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8/4/2019 Project Report Final03
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POROUS PLATE ANALYSIS
PROJECT REPORT
Submitted by
VARUN BASIL JOHN
VIGNESH KARTHIK
VAISAKH SOMANATH P
NIMAL NASER
Department of Mechanical Engineering
College of Engineering, Trivandrum-16.
April, 2009
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DEPARTMENT OF MECHANICAL ENGINEERING
COLLEGE OF ENGINEERING, TRIVANDRUM-16.
CERTIFICATE
This is to certify that this report entitled ‘ Porous Plate Analysis’ submitted
by Varun Basil John, Vignesh Karthik, Nimal Naser And Vaisakh
Somanath P to the University of Kerala in partial fulfillment of the
requirement for the award of the Degree of Bachelor of technology in
Mechanical Engineering is a bonafide record of work carried out by them
under our guidance and supervision. The contents of this work in full or in
parts, have not been submitted in any other institute or University for theaward of any degree or diploma
Dr.K.Krishna.Kumar
Professor
Department of Mechanical Engineering
Dr.B.Anil
Professor&Head
Department of Mechanical Engineering
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ACKNOWLEDGEMENTS
We would like take this opportunity to extend our sincere gratitude to Dr. K.
Krisshna Kumar, Department of Mechanical Engineering, College of
Engineering, Trivandrum for his invaluable inputs, kind assistance and
cooperation without which the completion of this project would have been a
mere dream
We express our sincere gratitude to Dr. B. Anil, Head of Mechanical
Department, College of Engineering, Trivandrum for the help rendered for the successful completion of the project.
We gratefully acknowledge the valuable help rendered to us by Anjan,
M.Tech student, College of Engineering, Trivandrum. The constructive
criticisms offered and the help rendered by our classmates and friends is also
gratefully acknowledged.
Finally the most importantly we are grateful to almighty God for His graceon us and guiding us all through this endeavor
VARUN BASIL JOHN
VIGNESH KARTHIK
VAISAKH SOMANATH P
NIMAL NASER
ABSTRACT
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A porous medium or a porous material is a solid (often called frame or
matrix) permeated by an interconnected network of pores (voids) filled with
a fluid (liquid or gas). Fluid flow through porous media is a subject of most
common interest and has emerged a separate field of study. Theoretical and
applied research in flow, heat, and mass transfer in porous media has
received increased attention during the past three decades. This is due to the
importance of this research area in many engineering applications.
This project aims at a theoretical evaluation of frictional and thermal
characteristics of a porous media using Fluent software and determining the
maximum slope and time at maximum slope from temperature response
diagram for different porosities and different velocities. These data were
further used to determine NTU from non-dimensionalized maximum slope
versus non-dimensionalized time at maximum slope diagram.
CONTENTS
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Introduction
Literature Review
Project Theory
Analysis Procedure
Results and Discussions
Result Summary
Conclusion
Reference
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LIST OF FIGURES
1. Contours for static pressure
2. Temperature Response Diagram
3. Trend line for ∆p v/s velocity
4. Trend line for f v/s Re
Literature review
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Reynolds no.
It is a dimensionless number which determines the state of flow, i.e
whether the flow is laminar or turbulent. It is the ratio of inertia force to
viscous force. It is denoted as Re.
Reynolds number,R e=
Porosity, φ
It defines the mass of fluid coming out through a porous media. Porous
media can be packed bed type like concrete beds or wire mesh type, where
we stagger wire meshes together to form a porous media
Porosity=
and
m = mass of matrix.=density of matrix.
r = radius of matrix.
l = length of matrix.
Fanning friction factor, f
It is the frictional resistance per unit wetted area.
Now fanning friction factor, f=
Theoretically fanning friction factor ,f=
Δp= Static pressure difference between inlet and outlet of pipe.
ρ = Density of the fluid.
= velocity of flow.
NTU (Number of Transfer unit)
It is a dimensionless parameter and is a measure of effectiveness of the heat
exchanger.
NTU=
U= overall heat transfer coefficients
Cmin = minimum specific heat capacity.
