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PHYSICAL AND COMPUTATIONAL FLUID DYNAMICS MODELING OF UNIT
OPERATIONS UNDER TRANSIENT HYDRAULIC LOADINGS
By
GIUSEPPINA GAROFALO
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2012
2
© 2012 Giuseppina Garofalo
3
To my family
4
ACKNOWLEDGMENTS
I would like to thank my advisor, Dr. John Sansalone for his encouragement and guidance.
He always believed in my potential and supported me. I also extend my sincere gratitude to the
members of my committee: Dr. James Heaney, Dr. Ben Koopman and Dr. Jennifer Curtis for
their valuable input, advice and accessibility. I am forever in debt to them for their guidance.
I thank my dear colleagues and friends who have helped me in the lab and in the field:
Dr. Jong-Yeop Kim, Dr. Srikanth Pathapati, Dr. Gaoxiang Ying, Dr. Josh Dickenson, Dr. Ruben
Kertesz, Dr. Tingting Wu, Dr. Hwan chul Cho, Saurabh Raje, Greg Brenner, Earendil Wilson,
Sandeep Gulati, Hao Zhang, Julie Midgette.
I thank the many friends I have made during these years and those in Italy, for being there
for me throughout this experience, no matter the distance, the differences in culture and
background. I thank my family for believing in me and supporting me in any moments with
unlimited strength, patience and love. They have been my greatest source of energy to overpass
the many obstacles present along the way.
5
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES ...........................................................................................................................9
LIST OF FIGURES .......................................................................................................................11
LIST OF ABBREVIATIONS ........................................................................................................17
ABSTRACT ...................................................................................................................................21
CHAPTER
1 GLOBAL BACKGROUND ...................................................................................................23
2 TRANSIENT ELUTION OF PARTICULATE MATTER FROM HYDRODYNAMIC
UNIT OPERATIONS AS A FUNCTION OF COMPUTATIONAL PARAMETERS
AND HYDROGRAPH UNSTEADINESS ............................................................................28
Summary .................................................................................................................................28
Introduction .............................................................................................................................28 Material and Methods .............................................................................................................32
Full-Scale Physical Model Setup .....................................................................................33 CFD Modeling .................................................................................................................35
Results and Discussion ...........................................................................................................42
Impact of Time Step (TS) and Mesh Size (MS) ..............................................................42 Event-Based Separated PSDs and DN for PSDs .............................................................45
Effect of Hydrograph Unsteadiness .................................................................................46 Conclusion ..............................................................................................................................47
3 STORMWATER CLARIFIER HYDRAULIC RESPONSE AS A FUNCTION OF
FLOW, UNSTEADINESS AND BAFFLING .......................................................................56
Summary .................................................................................................................................56 Introduction .............................................................................................................................56 Material and Methods .............................................................................................................59
RTD Curves and Assessment of Hydraulic Indices ........................................................60 CFD Modeling .................................................................................................................61
Results and Discussion ...........................................................................................................65
Steady Flow Hydraulic Indices as Function of Flow Tortuosity (equivalent L/W) ........65
Unsteady Flow Hydraulic Indices as Function of Flow Tortuosity (Equivalent L/W) ...68
4 CAN A STEPWISE STEADY FLOW CFD MODEL PREDICT PM SEPARATION
FROM STORMWATER UNIT OPERATIONS AS A FUNCTION OF
HYDROGRAPH UNSTEADINESS AND PM GRANULOMETRY? .................................78
6
Summary .................................................................................................................................78 Introduction .............................................................................................................................79 Methodology ...........................................................................................................................83
Physical Model Setup ......................................................................................................83
CFD Modeling of Fluid and PM Phases ..........................................................................87 CFD modeling under unsteady conditions ...............................................................90 Stepwise steady CFD modeling ...............................................................................91
Results and Discussion ...........................................................................................................94 Comparison of the Stepwise Steady and Fully Unsteady CFD Results ..........................94
Automatic Sampling, PM Granulometry and CFD Results ............................................97
Conclusion ..............................................................................................................................99
5 A STEPWISE CFD STEADY FLOW MODEL FOR EVALUATING LONG-TERM
UO SEPARATION PERFORMANCE ................................................................................111
Summary ...............................................................................................................................111 Introduction ...........................................................................................................................111
Methodology .........................................................................................................................115 Hydrology Analysis .......................................................................................................115
Physical Full-Scale Model for PM Separation ..............................................................116 Physical Full-Scale Model for PM Washout .................................................................118
CFD Modeling ...............................................................................................................119 CFD model for PM separation ...............................................................................120
CFD model of PM washout ....................................................................................121 Validation analysis for fully-unsteady CFD model ................................................123 Stepwise steady CFD model ..................................................................................124
Evaluation of PM Elution Due to Washout in the Continuous Simulation Model .......126 Time Domain Continuous Simulation Model and its Assumptions ..............................127
Results and Discussion .........................................................................................................128 CFD Model for PM Separation and Washout ...............................................................128 PM Washout as Function of Flow Rate and Pluviated PM Depth ................................129
Stepwise CFD Steady Flow Model and Time Domain Continuous Simulation ...........131
Conclusion ............................................................................................................................134
6 GLOBAL CONCLUSION ...................................................................................................147
APPENDIX
A SUPPLEMENTAL INFORMATION OF CHAPTER 2 “TRANSIENT ELUTION OF
PARTICULATE MATTER FROM HYDRODYNAMIC UNIT OPERATIONS AS A
FUNCTION OF COMPUTATIONAL PARAMETERS AND HYDROGRAPH
UNSTEADINESS” ...............................................................................................................151
Detailed Sampling Methodology and Protocol .....................................................................151 Effluent Sampling ..........................................................................................................151 Mass Recovery and Sample Protocol ............................................................................151 Laboratory Analysis ......................................................................................................152
7
Verification of Mass Balance ........................................................................................153 Verification of PSD Balance .........................................................................................153
Results under Steady Condition ............................................................................................154 Morsi and Alexander K – Values (Morsi and Alexander, 1972): .........................................154
Effect of Temperature ...........................................................................................................155
B SUPPLEMENTAL INFORMATION OF CHAPTER 3 “STORMWATER CLARIFIER
HYDRAULIC RESPONSE AS A FUNCTION OF FLOW, UNSTEADINESS AND
BAFFLING” .........................................................................................................................165
Full-scale Physical Model Setup ..........................................................................................165 Generation of Hydrographs Used for the Validation of the Full-Scale Physical Model of
Clarifier under Transient Conditions ................................................................................167
Hyetographs ...................................................................................................................167 Particle Size Distribution ......................................................................................................167
PSD Selection ................................................................................................................167 PSD Significance ...........................................................................................................168
Transformation of Rainfall Hyetographs to Runoff Hydrographs .......................................168 Definition of N ......................................................................................................................169
Geometry and Mesh Generation of Full-Scale Rectangular Clarifier ..................................170 Turbulent Dispersion Model .................................................................................................170
CFD Modeling and Population Balance ...............................................................................171 Validation Analysis of Steady RTDs and PM Separation Efficiency on Full-Scale
Physical Model of Rectangular Clarifier...........................................................................172
C SUPPLEMENTAL INFORMATION OF CHAPTER 4 “CAN A STEPWISE STEADY
FLOW CFD MODEL PREDICT PM SEPARATION FROM STORMWATER UNIT
OPERATIONS AS A FUNCTION OF HYDROGRAPH UNSTEADINESS AND PM
GRANULOMETRY?” .........................................................................................................191
Stepwise Steady Flow Model ...............................................................................................191
UDF for Fully Unsteady and Stepwise Steady Flow CFD Models ......................................193
D SUPPLEMENTAL INFORMATION OF CHAPTER 5 “A STEPWISE CFD STEADY
FLOW MODEL FOR EVALUATING LONG-TERM UO SEPARATION
PERFORMANCE” ...............................................................................................................211
Disaggregation Rainfall Method ...........................................................................................211 Full-Scale Physical Model Setup of the Rectangular Clarifier .............................................211 Generation of Hydrographs Used for the Validation of the Full-Scale Physical Model of
Clarifier under Transient Conditions ................................................................................212
Hyetographs ...................................................................................................................212
Transformation of Rainfall Hyetographs to Runoff Hydrographs ................................213
Particle Size Distribution ......................................................................................................214 PSD Selection ................................................................................................................214 PSD Significance ...........................................................................................................214
Geometry and Mesh Generation of Full-Scale Models ........................................................214
8
CFD Modeling and Population Balance ...............................................................................215 Liquid Phase Governing Equations ...............................................................................215 Particulate Phase Governing Equations (the DPM) ......................................................216 Numerical Solution ........................................................................................................218
Stepwise Steady Flow Model ...............................................................................................218
LIST OF REFERENCES .............................................................................................................243
BIOGRAPHICAL SKETCH .......................................................................................................250
9
LIST OF TABLES
Table page
2-1 Physical model (baffled HS) hydraulic and PM loading and PM separated......................49
4-1 Physical model (baffled HS and rectangular clarifier) hydraulic and PM loading and
PM separated ....................................................................................................................110
5-1 Physical and CFD model hydraulic loadings and washout PM results for the clarifier
subject to the hydrographs and the hetero-disperse gradation .........................................144
5-2 Measured and modeled washout PM are reported for two units, SHS (D = 1.7 m) and
SHS (D = 1.0 m) along with the characteristics of the washout runs ..............................145
5-3 Unsteady and steady CFD PM washout results for rectangular clarifier and SHS (D =
1.7m) ................................................................................................................................146
A-1 Experimental matrix and summary of treatment run results for the baffled HS unit
loaded by a hetero-disperse (NJDEP) gradation under 100 mg/L ...................................164
A-2 Morsi and Alexander constants for the equation fit of the drag coefficient for a
sphere ...............................................................................................................................164
B-1 Summary of measured and modeled treatment performance results for full-scale
rectangular clarifier (RC) and rectangular clarifier with 11 baffle clarifier (B11) ..........186
B-2 Summary of RTD test for pilot-scale rectangular cross-section linear clarifier
configuration loaded with sodium chloride injected as a pulse at t = 0. ..........................186
B-3 Number of baffles and corresponding value of tortuosity, Le/L for the clarifier with
transverse baffles and opening of 0.60 m and 0.20 m, with longitudinal baffles ............187
B-4 Parameter values of the curves used to fit the volumetric efficiency versus tortuosity
for the clarifier configuration with longitudinal baffles and opening of 0.20 m .............187
B-5 Parameter values of the curves used to fit the volumetric efficiency versus tortuosity,
for the clarifier configuration with transverse baffles ......................................................188
B-6 Parameter values of the curves used to fit the Morrill index, MI data versus
tortuosity, for the clarifier configuration with longitudinal baffles and opening of
0.20 m ..............................................................................................................................188
B-7 Parameter values of the curves used to fit the Morrill index, MI data versus
tortuosity, for the clarifier configuration with transverse baffles ....................................189
B-8 Parameter values of the curves used to fit the N data versus tortuosity for the clarifier
configuration with longitudinal baffles and opening of 0.20 m.......................................189
10
B-9 Parameter values of the curves used to fit the N data versus tortuosity for the clarifier
configuration with transverse baffles ...............................................................................189
B-10 Parameter values of the curves used to fit the MI data for degrees of unsteadiness for
the clarifier configuration with transverse baffles and opening of 0.20 m ......................190
B-11 Parameter values of the curves used to fit the N data for degrees of unsteadiness for
the clarifier configuration with transverse baffles and opening of 0.20 m ......................190
C-1 Computational time expressed in hour for the CFD stepwise steady flow and the
fully unsteady models. .....................................................................................................210
C-2 Example of the output from UDF developed for recording particle residence time,
injection time and diameter ..............................................................................................210
D-1 Summary of measured and modeled treatment performance results for full-scale
rectangular clarifier loaded by hetero-disperse silt particle size gradation ......................241
D-2 Morsi and Alexander constants for the equation fit of the drag coefficient for a
sphere ...............................................................................................................................241
D-3 Under-relaxation factors utilized in the CFD simulations ...............................................242
11
LIST OF FIGURES
Figure page
2-1 Schematic representation of the full-scale physical model facility setup with baffled
hydrodynamic separator (BHS) .........................................................................................50
2-2 Three hydrographs loading physical model (baffled HS shown in inset) and influent
and effluent measured and modeled particle size distributions (PSDs) for each
loading................................................................................................................................51
2-3 The effect of time step (TS) on modeled intra-event effluent PM as a function of
hydrograph unsteadiness () ..............................................................................................52
2-4 The CFD model error (en) and computational time simulating eluted PM as function
of TS and MS for hydrograph unsteadiness .......................................................................53
2-5 The effect of mesh size (MS) on CFD modeled intra-event effluent PM as a function
of hydrograph unsteadiness () ..........................................................................................54
2-6 Separated event-based PSDs from CFD model as compared to physical model data.
Separated event-based PSDs for Qp and Qmedian are also reported .....................................55
3-1 The conceptual process flow diagram for the stepwise CFD steady flow methodology ...71
3-2 Physical model and CFD model results for PM and PSDs for the validation analysis
for full-scale physical model of the rectangular clarifier ...................................................72
3-3 Comparison between rectangular and trapezoidal cross-section clarifier
configurations. ...................................................................................................................73
3-4 Volumetric efficiency as function of clarifier flow path tortuosity, Le/L for the
clarifier configurations with transverse and longitudinal internal baffling .......................74
3-5 N as function of clarifier flow path tortuosity, Le/L for the clarifier configurations
with transverse and longitudinal internal baffling .............................................................75
3-6 Pe as function of N tanks in series for the configurations with respectively transverse
baffles and opening of 0.20 m and longitudinal baffles.....................................................76
3-7 Modeled cumulative RTD function, F as function of time for highly unsteady,
unsteady and quasi-steady hydrographs respectively for rectangular clarifier ..................77
4-1 Influent hydraulic loadings and PSDs..............................................................................101
4-2 Effluent PM response of a baffled HS to the finer hetero-disperse PSD transported by
the hydrographs of varying unsteadiness .....................................................................102
12
4-3 Effluent PM response of a BHS to the coarser hetero-disperse PSD transported by
the hydrographs of varying unsteadiness ......................................................................103
4-4 Effluent PM response of a rectangular clarifier to each hydrograph (volume = 122
m3) loading of varying unsteadiness .............................................................................104
4-5 Each plot displays the influent PM mass recovery provided by auto sampling of the
BHS as a function of hydrograph unsteadiness () and PSD ..........................................105
4-6 Each plot displays the effluent PM mass recovery comparing auto and manual
sampling methods for the BHS as a function of hydrograph unsteadiness ( and
PSD ..................................................................................................................................106
4-7 Each plot displays the effluent PM response of the BHS to a coarser PSD as a
function of hydrograph unsteadiness ( .........................................................................107
4-8 Each plot displays the effluent PM response of the BHS to a finer PSD as a function
of hydrograph unsteadiness ( ........................................................................................108
4-9 Each plot displays the effluent PM response of the BHS to a source area PSD as a
function of hydrograph unsteadiness ( .........................................................................109
5-1 The subject Gainesville, Fl (GNV) watershed for physical, the continuous simulation
(SWMM) modeling and time of concentration as function of rainfall intensity .............138
5-2 Influent hydraulic loadings and PSDs. Influent particle size distribution (PSD) is
reported in A), the scaled hydrographs obtained from design hyetographs in B) ...........139
5-3 ntra-event effluent PM washout generated by physically-validated CFD model. Plot
A) and B) generated from a triangular hyetograph loading the subject watershed .........140
5-4 CFD model of event-based washout of PM at 50% and 100% of sediment capacity in
sump area and no PM depth in the volute area ................................................................141
5-5 CFD model of PM washout mass as a function of flow rate, Q for the rectangular
clarifier and SHS unit.......................................................................................................142
5-6 Effluent PM results generated through the continuous simulation model for 2007 ........143
A-1 Validation of measured vs. modeled PM separation for HS subject to hetero-disperse
PSD loading at a gravimetric PM concentration of 100 mg/L at steady flow rates .........156
A-2 Effluent PSDs for differing hydrographs. Effluent PSDs for highly unsteady
hydrograph, unsteady hydrograph, quasi unsteady hydrograph ......................................157
A-3 Effect of time step (TS) on modeled effluent PM at DN = 16 and MS = 3.1*106 for
three hydrologic unsteadiness ..........................................................................................158
13
A-4 Normalized root mean squared error (en) of CFD model effluent PM as function of
time step for three levels of hydrologic event unsteadiness investigated ........................159
A-5 Effect of mesh size on modeled effluent PM at DN = 16 and TS = 10 sec for three
hydrographs investigated respectively, highly unsteady, unsteady and quasi-steady. ....160
A-6 Captured CFD model particle size distribution (PSD) at TS = 10 sec, MS = 3.1*106,
DN = 16, 32, 64 generated by baffled HS loaded by an influent hetero-disperse PSD ...161
A-7 Effect of temperature on PM removal percentage of HS unit subject to the hetero-
disperse PM gradation of this study at the peak flow rate of 18 L/s ................................162
A-8 CFD model snapshots. Pathlines are colored by velocity magnitude (m/s) ....................163
B-1 Triangular hyetograph. Td is the recession time, ta is the time to peak, and r is the
storm advancement coefficient ........................................................................................173
B-2 Frequency distribution of rainfall precipitation for Gainesville, Florida. The
frequency distribution is obtained from a series of 1999-2008 hourly precipitation
data ...................................................................................................................................173
B-3 Historical event collected on 8 July 2008 ........................................................................174
B-4 Influent PSD for fine PM {SM I, <75m}. SM is sandy silt in the Unified Soil
Classification System (USCS). SM is SCS 75.................................................................174
B-5 Hydraulic loadings utilized for full-scale physical model. The rainfall-runoff
modeling is performed in Storm Water Management Model (SWMM) for the
catchment .........................................................................................................................175
B-6 Relationship between N-tanks-in-series and the difference between median and peak
residence time ..................................................................................................................176
B-7 Isometric view of full-scale physical model and mesh of the rectangular cross-section
clarifier with eleven baffles .............................................................................................177
B-8 Isometric view of full-scale physical model and mesh of the rectangular cross-section
clarifier .............................................................................................................................178
B-9 Grid convergence for full-scale rectangular clarifier. The mesh utilized comprimes
3.1*106 tetrahedral cells ...................................................................................................179
B-10 Physical and CFD Modeled RTDs for flow rates, representing 100%, 50%, 10% and
5% of Qd on no-baffle rectangular clarifier .....................................................................180
B-11 Physical model and CFD model results for the triangular hydrograph used for the
validation analysis for full-scale physical model of a rectangular clarifier .....................181
14
B-12 Velocity magnitude (m/s) contours at a horizontal plane at mid-depth for the
configuration with transverse baffles and opening of 0.60 m ..........................................182
B-13 Velocity magnitude (m/s) contours at a horizontal plane at mid-depth for the
configuration with transverse baffles and opening of 0.20 m ..........................................183
B-14 Velocity magnitude (m/s) contours at a horizontal plane at mid-depth for the
configuration with longitudinal baffles ............................................................................184
B-15 Morrill index as function of clarifier flow path tortuosity, Le/L for the clarifier
configurations with transverse and longitudinal internal baffling ...................................185
C-1 Schematic representation of the full-scale physical model facility setup with
rectangular clarifier ..........................................................................................................196
C-2 Schematic representation of the full-scale physical model facility setup with baffled
HS ....................................................................................................................................197
C-3 Triangular hyetograph. Td is the recession time, ta is the time to peak, and r is the
storm advancement coefficient (Chow et al., 1988) ........................................................197
C-4 Frequency distribution of rainfall precipitation for Gainesville, Florida. The
frequency distribution is obtained from a series of 1999-2008 hourly precipitation
data ...................................................................................................................................198
C-5 Historical event collected on 8 July 2008 ........................................................................198
C-6 Hydraulic loadings utilized for full-scale physical model of rectangular clarifier:
triangular hyetograph, Historical 8 July 2008 hydrologic event......................................199
C-7 Unit hydrograph (UH) theory (Chow et al., 1988) ..........................................................200
C-8 Stepwise steady flow model analogy with UH ................................................................201
C-9 Stepwise steady flow model. Particle residence time distribution, Up as function of
flow rate ...........................................................................................................................202
C-10 Stepwise steady flow model methodology ......................................................................203
C-11 Up as function of time for the finer PSD for two steady flow rates. The Up
distributions are fit by a gamma distribution with parameters, and ..........................204
C-12 Shape and scale gamma paremeters ( and ) as function of Q. The gamma
parameters are used to fit the Up,Q with a gamma distribution function ........................205
C-13 Effluent PM response of a rectangular clarifier to the highly unsteady (=1.54) and
unsteady (=0.33) hydrographs .......................................................................................206
15
C-14 Effluent PM for the fully unsteady CFD model and the stepwise steady model from
Pathapati and Sansalone (2011) .......................................................................................207
C-15 Effluent PM response of a rectangular clarifier to the highly unsteady (=1.54) and
unsteady (=0.33) hydrographs generated through the stepwise steady model ..............208
C-16 Influent coarser and finer PSDs as compared to measured effluent PSDs generated
through auto sampling for the three hydrographs shown in Figure 1B ...........................209
D-1 Precipitation data disaggregation (Orsmbee, 1988)) .......................................................221
D-2 Rainfall intensity frequency distribution for the period 1998-2011 and for 2007 and
time domain distribution of rainfall and runoff for June 2007 ........................................222
D-3 Total rainfall depth as function of month for the year 2007 ............................................223
D-4 Cumulative and incremental runoff frequency distribution for 2007 for a watershed
of 1.6 ha, with 1% slope, 75% of imperviousness and sand soil characteristics .............223
D-5 Schematic representation of the full-scale physical model facility setup with
rectangular clarifier ..........................................................................................................224
D-6 Frequency distribution of rainfall precipitation for Gainesville, Florida. The
frequency distribution is obtained from a series of 1999-2008 hourly precipitation
data ...................................................................................................................................225
D-7 Influent PSD for fine PM {SM I, <75m}. SM is sandy silt in the Unified Soil
Classification System (USCS). SM is SCS 75.................................................................225
D-8 Hydraulic loadings utilized for full-scale physical model. The rainfall-runoff
modeling is performed in Storm Water Management Model (SWMM) for the
catchment .........................................................................................................................226
D-9 Isometric view of full-scale physical model and mesh of the rectangular cross-section
clarifier. The number of computational cells is 3.5*106. D is diameter ..........................227
D-10 Grid convergence for full-scale rectangular clarifier. The mesh utilized comprimes
3.5*106 tetrahedral cells ...................................................................................................228
D-11 View of the full-scale physical model of screened HS (SHS) unit. D represents the
diameter............................................................................................................................228
D-12 Scour hole generated after a transient physical model test on the rectangular clarifier ..229
D-13 Schematic of scour CFD model by integrating across surfaces (not to scale) .................229
D-14 Particle residence time distributions, Up for RC and SHS as function of steady flow
rate. The flow rates vary from 1 to 50 L/s (maximum hydraulic capacity of RC) ..........230
16
D-15 Unit hydrograph (UH) theory (Chow et al., 1988) ..........................................................231
D-16 Stepwise steady flow model analogy with UH ................................................................232
D-17 Stepwise steady flow model. Particle residence time distribution, Up as function of
flow rate ...........................................................................................................................233
D-18 Stepwise steady flow model methodology ......................................................................234
D-19 Effluent PM generated from the stepwise steady model as function of the number of
flow rates ..........................................................................................................................235
D-20 Physical and CFD model results for PM and PSDs for the triangular hydrograph and
for 8th July 2008 storm for full-scale physical model of a rectangular clarifier .............236
D-21 CFD model of washout PM concentration as a function of flow rate, Q for the
rectangular clarifier and SHS unit....................................................................................237
D-22 CFD model of PM washout mass and concentration for the SHS unit for PM depths
in volute section ranging from 10 to 100 mm with 100% of PM capacity in sump
area. ..................................................................................................................................238
D-23 Effluent PM mass and PM mass depth as function of month for the screened HS unit
in the representative year 2007 for 100% of sediment capacity of sump area ................239
D-24 Normalized mean fluid velocity distributions inside the inner and outer volute area of
SHS, and RC. Bin sizes are consistent for SHS and RC..................................................240
17
LIST OF ABBREVIATIONS
BHS Baffled Hydrodynamic Separator
Ceff Effluent Concentration [mg L-1]
CDi Drag coefficient
Ci Influent concentration (mg L-1)
C1, C2 Empirical constants in the standard k- model
CFD Computational fluid dynamics
DN Discretization number
dp Particle diameter (m)
DPM Discrete particle model
d50 Particle diameter at which 50% of particle gradation mass is finer (m)
en Normalized root mean squared error
FDi Buoyancy/gravitational force per unit particle mass
gi Sum of body sources in the ith direction (m s-2
)
HS Hydrodynamic separator
k Turbulent kinetic energy per unit mass (m2 s
-2)
K1, K2, K3 Empirical constants as function of particle Rei
L Clarifier length (m)
Le Clarifier flow path tortuosity (m)
M PM mass associated to particle size range
MB Mass balance
Meff Effluent total mass (Kg)
Minf Influent total mass (Kg)
MI Morrill Index
MS Mesh size
18
Msep Separated total mass (Kg)
N Total number of particle injected
N-S Navier-Stokes
pn Mass per particle (Kg)
PM Particulate matter (Kg)
PBM Population balance model
PSD Particle size distribution
Q Normalized flow rate respect to the median flow rate
Qp Peak flow rate (L/s)
Q50 Median flow rate (L s-1
)
Q Flow rate (L s-1
)
pj Reynolds averaged pressure (Kg m-2
)
RANS Reynolds Averaged Navier Stokes
RC Rectangular clarifier
Re Reynold number
Rei Reynold number for a particle
RTD Residence Time Distribution
S Mean strain rate (m s-1
)
SC Sump capacity
SHS Screened Hydrodynamic Separator
SIMPLE Semi-Implicit Method for Pressure-Linked Equations
SSC Suspended sediment concentration (mg L-1
)
SWMM Storm Water Management Model
t50 Time at which 50% of tracer has exited the clarifier
t Normalized elapsed time respect to the duration of the storm
19
td Duration of the event (min)
ti Time instant (min)
tp Time of peak flow rate (min)
tr Total running time (min)
TS Time step (sec)
ui Reynolds averaged velocity in the ith direction (m s-1
)
uj Reynolds averaged velocity in the jth direction (m s-1
)
ui’uj’ Reynold Stresses (m2 s
-2)
Up Particle Residence Time Distribution
UDF User defined function
UO Unit Operation
UOP Unit Operation and Process
V Event Total Volume (L)
VE Volumetric Efficiency (%)
vi Fluid velocity (m s-1
)
vpi Particle velocity (m s-1
)
VF Volume fraction
xm Modeled variable
xm,max Maximum value of modeled variable
xi ith direction vector (m)
xj jth direction vector (m)
xo Measured variable
xo,max Maximum value of measured variable
Gamma distribution scale factor for Up
Gamma distribution scale factor for PSD
20
Gamma distribution shape factor for PSD
PM Mass PM separation (%)
t Temporal discretization (min)
Turbulent energy dissipation viscosity (m2 s
-2)
Unsteadiness parameter
Dynamic viscosity (Kg m-1
s-1
)
50 Median value
Fluid viscosity (m2 s
-1)
Eddy viscositym2 s
-1
Particle size range m
Fluid density (Kg m-3
)
p Particle density (Kg m-3
)
b Bulk density (Kg m-3
)
Gamma distribution shape factor for Up
Prandtl number (ratio eddy diffusion of k to the momentum eddy viscosity)
Prandtl number (ratio eddy diffusion of to the momentum eddy viscosity)
Injection time (min)
50 Theoretical residence time at median flow rate, Q50 (min)
21
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PHYSICAL AND COMPUTATIONAL FLUID DYNAMICS MODELING OF UNIT
OPERATIONS UNDER TRANSIENT HYDRAULIC LOADINGS
By
Giuseppina Garofalo
August 2012
Chair: John J. Sansalone
Major: Environmental Engineering Sciences
Unit operations (UOs) are used to manage the fate of urban rainfall-runoff particulate
matter (PM) and compounds in runoff that partition to and from PM. For UOs subject to runoff
loadings, computational fluid dynamics (CFD) is emerging as a design and analysis tool, albeit
utilization has been primarily for time-independent flows. In contrast to the common use of
steady CFD models there are few transient validated models of UOs.
This dissertation aims to investigate the transient hydraulic and PM response of common
runoff UOs. Utilizing a baffled hydrodynamic separator (BHS) the potential of CFD model to
predict PM elution as a function of hydrograph unsteadiness is investigated. The role of mesh
size (MS), time step (TS) and discretization number (DN) of particle size distribution (PSD) to
simulate PM elution is examined. The impact of baffle configuration, flow rate, and hydrograph
unsteadiness on hydraulic response of a rectangular clarifier (RC) is quantified through Morrill
index (MI), volumetric efficiency (VE) and N-tanks-in-series (N) metrics. A stepwise steady
flow CFD model is proposed and tested for transient events to predict PM separation with
reduced computational overhead. The stepwise steady approach models response of a BHS and a
RC to a hydrograph. The stepwise steady CFD flow model is extended to evaluate PM fate
(separation and washout) in a RC and a screened HS (SHS) on annual basis.
22
Results for BHS demonstrate MS, TS and DN significantly impact prediction of PM
elution, PSDs and computational effort as influenced by the unsteadiness level. For a RC with no
baffles, VE and N increase while MI decreases with flow rate. For a RC with baffles MI and N
are functions of unsteadiness level and number of baffles. The stepwise steady CFD model
produces effluent PM results in good agreement with measured physical model data at a
significantly reduced time compared to unsteady CFD models. The coupling of a stepwise-steady
CFD approach and time domain continuous simulation represents a valuable tool to estimate PM
fate on annual basis. Results provide a macroscopic evaluation for finding the optimal control
strategy and defining maintenance requirements to improve UO treatment.
23
CHAPTER 1
GLOBAL BACKGROUND
Urban rainfall-runoff particulate matter (PM) is a reactive substrate that is size hetero-
disperse. PM functions as a vehicle for chemical and microbial transport, and a discrete phase to
and from which chemicals partition (Sansalone, 2002; USEPA, 2000; Stumm and Morgan 1996;
Sansalone et al. 1998; Sansalone et al., 1998; Sansalone and Buchberger, 1997). Stormwater PM
represents a cause of impairment for surface waters (Heaney and Huber, 1984) and in 1972 the
Clean Water Act (revised in 1987) to mitigate PM stormwater discharges into receiving waters
introduced the use of unit operations (UOs) (USEPA, 2000).
CFD model based on numerically solving the fundamental equations of fluid flow, the
Navier-Stokes (N-S) equations is emerging as a design and analysis tool for modeling hydraulic
and PM response of UOs. In CFD a hydrodynamic model solves and simulates the flow field,
while a discrete phase model (DPM) coupled with granulometric data, such as PSD and specific
gravity (s), predicts three-dimensional particle trajectories and velocities (Pathapati and
Sansalone, 2009a,b). Recent CFD research is very active on the development of dependable
particle flow models which provide helpful insights into PM process phenomena and accelerate
the achievement of ameliorative process solutions (Curtis and Wachem, 2004).
Steady CFD models were utilized to reproduce PM settling and resuspension processes in
sedimentation storage tanks (Andersson et al., 2003; Dufresne, 2008). Pathapati and Sansalone
conducted a steady CFD model analysis of PM separation process of a passive radial cartridge
filter system and a hydrodynamic separator (Pathapati and Sansalone, 2009a,b). Dickenson and
Sansalone (2009) demonstrated the influence of PSD discretization (as DN) in steady CFD
model in predicting PM separation and provided DN guidance based on PM dispersivity. Steady
24
flow studies have also used a DPM to examine PM settling and scour processes in tanks and
basins (Dusfrene et al., 2009; Wals et al., 2010; Samaras et al., 2010).
Although steady PM performance evaluations of UOs represents a basic tier of testing
certification (TARP, 2001), final regulatory certification requires monitoring of unsteady runoff
events and PM delivery to assess actual UO behavior under in-situ conditions. In contrast to
wastewater and drinking water systems that are loaded by steady to quasi-steady flows,
stormwater UOs are, in fact, subjected to a very wide range of flows or highly unsteady episodic
flows. Validated unsteady CFD models are also necessary for design and analysis (Cristina and
Sansalone, 2003) given the current cost of an in situ unit operation certification program is
between 200 and 300 hundred thousand dollars.
Few validated or three-dimensional (3D) models of UOs subject to unsteady hydrologic
loads are present in literature (Pathapati and Sansalone, 2009) due to added computational efforts
to resolve variably unsteady hydrodynamics and the complexity of coupling a CFD model with a
monitored physical model for validation (Valloulls and List, 1984a-b; Wang et al., 2008). These
studies did not investigate PM elution as a function of differing levels of unsteadiness.
Furthermore, the influent particle size distributions (PSDs) were either uniform, divided into a
DN of six to eight, or simply simulated as a continuous function. Effluent PM reported in these
studies was not a function of time but lumped as PM removal efficiency, sludge thickness,
sludge or effluent PSD. Finally, these studies generated simulation results primarily without
physical model validation.
A major issue in highly polluted urban environments is that UOs, such as clarification
type-basins, are constrained by infrastructures and land uses. To improve hydraulic and PM
response, clarifiers are retrofit with baffles. The role of internal baffling on improving hydraulic
25
behavior of clarifiers was examined in previous literature by examining hydraulic indices, such
as Morrill Index residence time distribution (RTDs), volumetric efficiency and N-tanks indices
with steady CFD models. Studies have examined the hydraulic efficiency of baffled systems,
typically at constant flow (Wilson and Venayagamoorthy, 2010; Kim and Bae, 2007; Amini et
al., 2011; Kawamura, 2000). For example, Wilson and Venayagamoorthy (2010) analyzed a
baffled tank with up to 11 transverse baffles at the design flow; concluding that the maximum
hydraulic efficiency was reached at six baffles. However, for stormwater clarifiers the hydraulic
efficiency as a function of flow rate, unsteadiness ( and number of baffles (as an equivalent
L/W for baffling) has not been examined.
Although unsteady CFD modeling represents a tool to accurately predict hydraulic and PM
response in UOs, it also requires an added computational overhead with respect to steady
modeling. Pathapati and Sansalone (2011) in an attempt of balancing modeled error and
computational time, introduced a stepwise steady flow CFD model to reproduce unsteady PM
separation for stormwater UOs. The method is based on PM separation efficiency results
generated from steady CFD modeling. The steady CFD results at each discretized flow level are
flow-weighted across the unsteady runoff events (Pathapati and Sansalone, 2011). According to
this method, the UO instantaneously responses to each discretized flow level delivered into the
system. The study concluded the stepwise steady model does not accurately reproduce PM
separation for HS and clarifier units.
Previous literature has evaluated PM separation efficiency of UOs by using unsteady CFD
models solely on event basis. While in the design and analysis, the performance of UOs is
frequently assessed for either a single representative storm or a design storm, an annual basis
evaluation can provide the UO`s overall response to the wide spectrum of long-term rainfall-
26
runoff events. In addition to the PM elution from UOs, a long-term analysis can also include an
estimation of the PM washout. Recent studies demonstrated that PM washout strongly impacts
the overall response of UO, depending on the type of UO and maintenance frequency. While
coupling fully unsteady CFD model with a long-term continuous simulation can be a reasonable
concept, the computational overhead can be unreasonable. For this reason, transient CFD
modeling has never been implemented into a continuous model framework.
The second chapter`s objective is to perform a parameterization study for unsteady CFD
modeling. The assumption is that numerical parameters, such as MS, TS and discretization of
influent PM granulometry strongly affect the accuracy and running time of CFD unsteady
solution. CFD model is applied to a baffled HS, which represents a common unit operation used
in urban drainage system to separate PM constituents from stormwater flows through
gravitational settling (Type I settling). The system is loaded with coarse hetero-disperse PM
gradation at constant concentration. The analysis intends to model not only lumped descriptors
such as overall PM separation efficiency but also specific parameters, which provide a unique
signature of the system behavior, such as spatially distribution of PM mass and PSD as function
of flow rate.
The third chapter`s objective is to examine the role of baffle configurations, flow rate and
hydrograph unsteadiness on the hydraulic behavior of a clarifier subject to stormwater flows. A
validated CFD model of a RC with different baffling configurations is utilized to investigate the
hydraulic behavior of the unit using RTD, MI, VE, Peclet number (Pe) and N tanks-in-series
parameters (Hazen, 1904, Morrill, 1932; Metcalf and Eddy, 2003). The number of baffles is
indexed by flow tortuosity (Le/L) as a surrogate for flow path L/W ratio. Results are generated
using a CFD model validated with full-scale physical models.
27
The fourth chapter introduces a new stepwise steady model for predicting PM separation
by a clarifier and a HS. This model takes into account that UO response to a hydraulic and PM
loading is not instantaneous but varies according to the hydrodynamic characteristics of the
system (for example, residence time). Idealizing clarifier and HS as linear systems, the overall
response of the UO subject to an unsteady event is obtained by convoluting particle residence
time distributions across the series of flow rates in which the hydrograph is discretized. The CFD
model is utilized to produce the particle residence time distributions for a series of steady flow
rates and for specific PM gradations. The CFD model is validated with full-scale physical model
data. In addition, this chapter examines the efficiency of PM recovery produced through auto
sampling at the influent and effluent sections of the HS and illustrates the effect of influent auto
sampling in predicting the effluent time-dependent PM on CFD stepwise steady model.
The fifth chapter`s aim is to extend the stepwise steady flow CFD model to evaluate long-
term response of two common UOs, a RC and a BHS for PM separation and washout at a
reasonable computational overhead. The time domain continuous simulation model is performed
for a representative year of rainfall-runoff, by using a validated CFD model for PM separation
and washout and transient hydraulic loadings.
28
CHAPTER 2
TRANSIENT ELUTION OF PARTICULATE MATTER FROM HYDRODYNAMIC UNIT
OPERATIONS AS A FUNCTION OF COMPUTATIONAL PARAMETERS AND
HYDROGRAPH UNSTEADINESS
Summary
While computational fluid dynamics (CFD) is utilized to simulate particulate matter (PM)
separation and particle size distributions (PSDs) from unit operations, the role of computational
parameters and hydrograph unsteadiness to simulate intra-event elution of PM mass has not been
examined. An Euler-Lagrangian CFD model is utilized to simulate PM separation by a common
hydrodynamic unit operation subject to unsteady flow events and a hetero-disperse PM
gradation. Utilizing a baffled hydrodynamic separator (HS) this study illustrates CFD model
potential to predict eluted PM subject as a function of hydrograph unsteadiness. The study
hypothesizes that accurate simulation of unit behavior as a function of unsteadiness is dependent
on mesh size (MS), time step (TS) and PSD discretization number (DN). CFD and full-scale
physical model results are compared. Results demonstrate that MS, TS and DN significantly
influence prediction of transient PM mass, PSD and computational effort. Results demonstrate
that each parameter generates model error for transient PM elution that is significantly
influenced by the level of unsteadiness. In contrast, TS, MS and DN selection each have a
statistically significantly smaller influence on event-based PM mass.
Introduction
Urban rainfall-runoff PM is a reactive substrate that is size hetero-disperse. PM functions
as a vehicle for chemical and microbial transport, and a discrete phase to and from which
chemicals partition. Runoff PM is also impairment for receiving waters (Weiss et al., 2007).
Reprinted from Chemical Engineering Journal, 175, Garofalo, G., Sansalone, J., Transient elution of particulate matter from hydrodynamic unit
operation as a function of computational parameters and runoff hydrograph unsteadiness, 150-159, 2011, with permission from Elsevier.
29
Whether runoff unit operations are clarification-type basins (residence time of hours) or
hydrodynamic units of short residence time (minutes), PM mass separation is predominately
discrete Type I sedimentation (Wilson et al. 2009; MetCalf & Eddy, 2003).
