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University of WollongongResearch Online
University of Wollongong Thesis Collection University of Wollongong Thesis Collections
1988
Dispersion mechanics in underground mineventilationPeter Nicholas StandishUniversity of Wollongong
Research Online is the open access institutional repository for theUniversity of Wollongong. For further information contact ManagerRepository Services: [email protected].
Recommended CitationStandish, Peter Nicholas, Dispersion mechanics in underground mine ventilation, Doctor of Philosophy thesis, Department of Civiland Mining Engineering, University of Wollongong, 1988. http://ro.uow.edu.au/theses/1239
DISPERION MECHANICS IN UNDERGROUND MINE VENTILATION
A thesis submitted in fulfilment of the requirements for the award of the degree of
DOCTOR OF PHILOSOPHY
from
THE UNIVERISTY OF WOLLONGONG
by
PETER NICHOLAS STANDISH, BE (HONS)
DEPARTMENT OF CIVIL AND MINING ENGINEERING
1988
Candidates Certificate
This is to certify that the work presented in this thesis
is original and was carried out in the laboratories of
the Department of Civil and Mining Engineering in the
University of Wollongong and in the Elura Mine of the
North Broken Hill Pty Ltd Company in Cobar NSW, and has
not been submitted to any other university or institution
for a higher degree.
Peter Nicholas STANDISH
(i)
TABLE OF CONTENTS
Acknowledgements (i) Summary (ii) List of Symbols (iii) List of Figures (iv) List of Tables (ix)
1.0 INTRODUCTION 1
2.0 THEORETICAL CONSIDERATIONS 5
2.1 TRADITIONAL ASPECTS 5
2.2 DISPERSION MECHANICS - IDEAL FLOW 11
2.2.1 Ideal Mixed Flow Model 13 2.2.2 Ideal Plug Flow Model 14 2.2.3 Pure Convection Model 16
2.3 DISPERSION MECHANICS: NON-IDEAL FLOW 19
2.3.1 Dispersion Model 19 2.3.2 Multiparameters Models 31 2.3.3 Tracer Introduction and Measurement 34
2.4 UNDERGROUND TRACER EXPERIMENTS -LITERATURE DATA 37
2.5 SUMMARY 44
3.0 EXPERIMENTAL INVESTIGATIONS 46
3.1 LABORATORY TESTS 46
3.1.1 Tracer Selection and Detection 47 3.1.2 Apparatus 48 3.1.3 Calibration of Equipment 50 3.1.4 Laboratory Method 52
3.2 LARGE SCALE PROVING TESTS 54
3.3 UNDERGROUND STUDIES 56
3.3.1 Test Sites 56 3.3.2 Equipment Usage 57 3.3.3 Test Method 60
3.4 ADDITIONAL WORK 63
3.4.1 Balloon Release Characteristics 63 3.4.2 Detector Evase 65 3.4.3 2 Drill West Vent Shaft Monitor
Position 66 3.4.4 Lateral Position Detection Trials 67
3.5 TREATMENT OF DATA 69
4.0 RESULTS and DISCUSSIONS 72
4.1 LABORATORY TESTS 72
CONTENTS (continued)
4.2 LARGE TEST RIG RESULTS 74
4.3 UNDERGROUND TESTS 77
4.3.1 2/8 Cross Cut Tests 78 4.3.2 West Vent Shaft - Preliminary Tests 83 4.3.3 West Vent Shaft - Position Tests 90
4.4 POSITIONAL ANEMOMETER TRAVERSE 100
4.5 COMPUTER ANALYSIS OF POSITIONAL RESULTS 101
4.5.1 Tracer Results 102 4.5.2 Anemometer Results 106
4.6 COMPARISON OF TRADITIONAL AND TRACER RESULTS 109
5.0 SIGNIFICANCE OF RESULTS 113
5.1 THEORETICAL ASPECTS 114
5.2 PRACTICAL ASPECTS 120
6.0 CONCLUSIONS 124
7.0 REFERENCES 126
(i)
ACKNOWLEDGEMENTS
I would like to thank my supervisor, Dr. N.I. Aziz,
Senior Lecturer, Department of Civil and Mining
Engineering, for his advice and encouragement during the
course of this work.
I also wish to thank the management of NBH P/L, in
particular the Mine Manager Mr Paul Rouse, for permission
to conduct the underground work at Elura Mine Cobar NSW.
The assistance of the workshop staff in the Department of
Civil and Mining Engineering, University of Wollongong
and that of the staff of Elura Mine, Cobar in
constructing experimental equipment is gratefully
acknowledged.
My thanks also go to David Pelchen, Mining Engineer,
Elura Mine for ungrudgingly staying back after his normal
shift to provide periodic assistance with underground
tests when an extra pair of hands was essential for the
experimental work to be carried out.
Special thanks are also due to Associate Professor
R.W. Upfold for his guidance in the selection of computer
software and equipment.
To all those who have helped, in one way or another, in
the preparation of this thesis I extend my sincerest
thanks.
(ii)
SUMMARY
Application of Dispersion Mechanics to mine ventilation
surveys is studied using C2H2 tracer release and
detection on the 2 Drill level at Elura Mine, Cobar, NSW.
Preliminary calibration work of the measuring systems in
the laboratory and in a large test rig together with the
results obtained is reported. It is found that the
results in these non-mining systems closely follow the
results of Dispersion Mechanics theory for a dispersed
plug flow model.
For the underground conditions studied the results of
tracer studies show that the ventilating air flow is
layered or segregated in a "tube bundle" pattern. These
tracer results are reproduced by the results of
traditional anemometer readings obtained under the same
flow conditions. The results also show that the
ventilating air flow under actual underground conditions
is characterised by transient behaviour which appears to
be a normal behaviour of the ventilating air in
underground workings. Application of the results to
practice is included.
r
A a b C c D
—
-
— — -
-
D M " d E e F f H K L M N P Q R
R S t
t
E u V V
x,y,z
Greek Symbols
« , ^ , ^
A 6 £
V 2
Ah Subscripts
e f d t &
Special Symbols
(D/UL) (D/ud)
Sc R
-
-
—
— -
-
— -
-
-
--—
--
-
-
-
—
-—
-
--—
—
-
-
-
— --
-
—
—
-
(iii)
LIST OF SYMBOLS
Area Area ratio (eqn (2.57)) Time ratio (eqn (2.57)) Concentration constant Dispersion Coefficient Molecular diffusivity
Diameter Exit age distribution Exponential Step function Friction factor Height Constant Length, distance Mass Number of ideal tanks Pressure Mine air flow rate Radius
Specific Resistance Perimeter Time
Mean time
Mean of coordinate mean times Velocity Volume volumetric flow rate Spatial coordinates
Exponents Difference Dirac <5-function Roughness Viscosity
Variance Head Loss
Effective Flowing Dead Real time Dimensionless time
Dispersion Number Dispersion Intensity Schmidt Number
Reynolds' Number
(iv)
List of Figures
Number Title Page
2.1 Friction Factor as a function of Reynolds' number with relative roughness as a parameter after Skochinsky and Komarov (64). 7 A
2.2 Plug flow model. 15A
2.3 Step function response. 15A
2.4 Comparison of plug flow, perfect mixing and laminar flow residence time distributions after Butt (66) 18A
2.5 One dimensional dispersion model. 19A
2.6 Convective and molecular diffusion contributions to dispersion. 22A
2.7 Fe and EQ curves as calculated from
eqns (2.28) and (2.43) for different
values of n [= (D/uL)-1] after Butt (66). 25A
2.8 Intensity of dispersion as a function of Reynolds' number for different Schmidt numbers after Levenspiel (69). 27A
2.9 An example of tracer response curves for fluid flow behaviour in equipment after Levenspiel (69). 31A
2.10 An idealized response curve for parallel flow. 32A
2.11 Idealized response curves to step and pulse inputs for a recirculating flow after Levenspiel (69). 33A
2.12 Test layout of Higgins and Shuttleworth (2). 37A
2.13 Reported tracer response curves (2) for the layout in Fig 2.12. 37A
2.14 Face response curves of Higgins and Shuttleworth (2). 38A
2.15 Calculated Et curves of the data in
Fig 2.14. 3 8 A
2.16 Plan of the USBM experimental mine (3). 41A
(v)
List of Figures (continued)
Number Title Page
2.16 Plan of the USBM experimental mine (3). 41A
2.17 Reported tracer response at position S in the mine of Fig 2.16. 41A
2.18 Response curve of Thimons and Kissell of a recirculating situation (3). * 42A
2.19 Calculated flow model for the response of Fig 2.18. 42A
2.20 Recirculation response curves of Stokes and Stewart (7). 43A
2.21 Calculated flow model for the response of Fig 2.20. 43A
3.1 Line diagram of laboratory apparatus. 48A
3.2 Circuit diagram of detector Tandy
Electronics P/L. 49A
3.3 Calibration curve of pressure vs volume for the vacuum pump. 50A
3.4 Rotating collar flow control device. 50AA
3.5 Diagram of the setup used for detector calibration. 52A
3.6 Detector mV response vs concentration plot. 52AA
3.7 Typical response curve obtained in laboratory tests. 54A
3.8,3.9 Surface test rig and Tracer Input Devices. 54AA
3.10 Typical response curve obtained in the large test rig. 56A
3.11 ' Plan of 4 Drill level. 56AA
3.12 2 Drill Plan with test sites marked. 56AAA
3.13(a) Line of backs, 2/8 Cross cut. 57A
3.13(b) View along drive, 2/8 Cross cut. 57A
3.14 West Vent Shaft detection site. 61A
(vi)
List of Figures (continued)
Number Title Pa
3.15 In situ zeroing of the chart recorder. 61A
3.16 Balloon inflation procedure. 62A
3.17 Close up of tilt valve. 62A
3.18 Balloon in position and ready for release. 6 2 A A
3.19 Recorder tracer of (a) balloon release and (b) plastic bag release. 63A
3.20 Balloon burst from below.
3.21 Balloon burst from below - 1 metre downstream.
64A
64A
3.22 Balloon burst from below - 5 metres downstream. 6 4AA
3.23 Diagram of observed tracer spread. 64AA
3.24 Cone evasfe on site in WVS regulator. 65A
3.25 Evas^ detail. 65A
3.26 Box evasfe 65AA
3.27 Detector position, WVS. 66A
3.28 Expanded plan view of WVS area. 67A
3.29 Expanded plan view of WVS area with sites marked. 68A
3.30 Tracer release points across drive section. g9A
3.31 Relationship between D/uL and the dimensionless E curve (C_) for small
extents of dispersion, after Levenspiel (69). 71A
4.1 Mean time vs velocity. 72A
4.2 D/ud vs Reynolds' number. 72A
4*3 Plot of variance vs velocity - Laboratory Results. 73A
(vii)
List of Figures (continued)
Number Title Page
4.4 Mean time vs velocity for Large test rig 74A
4.5 Log-log plot variance vs velocity, Large test rig data. 74A
4.6 Head loss vs velocity (log-log), large test rig. 77A
4.7 Plot of mean time vs distance; Large test rig. 79A
4.8 Variance vs distance; Large test rig. 80A
4.9 Tracer response in an ideal plug flow vessel. 84A
4.10 Expanded plan view of WVS release points 84A
4.11 Response curve for Test 192. 97A
4.12 Flow model for the response of Fig 4.11. 97A
4.13 Hand drawn velocity contours - Site 1 101A
4.14 Computer generated contour plot - Site 1 101A
4.15 Site 1 positional velocities by tracer, all head positions. 102A
4.16 Site 1 Positional velocities by tracer, central head position only. 102A
4.17 Site 2 positional velocities by tracer. 102AA
4.18 Site 3 positional velocities by tracer. 102AA
4.19 Site 4 positional velocities by tracer. 102AAA
4.20 Site 1 positional velocities by anemometer. 106A
4.21 Site 2 positional velocities by anemometer. 10 6A
4.22 Site 3 positional velocities by anemometer. 1o 6AA
4.23 Site 4 positional velocities by anemometer. 106AA
Number
4.24
4.25
4.26
4.27
4.28
4.29
4.30
4.31
5.1
(viii)
List of Figures (continued)
Title
Site 5 positional velocities by anemometer.
Site 6 positional velocities by anemometer.
Site 7 positional velocities by anemometer.
Site 8 positional velocities by anemometer.
Site 1 positional velocities by anemometer (low velocity).
Site 2 Positional velocities by anemometer (low velocity).
Site 3 positional velocities by anemometer (low velocity).
Site 4 positional velocities by anemometer (low velocity).
Calculated variances () and residual concentrations, %. Site 1 calculated responses.
Page
106AAA
106AAA
106AAAA
106AAAA
108A
108A
108AA
108AA
117A
(ix)
List of Tables
Number Title Page
2.1 Resistance Coefficient Values - k (65) 10
3.1 Properties of C2H2 and Air 47
3.2 Chart Recorder Calibration Results 51
3.3 Chart Recorder Speeds 52
4.1 Results of Air Velocities (m/s) Measured by Two Measurement Techniques 79
4.2 Particulars of Tests 46=*64 85
Al Laboratory Test Results A2-2
A2 Large Test Rig Results Cross Sectional Injection A2-2
A3 Large Test Rig Results Point Injection A2-3
A4 2/8 Results A2-3
A5 Site 1 Results; Positional Release A2-5
A6 Site 2 Results; Positional Release A2-6
A7 Site 3 Results; Positional Release A2-7
A8 Site 4 Results; Positional Release A2-7
A9 Site 1, Anemometer Positional Velocities A3-2
A10 Site 2, Anemometer Positional Velocities A3-2
All Site 3, Anemometer Positional Velocities A3-3
A12 Site 4, Anemometer Positional Velocities A3-3
A13 .. Site 5, Anemometer Positional Velocities A3-4
A14 Site 6, Anemometer Positional Velocities A3-4
(x)
List of Tables (continued)
Number Title Page
A15 Site 7, Anemometer Positional Velocities A3-5
A16 Site 8, Anemometer Positional Velocities A3-5
1
CHAPTER 1
INTRODUCTION
A number of functions are required of air ventilating the
underground environment, beyond the provision of Oxygen
to underground workers. A concise statement of these
functions has been made in a recently published work by
Vutukuri and Lama (1):
1) "To dilute the concentration of the
explosive and toxic gases, fumes and
radon to environmentally safe levels and
to remove from the mine;
2) To dilute the concentration of the airborne
dust to physiologically acceptable levels
and to remove from the mine;
3) To provide a thermally acceptable
environment in which persons can work
without undue discomfort or any danger of
exhaustion from heat from the mine as may
be necessary."
From the above it is evident that in addition to the
knowledge of air quantity, velocity and pressure losses
involved, an understanding of the behaviour of the
ventilating air in actual roadways is necessary.
2
Flow parameters that may influence the above functions of
the ventilating air are its dispersion characteristics as
well as the actual flow patterns involved. Neither of
these flow characteristics can be evaluated by
traditional surveying methods. They can, however, be
measured by tracer gas techniques.
In 1958,Higgins and Shuttleworth (2) reported what may be
one of the earliest investigations into the use of tracer
gases in headings. These authors used NO as a tracer and
restricted their investigations to the measurement of
flow rates and turnover times.
Later, a series of investigations (3-6) was conducted by
the USBM using Sulfur Hexaflouride (SF^) as a tracer. In
addition to the measurement of flow rates and turnover
times, air recirculation, stopping leakage, coal face
ventilation and spray-fan versus conventional ventilation
were investigated.
Recently a tracer study of the behaviour of a tunnel
boring machine (TBM) was reported by Stokes and Stewart
(7). Tracers used were CH4 and CgH0. Although the study
was not carried out underground, the results give an
insight into the possible air movement patterns that may
occur at the face during the coal cutting with the TBM
design used.
3
None of the investigations referred to above considered
dispersion mechanics theory nor the flow models suggested
by this theory in the analysis of the tracer response
curves obtained in the respective works.
As far as is known, there have been no reports so far of
the use of dispersion mechanics to analyse ventilation in
actual underground mine workings. However, dispersion
mechanics has been used in a 1:100 scale hydraulic model
of a three-heading longwall development panel to explore
possible changes in mine ventilation characteristics of a
number of alternative operations as well as simulated
methane emissions at the coal face (8).
Presentation of this work at ventilation symposia (9,10)
raised interest from other investigators in the field of
mine ventilation. It was concluded from the investigation
and the comments arising from presentation of the
findings that the model results of Dispersion Mechanics
could be applied to mine ventilation surveys to provide
quantitative flow patterns and effective dispersion in
the ventilating air. It was also considered that the next
step in the development should involve evaluation of the
method under actual underground mining conditions to
enable general assessments to be made of this new method
in mine ventilation work.
4
The challenge suggested in that work viz: to evaluate
Dispersion Mechanics under actual operating conditions
has been attempted in the Elura mine, often under
difficult conditions. Elura mine, exploiting a Silver,
Lead and Zinc ore body near Cobar N.S.W. produces 1.2 MTA
and employs a main surface fan installation providing a
3
total throughput ventilation of 120 to 140 m /sec. More information on the mine can be obtained from the
proceedings of the 1986 Underground Mine Operators
Conference, held at Kalgoorlie, W.A. (11).
The results of developmental work leading to, and of
actual underground work conducted at the Elura Mine are
presented in this thesis.
7
5
CHAPTER 2
THEORETICAL CONSIDERATIONS
2.1 - TRADITIONAL ASPECTS
The quantity of flowing air underground has traditionally
been of primary interest to researchers in the field of
underground mining ventilation. The importance of the
knowledge of the air quantity is associated with the
assessment of: network designs (12-21), strata gas
control (22-34), ventilation and refrigeration (35-39)
and system analysis (40-45). Additionally, other
ventilation aspects including those associated with fans
(46-52) and diesel emissions (53-57) as well as aspects
of dust control (58-62) require a knowledge of the air
quantity flowing underground.
Historically, air quantity in mines has been evaluated by
the Atkinson's equation below:
An kSL rt2 AP = — j Q (2.1)
A
The sequence of theories culminating in Atkinson's
equation has been presented in Hartman's book entitled
Mine Ventilation and Air Conditioning (63). In reaching
the relationship in eqn (2.1) between the frictional loss
of pressure (Ap) along a driveage (of length L, perimeter
6
S and cross sectional area A) and the flow rate of air
(Q) consideration has been made of other works.
Skochinsky and Komarov (64), in their text on the subject
indicate that for most of the air-flows underground,
pressure losses are directly proportional to the square
of the velocity, ie.
AP=*i^i (2.2)
Equation (2.2) gives the relationship between the head
loss (Ap), the dimensions and properties of a pipeline
(d, k and L), and the flow velocity (u): It can also be
derived by dimensional analysis, ie. Ap = f.(p,u,/J,L#A,S)
where; p is the density of the flowing fluid, u is the
linear velocity of flow, v is the viscosity of the fluid,
L the length of the "pipe", A the cross sectional area
and S the wetted perimeter of the pipe.
Removing L and S from the right hand side of the
equation, allows it to be expressed as:
AP/LS = f(p,u,(JrA) (2.3)
Assuming a polynomial solution, ie. raising the unknown
parameters to the powers a, fif y, and X. respectively,
leads to Atkinson's solution where R, the specfic
resistance is given by
„ kLS R = ~ T (2.4)
A
with ot = fir/2*, (from the dimensional solution) ; L being
path length and S perimeter.
Figure 2.1 shows the relationship between the coefficient
of friction (k) and Reynolds number (R) for fluids moving
in pipes, with the linear k values plotted against the
log10 values of R, as given by Skochinsky and Komarov
(64). For Reynolds' numbers below 2,000 Fig 2.1 shows that
laminar flow regime applies, and k=64/R. Beyond the
transition zone, with Reynolds' numbers typically above
100,000 the dimensionless friction factor becomes
constant for various roughness "pipes". in most mining
situations Reynolds' number, given by eqn (2.5) is
usually greater than this value.
« = ^ (2-5)
where symbols retain their defined meaning, and v
represents the dynamic viscosity.
