by prof. zeinab s. abdel rehim & m. a. ziada and salwa el-deeb h mechanical engineering...

BY

Prof. Zeinab S. Abdel Rehim

&

M. A. Ziada and Salwa El-Deeb H

Mechanical Engineering Department

National Research Centre

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ICMCE 2015 : 17th International Conference on Mechanical and Control Engineering, Zurich, Switzerland, July 29 - 30, 2015

Numerical Study of Fluid Flow and Heat Transfer in the Spongy-Porous Media

Outlines

1- Abstract and introduction2- Theoretical work

◦Physical model◦Solid model◦Mathematical model ◦ Solution procedure

• 3- Results and discussion• 4- Conclusion and

recommendation• 5- References


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ABSTRACT

Numerical study of fluid flow, heat transfer and thermal energy storing or released in/from spongy-porous media to predict the thermal performance and characteristics of the porous media as packed bed system is presented in this work. This system is cylindrical channel filled with porous media (carbon foam). The system consists of working fluid (air) and spongy-porous medium; they act as the heat exchanger (heating or cooling modes) where thermal interaction occurs between the working fluid and the porous medium. The spongy-porous media are defined by the different type of porous medium employed in the storing or cooling modes. Two different porous media are considered in this study: Carbon foam, and Silicon rubber. The flow of the working fluid (air) is one dimensional in the axial direction from the top to downward and steady state conditions. The numerical results of transient temperature distribution for both working fluid and the spongy-porous medium phases and the amount of stored/realized heat inside/from the porous medium for each case with respect to the operating parameters and the spongy-porous media characteristics are illustrated.

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Aim of this study:

The study goals have been achieved through vital and advanced numerical simulation for fluid flow, heat transfer to obtain the temperature field inside the spongy porous media for both working fluid (air or water) and the porous medium.

Then, the amount of energy stored or released for case of different conditions and parameters are obtained for both air and water working fluid

A comprehensive survey and critical review of the literature related to the present problem and ending to the recent years (up to 2013)

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A special program was developed to find the numerical model for spongy porous media to use in heat exchangers as heating or cooling systems.


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Physical Model of the Present System

THEORETICAL WORK

•The physical model of the system considered in the present work is described as a cylindrical enclosure filled with porous media such as Carbon foam.

•The flow of the working fluid (air) is one dimensional in the axial direction from the top to downward and steady state conditions.

•The present system can mathematically be modeled using the appropriate conservation equations applied to the working fluid (air) and spongy-porous medium separately.

BA C

Solid modeling of carbon foamA solid model aims to approximate the carbon foam with a volumetric segment (C) obtained by subtracting a bed of spheres (B) from a solid volume (A), From the Figures: C = A – B.P

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MATHEMATICAL MODELING

The problem under investigation is forced convection of incompressible fluid flow through open-celled metal foams.

The general transport equations are commonly integrated over a representative elementary volume.


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The assumptions upon which the numerical model is based are summarized as follows:

1. The medium is homogeneous and isotropic .2. Forced convection dominates in the metal foams, i.e., natural

convection effects are negligible.

3. Variation of the thermo physical properties with temperature is ignored.

4. Due to the relatively low operating temperature (<100oC) considered in the present study, radiation heat transfer is neglected.

5. Fluid flow and heat transfer reach steady state in the channel.


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The governing equations are:•The conservation equations: Continuity, momentum and energy equations are applied for the present system.

•The equations of the present model provide the transient temperature distribution for both working fluid (air/water) and spongy-porous medium and the amount of heat stored or released within the system at any instant of time.

•The set of partial differential energy equations for the working fluid and solid phases can be simplified as:

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Initial and boundary conditions:

-For fluid at Z=0, Tf = Tin for all t

at t=0, Tf = Tin for Z=0

and Tf = To for Z≠0

-For solid at t=0 Ts=To for all Z

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1- Initial conditions

Physical Model of the Present System

2- Boundary conditions

The appropriate upstream and downstream boundaries conditions are specified by the solid temperature satisfies the energy equation at the upstream and downstream boundaries, respectively, i.e.