PROJECT THEORY
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In this project we undertake the analysis of a porous media using
Fluent. Here we use one of the most widely accepted and used
Computational Fluid Dynamics software to do the analysis. Modeling
for the analysis was created in GAMBIT. Proper meshing was given and
boundary conditions were specified. The model created in GAMBIT
was exported to Fluent for further analysis. Analysis was done for both
steady state and unsteady state and then maximum slope was
determined and maximum slope and time was non- dimensionalized
and NTU was determined from these data.
INTRODUCTION
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POROUS MEDIA CONCEPT
The employment of different types of porous materials in forced convection
heat transfer has been extensively studied due to the wide range of potential
engineering applications such as electronic cooling, drying processes, solid
matrix heat exchangers, heat pipe, grain storage, enhanced recovery of
petroleum reservoirs, etc.
The porous media model can be used for a wide variety of problems,
including flows through packed beds, filter papers, perforated plates, flow
distributors, and tube banks. When you use this model, you define a cell
zone in which the porous media model is applied and the pressure loss in the
flow is determined via your inputs. Heat transfer through the medium can
also be represented, subject to the assumption of thermal equilibrium
between the medium and the fluid flow.
The flow through porous media capability enables engineers to simulate
fluid flow through media such as ground rock, filters and catalyst beds. For
example, simulating underground flow through porous rock can enable
engineers to predict the movement of contaminated fluid from a solid waste
landfill into a drinking water supply. In industrial applications, harmful
particles can be filtered from a fluid stream by passing it through a porous
solid whose pores are too small to permit passage of the particles.Additionally, porous media may provide sites for chemical catalysis or
absorption of components of the fluid. The flow through porous media
capability supports both isotropic and orthotropic materials and can calculate
the velocity and pressure fields in a 2-D planar, 2-D axisymmetric or 3-D
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configuration. Multiple parts are supported, where each part may have a
different permeability. Regions of the flow where no porous media exists
can also be included. Both pressure and velocity loads can be applied. In
addition to the standard Darcy's law material model (which relates
volumetric flow and pressure drop with properties of the fluid and media),
the fractional power Darcy's law is also supported. This latter material model
incorporates inertial effects for high Reynolds number applications.
Limitations of the Porous Media Model
The porous media model incorporates an empirically determined flow
resistance in a region of your model defined as ``porous''. In essence, the
porous media model is nothing more than an added momentum sink in the
governing momentum equations. As such, the following modeling
limitations should be readily recognized:
• The fluid does not accelerate as it moves through the medium, since the
volume blockage which is present physically is not represented in the
model. This may have a significant impact in transient flows since it
implies that the transit time for flow through the medium is not
correctly represented by FLUENT.
• The effect of the porous medium on the turbulence field is only
approximated.
TYPICAL APPLICATIONS
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• Aquifer studies
• Catalyst bed testing
• Chemical leaching studies
• Chemical transport simulation
• Contaminant transport studies
• Filter design
• Foam flow studies
• Gas coolant system design
• Geologic flow simulation
• Groundwater remediation studies
• Heat exchanger design
• In-situ biorestoration studies
• Landfill design
• Natural gas exploration studies
• Nuclear waste transport studies
• Ocean hydrodynamics simulation
• Oil exploration studies
• Petroleum reservoir simulation
• Seabed simulation
• Sedimentary basin studies
• Underground flow simulation
• Well treatment studies
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Analysis Procedure
Modelling procedure in GambitPOROSITY, φ= 0.6.
Specifying solver for analysis
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Creating Geometry
Creating nodes
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Creating edges
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Creating Face from wireframe
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Meshing Procedure
Inputting spacing for mesh
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Creating the Mesh
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Specifying Boundary Conditions
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Specifying Continuum Type
Exporting Mesh
The 2-D mesh can now be exported to fluent by using the command
FILE→EXPORT→MESH
Enable the 2-D export mesh and it saves the file in 2d mesh format to be read in FLUENT
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Analysis In FLUENT
The desired mesh can now be read into FLUENT which will then run the geometry throughnumerical analysis.