The values of n marked on the curves in Fig 2.1 are given
by n = £/r, where c is the absolute roughness measured by
the mean value of the projections from the walls of the
pipeline and r is the radius of the pipe.
k
7A
M O O
O
1.0
0.8
0.6
OJt
0.2
\
\ \
V
n= 1066
ti* 0.0326
••• nz
i rl
n
0.015.1
.0081
.O.OO'i
0L — 2.6 3.0 3A 3,8 4.2 0.6 5.0 5.4
log Reynolds' Number
Fig 2.1: Friction Factor as a function of Reynolds' number with relative roughness as a parameter after
Skochinsky and Komarov (64).
8
The foregoing equations allow the calculation of energy
requirements based on experimentally determined friction
factors. Energy requirements, particularly the head loss
in the flowing fluid allow for the correct selection of
fans and forward planning determinations in overall
network designs.
Design of the ventilating system networks has been
greatly enhanced with the development of the digital
computer. Programs have been developed which allow input
of the various network parameters and the output of
information on the expected airflow performance with
various fans.
These programs involve an application of network theory,
combined with Atkinson's equation and, in general, use a
Hardy-Cross style iteration to reach a solution.
The fundamental relationships governing the flow about
the network are conservation of mass and energy.
Conservation of mass is maintained for the network by
ensuring that the sum of flows at a node is zero.
Equation (2.6) after Hartman (63) represents this
situation.
9
n
j=l
Qj = 0 (2.6)
Ensuring the total sum of pressure drops around all the
loops in the network is zero means that energy is
conserved. Equation (2.7) is formulated for each loop. An
iterative approach (63) is then required to reach a
solution.
m n
j=l i=l
A P i f j = 0 (2.7)
where Ap is the pressure drop for the ith branch of •••»]
the jth loop, with m total loops and n branches for each
loop.
The digital computer is ideal for solution of the set of
simultaneous equations developed in a network program. As
a general guide, these programs accept as input the drive
and fan specifications, and output tabulated information
on the amounts of air flowing through the network with
expected pressure drops.
To determine the resistance values for the various
drivages modelled, "standard" resistance factors are
used. Table 2.1 presents typical values of resistance
selected for various roadway types.
10
The values tabulated below provide the starting point for
the estimation of the most appropriate resistance values
to use in any network being modelled. Additional
information is determined for specific driveages
determining the pressure drop and airflow, to allow
calculation of specific "k" values for use.
Rearranging eqn (2.1), and expanding for R, gives:
k = A3AP
Q2SL (2.8)
Where the right hand side terms of eqn (2.8) are
determined at strategic locations underground.
TABLE 2.1 Coefficeint of Friction - k (65)
DESCRIPTION VALUE
Smooth concrete lined all around
Concrete slabs or other lagging between arch sets
Concrete slabs or timber lagging between arch sets to spring
Lagging behind arches -straight airways
Rough conditions with irregular roof floor and sides
0.0037
0.0074
0.0093
0.0121
0.0158
11
With k values selected, the network is modelled and
"tuned" to ensure that computed results are consistent
with observations.
A solution of the 2 Drilling level (2 Drill) ventilation
network at the Elura mine has been made using a network
program run on a Sperry, 64OK personal computer.
2.2 DISPERSION MECHANICS: IDEAL FLOW
Air may flow in underground mine workings with varying
extents of mixing on a molecular level and also on a
macroscopic level, which is the result of the different
flow paths of air within the mine workings.
The two contributions are independent of each other in
that definition of a state of macromixing does not, for
example, define a corresponding level of micromixing.
Extreme limits of mixing, ie. perfect mixing and no
mixing at all (or plug flow) define corresponding ideal
flow behaviours. These two flow patterns are most
conveniently characterised by considering the time
required for each volume element of air to traverse a
given length of the flow path. For ideal plug flow the
time is the same for each volume element, whilst for
5\
12
ideal mixed flow there is an exponential relationship of
these times. The mean residence time t is given by:
t = £ (2.9)
where: L is the path length traversed, and
u is the velocity of the flow
then for ideal plug flow the exit time (age) distribution
Et is:
Et = cS(t-tQ) =00 at t = t (2.10)
6(t-t ) = 0 elsewhere
and for ideal mixed flow:
E = ~ e t/t (2.11) r t
Equation (2.11) defines the exit age (Et) or residence
time distribution (RTD) for ideal mixed flow. In real
systems, the distribution of residence times may arise as
a result of micromixing and macromixing, or as a result
of radial velocity distribution of the flow.
Since it is difficult to define a measure for quantities
such as the degree of mixing or, indeed, to make
measurements on the hydrodynamic state of the internal
13
flow in engineering systems, extensive use has been made
of models that describe the observable behaviour in terms
of external measurements.
The most widely used method of measurement is a
stimulus-response method, employing an appropriate tracer
substance. The introduction of the tracer is most simply
performed by way of a pulse, but other methods such as
step or periodic introduction can also be used. It should
be noted that measurements of RTD by any method cannot
define micromixing.
In spite of this limitation, RTD is most valuable as it
provides as much information on the state of mixing as
can be obtained short of measurement on the microscopic
level.
2.2.1 Ideal Mixed Flow Model
Consider a flow compartment of volume V, through which
air flows at a steady volumetric flow rate v. At t=0, a
pulse of tracer <5 (t) is introduced at the inlet. By
definition, the concentration of the inlet tracer is
uniformly distributed within the compartment. Let this
concentration (C0) be equal to unity. The exit
concentration C is then obtained by solving the material
balance equation, viz:
14
CQV <5(t) = CV +~AJ!~L (2.12) dt
dividing by V, and noting that C =1 o
c ... C dC <5(t) = f + — (2.13) t dt
integrating:
C = i et <5(t)dt (2.14)
Using the property of the Dirac-6 function
f(x)6(X)dx = f(0) (2.15)
the resultant solution is given in eqn (2.16) which is
the result for E. given in eqn. (2.11) since C was made w o
equal to unity in the above derivation:
1 -t/t C = -e (2.16)
t
2.2.2 Ideal Plug Flow Model
The derivation is most conveniently performed by
considering a step function input (F) and then
differentiating the resultant equation to obtain the Ee
and Etexpressions, where EQ is the dimensionless exit age
distribution.
15
Consider a differential length, dz, of a cylindrical
conduit, as shown in Fig 2.2. Fluid with a uniform
velocity u in the axial direction is passing through the
differential volume Adz, where A is the cross section of
the tube. At a time t = 0, a step input of tracer is
introduced uniformly across the cross section at the
entrance to the tube at concentration CQ. The general
unsteady state mass balance for the differential volume
can be written as:
input - output = accumulation (2.17)
where
tracer input = uCA
tracer output = uA (C + -=—• . dz)
dC tracer accumulation = A dz TT
dt Equating the terms,
uCA - uA(C + |f.dz) =Adz| (2.18)
or
with the initial boundary conditions
t>0, z = 0, C = C max
t = 0, Z > 0 , C = 0
t = o, z < o, c = cmax
15A
Fig 2.2: Plug flow model.
u_
1.0 (t/t) = 0
Fig 2.3: Step function response.
16
The solution of eqn (2.19) for the tracer concentration
at the exit (z = L) is:
C = 0, t < £ (2.20)
C = C , t > -o' u
which is a step function response F(t) as shown in Fig.
2.3.
The equivalent E. response is given by eqn (2.10) and is
simply a Dirac 6 function of unit area and zero width at
t = £ ^ u*
The specific mixing assumptions involved in this model
are the absence of mixing in the axial direction, and
uniformity of concentration and velocity in the radial
direction.
2.2.3 Pure Convection Model
For laminar flow in pipes and also for short pipes at
high flow rates, molecular diffusion would not have
enough time to act - so all that needs to be considered
as causing a spread of residence times is the velocity
profile.
The model that considers this siutation is the pure
convection model. To derive the mixing model for laminar
17
flow, one starts with a definition of the velocity
profile (66), viz:
»<v-S[-R)] (2.21)
where R is the radius of the tube, o ' r is the radial position at which the velocity,
u(r ) is determined, and
v is the volumetric flow rate.
For length L of tubing, the residence time t(r ) P
corresponding to u(r ) is:
t(r ) = u(r ) v p'
(2.22)
and the average residence time is given by
u (2.23)
where u is the average velocity u = v rcR o J
Solving eqns (2.21) and (2.22) for r gives: hr
18
Now (66):
c J P 2u[ 1 - (r /R )2lc.27rr dr *<*> = § = L P ° J (2.25)
o r
r p -•J u C 2 ^ r dr o p p or:
*C 1 f/l-t/t r 2l
F(t) = 1 J K ^ w J 2"rPdrP <2-26)
o o
Evaluation leads to
t2
F(t) = 1 - (2.27) 4t
and the exit age distribution is
E ssm. = £ (2.28) dt 2t
A comparison of the laminar flow residence time
distribution with corresponding plug flow and perfect
mixing results is shown in Fig 2.4.
It may be of interest to note that the mixing model for
laminar flow is similar to that for plug flow, except for
the radial dependence of velocity.
i\
18A
1.0
0.8
0.6
0.4
0.2
0
I . Laminar
— flow
— \/y
i \
Perfect mixing
I I I I I
—
—
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
(t/t) =0
Fig 2.4: Comparison of plug flow, perfect mixing and laminar flow residence time distributions
after Butt (66)
19
This is made clear when it is considered that the analog
of eqn (2.19) is:
d c ( rP) dC
~U(rp)— = dt (2-29) dz
2.3 DISPERSION MECHANICS: NON-IDEAL FLOW
2.3.1 Dispersion Model
Departure from the ideals of plug flow is treated by the
dispersion model which is of wide generality and
applicability. This model considers plug flow of a fluid,
on top of which is superimposed some degree of backmixing
or intermixing, the magnitude of which is independent of
position along the flow path.
Considering the one-dimensional dispersion model,
illustrated in Fig 2.5, the mass balance around the
differential length dz is:
in: convection: uCA
j• • ~dC
dispersion: -D-r— . A dC
out: convection: u ( C + ^.dz ) A dz ' dispersion: -D [ |£ + S-( g ]dz]
dC accumulation: ^ . Adz
dt
19A
— • -
— > > -
u — ^
©— ^ z >-
B H dz
—*- u
—© -«
>-
•_
At(T): uCA+(-D ^ + i L - A )
dC
dz dz
At(T): u(C + —-dz) A + v-/ dz
D dC+_d_ d c . d z
dz dz dz
A = cross-sectional area
A
Fig 2.5: One dimensional dispersion model
20
Equating the difference in input/output terms to
accumulation in the volume element gives:
d c ^ dC J d dt ' d z = "ud£ • d z + D^(dCdz)dz (2.30)
which on rearrangement becomes
n <=l£ „ dC dC D dz2 "
U di = dt (2-31)
D, the axial diffusion (or dispersion) coefficient, is
the parameter employed to describe the deviations from
ideal flow. If u is taken to be constant in the radial
direction, the rightmost terms in eqn (2.30) constitute 2
the plug flow mixing model (eqn 2.19) and D(^-£ j
Fickian form of diffusional correction term
a dz"
Using the model to produce F(t) and Et responses the
equation is solved (noting that the equation is no longer
in the form of an initial value problem, but a boundary
value problem) by making a change of variable. Let v
represent the position of the moving interface
represented by all elements of fluid introduced into the
reactor at some given time. in terms of the length
variable, this transformation is:
v = z - ut (2.32)
21
Substituting for z in terms of v gives;
d C dC
dv dt (2.33)
The boundary conditions for a step function in inlet
concentration of tracer are:
C = 0
C = 1
C = 0
C = 1
(V > 0, t = 0)
(V < 0, t = 0)
(V = oo, t > 0)
(V = -oo, t > 0)
(2.34)
The corresponding solution (66) is
C = i 2
1 - erf L 2/5T J
where
erf(y) =
/ *
exp(-v )dv J O
(2.35)
and is again a tabulated function. The F(t) response
computed from the one-dimensional dispersion model is,
then,
F(t) = \ - \ erf L - ut
2/DlT . (2.36)
i.
22
Rewriting in terms Of dimensionless time, © = t/t:
F(e) = I - I erf l - e 2 /©(D/uL).
(2.37)
Since E(©) = dF(©)/d© and Efc = dFfc/dt, then on
differentiation of eqn (2.37) and for small extents of
dispersion we obtain:
E(©) = — - exp
27 n(D/uL)
_ (1-Q)2
4(D/uL) (2.38)
The presentation of the one dimensional dispersion model
so far has been a modification of the plug-flow model.
Hence, u is treated as uniform across the tubular cross
section. In fact, the general form of the model can be
applied to numerous instances when this is not so, in
which case the dispersion coefficient D becomes a
parameter describing the net effect of a number of
different phenomena. Taylor (67) has illustrated the
effect on the combined contributions of the velocity
profile and molecular diffusion to the residence-time
distribution for laminar flow in a tube. The situation
considered is illustrated in Fig 2.6. For moderate flow
velocities the dispersion of a tracer in laminar flow
will occur by axial and radial diffusion from the flow
front and, in the absence of eddy motion, this will be
22A
r Dr
u(r| ™
Fig 2.6: Convective and molecular diffusion contributions to dispersion
23
via a molecular diffusion mechanism. However, the net
contribuiton of diffusion in the axial direction can be
taken as small in comparison to the contribution of the
flow velocity profile. This leaves one with a
two-dimensional problem, diffusion in the radial
direction and convection in the longitudinal direction.
Following the procedures outlined for eqn (2.31), the
following can be derived (66):
dc n f dZC l ac 1 , , ac
at = Du[ ^ + r *x J ~ u ( r ) !ir (2'39>
where DM is the molecular diffusivity for the tracer and
u(r) represents the laminar flow velocity profile. Now
eqn (2.39) is a nonsteady-state partial differential
equation, the solution of which under the best of
circumstances is going to be a demanding task.
Taylor (67) presents a rational approximation to this
solution in:
<?C a2 c dc m m — m
_ = D _ u _ _ ( 2 . 4 0 )
«Z
where C is a mean radial concentration, u the average
velocity independent of r, and D an effective dispersion
coefficient. In terms of the parameters of eqn (2.34), D
is given by:
24
2-2
D « ^gg- (2.41) 171
where R is the tubular radius. Of course, this
representation is valid only under the conditions stated,
with molecular diffusion in the axial direction being
negligible. Taylor (67) further showed that, for this
condition to exist, it was necessary that:
* | - » ] p » 6 . 9 (2.42) m
Note in the inequality (2.42) that the quantity (uR/D )
can be considered an axial Peclet number. The right-hand
bound of 6.9 has been criticized by Ananthakrishnan et
al. (68) as not being sufficiently conservative. They
propose that (uR/D ) > 50 should be used as a criterion
for the use of the one dimensional approximation.
For large deviations from plug flow and open vessel
boundary conditions - the only physical criterion where
the analytical expression for E& can be derived, the
resultant expression is (69):
Ee = , exP y An(D/uL)e
(l-e)2
4e(D/uL) (2.43)
V
25
Equations (2.38) and (2.43) are easy to solve as they
represent normal or Gaussian curves with mean and
variance:
t © = — = 1 (2.44)
2
°© = ~?~r = 2(D/uL) (2.45) (t)Z
for small extents of dispersion of eqn (2.38) and
en = Z 2 = 1 + 2(D/UL) (2.46) t
and 2
J* O ~,~/T* „,„,,, 2 *€> = - 2
(t) = 2(D/UL) + 8(D/uL) (2.47)
for the larger extents of dispersion of eqn (2.43).
Examples of F0 and E& computed from eqns (2.38) and
(2.43) are shown in Fig 2.7.
It may be useful to note that the property of additivity
of variances applies for flow through a series of flow
regimes, provided they obey the condition of
independence. The latter simply means that the fluid
loses its memory as it passes from region to region. The
additivity of mean times does not require this
independence of regions. So:
i
A
25A
0 0.5 1.0 1.6 1.8
Fig 2.7: FQ and EQ curves as calculated from eqns (2.28)
and (2.43) for different values of n [s (D/uL)-±] after Butt (66).
a
26
2 7 2
and
^at =1\ (2-49)
It is also noted that the term D/uL in eqns (2.37) to
(2.47) is not the reciprocal of the Peclet number. This
mistake is often made in the literature. In the Peclet
number (uL/D), D is molecular diffusivity, and even if
this D is taken to be the eddy diffusivity the answer is
still incorrect. The diffusivity (D) in eqns (2.37) to
(2.47) is a new and different diffusivity which
characterises the movement of fluid by longitudinal
dispersion, ie fluid overtaking caused by all possible
simultaneous effects such as molecular diffusion,
velocity differences, turbulent eddies etc.
The term D/uL then compares movement by the combined
dispersion referred to above and movement by bulk flow.
The dispersion number (D/uL) is related to intensity of
dispersion and geometric factor by the following
equation.
(D/ ) = (D/Ud)(d/L) (2.50)
27
The intensity of dispersion as measured by D/ud has been
found to correlate well with the properties of the flow
and the fluid, ie Schmidt's and Reynolds' numbers, where
the former is defined as:
sc= J5D~ (2.51)
and the latter by eqn (2.5)
For a given fluid Sc is virtually constant over a wide
range of temperatures. Its value for air is 0.71.
The relationship between intensity of dispersion and K in
pipes is given in Fig 2.8. It is clear from Fig 2.8 that
for turbulent flow D/ud is independent of Schmidt's 5
number and for K > 10 its decrease is also slight.
By inspection of Fig 2.8 it is seen that the behaviour is
analogous to that of k vs K in Fig 2.1. In fact, the
analogy between fluid dispersion and fluid friction
becomes even more obvious if it is noted that from eqn
(2.2) the pressure loss (Ap) is:
AP « f(^) (2.52)
Since at constant K, friction factor (k) is constant at
any position in the pipe then it is obvious from eqn
27A
io4
Re = dtup/n
Fig 2.8: Intensity of dispersion as a function of Reynolds' number for different Schmidt
numbers after Levenspiel (69).
28
(2.52) that Ap will change with L/d. Similarly, since at
constant K, intensity of dispersion D/ud is constant at
any position in the pipe so it is obvious from eqn (2.50)
that the dispersion number D/uL will change with d/L
only. In other words, Ap and D/uL represent effects
which are additive with flow distance. Moreover, as the
pipe length increases the pressure loss also increases
but the dispersion number decreases, meaning that, for
example, a burst of a concentrated gas will progressively
loose its identity with distance downstream.
The above conclusion, of course, is not new in the sense
that it confirms observed effects in everyday practice.
However, the dispersion mechanics theory and its
resultant equations and relationships allow the
dispersion to be quantified more rationally, and to draw
conclusions of the effect of operating variables on the
actual dispersion and not just that caused by molecular
diffusion. The theory shows that for flow in the laminar
regime the dispersion coefficient (D) is proportionial to ,2 2.
d u and inversely proportional to DM (eqn (2.41) and Fig
2.8). In turbulent regimes (K > 10 ), on the other hand,
D is essentially directly proportional to ud, is
independent of DM but is affected by the physical
properties of the fluid to a small extent viz (u/p)
In the intermediate flow regime as Fig 2.8 shows, the
effect of ud on D is between (ud)~ and (ud) .
29
Additionally the effect of key operating variables on the
spread of residence times can be obtained by solving
simultaneously eqns (2.9) and (2.45). The resultant
relationship is:
a = / D^ (2.53) u
Noting that residence time distribution (E. ) and
concentration of a tracer-like substance introduced into
the flow are related, then eqn (2.53) gives directly the
spread of concentrations also. Thus, for example,
doubling the distance will increase the spread by a
factor of y 2 whereas doubling the velocity will decrease
it very markedly, in fact, by a factor ~. „ o
of/§. The relationship between maximum concentration of the
substance and flow parameters including distance is
readily calculated from the value of the spread {cr) once
it has been evaluated from eqn(2.53). Of course, given
the relationship of eqn (2.53), maximum concentrations
may also be predicted and the resultant values used to
assess whether the required standards are satisfied.