At Z=0 for all t

At Z=L for all t

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The solution procedure:The set partial differential equations that govern the thermal behavior of the foam thermal storage system are first reduced to finite difference equations along with their associated initial and boundary conditions.

The energy stored in the solid phase at each time step can be obtained by numerically integrating the following integral:

This yields as follows:

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Table: Numerical values of the parameter considered in the numerical analysis

Parameters Values

Mass flow rate, G, kg/s 0.1, 0.15, 0.2, 0.25, and 0.3

Bed diameter, m 0.4

Bed length, BL, m 0.3, 0.4, 0.5, and 0.6

Porosity, e 0.2, 0.25, 0.3, 0.35, and 0.38

Particles diameter, dp, m 0.003, 0.004, 0.005, and 0.007

Inlet working fluid (air) temperature, Ti, oC 60, 70, 80, and 85

Cooling or heating times, t, h 3, 4, 5, 6, and 7

Porous materials Carbon foam and Silicon rubber

Ambient temperature, To, oC 25

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RESULTS AND DISCUSSIONS

•The heat transfer, fluid flow and thermal behavior of spongy-porous media system are, generally, described by the temperature distribution for the working fluid and porous media phases in the axial direction and the energy stored or released at different time intervals

•The present model has suitable selected numerical values of constant parameters and matrix variables such as length, height of the channel, inlet temperature of the working fluid, mass flow rate, porous material, particle diameter of the porous media, and porosityP

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.The time is extended until saturation mode of the medium occurs, then, the amount of energy stored or released inside or from the medium, respectively.


•The behavior and performance of the present system has been evaluated by the computation of the temperature distribution for both working fluid and porous medium along the cylindrical enclosure at various operating parameters.

•The variation of working fluid temperature distribution and solid temperature distribution at different time intervals and various axial locations during the cooling process of the system are illustrated in the following Figures.

•Also, the variation of energy extracted with above the different parameter's effect are presented in the following Figures.

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The following figures show the variation for temporal and spatial of the air and solid temperature distribution during cooling and storing modes.

Also, variation of energy extracted with time and variation of energy stored with time for Carbon foam for different effected parameters.

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-Effect of working fluid mass flow rate-Effect of bed length -Effect of porosity-Effect of particle diameter-Effect of inlet working fluid temperature-Effect of the porous medium with effect other parameters

Z/L

=0

Z/L

=0.1

Z/L

=0.2

Z/L

=0.3

Z/L

=0.4

Z/L

=0.5

Z/L

=0.6

Z/L

=0.7

Z/L

=0.8

Z/L

=0.9

Z/L

=1.0

0

10

20

30

40

50

60

70

80

t = 0 mint = 15 mint = 30 mint = 60 mint = 90 mint = 120 mint = 150 min

Axial locations, Z/L

Air

tem

pera

ture

, Ta,

oC

Air temperature variation with axial locations at different times during bed

cooling

BL=0.4m, DP=0.003m,

e=0.38, Ta=25oC,Tf=80oC

G=0.1kg/s, Carbon

0 15 30 45 60 75 90 105 120 135 150 165 1800

10

20

30

40

50

60

70

80

Z/L=0 Z/L=0.1 Z/L=0.2 Z/L=0.3

Z/L=0.4 Z/L=0.5 Z/L=0.6 Z/L=0.7

Z/L=0.8 Z/L=0.9 Z/L=1.0

Time, min.

Air

tem

pera

ture

, Ta,

oC

BL=0.4m, DP=0.003m

e=0.38, Tf=25oC, Ts =80oC

G=0.1kg/s, Carbon

Air temperature variation with time at different axial locations during bed

cooling.

Fluid temperature distribution

•porous medium (Carbon foam) temperature distribution

0 15 30 45 60 75 90 105 120 135 150 165 1800

10

20

30

40

50

60

70

80

Z/L=0 Z/L=0.1 Z/L=0.2

Z/L=0.3 Z/L=0.4 Z/L=0.5

Z/L=0.6 Z/L=0.7 Z/L=0.8

Z/L=0.9 Z/L=1.0

Time, min.

