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



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


Dr.B.Anil

Professor&Head




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



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



Introduction

Literature Review

Project Theory

Analysis Procedure

Results and Discussions

Result Summary

Conclusion

Reference



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



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



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



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



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



• 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



Analysis Procedure

Modelling procedure in GambitPOROSITY, φ= 0.6.

Specifying solver for analysis



Creating Geometry

Creating nodes



Creating edges



Creating Face from wireframe



Meshing Procedure

Inputting spacing for mesh



Creating the Mesh



Specifying Boundary Conditions



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



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



Steady state analysis to find dependence of Friction

Specifying solver for analysis



Inputting the material Properties

Specifying the operating and boundary conditions



Solution Initialization for Steady State



Setting up the convergence criteria



THERMAL ANALYSIS



Inputting Unsteady state conditions



Specifying the Temperature for unsteady state



Solution initialization for unsteady state condition



Defining surface monitor



Specifying the time step for iteration

RESULTS AND DISCUSSION



Contours for static pressure

Temperature response diagram



Trend line for ∆p v/s velocity



y = 0.0003x3 - 0.0192x2 + 0.4403x

R2 = 0.9833

1

2

3

4

5

6

Trendline for Reynolds no: vs Friction factor



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)



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



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



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.



Plot of theoretical f Vs Re



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



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



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



occurrence of maximum variation in temperature response plot of

outlet.

project report final03

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