Two, at first sight curious corollaries of dispersion
mechanics theory are that:
i) for a given length of pipe the dispersion number
(D/uL) remains constant at high Reynold's
numbers and is independent of the flow velocity,
and
a
30
ii) if the fluid is subjected to local mixing then
the more often this occurs along the flow path
the less mixed or dispersed will the fluid be
at the end.
The first result is explained directly by Fig 2.8 and the
second result by the equivalence between the dispersion
model of this section and the tanks-in-series models
(69), viz
cf\ = 2 (D/uL) = | (2.54)
where N is the number of mixing tanks along the pipe
length considered.
It should be noted that Taylor's theory (67), which is
the basis of Dispersion Mechanics, has been applied to
studies of the dispersion of dust and toxic gas pulses in
mine working, as well as the dispersion of blasting fumes
and Methane (70-74). The prime objective of these studies
was to evaluate the dilution of the substances involved
and not to characterise the dispersion behaviour of the
ventilating air itself. Additionally, dispersion studies
in mines reported in the literature (75-81) have involved
essentially the mathematical models based on Taylor's
(67) convection-diffusion equations for essentially
straight flow conditions.
31
2.3.2 Multiparameter Models
The flow models considered so far are incapable of
dealing with complex flow behaviour induced by
channeling, by-passing, combining or branching of the
flows, recirculation as well as the presence of dead
volumes in the flow path. Combining and branching of the
air flows are self explanatory and a feature that is
inherent in all underground ventilation networks.
In channeling a path of least resistance in the network
exists such that some portion of the fluid passes through
the channel. In by-passing a significant amount of fluid
enjoys a much abbreviated residence time in some part(s)
of the network whereas dead volumes indicate regions of
stagnation in which there is no significant fluid motion.
In recirculation the fluid travels back before turning
again. This type of behaviour may occur with slow moving
fluid in short, wide vessels. Fig 2.9 illustrates the
tracer response curves for these situations.
Derivation of the appropriate dispersion function for
such models is not difficult, since they essentially
consist of assemblies of components of dispersion models
considered earlier.
31A
Expccled
( (a)
r
Inlornal recirculation
Parallel paths
i>-t
Fig 2.9: An example of tracer response curves for fluid flow behaviour in equipment after
Levenspiel (69).
32
Stagnant or dead volumes in the flow path are evaluated
from the difference between the calculated and measured
mean times, that is:
vf _ vlot tmeas = ~u~~ Z ^calc = u (2.54)
therefore with VT = Vf + Vd
(t . - t ) V d
t , v, caLc t
(2.55)
The response in Fig 2.9 showing tracer appearing later
than expected has three possible explanations: an error
in flow rate measurement, an error in volume available
for fluid; or the tracer is adsorbed and held back on the
surfaces of the "pipe" being traversed.
Parallel flow parameters are evaluated from the
consideration of the areas under the curves and the mean
time of each curve. Figure 2.10 shows the output trace
(E. ) generated by an idealised parallel flow regime.
This system can be quantified by noting:
Ai + A 2 = 1
V l V 2 V~ = Ai v~ = V a n d ' (2-56)
32A
0 Y V, v V, fi = — -J Q - ' '; 01 v, Y Q*--2V
Fig 2.10: An idealized response curve for parallel flow.
33
The over all mean time is given by
[ V* + Va ]
Figure 2.11 shows an idealized output trace (E. ) of a
recirculating flow. In this case the areas of consecutive
curves decrease in a geometric progression whilst their
mean time increases in an arithmetic progression. The
total area of the curve must, by definition, equal unity.
From the measured values of either a or b, the
recirculation ratio of the system can be calculated, ie.
R a ~ R+l
(2.57)
In eqn (2.57) the recirculation ratio (R) is defined as:
volume of fluid returned volume of fluid leaving
Because of other flow complexities that may be associated
with recirculation it is best to use both expressions in
eqn (2.57) to check for consistency of R. If two
different values of R are obtained, then this suggests
the presence of dead volume regions in the system.
33A
(R + 1)
a>
a = R/(R + 1) b = 1/(R+1)
I N
- - Area = 1 - -" ^
b . 2b 36
k -Area = 6
v /-Area = ab
tf* Area = a2b
b lb 3b
Fig 2.11: Idealized response curves to step and pulse inputs for a recirculating flow after Levenspiel (69).
34
2.3.3 Tracer Introduction and Measurement
There are many ways of introducing the tracer into a flow
stream and measuring the response. There are also strict
boundary conditions in the derivation of the mathematical
expressions for Et - the residence time distribution. In
addition to the open vessel boundary conditions of eqn
(2.43) which allowed the analytical expression to be
evaluated, there are also closed vessel boundary
conditions as well as a number of others in between these
two extremes.
The analytical expressions derived in the previous
sections were based on the assumption that the pulse is
injected across the flow in zero time in such a way that
injection is proportional to the flow rate.
If the velocity profile of the flow is flat then, in
principle, injection uniformly across the cross section
should be easier to achieve than if the velocity profile
is not flat as, for example in the case of pure
convection in Sect 2.2.3.
Assuming that correct injection is experimentally
possible the analysis still requires that the tracer used
must also be a correct tracer. This means a tracer which
is in all respects indistinguishable from the flowing
*T*
35
fluid, ie. it has the same physical properties as the
flowing fluid. The best tracer would be a radioactive
isotope of the fluid and the best tracer input and
measurement would be the so called "Mixing Cup"
measurement, where the entire flow is collected and
analysed continuously.
Although fine in principle, the experimental difficulties
of even approximating these requirements in practice, let
alone achieving them, are immense especially in large
conduits such as mine roadways. Of the foregoing
problems, viz tracer and its introduction and
measurement, the more important requirement is to ensure
that the tracer is not too different from the flowing
fluid particularly with respect to the density. If this
requirement is satisfied then non-ideal introduction and
measurement will give a response curve which, with proper
flow modelling, and the right mathematical manipulation,
may give the proper Et curve.
2
If, for example, a non-ideal pulse of known cr , has been
injected then as shown by Aris (82), the relationship:
. 2 A(y& = - 2 = 2 (D/UL) (2.58)
(At)2
applies for any kind of input and boundary conditions.
36
If the tracer is introduced in a local volume element of
the flow and not fully across the flow cross section then
analysis of the previous sections would be valid for the
"flow tube" involved, provided the contribution of
molecular diffusion in the radial direction is small by
comparison with the dispersion in the axial direction,
(see Fig 2.6). This situation is practically ensured at
all but very low Reynolds' numbers. For these conditions
this would also give the dispersion characteristics
(D/uL) for the pipe as a whole. This follows from the
fact that what is being measured is a sample of the full
flow and as noted earlier, at high Reynold's numbers,
(D/uL) is a flow independent constant when the velocity
varies.
Moreover, one of the advantages of point introduction and
measurement is that any local anomalies in the flow
pattern can be detected immediately. Although
theoretically this would also be possible with a full
cross-section pulse, real response curves obtained in
actual practice are always "noisy" and it is often
difficult to distinguish with certainty which is the
noise and which is the flow anomaly.
37
2.4 UNDERGROUND TRACER EXPERIMENTS: LITERATURE DATA
In the work of Higgins and Shuttleworth (2) both pulse
and step input of N20 tracer were used. Fig 2.12 details
the section of the heading investigated and Fig 2.13
gives their results at position C. The authors state that
with regard to Fig 2.13
"the two curves are the results of two identical
experiments on different days and that on both days
work was in progress in the heading while the
experiments were being carried out and the positions
of the tubs, drilling rigs etc. were constantly
changing", and that
"The effect of these changes upon the longitudinal
dispersion of the Nitrous Oxide in the airstrearn can
be seen in the marked difference in the shapes of
the curves".
The above conclusion is important as it highlights the
variability of the results under actual mining conditions
even when every attempt is made to' keep everything
constant. It is of interest to note the use of the term
longitddinal dispersion which is, of course, the basis of
the Dispersion Mechanics theory that at that time was
still in its infancy and was not considered by the
authors.
37A
—63 )n -*-• Bm •»-
PNESSUUE TAPPINGS AT OIWICE PLATE
NzO 1HJECTION P01UT
Fig 2.12: Test layout of Higgins and Shuttleworth (2).
B i6 ?A 32 TIME. MINUTES (Nj 0 OH AT I MIN.)
-10
Fig 2.13: Reported tracer response curves (2) for the layout in Fig 2.12.
38
If the curves in Fig 2.13 are analysed by the methods
given earlier the following is obtained:
t = 5.65 min t, = 6.42 min 1 2
(D/uL)± = 0.104 (D/uL)2 = 0.079
The difference of some 20% in the mean times and the
difference of about 30% in D/uL values may indeed be
regarded as marked differences in the simple straight
section of Fig 2.12. From theory D/uL should be the same
in both cases and since airflow rate and the dimensions
were the same in each case then it must be concluded that
the dispersion coefficient must have been different in
the two cases. The above conclusion therefore means that
mining activity and the movement of machinery in the
various nearbye roadways, stopes, etc. has an effect on
the dispersion coefficient. In other words, the
dispersion coefficient in working mines cannot be assumed
to have a constant value.
Tracer response curves of Higgins and Shuttleworth (2) at
different positions and distances from the face are shown
in Fig 2.14, and in their E. form, calculated by the
analog of eqn (2.38), are shown in Fig 2.15.
38A
3 6 9 12 TIME, MINUTES (N2O ON AT I MIN.)
Fig 2.14: Face response curves of Higgins and Shuttleworth (2).
1,5
1.0 —
0,5
0,0
0 100
15 metres, X 15 metres, Y
26 metres, Y
28 metres, X
1 T 200 300 400 500 600
Time (seconds)
Fig 2.15: Calculated E. curves of the data in Fig 2
39
Using the calculating procedures outlined in previous
sections gives at the 15 metre position:
tx = 1.9min (D/uL)x = 0.08
t = 3.2min (D/UL) =0.45
and at the 26 metre position:
tx = 5.8min (D/uL)x = 0.31
t = 4.1rnin (D/uL) =0.45 y \ / /y
By inspection of Fig 2.14 and Fig 2.15 it is obvious that
the break-through time cannot be identical for all cases
as is incorrectly shown in the original plot (Fig 2.14).
The mean time for each duct distance is very different
but the expected lengthening of the mean time in direct
proportion to distance is reasonably satisfied.
The most significant feature of the above results is the
large difference in the D/uL values at the 15 metre
position for the X and Y positions, and their reversal at
the 26 metre distance.
This indicates that the dispersion characteristics across
the cross section of headings may be different and also
be a function of the distance. Another possibility is
that the tracer used may have preferentially segregated
\
40
in the heading. Since the density of N„0 is 65% higher
than that of air, this possibility cannot be discounted
even though the authors suggest in their paper that this
effect was not significant. It is unfortunate that no
results are given for the other three sampling positions
shown in the insert in Fig 2.14, since they would help to
decide in favour of one or the other effect.
In the USBM series of investigations (3-6), which began
some 20 years later, the tracer employed was SF , which
is more than nine times heavier than air, so it becomes
questionable whether the dispersion mechanics theory of
Section 2.3.1 should be used. It is of interest to note
that in their first report Thimons and Kissell (3) found
"the major problem to be incomplete mixing of the dense
SF^ with the mine air in airways of low velocity". They
note, however, that "at high velocities there was no
problem". These comments, of course, relate to the
injection stage, and no mention was made of segregation
which may have taken place downstream.
Thimons and Kissel (3) used pulse input typically by
releasing SFtf as a jet spray from a pressurized lecture
bottle whilst at the same time moving the lecture bottle
around the mine airway to further improve mixing.
41
By reference to Sect 2.3.3 this technique of tracer
release is far, far away from even approximate ideals of
pulse input. Thus, although application of dispersion
mechanics may be doubtful, in so far as the absolute
values are concerned, the results can still be used on a
comparative basis.
The response curve of an experiment made by these
investigators (3) in which SF^ was released at location R
and measured at location S in the mine of Fig 2.16 is
shown in Fig 2.17.
By inspection the overall shape of the response curve in
Fig 2.17 is reasonably normal but the initial portion,
except for an unexpected low C , is suggestive of
parallel flow (see Fig 2.9(e)).
Considering the physical situation of Fig 2.16 the only
possible true parallel paths are the three parallel
North-south headings. Under normal conditions, of course,
the response from these would be expected to show up in
the curve later. A probable explanation for the early
appearing parallel-like signal is that some
SF^-containing air leaked through the various stoppings
in the cut-throughs separating intake and return
headings. The leaked portion was then united with return
air ahead of the main portion of the SF signal.
41A
ununrX^ 2 bull L-ii—'
Exhaustion
I V)
>*
LEGEND
—*- Intake air
'—< Return air :(tT Door ~t~ Regulator " T ~ Curtain
Temporary stopping
.30
IZ}|ZZ Permanent stopping 7- Brallice
X Release location A Sampling location
Fig 2.16: Plan of the USBM experimental mine (3).
,000
BOO —
600
Ll.
in 400 —
200
10 20 30 . 40 50 60
TIME FROM RELEASE OF SF6, min 70 BO 90
Fig 2.17: Reported tracer response at position S in the mine of Fig 2.16.
42
The mean time of the initial signal in Fig 2.17 is
approximately 15 minutes, suggesting leakage through the
door rather than other ventilation structures. The mean
time of the main portion of the response curve,
calculated from the airflow and distances given in the
paper (3), is 35.7 minutes* The D/uL for the main portion
of the curve is calculated as 0.038, meaning that this is
the characterizing value of the spreading process of the
mine air and not of the SF . ©
An interesting recirculation experiment in a deep copper
mine cooling plant, reported by Thimons and Kissell (3)
gave the response shown in Fig 2.18. Using the procedure
outlined in Sect 2.3.2 and noting that the first signal
appears early, the calculated model and its parameters
are given in Fig 2.19
Thimons and Kissell (3) gave the following interpretation
of Fig 2.18:
"Approximately 50% of the air passing through these
cooling plants is recirculated" and "the individual
peaks most likely represent recirculation along
different paths."
These conclusions were obtained by the authors (3), in
part, by a correct consideration of the geometric series
\
42A
1,000
800-
.o Q.
a
600 -
I? (/> 400-
200
10 20 30 40 50 60 70 80 90 100 TIME FROM SF6 RELEASE, min
Fig 2.18: Response curve of Thimons and Kissell of a recirculating situation (3).
Y = 1/2 (DM)^ 0.021
T»l
V1
Fig 2.19: Calculated flow model for the response of Fig 2.18
43
(see Fig 2.11) and in part, by spurious reasoning, are
supported by the calculations based on dispersion
mechanics theory in Fig 2.19. It is also evident from Fig
2.19 that dispersion mechanics enables the recirculation
system involved to be specified quantitatively, but for
reasons noted earlier, only in relative terms in this
case. Nevertheless, this may still be considered useful
as it gives the ventilation engineer a good basis on
which to carry out rational improvements in the
ventilation system.
A true recirculation response obtained in ventilation
trials of a full-face Lovat tunnel boring machine (TBM)
and reported by Stokes an</stewart (7) is given in Fig
2.20. These workers used propane (CHD)) which was "pulse
injected" from a pressure bomb by a quick acting solenoid
valve. It is notable that Stokes and Stewart (7) treated
the 50% density difference between C H and air as "a
matter of concern" and went to elaborate lengths to test
conditions where the density effect would be
insignificant. It is clear from the foregoing quotation
that Stokes and Stewart (7) understood the need to employ
proper tracer substances. However, as with previous
investigators in the trials they did not analyse their
data in Fig 2.20 by the dispersion mechanics theory. If
this is done then the model corresponding to the tracer
response curve in Fig 2.2 0 is that shown in Fig 2.21.
43A
10
9
8
/
6
5
2 4 C 3
I
0
IHOECTION POINT * 1?
HEAD ROTATION : <l RPH
15 SECOHO PERIOD
1(1 00 00 100 120 140
EI-AP5E0-TIHE. 51HI.ETn/\CEIt RCtfASE (SECONDS)
160 100
Fig 2.20: Recirculation response curves of Stokes and Stewart (7).
T ^ 2/3 (D/uI^- 0.08
V=l
nr*
Fig 2.21: Calculated flow model for the response of Fig 2.20.
44
In Fig 2.21 an average value of D/uL is shown. This is
because D/uL of successive curves was not constant,
although it should be, but varied in the range 0.0041 to
0.0062. A possible explanation is that the curves in Fig
2.20 were not exact copies of the original. This
explanation is also supported by the fact that the second
and first pass, which was ignored in the calculation of
Fig 2.21, have the same Cwi„ value. MAX
2.5 SUMMARY
In summary, the use of tracer techniques to study aspects
of ventilation in mines has been shown to be possible.
The workers referred to above, have all been unanimous in
their conclusions that the method offers a possibility of
evaluating ventilation characteristics and phenomena that
cannot be done by traditional methods. Examples of these
were given by the USBM investigators (3-6), for both coal
and metal mines, and by Higgins and Shuttleworth (2) for
an NCB colliery. The latter investigators also concluded
that "if the time of release of the tracer has to be
limited, or there is significant longitudinal diffusion
the Pulse Release Method is preferable (to step input
methods)". It can also be added that the pulse release
method is more practical underground and is less prone to
noise masking.
45
Finally, none of the above investigators examined their
work in the light of Dispersion Mechanics theory. It is
not known why, at least in the later investigations, this
had not been attempted. As noted earlier, what appears to
have been the first attempt to do so had been done in a
small hydraulic model (26->28) . The details of the work
presented at the Illawarra Branch Symposium on Mine
Ventilation (9) and the Third International Mine
Ventilation Congress, Harrogate (1984) (10) generated
considerable interest amongst the delegates.
46
CHAPTER 3
EXPERIMENTAL INVESTIGATIONS
Trials were conducted on the release and detection of
tracer gas in the ventilating airflow underground at the
Elura Mine N.S.W. The following sections detail the
development of the experimental method used in the
conduct of trials.
The provisional methodology and measuring equipment were
tested prior to mine investigations. These tests were
designed to investigate and ensure that reliable results
could be obtained from equipment, and that it was robust
enough to withstand the underground environment.
The initial tests were conducted in the laboratory and
then on a larger scale rig prior to actual underground
measurements being made.
3.1 LABORATORY TESTS
Laboratory tests were conducted in the Department of
Civil and Mining Engineering laboratories at the
University of Wollongong. The principal purpose of the
laboratory tests was to determine a suitable tracer and a
suitable detection system for use in further experimental
work.
47
3.1.1 Tracer Selection and Detection
In Residence Time Distribution (RTD) studies it is a
requirement of the method (Sect 2.3.2) that the tracer
used has similar properties to the bulk gas. For
practical purposes it is also essential that the tracer
gas can be adequately injected and measured.
As noted in Sect 2.3.2, tracers used to date have not met
the first of these requirements.
A search of chemical literature (83) showed that the gas
which meets the above requirements for use in air is C H Z Z
(Acetylene).
Table 3.1 shows the properties of CH, and Air at STP. It
is obvious from this table that the properties of the two
gases are very similar.
TABLE 3.1 - PROPERTIES OF C R AND AIR 2 2
PROPERTY C H AIR 2 2
28.84
1.265
1.83
3.617
2.06
Molecular Weight
3
Density kg/m -5
Viscosity,kg/m.s(xl0 )
Molecular Diameter, nm
Molecular diffusivity,
m2/s (* 10~5)
26.05
1.163
1.79
4.232
1.73
48
Being a hydrocarbon a number of standard techniques are
available for C2H2 detection. These techniques include
gas chromatography, flame ionization methods, bi-metallic
powder and conductivity methods.
On the basis of cost, simplicity and sensitivity, as well
as its ability to be continuously measured, the
bi-metallic powder method was selected as being the most
practical technique.
3.1.2 Apparatus
The apparatus used consisted of the release and detection
equipment arranged as shown schematically in Fig 3.1.
Equipment used included:
Vacuum Pump Electrolux model number 81743. This pump was
used to draw atmosphere samples over the detector as
preliminary tests revealed that the through flow
resistance of the head was too high and measurements
were not reliable without suction assistance.