For unit operations subject to runoff loadings CFD is emerging as a design and analysis
tool, albeit utilization has been primarily for time-independent (steady) flows (Dickenson and
Sansalone, 2009; Dufresne et al., 2009). CFD solves the Navier-Stokes (N-S) equations for the
continuous fluid phase and can allow coupling of PM transport through a discrete phase model
(DPM) (He et al., 2006; Wang et al., 2008; Wachem et al., 2003; Al-Sammaerraee et al., 2009).
CFD is a fundamental approach to model PM fate in unit operations as compared to lumped ideal
overflow methods for steady flows (Pathapati and Sansalone, 2009a-b). Using a steady CFD
model the role of discretization (as a DN) has demonstrated that the DN strongly influences
model error for PM separation by runoff unit operations, and provides DN guidance based on
PM hetero-dispersivity (Dickenson and Sansalone, 2009). Steady flow studies have also used a
DPM to examine PM settling and scour processes in tanks and basins (Dufresne et al., 2009;
Wols et al., 2010; Samaras et al., 2010).
While steady flow evaluations of unit operations are a basic tier of testing certification
(TARP, 2001), actual unit operation behavior and final regulatory certification requires
monitoring of unsteady runoff events and PM delivery. In addition to regulatory requirements,
validated CFD models of unsteady phenomena are needed for design and analysis (Cristina and
Sansalone, 2003) given the current cost of an in-situ unit operation certification program is
between 200 to 300 hundred thousand dollars.
In contrast to the common use of steady CFD models there are few validated or three-
dimensional (3D) models of unit operations such as an HS subject to unsteady hydrologic loads
30
and Type I settling (Dickenson and Sansalone, 2009). Whether for a clarifier or HS this is in part
due to added computational efforts to resolve variably unsteady hydrodynamics and the
complexity of coupling a CFD model with a monitored physical model for validation. There
have been many 2D modeling studies of wastewater clarifiers. Valloulls and List (Valloulls and
List, 1984a-b) developed a 2D model of effluent PM from a rectangular wastewater basin subject
to Type II settling under steady and periodic sinusoidal flows. The simulated input and output
demonstrated that effluent PM was influenced by mass concentration, PSDs, floc-density and
collision efficiency. Jin et al. (Jin et al., 2000) developed a 1D model for Type I settling in
rectangular tanks to evaluate separate efficiency, captured and effluent PSDs. The model
evaluated an unsteady process as a series of steady flow and concentration steps. The DN of the
influent PSD was eight. Huang et al. (Huang and Jin, 2011) proposed an unsteady 2D model for
circular Type I settling tanks based on the model of Jin et al. (Jin et al., 2000). While the model
was not validated a sensitivity analysis was performed. The DN of the influent PSD was six.
Zhou and McCorquodale (Zhou and McCorquodale, 1992) utilized a 2D model to simulate flow
and PM fate in rectangular wastewater tanks. The model was solved for transient flows until a
steady state solution was reached. The transient model was used to examine temporal density
variations and avoid divergence. Kleine and Reddy (Kleine and Reddy, 2005) proposed a 2D
unsteady finite element method to simulate steady hydrodynamics from an initially unsteady
condition. Velocity and pressure fields as well as wastewater sludge distribution were modeled.
In contrast to 2D simulations, Wang et al. (Wang et al., 2008) built a 3D model for a secondary
wastewater clarifier to simulate 3D velocity and PM concentration distributions as well as
dynamic sludge settling. He et al. (He et al., 2008) utilized a 3D model of a prismatic horizontal-
flow clarifier. The DPM was generated by injecting a fixed amount of PM at the clarifier inlet.
31
The PSD was mono-disperse; a single 50 m particle size. Clarifier designs were compared
based on inlet configurations.
Whether as 2D or 3D analysis of wastewater clarifiers these studies did not investigate PM
elution as a function of differing levels of unsteadiness. The studies that examined transience did
so as a transition to steady conditions or as a fixed periodic variation in influent flow rate.
Furthermore, the influent PSDs were either uniform, divided into a DN of six to eight, or simply
simulated as a continuous function. Effluent PM reported in these studies was not a function of
time but lumped as PM removal efficiency, sludge thickness, sludge or effluent PSD. Finally,
these studies generated simulation results primarily without physical model validation.
In comparison to wastewater clarifiers which are loaded by quasi-steady flows with
cohesive and largely organic PM subject to Type II settling, runoff unit operations are loaded by
unsteady flows with PM that is more hetero-disperse and inorganic. Pathapati and Sansalone
(Pathapati and Sansalone, 2009c) demonstrated that event-based steady flow indices for a CFD
model of unsteady runoff events can generate significant error as compared to physical model
data. In a follow-up study Pathapati and Sansalone (Pathapati and Sansalone, 2011) illustrated
that a stepwise steady CFD model of effluent PM and PSDs for unsteady runoff did not
reproduce physical model results for a HS and primary clarifier but in contrast did replicate the
response of a volumetric filter. The study demonstrated that unsteady CFD models provide an
accurate representation of PM fate for each unit operation. However these study or other studies
of urban runoff unit operations have not examined the role of MS, TS, DN or unsteadiness.
Towards the eventuality that validated CFD models will be relied upon to reproduce unit
operation behavior, a defensible unsteady CFD model requires investigation of the spatial
discretization (MS) of the computational domain, TS resolution of the hydrodynamics, and a DN
32
for the PM granulometry. It is hypothesized that these parameters impact the accuracy of the
unsteady CFD solution. Elucidation of computational effort as a function of unsteadiness is
needed if CFD is eventually coupled with continuous simulation models such as the Stormwater
Management Model (SWMM) to extend CFD beyond an intra-event time scale to simulate
longer term unit operation behavior and unit maintenance (Huber et al., 2005; Heaney and Small,
2003).
This study hypothesizes that CFD model accuracy for simulating elution of hetero-disperse
PM under transient hydraulic loadings is dependent on time resolution of the flow field, spatial
discretization of the computational domain, and the PSD size discretization. These
computational parameters have impacts on computational effort, hypothesizing that increasing
model accuracy as a function of unsteadiness comes at the expense of computational effort. This
study utilizes a baffled HS as a circular sedimentation tank. The HS is a unit operation for
separation of non-aqueous phase constituents such as PM in runoff with over 30,000 HS units
operating in North America. Objectives of this study are to develop an unsteady CFD model to
predict the effluent PM variation of a HS as a function of MS, TS and DN model parameters for
increasing unsteady loadings. Objectives also include prediction of time-dependent PM
measured as suspended sediment concentration (SSC) and PSDs. The computational expense of
model parameterization (MS, TS, DN) is also examined as a function of hydrologic unsteadiness.
Material and Methods
This study utilizes a common 1.83 m (~ 6 ft) diameter baffled HS that provides
gravitational settling (Type I) and retention of separated PM mass for small commercial, retail or
otherwise developed land parcels. Separate or combined sewers concrete appurtenances are
precast with this nominal diameter and most HS units are manufactured to insert into precast
appurtenances or tanks. A horizontal baffle separates oil, grease and floatables from PM that
33
settles in the HS. Without regular maintenance, buildup of coarser PM and anaerobic conditions
occur in the HS.
Full-Scale Physical Model Setup
A schematic process flow diagram of the physical model is illustrated in Figure 2-1. The
inset of Figure 2-2A illustrates the HS. Influent runoff to the HS is directed by a 200 mm high
inflow weir through an orifice plate into the clarification chamber as conveyed through a drop
tee inlet pipe. PM is separated in the clarification chamber. Runoff in the clarification chamber
is conveyed through the outlet riser to the downstream side of an effluent channel before
discharge through an outlet pipe. The HS volume is 4.62 m3.
The lower section of the
clarification chamber is approximately 1.82 m tall and the unit diameter is 1.8 m. The flow rate
through the clarification chamber is driven by the available head generated by the weir and
orifice plate.
Physical model runs are performed on a commercial HS for unsteady hydraulic loads at 20
˚C and PM mass recovered after each run. Hydrographs of differing unsteadiness are utilized as
shown in Figure 2-2A. Hydrograph formulations are based on the use of a step-function to model
the SCS dimensionless unit hydrograph (Malcom, 1989). The hydrographs are scaled based on
the HS maximum hydraulic capacity (18L/s), maintaining constant volume (V = 22,840 L) and a
constant time of peak flow, tp of 15 minutes (Sansalone and Teng, 2005). In Figure 2-2B the
event-based measured PSD is presented. The physical model of the HS is utilized to validate the
CFD model based on effluent PM as illustrated in the Appendix in Figure A-1. Selected
illustrations of CFD model flow pathlines and temporal variation of PSDs throughout each event
is reported in Figure A-2 and A-3. There is a range of hydrographs generated from small urban
watersheds (scaled at 0.1 to 0.2 impervious hectares for this HS) depending on rainfall depth-
duration-frequency, abstraction functions, geometrics and flow routing. Hydrographs with
34
differing unsteadiness are contained within this range (Fluent, 2006). In addition to differing
unsteadiness the peak flow of 18 L/s is the maximum hydraulic capacity of the full-scale
physical model with other peak flows selected to represent 50% and 25% of this hydraulic
capacity (2,500 < Re < 50,000). An unsteadiness parameter, is defined for each hydrograph
and the values of summarized in Table 2-1.
50medi
Q
1
dt
dV
In this Qmed represents the median flow rate. The values of for highly unsteady, unsteady
and quasi-steady hydrographs are 1.15, 0.24 and 0.09, respectively. The quasi-steady of 0.09
is comparable to 0.085 for the sinusoidal wastewater loading of Valloulls and List (Vallouls and
List, 1984) and a wastewater clarifier with a peaking factor of 4 has a of less than 0.09. The
for the unsteady and highly unsteady hydrographs are significantly higher. Based on monitoring
data of Pathapati and Sansalone (Pathapati and Sansalone, 2009) the of actual hydrographs
from a similar size paved watershed are typically 1 or greater; considered highly unsteady.
Physical model runs are conducted at constant influent PM concentration (Ci) and constant
hetero-disperse PSD with a d50 of 67 m as shown in Figure 2-2B. PSDs are modeled as
cumulative gamma distribution in which (shape factor) and (scale factor) represent the PSD
uniformity and the PSD relative coarseness, respectively (Dickenson and Sansalone, 2009). For
the physical model the unsteady influent flow rate is delivered by a pumping station and
measured by two calibrated magnetic flow meters and a volumetric meter for low flows. Flow
measurements are recorded by a data logger every second. PM is injected into the inlet drop box
mixing with the influent flow. Representative effluent samples are taken manually at the effluent
section of the HS unit as discrete samples in 1L wide-mouth bottles. Samples are collected in
(2-1)
35
duplicate for the entire run duration at variable sampling frequencies according to the flow rate
gradients and event duration to provide representative sampling of effluent variability for PM
concentration and PSD. The minimum sampling interval is 1 minute. After a treatment run,
supernatant samples and captured PM are collected. Samples are analyzed for PM
(gravimetrically as SSC) and PSDs. Separated PM mass is recovered, dried, weighted and
analyzed by laser diffraction to obtain PSDs.
A PM mass balance evaluation is conducted for each physical model run, summarized as:
00
inf
n
i
iieffsep
n
i
i ttQtCMtM
In the mass balance expression Minf is influent mass load and Ceff is effluent concentration
which varies with time, ti. Msep is separated PM recovered. The PM separation (%) is also
determined.
100
PMInfluent
PMEffluent - PMInfluent MassPM
PM separation and mass balance (MB) are reported in Table 2-1. Measured results
including effluent PSDs and PM obtained from physical modeling are utilized to validate the
CFD model.
Physical model runs at steady flow rates are also performed as described in the Supporting
Information.
CFD Modeling
A 3D unsteady CFD model is built for the full-scale HS physical model using FLUENT v
13.0. The code is finite volume based, written in C programming language and solves Navier-
Stokes (N-S) equations across a computational domain. CFD methodology comprises three
general steps: (1) geometry and mesh generation (pre-processing), (2) creating boundary and
(2-2)
(2-3)
36
initial conditions and (3) defining and solving the physical model (processing) and post-
processing model data. Due to the complex HS geometry, the mesh is completely comprised of
tetrahedral elements, a non-uniform meshing scheme where nodes do not reside on a grid. The
mesh is checked to ensure equi-angle skewness and local variations in cell size are minimized.
In this study, the liquid-particle phase flow in the HS is simulated by combining the
Eulerian fluid dynamics model with a discrete particle model (DPM). The model is based on
Euler-Lagrangian approach in which the fluid phase is treated as a continuum in an Eulerian
frame of reference and solved by integrating the time-dependent N-S equations. The particulate
phase behavior in the system is predicted by the DPM as a discrete phase in a Lagrangian frame
of reference. At each simulation time interval the flow field is solved first.
Liquid Phase Governing Equation. The governing equations for the continuous phase
are a variant of the N-S equations, the Reynolds Averaged N-S (RANS) equations for a turbulent
flow regime. The RANS conservation equations are obtained from the N-S equations by
applying the Reynolds’ decomposition of fluid flow properties into their time-mean value and
fluctuating component. The mean velocity is defined as a time average for a period t which is
larger than the time scale of the fluctuations. Time-dependent RANS equations for continuity
and momentum conservation are summarized.
,0
i
i
ux
i
j
i
iij
jji
j
i gx
u
x
puu
xuu
xt
u
2
2''
In these equations is fluid density, xi is the ith direction vector, uj is the Reynolds
averaged velocity in the ith direction; pj is the Reynolds averaged pressure; and gi is the sum of
(2-4)
(2-5)
37
body forces in the ith direction. Decomposition of the momentum equation with Reynolds
decomposition generates a term originating from the nonlinear convection component in the
original equation; these Reynolds stresses are represented by ''
jiuu . Reynolds stresses contain
information about the flow turbulence structure. Since Reynolds stresses are unknown, closure
approximations can be made to obtain approximate solution of the equations (Pope, 2000). In
this study the realizable k- model (Shi et al., 1995) is used to resolve the closure problem. This
model is suitable for boundary free shear flow (baffled HS) applications and consists of turbulent
kinetic energy and turbulence energy dissipation rate equations, respectively reported below (Shi
et al., 1995).
jx
iu
ju
iu
jx
k
k
t
jx
jx
k
ju
t
k''
kCSC
xxxu
t j
t
jj
j
2
21
ijij SSS
kSC
2,,
5,43.0max
1
In these equations σk = 1.0, σε = 1.2, C1 = 1.44, C2 = 1.9, k is the turbulent kinetic energy; ε
is the turbulent energy dissipation rate; S is the mean strain rate; νT is the eddy viscosity; ν is the
fluid viscosity; and uji, uj′u′i are previously defined.
Particulate Phase Governing Equations (DPM).
After solving the flow field, the DPM is applied. The DPM simulates 3D particle
trajectories through the domain to model PM separation and elution in a Lagrangian frame of
reference where particles are individually tracked through the flow field. This analysis assumes
PM motion is influenced by the fluid phase, but the fluid phase is not affected by PM motion
(2-6)
(2-7)
(2-8)
38
(one-way coupling) and particle-particle interactions are negligible. These assumptions are
applicable, since the particulate phase is dilute (volume fraction (VF) around 0.01%) (Brennen,
2005). The DPM integrates the governing equation of PM motion and tracks each particle
through the flow field by balancing gravitational body force, drag force, inertial force, and
buoyancy forces on the PM phase. The motion of a single particle without collisions is modeled
by the Newton`s law. Particle trajectories are calculated by integrating the force balance equation
in the ith-direction.
p
pipiiDi
pi gvvF
dt
dv
The first term on the right-hand side of the equation is the drag force per unit particle mass.
The second term is the buoyancy/gravitational force per unit particle mass. In these equations, p
is particle density, vi is fluid velocity, vpi is particle velocity, dp is particle diameter, Rei is the
particle Reynolds number, FDi is the buoyancy/ gravitational force per unit mass of particle and
CDi is the particle drag coefficient (Morsi and Alexander, 1972). The last three variables are
defined as follows.
24
Re18
2iDi
pp
DiC
dF
ipipi
vvd Re
3221
ReReK
KKC
iiiD
K1, K2, K3 are empirical constants as a function of particle Rei and tabulated in Table A-2.
(2-9)
(2-10)
(2-11)
(2-12)
39
Particle injections are uniformly released from the HS inlet surface and each particle is
tracked within the domain at each time step. To model the temporal PM fate, a computational
subroutine as a user defined function (UDF) is written in C to record PM injection properties,
residence time and size of each particle eluted from the system throughout the entire simulation.
A trap condition is defined for the HS lower boundary so that PM settling to this boundary
is not reflected and the particle trajectory is terminated. This assumption is physically reasonable
given the volumetric isolation of settled PM in the HS sump, and is verified by comparing
modeled results for trapping or reflecting boundary conditions. The difference in eluted PM is
approximately 1%, and for PSDs approximately 0.4%. The PM trapping assumption reduces the
DPM computational effort, since the particle numbers are reduced during the simulation. The
PSD is discretized into size classes with an equal gravimetric basis. Studies have demonstrated
that PM tracking lengths (TL) of 8 m and DN from 8 to 16 are generally able to reproduce
accurate results for hetero-disperse PM in this HS subject to steady flows (Dickenson and
Sansalone, 2009). The DN baseline of this study is 8 and higher DN (16, 32 and 64) values are
utilized to explore the impact of DN.
A population balance model (PBM) is utilized to model PM separation. Assuming no
flocculation in the dispersed PM phase, the PBM equation (Jakobsen, 2008) can be written.
max
min
max
min
max
min 0
,
0
,
0inf,
ddd t
sep
t
eff
t
ppp
In this equation and represent particle size range and injection time ranging from 0 to
the runoff event duration, td, respectively. The term ()inf indicates influent PM, ()eff effluent PM
and ()sep separated PM. p represents the mass per particle and is obtained as follows:
(2-13)
40
N
Mp
,
,
M is PM mass associated with the particle size range as function of injection time N
is the total number of particles injected at the inlet section, td is the event duration.
A constant temperature of 20º C is utilized in this study. Full-scale physical model water
temperature varied by ± 2º C. It is hypothesized that the temperature does not significantly
impact the PM separation in a Type I settling unit subject to a hetero-disperse PSD loading. This
assumption is shown to be reasonable based on the study conducted by Ying and Sansalone
(Ying and Sansalone, 2011) in which they examine the influence of temperature on Type I
settling in a screened HS unit by using a CFD model validated with physical model data. For a
hetero-disperse PSD their study illustrated a relatively small influence of temperature (< 5%
based on PM mass) or salinity as compared to particle density or PSD in a screened HS unit. The
role of temperature on PM separation efficiency of the baffled HS in this study is provided in the
Appendix.
Numerical solution. The numerical solver is pressure-based for incompressible flows that
are governed by motion based on pressure gradients. The spatial discretization schemes are
second order for pressure, the second order upwind scheme for momentum and the Pressure
Implicit Splitting of Operators (SIMPLE) algorithm for pressure-velocity coupling. Temporal
discretization of the governing equations is performed by a second-order implicit scheme. Table
A-3 summarizes the under-relaxation factors utilized. The under-relaxation factors summarized
in Table A-3 are based on a parametric evaluation of these factors from 0.1 to 1 at different TS.
It is observed that as the TS increases the impact of the under-relaxation factor on the results
increased. These factors are selected to ensure simulation stability and minimize model error
(2-14)
41
while balancing computational time. Convergence criteria are set so that scaled residuals for all
governing equations are below 0.001 (Ranade, 2002). All simulations are run in parallel on a
Dell Precision 690 with two quad core Intel Xeon® 2.33GHz processors and 16 GB of RAM.
A TS analysis quantifies modeling error and computational effort as a function of TS and
unsteadiness. TS values of 10, 30, 60, 300 and 900 seconds are investigated noting that a TS
below 10 seconds are computationally expensive while 10 seconds provides temporal grid
independence; and is therefore the baseline TS. A TL of 8 m is utilized for PM. The HS
geometry is spatially discretized into four mesh sizes (MS) of 0.2, 1, 3.1 and 5 million tetrahedral
computational cells. A MS less than 0.2 million cells does not satisfy convergence criteria.
Validation analysis. A normalized root mean squared error, en is used to evaluate CFD
model results with respect to the full-scale physical model. In this equation xo is measured, and
xm the modeled variable.
min,max,
1
2
,,
oo
n
i
imio
nxx
n
xx
e
The validation study consists of comparing the full-scale HS physical model results and the
results obtained from the full-scale CFD model. Validation is based on full-scale physical model
results (1) temporal intra-event eluted PM results, (2) event-based PM mass separation, (3)
event-based PSDs, and (4) PM mass separation at steady flow rates. In the validation process
CFD model results for PM mass and PSD are compared to physical model results measured for
each level of hydrograph unsteadiness.
(2-15)
42
Results and Discussion
CFD model results are validated with respect to physical model results for each
hydrograph’s level of unsteadiness that is illustrated in Figure 2-1B. Figure 2-2B illustrates the
CFD model replication of eluted PSDs. Effluent PSDs are represented as cumulative gamma
functions and parameters are shown in Figure 2-2B. The HS unit provides a transformation
between influent and effluent PSDs with the quasi-steady hydrograph of the lowest Qp,
generating the finest effluent PSD. For higher Qp the physical model and gamma parameter
results trend in the direction of influent PSD parameters; increasing larger particles are eluted.
The CFD model is also validated for steady flows with results in Figure A-1. Additionally,
selected instantaneous solutions of the CFD model are illustrated in Figure A-2.
Impact of Time Step (TS) and Mesh Size (MS)
For the TS analysis, physical and CFD model (DN = 8 and MS = 3.1 x 106) results are
summarized as temporal effluent PM mass in Figure 2-3 as a function of hydrograph
unsteadiness. For clarity only the modeled effluent PM mass values for TS of 10, 300 and 900
sec are reported. TS results indicate that the CFD model accurately simulates the temporal
distribution of the physical model effluent PM for a TS range of 10 to 300 sec at each level of
unsteadiness. CFD model error varies from approximately 4 to 9%. In comparison the CFD
model at TS of 900 sec is less accurate at each level of unsteadiness, varying from 8 to 37% with
larger error at higher unsteadiness. At higher hydrograph unsteadiness typical of small watershed
with a lag time similar to the TS of 900 sec (15 min) the CFD model results in an
underestimation during the hydrograph rising limb and an overestimated near the peak. With
higher unsteadiness the TS of 900 sec does not account for this unsteadiness and the “jump” in
cell properties across the TS leads to less accurate results. Results in Figure 2-3 illustrate the
largest change in en occurs around the hydrograph peak.
43
TS results are summarized in the three left-hand plots of Figure 2-4 (A, C, E). Figure 2-4A
illustrates an exponential decrease in CFD model error (DN = 8, MS = 3.1 x 106) that
asymptotically approaches 5% at 1 minute TS based on PM mass. While Figure 2-4A illustrates
an exponential decrease in model error for decreasing TS there is an increase in computational
time as illustrated in Figure 2-4C. The increase of computational time is not only influenced by
the duration of the event but also by the number of particles tracked (TL = 8 m) throughout the
entire event. Figure 2-4E compares the PM mass separation (%) between the physical and CFD
models. The CFD range bars define the range of event-based modeled results obtained across
the TS series. The maximum error in PM mass separation between measured and modeled data
for varying TS values is approximately 5% for this relatively coarse hetero-disperse PSD loading
the HS. Previous research has shown for steady flows that as this PSD becomes finer the model
error for PM mass separation can increase significantly (Dickenson and Sansalone, 2009). While
TS analysis demonstrates that the temporal distribution of effluent PM is significantly influenced
by the TS selection, TS influence is muted for event-based PM for this hetero-disperse PSD
modeled with a DN of 8.
For MS analysis, physical model and CFD model (DN = 8 and TS = 10 sec) results as
temporal eluted PM mass are compared in Figure 2-5 A, B, C. Parallel to the accumulation of
CFD error illustrated in Figure 2-3 for TS the accumulation of CFD model error is shown at the
top of each plot in Figure 2-5. As with TS results the highest variation in CFD model error
associated with MS corresponds to the rapidly varying flows around the hydrograph peak. The
CFD model accurately simulates temporal PM elution for a MS of 3.1 million cells while errors
are consistently larger than 10% for each coarser MS. Since the turbulent fluid flows and PM
44
loadings with a coarser mesh cross fewer computational cells at a given TS a mesh of fewer cells
produces less accurate results.
MS results are summarized in the three right-hand plots of Figure 2-4 (B, D, F).
Analogous to the TS analysis, the model error generated based on MS is illustrated in Figure 2-
4B. Model error for effluent PM mass in Figure 2-4B also illustrates an exponential decrease
approaching 2% with increasing MS. In contrast to the computation time increase with smaller
TS, there is an exponential and larger increase in computational time with an increase number of
computation cells as shown in Figure 2-4D. For 1 minute of real time operation of the full-scale
HS there is a corresponding 10-15 minute computational time for the full-scale HS CFD model.
The computational time considerations presented as a function of TS are further accentuated as a
function of MS. This is largely due to the DPM process which becomes more computational
expensive as the unsteady event duration increases; more particles enter and are tracked at each
computational cell in the domain. For a MS of 5 x 106
the computational time for a runoff event
of 125 minutes reaches 120 hours. The MS selection has a significant impact on the computing
time due to the tracking of particles in each cell of a highly discretized domain which increases
the computational time.
Parallel to TS results, results in Figure 2-4F compare the PM mass separation (%)
between the physical and CFD models for varying MS. Range bars for CFD results define the
CFD model results across the range of MS. Similar to TS results, model results of temporal
effluent PM mass is significantly influenced by the MS selection. In contrast to temporal results
there is a much more muted influence of MS on the event-based PM separation for this coarse
hetero-disperse PSD modeled with a DN of 8. The maximum error in PM mass separation
between physical model and event-based CFD model results for MS values is approximately 3%.
45
Event-Based Separated PSDs and DN for PSDs
The event-based separated PSDs as a function of unsteadiness are reported in Figure 2-6.
The CFD model (MS = 3.1 x 106, TS = 10 sec, DN = 8) PSDs are compared to the PSDs
separated by the physical model. The CFD model error varies from 2.4 to 6% as a function of
unsteadiness. Physically, results illustrate that the finer gradation of PM is eluted by higher
flows and the coarse PM dominates the separated PSD on a gravimetric basis.
As a function of TS a parallel set of CFD model results at a higher DN (MS = 3.1*106, TS
= 10 s, DN = 16) are summarized in Figures A-4 and 5. Results indicate that the CFD model
error with respect to the temporal distribution of effluent PM mass is further decreased as
compared to a DN of 8 for each TS but at the cost of increased computational time. This
reduction in model error is particularly apparent for the highly unsteady hydrograph. However,
while the modeling error does decrease with a DN of 16 the computational time almost doubles.
For this coarse hetero-disperse PSD and a baffled HS a DN of 16 may not provide a significant
benefit as compared to a DN of 8 based on PM mass given the additional computational time.
Additionally, as a function of MS a parallel set of CFD model results at a higher DN (MS
= 3.1*106, TS = 10 s, DN = 16) are summarized in Figure A-4 and 5. Parallel to the TS results at
a DN of 16 the CFD model error with respect to the temporal distribution of effluent PM mass is
further decreased, again at a cost of increasing computational time. Figure A-4 illustrates the
model error decreases slightly for each MS, in particular for the highly unsteady hydrograph as
compared to a DN of 8 results in Figure 2-4. As is the case for TS results at a DN of 16 the
resulting decrease in CFD model error is accompanied by increased computational time.
While temporal effluent PSD and PM mass are a function of TS and MS, separated PSD
are separately modeled to examine the role of MS on separated PSD results. Results in Table A-
4 through A-6 indicate no significant difference (p = 0.05) for the MS range tested with the
46
requirement that the MS selected satisfy convergence criteria. While these results indicate that
CFD model results for the separated PSD are independent of MS, this result is a function of the
relatively coarse hetero-disperse PSD and as with TS will vary with PSD granulometry.
The role of DN on captured PSD is also explored. Figure A-7 depicts the captured CFD
model PSDs. CFD model errors range from 2.4 to 5.7%. The captured PSDs obtained for varying
DNs are not statistically significantly different (p = 0.05); noting that captured PSDs are coarser
and less hetero-disperse than the effluent.
Effect of Hydrograph Unsteadiness
Figure 2-3 and 2-5 reports the CFD model results in comparison to physical model results
for effluent PM mass as a function of hydrograph unsteadiness. For example, results at TS of 900
sec illustrate increasing error with increasing unsteadiness. Results in Figure 2-3 indicate that as
unsteadiness decreases the model error decreases. As hydrograph unsteadiness increases coarser
TS and MS values do not capture the variability of computational cell properties in the
computational domain as compared to greater discretization in time and spatial grid resolution.
Figure 2-4 and Figure A-4 include a range of HS residence times. For each hydrograph the
normalized axis TS/50 is generated, where 50 is the theoretical residence time for the HS
median flow rate, Q50. With Q50, hydrograph Qp, and 50 of the HS the error for a given TS can
be determined. To illustrate TS results normalized to hydrograph duration the normalized axis
TS/td is generated. Previous studies model the PM response of a screened HS subject to
unsteady loadings in which one minute TS are utilized to reproduce actual runoff event effluent
PM. In these events the hydrograph td varies from 15 to 408 minutes and hydrograph Qp varies
from 0.6 L/s to 17.5 L/s for a small impervious urban watershed (Pathapati and Sansalone,
2009c). Results in Figure 2-4A are supported by physical and CFD model results from a
47
separate study for a screened HS. In that study the CFD model TS is 60 sec and MS is 3.86 x
106. From that study model results for a 14 March 2004 event (Qp = 6.4 L/s, td = 400 minutes,
V = 24,076 L) produced an error for effluent PM mass of 4.7% while for a 21 August 2005 event
(Qp = 17.3 L/s, td = 106 minutes, V = 50,002 L) produced an error of 6.6% (Pathapati and
Sansalone, 2009c). The small watershed hydrologic loading parameters, CFD model parameters
for the in-situ screened HS and error results are similar to those of this study.
Results in Figure 2-4E-F are compared to steady flow CFD model predictions of effluent
PM mass using the median and peak flow rates. The median and peak steady flow rates
underestimate (up to -13.5%) and overestimate (up to 6%), respectively the physical model
event-based effluent PM. Results indicate that steady flow statistics typically cannot represent
unsteady PM mass separation behavior, especially for highly unsteady hydrographs. These
results are supported by previous studies indicating a singular steady flow statistic (Pathapati and
Sansalone, 2009c) or steady flow rate steps do not reproduce unsteady phenomena controlling
PM mass separation in a baffled or screened HS or clarifier unless loadings approach a quasi-
steady condition.
Event-based separated PSD results for each hydrograph are compared to CFD model
results using steady peak or median hydrograph flows as shown in Figure 2-6. While steady flow
results diverge from physical model PSDs, only for the highly unsteady hydrograph, typical of
small watersheds, do steady flow indices not accurately reproduce separated PSDs (p = 0.05).
Conclusion
This study develops a validated CFD model to predict PM separation and eluted PM of a
hydrodynamic separator (HS), a treatment unit utilized worldwide for treatment of wet and dry
weather flows, subject to a hetero-disperse PSD gradation and unsteady hydrologic loadings. An
accurate parameterization of mesh size (MS), time step (TS) and PSD discretization number
48
(DN) is performed. Results (PM and PSD) demonstrate that the full-scale CFD model is able to
accurately predict the response of a full-scale physical model across the range of quasi-steady to
highly unsteady flow loadings. However, time-dependent profiles of PM indices are strongly
influenced by model parameterization. Results demonstrate that TS and MS have a significant
impact on time-dependent eluted PM mass and SSC. The influence of TS and MS also varies for
increasing unsteadiness. Hydrologic events with higher degree of unsteadiness require a finer
spatial discretization (higher MS) of the computational domain and finer time resolution (smaller
TS). Results also demonstrated that increasing the model accuracy through higher MS, higher
DN or smaller TS requires increasing computational effort. The matrix of results are applicable
to different geometries due to the scaling procedure applied to TS and MS. Results also indicate
that a DN of 8 to 16 for this coarser hetero-disperse PSD will reproduce effluent PM load. This
study serves as a benchmark for future CFD applications to facilitate modeling of unit operations
and processes (UOPs) under highly unsteady hydrologic loading typical of small watersheds.
Finally this investigation provides a quantitative assessment of modeling accuracy for different
TS and MS subject to hydrograph unsteadiness with results that are validated from a monitored
physical model. This set of results represents a detailed and useful guideline for modelers in
selecting or evaluating computational parameters as a function of loading unsteadiness in order
to balance model accuracy, computing time and computational resources.
49
Table 2-1. Physical model (baffled HS) hydraulic and PM loading and PM separated. Qp, V, tp,
Ci, td, MB PM, and are peak flow, volume, time to peak, influent PM,
hydrograph duration, mass balance, separated PM, gamma shape and scale factors,
and unsteadiness, respectively
Qp Qp V tp Ci td MB PM
Mass Influent PSD Hydrograph
(L/s) (%) (L) (min) [mg/L] (min) (%) (%) Description
18 100 22.75 15 200 74 93.9 64.03 0.58 271 1.15 Highly
unsteady
9 50 23.37 15 200 87 97.9 63.51 0.58 271 0.24 Unsteady
4.5 25 22.85 15 300 125 98 71.82 0.58 271 0.09 Quasi-
steady
50
Figure 2-1. Schematic representation of the full-scale physical model facility setup with baffled
hydrodynamic separator (BHS)
Baffled HS
cm pipe
cm pipe Flow meter Flow meter
Municipal water line
45,425 L
Storage
tank
45,425 L
Storage
tank
Pump skid
Drop Box: Influent
PM Injection
Effluent Sampling
Inflow
Outflow
Flow Control Valve
Flow
Valve
51
Elapsed time (min)
0 20 40 60 80 100 120
Q (
L/s
)
0
5
10
15
20
25Q
p = 18 L/s; td=74 min
Qp = 9 L/s; td=87 min
Qp = 4.5 L/s; td=125 min
V = 22,840 L
Particle diameter (m)
1101001000
% f
iner
by m
ass
0
20
40
60
80
100Modeled Influent ( = 0.58, =271)
Modeled Effluent
Qp = 18 L/s ( = 0.83, = 42.8)
Qp = 9 L/s ( = 0.85, = 38.3)
Qp = 4.5 L/s ( = 0.89, = 27.13)
Measured Influent
Measured Effluent
Qp = 18 L/s
Qp = 9 L/s
Qp = 4.5 L/s
Figure 2-2. Influent hydraulic loadings and PSD. A) illustrates three hydrographs loading
physical model (baffled HS shown in inset) and B) influent and effluent measured
and modeled particle size distributions (PSDs) for each loading
A B
Outflow
1.83 m
1.73 m
Inflow
Baffled HS
52
Qp
= 18 L/s; td
= 84 min
Eff
luen
t P
M (
g)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Model parameters:
DN = 8
TL = 8 m
MS = 3.1*106
Qp
= 9.06 L/s; td
= 87 min
Elapsed time (min)0 20 40 60 80 100 120
Eff
luen
t P
M (
g)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Qp
= 4.53 L/s; td
= 125 min
Elasped time (min)
0 20 40 60 80 100 120
Eff
luen
t P
M (
g)
0
100
200
300
400
500
e n (
%)
0
20
40
60
80
100
Measured
Modeled
TS = 10 sec
TS = 300 sec
TS = 900 sec
Qp
= 18 L/s; td
= 74 min
Qp
= 9.06 L/s; td
= 84 min
Model parameters:
DN = 8
MS = 3.1*106
Figure 2-3. The effect of time step (TS) on modeled intra-event effluent PM as a function of
hydrograph unsteadiness (). The model error (en) is calculated with respect to
physical model data. A, B, and C report respectively the effluent PM variation
throughout the highly unsteady (=1.15), unsteady (=0.24) and quasi-steady
(=0.09)
A
B
C
53
0
5
10
15
20
25
30
35
40
Qp = 4.5 L/s; td = 125 min; 50
= 11 min
Qp = 9 L/s; td = 87 min; 50
= 33.7 min
Qp = 18 L/s; td = 74 min; 50
= 58 min
(A.) Effluent PM mass
DN = 8
MS = 3.1*106
No
rmal
ized
ro
ot
mea
n s
qu
ared
err
or,
en
(%
)TS/
50
0.02 0.05 0.09 0.45 1.36
0.005 0.01 0.03 0.15 0.44
0.003 0.01 0.02 0.09 0.26
Co
mp
uta
tio
nal
tim
e (h
)
0
20
40
60
80
100
Qp = 4.5 L/s; td = 125 min
Qp = 9 L/s; td = 87 min
Qp = 18 L/s; td = 74 min
Time step, TS (minutes)
0.17 0.5 1.0 5.0 15.0
DN = 8
MS = 3.1*106
(C.)
No
rmal
ized
ro
ot
mea
n s
qu
ared
err
or,
en (
%)
0
2
4
6
8
10
12
14
Qp = 4.5 L/s; td = 125 min
Qp = 9 L/s; td = 87 min
Qp = 18 L/s; td = 74 min
2.3 0.9 0.5
Cell size (mL)
(B.) Effluent PM mass
DN = 8
TS = 10 sec
11.6
0.1
Co
mp
uta
tio
nal
tim
e (h
)
0
20
40
60
80
100
120
Qp = 4.5 L/s; td = 125 min
Qp = 9 L/s; td = 87 min
Qp = 18 L/s; td = 74 min
0.2 1 3.1 5
(D.)
DN = 8
TS = 10 sec
Mesh size, MS (millions)
0.2 1 3.1 5Mesh size, MS (millions)
0.02 0.05 0.09 0.45 1.36
0.005 0.01 0.03 0.15 0.44
0.003 0.01 0.02 0.09 0.26
0.001 0.004 0.008 0.040 0.120
0.0002 0.006 0.012 0.057 0.172
0.0023 0.007 0.013 0.068 0.203
TS/td
4.5
P
M m
ass
(%)
55
60
65
70
75
80
9 18 4.5 9 18
P
M m
ass
(%)
55
60
65
70
75
80
Qp (L/s) Q
p (L/s)
Measured
Qmedian
Qpeak
Event-based
Modeled
MS = 3.1*106
MS = 3.1*106
MS = 3.1*106 TS = 10 sec TS = 10 sec TS = 10 sec
Figure 2-4. CFD model error (en), computational time simulating eluted PM as function of TS
and MS for hydrograph unsteadiness and measured and modeled event-based overall
removal efficiency, as well as the modeled overall efficiency at Qpeak and Qmedian
A B
C
D
E F
54
Elasped time (min)
0 20 40 60 80 100 120E
fflu
ent
PM
(g)
0
100
200
300
400
e n (
%)
0
20
40
60
80
100
Measured
Modeled
MS = 0.2*106
MS = 1*106
MS = 3.1*106
Qp
= 18 L/s; td
= 74 min
Eff
luen
t P
M (
g)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Qp
= 9.06 L/s; td
= 87 min
Model parameters:
DN = 8
TS = 10 sec
Elapsed time (min)
0 20 40 60 80 100 120
Eff
luen
t P
M (
g)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Qp
= 4.53 L/s; td
= 125 min
Figure 2-5. The effect of mesh size (MS) on CFD modeled intra-event effluent PM as a function
of hydrograph unsteadiness (). The model error (en) is calculated with respect to
physical model data. A), B) and C) report respectively the effluent PM variation
throughout the highly unsteady (=1.15), unsteady (=0.24) and quasi-steady
(=0.09)
A
B
C
55
Particle diameter (m)1101001000
% f
iner
by m
ass
0
20
40
60
80
100 Measured
CFD Modeled ( = 1.2; = 150)
Qmedian
Qpeak
% f
iner
by m
ass
0
20
40
60
80
100Measured
CFD Modeled
(
Qmedian
Qpeak
Particle diameter (m)
1101001000
% f
iner
by m
ass
0
20
40
60
80
100Measured
CFD Modeled
(
Qmedian
Qpeak
DN = 8
TS = 10 sec
MS = 3.1*106
Qp
= 18 L/s; td
= 74 min
Qp
= 9 L/s; td
= 87 min
Qp
= 4.5 L/s; td
= 125 min
en= 3%
en = 2.4%
DN = 8
TS = 10 sec
MS = 3.1*106
en
= 5.6%
DN = 8
TS = 10 sec
MS = 3.1*106
Figure 2-6. Separated event-based PSDs from CFD model as compared to physical model data.
