Conjugate Heat Transfer In Porous Media

gartz89 · January 24, 2022, 16:00

Before 2 years we made a CFD model of the conjugate heat transfer in ceramic regenerative heat exchangers aiming a heat recovery in air conditioning systems is elaborated. The transient thermal and fluid flow fields in such a regenerator are obtained via numerical solutions by the finite volume method. The models are validated by comparing the computed and measured outlet temperatures and the heat transfer coefficients obtained by the simulations and the theory of similarity.

https://www.researchgate.net/publica...G_APPLICATIONS

Now we are doing more deep research, but at this time we can't apply the model of the above article. So we have to create a new CFD model Conjugate Heat Transfer in Porous Media, but we wondering how Fluent simulate the porous. We've got a honeycomb matrix with square channels and we would like to imitate as porous media. If we change the honeycomb structure and for example, we use rectangle channels how does influence the porous media, what do we have to change? How does Fluent know what is the structures of porous media or we must write a UDF for this problem. Thank you!

LuckyTran · January 24, 2022, 16:29

The porous media model in Fluent and just about any CFD software is LIH (linear, isotropic, homogeneous). It has no clue what is the microstructure.

A honeycomb is obviously not linear, not isotropic, and not homogeneous. That doesn't prevent you of course from applying a porous media model anyway. LIH porous media have two properties:

its pressure drop characteristics which is your Darcy (and sometimes Forchheimer) coefficients.
porosity, which tells you of the volume designated as being porous, the % occupation of solid and % occupation of fluid.

The porosity you can determine from just a simple CAD definition. Get the volume of the solid and divide by the total volume. The Darcy coefficient you can calculate if you have the pressure drop vs velocity (or flowrate) curve of your honeycomb.

gartz89 · January 25, 2022, 00:16

Thank you for your reply. Yes, you are quite right but if I calculate the porosity of the square structure and the rectangle structure the pressure drop and the Darcy coefficient will be different. Therefore the conjugate heat transfer will be rather different. I'm not quite sure but when I specified the different porosity of structures and the boundary conditions of the model as hydraulic diameter and inlet velocity (volume flow rate) is the same does is correct. Just I want to optimize the honeycomb structures and fix the velocity and hydraulic diameter through the channels so that the flow rate is approximately equal. And then I have to observe the different heat transfer that occurs and see which structure is the best in my case. So I really don't understand how the software can be solved only with the value of porosity. Thank you again.

NickFL · February 7, 2023, 03:24

This is a type of problem that I have run across in the past. The approach I have taken is the following:

1. Create a simple "mirco" model of a known length that simulates simply one hex and use the peroidic boundary conditions on the walls. Include an upstream and downstream section. Simulate this at several different flow conditions, i.e. velocities and temperatures. From these results you should be able to determine the coefficients for the porous media. Keep in mind this will only be in the 1 direction (streamwise). Because of the presence of the walls, the others will be infinity.

2. Create a "macro" model where the bed is modeled as a porous media. It may be best to orient your model so that the streamwise direction through the porous media is in one of the primary directions (X, Y or Z). Notice that you can put a directional dependence on this coefficient. So for the coefficient that is computed from 1, here is where you input it. For the other two directions, simply add a much higher coefficient. (For example if your coefficent is 3e5, make the other two 3e9 or something.) Here you can also input coefficients for the heat transfer and the interfacial area density.

I hope that helps point you in a direction to model it. Keep in mind, there are many different ways to model the same problem. Simulation is much an art as it is a science. The goal is to get a good solution that matches reality with the computing resources we are allocated.

January 24, 2022, 16:00	Conjugate Heat Transfer In Porous Media	#1
gartz89 Member Angel Penev Join Date: Apr 2016 Location: Bulgaria Posts: 47 Rep Power: 10	Before 2 years we made a CFD model of the conjugate heat transfer in ceramic regenerative heat exchangers aiming a heat recovery in air conditioning systems is elaborated. The transient thermal and fluid flow fields in such a regenerator are obtained via numerical solutions by the finite volume method. The models are validated by comparing the computed and measured outlet temperatures and the heat transfer coefficients obtained by the simulations and the theory of similarity. https://www.researchgate.net/publica...G_APPLICATIONS Now we are doing more deep research, but at this time we can't apply the model of the above article. So we have to create a new CFD model Conjugate Heat Transfer in Porous Media, but we wondering how Fluent simulate the porous. We've got a honeycomb matrix with square channels and we would like to imitate as porous media. If we change the honeycomb structure and for example, we use rectangle channels how does influence the porous media, what do we have to change? How does Fluent know what is the structures of porous media or we must write a UDF for this problem. Thank you!

January 24, 2022, 16:29		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	The porous media model in Fluent and just about any CFD software is LIH (linear, isotropic, homogeneous). It has no clue what is the microstructure. A honeycomb is obviously not linear, not isotropic, and not homogeneous. That doesn't prevent you of course from applying a porous media model anyway. LIH porous media have two properties: its pressure drop characteristics which is your Darcy (and sometimes Forchheimer) coefficients. porosity, which tells you of the volume designated as being porous, the % occupation of solid and % occupation of fluid. The porosity you can determine from just a simple CAD definition. Get the volume of the solid and divide by the total volume. The Darcy coefficient you can calculate if you have the pressure drop vs velocity (or flowrate) curve of your honeycomb. gartz89 likes this.

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January 25, 2022, 00:16		#3
gartz89 Member Angel Penev Join Date: Apr 2016 Location: Bulgaria Posts: 47 Rep Power: 10	Thank you for your reply. Yes, you are quite right but if I calculate the porosity of the square structure and the rectangle structure the pressure drop and the Darcy coefficient will be different. Therefore the conjugate heat transfer will be rather different. I'm not quite sure but when I specified the different porosity of structures and the boundary conditions of the model as hydraulic diameter and inlet velocity (volume flow rate) is the same does is correct. Just I want to optimize the honeycomb structures and fix the velocity and hydraulic diameter through the channels so that the flow rate is approximately equal. And then I have to observe the different heat transfer that occurs and see which structure is the best in my case. So I really don't understand how the software can be solved only with the value of porosity. Thank you again.

February 7, 2023, 03:24		#4
NickFL Senior Member Join Date: Jun 2009 Location: Technische Universität Chemnitz Posts: 107 Rep Power: 17	This is a type of problem that I have run across in the past. The approach I have taken is the following: 1. Create a simple "mirco" model of a known length that simulates simply one hex and use the peroidic boundary conditions on the walls. Include an upstream and downstream section. Simulate this at several different flow conditions, i.e. velocities and temperatures. From these results you should be able to determine the coefficients for the porous media. Keep in mind this will only be in the 1 direction (streamwise). Because of the presence of the walls, the others will be infinity. 2. Create a "macro" model where the bed is modeled as a porous media. It may be best to orient your model so that the streamwise direction through the porous media is in one of the primary directions (X, Y or Z). Notice that you can put a directional dependence on this coefficient. So for the coefficient that is computed from 1, here is where you input it. For the other two directions, simply add a much higher coefficient. (For example if your coefficent is 3e5, make the other two 3e9 or something.) Here you can also input coefficients for the heat transfer and the interfacial area density. I hope that helps point you in a direction to model it. Keep in mind, there are many different ways to model the same problem. Simulation is much an art as it is a science. The goal is to get a good solution that matches reality with the computing resources we are allocated.