Chart Recorder - Houston Instruments OmniScribe. A two
(2) Channel recorder, with a 2 Volt full scale
48A
Overall Length 1600mm
Fan-y r Flow Streightener •Dia lfiOmm
H; Tracer input /
37 Cable
Suction Line
—
Chart Recorder
Fig 3.1: Line diagram of laboratory apparatus
49
maximum input and a maximum resolution of 1 mV full
scale. 23cm wide paper was used. The possible paper
speed ranges varied between 2.5 cm/hour and 25
cm/min.
Detector and Power Supply: The detector used was a Tandy
Moel BT, hand held bi-metallic breath alcohol
detector modified to suit continuous remote
recording. Figure 3.2 gives a circuit diagram of the
detector. Power supply to the head was provided by
using a 24 0V, 115Hz transformer stepping down to 3V
DC.
Physical connection to the vacuum pump was made by a
flexible suction line.
Input and output cables led, respectively, to the
power supply and the chart recorder.
Release System: The tracer gas (C2H2) was contained in a
pressurised cylinder at 12 0 bar. The gas was
released by momentarily opening the main feed valve
on the C H cylinder.
^
49A *'
Ext 6 V o —
..2757
6V
d>Dn -•ff 9 Test
$ 3.3k
XZ y
3.9k. •co .SO
o •X)
3.3k
# &
Dn VRH
( » - / M ^ /.©—
o> Teste?
c»-
5 6
•n p "J O 03
^
ru o
> VR1
4 10k
Fig 3.2: Circuit diagram of detector Tandy Electronics P/L.
50
3.1.3 Calibration of Equipment
All the equipment used during the course of the
experimental trials was calibrated to determine the
response from known inputs.
Vacuum Pump Calibration y
Figure 3.3 shows a plot of Pressure vs Flowrate for the
Electrolux Vacuum Pump. The plot was obtained
experimentally using a rotameter and pressure meter on
the inlet to the flexible vacuum line. The pressure
volume flow characteristics define the operation of the
unit.
To ensure effective response from the detector it was
found necessary to include a flow bypass. This was a
simple finger operated rotating collar over an opening in
the metal tube mounted on the rear of the detector (see
Fig 3.4).
Chart Recorder Calibration
The voltage response and the chart speed of the chart
recorder were calibrated.
50A
1.1 -
1.0 4
0.9 J
0.8 J
/~\
6 Q-X \s
(b L
0.7
0.6
0.5
3 0.4 in
L 0.3
Q_ 0.2
0.1
0.0 I I I I 1 I 1 I I I I I I I I 1 I I I I 1 I I M I I I I I I I I 1 1 1 I T T
0.0 1 0.1
I I I I I I I I I I I I I I I I I I 1 I I
0.2 0.3 0.4
Flowrate (n /sec)
Fig 3.3: Calibration curve of pressure vs volume for the vacuum pump.
50AA
-o o X o>
c o 2
Rotating Collar
To Vacuum Pump
J
Elevation (Not to Scale)
Fig 3.4: Rotating Collar flow control device
51
In the first instance known voltages were input into the
channel used for the detector. The response of the chart
recorder to these voltages was marked on the chart.
Table 3.2 gives a listing of the input and measured
voltages recorded during this test. To determine the
actual chart speed the chart was run for a known period
of time. This time period was determined by a stop watch.
Table 3.3 lists the speed settings tested and the
recorded time and distance values made during the
calibration trials. Averaged values taken from these
calibration trials were used in later interpretation of
results.
TABLE 3.2 - CHART RECORDER CALIBRATION RESULTS
INPUT VOLTAGE (Volts)
1 1 0.9 0.8 0.7 0.6 0.5 0.5 0.4 0.3 0.2 0.2 0.1 0.1 0.05 0.05
SENSITIVITY (Marked)
1 V 2 V 1 V 1 V 1 V 1 V 1 V 500 500 500 500 200 200 100 100 50
mV mV mV mV mV mV mV mV mV
MEASURED VOLTAGE (Volts)
Off Scale 1.05 0.93 0.84 0.75 0.61 0.51 0.49 0.405 0.295 0.198 0.195 0.103 Off Scale 0.049 0.049
52
TABLE 3.3 - CHART RECORDER SPEEDS
INDICATED CHART SPEED MEASURED CHART SPEED
2.5 cm/min 5.0 10.0 12.5 20.0 25.0
2.4 cm/min 4.85 9.71 12.47 19.42 23.78
Detector Calibration
The detector was calibrated by introducing known
concentrations of a tracer/air mixture into a mixing
container and using the head to sample this mixture.
Figure 3.5 shows the layout of the equipment employed.
The response of the detector was approximately linear.
Figure 3.6 shows a plot of the results of measured
concentration (ie. chart recorder response) vs actual
concentration.
3.1.4 Laboratory Method
The method of employing the release and detection
equipment, shown in Fig 3.1 was developed through
repeated trials.
52A
KEY
Electrical Cable
Gas Flow
Tracer
Supply
Air
Supply
Mixing
Chamber
Chart
Recorder
A
Monitoring
Head
A
To Vacuum
Pump
Fig 3.5 Diagram of the setup used for detector calibration
52AA
0
nt i j i in 1111111111111 ri) 1111rn 111 ri in 1111)1111 ri i'
100 200 300 400 500
Input Concentration (ppm)
Fig 3.6: Detector mV response vs concentration plot
53
The method developed required the sequential performance
of the following:
- Switching on power to the detector. It was required
that the detector be powered up some five to ten
minutes prior to the commencement of testing. This
period allowed the head to "warm up" to give
consistent results.
- Starting the vacuum pump, at a reduced flow rate. The
vacuum pump was operated at an optimum flow rate of
25 cm /s to ensure the optimum reading on the
detector head. Flow rates above this level generated
inconsistent results and below this level
insufficient sample is drawn over the detector. The
reduced flow rate was achieved by using the bypass
arrangement on the intake line to the pump.
- Zeroing the chart recorder. A desired zero line
position is set using the zero set knob on the chart
recorder.
Setting the required sensitivity on the chart
recorder. Using the sensitivity switch the required
range is selected. For most of the laboratory trials
a 1 Volt range was used.
54
- Starting the chart recorder paper. A chart speed is
selected and the chart started. Nominal speeds
employed in the laboratory trials were 20 and 25 cm
per minute.
- Releasing the tracer gas. A short "burst" of gas was
released into the mouth of the perspex pipe using
the main control valve (see Fig 3.1).
- Shutting down the system. Once the trace had been fully
recorded (ie. the chart pen returns to its zero set
position) the equipment can be shut down, or
additional trials conducted.
This method was developed to allow for the consistent
detection of C2H tracer gas. Pulses of the tracer pass
along the perspex pipe and are detected at the detector
head. The output curves produced by the tracer gas are
concentration-time plots suitable for later analysis.
Figure 3.7 shows a typical example of the actual response
curve during initial trials.
3.2 LARGE SCALE PROVING TESTS
These were conducted using lengths of 900mm diameter
"Spirex" ventilation ducting, a compressed air auxilliary
fan and CH2 injection and measurement equipment as
54A
1 1 — j — • - . - — - T J —
Pi'INTED INALISTRAl
Fig 3.7: Typical response curve obtained in laboratory tests.
54AA
Figs 3.8 and 3.9: Surface test rig and Tracer Input Devices
55
described in Sect 3.1. A line diagram of the equipment
employed is shown in Fig 3.8.
Pressure tappings were made in the ducting as shown in
Fig 3.8 and these were connected to water manometers.
These were used to both measure the pressure drop and the
flow rates. The latter were calibrated using velocity
readings obtained with an anemometer. To test the
behaviour of point injection and that of the injection
across the cross-section two different injection devices
were used as shown in Fig 3.9. The procedure consisted
typically of switching on the air fan and setting the
flowrate at a predetermined value obtained by reference
to the calibration results between manometer (M2)
readings and the corresponding flowrate.
After the tracer measuring equipment had been prepared
according to the procedure in Sect 3.1.4, then for both
injection modes, the on-off valve on the CH2 cylinder
was momentarily hand activated, to release the tracer
into the airstream.
The above procedure was repeated at different airflow
rates and again with other different lengths of ducting.
The different lengths were made up by simply butting the
ends together and wrapping the join with ducting tape.
A
56
The required lengths of the ducting were inserted between
the intake and exit lengths which always remained in
place as they contained the injection and the measuring
devices. An example of the response curves recorded on
the chart recorder in these trials is shown in Fig 3.10.
3.3 UNDERGROUND STUDIES
With the methodology of the system proved in the
laboratory and on the large scale rig, the next step
required the adaptation of the experimental system for
use in the underground environment. In all 192 separate
runs were made underground at the Elura Mine (11).
3.3.1 Test Sites
Two sites were selected for the underground proving
studies.
The first site for preliminary trials was the 4 Drill
level entrance access (Refer Figure 3.11).
The second site was on the 2/8 North cross cut on the 2
Drill level. (Refer Fig 3.12 for a detailed plan.)
The 4 Drill site was selected for the simplicity of the
network in the area, and the flowrate of the ventilating
56/*
.._!...
J ! !
I : •• I • I
;-i L..t">...
Fig 3.10 Typical Response curve obtained in the large test rig
56AA
Fig 3.11: Plan of 4 Drill level
5 6 AAA
KEY 9 ConTBjor Belt Regulator
Grid Una (50x60) Pillar outline
"^>- Stoired mullock •topping (n> Looatlon of Slta n
Fig 3.12: 2 Drill Plan with test sites marked
i.
57
air along the driveage. At the time of testing, the 4
Drill level was acting as an exhaust airway, taking
polluted air from the Crusher/Loading station to the
upcasting exploration shaft.
The exploration shaft was fitted with a CY1615 Richardson
fan, expelling 95 m/s to atmosphere.
Changes in the mine production schedule required the
movement of production development to the 4 Drill level.
Trials were then continued on the 2 Drill level.
The 2/8 North cross cut offered a similar layout to the
straight driveage tested on the 4 Drill level, with the
added advantage of a regulator positioned at the exhaust
end of the drive. The conveyor belt regulator (see Figure
3.12) could be opened or closed to increase or decrease
the flowrate along the driveage. Photographs showing
typical driveage sections at the test site are presented
in Fig 3.13.
3.3.2 Equipment Usage
The equipment employed in the previous trials was
modified to suit the underground environment through a
number of refining steps.
57A
Fig 3.13 (a): Line of Backs, 2/8 Cross Cut
Fig 3.13 (b): View along drive, 2/8 Cross Cut
i
58
Initial underground trials conducted on the 4 Drill level
showed very unstable results. This instability was most
probably due to a number of contributing factors.
The lack of shielding between the detector and the chart
recorder, the instability of the chart recorder position
(mounted in the rear of the mobile vehicle) and the
proximity of the power generator to the chart recorder,
were the most significant factors.
To overcome these problems the chart recorder was moved
to a position remote from the mobile generator, and
plastic sheathed cables run from the detector to the
recorder.
All of these changes were made with the change of the
testing site to the 2 Drill level. Additionally a 25
metre single phase extension lead was connected to the
mobile generator allowing the chart recorder and
monitoring head to be set remote from the generator.
The detector was fitted with an intake evase to improve
the percentage of the available area sampled by the head.
This modification improved the detection of released
pulses of tracer gas.
59
Power supplied by the mobile generator in the 2/8 cross
cut location (Fig 3.12) required the nearby parking of
the underground vehicle. In the final location, (the
Western Vent Shaft access on the 2 Drill level) where
most of the results were obtained, this was undesirable,
as the airflow was interrupted about the vehicle.
To ensure consistent supply, a power line was run from a
distant sub-station transformer to the test site. This
provision alleviated the airflow problem and the need to
park the vehicle so close to the site. 240V, 115Hz supply
at a maximum of 10 amps was provided by the supply line.
The release system for the tracer gas was modified
through the course of testing. Initial release of gas
underground was made through the partial filling of a 20
litre plastic bag which was rapidly squeezed to expel the
tracer into the ventilating air stream.
Problems caused by inconsistent times for complete
expulsion of the tracer were noted.
After further experimentation with various alternatives
the system was upgraded to incorporate the use of
balloons, 2.5 litre capacity, which were filled and
punctured to release the tracer gas (C2H2) into the
ventilating air stream.
60
All main underground tests were conducted using balloons
for the release of tracer.
An equipment list for the tests in their final form
is:
Service vehicle for transport of equipment and power
generation. A Toyota 2.2 litre Diesel 4x4 Landrover.
Lighting: Two 1000 Watt, 240V AC sealed beam lights
operated as required.
Release system: C2H2 pressurised container, 120 Bar with
balloon filling nozzle fitted to main valve system.
Chart Recorder, Vacuum Pump, 240/3 V Transformer and
Detector as used in laboratory trials.
Consumables; balloons, chart paper and additional C2H2
cylinders.
Use of this equipment is detailed in section 3.3.3.
3.3.3 Test Method
Through trials conducted at the locations, detailed in
Sect 3.3.1, the optimum method of conducting the release
and detection tests was determined.
\
61
Prior to the commencement of release and detection tests,
"traditional" measurements of the airflow were taken. An
annemometer traverse was conducted in the roadways being
tested to determine the flowrate and velocity. Wet and
Dry temperatures and an Aneroid Barometer reading were
also taken. A repeat of these readings was made every two
hours during, and at the completion of testing.
A sequential list of actions required during the conduct
of a single test, after "traditional" values were
obtained, would include:
1) Transport all the equipment to the required location
and connect the power line to the established
monitoring site from the generator in the vehicle
(not required after the installation of the power
line to the West Vent Shaft location on the 2 Drill
level.) and set up (Fig 3.14).
2) Warm up the chart recorder and detector, switching the
main power supply on some five to ten minutes before
the first release. At the same time the chart span
(Fig 3.15) is zeroed.
3) Mark out the release points. The release areas were
marked out using reflective spray paint to ensure a
consistent release position was used. This work was
61A
-ar 1 r K li-.
¥* •
^UtfftaaaaB kaa^^^3l
Fig 3.14: West Vent Shaft detection site.
v;
T
1
^ *#/A
m Fig 3.15: In situ zeroing of the chart recorder.
62
considerably more involved in locations where
previous velocity profiles had been made. (Refer
Sect 3.4.2)
Additional markouts were made to allow for the
conduct of successive tests during a single session.
4) Inflate the balloons with the tracer (Fig 3.16) using
the touch valve on the cylinder (Fig 3.17). A number
of tracer balloons were prepared and stored
downstream from the detector awaiting release.
5) Record the run number, chart speed, sensitivity and
traditional ventilation details on the chart.
6) Release tracer and start chart recorder. A stopwatch
system was employed. The procedure was to first
start the chart drive on the recorder then walk to
the release location, release the tracer (Fig 3.18)
and start the watch at the instant the tracer was
released.
Leaving time for the tracer to move to the detector,
the release operator would then move to the chart
recorder position. The paper feed would be halted at
62A
Fig 3.17: Close up of tilt valve
62AA
Fig 3.18: Balloon in position and ready for release.
63
a given watch time. The elapsed time was then
marked on the chart to give the time of release.
The above procedure was particularly convenient at
release locations out of direct sight of the chart
recorder station. However, the shortcoming of the
procedure was that often the chosen mV span was not
large enough to record the full response curve, so
many runs had to be repeated at other spans to
obtain the full curves.
7) Repeat trials could be conducted by repeating steps
4,5 and 6.
3.4 ADDITIONAL WORK
Beyond the development of the testing procedure some
additional analysis was undertaken. This work defined
some of the performance characteristics of
equipment/systems used in the underground tests.
3.4.1 Balloon Release Characteristics
The use of balloons as a method of releasing tracer gas
into the ventilating air stream was developed after
unsuccessfully trying the bottle release (after Thimons
63A
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xsxxxxxxxxxxxx: rxxxxrx: X ...t cu :.:;:;"": xxixlxix :x_ ffl :::::::::::::::.:.-:::::.„:::.c::.::_. £ . .. . ..r.....t .. ..-. .-- - -4-»
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. J.luxiiu;lT t;_. x n l .1 TX:. ..nil ill 11.11 xixlr tmll..-.U . .11 Itlxi Fig 3.19: Recorder tracer of (a) balloon release and
(b) plastic bag release.
64
and Kisell (3)) and a plastic bag method referred to in
Sect 3.3.2.
A clear comparison of plastic bag and the balloon methods
of pulse release can be seen between the output traces
shown in Fig 3.19. These tests were made with a release
of gas from the same distance from the detector using the
two different methods. As can be seen from Fig 3.19, the
balloon release method shows a consistent rapid rise to
the maximum followed by a steady drop in concentration
after the maximum, whereas the response from the "plastic
bag" release shows a "bi-modal" response, the first peak
being due to irregular release.
To improve the clarity of interpretation of RTD results
it is desirable to have a consistent and reproducible
pulse shape. This was achieved using balloons.
Physical observation of the release characteristics of
the balloons was also made.
Balloons were partially filled with talcum powder prior
to the introduction of tracer. Agitating the balloons
prior to puncture ensured that the powder was "well
mixed" with the tracer gas. The balloon was then
punctured and the movement of the powder observed.
65
For any puncture position on the surface of the balloon
the tracer/powder appeared to form an ellipsoid along the
diameter punctured. Figure 3.20 shows a photograph of the
spread directly after the balloon was punctured.
Figures 3.21 and 3.22 are photographs from a series of
balloons burst in the same manner. For this sequence
photos were taken at differing distances from the burst
position.
Figure 3.23 shows a diagram of the ellipsoid formation
and movement during the conduct of a test.
The talcum powder "falls out" of suspension reasonably
quickly, but indications during the period where it was
well mixed with the tracer suggested that the air flow
may be laterally discrete.
3.4.2 Detector Evase
The final evase design shown in Fig 3.24 on site and
depicted in Fig 3.25, was the result of a number of test
runs on inlet shapes for the unit.
Initial trials on the 4 Drill level were conducted using
the head without any inlet control as was the case in
laboratory and large scale tests where the detector
k
65A
Fig 3.20: Balloon burst from below.
Fig 3-21: Balloon burst from below - 1 metre downstream
65AA
Fig 3.22: Balloon burst from below - 5 metres downstream.
1) Before buret 2) After buret
3) 6 metree from buret 4) 10 metree from buret
Fig 3.23: Diagram of observed tracer spread.
6 5 AAA
Fig 3.24: Cone evase on site in WVS regulator.
900
$ 375mm
pf 150mm
Elevation End Elevation
Fig 3.25: Evase Detail
66
performed well as such. In the underground situation,
however, this resulted in a poor relationship between
pulses released and detected.
Tests conducted in the 2/8 cross cut used a "box" evase1,
detailed in Fig 3.26. This system proved quite adeguate
in the relatively low flow rates (linear velocity less
than 1.0 m/s) along the 2/8 cross cut.
However, with a change of location to the West Vent Shaft
(WVS) position it was necessary to develop the final
system to overcome stability problems in the very high
flow velocities (up to 20.0 m/s). To this end, the mild
steel, rubber lined conical shape evase (Fig 3.24) was
employed. The weight and shape of this unit ensured its
stability and performance in the flow rates experienced
at the site.
3.4.3 2 Drill West Vent Shaft Monitor Position
A number of "lost pulses" (ie. tracer release trials
which were not detected at the detector) occuring in the
2/8 trials when the detector was located in the 2/8
drive, proved problematical.
66A
Elevation End Elevation
Fig 3.26: Box evas L
67
To overcome these problems a series of tests were
conducted with the monitoring head mounted in the
regulator in the access to the Western Vent Shaft of the
2 Drill level. Figure 3.27 shows a dimensioned drawing of
the head in the location with an inlet evase attached.
The size and shape of the inlet evase ensured that a much
greater percentage of the effective roadway area was
sampled. Previously tests had been dependent on the
detection by using a non-streamlined sampling head,
comprising 3% of the cross sectional area.