Separated event-based PSDs for Qp and Qmedian are also reported. en represents the
normalized root mean squared error between captured event-based measured and
modeled PSDs
A
B
C
56
CHAPTER 3
STORMWATER CLARIFIER HYDRAULIC RESPONSE AS A FUNCTION OF FLOW,
UNSTEADINESS AND BAFFLING
Summary
A primary function of clarifiers (basins) loaded by stormwater is separation of particulate
matter (PM). Clarifier geometry and response are often indexed by surface area (SA) or length
to width (L/W) ratio. In the built environs, clarifier geometry is constrained by infrastructure
and alternative opportunity land uses that impact SA and L/W. As a result, retrofitting clarifiers
with internal bafflers is often considered in order to improve hydraulic and PM response. While
most studies and practices evaluate hydraulic response based on steady flow, stormwater unit
operations (UO), including clarifiers, are also subject to highly unsteady flows. This study
quantifies the impact of baffle configuration, (direction and flow tortuosity (Le/L) as an analog
to L/W), flow rate and hydrograph unsteadiness () on hydraulic response using the Morrill
index (MI), volumetric efficiency (VE) and N-tanks-in-series (N) metrics. Data are generated
with both physical models and unsteady computational fluid dynamics (CFD) models of
clarifiers with rectangular (with and without baffles) and trapezoidal cross-sections. For un-
baffled configurations, VE and N increase while MI decreases with flow rate. For baffled
configurations, there is an asymptotic relationship between N and the Peclet number (Pe). MI
and N are functions of and Le/L as may be seen in the hydrograph results. A higher baffle
number (higher Le/L) generates greater PM separation.
Introduction
Urban stormwater PM is a cause of impairment and deterioration for surface waters
(Heaney and Huber, 1984). PM is also a mobile substrate for partitioning of chemicals such as
metals and nutrients (Sansalone, 2002; USEPA, 2000). Separation of PM from stormwater is
commonly facilitated with clarifier systems such as retention basins based on gravitational
57
settling. In many urban settings, clarifier dimensions such as SA, L/W and volume are limited.
As a result, internal retrofitting with bafflers is often considered to improve hydraulic behavior
and, commensurately, PM separation. While clarifiers are frequently idealized as approximating
plug flow with increasing L/W, the actual hydraulic behavior deviates from plug flow, not only
because of external constraints on L/W but also as a result of dispersion, channeling, recycling of
fluid or creation of stagnant zones (Levenspiel, 1999). Hydraulic behavior can be quantified with
MI, residence time distribution (RTDs), VE and N-tanks-in-series indices. MI is a mixing index,
accounting for the random spread of fluid due to stagnation zones, turbulent diffusion and
recirculation (Morrill, 1932). RTD is the time a fluid element resides in a clarifier, expressed as a
probability distribution function (Morrill, 1932). VE is the inverse of MI. N-tanks-in-series can
be determined from an RTD (Hazen, 1904). The N-tanks model idealizes a clarifier as a series of
completely mixed tanks with higher N values indicating an increasing similarity to ideal plug
flow behavior (Metcalf and Eddy, 2003). While physical modeling may facilitate the
determination of these indices, they are often prohibitively expensive. CFD modeling provides
an approach to more economically simulate the hydraulic (continuous phase) and the coupled
PM behavior (discrete phase) (Pathapati and Sansalone, 2011; Dickenson and Sansalone, 2009).
CFD also provides a tool to examine these hydraulic indices for UOs subject to design and load
variations.
Studies have examined the hydraulic efficiency of baffled systems, typically at constant
flow (Wilson and Venayagamoorthy, 2010; Kim and Bae, 2007; Amini et al., 2011; Kawamura,
2000). For example, Wilson and Venayagamoorthy (2010) analyzed a baffled tank with up to 11
transverse baffles; concluding that that maximum hydraulic efficiency was reached at six baffles.
Kim and Bae (2007) studied the hydraulic efficiency of a pilot-scale baffled contactor as a
58
function of the number of transverse baffles and demonstrated that the rate of plug flow
increased as the number of baffles (up to 25) increased. Amini et al. (2011) used a validated
scaled-down physical model of a chlorine contact tank (CCT) to conclude, using the MI, that the
recommended number of channels within the tank was 6 to 9. Kawamura (2000) recommended
that, for the design of CCTs, a tank should be divided into 2 to 4 longitudinal baffles, with a L/W
ranging from 5:1 to 15:1.
Not all studies agree on the relationship between flow rate and N. For example, Lopez et
al. (2008) analyzed a lab-scale clarifier as a function of flow rate steps and type of feed under
three flow regimes and concluded that as flow rate increases, N decreases. Conversely, Metcalf
& Eddy (2003) and Abu-Reesh (2003) argued that N should be proportional to Pe, and since for
increasing flow rate there is increasing advection, Pe also increases. Therefore they concluded
that N also increases. In contrast to wastewater and drinking water systems that are loaded by
steady to quasi-steady flows, stormwater UOs are subjected to a very wide range of flows or
highly unsteady episodic flows. For stormwater clarifiers, a determination of N or MI as a
function of flow rate, or Le/L (as an equivalent L/W for baffling) has not been examined.
The objective of this study is to elucidate the role of baffle configurations, flow rate and
hydrograph unsteadiness on the hydraulic behavior of a clarifier subject to stormwater flows.
Hydraulic behavior is indexed using RTD, MI, VE, Pe and N. The baffle configuration
parameters are direction (transverse or longitudinal) and the number of baffles. The number of
baffles is indexed by flow tortuosity (Le/L) as a surrogate for flow path length to width ratio.
Results are generated using a CFD model validated with a full-scale physical model.
59
Material and Methods
The physical modeling and tracer study was conducted on a full-scale primary rectangular
clarification basin typically used for PM separation from runoff collected in a small urban
catchment. Depending on land use and infrastructure constraints, this precast concrete clarifier
would be constructed at-grade or below-grade. In Figure 3-1, the conceptual process flow
diagram for the methodology and the scaling between the actual physical model and the
catchment characteristics is shown. Physical loadings and scaling are representative of
predominately impervious, developed urban parcels facilitating motor vehicle movement or
parking. The particle size distribution (PSD) and PM loadings represent the fine PM fraction (<
75 m) of urban runoff PM while the rainfall depth and duration generates a hydrograph with a
peak flow and volume that is representative of a one-hour event with a two year recurrence time
event for the North Florida catchment. The clarifier design flow, Qd was ~50 L/s as an open-
channel system. With programmable variable frequency drives for the pumping system,
hydrographs with differing peak flows (up to 50 L/s) and levels were generated with schedules
as shown in Figure 3-1. As a control, a constant concentration of 200 mg/L was also studied.
Monitoring of PM and PSDs was conducted. Tracer tests were conducted to determine RTDs for
steady flows (2, 5, 10, 25, 50, 75 and 100% of Qd). Full-scale physical models of an un-baffled
rectangular, an 11-baffle rectangular clarifier of the same surface area, and an un-baffled
trapezoidal clarifier were fabricated. In addition to steady flows, validation of the CFD model
was conducted with an unsteady event. A description of the physical modeling is provided in the
Appendix. Figure 3-2 summarizes the validation results of the 8 July 2008 storm for PM and
PSDs. Supporting figures (B-5) are provided in the Appendix.
60
RTD Curves and Assessment of Hydraulic Indices
RTD functions, E(t) and cumulative function, F(t) were derived from tracer tests and
calculated (Morrill, 1932). The definitions are as follows:
0
dttC
tCtE
dttEtF
t
0
MI is defined as (Morrill, 1932; Metcalf and Eddy, 2003):
10
90
t
tMI
In this expression t10 and t90 indicate the period of time necessary for 10 and 90% of the
mass of tracer that was injected at the inlet to reach the clarifier outlet. For ideal plug flow, MI =
1 and increases for a completely mixed clarifier. Metcalf & Eddy (2003) indicate 22 as an
approximate upper bound. The inverse of MI is the hydraulic VE (Morrill, 1932; Metcalf and
Eddy, 2003).
100
1(%)
MIVE
The N-tanks-in-series model introduced by Hazen (Hazen, 1904) conceptualizes a non-
ideal clarifier as consisting of a cascade of N equal-sized completely mixed tanks arranged in
series. As N increases from 1 to ∞, the hydraulic pattern in the clarifier changes from a single
completely mixed tank to that of a plug flow clarifier. N is defined for horizontal-flow settling
basins (Letterman, 1999; Fair et al., 1966).
ptt
tN
50
50
(3-1)
(3-2)
(3-3)
(3-4)
(3-5)
61
In this expression t50 is the time at which 50% of tracer has exited the clarifier and tp is the
time at which the peak tracer concentration is observed. In literature there are other definitions of
N which are related to equation 3-5 as shown in the Appendix.
CFD Modeling
The 3D geometry and mesh of the full-scale physical models were generated in a GAMBIT
(Fluent, 2010) environment as shown in Figure B-6, B-7, B-8, with details of the mesh
generation shown Figure B-9 and described in the Appendix. The CFD models were built for a
trapezoidal cross-section clarifier, a rectangular clarifier with a varying number of transverse
baffles, and separately with longitudinal baffles. The number of transverse baffles varied from 3
to 36 and from 2 to 9 for the longitudinal baffles. The CFD models were built using the finite-
volume based code Fluent (Fluent, 2010). The CFD developed in this study treated the fluid
phase as a continuum in an Eulerian frame of reference while coupled discrete phase model
(DPM) used a Lagrangian frame of reference for describing behavior of the PM in the system.
The turbulence model of this study is based on a variant of the Navier-Stokes (N-S) equations,
the Reynolds Averaged Navier-Stokes (RANS) equations (Pope, 2000):
,0
i
i
ux
2
2
''
j
i
i
ij
j
ji
j x
u
x
puu
xuu
x
The turbulence model used was the realizable k- model (Shih et al., 1995). This model is
suitable for boundary-free shear flow (baffled clarifier) applications and consists of turbulent
kinetic energy and energy dissipation rate equations recorded below (Shih et al., 1995).
jx
iu
ju
iu
jx
k
k
t
jx
jx
k
ju
t
k''
(3-6)
(3-7)
(3-8)
62
kCSC
xxxu
t j
t
jj
j
2
21
ijij SSS
kSC
2,,
5,43.0max
1
In these equations σk = 1.0, σε = 1.2, C1 = 1.44, C2 = 1.9, k is the turbulent kinetic energy; ε
is the turbulent energy dissipation rate; S is the mean strain rate; νT is the eddy viscosity; ν is the
fluid viscosity; and uji, uj′u′i were previously defined.
The numerical solver used was pressure-based, meaning that it was and suited for
incompressible flows where motion is mainly governed by pressure gradients. The SIMPLE
(Semi-Implicit Method for Pressure-Linked Equations) pressure-velocity coupling scheme was
used. Convergence criteria were set so that scaled residuals for all governing equations were
below 0.001 (Ranade, 2002). Regarding boundary conditions, the inlet velocity was specified
and the free surface was approximated as a shear free wall with velocity components normal to
the surface. From the balance of tangential stresses at the interface assuming air dynamic
viscosity is much less than water viscosity, shear stresses becomes negligible at the free surface.
All walls were defined as “reflective” boundaries, whereas the outlet is defined as an “escape”
boundary.
To model the RTDs, one hundred neutrally buoyant particles (1 m) were uniformly
released across the inlet as an instantaneous pulse at (t = 0) and tracked through the flow using
stochastic particle tracking. Since the dispersed phase was sufficiently dilute (volume fraction
(VF) was less than 10%) the DPM was used to predict PM transport and fate within the system
(2005). The DPM integrated the equations of motion of the discrete phase and tracked individual
particles through the flow field by balancing the forces acting on the particles. Particle trajectory
was calculated by integrating the force balance equation, written below in the ith-direction.
(3-9)
(3-10)
63
p
pipiiDi
pi gvvF
dt
dv
24
Re18
2iDi
pp
DiC
dF
ipipi
vvd Re
3221
ReReK
KKC
iiiD
The first term on the right-hand side of eq. 3-11 is the drag force per unit particle mass, in
which FDi is defined in eq. 3-12. The second term is buoyancy/gravitational force per unit
particle mass. Rei is Reynolds number for a spherical particle, and CDi is drag coefficient. From
Eq. 3-11 to Eq. 3-14, is the fluid density, p is particle density, vi is fluid velocity, vpi is particle
velocity, dp is particle diameter, is the dynamic viscosity, and K1,K2,K3 are empirical constants
as function of Rei.
The dispersion of particles due to turbulence in the fluid phase is predicted using a
stochastic tracking model, integrating the trajectory equation for individual particles (Eq. 3-11),
using the instantaneous fluid velocity, tuu ' , along the particle path during the integration
(Thomson, 1987; Hutchinson et al., 1971). The random effects of turbulence on the particle
dispersion were considered by computing the trajectory for a sufficient number of representative
particles. A user defined function (UDF) was written to record the time at which each particle
passed through the outlet surface. The CFD model was loaded with a constant flow rate at the
inlet and, after solving the flow field, the DPM equations were integrated numerically. For
transient RTD, the CFD model was loaded with the hydrographs of different (Equation 3-15)
(3-11)
(3-12)
(3-13)
(3-14)
64
and Qp, as shown in Figure 3-1. The UDF recorded the residence times of the particles passing
the outlet section during each time step. The dimensionless unit hydrograph was modeled as a
step-function (Sansalone and Teng, 2005). The physical model hydrographs are scaled by the HS
design hydraulic capacity (50 L/s), maintaining constant volume (V= 125,200 L) and a constant
time to peak flow, tp of 30 min. The time to peak flow is established from the SWMM (Storm
Water Management Model) (Huber and Dickinson, 1988), in which the size of a catchment is
matched to deliver peak runoff flow rate equal to the design flow rate of the unit operation. A
parameter, is determined to quantify the unsteadiness of each hydrograph (Garofalo and
Sansalone, 2011):
50
1
mediQdt
dV
In this equation, Qmedian represents the median flow rate. The values of for highly
unsteady, unsteady and quasi-steady were 1.54, 0.33 and 0.01, respectively.
The physical model of the rectangular and trapezoidal cross-section clarifiers without
baffles and the rectangular clarifier with transverse baffles were used to validate effluent PM and
PSD response generated by the CFD method detailed by Garofalo and Sansalone (Garofalo and
Sansalone, 2011). The physical models were loaded by two hydrographs, a triangular
hyetograph generating 0.5 inches of runoff and a simulation of a historical event of 8 July 2008
in Gainesville, Florida from the small catchment. The two hydrographs are described in the
Appendix and their characteristics are summarized in Table B-2. The validation analysis
consisted of comparison between measured and CFD modeled RTD curves. A root mean
squared error, RMSE was used to evaluate CFD model error in predicting RTDs with respect to
the physical model data. The errors reported in Table B-1 show RMSEs between measured and
(3-15)
65
modeled RTDs within ± 10%. The validated RTD curves from which the hydraulic indexes are
generated are reported in Figure B-10. The error between the measured and modeled event-based
PSDs was also calculated as a RMSE. The validation of CFD modeled data in terms of measured
PM mass removal was based on a relative percentage error, . The modeling error was within ±
10%. The validation analysis is described in detail in the Appendix.
Results and Discussion
Validation results from the physical and CFD model are shown in Figure 3-2 and B-10 for
effluent PM and PSDs. Results from both the CFD and the physical model are compared for the
full-scale rectangular cross-section clarifier with and without 11 baffles for the July 8, 2008
hydrograph (Figure 3-2). Figure 3-2 also illustrates the impact of baffling on PM eluted as a
function of time or as an event-based PM mass. As in Figure 3-2, Figure B-11 summarizes PM
elution results for a validation hydrograph generated from a triangular hyetograph. The CFD
model reproduces PM elution from the physical clarifier with and without baffles. PM
separation is related to the hydraulic behavior of the clarifier and increases with a higher number
of baffles. Figure 3-2 shows the measured effluent PM eluted from the system for the July 8th
hydrograph for the rectangular clarifier with 0 baffles and 11 baffles. PM removal efficiency for
the un-baffled clarifier is 56% and with 11 baffles it is 71%, as shown in Table B-2. The percent
difference between the two configurations of 26%, thus demonstrating the beneficial effect of
internal baffling on PM separation.
Steady Flow Hydraulic Indices as Function of Flow Tortuosity (equivalent L/W)
The results in Figure 3-3 compare the hydraulic indices for the un-baffled rectangular and
trapezoidal clarifiers. Figure 3-3A indicates that VE linearly increases as Qn increases and varies
from 5-10% and 12 - 22% for the rectangular and trapezoidal clarifiers. The results also indicate
that the trapezoidal cross-section is hydraulically more efficient than the rectangular cross-
66
section. In the rectangular clarifier, the areas proximate to the two lateral walls mostly represent
stagnant zones. The trapezoidal cross-section configuration with lateral inclined walls minimizes
the side stagnant areas and, therefore, offers a higher volume utilization than the rectangular
configuration. In contrast to the VE results, Figure 3-3B shows that MI decreases with Qn for
both clarifier configurations, but that the rate is significantly greater for the rectangular clarifier.
At the design flow rate, Qd, there is approximate convergence of the MI values for each
configuration. In a pattern similar to VE results, Figure 3-3C shows the value of N for the N-
tanks-in-series model increases linearly with Qn for the rectangular and trapezoidal no-baffle
configurations. The rectangular clarifier behaved as a mixed reactor with N varying from 1 to 1.7
while N for the trapezoidal clarifier ranged between 1.5 and 3. The trapezoidal clarifier deviated
from the completely mixed reactor behavior (N = 1), a result also supported by higher VE results
of the trapezoidal clarifier.
The impact of baffle configuration (e.g. number of baffles and orientation) was
investigated with the CFD model. While the physical models were constructed with either 0 or
11 baffles for the rectangular clarifier, the simulations were capable of modeling the rectangular
clarifier with various numbers and configurations of baffles, thus producing data for clarifier
flow path tortuosity, Le/L (Table B-3). In Figure 3-4, simulated VE results are reported as a
function of the number of baffles as indexed by tortuosity (as well as equivalent L/W) and fit by
two-parameter sigmoid curves with parameters summarized in Table B-4. VE results vary up to
approximately 50% across the range of steady flows tested and the tortuosity varied up to
approximately 70%. For all simulated baffling configurations, the maximum VE achieved was
80%; a significant increase with respect to the un-baffled configurations. Figure 3-3, 3-4
illustrates that the increase in VE is a function of increasing tortuosity and increasing Qn. The
67
rate of increase in VE, as a function of tortuosity, is greater at high Qn as compared to low Qn for
low values of tortuosity. For both baffle directions, at the highest values of tortuosity the VE
approaches a common asymptotic value beyond which VE does not significantly change. While
wastewater and drinking water unit operations and processes are subjected to fairly steady flows,
stormwater units are subjected to highly variable and transient flows that can vary by orders of
magnitude in an event. Therefore, to achieve a target VE in a baffled clarifier subjected to
rainfall-runoff events, the representative Qn range requires determination (for instance,
probabilistically) in order to identify a tortuosity range.
The velocity magnitude contours generated from the simulation results at the design flow
rate of 50 L/s are shown for the rectangular clarifier with 0, 3, 24 baffles in Figures B-12, B-13,
B-14. In the clarifier without baffles, the results show a direct flow path (short-circuiting) from
the inlet to the outlet. With an increasing number of baffles the dead zone areas (low velocity
areas) decreased with respect to the non-baffled rectangular configuration, as shown qualitatively
in these simulation results. As the number of baffles increased (increasing flow tortuosity) the
VE also increased. MI values from the validated steady CFD model are reported in Figure B-15.
MI curves, modeled as two parameter exponential functions (Table B-5), decrease with
increasing flow rates. MI curves reach an asymptote beyond 6 baffles (transverse baffling) at Qd,
in agreement with the results from Amini et al. (2011) However at lower Qn, the MI approaches
an asymptote at 11 to 24 baffles, indicating that the number of baffles beyond which MI is
constant varies as a function of Qn. In Figure B-15B the MI curve at Qd approaches a constant
value beyond 2-4 longitudinal baffles with a L/W of 38, in accordance with the rule of thumb
given by Kawamura (Kawamura, 2000); however at Qn values lower than Qd, MI reaches an
asymptote beyond 5-6 baffles with 100 L/W.
68
Since the work of Hazen (Hazen, 1932), there has been ongoing interest in conceptualizing
the behavior of a clarifier as series of N well-mixed tanks such that increasing values of N
approach plug flow behavior. In Figure 3-5, the simulation results for N-tanks-in-series are
shown as function of flow rate and flow path tortuosity. As the tortuosity increases N also
increases. The increase in N is a function of increasing flow rate, with an increase in N that is
much greater at higher flow rates for the same tortuosity. For an increasing number of baffles in
either direction the clarifier approaches plug flow conditions at higher flow rates. The baffling
has a higher impact on N at high Qn, enhancing plug flow condition (N up to 500). N turns out to
be proportional to Qn.
The Peclet (Pe) number is the ratio of the convective to dispersive transport. Convection is
quantified as the product of the fluid velocity, u, and the characteristic length, which in this case
it is selected as the clarifier flow path, Le. As Qn increases convection increasingly dominates
dispersion and Pe increases. N also increases in proportion to Pe. The fitting curve parameters
are reported in Table B-6. Figures 3-6A and 3-6B summarizes the relationship between the Pe
number and N for varying flow rates. Results are fit with a hyperbolic function.
Unsteady Flow Hydraulic Indices as Function of Flow Tortuosity (Equivalent L/W)
In addition to results generated at a series of steady flow rates up to Qd of the clarifier, and
separately from the unsteady validation loadings for the physical models, unsteady loading were
simulated for the hydrographs shown in Figure 3-1. The unsteadiness () of these hydrographs
ranged from a of 1.54 for the highly unsteady hydrograph to a of 0.01 for the quasi-steady
hydrograph. The MI and N-tanks-in-series results for each of these hydrographs are reported in
Figure 3-6C and 3-6D. At low values of tortuosity, the MI is higher (indicating lower efficiency)
and varies significantly across the degree of unsteadiness. As the tortuosity increases, the MI
69
decreases (approaching plug flow) and unsteadiness does not significantly impact the MI values.
For the given range of unsteadiness and tortuosity, the N values range from 1 to 80. N values are
influenced by increasing unsteadiness, but in contrast to MI results, this influence occurs for
increasing tortuosity values. The data are fit and the parameters are reported in Tables B-13, B-
14.
Hydrograph-based RTDs are modeled for each hydrograph shown in Figure 3-1 in order to
examine the behavior of the rectangular clarifier with transverse baffles as a function of
unsteadiness. In Figure 3-7, the cumulative RTDs are reported as function of tortuosity and
unsteadiness. At low tortuosity, (1 and 1.9 corresponding to 0 and 3 baffles) the clarifier
behavior approximates more of a plug flow behavior for the highly unsteady hydrograph. At
lower levels of unsteadiness the clarifier behavior increasingly approximates a mixed reactor
RTD. The RTD gradients increase as the degree of unsteadiness increases, indicating that
convective transport dominates dispersive transport for higher unsteadiness levels and lower
tortuosity. These results are similar to the Pe number results in Figure 3-6A and 3-6B. At higher
tortuosity (3.6 and 6.4, corresponding to 11 and 24 baffles) the clarifier increasingly
approximates plug flow behavior for all levels of unsteadiness. At higher tortuosity the RTD
curves are characterized by a similar constant slope and are offset in parallel along the time axis.
Therefore, regardless the level of unsteadiness, the hydraulic behavior remains invariant with a
higher number of baffles and tortuosity.
In contrast to wastewater and drinking water unit operations and processes, evaluation of
the hydraulic response of clarifiers (basins) retrofitted with internal baffles and loaded by
unsteady rainfall-runoff has not been conducted. Results indicate that the hydraulic response (as
N, MI or RTD) of a baffled or un-baffled basin is function of flow rate, unsteadiness and
70
tortuosity (as an equivalent L/W ratio). Given that stormwater systems are loaded by a wide
range of flows and unsteadiness, a singular hydraulic response, whether as N, MI, VE or RTD,
cannot be expected, although high tortuosity (high number of baffles) does confer a more
consistent, albeit dependable, response as a function of unsteadiness. Based on physical and
CFD model results, this study indicates that internal baffling does alter unsteady hydraulic
response and increase PM separation. For stormwater systems subject to a wide range of
uncontrolled loadings, hydrograph unsteadiness is an important parameter. While the full-scale
physical modeling system of this study was able to meter a constant PM concentration and PSD,
the quest for a unique relationship between a particular hydraulic response (for example N) and
PM or PSD elution from a rainfall-runoff clarifier is further complicated by the separate
unsteadiness of PM and PSD inflows. For future study, it is hypothesized that such a
relationship is not unique. Such a relationship would be tested as a function of hydrograph
unsteadiness, PM and PSD loadings and unsteadiness (the temporal or volumetric transport of
each) and the PM accumulation and PSD thereof in the system (maintenance interval). Such
relationships could most effectively be examined with a CFD model validated by physical model
data.
71
Elasped time (min)0 50 100 150 200 250
Q (
L/s
)
0
10
20
30
40
50
60Qp = 50 L/s, td = 150 min, = 1.54
Qp = 25 L/s, td = 200 min, = 0.33
Qp 12.5 L/s, td = 250 min, =0.01
Figure 3-1. This figure illustrates the conceptual process flow diagram for the methodology.
Clarifier configurations are either: a. rectangular or trapezoidal cross-section with no
baffles, b. clarifier of rectangular cross-section with transverse baffles that range from
n = 3 to 35 baffles, c. clarifier of rectangular cross-section with longitudinal baffles
that range from n = 2 to 8 baffles, Pt: rainfall depth, Td: rainfall duration, Lc:
watershed length, Vt: hydrograph volume, Qp: peak flow rate (L/s), Qd: design flow
rate of 50 L/s, VE: volumetric efficiency, RTD: residence time distribution, N: tanks
in series value, MI is Morrill dispersion index, V: clarifier volume, L: clarifier length,
Le: clarifier flow path tortuosity and PSD is particle size distribution. The watershed
area is 0.25 ha, slope of 1%, Pt of 50 mm and Td = 60 min. Length of catchment of
200 m. and represent the gamma function parameters
0.1110100
% f
iner
by m
ass
0
20
40
60
80
100
Particle Diameter, d (m)
Particle Diameter, d (m)
0.1110100
% f
iner
by
mas
s
0
20
40
60
80
100
L = 7.3 m
n
Clarifier configuration
RTD,
N,
VE,
Output
Vt = 125,200 L
a
.
b
.
c
.
Le
Watershed
Influent
PSD
Effluent
PSD
Inlet Outlet
1.8 m
V = 24,000 L
a
.
72
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
20
40
60
Eff
luent
PM
(kg)
0.0
0.2
0.4
0.6
0.8
1.0
eff
luen
t P
M (
kg)
0
2
4
6
8
10
12
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
20
40
60
Eff
luent
PM
(kg)
0.0
0.2
0.4
0.6
0.8
1.0
eff
luen
t P
M (
kg)
0
2
4
6
8
10
12
Q
Effluent PM
Measured PM
effluent PM
Rectangular
Qp = 50 L/s
td = 110 min
Influent PM = 16 kg
m = 9.30%
0.1110100
% f
iner
by
mas
s
0
20
40
60
80
100
s = 2.65 g/cm
3
Particle Diameter, d ( m)
Rectangular
RMSE = 3.6 %
Effluent
Influent
Effluent
Measured
Modeled
Rectangular clarifier
11 Transverse baffles
m = 4.65%
Particle Diameter, d ( m)
0.1110100
% f
iner
by
mas
s
0
20
40
60
80
100Rectangular clarifier
11 Transverse baffles
RMSE = 1.8 %
Figure 3-2. Physical model and CFD model results for PM and PSDs for the July 8, 2008
hydrograph used for the validation analysis for full-scale physical model of the
rectangular clarifier with no baffles and 11 transverse baffles. In A) and C) the dash
line represents the incremental effluent PM, the solid line the cumulative effluent PM
and the dot points the measured data with the range bars from duplicate samples. In
B), D) the shaded area indicates the range of variation of effluent PSDs throughout
the hydrological events. The dot points are the influent measured PSD (white) and the
minimum and maximum measured PSDs (black). RMSE is the root mean squared
error between effluent average measured and modeled PSDs. Qp is the peak influent
flow rate and td is the total duration of the hydrological event, s is the particle density
eff
luen
t P
M (
Kg)
eff
luen
t P
M (
Kg)
A
C
B
D
Rectangular
clarifier
Rectangular
clarifier
Rectangular
clarifier
Rectangular clarifier
73
Normalized flow rate, Qn
0.0 0.2 0.4 0.6 0.8 1.0V
olu
met
ric
effi
cien
cy,
VE
(%
)
0
5
10
15
20
25
RC (a = 5.5, c = 8, R2=0.99)
TC (a = 12, c = 10.3, R2=0.94)
Morr
ill
Ind
ex,
MI
0
5
10
15
20
RC (a = 17.8, c = 0.97, R2=0.96)
TC (a = 8.3, c = 0.66, R2=0.90)
Normalized flow rate, Qn
0.0 0.2 0.4 0.6 0.8 1.0
N t
ank
s in
ser
ies
0
1
2
3
4
RC (a = 1.53, c = 1.59, R2=0.99)
TC (a = 0.62, c = 1.07, R2=0.98)
Figure 3-3. Comparison between rectangular and trapezoidal cross-section clarifier
configurations. A) illustrates volumetric efficiency, VE as function of Qn, normalized
flow rate with respect to the hydraulic design flow rate, Qd. B) illustrates Morrill
index, MI as function of Qn. C) illustrates N as function of Qn. The parameter of the
fitting curves, a represents respectively in A) and C) the minimum value of VE and
N. The parameter of the fitting curves, b represents in B) the maximum value of MI.
The parameter c represents the slope of the fitting curves
Rectangular clarifier (L/W=4)
nQcaN
nQceaMI
nQcaVE
A
B
C
74
Clarifier flow path tortuosity, Le/L0 2 4 6 8 10
Vo
lum
etri
c ef
fici
ency
(%
)
0
20
40
60
80
100
Q=50 L/s
Q=37.5 L/s
Q=25 L/s
Q =12.5 L/s
Q=5 L/s
Q=2.5 L/s
Q=1 L/sCol 129 vs Col 130
Clarifier flow path tortuosity, Le/L0 2 4 6 8 10
Vo
lum
etri
c ef
fici
ency
(%
)
0
20
40
60
80
100
Qn
1
0.75
0.50
0.25
0.10
0.05
0.01
Figure 3-4. Volumetric efficiency as function of clarifier flow path tortuosity, Le/L for the
clarifier configurations with transverse and longitudinal internal baffling. O is the
opening between the baffle edges and the clarifier walls. Qn is the normalized flow
rate with respect to the hydraulic design flow rate, Qd of 50 L/s for the clarifier
.00
6.6 4 262 35 118
Equivalent length to width, L/W
Transverse baffles (O = 0.20 m)
Longitudinal baffles
A
B
4 38 103 328
Equivalent length to width, L/W
75
Clarifier flow path tortuosity, Le/L0 2 4 6 8 10
N t
ank
s in
ser
ies
0
50
100
150
200
250
300
Clarifier flow path tortuosity, Le/L0 2 4 6 8 10
N t
ank
s in
ser
ies
0
100
200
300
400
500
600
1
0.75
0.5
0.25
0.10
0.05
0.02
Qn
Transverse baffles (O = 0.20 m)
Longitudinal baffles
Figure 3-5. N as function of clarifier flow path tortuosity, Le/L for the clarifier configurations
with transverse and longitudinal internal baffling. O is the opening between the baffle
edges and the clarifier walls. Qn is the normalized flow rate with respect to the
hydraulic design flow rate, Qd of 50 L/s
4 262 35 118 Equivalent length to width, L/W
.00
Transverse baffles
(O = 0.20 m)
Longitudinal
baffles
A
B
4 38 103 328
Equivalent length to width, L/W
76
N tanks in series
0 25 50 75 100 125
Pe
0
20
40
60
80
100
120
1.00
0.75
0.50
0.25
0.10
0.05
0.02
N tanks in series
0 100 200 300 400
Pe
0
20
40
60
80
100
120
1.00
0.75
0.50
0.25
0.10
0.05
0.02
Le/L0 1 2 3 4 5 6 7
Morr
ill
Ind
ex,
MI
0
2
4
6
8
10
Highly unsteady (
Unsteady (
Quasi-steady (
N t
ank
s in
ser
ies
0
20
40
60
80
100
120
Highly unsteady (
Unsteady (
Quasi-steady (
Figure 3-6. Pe as function of N tanks in series for the configurations with respectively transverse
baffles and opening of 0.20 m and longitudinal baffles. The Peclet number illustrated
in A) and B) is calculated as ratio of convective forces to dispersion coefficient, D.
The convective forces are given by the product between the fluid velocity, u and the
characteristic length, Le. The data are fitted by a hyperbole function with parameter a,
representing the maximum value of Pe and b, the rate of Pe change as function of N
tanks in series. Morrill index, MI C) and N D) as function of clarifier flow path
tortuosity, Le/L for highly unsteady, unsteady and quasi-steady hydrographs
A
Nb
NaPe
Transverse baffles
a = 102
b = 18
R2=0.97
Longitudinal baffles
B
a = 121
b = 56
R2=0.91
C
D
4 35 118
Equivalent length to width, L/W 6.6
77
Elasped time (min.)
0 20 40 60 80 100
F (
t)
F (
t)
0.0
0.2
0.4
0.6
0.8
1.0
Le/L = 1.9
Elapsed time (min.)
0 20 40 60 80 100F
(t)
0.0
0.2
0.4
0.6
0.8
1.0
0.25 Qd
Highly unsteady (
Unsteady (
Quasi-steady (
Le/L = 1
Elasped time (min.)
0 20 40 60 80 100
F (
t)
0.0
0.2
0.4
0.6
0.8
1.0
Le/L = 3.6
Elasped time (min.)
0 20 40 60 80 100
F (
t)
0.0
0.2
0.4
0.6
0.8
1.0
Le/L = 6.4
Figure 3-7. Modeled cumulative RTD function, F as function of time for highly unsteady,
unsteady and quasi-steady hydrographs respectively for rectangular clarifier with no
baffle (Le/L = 1), 3 (Le/L=1.9), 11 (Le/L = 3.6) and 24 baffles (Le/L = 6.4)
78
CHAPTER 4
CAN A STEPWISE STEADY FLOW CFD MODEL PREDICT PM SEPARATION FROM
STORMWATER UNIT OPERATIONS AS A FUNCTION OF HYDROGRAPH
UNSTEADINESS AND PM GRANULOMETRY?
Summary
Computational fluid dynamics (CFD) is an emerging model used to predict PM separation
from runoff unit operations (UOs) loaded by hetero-disperse particulate matter (PM) and
unsteady hydraulics. However unsteady CFD modeling requires significantly more
computational overhead compared to steady modeling. As a result this study examines a stepwise
steady CFD model methodology designed to reproduce UO response to unsteady loadings with
lower computational overhead. The method assumes that the UO response for differing flow
rates and particle size distributions (PSDs) can be based on particle residence time distribution
(Up) in a UO. Conceptualizing the linearity and superposition of a UO response subject to a
hydrograph, each Up is convoluted across a hydrograph that was discretized into a series of
steady flow rates. The model is applied to a rectangular clarifier (RC) subjected to three
hydrographs with differing levels of unsteadiness () and PSDs. The role of representative PSD
sampling for the model is also shown for a baffled hydrodynamic separator (BHS). The stepwise
steady model loaded with accurately-monitored PSDs reproduced PM mass when compared to
RC physical model data while the BHS was used to elucidate the need for accurate PSDs.
Computational times for the RC were reduced by an order of magnitude compared to fully
unsteady CFD models. When applied to the measured PSD data from the BHS generated through
automatic sampling, the physical model PM mass balance ranged from 40 to 60% as a function
of hydrograph . Results from automatic sampling of the BHS translated into CFD modeling
errors from 15% to 70%.
79
Introduction
Urban runoff PM is a mobile, reactive hetero-disperse substrate for which chemical species
such as metals, organics and nutrients partition during mobilization, transport and treatment. PM
is recognized as a significant contributor for the impairment of receiving waters (USEPA, 2000).
One common category of unit operation (UO) to separate PM in runoff is hydrodynamic
separators (HS) as preliminary UOs with mean residence times on the order of minutes. A
second category of UO is primary clarifier-type basins (retention/detention/equalizing basins or
tanks with mean residence times that can range from approximately an hour to days). From an
urban water treatment perspective, clarifiers (basins) are more traditional, non-proprietary, more
commonly implemented given their potential to provide coupled hydrologic
(volumetric/hydraulic) and PM control. During the last decade regulatory programs have
developed to require physical modeling of UOs subject to steady flows and PM loadings for
initial certification of performance (TARP, 2003). Final certification of a UO in these programs
can require augmentation of the testing program with fully-unsteady performance testing of UOs
subject to unsteady hydrologic loadings (TARP, 2003). While these programs may require a
series of analyses beyond PM (either as total suspended solids (TSS), suspended sediment
concentration (SSC) and/or PSDs), the performance focus is separation of PM.
While physical modeling is increasingly required for UO, numerical models of UOs
utilizing computational fluid dynamics (CFD) have not developed to the same extent for
regulatory programs (Chen, 2003) despite recent research and engineering utilization of
numerical models (Al-Sammarrace et al., 2009; Tamburini et al., 2011). CFD is an emerging
model based on the Navier-Stokes (N-S) equations utilizing a finite-volume method that can
simulate the coupled hydrodynamics and particulate matter (PM) phenomena in UOs (Dickenson
and Sansalone, 2009; He et al., 2006; Pathapati and Sansalone, 2009a-b). CFD models have been
80
validated with steady flow UO physical models to examine requirements for numerical
simulations. For example, Dickenson and Sansalone (2009) investigated the PSD discretization
requirements of a steady flow CFD model of a baffled HS (BHS) to predict PM fate and
minimize CFD model error for size granulometry that ranged from mono- to hetero-disperse. He
et al. (2006) examined the performance of a combined sewer overflow (CSO) storage to improve
the maximum treatment flow rate by using a validated steady CFD model. Pathapati and
Sansalone (2009a-b) utilized a validated full-scale CFD model to predict PM separation as
function of particle size and flow rate for a radial filter and a screened HS (SHS) under steady
conditions.
Beyond steady flow modeling and initial certification of UOs, actual rainfall-runoff events
are unsteady flow phenomena and field-deployed physical model testing subject to actual
rainfall-runoff events and PM delivery is required for final regulatory certification. Unsteady or
transient loading CFD models are more complex than steady flow models because of coupling
variable hydrology with PM transport and require increasing computational overhead for a given
level of model accuracy. Recent studies employing unsteady CFD models have reproduced PM
separation by UOs subject to unsteady loadings (Pathapati and Sansalone, 2009c; Garofalo and
Sansalone, 2011). Pathapati and Sansalone (2009c) demonstrated CFD unsteady modeling
reproduces the PM mass response of a SHS subject to unsteady runoff with model errors of 10%
with respect to physical model data. However, in the same study the use of event-based steady
flow indices to predict PM separation generated significantly higher errors; in some cases over
100% albeit at a much lower level of computational overhead compared to the accurate fully-
unsteady model. Garofalo and Sansalone (2011) conducted a parameterization study on a CFD
model of BHS to balance model accuracy, computational overhead based on mesh size (MS),
81
time step (TS) and PSD discretization number (DN). The computational time for solving an
unsteady CFD model varied from 10 to 100 hours as a function of TS, MS, DN and the influent
hydrograph`s degree of unsteadiness ( commonly ranges from 0.09 to 1.15) (Garofalo and
Sansalone, 2011). In an attempt to balance CFD model error and computational overhead,
Pathapati and Sansalone (2011) introduced a simple first-generation stepwise steady flow
methodology for a CFD model to reproduce unsteady PM separation for UOs loaded by rainfall-
runoff. This CFD methodology was based on modeled at PM separation results generated at a
series of discrete steady flow levels across the unsteady hydrographs. The CFD results at each
discretized flow level were flow-weighted across the hydrograph (Pathapati and Sansalone,
2011). The method implicitly assumed an instantaneous PM response to each discretized flow
level loading a UO system which leaded to an inaccurate prediction of time-dependent effluent
PM distributions, especially for UOs with longer residence times. Subject to this methodology
and assumptions the study concluded that a stepwise steady model accurately reproduced PM
separation by filters but not HS and clarifier units.