Soli

d te

mpe

ratu

re, T

s, o

C

Z/L

=0

Z/L

=0.1

Z/L

=0.2

Z/L

=0.3

Z/L

=0.4

Z/L

=0.5

Z/L

=0.6

Z/L

=0.7

Z/L

=0.8

Z/L

=0.9

Z/L

=1.0

0

10

20

30

40

50

60

70

80

t = 0 min t = 15 mint = 30 min t = 60 mint = 90 min t = 120 mint = 150 min t = 180 min

Axial locations, Z/L

Soli

d T

empe

ratu

re, T

s, o

C

Solid temperature variation with time at different axial locations during bed cooling.

Solid temperature variation with axial locations at different times during bed cooling

BL=0.4m, DP=0.003m

e=0.38, Ta=25oC, Tf=80oC

G=0.1kg/s, Carbon

BL=0.4m, DP=0.003m

e=0.38, Ta=25oC, Tf=80oC

G=0.1kg/s, Carbon

0 15 30 45 60 75 90 105 120 135 150 165 1800

10

20

30

40

50

60

70

80

Z/L=0 Z/L=0.1 Z/L=0.2 Z/L=0.3Z/L=0.4 Z/L=0.5 Z/L=0.6 Z/L=0.7Z/L=0.8 Z/L=0.9 Z/L=1.0

Time, min.

Air

tem

pera

ture

, oC

Tin = 80oC

BL = 0.4m Dp = 0.003m

ε = 0.38

Z/L

=0

Z/L

=0.

1

Z/L

=0.

2

Z/L

=0.

3

Z/L

=0.

4

Z/L

=0.

5

Z/L

=0.

6

Z/L

=0.

7

Z/L

=0.

8

Z/L

=0.

9

Z/L

=1.

00

10

20

30

40

50

60

70

80

t = 0 min t = 15 min t = 30 mint = 60 min t = 90 min t = 120 mint = 150 min t = 180 min

Axial locations, Z/LA

ir te

mpe

ratu

re, T

a, o

C

Tin = 80oC, BL = 0.4m

Dp = 0.003m, ε = 0.38

Air temperature variation with time at different axial locations during storing mode, (G=0.1kg/s, Carbon).

Air temperature variation with axial locations at different times during storing mode, (G=0.1kg/s, Carbon).


0 15 30 45 60 75 90 105 120 135 150 165 180

-3000

-2500

-2000

-1500

-1000

-500

0

G=0.1kg/s

G=0.15kg/s

G=0.2kg/s

G=0.25kg/s

G=0.3kg/s

Time, minE

nerg

y, k

J

BL=0.4m, DP=0.003m

e=0.38, Ta=25oC, Ts

=80oC

0 15 30 45 60 75 90 105 120 135 150 165 180

-4000

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

BL=0.3

BL=0.4

BL=0.5

BL=0.6

Time, min

Ene

rgy,

kJ

G=0.1kg/s, DP=0.003m

e=0.38, Ta=25oC, Ts =80oC


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Variation of energy extracted with time at different air mass flow rate

Variation of energy extracted with time at different bed lengths .

G=0.1kg/s, DP=0.003m

BL=0.4m, Ta=25oC, Ts =80oC

0 15 30 45 60 75 90 105 120 135 150 165 180

-3000

-2500

-2000

-1500

-1000

-500

0

DP =0.003

DP=0.004

DP=0.005

DP=0.007

Time,min

Ene

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kJ

G=0.1kg/s, BL=0.4m, e=0.38, Ta=25oC,Ts =80oC

Variation of energy extracted with time at different porosities

Variation of energy extracted with time at different particles diameters .