Tests made during the early portion of this testing
period showed a more consistent appearance at the
detector, with 7 from 9 pulses being recorded.
It was noted during testing that the release point of the
tracer had a considerable effect on the extent of
detection of the tracer gas.
Carrying on from the first successful trials with power
supplied from the sub-station line trials 55 to 64 were
conducted. Only one pulse was recorded from ten releases.
The only notable difference between the trials 46-54 and
55-64 was in the position of release.
67A
Elevation - Looking West (NTS)
Fig 3.27: Detector position, WVS
68
Figure 3.28 shows an expanded plan view of the area, with
the release positions marked. The positions on this plan
which were detected by the detector all coincided with a
similar position to that in which the monitor head was
located in the West Vent Shaft access.
3.4.4 Lateral Position Detection Trials
A series of trials were developed and conducted to define
the performance of the flowing air.
These trials involved a two part analysis of the flowing
air. Traditional analysis requires the use of an
anemometer traverse to provide an average flow velocity
value for a given driveage. To generate a closer focus
analysis of the airflow a velocity profile measurement
technique was developed, as discussed below.
A more defined positional release of tracer gas, at sites
for which the velocity profile was known was indicated.
The technique adopted for this work is also discussed
below.
z 68A
Western Perimeter Drive Western Vent Shaft Release Point WPD Kink (e) - 2/6 int WPD 10 metre position 2/5 intersection WPD 2/4 intersection WPD
Fig 3.28: Expanded plan view of WVS area.
69
Velocity Flow Profiles
Figure 3.29 gives a plan layout of the 2 Drill level
showing the positions selected for cross sectional
velocity profile measurements.
The technique employed to measure the profile was as
follows:
- Mark the site using paint on the walls, floor and roof
to define the correct grid, using proportional
spacing. Positions 1-4 in both horizontal and
vertical directions were marked.
Conduct an anemometer (Vane style) traverse to
determine the "traditional" velocity.
- Locate the anemometer at each of the grid positions and
determine the flow velocity at this point. Repeat to
the completion of all the grid positions at the
site.
Analysis of the results is given in Chapter 4.0.
69A
Z
Scale 1:100
Fig 3.29: Expanded plan view of WVS area with sites marked.
70
Positional Tracer Gas Release
Trials 65 to 87 were conducted to determine the
performance of the flow using positional release.
Subsequently this method was adopted as a standard in all
trials.
Figure 3.30 shows a view of the release site looking
upstream, with the node numbers indicated.
A consistent relationship appeared to exist between
release point and detection level. It should be noted
that a consistent release was provided by initiating
rupture at the base of the balloon.
The practice of thoroughly marking sites, and testing at
a range of node positions was continued throughout the
remainder of the underground experimental work.
3.5 TREATMENT OF DATA
The response curves from the chart recorder were
digitized to form a computer data file. This file was
modified using an IMSL (84) online routine, RECSPL, which
fits a spline relationship to a two dimensional array.
The resultant E. vs t curves were then plotted out. These
are given in Appendix 1.
7 0 A
KEY
* Tracer Release point ___ Tunnel boundary
Grid Line
X 1 2 3 4
Elevation - Looking Into Flow
Fig 3.30: Tracer release points across drive section.
71
Using the digitized form of the data, the mean time (t) 2
and the variance (o- ) were calculated for each curve
according to the discrete form of their equation, viz:
t = t > t.E.At. £ 1 1 1
S E.At. /! l l
(3.1)
I t2iEiAti
1 EiAti
2 •*- -2
a = — t (3.2)
— 2
Using the values of t and & , so calculated for each
curve the dispersion number (D/uL) was then calculated by
eqn (2.45)
Care was taken to ensure that the resultant values
conformed to the limits of the validity of the dispersion
model. For this purpose both the values of the calculated
D/uL and the shape of the actual curve were examined.
If the calculated D/uL is greater than unity, the
assumption of the dispersion model breaks down (69).
However, even with D/uL < 1, if the shape of the curve is
either multimodal or the curve has a very long tail then
the dispersion model of Sect 2.3.1 cannot be used.
Instead, a multi-parameter model was applied or, for long
tailed curves a graphical calculation was adopted which
72
is not critically sensitive to long tails. The graphical
calculation is based on the properties of normal curves,
where 68% of the total area under the curve is located
one standard deviation from the mean as shown in Fig
3.31.
It is obvious from Fig 3.31 that if the mean is taken as
occuring at the peak value of the curve then the 68% area
criterion would clearly not be too sensitive to the tail.
It should be noted, that the graphical calculation
outlined above would lead to some inaccuracies in the
D/uL values. Nevertheless, the results of graphical
calculation may be considered to be good approximations
of the main flow reality, since the presence of long
tails would not be the principal feature (dispersion
characteristic)of that flow. Extended tails in otherwise
reasonably normal response curves are caused by some of
the fluid being held back. This can occur by adsorption,
or by tracer being trapped within pores or, more likely
in mine roadways, by being held up in the many
semi-stagnant pockets (See Fig 3.13).
72A
•'e, max
JS, Inl
¥- = 0.000625 ut,
Fig 3.31: Relationship between D/uL and the dimensionless E curve (C~) for small extents of dispersion, after
Levenspiel (69).
73
CHAPTER 4
RESULTS AND DISCUSSIONS
4.1 LABORATORY TESTS
The primary aim of these tests was to prove the
suitability of the tracer measuring apparatus (Sect
3.1.2) to detect and record small concentrations of
C2H2-air mixtures. As was shown earlier (Fig 3.6) the
detector-recorder possessed the reguired sensitivity and
linearity.
In addition to the above tests a series of runs were made
with the perspex pipe assembly (Fig 3.1) to obtain data
at different flow velocities for comparison with those
expected from theory (Sect 2.3.1). The experimental
results are given in Appendix 2, Table A.l and the
results of the calculations are shown here in Figs 4.1
and 4.2.
It should be noted that the small scale of the system
(Fig 3.1) restricted the velocity range that could be
used since the response time of the chart recorder was a 4
limiting factor. Hence K > 2 x 10 could not be used.
Also, since flow at K < 5 x 10 was not the main interest
in this study, tests were not conducted below this
Reynolds' number.
73A
1.0 1.5
Velocity (m/e) 2.0
Fig 4.1: Mean Time vs Velocity.
4x10^ 6 7 89 1x10* 2
R 3 4 5x10
Fig 4.2: D/ud vs Reynolds' Number,
74
In tracer studies, the first check of the system
performance is the conformity of the mean times between
measurement and theory (eqn (2.9)). The results in Fig
4.1 show that the observed relationship between t and u
closely agrees with theory, except for reasons noted
earlier, at the highest flow rate used (35 l/s).
2
Next using the o values, calculated from the response
curves, an example of which has been given in Fig 3.7, by
eqn (3.2), dispersion numbers (D/uL) were calculated (eqn
(2.45)), and then using eqn (2.50), values of D/ud were
extracted and plotted against 03 in Fig 4.2.
Comparing the results in Fig 4.2 with the published data
in Fig 2.8 it is obvious that agreement is very good. In
fact, good agreement of the data is not surprising since
the flow system used was for all purposes an ideal
system, viz a smooth pipe of constant diameter.
This ideality is further supported by the observed
relationship between variance and the flow velocity in
Fig 4.3. The slope of the line of best fit in Fig 4.3 is
very close to -3.0 which is the relationship predicted by
theory (eqn (2.53)).
74A
i nun .1 LO 10.0 100.
Velocity (m/s)
Fig 4.3: Plot of Variance vs Velocity Laboratory Results
75
4.2 LARGE TEST RIG RESULTS
As was the case in the work of Higgins and Shuttleworth
(2) , the aim of these tests was to examine the behaviour
of the technique in a large scale rig before taking the
technique underground. In fact, the duct assembly used
(Fig 3.8) parallelled the design employed by the above
authors.
The experimental results are given in Appendix 2, Tables
A2 and A3, respectively for cross-sectional and for point
injection. Figure 4.4 gives the measured mean times,
obtained from the tracer response curves by eqn (3.1), as
a function of the measured flow velocity. It is obvious
from Fig 4.4 that the results satisfactorily follow
theory. However, it is also clear from Fig 4.4 that the
mean times for point injection are, on average, slightly
higher than those for cross-sectional injection.
2
An examination of the measured o> values in Tables A2 and
A3 (Appendix 2) clearly indicates that these are higher
for point injection than for cross-sectional injection.
By way of illustration of differences involved Fig 4.5
2
shows a plot of c/ vs u for the case of L = 10m.
75A _ y
J m
o
1.0
0.9
0.8
0.7
0.4 _
P 0.6
3 0.5
A •o m
£ 0.3 1 0.2
0.1
0.0
£
® - Cron-Motlonal InJroUoa
X - Point toJsoUon
1 I ' I ' I ' I • I ' I ' I ' I ' I ' I 0 1 2 3 4 5 6 7 8 9 10
Velocity (m/s)
Fig 4.4: Mean Time vs Velocity for Large Tests Rig
LO 10.0 100.
Velocity Cn/s)
Fig 4.5: Log-Log plot of Variance vs Velocity, Large Test Rig Data
76
It is interesting to note that in addition to the
difference of the variances between the two injection
systems the relationship between cf and u is not quite
that expected from theory as was the case in the
laboratory tests (Sect 4.1) In this case (Fig 4.5) 2-2.5 2-3
o ck u rather than & & u. predicted by theory.
The larger variances in the case of point injection are
almost certainly caused by initial variance of the input
pulse. This is supported by the physical considerations
of the injection device which would inevitably impart a
lateral spread to the tracer on injection. In the case of
cross-sectional injection with the design of the injector
used and its position in the pipe (Fig 3.9), this initial
spreading of the tracer cannot occur.
Using eqn (2.48) the extent of this initial spread of the
tracer is estimated to have contributed a variation of
about 20. % to the total variance. From the view point of
the intensity of dispersion (D/ud) the two sets of data
(in Tables A2 and A3) are correlated for K > 10 by:
D/ud = 0.25 - 9.2xlO~aR (r*=0.87) (4.1)
for cross-sectional injection and
D/ud = 0.29 - 9.2xlO~aR (r2=0.81) (4.2)
for point injection.
77
In other words, the spread of the initial pulse with
point injection is equivalent to an increase of almost
10% in the measured intensity of dispersion of the flow.
It should be noted that this difference does not mean
that the main flow is more dispersed. The dispersion of
the flow remains the same - the difference is simply that
due to the difference of the injection method (Sect
2.3.3). After all, why should the way the tracer is
introduced change the flow pattern of the fluid if
everything else remains constant?
With regard to the observed proportionality of c with
u , rather than with u as predicted by theory, the
most likely explanation is the non-ideality of the piping
system used. This is supported by noting that in
non-circular tubes and channels it has been found (69)
that the dispersion coefficient (D) is affected by the
flow parameters to a slightly different extent than for
the ideal case given by eqn (2.41).
Additionally, a similar situation pertains also to head
losses in industrial flow systems. Thus, according to eqn 2
(2.2) Ap oi u , but this proportionality is seldom
observed in practice. It is more common to observe Ap a
1. <s-±. &
u . In the present case the head loss (Tables A2
and A3) have been found to be proportional to u as is
78
evident from the plot of the experimental results in Fig
4.6.
Finally, it is useful to give the range of the dispersion
coefficient values for the ducting system used. From eqn
(2.45) for L = 10m, D = 0.286 m2/s at the low velocity
(1.3m/s) and D = 1.604 m2/s at the high velocity
(6.8m/s). It is also pleasing to note that the dispersion
coefficients are in almost the same ratio as their
respective velocities and that this is in line with
theory (Sect 2.3.1). Additionally, the constancy of the
D/uL values for L = constant, evident in Tables A2 and
A3, is also in line with theory (Sect 2.3.1).
4.3 UNDERGROUND TESTS
Having established from the results of the large test rig
that the tracer injection and measurement technique was
satisfactory, preliminary underground tests were
commenced at the 4 Drill site. As the large test rig
results have shown that there was no difference between
cross-sectional and point injection techniques if the
initial variance of the latter was accounted for, the
point injection technique was adopted underground.
An additional advantage of this technique was that it
also made a one man operation possible.
78A
o
100.0 _
o h-
s = ,3 < 1.0
.1
—
M^WB
'm^m}
—
~ r
M
zz I
~i nun
o , ©/
(0/
Ik/TO
i n u n
K<ry
6> Test I
A - Test 2^
IIIIIII Mini! .1 1.0 10.0 100.0
U (m/s) - Velocity
Fig 4.6: Head Loss vs Velocity (log-log), Large Test Rig
79
Initial results at the 4 Drill level could best be
described as a failure of the support equipment as
detailed in Sect 3.3.1. The first successful results in
obtaining tracer response curves were at the 2/8 cross
cut on the 2 Drill level.
4.3.1 2/8 Cross-cut Tests
The results of tests 1=»64 conducted in the 2/8 cross cut
(Fig 3.12)are detailed in Appendix 1. By inspection of
the results in Appendix 1 the most obvious common feature
of the response curves obtained is their irregular
appearance. This contrasts quite sharply with the
response curves obtained in the laboratory and large
tests rig (Figs 3.7 and 3.10), but parallels the
underground results of other workers (Sect 2.4 and Figs
2.14, 2.17 and 2.18).
It should also be noted that the NCB (2) and the USBM
(3-6) results were obtained by analysing tracer
concentration in air samples, taken at discrete time
intervals following release.
In the present work tracer concentration was recorded
continuously, thus, all changes, both small and large,
were recorded, making the irregularities of the response
80
curves even more exaggerated than would be the case with
discrete sampling.
Following the laboratory and the large test rig data
analysis procedure, results were first checked to ensure
consistency of the mean times. Figure 4.7 gives the plot
of the experimental mean times vs distance between
release and measuring points for three different air flow
rates (as determined from an anemometer traverse or smoke
tube release and detection). The flow rates were varied
by adjusting the regulator at the Western end of the 2/8
drive (Sect 3.3.2).
It is evident from the results in Fig 4.7 that the mean
times are reasonably linear with distance for each test
series. The slope of the t vs L line is the average flow
velocity and these velocities are compared in Table 4.1
with those obtained by the traditional techniques
referred to above.
Table 4.1 - Results of Air Velocities (m/s) Measured by
Two Measurement Techniques
Traditional
0.25 0.45 0.84
Tracer
0.375 0.551 0.825
80A
60 -a P
50 -=
40 T . n
I 30 ~
20 ~
10 -=
0 l'i 1 | I I I I I I I I T | I I I I I J I I I | I I I I I J I I I | 1 1 I I I
10 20 30 40
Distance (m)
Fig 4.7: Plot of Mean Time vs Distance; Large Test Rig
81
The results in Table 4.1 show that the two techniques are
in reasonable agreement at the higher velocities but not
at the low velocities. The error at the lower velocities
is almost certainly in the traditional method since it is
well known in practice that traditional measurements of
low velocities are notoriously (60) unreliable.
With regard to the measurement of low air velocities it
is of interest to note that Higgins and Shuttleworth (2)
concluded from their tracer work that "The tracer
technique is especially valuable in the measurement of
small quantities of air where the velocities are too low
to be measured by vane anemometers".
Next a comparison of variances (Table A4) is shown
graphically in Fig 4.8. By inspection of Fig 4.8 it is
evident that although widely scattered, the results do
show a definite trend, both with respect to distance and
with respect to the flow velocity, but only when the
latter results for L > 15m are considered.
Before the results are analysed it is necessary to
establish which of the flow models in Sect 2.3 may be
involved. Inspection of the actual response curves shows
that apart from a few, obviously irregular shaped curves
and the true bi-modal response of Test 22, the responses
81A
Q- T « + Ser.es
O- Test SeKes
0
r W l i i u | u i 11 m i| 11 n 11111 | rr
10 20 30
Distance (m)
rr\ r i 111 40
Fig 4.8: Variance vs Distance; Large Test Rig
82
are of the kind that might be expected from a dispersion
model.
The dispersion model predicts (eqn (2.53)) that c/2 cx L , _ 2 3
and also c, a i/u . Figure 4.8 shows that for a constant
flow velocity the variance increases linearly with
distance. So, in this respect the results agree with
theory. However, this increase is not what it should be
for the results at the high velocity (u = 0.825 m/s).
Since reproducibility of the results could be considered
satisfactory (Table A4) it can be concluded that the
reason for the anomalous behaviour is connected in some
way with the actual flow pattern rather than with a
system malfunction. The effect of the flow velocity on
variance changes is also anomalous, not only for the
short distances (L < 15m), which is obvious from Fig 4.8,
but also for the larger distances, where variance is
inversely proportional only to u, and not to u as
predicted by theory. This difference may have been caused
by the non-ideality of the roadway.
Although the latter explanation was reasonable, and also
supported by literature findings, for the difference in
the velocity effect observed in the large test rig
results (Sect 4.2), the difference involved here is very
83
much greater for the same reasoning to be sustainable.
Unfortunately no data are available in the literature
that may confirm or negate such a possibility, and
research into this aspect of dispersion mechanics is
clearly indicated.
Table A4 includes the calculated values of the dispersion
number and the intensity of dispersion calculated by eqn
(2.50) using the equivalent diameter of the actual
roadway in the d/L term. Because the latter results are
an order of magnitude different from those expected (Fig
2.8) a reverse calculation was performed.
In this case the value of 0.22 corresponding to 03=10 was
used for D/ud (Fig 2.8). Then with the known L and D/uL,
independently calculated from the measured variances, the
values of d were obtained. By inspection of the results
in Table A4 the range of d values lies between 0.01 and
1.2m, with a tendency for an increase in d with the flow
velocity.
Since the diameter so calculated is much smaller than the
actual diameter of the roadway (d=4.95m) then these
diameters may be interpreted as those characterising some
"flow tubes" in the main airways. To investigate this
phenomenon the test site was transferred to the West Vent
84
Shaft area. The objective there was to measure much
larger cross-sectional area of the flow as the air
converges at the regulator.
4.3.2 West Vent Shaft: Preliminary Tests
The response curves of tests 46=*64 (Appendix 1) describe
the early results of the tests. Tests 46=^54 that were
detected with the box evase gave noisy responses
(Appendix 4) for which the cause was established as being
the "flapping" of the box in the high velocity airstream
at the detection position. The box was removed and tests
55 to 64 were then carried out with the detector head
alone, as was done previously in the large test rig with
good results. However, since only test 58 was detected,
it was felt that a large number of resultant "lost
pulses" made the use of an evase necessary. Subsequent
tests therefore employed the evase described in Fig 3.27.
The question that has to be addressed next is: should the
results obtained under the above conditions be analysed
at all or should they be scrapped altogether?
The answer to this question should rely on establishing
validity of the measurement, ie. deciding that what is
being measured does in fact represent the characteristics
of the flow that actually exist in the roadways.
85
Elementary considerations show that if the testing
equipment is reliable - and this was proved so earlier
(Sects 4.1 and 4.2) - then the response curve is
diagnostic of the features of the flow. As the general
shape of the curves (Appendix 1) is indicative of
dispersed flow with superimposed patterns of Fig 2.9 then
the dispersion model may be used with the only limiting
conditions being those of the model itself (Sect 2.3.1).
The fact that at the injection point the cross-sectional
area is much larger than at the measurement point, and
the air velocities are an order of magnitude different,
does not in any way invalidate the dispersion model and
its mathematics. The proof of this assertion follows
directly from eqn (2.43) and its result in eqn (2.45) and
also eqn (2.53). A non-mathematical explanation is to
consider the behaviour of an ideal plug flow vessel such
as depicted in Fig 4.9. Since ideal plug flow is always
ideal then a pulse injected at the entrance will appear
unchanged in no way at the exit, no matter if the flow
speeds up, slows down, converges or diverges during its
passage.
Table 4.2 summarises the particulars of tests 44=»64, and
Fig 4.10 shows the location plan in more detail with
positions of the test release points and detector marked.