Granulometric data (for example, PSD or specific gravity) required for physical or CFD
modeling of a UO have been collected through manual or automatic sampling with subsequent
granulometric analysis. Wastewater treatment plants (WWTPs) are characterized by fairly
constant flow rates (ranges from 0.08 to 0.095), largely organic with a range of specific gravity
from 1.03 to 1.05 g/cm3, relatively mono-disperse, finer PSDs (Dick, 1974; Fisher, 1975; Hettler
et al., 2011) and automatic sampling has been commonly used and accepted in conjunction with
wastewater treatment analysis (Koopman et al., 1989) including measurement of suspended PM
(as TSS, Standard Methods, 2540D (APHA, 1998)). While automatic sampling of urban runoff
UOs has been adopted from WWTP sampling there is increasing acceptance that the
82
convenience of automatic sampling may be outweighed by the potential mis-representation of
urban runoff separation and washout by UOs due to the pluviometric and granulometric
differences (Gettel et al., 2011). In contrast to wastewater, urban runoff flows are highly
unsteady (ranges from 0.09 to 1.2), with PM granulometry that is size hetero-disperse and
largely inorganic with a particle density in the range of 2.1 to 2.6 with PM that is not uniformly
distributed across the flow cross-section (Kim and Sansalone, 2010). Despite these differences
automatic sampling is commonly used for urban runoff UOs and gravimetric analysis of urban
runoff PM includes the traditional wastewater TSS method and increasingly suspended sediment
concentration (SSC) as developed by the United States Geological Survey (ASTM D3977-97
(ASTM, 2000)). A mass balance on PM for a field monitoring campaign of a UO has
demonstrated the representativeness of manual sampling and SSC (Sansalone et al., 2009). PM
misrepresentation with automatic sampling leads to inaccuracy in the PSD, SSC and therefore
PM separation (Sansalone et al., 1998). Despite the ongoing debate over the representativeness
of automatic or manual sampling for runoff UOs (Gettel and al., 2011), most monitoring of UOs
is performed with automatic samplers and TSS.
Building from these previous CFD model developments the current study proposes a
second generation stepwise steady CFD model to accurately predict PM separation by an HS and
clarifier unit. In contrast to the assumption of an instantaneous UO response this model
conceptualizes a UO as a linear system with a response that varies according to the
hydrodynamic characteristics of the system (for example, residence time distribution, RTD).
Conceptualizing a clarifier and HS as linear systems, the overall response of the UO subject to an
unsteady event is obtained by convoluting the RTDs of particle size ranges (based on a DN)
comprising a PSD across the series of steady flow rates for which the hydrograph is discretized.
83
The method hypothesizes that the CFD model can be used to produce the particle RTD for a
series of steady flow rates across the PSD. The study hypothesizes that the model based on the
particle RTD is able to properly predict flow and PM response times of UOs, in contrast to the
previous stepwise steady model approach (Pathapati and Sansalone, 2011). In addition, since the
PM eluted at a generic time ta, is modeled as a result of the influent mass PM delivered at times
equal and less than ta, the new approach models the transient behavior of UO as a continuously
evolving system, in which the output at each instant is also influenced by the previous conditions
in the UO.
As with the first generation stepwise steady CFD model (Pathapati and Sansalone, 2011)
and steady flow CFD models (Dickenson and Sansalone, 2009) an accurate of physical model
results requires representative PSD data.
The objective of this study is to demonstrate that PM separation and time-dependent PM
elution by a clarifier and a BHS loaded with unsteady hydraulic and PM loadings can be
reproduced with a stepwise steady flow model for three runoff hydrographs of differing levels of
. The accuracy of the stepwise steady CFD model will be validated with physical model data as
a function of hydrograph and PM granulometry. Finally this study examines the PM mass
balance produced through automatic sampling to illustrates the role of influent automatic
sampling for the prediction of effluent time-dependent PM with the stepwise steady CFD model.
Methodology
Physical Model Setup
This study utilizes a 1.83 m (nominal 6 feet) diameter BHS and a rectangular clarifier (RC)
with a length/width ratio of 4:1, designed to provide gravitational settling (Type I settling) and
retention of separated PM mass for small developed, largely paved parcels of urban land. The
84
two UOs are illustrated in the inset of Figure 4-1. The schematic representation of the full-scale
physical model and the testing setup are shown in Figures C-1 and C-2 of the Appendix. In the
BHS influent flow is conveyed by a 200 mm high inflow weir through the opening of the
horizontal baffle to the clarification chamber (where PM separation occurs) and directed to the
effluent pipe through an outlet riser. The RC and BHS are sedimentation-type UO. Physical
model runs were performed on the full-scale BHS and RC loaded by unsteady hydrographs at 20
˚C. Three hydrographs with differing levels were used for the BHS and RC as shown in Figure
4-1B and 4-1C. The unsteady inflow is delivered by a pumping station equipped with
programmable variable frequency drives and flows were measured by two magnetic flow meters
illustrated in Figures C-1 and C-2. The hydrograph formulations are based on the use of a step-
function to model a SCS Type II dimensionless unit hydrograph (Malcom, 1989). The physical
model hydrographs were scaled based on the maximum hydraulic capacity of 18 L/s for the BHS
and 50 L/s for the RC, maintaining constant volume for each (22,840 L and 125,000 L) and a
constant time of peak flow, tp of 15 minutes for BHS and 30 minutes for the RC (Sansalone and
Teng, 2005). In addition to differing levels the peak flow of 18 and 50 L/s were matched to the
maximum hydraulic capacity of the physical models with the other hydrograph peak flows
represent 50 and 25% of the hydraulic capacity. is defined for each hydrograph and
summarized in Table 4-1 (Garofalo and Sansalone, 2011):
50
1
mediQdt
dV
where i=1*dt.....td*dt
In this expression Qmed, dt, V, td represent the median value of Q, the time step, the storm
volume and the storm duration, respectively.
(4-1)
85
The values of for the BHS were from 0.09 to 1.15 and 0.015 to 1.54 for the RC. Physical
model runs of the BHS were conducted at 200 mg/L of PM and a constant PSDs. In Figure 4-1A
the two influent PSDs used are reported as compared to a measured source area PSD (Berretta
and Sansalone, 2012). The finer PSD is hetero-disperse ranging from 0.01 to 100 m with a d50
of 15 m. The coarser PSD is also hetero-disperse with a d50 of 67 m and a size range from 0.01
to 1000 m. The measured source area PSD with d50 of 107 m was collected from the outlet
section of a 500 m2 paved surface parking (Berretta and Sansalone, 2012). The influent and
effluent PSDs are modeled as cumulative gamma distribution in which (shape factor) and
(scale factor) represent the PSD uniformity and the PSD relative coarseness, reported in Table 4-
1. PM is released from a calibrated slurry system which works under transient conditions to the
inlet drop box and mixed with the influent flow (Figures C-1, C-2).
The three hydrographs shown in Figure 4-1B are used for the full-scale physical and CFD
modeling of the BHS loaded with finer and coarser PSDs. For the BHS an automatic sampler
was used to collect influent samples downstream the inlet drop box. All samples were taken in
duplicate, with a volume of 1 L each. In the effluent, automatic and manual sampling is
performed. The sampling interval varies according to the influent flow gradients. Less frequent
sampling intervals (5 to 10 min) are used in the beginning and ending parts of the hydrograph
(where the flow rate is fairly constant) with 1 to 3 minutes for the duration of the hydrograph
(where flow rate rapidly changes). The sampling intervals were the same for the influent and
effluent. To provide mass balance verification, separated PM and supernatant samples were also
collected after each run. Sample analyses included PSDs conducted by laser diffraction and PM
(as SSC). A PM mass balance (MB) was checked for each physical model run:
86
00
inf
n
i
iieffsep
n
i
i ttQtCMtM
In the mass balance expression Minf is influent mass load and Ceff is effluent
concentration which varied with time, ti. Msep is the separated PM recovered. The PM
separation is determined as:
100
PMInfluent
PMEffluent - PMInfluent MassPM
PM separation and the MB are reported in Table 4-1. Measured results including effluent
PSDs and PM obtained from physical modeling are utilized to validate the CFD model of the
BHS. The three hydrographs reported in Figure 4-1C were utilized for CFD modeling of the RC
loaded with finer PSD. The validation of the model is performed by using two hydrographs. The
physical model of the RC is loaded by two hydrographs. The first hydrograph was generated
from a triangular hyetograph with 12.7 mm of runoff volume and duration of 15 minutes. This
loading was selected as a common short and intense rainfall event during the wet season in
Florida (Figure C-3, C-4). The second hydrograph was generated from an historical event
collected on 8 July 2008 in Gainesville, Florida with total rainfall depth of 71 mm. This event
was chosen as an intense historical event, with a peak rainfall intensity of about 165 mm/h
(Figure C-5). The hyetographs were transformed as event-based hydrographs through the Storm
Water Management Model (SWMM) (Figure C-6) (Huber and Dickinson, 1988). In the rainfall-
runoff transformation for the scaled physical model basin the watershed peak runoff flow rate
approximated the design flow rate of the RC. The methodology used to retrieve the physical
model data for the validation of the unsteady CFD model is the same as the method described in
Garofalo and Sansalone (2011) and for brevity not reported herein. The influent PSD used for
RC is the finer PSD reported in Figure 4-1A.
(4-2)
(4-3)
87
CFD Modeling of Fluid and PM Phases
A three-dimensional (3D) CFD model was utilized to characterize the continuous phase
hydrodynamics and to predict PM phase transport and fate in the HBS and RC loaded by
hydrographs (Fluent, 2006). The CFD numerically solves the Navier-Stokes (N-S) equations
across a computational domain by using a finite volume approach. The physical model of BHS
and RC is built and meshed in Gambit environment (Fluent, 2010). The mesh was comprised of
tetrahedral elements. The size of the mesh was determined by a grid convergence study. The
CFD model developed for this study couples the continuous fluid phase with a discrete
particulate phase model (DPM) based on Eulerian and Langragian approaches. To solve the
continuous fluid phase the Reynolds Averaged Navier Stokes (RANS) formulation was utilized.
The RANS conservation equations were obtained from the N-S equations, by applying the
Reynold’s decomposition which decomposes the fluid flow properties into their time-mean value
and fluctuating component. The mean velocity is defined as a time average for a period t which
is larger than the time scale of the fluctuations. The time-averaged fluctuations tends to zero and
do not contribute to the bulk mass transport. The time-dependent RANS equations for continuity
and momentum conservation are summarized (Panton, 2000).
,0
i
i
ux
i
j
i
iij
jji
j
i gx
u
x
puu
xuu
xt
u
2
2''
In these equationsis fluid density, xi is the ith direction vector, uj is the Reynolds
averaged velocity in the ith direction; pj is the Reynolds averaged pressure; and gi is the sum of
body forces in the ith direction. The decomposition of the momentum equation with Reynolds
(4-4)
(4-5)
88
decomposition generates the Reynolds stresses term, ''
jiuu, from the nonlinear convection
component. Since the Reynolds stresses are unknown, the realizable k- model (Shih et al., 1995)
was used to resolve the closure problem. Studies have shown the realizable k- provides more
accurate results respect to the standard k- model where the flow features include strong
streamline curvature, vortices and rotation (Rahimi and Parvareh, 2005). The realizable model is
suitable for boundary free shear flow (BHS and RC) applications (Kim and Choudhury, 1995).
The realizable k- model consists of a turbulent kinetic energy equation and a turbulence energy
dissipation rate equation, respectively reported below (Shih et al., 1995).
jx
iu
ju
iu
jx
k
k
t
jx
jx
k
ju
t
k''
kCSC
xxxu
t j
t
jj
j
2
21
ijij SSS
kSC
2,,
5,43.0max
1
In these equations σk = 1.0, σε = 1.2, C2 = 1.9, k is the turbulent kinetic energy; ε is the
turbulent energy dissipation rate; S is the mean strain rate; νT is the eddy viscosity; ν is the fluid
viscosity; and uji and uj′u′i are defined in equations 4-5 and 4-6. The inlet is specified as velocity
inlet and each free surface is approximated as shear free wall with velocity components normal
to the surface. The numerical solver utilized is a pressure-based solver, suited for incompressible
flows governed by motion based on pressure gradients. The spatial discretization schemes
adopted are the second order for the pressure, the second order upwind scheme for the
momentum and the Pressure Implicit Splitting of Operators (SIMPLE) algorithm for pressure-
velocity coupling. The temporal discretization of the governing equations was performed by
(4-6)
(4-7)
(4-8)
89
using the second-order implicit scheme. Convergence criteria are set so that the scaled residuals
for all governing equations are below 0.001 (Ranade, 2002).
The DPM was used to simulate three-dimensional trajectories of discrete particles through
the computational domain and to model particle separation. The CFD model was based on
Eulerian-Lagrangian approach. While the fluid phase is treated as a continuum in an Eulerian
frame and solved by integrating the time-averaged N-S equations, the DPM tracks each
individual particle through the flow field in a Lagrangian frame of reference. The DPM model
assumes PM motion is influenced by the fluid phase, but not vice versa (one-way coupled model)
and particle-particle collisions are negligible. These assumptions were satisfied in this study
since the volume fraction (VF) was less than 10%, indicating that the dispersed phase was
sufficiently dilute (Brennen, 2005). The DPM tracks individual particles through the flow field
by balancing the forces acting on the particles such as gravitational body force, drag force,
inertial force, and buoyancy. Each particle trajectory therefore is calculated by integrating the
force balance equation written below in the ith-direction:
p
pipiiDi
pi gvvF
dt
dv
The first term on the right-hand side of equation 4-9 is the drag force per unit particle
mass, in which FDi is defined in equation 4-10. The second term is buoyancy/gravitational force
per unit particle mass.
24
Re18
2iDi
pp
DiC
dF
In this equation Rei is the Reynolds number for a particle, and CDi is the drag coefficient.
(4-9)
(4-10)
90
ipipi
vvd Re
3221
ReReK
KKC
iiiD
The first term on the right-hand side of the equation is the drag force per unit particle mass.
In these equations, p is particle density, vi is fluid velocity, vpi is particle velocity, dp is particle
diameter, K1,K2,K3 are empirical constants as a function of particle Rei. To model the influent
PSD, the PM gradation was discretized into discrete PM size classes on a symmetric gravimetric
basis. Studies have demonstrated that a DN of 8 to 16 is generally able to produce accurate
results for size hetero-disperse granulometry subject to steady (Dickenson and Sansalone, 2009)
or unsteady flows (Garofalo and Sansalone, 2011). The DN baseline of this study was 16 for the
finer PSD and 8 for the coarser PSD.
In transient CFD model, at each time step the fluid phase is solved. PM phase is then
tracked throughout the solved flow field by using Equation 4-9.
CFD Modeling under unsteady conditions
For a fully unsteady CFD model, the TS typically ranged from 10 to 60 seconds as a
function of for the hydrograph (Garofalo and Sansalone, 2011). PM particles were injected
from the inlet surface and tracked through the domain at each TS. A computational subroutine as
a user defined function (UDF) was developed to record PM injection properties, residence time
and particle size of each particle eluted from the system throughout the entire simulation. Further
details about the UDF are reported in Appendix.
A population balance model (PBM) was coupled with CFD to model particle separation.
Assuming no flocculation in the dispersed PM phase, a PBM (Jakobsen, 2008) is written.
(4-11)
(4-12)
91
max
min
max
min
max
min 0
,
0
,
0inf,
ddd t
sep
t
eff
t
ppp
In this equation and represent particle size range and injection time ranging from 0 to
the runoff event duration, td, respectively. The term ()inf indicates influent PM, ()eff effluent PM
and ()sep separated PM. p represents the mass per particle and is obtained as follows:
N
Mp
,
,
In this expression Mis PM mass associated with the particle size range and injected at
time N represents the total number of particles injected at the inlet section (Garofalo and
Sansalone, 2011). In Garofalo and Sansalone (2011) the CFD fully-unsteady model was used to
predict effluent PM from BHS subjected to storm events with differing level of unsteadiness.
The study illustrated modeling error and computing time produced by a transient CFD model as
function of computational parameters.
Stepwise steady CFD modeling
The conceptual foundation for stepwise steady flow model is analogous to unit hydrograph
theory used to predict surface runoff from a watershed (Bedient and Huber, 2002). The stepwise
steady model is based on the assumption that the temporal effluent PM distribution from a UO is
given by the superposition of PM residence times across the entire hydrograph.
For this analog, I is the event-based influent PM for a given PSD. The hydrograph is
discretized into a series of m steady flow rate, Qm for a fixed time step, t. Im represents the
influent PM for a given PSD and a fixed time step, t, delivered into the system at Qm. Up is
function of flow rate, Qm; therefore, let define Up,Qm the UO response to Im for the specific flow
rate, Qm (Figures C-7- C-9). Up,Qm is computed from steady CFD models. The UO is assumed to
(4-13)
(4-14)
92
be a linear system. Based on this assumption the event-based effluent mass PM, E can be
modeled as sum (convolution) of the responses Up,Qm to inputs Im. The effluent mass PM at each
time step t, En is given by the discrete convolution equation:
In these expressions, n and m are the number of steps in which the effluent PM distribution
and the influent hydrograph are respectively discretized. A schematic of this methodology is
shown in Figure C-10.
In this study the DPM loading of the CFD model was represented by three hetero-disperse
(finer, coarser and source area) PSDs. These PSDs loaded the physical models in this study.
The coarser and source area PSDs were discretized into 8 size classes (DN = 8) with an equal
gravimetric basis and a DN of 16 for the finer PSD. Throughout each stepwise steady flow
simulation a computational subroutine as a user defined function (UDF) was run to record
residence times of each particle size and generate Up,Q. UDF is described in the Appendix.
The temporal step is chosen to be less than the flow response time of the system. Since the
mean residence time of the BHS and RC is less than 2 min at the respective peak flow rates, a t
of 1 min is considered appropriate for both UOs. For each discrete flow rate a steady CFD
modeled Up,Qm is determined.
In this study the continuous phase loading of the CFD model was represented by the
hydrographs show in Figure 4-1 that were varied based on unsteadiness, and peak flow, Qp and
the UO. Each hydrograph was divided into one minute intervals, t and converted in a series of
discrete steady flow rates.
To associate to each discretized flow rate the corresponding Up, the following procedure
was used. The modeled CFD Up,Q obtained from the UDF was fit by a gamma distribution
(4-15)
93
function; therefore, Up,Q was uniquely described by two gamma distribution parameters, and
as shown in Figure C-11set of steady flow rates was run to derive the relationship between
Q and Up,Q gamma parameters as shown in Figure C-12. This relationship allowed to obtain Up
gamma parameters, and hence Up,Q for each discretized flow rate. From the findings shown in
Figure A-13, a set of 7 flow rates chosen as 100%, 75%, 50%, 25%, 10%, 5%, 2% of the UO`s
design flow rate produced accurate results (accuracy error of 6%). A higher number of flow rates
did not generate more accurate results. Therefore, in this study a number of seven flow rates was
run for each unit to obtain Up as function of flow rate.
The coupling of particle residence time, Up,Q and influent PM, Im at each time interval
through applying the convolution equation by Equation 4-15 was conducted in order to obtain
time-dependent effluent PM.
To evaluate the error in predicting the temporal effluent PM variation between the fully
unsteady and stepwise steady CFD models, the normalized root mean squared error, en was
introduced and represents the error generated by the stepwise steady model as compared to the
fully unsteady CFD model at each time interval. The en is computed as follows.
min,max,
1
2
, ,
unsteadyunsteady
n
i
isteadystepwiseiunsteady
nxx
xx
e
In this equation xunsteady represents the value obtained from the unsteady modeling and
xstepwise steady represents the value obtained from the stepwise steady modeling. CFD simulations
are solved in parallel on a Dell Precision T7500 Workstation equipped with two quad core Intel
Xeon® 3.33GHz (a total of eight cores) processors. The workstation has 48 GB of RAM.
(4-16)
94
Results and Discussion
Comparison of the Stepwise Steady and Fully Unsteady CFD Results
In Figure 4-2 the stepwise steady and unsteady CFD model results for the BHS are
compared to measured physical model data for the finer PSD and differing levels of . With
respect to the unsteady CFD model the stepwise steady model accurately reproduces the
temporal effluent PM distribution from the BHS. The modeling errors (en) ranged from 9.6 to
7.8%. As the hydrograph decreases to quasi-steady condition the performance of the stepwise
steady model further improves. Quasi-stationary conditions reduce the complexity of the model
and tend towards a steady solution with further improved model accuracy.
The computational time required for the unsteady and stepwise steady models are reported
in Figure 4-2D. The computing time for the fully unsteady model was represented by the sum of
the “processing” and “post-processing” times. The processing time was a function of the
unsteadiness degree and duration of the hydrograph, while the post-processing was constant
(about 1 hour) regardless the hydrograph`s characteristics. The fully unsteady model computing
time ranged from 15.5 to 55 hours for hydrograph loadings (durations, ) from (125 min, ) to
(84 min, ) with a mean of 30.3 hours. In contrast, the computational time for the stepwise
steady model was not dependent on the duration and the unsteadiness level of the hydrograph
and consisted of two computing components. The first component represents the processing time
to run a series of steady simulations. As previously described seven steady flow rates were run to
identify the relationship between Up and Q. For seven steady simulations the CFD model
required approximately 9 hours. The second part consisted of the post-processing time, the time
employed by the user to implement the excel spreadsheet for computing the convolution integral
defined by Equation 4-15. The post-processing time was approximately 2 hours. The total
95
computing time given by the sum of “processing” time and “post-processing” times was
approximately 12. Since in this study three hydrographs were analyzed, the computing time per
event was 4 hours as compared to the mean average of 30.3 hours for fully-unsteady model.
Since the processing and post-processing times were constant in a stepwise steady flow rate,
higher the number of events was, lower the computing time per event became. These results
showed that the stepwise steady model drastically drops the computing time from an average of
around 31 hours to 4 hours per event and this is due to the fact that the stepwise steady model is
based on the set of fixed steady flow rates run to generate the unique relationship between Up
and Q for the specific UO and remains invariant regardless the hydrographs run. In addition, this
stepwise steady flow model produced more accurate results in comparison to the previous steady
flow model for the BHS. In Figure C-14 effluent PM distributions from the BHS subjected to the
finer gradation and the highly unsteady hydrograph ( = 1.15) was shown by using new and
previous stepwise steady approaches and the fully unsteady CFD model. The results showed that
the previous stepwise steady model overestimated the effluent PM from the BHS, especially in
the first part of the hydrograph (Q < Qp). At the beginning of the storm, the BHS was filled with
clear water. Therefore, the PM initially injected at low flow rates is translated to the outlet with a
delay, depending on the PM response time of the unit. The previous stepwise steady approach
was not able to model this delay occurring at low flow rates, causing not only an earlier delivery
of PM at the outlet section but also an overestimation of it. The new stepwise steady model
instead was able to predict the PM delay by modeling the actual PM response for low flow rates
through the Up,Q distributions.
For the coarser PSD, Figure 4-3 summarizes the temporal effluent PM mass for differing
levels of . With respect to the unsteady CFD model the stepwise steady model accurately
96
reproduces the temporal effluent PM distribution from the BHS. The modeling errors (en) ranged
from 9.7 to 5.8%. The total computational time (processing and post-processing) time for the
stepwise steady model was approximately 11 hours. In contrast for the fully unsteady model the
mean total computational time for the fully unsteady CFD model was 28.6 with a range for
hydrograph loadings (durations, ) from (125 min, ) to (84 min,) of 15 to 52 hours. In
Table C-1 the computational time for fully unsteady and the stepwise steady model is reported
along with event characteristics, including influent PSD and hydrological parameters. While the
hydrograph’s influences the modeling errors, finer and coarser influent PSDs produce the same
order of error and therefore the granulometry did not influence the accuracy of the stepwise
steady CFD model.
To verify the applicability of the stepwise steady model to UOs different from a BHS, the
model was compared to the fully unsteady validated CFD model of the RC as shown in Figure 4-
4. Results indicate that the stepwise steady model accurately reproduced the effluent PM eluted
from the RC with modeling error that ranged from 8.5 to 5.6% for decreasing levels of . The
total computational time (processing and post-processing) for the stepwise steady model was
approximately 15 hours. In contrast for the fully unsteady model the mean total computational
time for the fully unsteady CFD model was with a range for hydrograph loadings (durations, )
from (282 min,) to (124 min,) of 21.5 to 70 hours. Figure C-15 showed the selection
of t of 1 min was able to produce the most accurate results. In Figure C-14 effluent PM
distributions from the RC subjected to the finer gradation and the highly unsteady hydrograph (
= 1.54) was shown by using new and previous stepwise steady approaches and the fully unsteady
CFD model. The results showed that the previous stepwise steady model overestimated the
effluent PM from the RC, especially in the first part of the hydrograph (Q < Qp).
97
These results show that the assumptions on which the stepwise steady model is based; the
linearity of the UO system response, the superposition of discrete loadings, and uniqueness of the
RTD for each particle within the PSD, U are valid for BHS and RC. The stepwise steady CFD
results also demonstrate the conceptual analog for this second generation model is applicable to
volumetric clarifiers or settling tanks and for HS units.
Automatic Sampling, PM Granulometry and CFD Results
Figure 4-5 summarizes the automatic sampling data collected for the BHS influent for the
finer (d50 = 15 m) and coarser (d50 = 67 m) PSDs. In Figure 4-5A the influent cumulative PM
dry mass from automatic sampling is reported as function of elapsed time. Throughout the entire
storm the metered (measured) overall influent PM is 4.5 kg. The results show for the highly
unsteady hydrograph ( = 1.15) the automatic sampling was able to recover around 62% of the
total influent mass for the finer PSD, and approximately 50% for coarser PSD. For the source
area PSD (d50 = 130 m) the recovery was approximately 40%. As the level of increased the
recovery of influent PM decreased. For the coarser PSD the percentage of influent PM recovered
by automatic sampling for the unsteady ( = 0.24) event drops slightly to 58% and for the quasi-
steady ( = 0.09) to approximately 45%. For the finer PSD (d50 = 15 m) the percentage of
influent PM samples for the unsteady event ( = 0.24) decreases to 65%, for the quasi-steady (
= 0.24) to approximately 63%. For the coarser PSD (d50 = 67 m) the percentage of influent PM
samples for the unsteady event ( = 0.24) decreases to 50%, for the quasi-steady ( = 0.24) to
approximately 48%. For the source area PSD (d50 = 130 m) the percentage of influent PM
samples for the unsteady event ( = 0.24) decreases to 40%, for the quasi-steady ( = 0.24) to
approximately 47%. For the coarser PSD the PM fraction greater than 75 m represents 50% of
PM mass in the gradation. The automatic sampling tube which was placed at the mid-depth of
98
the inlet section was not able to collect the coarser particles which settled and became bed load
transport in the inlet channel. The lower the flow rate the higher the rate of settling of this
sediment PM fraction. In fact the turbulent mixing generated by higher flows in the influent
channel can resuspend coarser PM, allowing the automatic sampler to collect a component of the
PM fraction greater than 75 m. This explains the low percentage of PM recovery from the
influent as the level of decreases. For the finer PSD, the PSD is predominately suspended
particles that are mixed more uniformly in the influent especially for high flow rate and these
particles have the potential to be collected more accurately by the automatic sampler.
In Figure C-16 the influent target PSDs are compared to measured influent PSDs generated
through automatic sampling for the three hydrographs shown in Figure 4-1B. The influent PSDs
is represented as the median PSDs for each hydrograph with range bars representing the
variability of PSDs across the entire hydrograph. Figure C-16A shows for the coarser PM
gradation that the measured PSDs are coarser as increases. Figure C-16B shows that the
influent PSDs from the BHS for the finer gradation are not statistically different ( = 0.05)
regardless the hydrograph`s level of . For the effluent the automatic sampling results are not
significantly different from the manual sampling results (=0.05) since PM larger than 75 m
and which is less likely to be sampled representatively by an automatic sampler has been settled
by the UO. This mixture of finer suspended PM in the effluent was also distributed more
homogenously in the effluent flow section. Therefore, automatic sampling of the effluent was
able to provide representative samples similar to those collected through effluent manual
sampling.
The stepwise steady CFD model utilized to generate Figure 4-3 results was applied using
the coarser PSD results generated from automatic sampling as shown in Figure 4-5 (as PM). The
99
results illustrated in Figure 4-7 demonstrated that the modeling error significantly increases when
an underestimated influent PM generated from automatic sampling is utilized in the CFD model.
The accuracy errors ranging from 49% ( = 1.15) to 69% ( = 0.09) became larger as the
hydrograph`s unsteadiness degree decreased. The stepwise steady CFD model used to generate
Figure 4-2 results was applied using the fine PSD results produced through automatic sampling
as shown in Figure 4-5 (as PM). The results shown in Figure 4-8 demonstrated accuracy errors
ranging from 45% ( = 1.15) to 77% ( = 0.09) became larger as the hydrograph`s unsteadiness
degree decreased. This is due to the underestimation of the influent PM produced by the
automatic sampling which increases as the degree of unsteadiness decreases. Figure 4-9 reports
the unsteady CFD model used to generate Figure 4-3 results for a source area PSD with
concentration of 200 mg/L and the stepwise steady CFD model results generated by using the
automatic sampling of source area influent PM illustrated in Figure 4-5. The results shown in
Figure 4-9 demonstrated accuracy errors ranging from 12% ( = 1.15) to 17% ( = 0.09) became
larger as the hydrograph`s unsteadiness degree decreased. For the source area PSD the accuracy
errors were lower than those generated for the finer and coarser PSDs. This is because for the
source gradation all the particles not captured by the samplers at the influent section settle
nevertheless inside the BHS. These results demonstrated that the inaccuracy of influent PM data
produced through automatic sampling leads to an underestimation of time-dependent PM eluted
from the BHS, and therefore, to an overestimation of unit`s PM separation efficiency.
Conclusion
The stepwise steady CFD model is validated with measured physical model and it shows
good agreement with results generated through unsteady CFD modeling for two Type I settling
units. The method proposed requires a series of steady state CFD simulations which require less
100
computational time. The convolution equation is applied to this series of steady CFD results for
coupling hydrodynamics and PM gradations. The computing time per event drops from several
hours of unsteady CFD modeling to few hours (approximately 5 hours).
The CFD model accuracy relies on the input PM data, which if not properly collected can
generate significant modeling errors. This study demonstrates the automatic sampling produces
representative samples of PM eluted from a BHS for both finer and coarser PSDs, but it does not
accurately characterize the influent samples for either PSDs. The automatic sampling is not able
to collect the coarser fraction of PSD (>75m) to which is associated most of the influent PM
mass. This study investigates the effect of influent automatic sampling in predicting effluent PM
for a BHS and rectangular clarifier by using CFD model, demonstrating the importance of
representative and accurate influent PM recovery is crucial not only in monitoring and testing but
also for modeling purposes.
101
Diameter, d (m)0.010.11101001000
Fin
er b
y m
ass
(%)
0
20
40
60
80
100
Diam vs Hao.PSD
Elapsed time (min)0 20 40 60 80 100 120
Infl
uen
t fl
ow
rat
e, Q
i (L
/s)
0
5
10
15
20
25Highly unsteady (= 1.54)
Unsteady ( = 0.24)
Quasi-steady ( = 0.09)
Finer PSD
Coarser PSD
Elapsed time (min)
0 50 100 150 200 250
Infl
uen
t fl
ow
rat
e, Q
i (L
/s)
0
10
20
30
40
50Highly unsteady (= 1.51)
Unsteady ( = 0.33)
Quasi-steady ( = 0.015)
Source area PSD
Figure 4-1. Influent hydraulic loadings and PSDs. In A) influent particle size distributions
(PSDs) as compared to a measured source area PSD, in B) three hydrographs loading
the physical model of the baffled HS, BHS (v ≈ 3.4 m3), and in C) three hydrographs
loading the rectangular clarifier (v ≈ 12 m3)
A
B
C
Inflow
Outflow
1.83 m
1.73 m
Inflow
Outflow
7.3 m
1.8 m
102
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.2
0.4
0.6
0.8Flow rate
MeasuredModel:
Unsteady
Stepwise steady
Finer PSD
(d50
= 15 m)
Qp=18 L/s
td
=84 min
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.2
0.4
0.6
0.8
Qp=9 L/s
td
=87 min
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.2
0.4
0.6
0.8
Qp=4.5 L/s
td
=125 min
(A) = 1.15
(B) = 0.24
(C) = 0.09
Figure 4-2. Effluent PM response of a baffled HS (BHS), diameter = 1.83 m, unit volume = 3.4
m3 to the finer hetero-disperse PSD (Figure 4-1A) transported by the hydrographs
(Figure 4-1B) (volume = 22 m3) of varying unsteadiness The range bars indicate
the variability of the measured data. The en represents the normalized root mean
square error between the unsteady and stepwise steady model results
en= 9.6 %
en= 9.1%
en= 7.8%
A
B
C
103
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.1
0.2
0.3
0.4Hydrograph
MeasuredModel:
Unsteady
Stepwise steady
Coarser PSD
(d50
= 67 m)
Qp=18 L/s
td
=84 min
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.1
0.2
0.3
0.4
Qp=9 L/s
td
=87 min
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.1
0.2
0.3
0.4
Qp=4.5 L/s
td
=125 min
(A) = 1.15
(B) = 0.24
(C) = 0.09
Figure 4-3. Effluent PM response of a baffled HS (BHS), diameter = 1.83 m, unit volume = 3.4
m3 to the coarser hetero-disperse PSD (Figure 4-1A) transported by the hydrographs
(Figure 4-1B) (volume = 22 m3) of varying unsteadiness The range bars indicate
the variability of the measured data. The en represents the normalized root mean
square error between the unsteady and stepwise steady model results
en= 9.7 %
en= 6.7 %
en= 5.8 %
A
B
C
104
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (k
g)
0.0
0.1
0.2
0.3
0.4
0.5
0.6Flow rateModel:
Unsteady
Stepwise
Finer PSD
(d50
= 15 m)
Qp=50 L/s
td
=124 min
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (k
g)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Qp=25 L/s
td
=136 min
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (k
g)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Qp=12.5 L/s
td
=282 min
(A) = 1.54
(B) = 0.33
(C) = 0.015
Figure 4-4. Effluent PM response of a rectangular clarifier, unit volume = 12 m
3 to each
hydrograph (volume = 122 m3) loading of varying unsteadiness Each hydrograph
transports a constant finer PSD (Figure 4-1A). The en represents the normalized root
mean square error between the unsteady and stepwise steady model results
en= 8.5 %
en= 6.5%
en= 5.6%
A
B
C
105
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Cu
mu
lati
ve
Infl
uen
t M
ass,
Mi/
Mt
0.0
0.2
0.4
0.6
0.8
1.0
Cu
mu
lati
ve
Infl
uen
t M
ass,
Mi
(kg
)
Coarser PSD
Finer PSD
Source area
(A)
(B)
Cu
mu
lati
ve
Infl
uen
t M
ass,
Mi/
Mt
0.0
0.2
0.4
0.6
0.8
1.0
(B)
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Cu
mu
lati
ve
Infl
uen
t M
ass,
Mi/
Mt
0.0
0.2
0.4
0.6
0.8
1.0
(C)
Qp=18 L/s
td
=84 min
Mt = 4.5 kg
Qp=9 L/s
td
=87 min
Qp=4.5 L/s
td
=125 min
Auto sampling
Cu
mu
lati
ve
Infl
uen
t M
ass,
Mi
(kg
) C
um
ula
tiv
e In
flu
ent
Mas
s, M
i (k
g)
Figure 4-5. Each plot displays the influent PM mass recovery provided by auto sampling of the
BHS as a function of hydrograph unsteadiness () and PSD. Each PM mass result is
normalized to the total influent dry mass (Mt) of 4.50 kg delivered at a constant 200
mg/L for each hydrograph (volume = 22 m3) displayed in Figure 4-1B
A
B
C
106
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Cu
mu
lati
ve
Eff
luen
t M
ass,
Me
(kg
)
Cu
mu
lati
ve
Eff
luen
t M
ass,
Me/
Mt
(A)
Cu
mu
lati
ve
Eff
luen
t M
ass,
Me/
Mt
0.0
0.2
0.4
0.6
0.8
1.0
Cu
mu
lati
ve
Eff
luen
t M
ass,
Me
(kg
)
(B)
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Cu
mu
lati
ve
Eff
luen
t M
ass,
Me/
Mt
0.0
0.2
0.4
0.6
0.8
1.0
Cu
mu
lati
ve
Eff
luen
t M
ass,
Me
(kg
)
(C)
Qp=18 L/s
td
=84 min
Qp=9 L/s
td
=87 min
Qp=4.5 L/s
td
=125 min
Mt = 4.5 Kg
Manual
Auto
Manual
Auto
Coarser PSD
Finer PSD
Figure 4-6. Each plot displays the effluent PM mass recovery comparing auto and manual
sampling methods for the BHS as a function of hydrograph unsteadiness ( and PSD.