Open the FLUENT and select the 2D double precision operation for two dimensional operations.The
GAMBIT mesh is read into FLUENT by selecting File Read Case and selecting the correct meshfile.
Smooth/Swap Function
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Steady state analysis to find dependence of Friction
Specifying solver for analysis
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Inputting the material Properties
Specifying the operating and boundary conditions
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Solution Initialization for Steady State
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Setting up the convergence criteria
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THERMAL ANALYSIS
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Inputting Unsteady state conditions
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Specifying the Temperature for unsteady state
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Solution initialization for unsteady state condition
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Defining surface monitor
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Specifying the time step for iteration
RESULTS AND DISCUSSION
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Contours for static pressure
Temperature response diagram
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Trend line for ∆p v/s velocity
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y = 0.0003x3 - 0.0192x2 + 0.4403x
R2 = 0.9833
1
2
3
4
5
6
Trendline for Reynolds no: vs Friction factor
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y = 63413x3 - 219252x2 + 252918x - 9688
R2 = 0.9818
100
200
300
400
500
600
RESULT SUMMARY
NON-DIMENSIONALISATION
Results for velocity 1.2 m/s
y = 82945x3 - 73317x2 + 20362x - 1350.R² = 0.998
0
100
200
300
400
500
600
0 0.1 0.2 0.3 0.4 0.5
Series1
Poly. (Series1)
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Time Temperature Slope Non d Time Non d slope
1 300.13046 0.49207 0.061 0.49207 0.049207
2 300.62253 0.58011 0.122 0.58011 0.058011
3 301.20264 0.56930 0.183 0.56930 0.05693
4 301.77194 0.53806 0.244 0.53806 0.053806
5 302.31000 0.50412 0.305 0.50412 0.050412
6 302.81412 0.47131 0.366 0.47131 0.047131
7 303.28543 0.44034 0.427 0.44034 0.044034
8 303.72577 0.41162 0.488 0.41162 0.041162
9 304.13739 0.37678 0.549 0.37678 0.037678
10 304.51417 0.36730 0.61 0.36730 0.03673
11 304.88147 0.33582 0.671 0.33582 0.033582
12 305.21729 0.31378 0.732 0.31378 0.031378
13 305.53107 0.29318 0.793 0.29318 0.029318
14 305.82425 0.27396 0.854 0.27396 0.027396
15 306.09821 0.25595 0.915 0.25595 0.025595
16 306.35416 0.46177 0.976 0.46177 0.0461772
17 306.81593 0.00078 1.037 0.00078 7.78E-05
18 306.81671 0.20883 1.098 0.20883 0.020883
19 307.02554 0.19513 1.159 0.19513 0.019513
20 307.22067 0.18235 1.22 0.18235 0.018235
21 307.40302 0.17037 1.281 0.17037 0.017037
22 307.57339 0.15921 1.342 0.15921 0.015921
23 307.73260 0.14875 1.403 0.14875 0.014875
24 307.88135 0.13901 1.464 0.13901 0.013901
25 308.02036 0.13000 1.525 0.13000 0.013
26 308.15036 0.12122 1.586 0.12122 0.012122
27 308.27158 0.11340 1.647 0.11340 0.01134
28 308.38498 0.10635 1.708 0.10635 0.010635
29 308.49133 0.08867 1.769 0.08867 0.008867
30 308.58000 ####### 1.83 ######## -30.858
Results for velocity 2.4 m/s
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Results
velocitym/s
Time Temperature Slope Non d Time Non d Slope
1 300.51971 1.60392 0.183 1.60392 0.160392
2 302.12363 1.55832 0.366 1.55832 0.155832
3 303.68195 1.28503 0.549 1.28503 0.128503
4 304.96698 1.02927 0.732 1.02927 0.102927
5 305.99625 0.81964 0.915 0.81964 0.081964
6 306.81589 0.65201 1.098 0.65201 0.065201
7 307.46790 0.51852 1.281 0.51852 0.051852
8 307.98642 0.41235 1.464 0.41235 0.041235
POROSITY, φ= 0.8.