85A
Response
Input Pulse
Fig. 4.9: Tracer Response in an Ideal Plug Flow Vessel
2/4 x WPD
2/5 xT .WPD
1
Kink >> MWP
\ A Detector
Fig. 4.10: Expanded view of WVS Release points
86
Table 4.2 Particulars of Tests 46= 64
Location
WPD Kink
2/5XWPD
2/4XWPD
2/5XEPD
Mid WPD
L (m)
10
22
51
350
6
Test No.
46,47*,52,59,60
48^49^55,56/57
50^54,62,63
51,53.64 * *
58,61
Comments
Long Tail
Bi-Modal
Tri-Modal
Lost Pulses
Normal
Velocity
2.1
0.8
0.4
0.7
1.3
NOTE: nn, indicates a detected pulse rm indicates a pulse released toward the detector
without the box evase Velocities indicated are at point of release
The analysis of the result of tests in Table 4.2,
follows.
At the WPD Kink the response shows . a long tail,
indicating that some air is slow moving. From the
physical situation in Fig 4.10, some flow from the WPD
Kink to the regulator via the Northern wall may be
expected, and this was picked up by the detector in the
form of the long tail. Ignoring the tail, the
characteristics of the main flow are calculated (Sect
3.5 and eqn 2.45) as:
t = 12.6 s o"2 = 29.1 s2
u = 0.8 m/s D/uL = 0.096 D/ud =0.2
87
The above results are most reasonable and consistent with
the physical reality in Fig 4.10. The calculated
dispersion coefficient is 0.77 m2/s which is slightly
more than double the value of 0.286 m2/s in the large
test rig for similar conditions. This is also reasonable
since increased dispersion activity can almost certainly
be expected in the underground environment of the test
site.
2/5 x WPD - The two response curves are considered to be
a satisfactory duplication of results for what must be
considered a potentially unstable flow region. The
bi-modal nature of the response suggests branching flow
in an approximately 60:40 split. Using the procedure in
Sects 2.3.2 and 3.5 the following results are obtained:
TEST 48: t = 43 s — — — ^
tL = 61 s 2
TEST 49: t = 48 s ^ — — — — • ^
tL = 68 s 2
Since variances were obtained by approximate graphical
separation techniques they are only reasonable estimates
and therefore not suitable for further calculations. This
explains the absence of dispersion parameters in the
above list.
2 2
c = 26 S I
2 2
& „ = 35 S 2
2 2
«y = 55 s i
2 2
88
However, the available results show that in both cases
— — 2 2
t±/t2=1.4 and o'i/©2=1.4. This again confirms satisfactory
duplication of results.
The calculated mean flow velocity in the main path
(L=22m) is 0.48 m/s and the length of the second path is
31m (ie 1.4 x 22 = 31m) assuming that the increased time
(t ) is due to the longer distance and not to any
velocity reduction. In all likelyhood, both effects are
involved and this would be more consistent with the
physical situation shown in Fig 4.10.
2/4 x WPD: The response curve suggests that the flow
takes three different paths which is a distinct
possibility from the geometry of the area (Fig 4.10) and
the very low anemometer velocity measured at the release
point (Table 4.2). The calculated parameters are:
Volume of flow regions 30:50:20 (approx.)
tL = 118 s vz = 28 s2
i I
t = 136 s cf\ = 42 s2
2 2
t = 160 s vZ = 65 s2
The explanation here parallels that given earlier for the
2/5 cross cut response. However, the third peak suggests
that the third path was that of a slow flow along the
89
wall possibly the Northern side wall. An estimate (from
mean times) of the distances involved is
L± = 51 m L2 = 59 m Lg = 69 m
The above results appear reasonable and the flow paths
suggested by the results are not impossible for the
physical area (and network) being considered.
Mid WPD The two duplicate response curves are for all
practical purposes identical. The differences between the
two responses are minimal and are caused by the normal
variations in the flow due to nearby mining activity as
demonstrated by Higgins and Shuttleworth's results (2) in
Fig 2.13. The calculated parameters of the two response
curves are:
ii = 1.18 m/s
D = 0.216 m /s
u = 1.17 m/s
D/uL = 0.024 d = 0.7 m D = 0.158 m2/s
The calculated velocity is in reasonable agreement with
that measured by the anemometer (cf 1.3 m/s Table 4.2).
Because the release distance was short, the calculated
intensity of dispersion was low (=0.03) but the "flow
TEST 58:
TEST 59:
t = 5.08 S
D/uL = 0.029
t = 5.12 s
2 2
& = 1.5 s
d = 0.9 m
2 2 <y = i.l s
90
tube" diameter of =*0.8m is in line with the 2/8 cross cut
results (Sect 4.3.1).
Likewise, the values of the dispersion coefficient are in
line with those obtained in the large test rig (Sect 4.2)
and are about one-third of those calculated from the
results of WPD Kink response curves given in this
section. The reasons given there for the difference in
the values of the dispersion coefficients apply here
without modification.
2/5 x EPD this test gave a "lost pulse" result, which
can be readily explained by the fact that the distance
involved was 350m and the dilution of the tracer was such
that the final concentration was below the sensitivity
level of the detector. However, there were other releases
much closer-bye (Table 4.2) which also gave "lost pulse"
results. The only possible explanation for these is that
the signal travelled outside the detector head or its box
evase.
This was actually proved by chance when one of the
balloons, prepared for a test at one of the release
positions, burst at the same time as the operator was
adjusting the span of the recorder. In the event, the
arrival of the C2H2 was detected by smell but not
91
recorded by the detector. However, when a burst of
C2H2 was released in front of the detector head the pulse
was recorded immediately. This chance occurence,
indicated a "layering" phenomenon and as this was
something unexpected a different plan of tests was
initiated and results are described in the next section.
4.3.3 West Vent Shaft - Positional Release
These tests were conducted at five different sites as
shown in Fig 4.10 with systematic tracer releases at
points over the site cross section as detailed by the
coordinate view in Fig 3.30. The measurement equipment
and procedure used were as given in Sect 3.3.3 using the
final design evase (Fig 3.24).
Unfortunately, standard balloon releases at Site 5 could
not be detected because the final concentration of the
tracer was again below the sensitivity level of the
detector. In other words, the same problem was
experienced here as that encountered with the test at the
2/5 cross cut-Eastern Perimeter Drive intersection
release described in Sect 4.3.2. Although the detection
of positional releases failed, a cross-sectional release,
to be described later, was successful.
92
The response curves obtained in the Site 1 - 4 tests are
given in Appendix 1 and Tables A5-A8 in Appendix 2 give
the results obtained.
An examination of the response curves 65=^191 (Appendix 1)
indicates that overall the curves are indicative of
dispersed flow. There are some anomalies to this and a
number of "noisy" responses. Considering that the tests
were made over a period of time with different levels of
mining activity occuring, differences in the results are
not only inevitable but what may be more important is
that they have to be considered normal behaviour.
Table A5 (Appendix 2) gives the Site 1 results which
include the calculated dispersion parameters and
velocities in addition to the measured t and &z. The
initial detector head position (Tests 65-»78) was central
(see Fig 3.24) and this resulted in a number of lost
pulses from certain release positions. As this result,
also observed earlier (Table 4.2), indicated "layering"
flow further releases were made with the detector head
located at various positions other than central in the
regulator, eg left, right and centre-up.
As shown in Table A5, a release from every grid
coordinate was detected if the head was in the
93
appropriate position. This result, therefore, provides
strong evidence that the air flow (at Site 1) is layered
or segregated. Inspection of the last column (d ) in calc
Table A5 gives an approximate indication of diameters
characterising the dimensions of the "flow tubes". By
inspection of the calculated values there are some
anomalies, viz some values exceed the measured diameter
of the roadway at Site 1 of 4.87m.
The reason is most probably associated with an
instability of air flow at some test times caused by
events of short duration such as fan surges, ore dumps,
stope rills, upcast shaft water curtain
formation/release,truck haulage and so forth. Because
such events may be expected to have a much greater effect
on the variance compared with mean time (eqns (2.53) and
(2.23)) then large variations in d 1 are inevitable. caic
This is because the magnitude of variance strongly
influences D/uL from which d is calculated by eqn (2.50)
with constant D/ud taken as before, equal to 0.22 for
K > 105.
— 2
The above explanation is supported by comparing t and o
for a duplicated result, eg:
94
Position 3,1
Curve 67 91 94
Position 3,2
Curve 92 95
Position 3,4
Curve 111 112
Position 4,2
Curve 79 80
Date
9.8.86 21.8.86 21.8.86
Date
21.8.86 21.8.86
Date
21.8.86 21.8.86
Date
15.8.86 15.8.86
t
13.5 9.5 9.2
t
8.2 10.8
t
18.6 19.1
t
7.16 8.4
2
a 21.83 1.41 0.04
2
0.17 8.40
2
a
26.29 112.36
2
8.47 0.06
d
6.26 0.82 0.03
d
0.13 3.76
d
3.97 16.10
d
8.78 0.04
It is clear from the above results for position 3,1 that
mean times can also be different on different days when
as far as it could be ascertained there were no
significant changes in the mine operation.
Additional evidence for the existence of transient
changes and flow instabilities, referred to above, is
provided by the observed results in all tests that a
consistently detected release position may once in a
consecutive number of releases report as a "lost pulse".
It should be noted that a single test number in all
underground tracer tests sometimes represents 5 or 6
consecutive individual releases because of "off chart"
95
recording (see Section 3.3.3). So when the chart span was
correctly adjusted for an "on-chart" recording to then
have a "lost pulse" was more than an annoying experience.
Because of the above transient effects and the normal
differences in the flow of the ventilating air, referred
to earlier and also noted by other investigators (2-6) in
their tracer work, the guestion of the reproducibility of
the results should always be borne in mind. In tracer
work the most sensitive reproducibility test is the
reproducibility of the mean times. If these are not
reasonably reproducible then the validity of the tests
must be regarded at best as questionable and at worst as
useless.
On this basis, the reproducibility of the present results
have a maximum relative error of 31,7% (Position 3,2 Site
1) and a minimum relative error of 3.2%. Since most
duplications have been well below the maximum error of
31.7%, it is therefore considered that the reproducibility
of the results is reasonable.
2
As far as the differences in ct r and hence d, are
concerned, it is considered that they still provide
reasonable relativity. In other words, a "flow tube" with
a low d , value may be expected to be smaller in extent
than a "flow tube" with a large d -. value.
96
A final estimate of difference from Site 1 t and ctz data
in Table A5 that can be made is to pool all the t and ct
values to obtain a grand mean time and a mean variance to
calculate the diameter of the roadway.
The calculating procedure is equivalent to considering
that a single cross sectional release gave the mean time
and variance used in calculations. The result is:
t = 13.1s and ct = 10.3 s
Then, combining eqns (2.50) and (2.58) and solving for d
with D/ud=0.22 for R > 10°
d = "2" L _ 2 (4.1) 2x0.22*(t)
The term not precisely known in eqn (4.1) is L, the
distance from Site 1 to the regulator. As is evident from
Fig 3.29, many possible tracer paths may be involved.
Taking the mean distance of 29.8m then on substitution in
eqn (4.1) the result is:
, 10.3x29.8 . __ d = — = 4.07m
2x0.22x(13.1)
Since the measured diameter of the roadway at Site 1 is
4.87 m the calculated value of 4.07m is in reasonable
agreement - the difference being less than 20%. This
97
result therefore may be viewed as supporting the
applicability of dispersion mechanics theory in
underground mine ventilation.
Release tests at Sites 2, 3 and 4 concentrated on
delineating the flow layering detected at Site 1 with
the particular aim of finding out where it may originate.
Consequently, only the central detection position in the
regulator was used. The results of the tests are given in
Tables A6-A8 (Appendix 2). By inspection of the results
obtained at these sites it is evident that the flow is
layered at these sites also. Unfortunately, and for
reasons noted earlier in this section, tracer tests using
the standard balloon procedure could not be extended to
distances beyond that of Site 4.
Therefore it is not possible to answer, at least by the
positional tracer release technique, how far upstream did
the observed flow layering extend. However, it will be
shown later that an indirect answer to this question may
exist.
It is of interest to note that the results in Tables
A6=>A8 also show the expected range of dispersion
parameters when the distances involved are accounted for.
Hence, analysis of these are omitted, but they of course
98
can be readily obtained if needed by simply repeating the
analytical procedure given in the previous few pages for
the Site 1 results.
Next, the response curve given in Fig 4.11, of the cross
sectional release test at Site 5 (Test 192) is analysed.
This test was carried out by inflating a meteorological
balloon (obtained from the Meteorological station) with 3
approximately 1.2 m of C2H2 and then bursting the
balloon at the site and recording the response at the
West Vent Shaft regulator in the usual manner, with the
detector head in the central position.
Figure 4.11 shows that the response curve of this test is
clearly bi-modal and that the slow rise at the beginning
and a slow fall at the end are a clear indication of a
dispersed flow. The bi-modal nature of the response curve
on the other hand is indicative of a parallel flow (Sect
2.3.2) .
Although as is usual in practice the response curve in
Fig 4.11 does not show the idealized separation of the
two flow paths of Fig 2.10, calculations of the flow
parameters using eqn (2.56), and that of the two D/uL
values involved, using Fig 3.31 procedure, can still be
performed with graphical separation. This, it will be
98A
0.2
O 8) 0.1 -J
Ui
0.0 rTjfrrm i n [rm i riTT[TmTTni{nTTTnrrpTrnrrnT|rrriT 50 100 150 200 250 300 350 400
TIME (sec)
Fig 4.11: Response curve for Test 192
Vi= 0.45 (D/uL) =- 0.021
Fig 4.12: Flow model for the response of Fig 4.11
99
recalled, was the procedure used in analysing the
underground tracer results of other workers (Sect 2.4).
The results of the analysis of the response curve in Fig
4.11 are:
t„ = 240s ctz = 1470s2 1 1
t, = 325s cfZ = 1690s2
2 2
The corresponding flow model and its relevant parameters
are given in Fig 4.12.
It is noted that the "size" of the two flow branches are
given in Fig 4.12 in terms of their volumes. This is a
necessary result of eqn (2.56). It is also noted that the
flow model in Fig 4.12 corresponds to the underground
physical situation of the relevant area in Fig 3.12, with
Site 5 being at the exit of the 2/7 North cross cut.
Therefore, whilst it is possible to accurately measure
the distances involved as has been done in Fig 3.29, it
is clear that they cannot be calculated accurately in
this case by the relationship L = V/A since the cross
sectional area of the two flow paths, viz paths 5-*2-»l->0
and 5-»4=»3->l=>0 (Figs 3.12 and 3.29), are not constant.
100
Nevertheless, with the reasonable assumption that in the
Western end of the 2/7 roadways the cross sectional area
of the Path 1 circuit is twice the volume of the Path 2
circuit, and both paths thereafter have a "constant"
cross sectional area of 25 m , then 1,± = 135m and
L2 = 180m. By inspection of Fig 3.29 the above calculated
distances are not too different from those actually
measured viz. 146m and 175m, respectively.
It is also of interest to note that the calculated D/uL
parameters for the flow model in Fig 4.12 are not as
different as may have been expected.This indicates that
the operative dispersion intensities are somewhat
different in each branch and possibly caused by the
different flow path geometries evident in Fig 3.29.
Although cross sectional release test like the one
described above, would have been of interest the cost of
conducting such tests was prohibitive. Additionally,
cross sectional release, although theoretically capable
of detecting "layered flow" if it closely corresponds to
the pure convection model of Sect 2.2.3, would be most
unlikely to be as successful (and as practical) in the
underground conditions as the point release method used
in this study.
101
4.4 POSITIONAL ANEMOMETER TRAVERSE
Anemometric positional velocity data were obtained at the
same sites as the tracer release was carried out; using
the vane anemometer and the measuring technique as
described in Section 3.4.4. Measurements were made at the
nodes according to Fig 3.30, ie at the same points used
for the tracer release. Additional to Sites 1-4, four
other sites, including Site 5, were also investigated,
with Sites 6,7 and 8 being in the vicinity of the 2 Drill
entrance some 600m distant from the West Vent Shaft
regulator.
The location of Sites 6,7 and 8 are indicated in Fig 3.12
The results of the anemometer survey in terms of
positional velocity are given in Appendix 3. It should be
noted that the measured raw velocity values have been
adjusted. This adjustment was based on two sources; the
standard calibration corrections for the anemometers
(determined by Scientific Instruments P/L) and secondly
by comparison with the centre line reading. Due to the
length of time spent at each site, a "drift" in
velocities, inherent to the mine ventilation, was
expected. To account for this drift a centre line
velocity was taken parallel to velocities measured at the
individual positions. The expected drift was found to not
102
be significant (=*2%), and a correction to the average
centre line velocity was applied on a linear basis for
each positional velocity.
Using the data in Appendix 3 traditional velocity
contours exemplified by the Site 1 results in Fig 4.13,
were prepared. However, this simple form of data
representation and its computer aided equivalent in Fig
4.14 was not found useful for analysis and was abandoned.
Instead, suitable data representation and analysis was
achieved by using commercially available software that
allowed the plotting of a topographical surface for the
positional velocities. The program, PLOTCALL distributed
by Golden Software P/L (1984) uses a Kriging method (85)
to determine the data values at each point of a 50 by 50
grid for the test site velocities.
4.5 COMPUTER ANALYSIS OF POSITIONAL RESULTS
Analysis of both tracer release and anemometer results
were carried out using the PLOTCALL package. After
several trials at different extents of smoothing, a 0.99
value was selected (where 1.0 gives no smoothing and 0
complete averaging of input data) as the standard for all
generated results. The reason for this choice is both
mathematical and physical as may be seen by comparing the
102A
CALCULATION iHin
Fig 4.13: Hand Drawn Velocity Contours - Site 1
1 i " * — ' • * • - ' ' - • • - * •
UL.I I wT*i
Site 1 - Contours, 0.99 SMooth, 0-04 ty 0.(
Fig 4.14: Computer Generated contour Plot - Site 1
103
results of the smoothing levels at 0.9 and 1.0 values
(Appendix 4) and the companion results at 0.99 level in
Fig 4.15.
Mathematical reasons are associated with the number of
degrees of freedom available and the fact that all points
at the flow boundary region, ie. the walls of the
roadway, must be set at zero as required by the boundary
layer theory (86). Physical reasons are actually a
compromise amongst the accepted physical reality of the
continuum (0.90 level), and the improbability (1.0) level
and the conceptually acceptable physical representation
of the segregated flow (0.99 level).
An important point to note, however, is that in each case
exactly the same data computation is performed so
similarities and differences can be compared exactly even
though they may not exactly correspond to the actual
macroscopic (and microscopic) distribution of the flowing
volume elements bounded by an impervious surface (ie. the
tunnel walls).
4.5.1 Tracer Results
The results in Tables A5=>A8 of the analysis of tracer
release data are shown in Figs 4.15=#4.19. Fig 4.15 shows
1037A
Fig 4.15: Site 1 Positional velocities by tracer all head positions
Fig 4.16: Site 1 Positional Velocities by Tracer, central head position only.
103AA
Fig 4.17: Site 2 Positional velocities by tracer.
Fig 4.18: Site 3 Positional velocities by tracer.
103AAA
Fig 4.19: Site 4 Positional velocities by tracer.
104
all the Site 1 data, whilst Fig 4.16 gives the data of
the central detector head position only. The latter is
therefore comparable to the results of sites 2-4 (Figs
4.17=^4.19) which featured a central detector location
only.
Inspection of Figs 4.15=»4.19 shows that all results are
similar in appearance which is not unlike a bundle of
tubes, the tips of which extend forward to a lesser or
greater extent.
Figure 4.15, viz the complete results in Table A5
(Appendix 2), clearly shows low velocity "flow tubes" in
the x = 1 position and high velocity "flow tubes" at the
x = 4 position, except for the x,y = 4,1 "tube" which is
low.
The positional features of the all-positions results in
Fig 4.15 are parallelled in Fig 4.16 which displays only
the central detector head location results. This,
therefore, indicates that the properties of the
positional "tubes" are constant. In other words, a "flow
tube" at any given x,y position in the coordinate grid of
Fig 3.30 has exactly the same characteristics at all
times.