Each PM mass result is normalized to the total influent dry mass (Mt) of 4.50 kg
delivered at a constant 200 mg/L for each hydrograph (volume = 22 m3) displayed in
Figure 4-1B. The measured results from manual and auto sampling are not
statistically different (=0.05)
A
B
C
107
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rate
, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.1
0.2
0.3
0.4Hydrograph
MeasuredModel:
Stepwise steady
Coarser PSD
(d50
= 67 m)
Qp=18 L/s
td
=84 min
Infl
uen
t fl
ow
rate
, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.1
0.2
0.3
0.4
Qp=9 L/s
td
=87 min
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rate
, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M ,
Mi (k
g)
0.0
0.1
0.2
0.3
0.4
Qp=4.5 L/s
td
=125 min
(A) = 1.15
(B) = 0.24
(C) = 0.09
Figure 4-7. Each plot displays the effluent PM response of the BHS to a coarser PSD as a
function of hydrograph unsteadiness (The en represents the normalized root mean
square error between the measured and stepwise steady model results. The stepwise
steady CFD model utilized to generate Figure 4-3 results was applied using the
coarser influent PSD produced through auto sampling as shown in Figure 4-5 (as PM)
in order to demonstrate the error associated with using auto sampling
en= 28%
en= 24%
en= 34%
A
B
C
108
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (K
g)
0.0
0.2
0.4
0.6
0.8
Flow rate
MeasuredModel
Stepwise steady
Finer PSD
(d50
= 15 m)
Qp=18 L/s
td
=84 min
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (K
g)
0.0
0.2
0.4
0.6
0.8
Qp=9 L/s
td
=87 min
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (K
g)
0.0
0.2
0.4
0.6
0.8
Qp=4.5 L/s
td
=125 min
(A) = 1.15
(B) = 0.24
(C) = 0.09
Figure 4-8. Each plot displays the effluent PM response of the BHS to a finer PSD as a function
of hydrograph unsteadiness (The en represents the normalized root mean square
error between the measured and stepwise steady model results. The stepwise steady
CFD model utilized to generate Figure 4-3 results was applied using the finer influent
PSD produced through auto sampling as shown in Figure 4-5 (as PM) in order to
demonstrate the error associated with using auto sampling
en= 31%
en= 41%
en= 32%
A
B
C
109
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (k
g)
0.0
0.2
0.4
0.6
0.8Flow rateModel
Unsteady
Stepwise steady
Source Area PSD
(d50
= 15 m)
Qp=18 L/s
td
= 84 min
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (k
g)
0.0
0.2
0.4
0.6
0.8
Qp=9 L/s
td
=87 min
Time, t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
/Qp
0.0
0.2
0.4
0.6
0.8
1.0
Eff
luen
t P
M , M
i (k
g)
0.0
0.2
0.4
0.6
0.8
Qp=4.5 L/s
td
=125 min
(A) = 1.15
(B) = 0.24
(C) = 0.09
en = 46.4%
en = 64%
en = 23%
Figure 4-9. Each plot displays the effluent PM response of the BHS to a source area PSD as a
function of hydrograph unsteadiness (The en represents the normalized root mean
square error between the measured and stepwise steady model results. The unsteady
CFD model utilized to generate Figure 4-3 results was applied using the source area
influent PSD delivered at a constant concentration of 200 mg/L. The stepwise steady
CFD model utilized to generate Figure 4-3 results was applied using the source area
influent PSD produced through auto sampling as shown in Figure 4-5 (as PM) in
order to demonstrate the error associated with using auto sampling
A
B
C
110
Table 4-1. Physical model (baffled HS and rectangular clarifier) hydraulic and PM loading and PM separated. Qp, V, tp, PM, td, MB,
PM mass, PSD, are peak flow, hydrograph volume, time to peak, influent particle matter, hydrograph duration,
mass balance, PM removal efficiency, influent particle size distribution, gamma shape and scale factors, and unsteadiness
factor, respectively
Qp Qp V tp C td MB PM mass Influent PSD Hydrograph
(%) L/s) (m3) min mg/L min (%) (%) Description
Baffled HS (1 turnover v = 3.4 m3)
18 100 22.8 15 200 74 93.9 64.03 0.64 177 1.15 Highly Unsteady
9 50 23.4 15 200 87 97.9 63.53 0.64 177 0.24 Unsteady
4.5 25 22.9 15 200 125 98.2 71.82 0.64 177 0.09 Quasi-steady
18 100 22.8 15 200 74 100.3 33.00 0.79 28 1.15 Highly Unsteady
9 50 22.7 15 200 87 92.8 34.26 0.79 28 0.24 Unsteady
4.5 25 22.8 15 200 125 107.1 57.60 0.79 28 0.09 Quasi-steady
Rectangular clarifier (1 turnover v = 12 m3)
50 100 124.1 30 200 74 0.79 28 1.54 Highly Unsteady
25 50 125.1 30 200 87 0.79 28 0.33 Unsteady
12.5 25 125.8 30 200 125 0.79 28 0.01 Quasi-steady
111
CHAPTER 5
A STEPWISE CFD STEADY FLOW MODEL FOR EVALUATING LONG-TERM UO
SEPARATION PERFORMANCE
Summary
Computational fluid dynamics (CFD) is an emerging tool to predict the coupled
hydrodynamics and PM fate in unit operations (UOs) subject to transient rainfall-runoff events.
Frequently, CFD is applied for the rapid analysis of steady flows. Recently an integrated
stepwise steady flow CFD model for transient events predicted separation PM with reduced
computational overhead as compared to transient CFD modeling. This study extends the
stepwise steady CFD model to evaluate long-term UO performance on annual basis. A validated
stepwise steady flow CFD model simulated PM fate (separation and washout) in a rectangular
clarifier (RC) and a screened hydrodynamic separator (SHS) for a representative year of rainfall-
runoff. Throughout the year, prediction of PM washout for transient events was integrated into
the time domain continuous simulation model. The CFD model was validated with measured PM
separation and washout data from full-scale physical models. In comparison to the RC, results
show that the SHS is prone to washout and that neglecting PM washout from the SHS
overestimates SHS performance. The coupling of a stepwise-steady CFD approach and time
domain continuous simulation represents a valuable tool to estimate the fate of PM on an annual
basis. The model can provide a macroscopic evaluation for finding the overall optimal control
strategy and for defining maintenance requirements to improve UO treatment.
Introduction
The relative imperviousness and conveyance of constructed urban surfaces such as
pavements facilitates the transformation of rainfall to runoff. These unsteady processes at the
urban interface mobilize and transport a hetero-disperse gradation of particulate matter (PM),
inorganic and organic compounds generated by urban infrastructure and activities. PM has been
112
identified as a major contributor to the deterioration of surface waters (USEPA, 2000) and a
significant vector for many reactive PM-bound compounds, including metals and nutrients
(Sansalone and Kim, 2007). To manage the fate of PM and compounds in runoff that partition to
and from PM, unit operations (UOs) have been applied to control loads otherwise discharged
through runoff to receiving waters (USEPA, 2000) and to address regulations for watersheds
such as total maximum daily loads (TMDLs). These UOs range from the common
retention/detention clarifier to less common adsorptive-filtration and a primary function of these
units is PM and PM-bound compound separation (Nix et al., 1988; Sansalone, 1999).
Simulation of rainfall to runoff transformations and UO treatment can be based on
deterministic equations or derived probability distributions of meteorological event statistics.
Deterministic models can be viable for a wide range of hydraulic conditions and basin
configurations, but can require more computational effort than statistical methods (Medina et al.,
1981; Ferrara and Hildick-smith, 1982; Amandens and Bedient, 1980). In a deterministic model
introduced by Nix et al. (1988), PM separation of a detention basin was estimated by
characterizing the settleability of PM (as total suspended solids, TSS) load with a “typical”
settling velocity distribution (Nix et al. 1988). In this study a time domain continuous simulation
model, Storm Water Management Model (SWMM) (Huber and Dickinson, 1988) was used to
generate event-based as well as long-term transformation of rainfall to runoff for the given
watershed and conveyance conditions. The statistical techniques rely, instead, on a set of
statistics of rainfall or runoff and a relatively simple representation of the detention facility
(DiToro and Small, 1979; Goforth et al. 1983; Adams and Papa, 2000; Lee et al., 2010). Lee et
al. (2010) proposed a frequency analysis model based on system response time using long-term
precipitation data to examine the behavior of an infiltration UO. This model is able to analyze
113
the response of UOs to the wide spectrum of long-term rainfall-runoff phenomena, avoiding the
selection of a single representative storm for water quality control. However, it is not as accurate
as a continuous simulation because it ignores the actual timing of the precipitation and storage
effects.
These models have been a major advancement in the field of urban drainage; however
these models were not designed to provide a description of hydrodynamics and particle fate for
UOs loaded by different PSDs. In addition, clarification methods in these models are commonly
based on concepts of as ideal overflow theory, reasonably steady influent hydraulics as well as
sparse PM characteristics such as PSDs. Therefore, the clarification components of these models
do not account for the dynamic, unsteady nature of the runoff hydrodynamics flows, constitutive
properties of PM loads, and the state of the UO system.
Computational fluid dynamics (CFD) modeling is an emerging tool capable of predicting
the flow field and PM fate within UOs subjected to either steady and unsteady hydraulic and PM
loadings (Dickenson and Sansalone, 2009; Pathapati and Sansalone, 2009; He et al., 2008; Wang
et al., 2008). Previous studies analyzed the performance of CFD models for UOs subjected to a
series of runoff events. Pathapati and Sansalone (2011) demonstrated CFD unsteady modeling
reproduces the response of a HS to unsteady runoff with modeling errors within 10% respect to
physical model data, while the use of event-based steady flow indices to predict PM separation
generated much larger errors. Garofalo and Sansalone (2011) conducted a parameterization study
on the CFD model of a baffled hydrodynamic separator (HS) to balance model accuracy and
computing time based on mesh size (MS), time step (TS) and PSD discretization number (DN).
Despite the precise and accurate representation of the physical model behavior, the
computational detailed information provided by unsteady CFD modeling, the computational
114
overhead was significant. For a single unsteady rainfall-runoff event the computational time
required for solving a fully unsteady CFD model varied from 10 to approximately 100 hours (on
a Dell Precision 690 with two quad core Intel Xeon® 2.33GHz processors and 16 GB of RAM),
depending on the TS, MS and DN required for the input hydrograph`s unsteadiness and the
PSD’s size-dispersivity (Garofalo and Sansalone, 2011). While coupling a fully unsteady CFD
model with a long-term continuous simulation to evaluate the response of an UO for a time series
of rainfall-runoff events is a reasonable concept, the computational overhead can be
unreasonable. To reduce computational overhead while ensuring an accurate representation of
the physical model response, Pathapati and Sansalone (2011) introduced a stepwise steady flow
CFD model to reproduce unsteady PM separation for stormwater UOs. However the model was
based on a single storm event. In contrast, this study develops a stepwise steady flow CFD
model providing an accurate long-term UO response to unsteady loading for PM response with
reasonable computational overhead.
While the importance of a UO to separate and retain captured PM is recognized, physical
modeling and quantification of washout of previously separated PM from a UO has been
examined for less than a decade. Recent studies have shown that PM washout can impact the
overall response of a UO, and in part depends on the type of UO and the maintenance frequency
(Avila et al., 2011). Pathapati and Sansalone (2012) demonstrated the Eulerian-Lagrangian
approach in a validated CFD model is able to accurately predict PM washout. Avila and al.
(2011) utilized a validated CFD model to estimate the PM washout for catch basin sumps with an
Eulerian-Eulerian approach, considering a bed fluidized bed.
This study develops and tests a stepwise steady flow CFD model with the goal of
simulating the long-term response of an UO (rectangular clarifier, RC and screened
115
hydrodynamic separator, SHS) to unsteady hydrologic loading for PM separation and also
washout at a reasonable computational overhead. For a representative year of rainfall depth over
a small impervious watershed, the continuous simulation unsteady runoff response results was
coupled with CFD to quantify the separate responses of separation and washout for each UO.
Methodology
Hydrology Analysis
The UOs investigated in this study are primary applied in relatively small developed urban
parcels of land. A largely impervious catchment translates the rainfall to runoff and the runoff is
transported by gravity to the RC or SHS in SWMM. The catchment generates flows that are
equal to or less than the maximum hydraulic capacity of the RC, 50 L/s. A long-term
precipitation data series is collected for Gainesville, FL (KGNV) for the period 1998-2011 as
hourly rainfall data from the National Climatic Data Center (NCDC) with rainfall depth
resolution of 2.54 mm (0.01 in.). The hourly rainfall data are downloaded from the NCDC
website (http://www.ncdc.noaa.gov). Since the catchment is small with times of concentration
time less than 1 h, the hourly rainfall data was disaggregated into 15 minute data. The
deterministic disaggregation procedure utilized was proposed by Ormsbee (1989) (Nix et al.,
1988) and the procedure is summarized in Figure D-1 of the Appendix D. From the resulting 15
minute rainfall data series, total rainfall volume, number of events and rainfall intensity
frequency distribution were evaluated for each year from 1998 to 2011 and the overall period.
The rainfall intensity frequency distribution is shown in Figure D-2. For the period of 1998-2011
mean annual rainfall depth and mean number of events per year is respectively 1214 mm and
133. The mean number of events for the wet season is 81 and for dry season 52. A
representative year (2007) with hydrological characteristics similar to the annual mean for
Gainesville was selected and is shown in Figure D-2. In 2007 the total rainfall depth and the
116
number of events are 1171 mm and 147 respectively. The rainfall intensity frequency
distributions shown in Figure D-2A for the period 1998-2011 and for 2007 are not statistically
different (p > 0.05). Therefore, the year 2007 is chosen to be representative of the period 1998-
2011. Figure D-3 shows monthly rainfall depth for the year 2007.
SWMM is used to generate unsteady runoff flow loadings from the rainfall time series data
of 2007. A catchment which delivers runoff to the RC and SHS was input into SWMM. The
catchment area generated a runoff time series with 99% of flows less than 50 L/s, the design flow
rate of the RC. The SWMM model parameters are summarized in Figure 5-1A, and represent a
catchment from the paved surface parking source area described by Berretta and and Sansalone
(2012). The catchment area is 1.6 ha.
The catchment time of concentration is based on the kinematic wave approach and is
approximately 30 minutes for the median intensity of 1 mm/h as shown in Figures 5-1B and D-1.
The minimum inter-event time (MIT) utilized the approach of Adams and Papa (2000) and
based on the annual average number of events the MIT was 1.36 h as shown in Figure 5-1C.
Therefore, since the MIT for a small catchment can approach the time of concentration, a MIT of
1.0 hours was utilized for this catchment. The cumulative runoff and discrete frequency
distributions generated at one minute interval are reported in Figure D-4.
Physical Full-Scale Model for PM Separation
PM separation validation was performed with a full-scale physical model of the RC under
unsteady hydrograph conditions as shown in Figure D-5. The RC is shown in the inset of Figure
5-2. The RC is 1.87 m high, 1.8 m wide and 7.31 m long with a volumetric capacity of
approximately 12,000 L. The design flow rate, Qd of the physical model (50 L/s) corresponds to
the hydraulic capacity of physical model. Further information about the geometry of the system
and a plan view are reported in the Appendix in Figure D-5.
117
PM separation validation was performed with a full-scale physical model of the SHs under
steady hydrograph conditions (Pathapati and Sansalone, 2012). The SHS unit consists of two
concentric cylindrical chambers separated by a static-screen with 2,400 m apertures. The HS
inlet is tangential to the inner sump chamber which has a diameter of 1.7 m. Surrounding the
sump chamber is the outer annular volute chamber with a diameter of 1.7 m. The volute
chamber functions as a settling tank and flow exits the volute chamber through the effluent
section. A sump is located at the bottom of the unit where PM is deposited after separation or
subsequently re-suspended by incoming flows. The volute area also functions as a PM separation
and re-suspension area. The SHS is shown in the inset of Figure 5-2D. The Appendix provides
information about the geometry and the plan view of the physical model.
Two hydrographs were delivered to the physical model of the RC. The first hydrograph
was generated from a triangular hyetograph with 12.7 mm (0.5 inch) of rainfall depth and
duration of 15 minutes. This loading is selected as a common short and intense rainfall event
during the wet season in Florida and is shown in Figure D-6. The second hydrograph was
generated from an 8 July 2008 in Gainesville, Florida with total rainfall depth of 71 mm. This
event was chosen as a high intensity event with a peak rainfall intensity of about 165 mm/h as
shown in Figure D-7. An unsteadiness parameter, is defined for each hydrograph and the
values of are summarized in Table 5-1 (Garofalo and Sansalone, 2011).
50
1
mediQdt
dV
where i=1*dt.....td*dt
In this expression Qmed represents the median value of Q, dt is the time step.
The particle size distribution (PSD) used for the physical testing is reported in Figure D-8
and is a fine hetero-disperse gradation classified as sandy silt based on the Unified Soil
(5-1)
118
Classification System (USCS) with a d50 of 15 m. More detailed information regarding the
generation of the two hydrographs utilized for the validation are reported in Section 3 of the
Appendix D. The physical model results are reported in Table D-1. Physical model testing was
conducted at constant influent PM concentration (Ci) of 200 mg/L and constant PSD shown in
Figure 5-2A. For each run discrete duplicate samples were taken manually with a frequency that
ranged from 2 to 5 minutes. Analysis included PSD by laser diffraction and PM gravimetric
analysis as suspended sediment concentration (SSC). A PM mass balance was conducted for
each physical model test.
00
inf
n
i
iieffsep
n
i
i ttQtCMtM
In the mass balance expression Minf is influent mass load and Ceff is effluent concentration
which varies with time, ti. Msep is separated PM recovered. The PM separation (%) is also
determined.
100
PMInfluent
PMEffluent - PMInfluent MassPM
PM separation and mass balance (MB) are reported in Table D-1. Measured results
obtained from physical modeling were utilized to validate the CFD model.
Physical Full-Scale Model for PM Washout
PM washout was also examined for each UO. Physical model runs for PM washout were
performed on the full-scale RC physical model for unsteady hydraulic loads at 20 ˚C as shown in
Figure D-5. The runs are carried out to evaluate washout PM from the RC. The PSD of the pre-
deposited PM bed in the RC is reported in Figure 5-2A and is a fine hetero-disperse gradation
classified as an SM with a d50 of 15 m. The dry bulk density of the deposit was 1.04 g/cm3.
The PSD was modeled as cumulative gamma distribution in which (shape factor) and (scale
(5-2)
(5-3)
119
factor) represent the PSD uniformity and the PSD relative coarseness. The washout hydrographs
are those reported in Figure 5-2B-C. The July 8th storm and the triangular hydrograph with peak
flow rates of 50 L/s and 28 L/s, respectively were previously described. For washout other two
hydrographs were considered. These hydrographs are scaled based on the RC maximum
hydraulic capacity (50 L/s), maintaining constant shape, volume (V = 15,000 L) and time of peak
flow, tp of 15 min of the triangular hydrographs. The two hydrographs has peak flow rate of 21
L/s and 35 L/s, respectively.
For the RC, each washout run was conducted by first pluviating PM across the entire
surface area of the RC for two depths of PM deposits: 5 and 15 mm. The RC was then filled with
water at a flow rate of around 0.2 L/s to avoid any re-suspension of the PM bed. For each
washout test, discrete duplicate effluent samples were taken manually within a frequency range
of 2 to 5 minutes. Analysis included PSD by laser diffraction and PM gravimetric analysis as
suspended sediment concentration (SSC). Measured effluent PSDs and PM obtained from
physical modeling were utilized to validate the CFD model.
The measured data for the SHS was generated from a mono-disperse PM gradation
described in Appendix. The methodology is the same of that described for the RC. PM
deposition depths investigated were 50% and 100% of sump storage capacity with no PM in the
volute chamber, and 50% of sump capacity and 2.5 cm of PM deposit in the volute chamber.
Further details about the physical modeling methodology of the SHS are reported in Pathapati
and Sansalone (2012).
CFD Modeling
A three-dimensional (3D) unsteady CFD model was built based on the full-scale physical
model of the RC and the SHS units using FLUENT version 13.0 (Fluent, 2010). The code is
finite volume based, written in C programming language and solves the Navier-Stokes (N-S)
120
equations within the computational domain boundaries of each unit. The geometry and mesh of
the RC physical model were built in Gambit (Fluent, 2010) and shown in Figure D-9. After a
grid convergence study, the final grid was comprised of 3.5 million tetrahedral elements. Further
information about the grid convergence is reported in Figure D-10 of the Appendix. The
validated CFD model for the SHS is described in details in Pathapati and Sansalone (2012). The
mesh of SHS consists of 2.1 million cells as shown in Figure D-11.
The CFD model is based on Euler-Lagrangian approach in which the fluid phase is treated
as a continuum in an Eulerian frame of reference and solved by integrating the time-dependent
N-S equations. The particulate phase behavior in the system is predicted by the discrete phase
model (DPM) in a Lagrangian frame of reference. To simulate the time-dependent PM eluted
from the units during separation (treatment) and also washout testing a fully-unsteady CFD
model and physical model validation thereof are summarized for the RC in Section 4 of the
Appendix (B). This physically-validated CFD model is then utilized to generate the stepwise
steady flow CFD model.
CFD model for PM separation
In a fully-unsteady CFD model the TS is typically in the range of 10 seconds to 1 minute
depending in the hydrograph unsteadiness, (Garofalo and Sansalone, 2011). The individual
particles across the PSD were injected into the UO inlet (at the computational domain boundary)
and tracked within the computational domain at each TS. The number of TS used to integrate the
particle motion (Equation D-8 of the Appendix D) was based on a tracer study. Buoyant, 1m
particles were injected from the inlet surface and then tracked through the computational domain
of each unit at a flow rate equal to 1% of the unit’s Qp. This flow rate is adopted to determine the
maximum number of steps needed to track the particles thought the system. A computational
121
subroutine as a user defined function (UDF) written in C records PM injection properties, tracer
elution, residence time and particle size of each particle eluted from the system throughout the
entire simulation. A population balance model (PBM) was coupled with CFD to model particle
separation. Assuming no flocculation in the dispersed PM phase, the PBM equation (Jakobsen,
2008) can be written.
max
min
max
min
max
min 0
,
0
,
0inf,
ddd t
sep
t
eff
t
ppp
In this equation and represent particle size range and injection time ranging from 0 to
the runoff event duration, td, respectively. The term ()inf indicates influent PM, ()eff effluent PM
and ()sep separated PM. p represents the mass per particle and is obtained as follows:
N
Mp
,
,
In these expressions, Mis PM mass associated with the particle size range as function
of injection timeN represents the total number of particles injected at the inlet section and td is
the event duration (Garofalo and Sansalone, 2011).
CFD model of PM washout
The pluviated PM bed consists of sandy-silt PM. The re-suspended PM is sufficiently
dilute to have negligible effect on the turbulence structure in the carrier fluid. Due to the dilute
nature of these PM laden-flows the use of a Lagrangian-Eulerian approach is appropriate to
describe the re-suspension and washout of PM (Elgobashi, 1991). From the physical model
testing the formation of a scour hole was observed after each run and corresponded to the area
where the incoming flow jet plunged downward through the water column of the RC and
impinged on the PM deposit. This observation aided in the CFD methodology for washout. The
(5-4)
(5-5)
122
geometry of this area is shown in Figure D-13 and was used in the modeling and mass balance
process.
In order to support the methodology for washout, from the physical model testing a semi-
circular scour hole was observed in the inlet section of the clarifier. This suggests the PM mass
washout from the system was mainly generated from the scour hole due to the impinging jet. The
scour hole was measured and subsequently, was represented in CFD by an equivalent rectangular
area (60 x 20 cm) shown in Figure D-13.
Layers were created in the region of computational domain that consisted of the pluviated
PM bed, where the scour hole was produced. A series of 60 x 20 cm layers were built in CFD
based on visual observations and physical measurements of the scour area. The interval size
between these layers was 1.0 mm and smaller intervals did not produce more accurate results. A
horizontal grid of 1,600 nodes with spacing of 0.5 mm was built in each horizontal layer. Further
refinement of the horizontal grid did not result in significant change in PM washout (= 0.05).
From each node 16 PSD particle sizes (Garofalo and Sansalone, 2011) are released for a total of
25,600 particles for each horizontal plane. A schematic of the methodology is shown in Figure
D-13. The number of steps utilized to integrate the particle motion (Equation D-8 in the
Appendix) was determined based on a tracer study. A neutrally buoyant tracer was released from
each plane and the number of steps is modified until all the tracer is eluted from the unit. The
largest TS number obtained for each layer was selected for the entire simulation. PSD particles
were then tracked through the computational domain with the DPM. A computational subroutine
as a user defined function (UDF) was written in C to record the number of particles eluted and
retained in the computational domain of the unit and their residence times shown in Figure D-14.
The effluent mass load is calculated.
123
NN Load MassEffluent
p n
,,retainedreleased npnp M
In this expression, p, n, Mp,n are the DN (number of PSD size classes), the number of
layers in which the pluviated PM bed is discretized, and PM mass between layers associated with
PSD size classes, respectively. The clarifier is loaded with the hydrographs and the PSD shown
in Figure 5-1 for pre-deposited PM depths of 5 and 15 mm.
For the SHS unit a similar methodology described in details in Pathapati and Sansalone
(2012) is applied. For washout CFD modeling the SHS was loaded with a fine hetero-disperse
PSD shown in Figure 5-2D and four hydrographs reported in Figures 5-2E and 5-2F. The
hydrographs were scaled based on the SHS design flow rate (31 L/s), maintaining constant the
shape of the RC`s hydrographs illustrated in Figures 5-2B and 5-2C.
Validation analysis for fully-unsteady CFD model
Measured PM separation and also washout results were utilized to validate the fully
unsteady CFD models. The measure of error between measured and modeled results is the
relative percent difference (RPD).
100% PM
RTD modmeasured
measured
eled
PM
PM
PMmeasured and PMmodeled are the event-based PM mass from the physical and CFD
model. The validation was considered satisfactory when RPD is less than 10%. The events used
to validate the CFD model for PM separation by the RC are the runoff events show in Figure 5-
2C and 5-2D with Qp of 28 and 50 L/s. The hydrographs reported in Figure 5-2C and 5-2D are
used for the pluviated PM depths of 5 and 15 mm in the CFD washout model. For the SHS the
measured data reported by Pathapati and Sansalone (2012) were compared to the CFD model
results. The CFD validation results are reported in Figure 5-4 in which the washout PM at 50 and
(5-6)
(5-7)
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100% of sump PM capacity, and for two different PM depths in the volute area (0 and 2.54 cm),
are analyzed at 100 % (31.1 L/s) and 125% (38.8 L/s) of Qd for the SHS.
Subsequently, fully unsteady model results for RC were validated against the stepwise
CFD steady model results.
Stepwise steady CFD model
In this study a stepwise steady flow CFD model was developed with the goal of simulating
the long-term response of the RC and SHS to unsteady hydrologic loading for PM separation and
washout at a reasonable computational overhead. The analogous conceptual basis for a stepwise
steady flow model is the unit hydrograph (Chow et al. 1988) used to predict runoff from a
watershed. The analogy is described in details in SI and shown in Figure D-15 and D-16. The
stepwise steady model is based on the assumption that the temporal distribution of effluent PM
from a specific UO can be represented as the superposition of the residence time distributions
(RTDs) of mass PM for a given PSD, Up. For this analog, I is the event-based influent PM for a
given PSD. The hydrograph is discretized into a series of m steady flow rate, Qm for a fixed time
step, t. Im represents the influent PM for a given PSD and a fixed time step, t, delivered into
the system at Qm. Up is function of flow rate, Qm; therefore, let define Up,Qm the UO response to
Im for the specific flow rate, Qm (Figure D-15). Up,Qm is computed from steady CFD models.
The UO is assumed to be a linear system. Based on this assumption the event-based effluent
mass PM, E can be modeled as sum (convolution) of the responses Up,Qm to inputs Im. The
effluent mass PM at each time step t, En is given by the discrete convolution equation:
(5-8)
125
In these expressions, n and m are the number of steps in which the effluent PM distribution
and the influent hydrograph are respectively discretized. A schematic of this methodology is
shown in Figure D-17 and D-18.
The methodology has the following steps. The CFD model is loaded with the fine hetero-
disperse PM gradation shown in Figure 5-1A and is run under steady conditions for stepwise
steady levels. The influent PSD is discretized into 16 size classes on an equal gravimetric basis.
Particles from each PSD size classes are injected at the inlet surface of the UO. Throughout each
simulation a computational subroutine, written as a user defined function (UDF) in C, is run to
record residence times of influent PSD and generate Up,Q.
The influent hydrographs are divided into 1 minute intervals, t and converted in a series
of discrete steady flow rates. The temporal step is chosen to be less than the flow response time
of the system. Since the mean residence time of the RC is 1.5 min at the peak flow rate of 50 L/s,
a t of 1 min is considered appropriate. For each discrete flow rate a steady CFD modeled Up,Qm
is determined. Finally Up,Qm is coupled to Im at each time interval by using the convolution
equation in order to obtain the temporal effluent PM distribution. A more detailed description of
the methodology is reported in the Appendix.
To associate to each discretized flow rate the corresponding Up, the following procedure is
used. The modeled CFD Up is well fit by a gamma distribution function; therefore, a Up can be
uniquely described by two gamma distribution parameters, and set of steady flow rates is
run to derive the relationship between flow rate and Up gamma parameters. This relationship
allows to obtain Up gamma parameters, and hence Up, for each discretized flow rate. From the
findings shown in Figure D-19, a set of 7 flow rates chosen as 100%, 75%, 50%, 25%, 10%, 5%,
2% of the UO`s design flow rate produces accurate results. A higher number of flow rates does
126
not produce more accurate results. Therefore, in this study a number of seven flow rates was run
for each unit to obtain Up for each discretized flow rate.
Previous studies proposed a stepwise steady model based on discretizing the hydrograph
into a series of steady flow rates and then, simply integrating the results for each discretized flow
level (Pathapati and Sansalone, 2011). This methodology implicitly assumes the flow response of
the system is nearly instantaneous (very short residence times) regardless the flow rate. In
addition, the difference between PM and flow response times is also assumed negligible.
The stepwise steady approach used in this study takes into account the actual PM response
times of the system as function of flow rate by modeling the PM residence time distributions
(Um,Qm) shown in Figure D-14. In addition, the PM eluted at a generic time ta, is given not only
by the influent mass PM delivered at ta, but also by the influent mass PM previously delivered
and still in suspension in the UO. The model, therefore, recognizes the transient behavior of UO
as a continuously evolving system, in which the outputs at each instant are influenced by the
previous conditions in the UO. For such reasons the stepwise steady model presented in this
study is able to reproduce fully unsteady results.
Evaluation of PM Elution Due to Washout in the Continuous Simulation Model
An approach to evaluate PM washout from UOs within a continuous simulation framework
is defined. Pathapati and Sansalone (2009) demonstrated that from a comparison of steady flow
statistical indices (mean, median, peak) that the peak flow rate (Qp) provides the most accurate
estimation of the total PM mass eluted from a UO subject to unsteady event-based hydrograph
loadings. For unsteady flow in open-channels, Qp has been used to estimate the maximum depth
of scour and therefore, the maximum mass eroded from the channel bed for no-cohesive PM
(Tregnaghi et al., 2010). In this study Qp is utilized to provide a prediction of the effluent PM
mass due to washout. This re-suspended mass represents potential washout from the UO system.
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To verify whether Qp reproduces physical model results, the PM washout mass from the
hydrographs reported in Figure D-2 for the RC and SHS are compared to the results obtained at
flow rates equal to each hydrograph`s Qp. For this purpose, a relationship between a range of Qp
values and PM washout mass is built for several PM depths for the RC and SHS. The errors are
measured as RPD. If results based on Qp can reproduce physical model results, then the
relationship between PM washout mass and hydrograph Qp can be implemented in the stepwise
steady flow CFD model to account for washout phenomena.
Time Domain Continuous Simulation Model and its Assumptions
Outside of CFD, a MatLab code was written to discretize the hydrograph in a series of
steady flow rates and to compute the convolution equation (Equation 5-8) described in previous
section. The code is implemented to run across an annual time series of runoff data computed
from the time domain continuous simulation and shown in Figure D-4 of the Appendix for the
RC. The assumptions for the time domain continuous simulation model were: (1) an event-based
PM influent concentration of 200 mg/L and the influent PSD is shown in Figure 5-1A are
maintained constant throughout the runoff event, (2) the distribution of settled PM mass is
approximately uniform across the bottom of the RC, and (3) the PM remained in suspension after
the storm event is predominately settled before the beginning of the subsequent event. For the
SHS, PM is primarily settled in the sump and as the sump capacity exceeds 50%, there is also a
net PM settling in the volute chamber (Kim and Sansalone, 2008). The relationship between the
washout of PM mass and flow rate is implemented in the stepwise steady flow CFD model to
account for PM washout. After generating the runoff distribution for each rainfall event of the
rainfall time series, the PM washout as a function of flow rate relationship is applied to
determine the mass of PM washout from the UO based on the event`s peak flow rate. As a result
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of the PM washout the total PM depth in the UO is updated and the next hydrologic event is run.
This process is continued for the entire time series of interest, in this case for 2007.
Results and Discussion
CFD Model for PM Separation and Washout
A mass balance validation was performed on the physical model for RC and SHS to ensure
the validity of the measured mass data. For RC and SHS the RPDs were within 10 %.
Subsequently, the fully unsteady CFD modeled PM results were compared to physical
model data as shown in Figure D-20. The RPDs for each hydrograph loading were computed to
estimate the CFD model error in predicting PM elution with respect to the physical model data.
The RPDs were less than 10%.
The validation results for PM washout from the RC and SHS are reported in Figure 5-3
and 5-4.
In the CFD model the pluviated PM bed was discretized into a series of layers with an interval
size of 1 mm. The selection of 1 mm interval size was able to reproduce accurate results. A
smaller interval sizes up to 0.3 mm did not generate more accurate results. The method reduces
the computational overhead respect to the approach used from Pathapati and Sansalone (2012)
where the interval size was approximately equal to one particle diameter. In Figure 5-3 the intra-
event effluent PM generated by the fully unsteady CFD model for the RC as compared to the
measured effluent PM data from the physical model. The washout PM results are reported for the
triangular hyetograph loading and the 8 July 2008 loading; each for 5 and 15 mm of PM
uniformly pluviated across the bottom of the RC and SHS.
The measured and fully unsteady modeled results are also reported for the hydrographs
shown in Figure 5-2B with a Qp of 28 L/s and 21 L/s, respectively. The results show agreement
between the fully unsteady CFD model and washout measured data. Also the trend of the time-
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dependent washout measured PM data is accurately modeled by CFD. In Table 5-1 the physical
and CFD model results are reported along with their RPDs. All RPDs were less than 10%.
Results show the mass of PM washout mass increased as Qp and PM bed depth increased. Flow
duration aside, results suggest that the hydrograph Qp is a primary parameter which influences
the PM re-suspension and washout phenomena. Based on the CFD model, Figure 5-4
summarizes the PM washout for the SHS at 50% and 100% of sump capacity for PM and for 0
and 2.54 cm of PM depths in the volute area. Results are obtained at 100 and 125% of Qd; for a
coarser (d50 = 110 m) and finer PM gradation (d50 = 67 m). Results show the SHS is more
conductive to washout than the RC. Table 5-2 summarizes RPDs for the validation; showing
agreement between measured and modeled results.
PM Washout as Function of Flow Rate and Pluviated PM Depth
After validating the CFD model, the PM washout mass for both UOs was modeled for
different pluviated PM depths and flow rates. Figure 5-5A summarizes PM washout mass as
function of flow rate (up to 50 L/s, Qd) for the RC for PM depths ranging from 5 to 50 mm. As
anticipated, the washout mass increases for increasing flow rate and PM depth. The washout
from the SHS unit is explored as function of flow rate ranging from 1.5 to 31.1 L/s (Qd) and PM
depths in the SHS sump and volute chamber. In Figure 5-5B the washout mass from the SHS
unit is modeled for 50% of sump capacity of PM and depths ranging from 10 to 100 mm in the
volute chamber. As anticipated, the PM mass washout increases as flow rate and sediment depth
increase. In Figure 5-5C the PM washout from the SHS sump is shown for PM depths ranging
from 25 to 450 mm (no PM pluviated in volute area). At the design flow rate of 31.1 L/s with the
sump capacity filled to 50% of capacity the PM washout mass is 4.3 Kg, while at the same flow
rate with a PM depth of 10 mm in the volute area the washout mass is 5 Kg. For lower PM
130
depths the volute area with a lower velocity distribution is more conducive to retain PM as
compared to the sump area (Kim and Sansalone, 2008). However when the volute PM depth is
higher than 50 mm, the PM washout mass from the volute chamber significantly increase.
In Figure D-21 the effluent PM concentrations due to the washout are reported for the RC
and SHS. The PM bed load PSD used for both units is the fine hetero-disperse PSD characterized
by = 0.79, = 28 and d50 = 15 m, as shown in Figure 5-2A. The concentration values are
based on 6.5 turnovers (1 turnover is equal to the runoff volumetric capacity of each unit) (Cho
and Sansalone, 2012). For the RC the effluent PM ranged from approximately 10 to 70 mg/L at
Qd, while for the SHS at 50% of sump capacity and PM in the volute chamber, the effluent PM
ranged from 200 to 700 mg/L, an order of magnitude higher. The PM from solely the volute
chamber was approximately from 30 to 670 mg/L. While at 50% of the sump capacity, effluent
PM is approximately 200 mg/L, at 100% of the sump capacity 350 mg/L at Qd. From 10 to 100
mm of PM depth in the volute area and 100% of sump capacity the effluent concentration varies
from around 400 to 900 mg/L as show in Figure D-22.
Results indicate that the PM washout from the RC is significantly less than the SHS. The
RC provides volumetric isolation of previously separated PM and produced lower washout
respect to the SHS as both modeled with a fine hetero-disperse PSD. By comparison, the SHS
does not provide volumetric isolation. Instead, the flow entering into the screen area tangentially
generates a vortex throughout the inner screen chamber with the flow momentum transferred
directly into the sump region and given conservation of momentum, reflected upward and
through the volute chamber towards the SHS outlet (Pathapati and Sansalone, 2012). This high
velocity field, established within the inner chamber, re-suspends previously separated PM in the
sump. Therefore, the sump is prone to significant re-suspension; while the volute chamber is
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prone to a lesser degree except at greater PM depths. Results corroborate the need for regular
maintenance of the SHS and that the net treatment functionality of unit operations deteriorates
without regular maintenance.
To further assess the role of the hydrograph`s peak flow rate as a statistical index to predict
PM mass washout, the results from Table 5-1 and 5-2 are compared to those in Figure 5-5 for
flow rates equal to the hydrograph`s peak flow rate. The errors generated are reported in Table 5-
3. The mean RPDs are 10%. The washout mass results obtained from each hydrograph
reasonably match those generated from the hydrograph`s peak flow rate. Under steady conditions
the flow rate is kept invariant for a number of 6.5 turnovers and the washout mass is associated
with the total volume passing through the UO. Once the peak flow rate(s) of an event re-
suspends mass, this mass is available for washout by the remaining storm hydrograph. Therefore,
the washout mass may be less under unsteady conditions respect to that under steady conditions.
The RPDs between the fully unsteady and steady washout CFD model results reported in Table
5-3 are negative, demonstrating in fact the steady CFD model results slightly overestimate the
unsteady CFD model results.
Stepwise CFD Steady Flow Model and Time Domain Continuous Simulation
The stepwise steady flow model was applied for the entire runoff time series generated
from SWMM for 2007 and the catchment shown in Figure 5-1A by using the MatLab code.
Subsequently, the results shown in Figure 5-5 are used to account for washout into the
continuous simulation model. Specifically, the washout PM produced by a storm event is
predicted by linearly interpolating the results from Figure 5-5 based on the hydrograph`s peak
flow rate and the PM depth accumulated within the unit during previous storms. The total
effluent mass for a storm event is given by the sum of the effluent mass predicted by the stepwise
steady model and the washout mass from Figure 5-5. Based on the amount of mass settled and
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washout during a storm event, the PM depth within the unit is then updated and the model set to
run the subsequent storm event.
The computational time required to run a time domain simulation model is given by the
time needed for solving and post-processing steady CFD runs and the time for running the
MatLab code for a long-term series of runoff events. As previously mentioned, 7 steady flow
rates run were sufficient to build the stepwise steady model and produce accurate results. The
computing time for the steady CFD runs was approximately 7 hours for RC and SHS (on a Dell
Precision 690 with two quad core Intel Xeon® 2.33GHz processors and 16 GB of RAM), while
for post-processing was 4 hours. The MatLab code for one year of runoff events (2007) run in 2
hours. Therefore, the total computing time required by the time domain simulation model is 13
hours. The computing time is significantly reduced respect to that required for running a fully
unsteady CFD model over a year of rainfall-runoff events (for the watershed studied,
approximately a number of 133 events).
An example of the output of the time domain continuous simulation model is illustrated in
Figure 5-2B, where PM mass eluted from the RC loaded with the runoff data series from Figure
D-2B is reported for June 2007.
Figure 5-6A reports the cumulative effluent PM mass as function of cumulative runoff
volume for 2007 for the RC loaded with fine hetero-disperse PSD shown in Figure 5-2A and
constant influent concentration of 200 mg/L. One set of results is obtained by applying the
stepwise steady CFD model without accounting for PM washout. A second set of results is
produced by applying the relationships in Figure 5-5A to account for PM washout. The two sets
of results are modeled and interpolated by power law model. The PM washout from the RC is
reasonably flow-limited; indicating the washout is limited by the flow and not by the PM mass
133
available in the RC. The effluent PM mass and the PM depth for 2007 are also shown as
function of month in Figure 5-6B and 5-6C. For the RC during 2007, 522 Kg are separated by
the unit (no washout). When accounting the washout phenomena, the results do not change
significantly; with a washout of 543 Kg. The RPD between the total effluent PM mass with scour
and the total effluent PM mass without scour is 4%. For the RC the final PM depth in the end of
2007 is 25 mm (no washout). When accounting for washout, the results do not vary significantly;
with a depth of 27.5 mm.