Values of constantsA) Viscous coefficients, α= 1062812.205.φ
B)Inertial coefficients, β= 78.3505.
The pipe inside which wire mesh is placed has a diameter of
38.1mm.
Wire mesh diameter=38.1mm
Length of wire mesh=50mm
Grit width=2mmGrit height=1.5mm
Porosity=
and
Time Temperature Slope Non d Time Non d slope
1 300.30234 1.03418 0.122 1.03418 0.103418
2 301.33652 1.11108 0.244 1.11108 0.111108
3 302.44760 1.00348 0.366 1.00348 0.100348
4 303.45108 0.87674 0.488 0.87674 0.087674
5 304.32782 0.76062 0.610 0.76062 0.076062
6 305.08844 0.65887 0.732 0.65887 0.065887
7 305.74731 0.57053 0.854 0.57053 0.057053
8 306.31784 0.49399 0.976 0.49399 0.049399
9 306.81183 0.42773 1.098 0.42773 0.042773
10 307.23956 0.37033 1.220 0.37033 0.037033
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m= Mass of the aluminium matrix.
ρa= Density of aluminium.
Reynolds number,R e=
Density of air ,ρ=1.225kg/m3
d = characteristic length considering small grit= =1.71mm
Area of grit, A=3mm2
Perimeter of grit, P=7mm.
Now fanning friction factor, f=
Theoretically fanning friction factor ,f=
Sl.no Velocity(m/sec)
Reynoldsno
Pressuredrop
Δp
(pascal)
Fanningfriction
Factor,f
Theoreticalfanning friction
factor,f
1 1.2 141.16 4.7912 1.0348 0.1133
2 2.4 282.32 16.470 0.8893 0.0567
3 3.6 423.48 35.027 0.8406 0.0378
4 4.8 564.64 60.463 0.8162 0.0283
5 6.0 705.80 92.778 0.8015 0.0226
Graph showing variation of f vs re.
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Plot of theoretical f Vs Re
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Finding NTU from maximum slope and time corresponding to it.
Velocity=1.2m/sec
Time Temperature Slope N-D
Time
N-D
Temperature
Slope
0 300 .00079 0 1 .001295
1 300.00079 .05991 .061 .999921 .098213
2 300.0607 .24149 .122 .99393 .395885
3 300.30219 .41156 .183 .969781 .674689
4 300.71375 .51388 .244 .928625 .842426
5 301.22763 .56052 .305 .877237 .918885
6 301.78815 .
57034
.366 .821185 .934984
7 302.35489 .55841 .427 .764151 .915426
8 302.9169 .53445 .488 .70831 .876148
9 303.45135 .50433 .549 .654865 .826934
10 303.95578 .47183 .610 .604422 773492
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Temperature response graph at outlet has a s shape
Velocity=2.4m/sec
Time Temperature Slope N-D
Time
N-D
Temperature
Slope
0 300 .00351 0 1 .002877
1 300.00351 .21967 .122 .999649 .180057
2 300.22318 .74887 .244 .977682 .613828
3 300.97295 1.08743 .366 .903795 .891366
4 302.05948 1.1676
6
.488 .794052 .957098
5 303.22714 1.0147 .610 .677286 .902844
6 304.32861 .97425 .732 .567139 .798566
7 305.30286 .83386 .854 .469714 .683492
8 306.13672 .69836 .976 .386328 .572426
9 307.41179 .57682 1.098 .25881 .472803
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10 307.88821 .47631 1.22 .211179 .390418
Similarily for velocity=3.6m/sec, we have
Maximum slope= .99839
Time at maximum slope=.549s
Re NTU
141.16 3.5
282.32 4.1
423.48 4.4
RESULT
NTU for various values where found out from the graph showingVariation of maximum slope with time of maximumslope for various ntu and λ.There is a slight increase in NTU with Reynolds number
Conclusion
The increase in NTU with Re is due to the increase in mass flow
rate with velocity which predominates over the decrease in time of
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occurrence of maximum variation in temperature response plot of
outlet.