105
Moreover, the "tube" also exists at all times and does
not disappear just because the detection system fails to
detect it. The results in Fig 4.15 of the high velocity
"tubes" at the 4,2=»4,4 and 3,2=>3,4 x,y positions are in
line with the physical situation (Fig 3.28) of the area
involved, in that it is a shorter, lower resistance path
to the West Vent Shaft Regulator on this side of the
drive. The low velocity "tubes" in Fig 4.15 at the other
positions, except 4,1 are likewise in accordance with the
physical situation at the other wall of the Western
Perimeter Drive to West Vent Shaft path. The low velocity
"4,1 tube" is however, puzzling.
The only reasonable explanation is that the flow there is
a low flow along the floor before ascending at the
regulator. This explanation is supported by the generally
lower velocities at the y = 1 level. Since the 1,4 "tube"
is also a low velocity tube then the same explanation
must apply there also. This is not unreasonable from the
physical point of view of the flow path involved (Fig
3.29) .
Comparison of Figs 4.18 and 4.19 shows quite clearly that
for all practical purposes they are identical.
Considering the fact that the two sites involved (Sites 3
and 4, Fig 3.29) are in the same section of the exhaust
106
flow from the 2/7 cross cuts, the result is not
surprising. However, the result does give added support
that dispersion mechanics also works underground.
With respect to the Site 2 results of Fig 4.17 inspection
shows that they are very nearly reproduced in the Site 1
results (Fig 4.16). In fact the Site 1 results are an
almost exact combination of the Sites 2 and 3 results ie.
Fig 4.15 = Fig 4.17 + Fig 4.18.
The reason for this may not be immediately obvious.
However, it becomes so when it is remembered that, unlike
traditional velocity surveys at a given cross section of
a roadway, tracer test velocities are the velocities for
the whole path length involved. This is made more clear
by referring to eqn (2.9) from which:
L u = —
t
Finally, from the results presented here, it can be
firmly concluded that the "layering" character of the
flow extends upstream of the West Vent Shaft to Site 4 in
the Western End of the 2/7 South cross cut and to Site 2
in the 2/6 South cross cut.
107
4.5.2 Anemometer Results
The results of the analysis of the anemometer data
(Appendix 3) for Sites 1=*8 are shown in Figs 4.20«*>4.27
inclusive. It should be noted that these tests were
performed at the same West Vent Shaft regulator opening
as all of the tracer release tests were carried out.
Therefore, flow conditions may be expected to have been
essentially the same in both cases.
Inspection of Figs 4.20=»4.27 shows that again the "tube
bundle" character is a common feature of the flow - from
Site 8 at the 2 Drill entrance (Fig 4.27) to the West
Vent Shaft exit, or more correctly to Site 1. With some
notable exceptions the "tube bundle" is more or less
symmetrical about the centre axis, ie. the highest
velocity is in the centre. Notable exceptions are Figs
4.20, 4.26-M.27.
By reference to Figs 3.12 and 3.29 the above exceptions,
apart from that in Fig 4.26, can be readily understood
since they correspond to the sites (Site 1, 6 and 8) at
which the flow is about to, or has already turned around
a corner. In the case of Site 6 (Fig 4.25) the flow is
not only segregated but the velocities are relatively low
compared to those at most other sites. These low
Fig 4.20: Site 1 Positional velocities by anemometer.
Fig 4.21: Site 2 Positional velocities by anemometer,
107AA
Fig 4.22: Site 3 Positional velocities by anemometer.
••'-TuVVV-'
Fig 4.23: Site 4 Positional velocities by anemometer.
107AAA
Fig 4.24: Site 5 Positional velocities by anemometer.
Fig 4.25: Site 6 Positional velocities by anemometer,
107AAAA
Fig 4.26: Site 7 Positional velocities by anemometer.
"•Car
Fig 4.27: Site 8 Positional velocities by anemometer,
108
velocities at Site 6 are expected since as Fig 3.12
shows, a part of the intake air after passing Site 8
enters the 2/8 North cross cut (Site 6) while the
majority continues along the Eastern Perimeter Drive to
the 2/7 cross-cuts. The flow is later recombined, mostly
at the Western Perimeter Drive and through the slot
connecting the 2/8 and 2/7 drives, and essentially
completely at the West Vent Shaft.
The profile of an increasing velocity from points 1 to 4
along the x coordinate in Fig 4.26 is an interesting
results considering the test location viz. Site 7.
Intuitively, in view of the result at Site 6 (Fig 4.25),
one would expect a reverse result at Site 7 to that in
Fig 4.26, or a symmetrical pattern. The explanation which
is suggested by the above results is that the different
kinetic energies of the "flow tubes", clearly already
present at Site 8 (Fig 4.27), have a long lasting
influence on the flow distribution downstream. Thus, the
highest velocity at x = 4 in Fig 4.27 and consequently 1 2
very much higher kinetic energy (=~Pu ) volume elements
are easily carried across the entrance into the 2/8 North
to Site 7 and probably well beyond it. In fact some trace
of the Site 7 pattern (Fig 4.26) appears to still exist
at Site 5 (Fig 4.24) but not beyond (cf Figs 4.21 and
4.23).
109
The interpretation of the essentially symmetrical flow in
Figs 4.16=^4.19 and Fig 4.21 can also be readily made by
reference to the location of the respective sites, but is
omitted here for the sake of brevity.
Finally, it should be noted again that the results in
Figs 4.15-4.27 were all obtained at the same regulator
setting. However, additional anemometer surveys were also
carried out at a different regulator setting which gave
an average velocity of about two thirds of the original
value, viz 0.96 m/s as against 1.53 m/s. The
corresponding Reynolds' Numbers are 3.1*10 and 5.0x10 .
Figures 4.28-M.31 show the Sites l-»4 results for the low
flow velocity. If these results are compared with the
high velocity results obtained at the same sites (Figs
4.20 •* 4.23) it is obvious that the two patterns are for
all practical purposes identical. This therefore means
that the velocity of the general body of air - at least
within the above range and most probably well outside it
too - does not have a significant effect in changing the
"tube bundle" character of the flow.
109A
Fig 4.28: Site 1 Positional velocities by anemometer (low velocity)
Fig 4.29: Site 2 Positional velocities by anemometer (low velocity)
109AA
Fig 4.30: Site 3 Positional velocities by anemometer (low velocity)
Fig 4.31: Site 4 Positional velocities by anemometer (low velocity)
110
4.6 COMPARISON OF TRADITIONAL AND TRACER RESULTS
It is evident from Figs 4.15=^4.31 of the previous
sections that both sets of results show the same "tube
bundle" feature of the flow. Hence, in this respect
traditional and tracer results compare very well. The two
sets of results are also complementary in that one set of
results alone may still leave doubt, particularly the
traditional ones, as to the reality of the results. This
is because, for example, the traditional results in Figs
4.20=>4.31 do not by themselves prove the reality of a
"tube bundle" or layered flow. Moreover, the very nature
of the anemometer survey method is incapable of any
confirmation of this sort.
The tracer tests on the other hand, can resolve this
impasse, and also provide other information that simply
is not obtainable by traditional methods. Thus, the
positional tracer release results in Sect 4.5.1 leave no
doubt about the layering of the flow since this feature
of the flow is confirmed physically, ie. depending on its
release point at a site the tracer either flows into the
evase and is detected or it bypasses the evase and is not
detected.
Ill
In other words, the tracer tests and specifically the
point injection technique, give a straightforward Yes/No
answer.
Although as shown in Sect 4.1.5, tracer tests also give
the flow velocity results in the same way as the
traditional methods do, the latter are still necessary
if for no other reason than to confirm the finding of the
tracer tests. However, there are some instances where
this cannot be done. For example, the result of the
meteorological balloon test at Site 5 (Fig 4.12) cannot
be confirmed by traditional methods. Other examples of
this kind were included in Sect 2.4.
One important difference between the two methods concerns
air balance and velocity questions. For example the air
flow at Site 1 must equal the sum of the airflows at
Sites 2 and 3 (Fig 2.39), ie.
UA = U2A2 + uaA3 <4-2>
From anemometer results in Appendix 3 and making the
usual assumption of equal cross sectional areas
throughout, the air balance is:
1.53 = 0.69 + 0.76
^ 1.45 (High u)
112
0.96 = 0.43 + 0.48
=* 0.91 (Low u)
By inspection the balance at both velocities is
satisfactory.
However, if the tracer determined velocities were to be
used in eqn (4.2) the result would be:
1.83 = 1.69 + 1.67
* 3.36
Comparison of the above results forcefully confirms the
difference between traditional and tracer results
referred to in Sect 4.5.1, viz., that traditional
velocity is an average velocity at a roadway
cross-section whereas the tracer velocity is the average
velocity in the roadway for the length considered (ie.
from release point to detector).
It is this property of the tracer velocity which is the
more significant since it includes implicit statements of
the history of the flowing volume element from its source
to its sink.
Nevertheless, if it is desired to use the tracer
velocities for air balance purposes, then path geometry
has to be accounted for in the calculations also.
113
It should also be pointed out that considering the
physical estimation of the area (Fig 3.12) it would be
expected that for Site 1 both the anemometer and the
tracer determined velocities should agree closely, but
not exactly. By inspection the two results viz. 1.53 m/s
(anemometer) and 1.83 m/s (tracer) are indeed close. The
fact that the tracer determined velocity is higher is not
surprising as it is expected to be the higher of the two
velocities. The reason for this is that the tracer
velocity at Site l is calculated from the mean time
recorded at the West Vent Shaft regulator where all the
air from the 2 Drill level is exhausted to the main
surface fan. This, of course, includes the air travelling
through the Northern drives (ie. through the 2/1, 2/2,
2/3, 2/4 and 2/5) with the determined velocity (by
anemometer) of 0.4 m/s total (Table 4.2). Assuming
an algebraic summation of the flows, then the tracer
velocity becomes 1.43 m/s. This value is therefore not
too different from the anemomter value of 1.53 m/s and
for actual underground conditions the agreement may be
regarded as excellent.
To summarise, the distinction between traditional and
tracer methods is most succinctly expressed by saying
that traditional methods measure how much air flows
whereas tracer methods measure how it does flow.
114
CHAPTER 5
SIGNIFICANCE OF RESULTS
In the introduction (Sect 1.0) it was stated that for the
essential functions of the ventilating air to be
satisfied (1) then an understanding of the behaviour of
ventilating air in actual roadways is necessary. It was
also stated that this cannot be done by the traditional
methods but it can be done by the tracer methods. Knowing
how the air flows, rather than simply how much air flows,
allows the calculation of these factors.
The tracer results presented in this thesis characterize
the behaviour of the ventilating air in an actual
underground mine roadway. These measured characteristics
of the ventilating air are the property of the
ventilating air itself for the regulator settings used.
These properties would probably apply for a range of
other settings also as the properties of the tracer used,
particularly its density, matched that of air very
closely, as is evident from Table 3.1. In fact, the
tracer selection was given considerable attention at the
outset to ensure the closest similarity possible with the
practical requirements of ease of detection, of cost and
of safety.
115
Hence the first significance of the results is that some
confidence can be placed in the conclusion that the
results represent those of the ventilating air and not of
the tracer. This is very important if an understanding of
the behaviour of ventilating air is to be obtained. Once
this close similarity has been recognised then a rational
basis would become available for considering the Vutukuri
and Lama (1) essential functions, viz. whether the
dilutions of the various substances to statutory levels
are met, and if not then what can be done for these
levels to be met.
5.1 THEORETICAL ASPECTS
The results of the present work clearly indicate a flow
layering, ie. flow regions that are distinctly separate.
Of course, there is no sharp separation in a physical
sense, but a more or less diffuse intermediate region.
However, no matter how the situation is viewed
conceptually, the fact remains that the flow is layered
and this would have a concentration interaction effect on
dilution rates. In this thesis the term "flow tube" has
been used to express the experimentally observed results
of the air flow layering characteristics in actual
underground cond it i ons.
116
The latter, viz. that the results were obtained under
actual underground conditions in an operating mine is the
second significance of the results. This is considered to
be of particular value in theoretical and computer
simulation work for predicting the dilution of noxious or
undesirable substances in the mine air.
There have been a number of research programs of the
above kind reported in the literature and they have been
reviewed recently by Bandopadhyay and Ramani (75) in
connection with their own work on the modelling of the
dispersion of diesel exhaust fumes.
In the above study Bandopadhyay and Ramani (75) adopted a
generalized mass transfer model, viz.:
£C at
d_ ax x a^ + dy E
£c y dy
+
, .ac , ^ c - u(x)3£ - v(y)gy
, .ac w^al
az z az
X(x,y,z,c) + jf(x,y,z,t) (5.1)
Where E , according to the authors are turbulent x,y, z
dispersion coefficients in x,y and z directions, >v is a
generalized decay coefficient for the pollutant and
r"(x,y,z,t) is the source term for the pollutant in the
roadway.
117
Equation (5.1) being a non-linear partial differential
equation with non-homogeneous terms had to be solved with
a number of assumptions and initial conditions,as well as
boundary conditions. The results of the calculations did
not match the reality very well.
It is of interest to note that in an earlier
investigation of the above question in the USSR Skobunov
(76) summarized the situation as follows:
"It must be evidently admitted that
mathematical models of physico-technical
ventilation systems give discrepancies of
magnitudes that in addition to being
unacceptable are very dangerous to safety."
In commenting on the disparity between computed and
measured results Bandopadhyay and Ramani (75) concluded
that:
"It is necessary to identify the existence of
the variations between model predicted and in
mine concentrations" and "It is important to
quantify the magnitude of the differences and
to identify the potential sources of their
origin. Only then can models be used as valid
predictions for more practical purposes"
118
The significance of the present results to the above
conclusions is that the foregoing mathematical
developments followed a mathematical model without due
regards to the assumptions of the model.
In short, mathematical modelling so far has assumed flow
conditions of the ventilating air that in reality may not
exist. The significance of the present results, obtained
in an actual operating mining environment, is that the
previous assumptions may be reconsidered in favour of
those that better represent the reality of actual mine
ventilation situations.
For example, from this study and taking the results of
Site 1 (Table A5) the dilution of a substance is shown in
Fig 5.1. This figure gives the mean value of the variance
for each node position obtained from Table A5 and the
calculated maximum concentration of the substance where
the initial concentration was 100%. The calculations for
CWAV were performed by the method of Fig 3.31.
The results in Fig 5.1 show that depending on the
position at which the air sample is taken so a different
resultant concentration of the substance would be
recorded. On the other hand, if a whole section is
sampled, then a mean value of 64.6% would be obtained.
118A
klB.l) jff.B) 48
.(H.9)
71
.(7.2)
57
61
\ 6 1
Jll.2)
(11.3)
77
71
74
.(7.9)
X7.5)
62
62
66
(10.5) U.
(10.3)
^a.v)
(0.2)
1(12-^ ••"•"Ji
57
24
44
(69.8)
J20.8)
.(o.i)
99 99 s 2 3
X
Fig. 5.1: Calculated Variances () and Residual Concentrations %. Site 1 calculated responses.
119
However, there will still be regions at this section with
concentrations below and above this value which may be
potentially hazardous.
The above calculations exclude mass transfer in the
direction normal to the flow. If required, this may be
done readily by, for example, a Fickian term (Sect 2.3.1)
and if flow velocity is assumed constant then dt and dL
terms are related, hence:
^ = D dL eff
dC d(z,y) (5.2)
Making a reasonable assumption that the concentration
gradient corresponds to a log mean concentration
difference (Ac)_ , then after integration of eqn (5.2)
and collecting terms the resultant expression is:
D ff £-= 1 -X- (AC)lmL (5.3) o o
With known values of D ff and (Ac), it should then be
possible to calculate the decrease of concentration for
given values of L due to mass transfer in the direction
normal to the flow. For molecular diffusion only (See Fig
2.11) D ff becomes simply DM- If eddying is present in
the transfer direction then D e^ should include the eff
contribution of this mechanism also, ie. terms such as E Y and E of eqn (5.1).
120
However, with dusts and gases of different density to
air, coupled phenomena have to be taken into account. In
other words, transport of species in the direction normal
to the flow is governed by the suimultaneous action of
the concentration driving force (eqn (5.2)) and the
gravitational (buoyancy) force. Interactions of this kind
were outside the scope of this thesis, but it is obvious
that future research should address such coupled
phenomena. Moreover, the results of this work indicate
that a model for the flow of the ventilating air should
also include some features of the convection model (Sect
2.2.3) in addition to the dominant features of the
dispersion model (Sect 2.5).
The above consideration of the significance of the
results have involved theoretical questions. These are
important since theory provides answers to how existing
operations may be improved as well as guidance to what
may be expected in new and untried situations.
121
5.2 PRACTICAL ASPECTS
The significance of the results from a practical point of
view are:
A recognition of the variability of the air flow, as
a certainty.
Here, the variability of the actual underground results
can be compared with the certainty of constancy of the
laboratory (Sect 4.1) and the large test rig (Sect 4.2)
results.
On the basis of Quantity surveys conducted as part of the
regular monitoring undertaken at the Elura Mine - along
with specific changes in the ventilation airflow noted in
this thesis (Sect 4.3.3) it is clear that local
variations in the flow do occur. This flow instabilities
appear to be common to all mine ventilation systems
where the flow velocities lie below some undetermined
critical velocity.
The certainty of change must be recognized and addressed
in all ventilation design work. The extent of the
expected variability should be determined by the
traditional/tracer analysis of a specific area. The
observed level of variability can then be included as a
122
design guide for correct network implementation, ie. the
correct fans, stoppings, ducts etc.
The layered or "flow tube" character of the
ventilating air.
This feature of the flow can give rise to a number of
undesirable consequences, including:
the presence of high concentrations of contaminants in
return roadways at a considerable distance from
their source. Specifically methane released during
the mining of Coal could exist in significantly
higher concentrations than the general body level in
"flow tubes" defined by the geometry of the mining
layout.
the lack of dilution of Nitrous Oxide exhaust gases from
diesel engines. High N02 levels could then be
expected remote from operating equipment.
The implications of this phenomenon include a necessity
for revision of the approach made to the calculation of
"adequate" amounts of diluting air for known levels of
contaminants. Flow patterns in the vicinity of
123
contaminant sources may: (i) be inferred from the results
reported in this thesis; (ii) cause an unsafe
concentration of the contaminant to exist, and; (iii)
continue to exist in the ventilating air stream.
Confident applications of the tracer technique in
analysis and in trouble shooting in underground
ventilation problems.
Problems inherent in the provision and control of
ventilating air underground could be easily assessed and
identified through the use of tracer techniques. Problems
such as leaky ventilation structures and undesired
recirculation could be quickly identified using a tracer
technique. Additionally, the extent of bypassing or
recirculation would be given as a result of the
measurements.
Prior to the continued development of the tracer release
and detection system for the conduct of whole of mine
surveys (which will be possible with the development of a
tracer/detection system capable of reading to a very
small concentration) the technique could be applied to
smaller studies. Some of the bypassing problems which
could be addressed would include leakage through bins,
stoppings and excessively open regulators - and the
124
recirculation by auxilliary fans could readily be
conducted.
Finally, it may be suggested that the findings reported
in this work may stimulate a review of some of the
statutory requirements concerning sampling methods and
permissible levels of pollutant in the mine airways.
125
CHAPTER 6
CONCLUSIONS
The results of this study have shown that:
1. Dispersion Mechanics can be applied to mine
ventilation surveys to provide quantitative flow
patterns and effective dispersion data in the
ventilating air. This therefore confirms the
expectations in this regard proposed in 1984 from
the results of a laboratory scale hydraulic model of
a section of a coal mine (10).
2. The ventilating air in the 2 Drill level network in
Elura Mine is characterised by layered segregated
flow patterns. This result of a Dispersion Mechancis
study is also supported by the results of
traditional velocity surveys.
3. The single observed constant feature of the
ventilating air is its short time scale transient
behaviour. This therefore supports similar results
reported in the literautre (2-6,64).