In Figure 5-6D the cumulative effluent PM mass as function of cumulative runoff volume
during 2007 for the SHS with fine hetero-disperse PSD shown in Figure 5-2A and constant
influent concentration of 200 mg/L is reported. The time domain simulation model is based on
the assumption that PM mass mainly deposits in the sump region for up to 50% of the sump
capacity before there is any significant accumulation in the volute chamber. The cumulative
effluent PM results for SHS in Figure 5-6D are modeled and interpolated by power law
functions, also suggesting the washout in the SHS is flow-limited. As previously observed, the
SHS is significantly more prone washout as compared to the RC. These results for one year of
separation and washout demonstrate that the long-term performance of the SHS was significantly
influenced by washout. In Figure 5-6E the effluent mass is reported as function of months. The
total annual PM effluent with no washout is 600 Kg, and with washout is 800 Kg. The difference
between these two results of annual effluent mass is 33%. More specifically, the difference
between the two sets of results as shown in Figure 5-6F is accentuated beginning in June when
the wet weather season starts for Gainesville.
In Figure D-23 the time domain simulation model results are reported based on the
assumption that the sump is at 100% of PM capacity, before PM accumulation occurs in the
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volute section. In this maintenance condition the effluent PM mass also increases. Figure D-23B
shows that under the assumption of no PM washout the sump fills to 100% of capacity from
January to the beginning of July with a PM accumulation of 60 mm in the volute chamber
between July and the end of the 2007. By comparison when washout is considered the sump
capacity is exceeded by July 29th with a subsequent PM accumulation of 20 mm in the volute
section. After August the PM accumulated in the volute chamber decreases due to washout and
in the end of year approaches to zero.
The continuous simulation model for the SHS indicates that a significant difference
between the results with and without washout occurs after the month of July. The slopes of the
curves reported in Figure 5-6E show that the period in which most of the PM elution occurs is
between July and October (summer season). The reason is that during the summer season the
runoff volume largely increases, generating larger amount of PM wash off from the watershed
and delivered into the system. Consequently, during summer season larger fractions of PM is
eluted or re-suspended and washout from the system.
Conclusion
This study developed and tested a stepwise steady flow CFD model coupled with a time
domain continuous simulation model to simulate the long-term response of two common UOs
(rectangular clarifier, RC and screened hydrodynamic separator, SHS) subject to unsteady
hydrologic loading for PM separation and also washout at a reasonable computational overhead.
Full-scale physical model testing of the two UOs was performed to validate the CFD
models of PM separation and washout. These UO physical models were hydraulically-loaded
with unsteady hydrographs as well as a series of hydrograph peak flow (Qd) steady loadings.
These hydraulic loadings were coupled with a range of particle size distributions (PSD). For the
RC, PM separation as well as washout was tested with a finer PSD (d50 = 15 m, = 0.79, =
135
28) while for the SHS, PM separation was tested with a finer PSD (d50 = 15 m, = 0.79, =
28) and PM washout was tested with a medium (d50 = 67 m, = 0.58, = 271) and coarse PSD
(d50 = 110, = 9.81, = 15.8). The fully unsteady CFD model and subsequently the stepwise
steady model reproduced the PM separation and washout of the physical model testing for the
RC and SHS.
The findings from the washout CFD model demonstrate that neglecting PM washout leads
to significantly underestimate PM mass eluted from UOs such as the SHS where the PM storage
zones are not volumetrically or hydraulically isolated from flows capable of re-suspending and
transporting PM from the UO (Figure D-24). The validated fully unsteady CFD model for PM
washout was then used to predict PM washout as function of flow rate (as the Qp of a
hydrograph) and separated PM depth in the UO under steady conditions. These results allowed
the integration of washout phenomena into the continuous simulation model. Based on the time
series of results generated from rainfall loadings for the representative year of 2007 on a 1.6 ha
largely impervious Gainesville, FL catchment, the SHS unit is significantly more prone to PM
washout than the RC. In comparison to the RC the washout of previously separated PM mass
significantly deteriorates the annual performance of the SHS.
The coupling of the stepwise steady CFD model with time domain continuous simulation
also quantified the temporal evolution of PM separation, accumulation and washout for the RC
and SHS. This temporal evolution across the year for any UO under any set of climate and
catchment conditions is crucial to for maintenance and management of the UO to achieve
targeted or promoted levels of treatment.
The primary advantage of the continuous simulation model based on the stepwise steady
CFD approach is the reduced computational overhead respect to fully unsteady CFD modeling.
136
The computational time is given by the sum of the modeling time to run steady flow CFD
simulation and post- processing time for the steady CFD results (total of 11 hours) and modeling
time for running the MatLab code for a year of storm events (2 hour). The total time required for
the time domain continuous simulation model presented in this study is 13 hours for a year of
rainfall-runoff events (133 events for the given watershed), in contrast to a fully unsteady CFD
model which requires at least 20 hours to run only a single storm event.
Time domain continuous simulation model based on the stepwise steady CFD approach is
valid for UOs, such as clarifier or HS subject to constant influent PM concentration and PSD. In
future study, the continuous simulation model may be developed to consider variable influent
PM concentration and PSD throughout the storm events.
The coupling of a stepwise steady CFD model and time domain continuous simulation
model provides a set of tools to quantify the capability of UOs to separate and retain PM on
annual basis. Results are directly applicable to not only UO separation behavior but also washout
mis-behavior; providing information needs to effectively maintain and manage UOs. Outcomes
of this study indicate that, irrespective of intra-SHS water chemistry degradation between events
that the SHS should be maintained (cleaned) every half year. Specifically for the Gainesville, FL
climate that exhibits two distinct seasons, wet and dry, maintenance of the SHS is required
before the start and after the end of the wet season to reduce the impacts of PM washout from the
SHS. By comparison, the RC illustrated only a nominal quantity of PM mass washout through
an entire year of loadings, with a maintenance interval that is at least one year and potentially up
to two years, irrespective of intra-RC water chemistry degradation.
Although UOs, whether manufactured or constructed, are subject to testing and
certification requirements before installation in situ, their treatment performance will deteriorate
137
without regular operation and maintenance inputs. Indeed, the storage of rainfall-runoff and
accumulation of PM mass will generate changing of water chemistry that can occur as rapidly as
the mean time between events (2.5 days on an annual basis for 2007 in GNV) and an increasing
intra-event washout response with an increasing interval between UO maintenance. In particular
the SHS demonstrated increasing washout during the year where the washout from the RC was
only nominal event across the entire year. A stepwise steady CFD model coupled with time
domain continuous simulation is a method to predict the temporal PM elution and PM
accumulation for a UO on a long-term basis.
138
0.1 1 10 100 1000
Tim
e o
f co
nce
ntr
atio
n,
t c (m
in)
1
10
100 tc = 25 i
r
-0.4
R2= 0.99
Rainfall intensity, ir (mm/h)
Minimum inter-event time, MIT (h)
0 4 8 12 16 20 24
An
nu
al
nu
mb
er
of
rain
ev
en
ts
50
100
150
200
250
MIT at breakpoint = 1.36 hours
1998-2011
Elasped time (h)0 20 40 60 80
Eff
luen
t P
M m
ass
(K
g)
0.0
0.1
0.2
0.3
0.4
Infl
eu
nt
run
off
(L
/s)
0
10
20
30
40
Effluent PM mass
Influent runoff
Figure 5-1. Hydrology analysis. In A) the subject Gainesville, Fl (GNV) watershed for physical
and continuous simulation (SWMM) modeling. In B) time of concentration as
function of rainfall intensity for the watershed of 1.6 ha, with 1% slope, 75% of
imperviousness and silty sand soil. Ksat, Di, represents the soil saturated hydraulic
conductivity, initial soil moisture deficit and soil capillary suction head, respectively.
In C) the mean number of rainfall events for the period 1998-2011 as function of
MIT. The knee of the curve represents the appropriate minimum inter-event time,
MIT. In D) Runoff and effluent PM mass eluted from the rectangular clarifier subject
to the hydraulic loading generated from the watershed in the month June 2007. The
June 2007 results are illustrative of monthly time domain continuous results
generated by the CFD stepwise steady model
Watershed properties:
Area is 75% paved
ksat = 10.9 mm/h
mm
Di = 0.2
Manning’s N (impervious) = 0.017
Manning’s N (pervious) = 0.15
A B
L = 160 m
Watershed area = 1.6 ha
C D
June 2007 MIT
139
Diameter, d (m)0.010.11101001000
Fin
er b
y m
ass
(%)
0
20
40
60
80
100
Elapsed time (min)0 10 20 30 40
Infl
uen
t fl
ow
rat
e, Q
i (t)
0
10
20
30
40
Elapsed time (min)
0 20 40 60 80 100
Infl
uen
t fl
ow
rat
e, Q
i (t)
0
10
20
30
40
50
Qp = 50 L/s
V = 89 m3
V = 15 m3
Qp = 28 L/s
Qp = 35 L/s
Qp = 21 L/s
Diameter, d (m)0.010.11101001000
Fin
er b
y m
ass
(%)
0
20
40
60
80
100
Elapsed time (min)0 10 20 30 40
Infl
uen
t fl
ow
rat
e, Q
i (t)
0
10
20
30
40
Elapsed time (min)
0 20 40 60 80 100
Infl
uen
t fl
ow
rat
e, Q
i (t)
0
10
20
30
40
50
Qp = 31 L/s
V = 51 m3
V = 10 m3
Qp = 17 L/s
Qp = 21 L/s
Qp = 13 L/s
Figure 5-2. Influent hydraulic loadings and PSDs. In A) influent particle size distribution (PSD)
(plan view of clarifier shown in inset A)). B) reports the scaled hydrographs obtained
from design hyetographs described in Appendix. In C) an historical hydrograph
collected on 8 July 2008 from Gainesville, Fl. In E) and F) hydrographs loading the
physical model of the SHS (D = 1.7m) unit (unit volume, v ≈ 4 m3). In E)
hydrographs generated from the scaling of hydrographs in B) respect to the maximum
hydraulic capacity of the unit, Qd of 31.1 L/s. In F) hydrograph generated from the
scaling of historical hydrograph collected on 8 July 2008 in Gainesville, Florida in C)
respect to the SHS`s Qd.
In
flow
O
utf
low
A
B
C
D
E
F
7.3 m
1.8 m Influent PSD
= 0.79
= 28
d50= 15 m
s = 2.63 g/cm3
b = 1.04 g/cm3
Influent PSD
= 0.79
= 28
d50= 15 m
s = 2.63 g/cm3
b = 1.04 g/cm3
VC ≈ 12 m3
VSHS ≈ 4 m3
1.8 m
Outflow
D = 1.7m
Inflow
140
t/td
0.0 0.2 0.4 0.6 0.8 1.0
0
10
20
30
40
50
Influent Q
Measured (PM = 8 mg/L)
Modeled
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Cla
rifi
er e
fflu
ent
PM
(g
)
0
20
40
60
80
100Influent Q
Measured (PM = 6 mg/L)
Modeled
Qp = 28 L/s
td = 44 min
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Infl
uen
t fl
ow
rat
e, Q
(L
/s)
0
5
10
15
20
25
30Influent Q
Measured (PM = 15 mg/L)
Modeled PM Depth = 5 mm
Measured PM = 142 g Modeled PM = 133 g
PM Depth = 15 mm
Measured PM = 325 g Modeled PM = 311 g
Qp = 28 L/s
td = 44 min
Cla
rifi
er e
fflu
ent
PM
(g
)
0
10
20
30
40
50
Influent Q
Measured (PM = 4 mg/L)
Modeled
Qp = 50 L/s
td = 110 min
15 mm (PM = 14 mg/L)
Infl
uen
t fl
ow
rat
e, Q
(L
/s)
0
10
20
30
40
50
60
Influent Q
Measured (PM = 10 mg/L)
Modeled
Qp = 50 L/s
td = 110 min
PM Depth = 5 mm
Measured PM = 385 gModeled PM = 380 g
PM Depth = 15 mm
Measured PM = 1071 gModeled PM = 1025g
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Cla
rifi
er e
fflu
ent
PM
(g
)
0
20
40
60
80
100Influent Q
Measured (PM = 4 mg/L)
Modeled
PM Depth = 5 mm
Measured PM = 75g Modeled = 82 g
Qp = 22 L/s
td = 44 min
PM Depth = 5 mm
Measured PM = 160 g Modeled PM = 158 g
Qp = 35 L/s
td = 44 min
Infl
uen
t fl
ow
rat
e, Q
(L
/s)
Figure 5-3. Intra-event effluent PM washout generated by physically-validated CFD model. Plot
A) and B) generated from a triangular hyetograph loading the subject watershed; plots
C) and D) generated from the 8 July 2008 hydrograph. Plot E) and F) generated from
hydrographs of Figure 5-2B with Qp of 22 L/s and 35 L/s, respectively. Plots A), C),
E), F) generated with uniformly pluviated PM depth of 5 mm while plot B) and D)
generated with 15 mm of PM across the bottom of the rectangular clarifier. The range
bars represent duplicate samples taken at each discrete time across each hydrograph
A B
C D
E F
141
Modeled washout PM (kg)0 1 2 3 4 5 6
Mea
sure
d w
ash
ou
t P
M (
kg
)
0
1
2
3
4
5
6
Figure 5-4. CFD model of event-based washout of PM at 50% and 100% of sediment capacity in
sump area and no PM depth in the volute area, and also for 50% of PM capacity in
sump area and 2.54 cm sediment depth in volute area for SHS (D =1.7m). The results
are obtained at maximum hydraulic capacity, Qd of 31.1 L/s and for 1.25·Qd. In
addition, CFD modeled overall washout results are reported for SHS unit (D = 1 m)
subject to a hetero-disperse PSD at flow rate of 10 L/s at 50% and 100% of PM
capacity of sump area (no pre-deposited PM in the volute area). The range bars
indicate the variability of the measured duplicated physical model results
SHS (D = 1.7 m)
Influent PSD
= 9.81
= 15.8
d50 = 110 m
s = 2.63 g/cm3
b = 1.04 g/cm3
SHS (D = 1 m)
Influent PSD
= 0.58
= 271
d50 = 67 m
142
Flow rate,Q (L/s)0 10 20 30 40 50
Was
ho
ut,
Mw (
kg
)
0
1
2
3
4
5
6
PM
dep
th
(mm
)
0 10 20 30 40
Sum
p a
nd
volu
te w
asho
ut,
Mw (
kg
)
0
10
20
30
Rectangular Clarifier
SHS
Volute (50 % sump capacity, SC)
5
50
40
35
15
100
25
10
Vo
lute
PM
dep
th (
mm
)
Flow rate,Q (L/s)0 10 20 30 40
Sum
p w
ash
ou
t, M
w (
kg
)
0
2
4
6
8
10SHS
Sump450
150
100
25
Su
mp
PM
dep
th (
mm
)
228
50
(100% SC)
(50% SC)
Figure 5-5. CFD model of PM washout mass as a function of flow rate, Q for the rectangular
clarifier and SHS unit. In A) washout PM mass from the rectangular clarifier is
shown for different PM depths ranging from 5 to 50 mm. In B) washout PM mass
from the SHS is reported for 50% of PM capacity in sump area and PM depths in
volute section ranging from 10 to 100 mm. In C) washout PM mass from the sump of
SHS unit is shown for different PM depths ranging from 25 to 450 mm (no PM in
volute region)
A
Influent PSD
= 0.79
= 28
d50 = 50 mm
s = 2.63 g/cm3
b = 1.04 g/cm3
B
C
143
Cum
ula
tive e
fflu
ent
mass
(k
g)
0
200
400
600
800 No washout
Washout
Month (2007)1 2 3 4 5 6 7 8 9 10 11 12
PM
depth
(m
m)
0
5
10
15
20
25
30No washout
Washout
2007 cumulative runoff volume (m3)
0 1000 2000 3000 4000 5000
Cum
ula
tive e
fflu
ent
mass
(k
g)
0
100
200
300
400
500
600
700Washout (M
o = 0.033, b = 1.15)
No washout (Mo = 0.039, b = 1.13)
Cum
ula
tive e
fflu
ent
mass
(k
g)
0
200
400
600
800No washout
Washout
2007 cumulative runoff volume (m3)
0 1000 2000 3000 4000 5000
Cum
ula
tive e
fflu
ent
mass
(k
g)
0
200
400
600
800
1000No washout (M
o = 0.132, b = 0.99)
Washout (Mo = 0.067, b = 1.11)
M = Mo V
b
M = Mo V
b
Month (2007)1 2 3 4 5 6 7 8 9 10 11 12
0.0
0.1
0.2
0.3
0.4
0.5
-0.08
-0.04
0.00
0.04
0.08
0.12No washout
Washout
Sump region
Volute region
Screened HS
Volu
te P
M
depth
(m
)S
um
p P
M
depth
(m
)
50% sump
capacity
Figure 5-6. Results from the continuous simulation model for 2007. In A) and D) illustrate the
flow limited washout from the RC and SHS where physical model data are fit by a
power law. B) and E) compare the effluent PM mass from a RC and SHS with and
without PM washout as a function of month runoff. C) and F) compare the
accumulated uniform PM depth with and without washout for the RC and SHS.
Results in F) produced by assuming PM mass accumulates first in the sump area
(negligible PM deposition in the volute area) and subsequently as the PM mass
reaches 50% of the sump capacity, PM accumulates in the volute area.
Influent PSD
= 0.79; = 28
s = 2.63 g/cm3
= 1.035 g/cm3
Cinf = 200 mg/L
D
C F
A
B E
144
Table 5-1. Physical and CFD model hydraulic loadings and washout PM results for the clarifier
subject to the hydrographs shown in Figure 5-1(B) and (C) and the hetero-disperse
gradation shown in Figure 5-1(A). Qp, Qd, td, V, , PM depth, RPD are peak flow,
design flow rate, hydrograph duration, hydrograph volume, unsteadiness factor, depth
of PM mass inside the system and relative percent difference, respectively
Rectangular clarifier, Qd =50 L/s
Hydrologic event Washout results
Qp td V
PM
pluviation
depth
Effluent mass PM load
RPD Measured Modeled
(L/s) (min) (m3)
(-) (mm) (g) (g) (%)
28 44 15 1.87 5 142 133 -6.77
28 44 15 1.87 15 305 311 -4.18
50 110 89 4.39 5 385 388 -1.21
50 110 89 4.39 15 1071 1025 -4.50
35 44 15 2.14 5 160 158 -1.27
22 44 15 1.61 5 75 82 8.54
145
Table 5-2. Measured and modeled washout PM are reported for two units, SHS (D = 1.7 m) and
SHS (D = 1.0 m) along with the characteristics of the washout runs. RPD is the
relative percent difference and Qd represents the design flow rate of the system
Screened HS (D = 1.7 m), Qd = 31.1 L/s and (D = 1.0 m), Qd = 10 L/s
PM pluviation Effluent mass
depth in : PM load
Q Unit dia. Volute Sump Measured Modeled RPD
(L/s) (m) (mm) (mm) (Kg) (Kg) (%)
31.1 1.7 0 228 2.76 2.86 -3.62
31.1 1.7 25.4 228 2.98 3.20 -7.42
31.1 1.7 0 456 4.51 4.50 0.22
38.8 1.7 0 228 3.22 3.53 -9.64
38.8 1.7 25.4 228 3.16 3.37 -6.61
38.8 1.7 0 456 5.48 5.97 -8.90
10.0 1.0 0 228 0.05 0.04 10.64
10.0 1.0 0 456 0.08 0.09 -11.31
146
Table 5-3. Unsteady and steady CFD PM washout results for rectangular clarifier and SHS (D =
1.7m). The unsteady results are obtained for the hydrographs shown in Figure 5-2(B)
and (C) and Figure 5-2(E) and (F). Steady PM results are obtained from the steady
CFD model subject to flow rate equal to peak flow rate of each hydrograph shown in
Figure 5-2. RPD represents the relative percent difference between the fully unsteady
and steady CFD model results
Rectangular clarifier, Qd =50 L/s
Q
PM pluviation Effluent mass PM load
RPD depth Steady Unsteady
(L/s) (mm) (g) (g) (%)
28 5 147 133 -10.38
28 15 342 311 -10.12
50 5 410 380 -7.78
50 15 1077 1025 -5.09
35 5 180 158 -13.67
22 5 91 82 -11.41
Screened HS (D = 1.7m), Qd = 31.1 L/s
Q
PM pluviation
depth Effluent mass PM load
RPD Volute Sump Steady Unsteady
L/s (mm) (mm) (Kg) (Kg) (%)
31.1 0 228 4.7 4.20 -11.90
31.1 25.4 228 6.9 6.30 -9.52
21.0 0 228 3.0 2.74 -8.76
17.0 0 228 2.8 2.55 -7.84
17.0 25.4 228 4.2 3.90 -8.72
13.0 0 228 2.4 2.15 -13.02
147
CHAPTER 6
GLOBAL CONCLUSION
This study developed a validated fully unsteady CFD model to predict PM separation and
time-dependent effluent PM of a BHS, a SHS and a RC, treatment units utilized worldwide for
treatment of wet and dry weather flows subjected to fine and coarse hetero-disperse PSD
gradations.
An accurate parameterization of MS, TS and DN was performed on the fully unsteady
CFD model for BHS. Results (PM and PSD) demonstrated that the full-scale CFD model was
able to accurately predict the response of a full-scale physical model across the range of quasi-
steady to highly unsteady flow loadings. Results also showed that TS and MS had a significant
impact on time-dependent profiles of PM indices. The influence of TS and MS also varied for
increasing . A DN of 8–16 for this coarser hetero-disperse PSD reproduced effluent PM load.
Results also demonstrated that increasing the model accuracy through higher MS, higher DN or
smaller TS requires increasing computational effort.
The validated CFD model of the RC was utilized to examine the hydraulic response of
clarifiers retrofitted with baffles and loaded by unsteady stormwater inflows. Results indicated
that the hydraulic response (as N, MI or RTD) of a baffled or un-baffled basin was function of
flow rate, and Le/L (as an equivalent L/W ratio). Given that stormwater systems are loaded by
a wide range of flows and , a singular hydraulic response (whether as N, MI, VE or RTD)
cannot be expected, although high number of baffles did confer a more consistent, reproducible
response even subject to unsteadiness. Based on physical and CFD model results, this study
indicated that internal baffling did alter unsteady hydraulic response and increased PM
separation. For stormwater UOs subject to a wide range of uncontrolled loadings, hydrograph
was an important parameter. While the full-scale physical modeling system of this study
148
metered a constant PM concentration and PSD, the quest for a unique relationship between a
particular hydraulic response (for example N) and PM or PSD elution from a stormwater clarifier
was further complicated by the separate unsteadiness of PM and PSD inflows.
To reduce the computational overhead of fully-unsteady CFD model the stepwise steady
CFD model based on the UH analog was introduced and tested. The stepwise steady flow model
was validated with measured physical model and it showed good agreement with results
generated by unsteady CFD modeling for two Type I settling units, a RC and a BHS. The
primary advantage of the stepwise steady CFD approach was to achieve a satisfactory modeling
accuracy at a reduced computational overhead. The computational time required for the time
domain continuous simulation model which included steady CFD modeling, post-processing and
running the MatLab code for a year of storm events (a number of 133 events) was 13 hours in
total. In contrast, a fully unsteady CFD model required 13 hours at minimum to solely run one
single hydrological event.
This study demonstrated the auto sampling produced representative samples of PM eluted
from a BHS for both finer and coarser PSDs, but it did not accurately characterize the influent
samples for either PSDs. The auto sampling was not able to collect the coarser fraction of PSD
(>75m) to which was associated most of the influent PM mass. This study investigated the
effect of influent auto sampling in predicting effluent PM for a BHS and RC by using CFD
model, demonstrating the importance of representative and accurate influent PM recovery was
crucial not only in monitoring and testing but also for modeling purposes.
Finally this study tested the stepwise steady flow CFD model coupled with a time domain
continuous simulation model to simulate the long-term response of the RC and SHS subject to
unsteady hydrologic loading for PM separation and also washout at a reasonable computational
149
overhead. The findings from the washout CFD model demonstrated that neglecting PM washout
leaded to significantly underestimate PM mass eluted from UOs such as the SHS where the PM
storage zones were not volumetrically or hydraulically isolated from flows capable of re-
suspending and transporting PM from the UO. The validated fully unsteady CFD model for PM
washout was then used to predict PM washout as function of flow rate (as the Qp of a
hydrograph) and separated PM depth in the UO under steady conditions. These results allowed
the integration of washout phenomena into the continuous simulation model. Based on the time
series of results generated from rainfall loadings for the representative year of 2007 on a 1.6 ha
largely impervious Gainesville, FL catchment, the SHS unit was significantly more prone to PM
washout than the RC. In comparison to the RC the washout of previously separated PM mass
significantly deteriorates the annual performance of the SHS.
The coupling of the stepwise steady CFD model with time domain continuous simulation
was able to quantify the temporal evolution of PM separation, accumulation and washout for the
RC and SHS. This temporal evolution across the year for any UO under any set of climate and
catchment conditions is crucial for maintenance and management of the UO to achieve targeted
or promoted levels of treatment.
In conclusion, this investigation provided a quantitative assessment of modeling accuracy
for different TS and MS subject to hydrograph unsteadiness with results that were validated from
a monitored physical model. This set of results represented a detailed and useful guideline for
modelers in selecting or evaluating computational parameters as a function of loading
unsteadiness in order to balance model accuracy, computing time and computational resources.
Furthermore, the coupling of a stepwise steady CFD model and time domain continuous
simulation model represented a valuable set of tools to quantify the capability of UOs to separate
150
and retain PM on annual basis and to provide necessary information to effectively maintain and
manage UOs.
151
APPENDIX A
SUPPLEMENTAL INFORMATION OF CHAPTER 2 “TRANSIENT ELUTION OF
PARTICULATE MATTER FROM HYDRODYNAMIC UNIT OPERATIONS AS A
FUNCTION OF COMPUTATIONAL PARAMETERS AND HYDROGRAPH
UNSTEADINESS”
Detailed Sampling Methodology and Protocol
Effluent Sampling
The sampling is conducted according the following procedure. During the test running
time, representative effluent samples are taken manually across the entire cross section of the
effluent section of the unit as discrete samples in 1L wide mouthed bottles. Samples are collected
in duplicate through the entire duration of the run at variable time sampling frequency according
to the flow rate gradients and event duration to provide a reasonable estimate of effluent
variability of PM concentration and PSD. The minimum sampling time interval is 1 minute. The
sampling protocol used to characterize the supernatant PSD consists of taking a duplicate sample
at the geometric midpoint of the supernatant after overnight settling. In particular, four PSD and
SSC duplicate samples are taken at four evenly spaced intervals of height of the stored
supernatant volume.
Mass Recovery and Sample Protocol
After the supernatant sample has been collected the wet slurry from the system is
recovered from the bottom of the unit by manually sweeping it through the washout points into
buckets and taken to the laboratory where they are allowed to stand for quiescent settling and
dried in glass trays at 105 degrees Celsius in an oven. After the slurry completely dries the dry
silica is disaggregated and collected in pre-weighed glass bottles and the gross weight is recorded
to find the overall efficiency of the system based on mass and for the mass balance. Laser
diffraction analysis for the collected dry sample is then performed to analyze the PSD of the
captured particle.
152
Laboratory Analysis
The experimental analyses include PSD measurements for influent, effluent and captured
PM by laser diffraction analysis, effluent gravimetric analysis based on PM concentration as
suspended solid concentration (SSC). SSC analysis is performed to quantify particle
concentration for each effluent composite sample as collected from each run and to calculate the
effluent mass load for the operating flow rates. Fully characterizing the entire PSD and utilizing
SSC allow a mass balance to be conducted which is not possible when utilizing an index
component and method of PM, such as total suspended solids, TSS. The protocol specifically
followed for this laboratory analysis is the ASTM D 3977 (Jillavenkatesa et al., 2001).
To perform the PSD analysis the Malvern Mastersizer 2000, a commercial laser diffraction
analyzer is utilized in this experimental analysis. The instrument technology is based on laser
diffraction, occurring when a laser beam passing through a dispersion of particles in air or in a
liquid is diffracted at the particle surface. The angle of diffraction is influenced by the size and
the shape of the particle. As the particle size decreases, the scattering angle increases (Kim and
Sansalone, 2008). The Mastersizer 2000 detects particle sizes in the range of ~0.02 to 2000 μm
in spherical diameter. During a sample measurement, the instrument is programmed to
characterize the PSD three times. These three PSD curves are then analyzed for stability to
ensure that the measurement settings for the instrument are adequately suited for the sample and
to ensure that any bubbles that might be present and affect the reliability of the measurement are
purged from the system. The three measured and stable PSDs for the individual sample are
averaged into a representative curve for that sample. An event mean PSD is generated from
averaging the individual Mastersizer measurements (both A and B).
Finally, the captured PSD is measured with the laser diffraction analyzer in dry phase. In
order to representatively sub-sample the dry mass the silica is uniformly mixed to obtain a sub-
153
sample as representative as is physically obtainable. Duplicate 20 g samples are taken for the
dry phase of the laser diffraction analyzer. The dry dispersion cell is connected to the laser
diffraction analyzer and the dry sample is measured by forming a PM aerosol with a high
pressure, high velocity air stream. The PSDs measured are observed for stability and averaged.
Verification of Mass Balance
A mass balance evaluation is conducted to ensure representative and defensible event-
based treatment performance results for the unit. The PM mass balance is calculated from dried
captured mass, effluent mass load, and supernatant mass load. The mass balance error (MBE)
criteria is ±10% MBE and determined by the following equation (ASTM, 2000):
100
load mass Influent
load mass Influentload mass Captured load mass Effluent (%) BEM
where
ttQt
t
ii
i
C load massEffluent
M load massInfluent
n
0i
eff
n
0i
inf
In the mass balance expression Minf is influent mass load and Ceff is effluent concentration
which varies with time, ti. Msep is separated PM recovered.
Verification of PSD Balance
The gravimetric PSD of the effluent, supernatant and recovered mass is measured and
compared with that of the influent to verify the balance of influent and effluent PSDs. This QC
measurement is performed by quantifying the deviation between the representative silt influent
loading and the summation PSD of the effluent, recovered, and supernatant mass.
(A-1)
(A-2)
(A-3)
154
n
1i
i
n
1i
iiii
error
PSDInfluent
PSDt Supernatan PSD Recovered PSDEffluent - PSDInfluent
PSD
In this expression each i is a discrete measurement at a specific particle size of the cumulative
PSD.
Results under Steady Condition
Experimental testing runs were performed on a full scale baffled HS unit located at the testing
facility “Stormwater Unit Operations and Processes Laboratory” at the University of Florida in
Gainesville, FL. In this section, the monitoring data collected from the experimental tests are
reported. In this analysis the particulate matter removal efficiency of the system is analyzed
when it is subjected to the influent NJDEP gradation. Testing experiments were carried out at 2,
5, 10, 25, 50, 75, 100, and 125 percent of the design flow rate (018 L/s) and at influent NJCAT
sediment concentrations of 100 mg/L. The run operational parameters and the treatment run
results for baffled HS are summarized in Table A-1.
The treatment efficiencies obtained from the physical model are compared graphically below to
the CFD modeled efficiencies under steady conditions. To assess the accuracy of the CFD
results with the monitoring data, the relative percentage difference (RPD) is computed. In
particular, the RPD is calculated on the basis of the baffled HS removal efficiency values
calculated experimentally as effluent event mean concentration (EMC). The RPDs computed
are 4.5% for influent PM concentration of 100 mg/L. The values obtained are within the control
limit defined for RPD, which is 10%.
Morsi and Alexander K – Values (Morsi and Alexander, 1972)
In equations 2-10 to 2-12 Rei is the Reynolds number for a particle, and CDi is the drag
coefficient.
(A-4)
155
ipipi
vvd Re
(A-5)
3221
ReReK
KKC
iiiD
(A-6)
In these equations is fluid density, p is particle density, vi is fluid velocity, vpi is particle
velocity dp is particle diameter, is dynamic viscosity, K1,K2,K3 are empirical constants as a
function of particle Rei.
Morsi and Alexander K – values as function of Reynolds number are reported in Table A-2.
Effect of Temperature
To verify the hypothesis that the temperature does not significantly impact the PM removal
efficiency of Type I settling unit, a set of steady-state simulations are performed in CFD on a HS
system. The unit is loaded with a hetero-disperse PM gradation and the effluent PSDs are
predicted for a wide range of temperature. The temperatures investigated are 1º, 5º, 10º, 15º and
20º. The results showed in Figures A-7 demonstrate that temperature variation does not
significantly influence the effluent PSD of PM eluted from a HS unit.
156
Overall Efficiency - Modeled vs. Measured
Percentage of maximum hydraulic capacity (0.64 cfs)
0 20 40 60 80 100 120 140
Per
cent
(%)
30
40
50
60
70
80
90
100
Measured
Modeled
Absolute RPD = 4.5 %
Cinfluent = 100 mg/L
Figure A-1. Validation of measured vs. modeled PM separation for the HS subject to the hetero-
disperse PSD loading at a gravimetric PM concentration of 100 mg/L at steady flow
rates
157
% f
iner
by
mass
0
20
40
60
80
100
% f
iner
by
mass
0
20
40
60
80
100
0.2<t/td<1
% f
iner
by
mass
0
20
40
60
80
100
% f
iner
by
mass
0
20
40
60
80
100
Particle diameter, d (m)
0.11101001000
% f
iner
by m
ass
0
20
40
60
80
100
Particle Diameter, d (m)0.11101001000
% f
iner
by m
ass
0
20
40
60
80
100
Figure A-2. Effluent PSDs measured by laser diffraction analysis for differing hydrographs.
Effluent PSDs for highly unsteady hydrograph (A-B), unsteady hydrograph (C-D),
quasi unsteady hydrograph (E-F). The PSDs reported are produced in effluent by the
baffled HS loaded by a hetero-disperse PSD. The measured influent gradation is in
each plot shown in gray dots on the left side
Q+ Q
-
Influent gradation
0 < t/td<0.2
Q+ Q
-
Influent gradation
0 < t/td<0.4 0.4 < t/td<1
Q+ Q
-
Influent gradation
0 < t/td<0.2 0.2 < t/td<1
Influent gradation
Influent gradation
Influent gradation
Qp = 18 L/s
td = 74 min
Qp = 18 L/s
td = 74 min
Qp = 9 L/s
td = 87 min Qp = 9 L/s
td = 87 min
Qp = 4.5 L/s
td = 125 min
Qp = 4.5 L/s
td = 125 min
A B
C D
E F
158
Elasped time (min)
0 20 40 60 80 100 120
Esc
aped
Eff
luen
t (g
)
0
100
200
300
400
e n (
%)
0
20
40
60
80
100
Measured
Modeled
TS = 10 sec
TS = 300 sec
TS = 900 sec
Model parameters:
DN = 16
MS = 3.1*106
Qp
= 18 L/s; td
= 84 min
Esc
aped
Eff
luen
t (g
)
0
100
200
300
400
e n (
%)
0
20
40
60
80
100
Qp
= 9.06 L/s; td
= 87 min
Elapsed time (min)
0 20 40 60 80 100 120
Esc
aped
Eff
luen
t (g
)
0
100
200
300
400
e n (
%)
0
20
40
60
80
100
Qp
= 4.53 L/s; td
= 125 min
Figure A-3. Effect of time step (TS) on modeled effluent PM at DN = 16 and MS = 3.1*10
6 for
three hydrologic unsteadiness levels investigated respectively, highly unsteady,
unsteady and quasi-steady. The CFD model results are compared to the measured
data. The value of en calculated respect to the measured data is reported for each time
step explored
A
B
C
159
No
rmal
ized
ro
ot
mea
n s
qu
ared
err
or,
en(%
)
0
5
10
15
20
25
30
35
40
Qp = 4.5 L/s; td = 125 min; 50
= 11 min
Qp = 9 L/s; td = 87 min; 50
= 33.7 min
Qp = 18 L/s; td = 84 min, 50
= 58 min
(A.) Effluent PM mass
DN = 16
MS = 3.1*106
0.02 0.45 1.36
0.003 0.09 0.26
0.005 0.15 0.44
TS/50
Norm
aliz
ed r
oot
mea
n s
quar
ed e
rror,
en
(%
)
0
2
4
6
8
10
12
14
Qp = 4.5 L/s; t
d = 125 min
Qp = 9 L/s; t
d = 87 min
Qp = 18 L/s; t
d = 84 min
DN = 16
TS = 10 sec
Cell size (mL)
2.3 0.9 0.511.6
(B.) Effluent PM mass
Mesh size, MS (millions)
Co
mp
uta
tio
nal
tim
e (h
)
0
50
100
150
200Qp = 4.5 L/s; td = 125 min
Qp = 9 L/s; td = 87 min
Qp = 18 L/s; td = 84 min
(D.)
DN = 16
TS = 10 sec
0.2 1 3.1 5
DN = 16
TL = 8 m
MS = 1.3*106
Com
pu
tati
onal
tim
e (h
)
0
20
40
60
80
100
Qp = 4.5 L/s; td = 125 min
Qp = 9 L/s; td = 87 min
Qp = 18 L/s; td = 125 min
DN = 16
MS = 3.1*106
0.17 5.0 15.0
(C.)