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0 30 60 90 120 150 1800

500

1000

1500

2000

2500

3000

G=0.1kg/s

G=0.15kg/s

G=0.2kg/s

G=0.25kg/s

G=0.3kg/s

Ene

rgy,

kJ

Time, min

Tin = 80oC, BL = 0.4m

Dp = 0.003m, ε = 0.38

Variation of energy stored with time at different air mass flow rate

0 15 30 45 60 75 90105

120135

150165

1800

500

1000

1500

2000

2500

3000

3500

4000

BL=0.3

BL=0.4

BL=0.5

BL=0.6

Ene

rgy,

kJ

Time, time

Tin = 80oC, G= 0.1kg/s

Dp = 0.003m, e = 0.38

Variation of energy stored with time at different bed lengths

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0 30 60 90 120 150 1800

500

1000

1500

2000

2500

3000

3500

4000

ε=0.2

ε=0.25

ε=0.3

ε=0.35

ε=0.38

Ene

rgy,

kJ

Time, min.


Dp = 0.003m, BL = 0.4m

Variation of energy stored with time for Carbon foam at different values of the porosity.

0 15 30 45 60 75 90105

120135

150165

1800

500

1000

1500

2000

2500

3000

Dp=0.003

Dp=0.004

Dp=0.005

Dp=0.006

Dp=0.007

Time, min

Ene

rgy,

kJ

G=0.1kg/secBL=0.4mε=0.38Tin=80oC

Variation of energy stored with time for Carbon foam at different values of the particles

diameter .


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Verification of the present numerical model

The validity of the present model is demonstrated by comparison with experimental measurements recorded by Master's Thesis of Michael Paul Trammell [59] which entitled evaluation of the transient thermal performance of a Graphite foam. Graphite foam is a rigid open-celled porous carbon material.

The data collection was taken at positions which are located at Z/L=0.2, 0.6 and 1.0 of the sample and the water mass flow rate was 0.3 kg/s.


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0 90 180

270

360

450

540

630

720

810

900

990

0

10

20

30

40

50

60

70

80

90

100

Z/L=0.2 (presen)

Z/L=0.6 (present)

Z/L=1.0 (present)

Z/L=0.2 (Ref. [59])

Z/L=0.6 (Ref. [59])

Z/L=1.0 (Ref. [59])

Sol

id T

empe

ratu

re, T

s o C

Time, s

The transient temperature for the Carbon foam (present work) and Graphite foam sample of Ref. [59]

From the figures, fair agreement between the present work and the experimental work of the Ref. [59] with maximum diviation of 8% for Z/L=1.0.

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Dp = 0.003m, BL = 0.4m

ConclusionsBased on this study, the following conclusions can be reached:

•The mathematical model and the used numerical technique are powerful to predict the performance and characteristics of the heat transfer and fluid flow through the porous spongy material systems.

•Increasing the working fluid mass flow rate pronouncedly enhances the heat transfer rate between both working fluid and porous medium phases and, consequently, decreases markedly the time required for fully heating or cooling the system. However, it does not affect the total amount of heating or cooling capacity of the system.

•The increase of the system length increasing the capacity of the heating or cooling the enclosure, but does not affect the heating or cooling a longer system, keeping the diameter constant..

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•The higher porosity of the porous media results in a longer time needed to reach the saturation. On other hand, the capacity of heating or cooling for the system is lowered due to the smaller volume of the absorbing material.

•Increasing the particle diameter results in an increasing in the rate of heating or cooling process with no effect on the heat or cool capacity of the system.

•The thermal heating or cooling of the present system at any time increases linearly with increase of the inlet working fluid temperature, on the other hand, the increase in the inlet working fluid temperature decreases the time required to heat or cool the system with a certain amount of the heating or cooling.

•The comparison between the present work and the pervious experimental work of Ref. [59] is good agreement.•A good agreement between the present work and the pervious experimental work is concluded


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Recommendation for future work

It is recommended that more research is required to investigate the following points:

•The thermal performance of the various porous spongy materials with different thermal and physical properties used as layers in present system to utilize in heat exchangers applications.

•Two and three dimensional model is needed take into consideration the radial and angular variation of the temperature through the porous spongy media. This, also, will allow the study of losses to the surrounding.

•The effect of the heat transfer by radiation through the porous media system may be considered in further analysis.•Economical studies to determine the optimum porous spongy media system.P

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by prof. zeinab s. abdel rehim & m. a. ziada and salwa el-deeb h mechanical engineering...

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