4. Acetylene (C_H ) is a suitable and practical tracer
gas for ventilation studies in metalliferous mines.
5. The release and detection system developed and
tested in laboratory and in a large scale test rig,
126
was, with subsequent modifications for underground
conditions, found to be a satisfactory system and
suitable for a one-person operation.
Other conclusions which emerge from this study are that
consideration should be given to (i) introducing the
"constant variability" of the ventilating air into
network calculations and (ii) examining statuatory
regulations governing concentration levels of noxious
substances in the ventilating air and the sampling
methods used.
Future research should address the guestion of the
interaction between the "flow tube" character of the
ventilating air, observed in this study, and the dilution
of the explosive and toxic gases in mines - these being,
of course, the three essential functions of the
ventilating air (1).
127
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th
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Al - 1
APPENDIX 1
UNDERGROUND TRACER RESULTS
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71
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A2 - 1
APPENDIX 2
TABULATED TRACER RESULTS
A2 - 2
TABLE Al Laboratory Test Results
Run Q t c2 u R D/UL D/ud (l/s) (s) (s ) (m/s) (-) (-) (-)
1 2 3 4 5 6 7 8 9 10 11 12
10 10 10 20 20 20 30 30 30 35 35 35
5.1 4.9 5.2 2.5 2.8 2.7 1.7 1.6 1.8 1.5 1.2 1.4
2.34 2.30 2.32 0.26 0.38 0.33 0.10 0.09 0.12 0.06 0.05 0.07
0.57 0.57 0.57 1.14 1.14 1.14 1.71 1.71 1.71 1.99 1.99 1.99
5. 5. 5. 1. 1. 1. 2. 2. 2. 2. 2. 2,
.1x10
.1x10
.lxl04
.4x10
.4xl04
.4xl04 ,oxio4 .0x10 .0xl04 .4x10^ .4xl04 .4x10
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0, 0.
045 048 ,043 ,021 ,024 .023 .018 .017 .019 .015 .017 .017
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0, 0,
,90 ,96 ,86 .42 .48 .46 .36 .34 .38 .30 .34 .34
TABLE A2 Large Test Rig Results Cross Sectional Injection
Run L Q Ah t & u R D/uL D/ud (m) (m/s) (mmH20) (s) (s ) (m/s) (-) (-) (-)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10 10 10 10 10 10 10 17 17 17 24 24 24 24 24
0.83 1.77 2.01 2.89 3.68 4.32 1.93 1.89 2.78 1.85 2.02 2.83 1.78 3.65 0.96
2.5 12 14 27 40 55 14 24 42 22 36 60 . 31
101 10
7.51 3.43 3.04 2.30 1.55 1.26 3.15 5.58 3.96 5.73 7.65 5.46 8.65 4.01 15.63
2.53 0.53 0.42 0.24 0.11 0.07 0.44 0.81 0.41 0.87 0.95 0.46 1.25 0.23 3.74
1.30 2.78 3.16 4.54 5.79 6.80 3.03 2.97 4.37 2.90 3.17 4.45 2.80 5.74 1.51
7.8x10 1.7x10^ 1.9xl0„ 2.7x10^ 3.4x10,, 4.1x10^ 1.8xl05 1.8x10,, 2.6xl0„ 1.7x10 1.9xl05 2.7xl05 1.7x10,, 3.4xl05 9.0x10
0.022 0.021 0.023 0.023 0.023 0.022 0.022 0.013 0.013 0.013 0.008 0.007 0.008 0.007 0.008
0.25 0.23 0.22 0.21 0.21 0.23 0.24 0.25 0.25 0.25 0.23 0.21 0.22 0.19 0.21
A2 - 3
TABLE A3 Large Test Rig Results Point Injection
Run
1 2 3 4 5 6 7 8 9 10 11 12 13 14
L
(m)
24 24 24 24 24 24 10 10 10 10 17 17 17 17
Q (m/s)
1.82 3.02 4.47 3.71 0.93 2.24 0.78 1.65 2.36 3.18 0.95 1.81 3.02 3.11
Ah (mmH20)
29 81
178 122
8 45 2
10 21 38 6
21 58 61
t (S)
8.76 5.23 3.48 4.33 16.71 6.95 8.41 3.98 2.79 2.21 11.83 6.20 3.91 3.68
2
a 2
(s2)
1.37 0.48 0.26 0.45 6.43 1.04 3.45 0.75 0.39 0.21 4.18 1.06 0.46 0.43
U
(m/s)
2.86 4.75 7.03 5.83 1.56 3.53 1.23 2.59 3.71 5.00 1.49 2.84 4.75 4.89
R
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1.6x10° 2.8xl05 4.2xl0„ 3.5xl04 8.4xl05 2.1x10 7.2xl0„ 1.6x10^ 2.2x10^ 3.5xl05 9.0xl0„ 1.7xl05 2.8xl05 2.9x10
D/uL (-)
0.009 0.009 0.010 0.009 0.011 0.011 0.024 0.023 0.024 0.022 0.015 0.014 0.015 0.016
D/ud (-)
0.25 0.24 0.27 0.24 0.29 0.29 0.27 0.26 0.27 0.24 0.28 0.26 0.26 0.30
TABLE A4 - 2/8 Results
Test Len u m M C . t „ meas No.
ct
1 2 5 6 12 13 14 15 17 18 20 21 22 23 24 25
P
(s) (s)
u , D/uL Reynolds D/ud d .p
C S lC ,T_ etc
No. (s ) (m/s) (-) (-) (-) (m)
3 0.25 8.1 0.18 6 0.25 16.3 3.19 9 0.27 23.8 4. 15 0.27 12.9 45.8 1, 5 0.84 6.6 3, 5 0.84 5.8 3
10 0.84 11.4 3, 10 0.81 12.6 15 0.81 18.3 15 0.81 18.6 22.5 20 0.86 24.8 20 0.86 21.2 24.1 20 0.86 28.8 19.2 3 0.45 5.2 3 0.45 5.8 5 0.45 10.3
53 00 05 30 90
5.08 6.70 6.23 0.12 5.39 11.61 0.69 1.95 0.58 1.48 0.52 0.85 0.49
0.37 0.37 0.38 1.16 0.76 0.86 0.88 0.79 0.82 0.81 0.81 0.94
0.001 8.2E+04 0.002 0.02 0.006 8.2E+04 0.005 0.16 0.004 8.9E+04 0.002 0.16 0.003 8.9E+04 0.001 0.20 0.035 2.8E+05 0.035 0.80 0.049 2.8E+05 0.049 1.11 0.015 2.8E+05 0.007 0.68 0.016 2.7E+05 0.008 0.73 0.010 2.7E+05 0.003 0.68 0.009 2.7E+05 0.003 0.61 1E-04 2.8E+05 0.000 0.01 0.006 2.8E+05 0.001 0.55 0.007 2.8E+05 0.002 0.64 0.036 1.5E+05 0.060 0.49 0.022 1.5E+05 0.036 0.30 0.004 1.5E+05 0.004 0.09
A2 - 4
TABLE A4 - 2/8 Results
(continued)
Test No.
26 27 28 29 34 35 36 37 39 40 43 44
Len
5 5 5
10 10 15 15 15 20 20 25 35
U t meas
0.39 0.39 0.39 0.48 0.48 0.48 0.44 0.44 0.44 0.44 0.46 0.46
(S)
9.7 11.2 10.4 18.6 17.3 26.5 27.4 24.0 34.1 35.6 42.5 65.2
t P
(S)
36.6 35.9 46.4
2
a 2
(s )
2.45 6.27 5.84 5.54 6.58 9.83 21.02 6.91 6.98 10.14 14.45 17.00
calc
(m/s)
0.52 0.45 0.48 0.54 0.58
-----
0.541 0.353
D/uL Reynolds D/ud No.
(")
0.013 0.025 0.027 0.008 0.011 0.007 0.014 0.006 0.003 0.004 0.004 0.002
(")
1.3E+05 1.3E+05 1.3E+05 1.6E+05 1.6E+05 1.6E+05 1.4E+05 1.4E+05 1.4E+05 1.4E+05 1.5E+05 1.5E+05
(")
0.013 0.025 0.027 0.004 0.005 0.002 0.005 0.002 0.001 0.001 0.001 0.000
d e ff
(m)
0.30 0.57 0.61 0.36 0.50 0.48 0.95 0.41 0.27 0.36 0.45 0.32
NB. t indicates the mean time for the parallel peak of the tr
trace if present.
A2 - 5
TABLE A5 - Site 1 Results; Positional Release
Test No.
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115
Cord
x,y
1/1 2,1 3,1 1,1 1,2 1,3 1/4 3,2 3,3 3,4 2,4 2,3 2,2 4,2 4,2 4,2 4,2 1,3 1/4 4,4 4,3 2,1 1/1 1,2 1,3 1/4 3,1 3,2 3,3 3,1 3,2 3,3 2,1 2,2 2,3 2,4 4,1 4,2 4,3 4,4 2,4 3,4 1/4 4,4 2,4 3,4 3,4 3,4 2,4 3,4 3,3
t s
(s)
13.5 12.9 11.2
-—
13.9 10.4
--
10.6 12.3
-
7.1 8.4 —
11.7 17.6
---
-
--
—
9.5 8.2
11.5 9.2
10.8 12.1 13.3 15.5
-
-
16.1 -
----
—
13.1 --
18.6 19.1 16.5
—
—
c2
(s2)
21.83 5.92 1.10
— —
6.57 0.93
— —
9.44 16.34
-
8.47 0.06
-
0.19 0.08
— — —
-
---
1.41 0.17
13.49 0.04 8.40 0.70 2.02 0.25
-
-
6.74 -
- • --
-
-
0.48 —
-
26.29 112.36 20.15
-
-
calc (m/s)
1.704 1.783 2.054
_ _
1.655 2.212
— —
2.170 1.870
—
3.239 2.738
-
1.966 1.307
— — —
—
— —
-
2.421 2.805 2.000 2.500 2.130 1.901 1.729 1.484
-
-
1.429 -
---
-
-
1.756 —
-
1.237 1.204 1.394
— —
D/uL
(")
0.060 0.018 0.004
_ _
0.017 0.004
_ _
0.042 0.054
—
0.084 0.000
—
0.001 0.000
— — —
—
— —
—
0.008 0.001 0.051 0.000 0.036 0.002 0.006 0.001
-
-
0.013 -
--
-
-
-
0.001 -
—
0.038 0.154 0.037
— _
D/ud
(")
0.276 0.082 0.020
—_ _
0.078 0.020
— _
0.193 0.248
0.386 0.002
—
0.003 0.001
— — —
—
— —
-
0.036 0.006 0.235 0.001 0.166 0.011 0.026 0.002
-
—
0.060 —
-— -
-
-
0.006 —
—
0.175 0.708 0.170
— _
cal (m)
6.26 1.86 0.46
1.78 0.45
4.39 5.65
8.78 0.04
0.07 0.01
0.82 0.13 5.33 0.03 3.76 0.25 0.60 0.05
1.36
0.15
3.97 16.10 3.87
A2 - 6
TABLE A5 - Site 1 Results; Positional Release (continued)
Test No.
116 117 118 119 120 154 156 157 158 165 166 171
Cord
x,y
3,3 4,1 2,1 3,1 1,1 4,4 4,3 1,1 4,2 4,4 4,3 1,2
t s
(s)
—
18.2 22.9
-
-
13.2 11.9 16.4 8.5
11.6 9.2
13.8
Cf2
(s )
—
30.47 9.44
—
-
12.89 11.05 6.46 0.16 0.43 5.25 0.76
calc (m/s)
_
1.264 1.004
—
—
1.742 1.933 1.402 2.706 1.983 2.500 1.667
D/uL
(-)
wm.
0.046 0.009
—
—
0.037 0.039 0.012 0.001 0.002 0.031 0.002
D/ud
(-)
__
0.212 0.041
—
—
0.170 0.179 0.055 0.005 0.007 0.143 0.009
d -, calc (m)
4.81 0.94
3.87 4.08 1.25 0.12 0.17 3.24 0.21
Head Posn.
CU L L L L L L R L L L C
TABLE A6 - Site 2 Results; Positional Release
Test No.
Cord
x,y
t s
(s) / 2* (s )
u calc (m/s)
D/uL
(-)
D/ud
(")
calc (m)
121 122 123 140 141 142 143 144 145 146 147 148 149 150 151 152 153 155 173 174 182
4,1 4,2 4,3 4,1 4,2 4,3 3,1 3,1 3,2 3,3 2,1 2,2 2,3 1,1 1,2 1,2 1,3 3,2 2,2 2,3 2,3
46.0 0.97 1.51
57.2 549.67 1.22
36.3 250.36 1.92 41.5 34^45 1.68 37.1 0.02 1.88
0.000
0.084
0.095 0.010 0.000
0.003 0.07
1.169 26.57
1.322 30.05 0.139 3.16 0.000 0.00
A2 - 7
TABLE A7 - Site 3 Results; Positional Release
Test No.
124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139
Cord
X/Y
4,1 4,1 4,1 4,2 4,3 3,1 3,1 3,2 3,3 2,1 2,2 2,3 1,1 1,1 1,2 1,3
t S
(s)
48.3 49.6
---
43.4 41.2 37.1
-39.5 40.1
--
45.3 -—
a2
i 2,
(s )
60.66 34.93
---
34.28 16.30 0.25
-3.06 0.48
--
4.51 -—
calc (m/s)
1.44 1.40
-— -
1.60 1.69 1.88
-1.76 1.74
--
1.54 -—
D/UL
(-)
0.013 0.007
— — -
0.009 0.005 0.000
0.001 0.000
--
0.001 -—
D/ud
(")
0.181 0.099
_ — —
0.127 0.067 0.001
-
0.014 0.002
--
0.015 -—
calc (m)
4.11 2.25
— _ —
2.88 1.52 0.03
-
0.31 0.05
--
0.35 -—
TABLE A8 - Site 4 Results; Positional Release
Test
No.
183 184 185 186 187 188 189 190 191
Cord
x,y
2,3 4,1 3,2 2,2 1/1 4,1 3,1 2,1 1,1
t s
(s)
80.9 101.3 82.2 54.8 80.3 118.2 91.3 70.2 66.8
a2
i 2,
(s )
52.358 51.308 41.892 198.20 27.082 64.268 58.350 98.561 33.021
calc (m/s)
0.860 0.687 0.847 1.270 0.867 0.589 0.762 0.991 1.042
D/uL
(")
0.0040 0.0025 0.0031 0.0330 0.0021 0.0023 0.0035 0.0100 0.0037
D/ud
(-)
0.0557 0.0348 0.0432 0.4594 0.0292 0.0320 0.0487 0.1392 0.0515
calc (m)
1.265 0.791 0.981 10.44 0.664 0.728 1.107 3.164 1.171
A3 - 1
APPENDIX 3
SITE ANEMOMETER RESULTS
A3 - 2
TABLE A9: site 1, Anemometer Positional Velocities
Position u, VL - *. low hxgh
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2.2 2,3 2,4 1,1 1,2 1,3 1/4
1.172 1.172 1.042 0.846 1.205 1.14
1.079 0.96
1.074 0.878 1.137 0.951 0.951 0.486 0.682 0.633
1.75 1.83 1.37 0.96 1.71 1.87 1.82 1.61 1.83 1.53 1.82 1.80 1.61 1.05 1.22 0.75
Average 0.963 1.532
TABLE A10 - Site 2, Anemometer Positional velocities
tion
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2.2 2,3 2,4
1/1 1,2 1,3 1,4
U-. u, . . low high
0.456 0.331 0.17 0.18
0.549 0.393 0.465 0.218 0.568 0.584 0.582 0.504 0.584 0.599 0.532 0.155
0.731 0.525 0^284 0.281 0.885 0.648 0.734 0.341 0.925 0.731 0.957 0.791 0.921 0.969 0.877 0.288
Averages 0.429 0.680
A3 - 3
TABLE All: Site 3, Anemometer Positional Velocities
low high
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2.2 2,3 2,4 1,1 1,2 1,3 1,4
0.538 0.566 0.582 0.399 0.442 0.445 0.538 0.532 0.46 0.46
0.398 0.471 0.429 0.465 0.472 0.448
0.875 0.884 0.931 0.657 0.701 0.703 0.811 0.875 0.745 0.751 0.639 0.764 0.691 0.728 0.775 0.718
Averages 0.477 0.765
TABLE A12: Site 4, Anemometer Positional Velocities
high
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2.2 2,3 2,4 1,1 1,2 1,3 1,4
0.210 0.159 0.159 0.110 0.257 0.159 0.240 0.262 0.257 0.175 0.164 0.119 0.240 0.248 0.235 0.257
0.318 0.268 0.275 0.161 0.501 0.224 0.361 0.402 0.409 0.288 0.275 0.180 0.399 0.316 0.392 0.486
Average 0.203 0.328
A3 - 4
TABLE A13: Site 5, Anemometer Positional Velocities
Position
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2.2 2,3 2,4 1,1 1,2 1,3 1,4
Average
low
0.201 0.148 0.221 0.184 0.301 0.184 0.221 0.164 0.201 0.195 0.224 0.201 0.194 0.162 0.201 0.215
0.201
high
0.339 0.218 0.327 0.284 0.488 0.239 0.320 0.213 0.365 0.347 0.347 0.388 0.353 0.273 0.339 0.341
0.324
TABLE A14: Site 6, Anemometer Positional Velocities
Position
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2,2 2,3 2,4 1,1 1,2 1,3 1,4
low
0.123 0.088 0.060 0.250 0.098 0.268 0.410 0.541 0.499 1.304 0.964 1.415 0.763 0.672 0.840 0.493
high
0.191 0.151 0.113 0.354 0.123 0.448 0.667 0.815 0.852 2.423 1.486 2.188 1.451 0.994 1.276 0.751
Average 0.549 0.893
A3 - 5
TABLE A15: Site 7, Anemometer Positional Velocities
Position
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2,2 2,3 2,4 1/1 1,2 1,3 1/4
Average
low
2.230 2.109 2.049 1.817 2.049 1.963 2.161 0.174 1.950 1.973 1.889 1.672 1.851 1.721 1.431 1.252
1.768
high
3.461 3.476 3.333 2.805 3.318 3.224 3.468 0.265 3.155 3.184 3.164 2.675 2.964 2.751 2.281 2.015
2.846
TABLE A16: Site 8, Anemometer Positional Velocities
Position u, „ u, . . low high
4,1 4,2 4,3 4,4 3,1 3,2 3,3 3,4 2,1 2,2 2,3 2,4 1,1 1,2 1,3 1,4
3.460 3.799 3.203 2.578 2.435 2.261 2.475 2.894 1.170 1.416 1.558 2.043 1.008 1.160 1.543 1.199
4.951 4.842 4.154 4.052 3.994 3.815 3.990 4.516 2.164 2.431 2.164 3.468 1.846 1.973 2.611 2.073
Average 2.138 3.315
A4 - 1
APPENDIX 4
COMPARATIVE SURFACE DATA REPRESENTATION
A4 - 2
Figures A4-1 and A4-2 detail the results of two separate
smoothing systems. Figure A4-1 shows the results obtained
where no smoothing was invoked during grid preparation in
the Plotcall program. The "spiky" nature of the results
and the tendency of the central areas to approach zero,
reduce the suitability of this smoothing regime.
Figure A4-2 shows the results obtained where 0.90
smoothing was invoked. Under this regime all of the
influence of the lower and higher readings obtained at
the positions across the drive section has been smoothed
out. This final shape is "too" perfect for use in drawing
comparisons with tracer results. Additionally evidence on
"flow tubes" returned from the tracer results, and
the surety of a convection flow regime discount this
extent of smoothing.
The final adopted system of 0.99 smoothing combines the
benefits of both these extents of smoothing in giving a
valuable representation of the velocity profile data.
A4 - 3
Fig A4-1: Site 1 results - 1.00 smoothing,
iWVWSy
mmw
Fig. A4-2: Site 1 results - 0.90 smoothing,