0.02 0.05 0.09 0.45 1.36
0.005 0.01 0.03 0.15 0.44
0.003 0.01 0.02 0.09 0.26
0.001 0.004 0.008 0.040 0.120
0.0002 0.006 0.012 0.057 0.172
0.0023 0.007 0.013 0.068 0.203
Time Step, TS (min) Mesh size, MS (millions)
0.2 1 3.1 5
TS/td
Figure A-4. Normalized root mean squared error (en) of CFD model effluent PM as function of
time step for three levels of hydrologic event unsteadiness investigated The error is
calculated based on the measured effluent data. The model parameters are PSD
discretization number (DN) of 16 and computational domain mesh size (MS) of 3.1 x
106
A B
C D
160
Elasped Time (min)
Esc
aped
Eff
luen
t (g
)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Measured
Modeled
MS = 0.2*106
MS = 1*106
MS = 3.1*106
Model parameters:
DN = 16
TS = 10 sec
Qp
= 18 L/s; td
= 84 min
Esc
aped
Eff
luen
t (g
)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Qp
= 9.06 L/s; td
= 87 min
Elapsed time (min)
0 20 40 60 80 100 120
Eff
luen
t P
M (
g)
0
100
200
300
e n (
%)
0
20
40
60
80
100
Qp
= 4.53 L/s; td
= 125 min
Figure A-5. Effect of mesh size (MS) on modeled effluent PM at DN = 16 and TS = 10 sec for
three hydrographs investigated respectively, A) highly unsteady, B) unsteady and C)
quasi-steady. The CFD model results are compared to the measured data. The value
of en calculated respect to the measured data is reported for each time step explored
A
B
C
161
Particle diameter (m)1101001000
% f
iner
by
mas
s
0
20
40
60
80
100
% f
iner
by
mas
s
0
20
40
60
80
100 Measured
Modeled
DN = 16 (tr = 37.5 hr; e
n = 2.4% )
DN = 32 (tr = 59 hr; e
n = 2.4% )
DN = 64 (tr = 267 hr; e
n = 2.4%)
Particle diameter (m)
1101001000
% f
iner
by
mas
s
0
20
40
60
80
100 Measured
Modeled
DN = 16 (tr = 103 hr; e
n = 5.7% )
DN = 32 (tr = 178 hr; e
n = 5.7%)
TS = 10 sec
MS = 3.1*106 Q
p = 18 L/s; t
d= 74 min
Qp
= 9 L/s; td
= 87 min
Qp
= 4.5 L/s; td
= 125 min
TS = 10 sec
MS = 3.1*106
TS = 10 sec
MS = 3.1*106
MeasuredModeled
DN = 16 (tr = 32 hr; e
n = 2.8%)
DN = 32 (tr = 51.3 hr; e
n = 2.9%)
DN = 64 (tr = 251 hr; e
n = 3.1%)
Figure A-6. Captured CFD model particle size distribution (PSD) at TS = 10 sec, MS = 3.1*10
6,
DN = 16, 32, 64 generated by baffled HS loaded by an influent hetero-disperse PSD
for three hydrographs investigated, respectively, A) highly unsteady, B) unsteady and
C) quasi-steady. The modeled PSD results are compared to measured data. tr
represents the overall computational time employed to run each simulation
A
B
C
162
Figure A-7. Effect of temperature on PM removal percentage of HS unit subject to the hetero-
disperse PM gradation of this study at the peak flow rate of 18 L/s
Temperature variation
Particle diameter, m
110100100010000
Fin
er b
y m
ass,
%
0
20
40
60
80
100
Measured Influent
Measured EffluentModeled
Effluent at 1 oC (54.5%)
Effluent at 5 oC (55.6%)
Effluent at 10 oC (56.2%)
Effluent at 15 oC (57.8%)
Effluent at 20 oC (58.0%)
163
Figure A-8. CFD model snapshots. Pathlines are colored by velocity magnitude (m/s)
164
Table A-1. Experimental matrix and summary of treatment run results for the baffled HS unit
loaded by a hetero-disperse (NJDEP) gradation under 100 mg/L and various
operating flow rates
Flow rate Influent conc. Influent
mass
load
Effluent
conc.a
Effluent
mass
load
Total
mass
capturedb
MBE Design Actual Target Actual
(%) (gpm) [mg/L] [mg/L] (g) [mg/L] (g) (g) (%)
100 294.0 100 97.8 3375 48.0 1655 1802 -2.4
125 364.6 100 98.5 3375 46.3 1588 1747 1.2
10 29.3 100 97.8 3375 29.8 1028 2660 -9.3
25 73.2 100 96.5 3375 36.0 1242 2225 -2.7
75 220.1 100 96.9 3375 44.5 1551 1885 -1.8
2 5.4 100 106.0 1042 11.1 109 917 1.5
50 146.8 100 97.8 3375 37.6 1295 2318 -7.1
5 16.6 100 86.3 2606 14.8 448 2186 -1.1
Note: a Effluent event mean concentration
b Total mass captured is the sum of suspended PM in supernatant and settled PM recovered as wet slurry
from the unit
Table A-2. Morsi and Alexander constants for the equation fit of the drag coefficient for a sphere
Reynolds Number K1 K2 K3
<0.1 24.0 0 0
0.1 < Re < 1 22.73 0.0903 3.69
1 < Re < 10 29.16 -3.8889 1.222
10 < Re < 100 46.5 -116.67 0.6167
100 < Re < 1000 98.33 -2778 0.3644
1000 < Re < 5000 148.62 -4.75 *104 0.357
5000 < Re < 10,000 -490.54 57.87 * 104 0.46
10,000 < Re < 50,000 -1662.5 5.4167 * 106 0.5191
165
APPENDIX B
SUPPLEMENTAL INFORMATION OF CHAPTER 3 “STORMWATER CLARIFIER
HYDRAULIC RESPONSE AS A FUNCTION OF FLOW, UNSTEADINESS AND
BAFFLING”
Full-scale Physical Model Setup
The analysis is carried out on full-scale physical models of primary clarifiers, which
represent the most traditional and common clarification systems used in rainfall-runoff PM
treatment. The first configuration is a rectangular clarifier, approximately 1.87 m tall, 1.8 m wide
and 7.31 m long with hydraulic capacity of approximately 12,000 L. The second configuration
has the same geometrical characteristics of the first one, but with eleven baffles placed in the unit
to avoid the potential for short-circuiting. The baffles have a length of 1.22 m and inter-distance
of 0.61 m. The distance from the edge of the baffles to the wall, O, is 0.60 m. The influent and
effluent pipe diameters are of 0.2 m. Two units are characterized by the same surface area. The
design flow rate, Qd of the physical model is about 50 L/s, corresponding to the hydraulic
capacity of physical model as an open-channel system.
Tracer tests are conducted to determine RTDs at 20˚C. The tracer used is sodium chloride
(NaCl). The flow rates tested are 1, 2.5, 5, 12.5, 25, 37.5 and 50 L/s (respectively, 2, 5, 10, 25,
50, 75 and 100% of the design flow rate, Qd). RTD experiments are conducted at constant flow
rate by injecting a single pulse of a known volume of tracer into the drop box upstream of the
clarifier. Prior to tracer injection, the conductivity of the potable water used for background
testing is measured. A calibrated conductivity probe, manufactured by YSI Inc., is placed fully
submerged at the outlet section of the clarifier to take real-time conductivity measurements every
5 seconds. The running time of the experiments is based on the time taken by the conductivity to
drop back to the background (potable water) conductivity. A calibration curve is developed to
establish the relationship between concentrations and conductivity. The concentrations are thus
166
calculated from conductivity measurements. Each tracer run is validated by a mass balance check
with an allowable error of +/-10 %. The mass recovery percent is reported in Table B-1 for the
tracer tests.
To validate the CFD model under transient conditions, effluent PM and PSDs eluted from
the full-scale rectangular clarifier with no baffles and 11 transverse baffles subjected to two
hydrological events are collected. The first hydrograph is generated from a triangular hyetograph
with 12.7 mm (0.5 inch) of rainfall depth and duration of 15 minutes. This loading is selected as
a common short and intense rainfall event during the wet season in Florida (Figure B-1-2). The
second hydrograph is generated from a historical event collected on 8 July 2008 in Gainesville,
Florida with total rainfall depth of 71 mm. This event is chosen since it is an extremely intense
historical event, with a peak rainfall intensity of about 165 mm/h (Figure B-3). The particle size
distribution (PSD) used is reported in Figure B-4 and is a fine hetero-disperse gradation
classified from Unified Soil Classification System (USCS) as SM I with a d50 of 18 m. The
hyetographs are transformed to event-based hydrographs by using Storm Water Management
Model (SWMM) (Huber and Dickinson, 1988) for each physical and CFD model. The objective
of the rainfall-runoff simulations is to generate unsteady runoff flow loadings for the scaled
physical model and CFD model. In this transformation from rainfall to runoff for the scaled
physical basins, the watershed area is matched to deliver peak runoff flow rates equal to the
design flow rate of the unit operation. More details information about the two hydrographs
utilized for the validation are reported in Appendix (Figure B-5). The protocol used to retrieve
the experimental data for the validation of transient CFD model is the same as that described in
Garofalo and Sansalone (Garofalo and Sansalone, 2011) and for brevity not reported here. In
167
Appendix, the generation of the two hydrographs utilized is explained in detail. The results
retrieved from the experiments are reported in Table B-2.
Generation of Hydrographs Used for the Validation of the Full-Scale Physical Model of
Clarifier under Transient Conditions
Study Hyetographs
An essential component of this study is the definition of the hydrological loadings. The
three hyetographs selected are:
Triangular hyetograph with 12.7 mm (0.5 inches) of rainfall volume and duration of 15
minutes. This loading is selected as a common short and intense rainfall event during the
wet season in Florida. A triangular shape is used to define the hyetograph as shown in
Figure B-1 (Chow et al., 2008). The maximum rainfall intensity of the triangular
hyetograph is approximately 101 mm per hour (4 inches per hour) and the total excess
precipitation depth is 12.7 mm (0.5 inches). The hyetograph selected is considered a fairly
extreme event, since 80% of storm events occurring in Gainesville are characterized by a
total precipitation depth equal or less than 12.7 mm (0.5 inches). Figure B-2 reported
below depicts the frequency distribution of 1999-2008 hourly rainfall data for Gainesville
Regional Airport (KGNV).
Historical event collected on 8 July 2008 by UF with total rainfall depth of 71 mm. This
event is chosen since it is an extremely intense historical event, with a peak rainfall
intensity of about 165 mm/h (Figure B-3). This value is higher than peak precipitation
intensity of the 24 hour-25 year design storm described in the following paragraph.
Particle Size Distribution
PSD Selection
The influent particulate loading used throughout the entire study for CFD wet-pond
simulation runs and experimental full-scale physical model testing consists of a PSD that is in
the silt-size range. The PSD, ranging from less than 1 m to 75 m is reported in Figure B-4.
The PM specific gravity is 2.63 g/cm3. The mass-based PSD is well described by a gamma
distribution function. The probability density function is given by Equation B-1 as a function of
particle diameter d, where is a distribution shape factor and a scaling parameter. The
cumulative gamma distribution function is expressed in Equation B-2.
168
PSD Significance
PM is widely recognized as a primary vehicle for the transport and partitioning of
pollutants. Moreover, PM is a pollutant itself that impacts the deterioration of receiving surface
waters. The potential for water chemistry impairment strongly depends on PM loading and PSD.
Furthermore, many PM-bound constituents, such as metals, nutrients and other pollutants,
partition to and from PM while transported by PM through rainfall-runoff events. Therefore,
PSD plays an important role in the transport and chemical processes occurring in urban
stormwater runoff and an understanding of its behavior is crucial for the analysis and the
selection of unit operations.
Transformation of Rainfall Hyetographs to Runoff Hydrographs
The hyetographs reported in Figure B-1 and B-3 are transformed to event-based
hydrographs by using the Storm Water Management Model (SWMM) (Huber and Dickinson,
1988) for each physical and CFD model. The objective of the rainfall-runoff simulations is to
generate unsteady runoff flow loadings for the scaled physical model and CFD model. SWMM
translates rainfall in runoff for the specific catchment properties.
In this transformation the watershed area is matched to deliver peak runoff flow rate equal
to the design flow rate of the unit operation. As shown pereviously, July 8th
2008 historical
hyetograph is characterized by the highest rainfall peak intensity (approximately 165 mm/h) in
comparison to the other selected hyetographs. Therefore, the historical hyetograph is utilized as a
reference to perform the flow scaling of the physical testing model. Since the maximum
(B-1)
x
ex
xf
1
dxxfxF
x
0
(B-2)
169
hydrualic load of the physical models is 50 L/s, the area of the catchment implemented in
SWMM is defined to deliver peak flow rate equal to 50 L/s for the historical storm of 8 July
2008.
The modeling parameters adopted are referred to an asphalt-pavement of a typical airport
runway/taxiway. Green-Ampt method is used to model infiltration process. The rainfall-runoff
modeling for the three hyetographs are shown in Figure B-5.
Definition of N
The tanks in series model equation is given by (Levespiel, 2002):
it
ni
n
en
ttE
!1
1
Because the total reactor volume is nVi, then the residence time in one of the reactor, i is
equal to /n, where t is the total volume divided by the flow rate, Q:
n
n
en
nntEE
!1
1
where =t/
The number of tanks in series can be determined by calculating the dimensionless variance
from a tracer study:
which can be proved equal to:
(B-3)
(B-4)
(B-5)
(B-6)
170
For the tanks in series model it is possible to define simple relations between the
parameters of the distribution and the variance (Kandlec and Wallace, 2009). For instance the
tanks-in-series model has a dimensionless variance given by:
From this expression we can derive that (Letterman, 1999)
In Figure B-6 the relationship between N tanks in series parameter obtained from Equation
B-7-8 is shown. The relationship is linear and the coefficients of the regression line suggest that
is approximately a bisector.
Geometry and Mesh Generation of Full-Scale Rectangular Clarifier
The mesh is comprised of tetrahedral elements and it is checked carefully to ensure that
equiangle skewness and local variations in cell size are minimized in order to produce a high
quality mesh. Several iterations of grid refinement are performed to determine the necessary
mesh density that balances the accuracy of the solution with the exponentially increasing demand
on computational resources. The final mesh used in this study is discretized into approximately
3.5 million cells (Figure B-7-8).
Turbulent Dispersion Model
The dispersion of particles due to turbulence in the fluid phase is predicted using stochastic
tracking model as mentioned (Thomson, 1987; Hutchinson et al., 1971; Jacobsen, 2008). In this
model, the turbulent dispersion of particles is predicted by integrating the trajectory equation for
individual particles (Eq. B-3-11) using the instantaneous fluid velocity, tuu ' , along the
particle path during the integration. The random effects of turbulence on particle dispersion are
(B-7)
(B-8)
171
considered by computing the trajectory for a sufficient number of representative particles. In this
approach, the interaction of a particle with a succession of discrete turbulent eddies is simulated.
Each eddy is characterized by Gaussian distributed random velocity fluctuations, u’, v’ and w,’
and a timescale of interaction. The velocity fluctuations are related to the local turbulent kinetic
energy as:
3/2' ku
where is a normally distributed random number. The characteristic eddy lifetime is
expressed in terms of the local values of k and e:
r
kCLe log
where r is the uniformly distributed random number between 0 and 1 and CL is a constant
having a value of about 0.15. The particle is assumed to interact with the fluid-phase eddy over
this lifetime, after which a new value of the instantaneous velocity is obtained by sampling
again.
CFD Modeling and Population Balance
A population balance model (PBM) is coupled with CFD to model PM separation.
Assuming no flocculation in the dispersed particle phase, the PBM equation (Jacobsen, 2008)
and mass per particle, pn are as follows.
max
min
max
min
max
min 0 1
,,
0 1
,,
0 1inf,,
ddd t N
nsepn
t N
neffn
t N
n
n ppp
N
n
nN
Mp
1
,
,,
M is PM mass associated with the particle size range, ξ as function of injection time,
N is the total number of particles injected at the inlet section, and td is the event duration.
(B-9)
(B-10)
(B-11)
(B-12)
172
Validation Analysis of Steady RTDs and PM Separation Efficiency on Full-Scale Physical
Model of Rectangular Clarifier
The validation analysis consists of two parts. First part comprises a comparison between
measured and CFD modeled RTD curves for the full-scale physical model of the no-baffle
rectangular clarifier. The second part includes the validation of CFD modeled data in terms of
PM removal efficiency for the trapezoidal cross section clarifier and the rectangular clarifier with
no baffle and with 11 baffles. The CFD model is loaded with two hydrographs summarized in
Table B-2.
For RTD validation, a root mean squared error, RMSE was used to evaluate CFD model
error in predicting RTDs with respect to the full-scale physical model data:
n
xx
RMSE
n
i
imio
1
2
,,
In this equation xo is the measured and xm the modeled variable. The error reported in
Table S1 shows that RMSEs between CFD model RTDs and measured RTDs are within 10%.
The comparison between measured and CFD- modeled RTDs are graphically reported in Figure
B-3-6. The validation of CFD-modeled data in terms of PM removal efficiency is performed as
follows. The error between the measured and modeled removal efficiency is computed as relative
percentage error, given by:
100% mod
meas
meas
Where mod is the modeled PM removal efficiency and meas is the measured PM removal
efficiency. The error between the measured and modeled event-based PSDs is also calculated as
a RMSE.
(B-13)
(B-14)
173
Time (hour)
0.00 0.05 0.10 0.15 0.20 0.25
Pre
cip
itati
on
in
tensi
ty (
in/h
r)
0
1
2
3
4Total excess rainfall = 0.5 inta = 0.125 hr
Td = 0.25 hr
5.0d
a
T
tr
Figure B-1. Triangular hyetograph. Td is the recession time, ta is the time to peak, and r is the
storm advancement coefficient
Rainfall depth, in
0.0001 0.001 0.01 0.1 1 10 100 1000
Cum
ula
tive f
requency d
istr
ibuti
on, %
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 101112
Mean
# o
f E
ven
ts
05
1015202530
hra
infa
ll (
mm
)
0
40
80
120
160
200
# events
mean hrainfall
Figure B-2. Frequency distribution of rainfall precipitation for Gainesville, Florida. The
frequency distribution is obtained from a series of 1999-2008 hourly precipitation
data for Gainesville Regional Airport (KGNV)
174
Time (hour)0.0 0.2 0.4 0.6 0.8 1.0
Pre
cip
itati
on
in
ten
sity
(in
/hr)
0
1
2
3
4
5
6
7Total rainfall = 2.92 inta = 0.3 hr
Td =0.92 hr
Figure B-3. Historical event collected on 8 July 2008
Particle Diameter, d (m)
0.1110100
% f
iner
by
mass
0
20
40
60
80
100Silt PSD ( 75m)
GF (= 0.8, = 29)
Figure B-4. Influent PSD for fine PM {SM I, <75m}. SM is sandy silt in the Unified Soil
Classification System (USCS). SM is SCS 75. PSD data are fit by gamma function
(GF) based on distribution parameters, shape factor, and scale factor,
g
/
c
m
3
≤
175
t/tmax0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate
s (
L/s
)
0
10
20
30
40
50
Rain
fall
Inte
nsit
y (
mm
/hr)
0
50
100
150
200
250
Flo
w r
ate
(L
/s)
0
20
40
60
80R
ain
fall
Inte
nsit
y (
mm
/hr)
0
100
200
300
400
Figure B-5. Hydraulic loadings utilized for full-scale physical model. The rainfall-runoff
modeling is performed in Storm Water Management Model (SWMM) for the
catchment. The two hydrologic events investigated are: A) triangular hyetograph and
B) historical 8 July 2008 loading hydrologic event
Qp = 28.3 L/s
Ttot = 93 min
V = 1,541 L
Qp = 50 L/s
Ttot = 248 min
V = 89,000 L
A
B
176
N tanks in series, N = 50
/(50
-p
1.0 1.2 1.4 1.6 1.8
N t
ank
s in
ser
ies,
N =
1/
0.8
1.0
1.2
1.4
1.6
1.8
50/(
50-
p
R= 0.99
Figure B-6. Relationship between N-tanks-in-series computed from the inverse of the RTD
variance and the ratio between median residence time and the difference between
median and peak residence time
177
Figure B-7. Isometric view of full-scale physical model and mesh of the rectangular cross-
section clarifier with eleven baffles
Outlet
7.3 m
0.60 m
1.2 m
1.67 m
Vertical Wall
Free surface
178
Figure B-8. Isometric view of full-scale physical model and mesh of the rectangular cross-
section clarifier
Inlet
Outlet
7.3 m
1.67 m
1.4 m
179
Figure S9. Grid convergence
Figure B-9. Grid convergence for full-scale rectangular clarifier. The mesh utilized comprimes
3.1*106 tetrahedral cells
Mesh size (1*106)
0 1 2 3 4 5 6
Ro
ot
mea
n s
qu
ared
err
or,
en
(%
)
0
2
4
6
8
10
12
14
Mesh size utilized
180
E (
t)
0.000
0.002
0.004
0.006
0.008
0.010Q
n= 50 L/s (100% Q
d)
Elasped time (sec)
0 1000 2000 3000 4000
E (
t)
0.000
0.002
0.004
0.006
0.008
0.010Q
n= 25 L/s (50% Q
d)
E (
t)
0.000
0.002
0.004
0.006
0.008
0.010Q
n= 5 L/s (10% Q
d)
Elasped time (sec)
0 2000 4000 6000 8000 10000 12000
E(t
)
0.000
0.002
0.004
0.006
0.008
0.010Q
n= 2.5 L/s (5% Q
d)
= 1.5 min
50
= 5.6 min
min
= 43.3 min
50
= 77.3 min
min
= 2.9 min
50
= 10.7 min
min
= 42.5 min
50
= 68.5 min
min
Measured RTD
Modeled RTD
Figure B-10. Physical and CFD Modeled RTDs for flow rates, representing 100%, 50%, 10%
and 5% of Qd on no-baffle rectangular clarifier
181
t/td
0.0 0.2 0.4 0.6 0.8 1.0F
low
rat
e, Q
(L
/s)
0
5
10
15
20
25
30
Eff
luen
t P
M (
g)
0
20
40
60
80
100Influent Q
Modeled Effluent PM
Measured Effluent PM Q
p = 28.33 L/s
td = 44 min
Rectangular
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
5
10
15
20
25
30
Eff
luen
t P
M (
g)
0
2
4
6
8
10Influent Q
Modeled Effluent PM
Measured Effluent PM
11 transverse baffles
Influent PM = 3.03 Kg
m
= -0.07%
m
= 0.34%
Particle Diameter, d (m)
0.1110100
% f
iner
by m
ass
0
20
40
60
80
100
Qp= 28.33 L/s
td= 44 minC
inf = 200 mg/L
s = 2650 g/cm
3
0.1110100
% f
iner
by m
ass
0
20
40
60
80
100
11 transverse baffles
Cinf
= 200 mg/L
RMSE = 1.6 %
Rectangular
RMSE = 6.9 %
Particle Diameter, d (m) Figure B-11. Physical model and CFD model results for the triangular hydrograph used for the
validation analysis for full-scale physical model of a rectangular clarifier and a
rectangular clarifier with 11 transverse baffles. In A) and C) results for PM and PSDs
for the rectangular clarifier. In B) and D) results for PM and PSDs for the rectangular
clarifier with 11 baffles. Qp is the peak influent flow rate and td is the total duration of
the hydrological event. In C), and D) the shaded area indicates the range of variation
of effluent PSDs throughout the hydrological events. RMSE is the root mean squared
error between effluent average measured and modeled PSDs, s is the particle
density, Qp is the peak influent flow rate and td is the total duration of the
hydrological event
A
B
C
D
182
Figure B-12. Velocity magnitude (m/s) contours at a horizontal plane at mid-depth for the
configuration with transverse baffles and opening of 0.60 m
Inlet
Outlet
Inlet
Outlet
Inlet
Outlet
183
Figure B-13. Velocity magnitude (m/s) contours at a horizontal plane at mid-depth for the
configuration with transverse baffles and opening of 0.20 m
Inlet
Outlet
Inlet
Outlet
Inlet
Outlet
184
Figure B-14. Velocity magnitude (m/s) contours at a horizontal plane at mid-depth for the
configuration with longitudinal baffles
Inlet
Outlet
Inlet
Outlet
Inlet
Outlet
185
Clarifier flow path tortuosity, Le/L
2 4 6 8 10M
I
0
5
10
15
20
Clarifier flow path tortuosity, Le/L2 4 6 8 10
MI
0
5
10
15
20
1
0.75
0.50
0.25
0.10
0.05
0.01
Qn
Figure B-15. Morrill index as function of clarifier flow path tortuosity, Le/L for the clarifier
configurations with transverse and longitudinal internal baffling. O is the opening
between the baffle edges and the clarifier walls. Qn is the normalized flow rate with
respect to the hydraulic design flow rate, Qd of 50 L/s
A
B
Equivalent length to width, L/W 6.6 4 262 35 118
.00
Clarifier flow path tortuosity, Le/L0 2 4 6 8 10
N t
ank
s in
ser
ies
0
50
100
150
200
250
300
Clarifier flow path tortuosity, Le/L0 2 4 6 8 10
N t
ank
s in
ser
ies
0
100
200
300
400
500
600
1
0.75
0.5
0.25
0.10
0.05
0.02
Qn
Transverse baffles (O = 0.20 m)
Longitudinal baffles
4 38 103 328 Equivalent length to width, L/W
Transverse baffles (O = 0.2 m)
Longitudinal baffles
186
Table B-1. Summary of measured and modeled treatment performance results for full-scale
rectangular clarifier (RC) and rectangular clarifier with 11 baffle clarifier (B11)
loaded by hetero-disperse silt particle size gradation for two different hydrological
events. Vt is the total influent volume, Qp is the peak influent flow rate, Ttot is the
duration of the hydrological event, measured is measured PM removal efficiency,
modeled is modeled PM removal efficiency and is absolute percentage error, and
represent the gamma parameters for effluent measured PSDs. The gamma
parameters for the influent PSD are respectively 0.8 and 29
Hydrograph Type Qp Vt td measured modeled PSD model
(L/s) (L) (min) (%) (%) %
Triangular RC 28.4 15.1 44 88.38 88.4 0.07 0.97 20.15
8 July 08 RC 50.8 88.9 110 56.78 51.7 9.03 0.90 18.00
Triangular B11 28.4 15.1 44 98.34 98 0.34 0.87 23.00
8 July 08 B11 50.8 88.9 110 71.32 68 4.65 1.20 16.60
Table B-2. Summary of RTD test for pilot-scale rectangular cross-section linear clarifier
configuration loaded with sodium chloride injected as a pulse at t = 0. Qn is the
normalized flow rate, Q respect to the design flow rate, Qdof 50 L/s is residence
time and RMSE is root mean squared error
Qn Q Mass Recovery RMSE
- L/s min % %
1.00 50.00 6.2 92.0 0.3
0.75 37.50 8.3 93.5 0.2
0.50 25.00 12.4 95.7 0.4
0.25 12.50 24.9 95.8 0.5
0.10 5.00 62.2 96.9 0.4
0.03 2.50 248.8 95.5 1.7
0.01 1.00 622.0 97.4 2.5
187
Table B-3. Number of baffles and corresponding value of tortuosity, Le/L for the rectangular
clarifier with (1) transverse baffles and opening of 0.60 m, (2) with transverse baffles
and opening of 0.20 m, (3) with longitudinal baffles
Number of baffles Le/L(1)
Le/L(2)
Le/L(3)
0 1.00 1.00 1.00
2 3.16
3 1.66 1.88
4 5.11
5 1.99
8 9.00
11 2.97 3.63
17 3.96
23 4.95 6.48
29 5.93
35 7.08 9.11
Table B-4. Parameter values of the curves used to fit the volumetric efficiency, VE data versus
tortuosity, Le/L for each flow rate, Qn for the clarifier configuration with longitudinal
baffles and opening of 0.20 m. In the equation, a represents the maximum value of
VE, b the rate of VE variation for unity change of tortuosity
Qn Q (L/s) a b xo R2
1.00 50.0 83.84 1.12 2.72 0.99
0.75 37.5 84.27 1.11 2.84 0.99
0.50 25.0 84.92 1.09 3.06 0.99
0.25 12.5 85.00 1.14 3.43 0.99
0.10 5.0 85.38 1.35 3.80 0.99
0.05 2.5 87.96 1.65 4.25 0.99
0.02 1.0 98.46 2.22 5.33 0.98
188
Table B-5. Parameter values of the curves used to fit the volumetric efficiency, VE data versus
tortuosity, Le/L for each flow rate, Qn for the clarifier configuration with transverse
baffles. In the equation, a represents the maximum value of VE, b the rate of VE
variation for unity change of tortuosity
Qn Q (L/s) a b xo R2
1.00 50.0 88.20 0.96 2.75 0.99
0.75 37.5 87.70 0.94 2.87 0.99
0.50 25.0 86.52 0.88 3.04 0.99
0.25 12.5 88.20 0.94 3.48 0.99
0.10 5.0 87.24 0.98 3.95 0.99
0.05 2.5 88.50 1.23 4.27 0.99
0.02 1.0 93.37 1.64 4.92 0.99
Table B-6. Parameter values of the curves used to fit the Morrill index, MI data versus tortuosity,
Le/L for each flow rate, Qn for the clarifier configuration with longitudinal baffles
and opening of 0.20 m. In the equation, a represents the maximum value of MI, b the
rate of MI variation for unity change of tortuosity, yo the minimum value of MI
Qn Q (L/s) a b yo R2
1.00 50.0 19.13 1.11 1.26 0.99
0.75 37.5 23.75 1.17 1.26 0.99
0.50 25.0 29.46 1.17 1.26 0.99
0.25 12.5 36.45 1.11 1.28 0.99
0.10 5.0 50.31 1.31 1.46 0.99
0.05 2.5 82.53 1.67 1.68 0.99
0.02 1.0 83.22 1.60 1.70 0.99
189
Table B-7. Parameter values of the curves used to fit the Morrill index, MI data versus tortuosity,
Le/L for each flow rate, Qn for the clarifier configuration with transverse baffles. In
the equation, a represents the maximum value of MI, b the rate of MI variation for
unity change of tortuosity, yo the minimum value of MI
Qn Q (L/s) a b yo R2
1.00 50.0 17.10 0.98 1.12 0.99
0.75 37.5 20.23 0.99 1.13 0.99
0.50 25.0 25.30 1.00 1.13 0.99
0.25 12.5 30.37 0.91 1.09 0.99
0.10 5.0 30.00 0.75 1.02 0.99
0.05 2.5 36.06 0.81 1.13 0.99
0.02 1.0 41.38 0.88 1.33 0.99
Table B-8. Parameter values of the curves used to fit the N data versus tortuosity, Le/L for each
flow rate, Qn for the clarifier configuration with longitudinal baffles and opening of
0.20 m. In the equation, a represents the maximum value of N, b the rate of N
variation for unity change of tortuosity, xo the minimum value of N
Qn Q (L/s) a b xo R2
1.00 50.0 313.50 1.23 7.42 0.99
0.75 37.5 160.90 1.34 6.95 0.99
0.50 25.0 2061.00 2.34 16.07 0.99
0.25 12.5 12680.00 2.40 21.17 0.99
0.10 5.0 120.00 1.61 8.60 0.99
0.05 2.5 95.00 1.49 8.12 0.99
0.02 1.0 43.42 0.82 6.36 0.99
Table B-9. Parameter values of the curves used to fit the N data versus tortuosity, Le/L for each
flow rate, Qn for the clarifier configuration with transverse baffles. In the equation, a
represents the maximum value of N, b the rate of N variation for unity change of
tortuosity, xo the minimum value of N
Qn Q (L/s) a b xo R2
1.00 50.0 646.40 1.12 7.60 0.99
0.75 37.5 398.90 1.14 7.08 0.99
0.50 25.0 216.00 1.03 6.19 0.99
0.25 12.5 60.88 0.57 4.32 0.99
0.10 5.0 28.88 0.54 4.87 0.99
0.05 2.5 20.22 0.53 3.65 0.99
0.02 1.0 13.45 0.51 3.21 0.99
190
Table B-10. Parameter values of the curves used to fit the MI data for different degrees of
unsteadiness, Qn for the clarifier configuration with transverse baffles and opening of
0.20 m. In the equation, a represents the maximum value of MI, b the rate of MI
variation for unity change of tortuosity, yo the minimum value of MI
Descriptor a b yo R2
Quasi-steady 0.01 22.67 1.18 1.24 0.99
Unsteady 0.33 11.39 0.92 1.26 0.99
Highly Unsteady 1.54 5.61 0.62 1.27 0.97
Table B-11. Parameter values of the curves used to fit the N data for different degrees of
unsteadiness, Qn for the clarifier configuration with transverse baffles and opening of
0.20 m. In the equation, a represents the maximum value of N, b the rate of N
variation for unity change of tortuosity, xo the minimum value of N
Descriptor a b xo R2
Quasi-steady 0.01 77.21 1.26 5.60 0.99
Unsteady 0.33 83.30 1.20 5.46 0.99
Highly Unsteady 1.54 84.10 0.89 4.27 0.99
191
APPENDIX C
SUPPLEMENTAL INFORMATION OF CHAPTER 4 “CAN A STEPWISE STEADY FLOW
CFD MODEL PREDICT PM SEPARATION FROM STORMWATER UNIT OPERATIONS
AS A FUNCTION OF HYDROGRAPH UNSTEADINESS AND PM GRANULOMETRY?”
Stepwise Steady Flow Model
The conceptual foundation for stepwise steady flow model is analogous to the unit
hydrograph theory used to predict surface watershed runoff (Chow et al., 1988). The unit
hydrograph represents the unit response function of a linear hydrologic system. The assumptions
of the unit hydrograph theory are the system (watershed) is linear and the unit hydrograph
response function, U is time invariant and unique for a given watershed (Chow et al., 1988).
Define Pn the “excess” rainfall and Qm the effluent flow rate as shown in Figure C-7. The
discrete convolution equation allows the computation of direct runoff Qm given excess rainfall
Pn:
Mn
mmnmn UPQ
11
Based on the assumption that a unit operation can be idealized as a hydrological watershed,
in this study, the concept of UH is applied to unit operations, subjected to unsteady hydraulic and
PM loadings as shown in Figure C-8. The main assumptions of the stepwise steady flow model
are:
UO is a linear system
Up is unique for a given UO, flow rate and PSD
Let I be the event-based influent PM for a given PSD. Im represents the influent PM for a
given PSD and a fixed time step, t, delivered into the system at Qm. Up is function of flow rate,
Qm; therefore, let define Up,Qm the UO response to Im for the specific flow rate, Qm (Figure C-9-
10). Up,Qm is computed from steady CFD models. The UO is assumed to be a linear system.
(C-1)
192
Based on this assumption the event-based effluent mass PM, E can be modeled as sum
(convolution) of the responses Up,Qm to inputs Im. The effluent mass PM at each time step t, En
is given by the discrete convolution equation:
In these expressions, n and m are the number of steps in which the effluent PM distribution
and the influent hydrograph are respectively discretized.
The stepwise steady CFD model approach consists of the following steps.
Steady CFD model is run for seven steady flow rates (100%, 75%, 50%, 25%, 10%, 5%,
2% of the design flow rate) for each unit. The CFD model is loaded a constant PM loading. For
coarser gradations PSD is discretized into 8 size classes with an equal gravimetric basis and for
finer gradation into 16 size classes (Garofalo and Sansalone, 2011). Throughout each steady
simulation a computational subroutine as a user defined function (UDF) is run to record
residence times of each particle size and generate Up,Qm.
The particle residence time distribution, Up for each Q is fit by a gamma distribution as
shown in Figure S11. The and gamma factors are determined by minimizing the error
between the CFD modeled particle size distributions and gamma fitting curves. The gamma
factors are considered satisfactory when producing a R2 greater than 0.95. A relationship
between gamma factors and steady flow rates is determined as shown in Figure C-12.
The hydrograph is divided into a series of discrete steady flow rates based on a fixed time
interval, t (for example, 1 min). Based on the relationship derived between particle residence
time distribution and flow rate, a CFD modeled Up,Qm is associated to each discrete flow rate in
the hydrograph. Each flow rate generates a unique Up for the specific PM gradation. For example,
(C-2)
193
Q1 and Q2 produce respectively Up,1 and Up,2. If Q1 is lower than Q2, Up,1 is longer than UP,2 and
has a peak lower than UP,1.
The influent PM and the particle residence time distributions are coupled by using the
discrete convolution equation to produce the effluent PM, by using Equation C-2. Figure C-10
illustrates the convolution formula concept. The effluent PM is given by the sum of the products
between Im and Up,Q for each discretization time step.
The mathematical operation of the discrete convolution integral is here derived:
UDF for Fully Unsteady and Stepwise Steady Flow CFD Models
The user-defined function (UDF) built in this study is a function that can be loaded with the
FLUENT solver to enhance and customize the standard features of the code and it is written in C
programming language. The UDF developed consists of a series of commands which allows to
record the particles eluted from the computational domain and their residence times during
steady and unsteady CFD simulations. The UDF code is as follows.
#include "udf.h"
#define REMOVE_PARTICLES FALSE
DEFINE_DPM_OUTPUT(discrete_phase_sample,header,fp,p,t,plane)
{
char name[100];
real flow_time = solver_par.flow_time;
if(header)
par_fprintf_head(fp,"\"Particle Size Range Name\" \"Injection Time [s]\"
\"#Residence Time [s]\" \"Diameter [m]\"\n");
……..
194
if(NULLP(p))
return;
sprintf(name,"%s:%d",p->injection->name,p->part_id);
#if PARALLEL
par_fprintf(fp,"%d %d %s %e %e %f\n",p->injection->try_id,p->part_id, name,
p->time_of_birth, P_TIME(p),P_INIT_DIAM(p));
#else
par_fprintf(fp,"%s %e %e %f\n",name, p->time_of_birth, P_TIME(p),
P_INIT_DIAM(p));
#endif
#if REMOVE_PARCELS
p->stream_index=-1;
#endif
}
The output is reported in a notepad file as follows in Table C-2.
This UDF is used for the fully unsteady and the stepwise flow CFD models. For the fully
unsteady model, injection time is used in the following equation to evaluate the mass per
particle, p:
N
Mp
,
,
In this expression Mis PM mass associated with the particle size range ξ and injected at
time N represents the total number of particles injected at the inlet section (Garofalo and
Sansalone, 2011). The residence time output is used to evaluate the number of particles which
injected at time for the particles size range are eluted from the system at each time step. The
total effluent mass is determined as follows:
max
min 0
, MassEffluent
dt
effp
In this equation ξ and represent particle size range and injection time ranging from 0 to
the runoff event duration, td, respectively. The term ()eff represents PM recorded in effluent. The
(C-3)
(C-4)
195
particle size fractions are not including on the calculations, simply because the particle size
ranges are equally weighted due to the symmetric, gravimetric PSD discretization on an
arithmetic scale.
For the stepwise steady model the same UDF is used to evaluate the particle residence time
distribution, Up. After each steady simulation, Up is determined by computing the number of
particles escaped from the computational domain as function of time (from UDF`s residence
time output) over the total number of particles injected.
196
Figure C-1. Schematic representation of the full-scale physical model facility setup with
rectangular clarifier
cm pipe
cm pipe Flow meter Flow meter Supplied Water
45,425 L
Storage
tank
45,425 L
Storage
tank
Pump skid
Drop box
(PM influent
sampling point)
PM delivery
system
Tank
Drop box (manual and
automatic effluent sampling point for eluted PM)
197
Figure C-2. Schematic representation of the full-scale physical model facility setup with baffled
HS
Time (hour)
0.00 0.05 0.10 0.15 0.20 0.25
Pre
cip
itat
ion
in
tensi
ty (
in/h
r)
0
1
2
3
4Total excess rainfall = 0.5 inta = 0.125 hr
Td = 0.25 hr
5.0d
a
T
tr
Figure C-3. Triangular hyetograph. Td is the recession time, ta is the time to peak, and r is the
storm advancement coefficient (Chow et al., 1988)
Td
ta
Baffled tank
cm pipe
cm pipe Flow meter Flow meter Supplied Water
45,425 L
Storage
tank
45,425 L
Storage
tank
Pump skid
Drop box
(PM influent
sampling point)
Manual Effluent sampling
point for eluted PM
PM delivery
system
Automatic Effluent sampling
point for eluted PM
198
Rainfall depth, in
0.0001 0.001 0.01 0.1 1 10 100 1000
Cum
ula
tive f
requency d
istr
ibuti
on, %
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 101112
Mean
# o
f E
ven
ts
05
1015202530
hra
infa
ll (
mm
)
0
40
80
120
160
200
# events
mean hrainfall
Figure C-4. Frequency distribution of rainfall precipitation for Gainesville, Florida. The
frequency distribution is obtained from a series of 1999-2008 hourly precipitation
data for Gainesville regional airport (KGNV)
Time (hour)0.0 0.2 0.4 0.6 0.8 1.0
Pre
cip
itati
on
in
ten
sity
(in
/hr)
0
1
2
3
4
5
6
7Total rainfall = 2.92 inta = 0.3 hr
Td =0.92 hr
Figure C-5. Historical event collected on 8 July 2008
199
t/tmax0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate
s (
L/s
)
0
10
20
30
40
50
Rain
fall
Inte
nsit
y (
mm
/hr)
0
50
100
150
200
250
Flo
w r
ate
(L
/s)
0
20
40
60
80R
ain
fall
Inte
nsit
y (
mm
/hr)
0
100
200
300
400
Figure C-6. Hydraulic loadings utilized for full-scale physical model of rectangular clarifier:
triangular hyetograph, Historical 8 July 2008 hydrologic event. The rainfall-runoff
modeling is performed in Storm Water Management Model (SWMM) for the
catchment
Qp = 28.3 L/s
Ttot = 93 min
V = 1,541 L
Qp = 50 L/s
Ttot = 248 min
V = 89,000 L
A
B
200
Figure C-7. Unit hydrograph (UH) theory (Chow et al., 1988)
Input Pm
P1
P
2
P3
1 2 3 ….. m
n-m+1
n-m+1 Output
Qn
0 1 2 3 4 ….. n
Un-m+1
Un-m+1
Mn
mmnmn
UPQ1
1
U1 U
2 U
3
P1
U1
P1
U2
P2
U2
P2
U1
P2
U3
201
Figure C-8. Stepwise steady flow model analogy with UH
202
Figure C-9. Stepwise steady flow model. Particle residence time distribution, Up as function of flow rate
203
Figure C-10. Stepwise steady flow model methodology
204
Elasped Time, t (min)
0 4 8 12 16 20
Cu
mu
lati
ve
UP
0.0
0.2
0.4
0.6
0.8
1.0
Elasped time , t (min)
0 10 20 30 40 50 60 70 80 90 100
Cu
mu
lati
ve
Up
0.0
0.2
0.4
0.6
0.8
1.0
Figure C-11. Up as function of time for the finer PSD for two steady flow rates. The Up
distributions are fit by a gamma distribution with parameters, and
BHS
Finer PSD
= 0.79
= 28
Q = 18 L/s
= 0.8
= 2.70
BHS
Finer PSD
= 0.79
= 28
Q = 1.8 L/s
= 1.2
= 33.73
205
Flow rate, Q (L/s)
0 4 8 12 16 20
,
shap
e g
amm
a p
aram
eter
0.4
0.8
1.2
1.6
2.0
2.4
Flow rate, Q (L/s)0 4 8 12 16 20
,
scal
e g
amm
a p
aram
eter
0
20
40
60
80
100
Figure C-12. Shape and scale gamma paremeters ( and ) as function of Q. The gamma
parameters are used to fit the Up,Q with a gamma distribution function
BHS
Finer PSD
= 0.79
= 28
R2 = 0.99
BHS
Finer PSD
= 0.79
= 28
R2 = 0.98
206
Elasped time (min)
0 20 40 60 80 100 120 140E
fflu
ent
PM
(k
g)
0.0
0.1
0.2
0.3
0.4
0.5
3 (6.31%)
7 (6.27 %)
10 (6.30%)
Elasped time (min)0 20 40 60 80 100 120 140 160 180
Eff
luen
t P
M (
kg
)
0.00
0.05
0.10
0.15
0.20
0.25
(28.20%)
3 (6.28%)
7 (6.53%)
10 (6.09%)
Q (NRMSE)
Q (NRMSE)
Finer PSD
= 1.54
Finer PSD
= 0.33
Figure C-13. Effluent PM response of a rectangular clarifier to the highly unsteady (=1.54) and
unsteady (=0.33) hydrographs generated through the stepwise steady model as
function of number of steady flow rates used to determine the relationship between
gamma parameters and Q. NRMSE is the normalized root mean squared error respect
to the unsteady modeling data
207
Elapsed time, t (min)
0 20 40 60 80 100 120 140 160
Flo
w r
ate,
Q (
L/s
)
0
10
20
30
40
50
Eff
luen
t P
M (
Kg
)
0.0
0.2
0.4
0.6
0.8
Elasped time, t (min)0 20 40 60 80
Flo
w r
ate,
Q (
L/s
)
0
5
10
15
20
Eff
luen
t P
M (
Kg
)
0.00
0.05
0.10
0.15
0.20
0.25
Q
Pathapati and Sansalone (2011)
Fully unsteady
Stepwise
Figure C-14. Effluent PM for the fully unsteady CFD model and the stepwise steady model from
Pathapati and Sansalone (2011). The models are applied to a RC and a BHS subjected
to a highly unsteady hydraulic load. The stepwise steady model overestimates PM
eluted from both systems, especially during the first part of the hydrographs (Q<Qp,
peak flow rate). This is because in the stepwise steady model the effluent PM
distribution is not translated in time according to the actual PM response of the
system
BHS
Finer PSD
= 0.79
= 28
Qp = 18 L/s
td = 84 min
RC
Finer PSD
Qp = 50 L/s
td = 124 min
New
208
Elasped time (min)
0 20 40 60 80 100 120 140
Eff
luen
t P
M (
kg
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 min (8.5%)
5 min (9.12%)
15 min (13.78%)
30 min (21.42%)
Elasped time (min)0 20 40 60 80 100 120 140 160 180
Eff
luen
t P
M (
kg
)
0.0
0.1
0.2
0.3
0.4
0.5
1 min (6.5%)
5 min (8.82%)
15 min (15.75%)
30 min (32.60%)
t (NRMSE)
t (NRMSE)
Finer PSD
= 1.54
Finer PSD
= 0.33
Figure C-15. Effluent PM response of a rectangular clarifier to the highly unsteady (=1.54) and
unsteady (=0.33) hydrographs generated through the stepwise steady model as
function of hydrograph time discretization, t. NRMSE is the normalized root mean
squared error respect to the unsteady modeling data
209
Particle size, dp (m)
0.010.11101001000F
iner
by
Mas
s (%
)
0
20
40
60
80
100
Highly Unsteady
Target Influent
Unsteady
Quasi-steady
Particle size, dp (m)
0.010.11101001000
Fin
er b
y M
ass
(%)
0
20
40
60
80
100
Figure C-16. Influent coarser and finer PSDs as compared to measured effluent PSDs generated
through auto sampling for the three hydrographs shown in Figure 1B. The effluent
PSDs represent the median PSDs for each hydrograph. The range bars represent the
variability of PSDs across the entire hydrograph
Coarser PSD
(d50 = 67 m)
Finer PSD
(d50 = 15 m)
(B)
(A)
210
Table C-1. Computational time expressed in hour (hr) for the CFD stepwise steady flow and the
fully unsteady models. Qp, td, are peak flow, hydrograph duration,
unsteadiness factor, shape and scale parameters of the gamma distribution,
respectively
Unit Qp td Stepwise Unsteady
(L/s) (min) (-) (-) (-) (hr) (hr)
RC 50 124 1.54 0.79 28 4.8 21.5
RC 25 136 0.33 0.79 28 4.8 35.5
RC 12.5 282 0.015 0.79 28 4.8 69.5
BHS 18 84 1.15 0.79 28 3.9 15.5
BHS 9 87 0.24 0.79 28 3.9 20.5
BHS 4.5 125 0.09 0.79 28 3.9 55
BHS 18 84 1.15 0.79 28 3.7 15.1
BHS 9 87 0.24 0.79 28 3.7 19.2
BHS 4.5 125 0.09 0.79 28 3.7 52.3
Table C-2. Example of the output from UDF developed for recording particle residence time,
injection time and diameter
Particle size class name Injection Time (s) Residence Time (s) Diameter (m)
njcat-dn8-d6-1.4um:0 2.900000e+002 1.623725e+003 0.000001
njcat-dn8-d6-1.4um:0 1.310000e+003 3.092848e+003 0.000001
njcat-dn8-d6-1.4um:0 3.590000e+003 5.194801e+003 0.000001
…………….. …………… …………… ………
211
APPENDIX D
SUPPLEMENTAL INFORMATION OF CHAPTER 5 “A STEPWISE CFD STEADY FLOW
MODEL FOR EVALUATING LONG-TERM UO SEPARATION PERFORMANCE”
Disaggregation Rainfall Method
The hourly rainfall data for the period of 1998-2011 downloaded from the National
Climatic Data Center (NCDC) are disaggregated in 15 min by using Ormsbee`s continuous
deterministic disaggregation procedure. The basic assumptions of Ormsbee`s method is the
distribution of precipitation within a time step is proportional to the distribution of precipitation
over three time step sequence with adjacent before and after time steps (Ormsbee, 1989; Lee et
al., 2010). Figure D-1 shows a schematic of the precipitation data disaggregation method. Using
this deterministic linear assumption, precipitation data can be disaggregated into smaller time
steps of, e. g., 1, 2, 3, 5, 10, 15, 20 or 30 min. A unique disaggregated time series data set will be
obtained from an input precipitation data set on basis of the applied temporal and volumetric
resolutions for output data. This disaggregation feature is particularly important for small
catchments with short system response times (Lee et al., 2010).
Full-Scale Physical Model Setup of the Rectangular Clarifier
The analysis is carried out on full-scale physical model of a rectangular clarifier, which
represents the most traditional and common clarification systems used in rainfall-runoff PM
treatment. The rectangular clarifier is 1.87 m tall, 1.8 m wide and 7.31 m long with hydraulic
capacity of approximately 12,000 L. The influent and effluent pipe diameters are of 0.2 m. The
design flow rate, Qd of the physical model is about 50 L/s, corresponding to the hydraulic
capacity of physical model as an open-channel system (Figure D-5).
To validate the CFD model under transient conditions, effluent PM and PSDs eluted from
the full-scale rectangular clarifier subjected to two hydrological events are collected. The first
hydrograph is generated from a triangular hyetograph with 12.7 mm (0.5 inch) of rainfall depth
212
and duration of 15 minutes. This loading is selected as a common short and intense rainfall event
during the wet season in Florida (Figure D-7). The second hydrograph is generated from a
historical event collected on 8 July 2008 in Gainesville, Florida with total rainfall depth of 71
mm. This event is chosen since it is an extremely intense historical event, with a peak rainfall
intensity of about 165 mm/h (Figure D-7). The particle size distribution (PSD) used is reported in
Figure D-8 and is a fine hetero-disperse gradation classified from Unified Soil Classification
System (USCS) as SM I with a d50 of 18 m. The hyetographs are transformed to event-based
hydrographs by using Storm Water Management Model (SWMM) (Huber and Dickinson, 1988)
for each physical and CFD model. The objective of the rainfall-runoff simulation is to generate
unsteady runoff flow loadings for the scaled physical model and CFD model. In this
transformation from rainfall to runoff for the scaled physical basin, the watershed area is
matched to deliver peak runoff flow rates equal to the design flow rate of the unit operation.
More details information about the two hydrographs utilized for the validation are reported in
Section 3 of the Appendix (Figure D-11). In Supplemental information section, the generation of
the two hydrographs utilized is explained in detail. The results retrieved from the experiments
are reported in Table D-1.
Generation of Hydrographs Used for the Validation of the Full-Scale Physical Model of
Clarifier under Transient Conditions
Study Hyetographs
An essential component of this study is the definition of the hydrological loadings. The
three hyetographs selected are:
Triangular hyetograph with 12.7 mm (0.5 inches) of rainfall volume and duration of 15
minutes. This loading is selected as a common short and intense rainfall event during the
wet season in Florida. A triangular shape is used to define the hyetograph as shown in
Figure D-7 (Chow et al., 1988). The maximum rainfall intensity of the triangular
hyetograph is approximately 101 mm per hour (4 inches per hour) and the total excess
precipitation depth is 12.7 mm (0.5 inches). The hyetograph selected is considered a fairly
213
extreme event, since 80% of storm events occurring in Gainesville are characterized by a
total precipitation depth equal or less than 12.7 mm (0.5 inches). Figure D-6 reported
below depicts the frequency distribution of 1999-2008 hourly rainfall data for Gainesville
Regional Airport (KGNV).
Historical event collected on 8 July 2008 by UF with total rainfall depth of 71 mm. This
event is chosen since it is an extremely intense historical event, with a peak rainfall
intensity of about 165 mm/h (Figure D-7). This value is higher than peak precipitation
intensity of the 24 hour-25 year design storm described in the following paragraph.
Transformation of Rainfall Hyetographs to Runoff Hydrographs
The hyetographs reported in Figure D-7 are transformed to event-based hydrographs by
using the SWMM (Huber and Dickinson, 1988) for each physical and CFD model. The objective
of the rainfall-runoff simulations is to generate unsteady runoff flow loadings for the scaled
physical and CFD model. SWMM translates rainfall in runoff for the specific catchment
properties.
In this transformation the watershed area is matched to deliver peak runoff flow rate equal
to the design flow rate of the unit operation. As shown pereviously, July 8th
2008 historical
hyetograph is characterized by the highest rainfall peak intensity (approximately 165 mm/h) in
comparison to the other selected hyetographs. Therefore, the historical hyetograph is utilized as a
reference to perform the flow scaling of the physical testing model. Since the maximum
hydrualic load of the physical models is 50 L/s, the area of the catchment implemented in
SWMM is defined to deliver peak flow rate equal to 50 L/s for the historical storm of 8 July
2008.
The modeling parameters adopted are referred to an asphalt-pavement of a typical airport
runway/taxiway. Green-Ampt method is used to model infiltration process. The rainfall-runoff
modeling for the three hyetographs are shown in Figure D-7.
214
Particle Size Distribution
PSD Selection
The influent particulate loading used for CFD and full-scale physical model consists of a
PSD that is in the silt-size range. The PSD, ranging from less than 1 m to 75 m is reported in
Figure S8. The PM specific gravity is 2.63 g/cm3. The mass-based PSD is well described by a
gamma distribution function. The probability density function is given by Equation D-1 as a
function of particle diameter d, where is a distribution shape factor and a scaling parameter.
The cumulative gamma distribution function is expressed in Equation D-2.
PSD Significance
PM is widely recognized as a primary vehicle for the transport and partitioning of
pollutants. Moreover, PM is a pollutant itself that impacts the deterioration of receiving surface
waters. The potential for water chemistry impairment strongly depends on PM loading and PSD.
Furthermore, many PM-bound constituents, such as metals, nutrients and other pollutants,
partition to and from PM while transported by PM through rainfall-runoff events. Therefore,
PSD plays an important role in the transport and chemical processes occurring in urban
stormwater runoff and an understanding of its behavior is crucial for the analysis and the
selection of unit operations.
Geometry and Mesh Generation of Full-Scale Models
The mesh is comprised of tetrahedral elements and it is checked carefully to ensure that
equiangle skewness and local variations in cell size are minimized in order to produce a high
(D-1)
x
ex
xf
1
dxxfxF
x
0
(D-2)
215
quality mesh. Several iterations of grid refinement are performed to determine the necessary
mesh density that balances the accuracy of the solution with the exponentially increasing demand
on computational resources. The final mesh used in this study is discretized into approximately
3.5 million cells (Figures D-9 and D-10). The mesh generated for the screened hydrodynamic
separator (SHS) is described in Pathapati and Sansalone (2012) (Figure D-11).
CFD Modeling and Population Balance
Liquid Phase Governing Equations
The governing equations for the continuous phase are a variant of the N-S equations, the
Reynolds Averaged N-S (RANS) equations for a turbulent flow regime. The RANS conservation
equations are obtained from the N-S equations by applying the Reynolds’ decomposition of fluid
flow properties into their time-mean value and fluctuating component. The mean velocity is
defined as a time average for a period t which is larger than the time scale of the fluctuations.
The RANS equations for continuity and momentum conservation are summarized.
,0
i
i
ux
i
j
i
iij
jji
j
i gx
u
x
puu
xuu
xt
u
2
2''
In these equations is fluid density, xi is the ith
direction vector, uj is the Reynolds
averaged velocity in the ith
direction; pj is the Reynolds averaged pressure; and gi is the sum of
body forces in the ith
direction. Decomposition of the momentum equation with Reynolds
decomposition generates a term originating from the nonlinear convection component in the
original equation; these Reynolds stresses are represented by ''
jiuu . Reynolds stresses contain
information about the flow turbulence structure. Since Reynolds stresses are unknown, closure
(D-3)
(D-4)
216
approximations can be made to obtain approximate solution of the equations (Panton, 2005). In
this study the realizable k- model (Shih and al., 1995) is used to resolve the closure problem.
This model is suitable for boundary free shear flow applications and consists of turbulent kinetic
energy and turbulence energy dissipation rate equations, respectively reported below (Shih and
al., 1995).
jx
iu
ju
iu
jx
k
k
t
jx
jx
k
ju
t
k''
kCSC
xxxu
t j
t
jj
j
2
21
ijij SSS
kSC
2,,
5,43.0max
1
In these equations σk = 1.0, σε = 1.2, C1 = 1.44, C2 = 1.9, k is the turbulent kinetic energy; ε
is the turbulent energy dissipation rate; S is the mean strain rate; νT is the eddy viscosity; ν is the
fluid viscosity; and uji, uj′u′i are previously defined.
The free surface of the rectangular clarifier is modeled as a fixed shear-free wall defined
by zero normal velocity and zero gradients of all variables. The boundary conditions for the
screened HS are described in Pathapati and Sansalone (2012).
Particulate Phase Governing Equations (the DPM)
The DPM simulates 3D particle trajectories through the flow domain to model PM
separation and elution in a Lagrangian frame of reference where particles are individually
tracked through the flow field. This analysis assumes PM motion is influenced by the fluid
phase, but the fluid phase is not affected by PM motion (one-way coupling) and particle-particle
interactions are negligible, since the particulate phase is dilute (volume fraction (VF) around
0.01%) (Brennen, 2005). The DPM integrates the governing equation of PM motion and tracks
(D-5)
(D-6)
(D-7)
217
each particle through the flow field by balancing gravitational body force, drag force, inertial
force, and buoyancy forces on the PM phase. The motion of a single particle without collisions is
modeled by the Newton`s law. Particle trajectories are calculated by integrating the force balance
equation in the ith
-direction.
The first term on the right-hand side of the equation is the drag force per unit particle mass.
The second term is the buoyancy/gravitational force per unit particle mass. In these equations, p
is particle density, vi is fluid velocity, vpi is particle velocity, dp is particle diameter, Rei is the
particle Reynolds number, FDi is the buoyancy/ gravitational force per unit mass of particle and
CDi is the particle drag coefficient (Morsi and Alexander, 1972). The last three variables are
defined as follows.
24
Re18
2iDi
pp
DiC
dF
ipipi
vvd Re
3221
ReReK
KKC
iiiD
K1, K2, K3 are empirical constants as a function of particle Rei, reported in Table D-2.
The PSD is discretized into PM size classes with a symmetric gravimetric basis. Studies have
demonstrated that a discretization number (DN) of 16 is generally able to reproduce accurate
results for fine hetero-disperse PM gradations subject to steady flows (Dickenson and Sansalone,
2009). Particles are defined as silica particles with specific gravity of 2.65 g/cm3.
p
pi
piiDi
pi gvvF
dt
dv
(D-8)
(D-9)
(D-10)
(D-12)
218
Numerical Solution
The numerical solver is pressure-based for incompressible flows that are governed by
motion based on pressure gradients. The spatial discretization schemes are second order for
pressure, the second order upwind scheme for momentum and the Pressure Implicit Splitting of
Operators (SIMPLE) algorithm for pressure-velocity coupling. Temporal discretization of the
governing equations is performed by a second-order implicit scheme. Under relaxation
parameters used in the CFD simulations are reported in Tables D-3. Convergence criteria are set
so that scaled residuals for all governing equations are below 0.001 (Ranade, 2002). All
simulations are run in parallel on a Dell Precision 690 with two quad core Intel Xeon® 2.33GHz
processors and 16 GB of RAM.
A population balance model (PBM) is coupled with CFD to model PM separation.
Assuming no flocculation in the dispersed particle phase, the PBM equation (Jacobsen, 2008)
and mass per particle, pn are as follows.
max
min
max
min
max
min 0 1
,,
0 1
,,
0 1inf,,
ddd t N
nsepn
t N
neffn
t N
n
n ppp
N
n
nN
Mp
1
,
,,
M is PM mass associated with the particle size range, ξ as function of injection time,
N is the total number of particles injected at the inlet section, and td is the event duration.
Stepwise Steady Flow Model
The conceptual foundation for stepwise steady flow model is analogous to the unit
hydrograph theory used to predict surface watershed runoff (Chow et al., 1988). The unit
hydrograph represents the unit response function of a linear hydrologic system. The assumptions
(D-14)
(D-13)
219
of the unit hydrograph theory are the system (watershed) is linear and the unit hydrograph
response function, U is time invariant and unique for a given watershed (Chow et al., 1988).
Define Pn the “excess” rainfall and Qm the effluent flow rate (Figure D-15). The discrete
convolution equation allows the computation of direct runoff Qm given excess rainfall Pn:
Mn
mmnmn UPQ
11
Based on the assumption that a unit operation can be idealized as a hydrological watershed,
in this study, the concept of UH is applied to unit operations, subjected to unsteady hydraulic and
PM loadings (Figure D-16). The main assumptions of the stepwise steady flow model are:
UO is a linear system
Up is unique for a given UO, flow rate and PSD
Let I be the event-based influent PM for a given PSD. Im represents the influent PM for a
given PSD and a fixed time step, t, delivered into the system at Qm. Up is function of flow rate,
Qm; therefore, let define Up,Qm the UO response to Im for the specific flow rate, Qm (Figure D-
15). Up,Qm is computed from steady CFD models. The UO is assumed to be a linear system.
Based on this assumption the event-based effluent mass PM, E can be modeled as sum
(convolution) of the responses Up,Qm to inputs Im. The effluent mass PM at each time step t, En
is given by the discrete convolution equation:
In these expressions, n and m are the number of steps in which the effluent PM distribution
and the influent hydrograph are respectively discretized.
The stepwise steady CFD model approach consists of the following steps.
Steady CFD model is run for seven steady flow rates (100%, 75%, 50%, 25%, 10%, 5%,
2% of the design flow rate) for each unit. The CFD model is loaded a constant PM loading.
(D-15)
(A5-15) (D-15)
220
For coarser gradations PSD is discretized into 8 size classes with an equal gravimetric
basis and for finer gradation into 16 size classes (Garofalo and Sansalone, 2011).
Throughout each steady simulation a computational subroutine as a user defined function
(UDF) is run to record residence times of each particle size and generate Up,Qm.
The particle residence time distribution, Up for each Q is fit by a gamma distribution. The
and gamma factors are determined by minimizing the error between the CFD modeled
particle size distributions and gamma fitting curves. The gamma factors are considered
satisfactory when producing a R2 greater than 0.95. A relationship between gamma factors
and steady flow rates is determined.
The hydrograph is divided into a series of discrete steady flow rates based on a fixed time
interval, t (for example, 1 min). Based on the relationship derived between particle
residence time distribution and flow rate, a CFD modeled Up,Qm is associated to each
discrete flow rate in the hydrograph. Each flow rate generates a unique Up for the specific
PM gradation. For example, Q1 and Q2 produce respectively Up,1 and Up,2. If Q1 is lower
than Q2, Up,1 is longer than UP,2 and has a peak lower than UP,1. The influent PM is
discretized into a series of pulse inputs, Im with t equal to 1 min.
The influent PM and the particle residence time distributions are coupled by using the
discrete convolution equation to produce the effluent PM, by using Equation D-15. Figure
D-18 illustrates the convolution formula concept. The effluent PM is given by the sum of
the products between Im and Up,Q for each discretization time step.
The mathematical operation of the discrete convolution integral is here derived:
……..
221
Figure D-1. Precipitation data disaggregation (Orsmbee, 1988))
Rainfall
Time
(A) Input data
Rainfall (B)
Disaggregated
data
222
Rainfall Intensity, Ir (mm/h)
0 10 20 30 40 50 60
Rai
nfa
ll i
nte
nsi
ty f
req
uen
cy d
istr
ibu
tio
n
(%)
0
20
40
60
80
100
1998-2011
2007
2007
N. events = 147 i
r50 = 1 mm/h
Mean ir = 3.1 mm/h
1998-2011
N. events = 166 i
r50 = 1.8 mm/h
Mean ir = 4 mm/h
MIT = 1 hr
Elasped time (h)0 200 400 600
Ru
no
ff,
Q (
L/s
)
0
10
20
30
40
50
60
Rai
nfa
ll,
(mm
)
0
2
4
6
8
10
Runoff
Rainfall
Figure D-2. Hydrology analysis. Rainfall intensity frequency distribution for the period 1998-
2011 and for 2007 is illustrated in A). Ir represents the rainfall intensity, ir50 represents
the median rainfall intensity. The number of events is calculated based on a minimum
inter-event time, MIT of 1 h. Time domain distribution of rainfall and runoff for June
2007 is reported in B)
A B
June 2007
223
Month
1 2 3 4 5 6 7 8 9 10 11 12
An
nu
al t
ota
l d
epth
(m
m)
0
50
100
150
200
250
Figure D-3. Total rainfall depth as function of month for the year 2007
Runoff, Q (L/s)
0 10 20 30 40 50
Cu
mu
lati
ve
freq
uen
cy d
istr
ibu
tio
n
(%)
0
20
40
60
80
100
2007Mean Q = 1.54 L/s Q
50 = 0.12 L/s
Runoff, Q (L/s)
0 10 20 30 40 50
Incr
emen
tal
cou
nt
1
10
100
1000
15 min
30 min
2007
Runoff data based on:
Figure D-4. Runoff frequency distribution for 2007 for a watershed of 1.6 ha, with 1% slope,
75% of imperviousness and sand soil characteristics. The cumulative frequency
distribution in A) is based 15 minute runoff data. In (B) the incremental runoff
frequency distribution is also based on 30 minute runoff data
Watershed area = 1.6 ha
A B
2007
224
Figure D-5. Schematic representation of the full-scale physical model facility setup with
rectangular clarifier
cm pipe
cm pipe Flow meter Flow meter Supplied Water
45,425 L
Storage
tank
45,425 L
Storage
tank
Pump skid
Drop box
(PM influent
sampling point)
PM delivery
system
Drop box (manual effluent
sampling point for eluted PM)
Clarifier
225
Rainfall depth, in
0.0001 0.001 0.01 0.1 1 10 100 1000
Cum
ula
tive f
requency d
istr
ibuti
on, %
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 101112
Mean
# o
f E
ven
ts
05
1015202530
hra
infa
ll (
mm
)
0
40
80
120
160
200
# events
mean hrainfall
Figure D-6. Frequency distribution of rainfall precipitation for Gainesville, Florida. The
frequency distribution is obtained from a series of 1999-2008 hourly precipitation
data for Gainesville Regional Airport (KGNV)
Particle Diameter, d (m)
0.1110100
% f
iner
by m
ass
0
20
40
60
80
100Silt PSD ( 75m)
GF (= 0.8, = 29)
Figure D-7. Influent PSD for fine PM {SM I, <75m}. SM is sandy silt in the Unified Soil
Classification System (USCS). SM is SCS 75. PSD data are fit by gamma function
(GF) based on distribution parameters,shape factor, and scale factor,
g
/
c
m
3
≤
226
t/tmax0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate
s (
L/s
)
0
10
20
30
40
50
Rain
fall
Inte
nsit
y (
mm
/hr)
0
50
100
150
200
250
Flo
w r
ate
(L
/s)
0
20
40
60
80R
ain
fall
Inte
nsit
y (
mm
/hr)
0
100
200
300
400
Figure D-8. Hydraulic loadings utilized for full-scale physical model. The rainfall-runoff
modeling is performed in Storm Water Management Model (SWMM) for the
catchment. The two hydrologic events investigated are: triangular hyetograph (A),
historical 8 July 2008 loading hydrologic event (B). Td is the recession time, ta is the
time to peak, and r is the storm advancement coefficient (Chow et al., 2008)
Qp = 28.3 L/s
Ttot = 93 min
V = 1,541 L
Qp = 50 L/s
Ttot = 248 min
V = 89,000 L
Td = 0.15 h
ta = 0.25 h
r = ta/Td = 0.5
A
B
227
Figure D-9. Isometric view of full-scale physical model and mesh of the rectangular cross-
section clarifier. The number of computational cells is 3.5*106. D is diameter
7.3 m
1.67 m
1.4 m
1.8 m
Influent and effluent
pipe D = 0.2 m
Inlet
Outlet
228
Figure S9. Grid convergence
Figure D-10. Grid convergence for full-scale rectangular clarifier. The mesh utilized comprimes
3.5*106 tetrahedral cells
Figure D-11. View of the full-scale physical model of screened HS (SHS) unit. D represents the
diameter
Mesh size (1*106)
0 1 2 3 4 5 6
Ro
ot
mea
n s
qu
ared
err
or,
en
(%
)
0
2
4
6
8
10
12
14
Mesh size utilized
1.8 m
Outflow
(Effluent pipe
D = 0.25 m) Inflow (Influent
pipe D = 0.25 m
equivalent)
D = 1.7 m
Sump
(D = 0.65 m)
2400 m screen
0.46 m
0.62 m
229
Figure D-12. Scour hole generated after a transient physical model test on the rectangular
clarifier. While a scour hole is produced by the impinging jet (A), indicating a
fraction of PM mass is resuspended in the inlet section of the system, in the rest of the
tank (B) no a visually appreciable scour occurs
Figure D-13. Schematic of scour CFD model by integrating across surfaces (not to scale). Based
on Figure D-12 is assumed washout PM mass is generated from the scour hole
located in the inlet section of the rectangular clarifier. Therefore, in CFD a squared
grid (60 by 20 cm) is built where the scour hole may occur. From the nodes of this
grid are injected the DPM particles. The grid is generated on different planes, n with
heights equal to the pre-deposited PM depth divided by n. W is the width of the
layer, L is the length of the layer, D is the pre-deposited PM depth
(A) (B)
W = 60 cm
W = 60 cm
D
D
n layers
Inlet
Outlet
Scour hole
L = 20 cm
L = 20 cm
230
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1020
3040
50
20
40
60
E (
t)
Flow rate, Q (L/s)
Elapsed time, t (sec)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1020
3040
50
150300
450
600
E (
t)
Flow rate, Q (L/s)
Elapsed time, t (sec)
Figure D-14. Particle residence time distributions, Up for RC and SHS as function of steady flow
rate. The flow rates vary from 1 to 50 L/s (maximum hydraulic capacity of RC). Both
units are loaded with the fine hetero-disperse gradation shown in Figure 5-2A
Elapsed time,
t (sec)
Influent PSD
= 0.79
= 28
Influent PSD
= 0.79
= 28
SHS
RC
Up
Up
SHS
231
Figure D-15. Unit hydrograph (UH) theory (Chow et al., 1988)
Input Pm
P1
P
2
P3
1 2 3 ….. m
n-m+1
n-m+1 Output
Qn
0 1 2 3 4 ….. n
Un-m+1
Un-m+1
Mn
mmnmn
UPQ1
1
U1 U
2 U
3
P1
U1
P1
U2
P2
U2
P2
U1
P2
U3
232
Figure D-16. Stepwise steady flow model analogy with UH
233
Figure D-17. Stepwise steady flow model. Particle residence time distribution, Up as function of
flow rate
234
Figure D-18. Stepwise steady flow model methodology
235
Elasped time (min)
0 20 40 60 80 100 120 140E
fflu
ent
PM
(k
g)
0.0
0.1
0.2
0.3
0.4
0.5
3 (6.31%)
7 (6.27 %)
10 (6.30%)
Elasped time (min)0 20 40 60 80 100 120 140 160 180
Eff
luen
t P
M (
kg
)
0.00
0.05
0.10
0.15
0.20
0.25
(28.20%)
3 (6.28%)
7 (6.53%)
10 (6.09%)
N. of Q (NRMSE)
N. of Q (NRMSE)
Finer PSD
= 1.54
Finer PSD
= 0.33
Figure D-19. Effluent PM generated from the stepwise steady model as function of the number
of flow rates used to generate the relationship between gamma parameters describing
particle residence time distribution, Up and flow rate. The results show a set of
minimum 3 flow rates chosen as 5%, 25% and 100% of RC`s design flow rate, Qd
generates a accurate results (6%). A higher number of flow rates does not produce
more accurate results. In this study a number of 7 flow rates were used since CFD
model results were already available. NRMSE is normalized root mean squared error
236
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
5
10
15
20
25
30
Eff
luen
t P
M (
g)
0
20
40
60
80
100Influent Q
Modeled Effluent PM
Measured Effluent PM Q
p = 28.33 L/s
td = 44 min
Rectangular
Flo
w r
ate,
Q (
L/s
)
0
5
10
15
20
25
30
Eff
luen
t P
M (
g)
0
100
200
300
400Influent Q
Modeled Effluent PM
Measured Effluent PM
Trapezoidal
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
5
10
15
20
25
30
Eff
luen
t P
M (
g)
0
2
4
6
8
10Influent Q
Modeled Effluent PM
Measured Effluent PM
11 transverse baffles
Influent PM = 3.03 Kg
m
= -0.07%
m
= 9.87%
m
= 0.34%
Particle Diameter, d (m)
0.1110100
% f
iner
by m
ass
0
20
40
60
80
100
% f
iner
by m
ass
0
20
40
60
80
100
Effluent Modeled
Influent Measured
Effluent Measured
Qp= 28.33 L/s
td= 44 min
Trapezoidal
Cinf
= 200 mg/L
RMSE = 1.9 %
s = 2650 g/cm
3
0.1110100
% f
iner
by m
ass
0
20
40
60
80
100
11 transverse baffles
Cinf
= 200 mg/L
RMSE = 1.6 %
Rectangular
RMSE = 6.9 %
Particle Diameter, d (m)
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
20
40
60
Eff
luent
PM
(kg)
0.0
0.2
0.4
0.6
0.8
1.0
eff
luen
t P
M (
kg)
0
2
4
6
8
10
12
t/td
0.0 0.2 0.4 0.6 0.8 1.0
Flo
w r
ate,
Q (
L/s
)
0
20
40
60E
fflu
ent
PM
(kg)
0.0
0.2
0.4
0.6
0.8
1.0
eff
luen
t P
M (
kg)
0
2
4
6
8
10
12
Q
Effluent PM
Measured PM
effluent PM
Rectangular
Qp = 50 L/s
td = 110 min
Influent PM = 16 kg
m = 9.30%
0.1110100
% f
iner
by
mas
s
0
20
40
60
80
100
s = 2.65 g/cm
3
Particle Diameter, d ( m)
Rectangular
RMSE = 3.6 %
Effluent
Influent
Effluent
Measured
Modeled
Rectangular clarifier
11 Transverse baffles
m = 4.65%
Particle Diameter, d ( m)
0.1110100
% f
iner
by
mas
s
0
20
40
60
80
100Rectangular clarifier
11 Transverse baffles
RMSE = 1.8 %
Figure D-20. Physical model and CFD model results for PM and PSDs for the triangular
hydrograph and for 8th July 2008 storm used for the validation analysis for full-scale
physical model of a rectangular clarifier. These results are showed in A) and B). Qp is
the peak influent flow rate and td is the total duration of the hydrological event. In B)
and D) the shaded area indicates the range of variation of effluent PSDs throughout
the hydrological events. RPD is the relative percentage difference between the
measured and modeled data. RMSE is the root mean squared error between effluent
average measured and modeled PSDs, s is the particle density, Qp is the peak
influent flow rate and td is the total duration of the hydrological event
eff
luen
t P
M (
Kg)
A
C
B
D
RPD = -0.07%
RPD = 9.30%
Rectangular Clarifier
Rectangular Clarifier
Rectangular Clarifier
Rectangular Clarifier
237
Flow rate, Q (L/s)0 10 20 30 40 50
Was
ho
ut,
Cw (
mg/L
)
0
20
40
60
80
100
PM
dep
th
(mm
)
Flow rate, Q (L/s)
0 10 20 30 40
0
200
400
600
800
1000
1200
Rectangular Clarifier
SHS
Volute (50 % sump capacity, SC)
5
50
40
35
25
100
2510
Vo
lute
PM
dep
th (
mm
)
Flow rate, Q(L/s)0 10 20 30 40
0
100
200
300
400SHS - Sump
450
150
100
25
Su
mp
PM
dep
th (
mm
)
228
50
(100% SC)
(50% SC)
Sum
p w
ash
ou
t, C
w (
mg/L
)S
um
p a
nd
volu
te w
asho
ut,
Cw (
mg/L
)
Figure D-21.CFD model of washout PM concentration as a function of flow rate, Q for the
rectangular clarifier and SHS unit. In (A) washout PM concentration from the
rectangular clarifier is shown for different PM depths ranging from 5 to 50 mm. In
(B) washout PM mass from the SHS is reported for 50% of PM capacity in sump area
and PM depths in volute section ranging from 10 to 100 mm. In (C) washout PM
concentration from the sump of SHS unit is shown for different PM depths ranging
from 25 to 450 mm (no PM in volute region)
A
B
C
238
Flow rate, Q (L/s)0 10 20 30 40
Vo
lute
an
d s
um
p w
ash
ou
t, M
w (
kg
)
0
10
20
30SHS
Volute (100 % sump capacity, SC)
100
2510
Vo
lute
PM
dep
th (
mm
)
50
Flow rate, Q (L/s)0 10 20 30 40
Vo
lute
an
d s
um
p w
ash
ou
t, C
w (
mg
/L)
0
200
400
600
800
1000
1200SHS
Volute (100 % sump capacity, SC)
100
2510
Vo
lute
PM
dep
th (
mm
)
50
Figure D-22. CFD model of PM washout mass and concentration as a function of flow rate, for
the SHS unit for PM depths in volute section ranging from 10 to 100 mm with 100%
of PM capacity in sump area. In (A) the PM washout mass is reported, in (B) PM
washout concentration
A B
239
Month (2007)1 2 3 4 5 6 7 8 9 10 11 12
Cum
ula
tive
effl
uen
t m
ass
(kg)
0
200
400
600
800No washout
Washout
0.0
0.2
0.4
0.6
0.8
1.0
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08WashoutNo washout
Sum
p P
M
dep
th (
m)
Volu
te P
M
dep
th (
m)
Sump region
Volute region
100% sump
capacity
Figure D-23. Effluent PM mass and PM mass depth as function of month for the screened HS
unit in the representative year 2007 for 100% of sediment capacity of sump area. The
results in (A) are generated by using the stepwise steady flow model with and without
considering washout phenomena for the hetero-disperse PM gradation shown in
Figure 1A ( and , respectively 0.79 and 28). In (B) the results are produced by
assuming PM mass accumulates first in the sump area (negligible PM deposition in
the volute area) and subsequently as the PM mass reaches 100% of the sump
capacity, it starts to build-up in the volute area. Cinf is the influent concentration
A
Influent PSD
= 0.79; = 28
s = 2.63 g/cm3
= 1.035 g/cm3
B
Cinf = 200 mg/L
Representative
year: 2007
SHS
SHS
240
Mean fluid velocity (m/s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
No
rmal
ized
fre
qu
ency
(%
)
0
2
4
6
8
10
12
14
16
Mean fluid velocity (m/s)
0.00 0.05 0.10 0.15 0.20 0.25 0.30
No
rmal
ized
fre
qu
ency
(%
)
0
2
4
6
8
10
12
14
16
No
rmal
ized
fre
qu
ency
(%
)
0
2
4
6
8
10
12
Figure D-24. Normalized mean fluid velocity distributions inside the inner and outer volute area
of SHS, and RC. Bin sizes are consistent for SHS and RC
RC
SHS
Inner area
SHS
Outer volute area
241
Table D-1. Summary of measured and modeled treatment performance results for full-scale
rectangular clarifier loaded by hetero-disperse silt particle size gradation for two
different hydrological events. Vt is the total influent volume, Qp is the peak influent
flow rate, Ttot is the duration of the hydrological event, measured is measured PM
removal efficiency, modeled is modeled PM removal efficiency and RPD is absolute
percentage error, and represent the gamma parameters for effluent measured
PSDs. The gamma parameters for the influent PSD are respectively 0.8 and 29
Hydrograph Type Qp Vt td measured modeled RPD PSD model
(L/s) (L) (min) (%) (%) %
Triangular RC 28.4 15.1 44 88.38 88.4 0.07 0.97 20.15
8 July 08 RC 50.8 88.9 110 56.78 51.7 9.03 0.90 18.00
Table D-2. Morsi and Alexander constants for the equation fit of the drag coefficient for a sphere
Reynolds Number K1 K2 K3
<0.1 24.0 0 0
0.1 < Re < 1 22.73 0.0903 3.69
1 < Re < 10 29.16 -3.8889 1.222
10 < Re < 100 46.5 -116.67 0.6167
100 < Re < 1000 98.33 -2778 0.3644
1000 < Re < 5000 148.62 -4.75 * 104 0.357
5000 < Re < 10,000 -490.54 57.87 * 104 0.46
10,000 < Re < 50,000 -1662.5 5.4167 * 106 0.5191
242
Table D-3. Under-relaxation factors utilized in the CFD simulations
Parameters Under-Relaxation Factors
Pressure 0.3
Density 1
Body Forces 1
Momentum 0.5
K energy 0.5
243
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BIOGRAPHICAL SKETCH
Giuseppina Garofalo received her bachelor`s and master`s degrees in civil engineering at
University of Calabria, Italy. She came to the United States in August 2007 to pursue her Ph.D.,
in environmental engineering sciences. In May 2012 she received her M.E. in environmental
engineering sciences from University of Florida. Her doctoral research focuses on physical and
CFD modeling of unit operations for rainfall-runoff. She worked under the guidance of Dr.
Sansalone in the Department of Environmental Engineering Sciences.
