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Inlet outlet mass flux is not identical
Posted May 14, 2013, 2:24 a.m. EDT Fluid & Heat, Heat Transfer & Phase Change, Results & Visualization Version 4.3 5 Replies
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Hi all,
I am trying to measure the bulk temperature, but initial testing on the conservation of mass failed as it gave me different results between the inlet and the outlet mass flux. This result makes me doubt all my simulation results so I would like to know what's going on. The model is a rectangular duct flow with 1) heat transfer on one side and 2) prescribed temperature at one of the walls and the channel inlet.
I used two 'general projection' planes to measure the mass flow rate over the entire channel length. As you can see in the graph, there is a sharp rise at x=0 (not to mention the fluctuations. I would say it's a numerical uncertainty due to the meshing). I don't understand why this is happening as this happens even if I refine the mesh, which is very concerning.
Any suggestions on why there is a discrepancy in the mass flux along the channel? Please let me know if there is any mistakes in my model.
Thanks!
Best,
Tae Jin Kim
ps: I also quantified the bulk temperature based on some discussions threads and extensive trial and error. At this point, I think it's almost correct, but please let me know if there is an error.
I am trying to measure the bulk temperature, but initial testing on the conservation of mass failed as it gave me different results between the inlet and the outlet mass flux. This result makes me doubt all my simulation results so I would like to know what's going on. The model is a rectangular duct flow with 1) heat transfer on one side and 2) prescribed temperature at one of the walls and the channel inlet.
I used two 'general projection' planes to measure the mass flow rate over the entire channel length. As you can see in the graph, there is a sharp rise at x=0 (not to mention the fluctuations. I would say it's a numerical uncertainty due to the meshing). I don't understand why this is happening as this happens even if I refine the mesh, which is very concerning.
Any suggestions on why there is a discrepancy in the mass flux along the channel? Please let me know if there is any mistakes in my model.
Thanks!
Best,
Tae Jin Kim
ps: I also quantified the bulk temperature based on some discussions threads and extensive trial and error. At this point, I think it's almost correct, but please let me know if there is an error.
5 Replies Last Post May 15, 2013, 2:15 a.m. EDT
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Posted:
1 decade ago
Hi,
I didn't see any graph nor model attached to you message ;)
Anyway, conservation of mass with Finite Elements Method cannot be guaranteed!
You can test it yourself if you simplify your model: forget the temperature...solve just for the velocity fields and you'll see that, independently on you mesh refinement, the mass isn't perfectly conserved.
Hope it helps,
Mattia
I didn't see any graph nor model attached to you message ;)
Anyway, conservation of mass with Finite Elements Method cannot be guaranteed!
You can test it yourself if you simplify your model: forget the temperature...solve just for the velocity fields and you'll see that, independently on you mesh refinement, the mass isn't perfectly conserved.
Hope it helps,
Mattia
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Posted:
1 decade ago
Hi Mattia,
Thank you for the response. I thought I attached the file but just noticed it wasn't there.
I didn't know that the mass flux may not be identical between the inlet and outlet (I guess I need to understand FEM better). I think this is indeed the main issue here, but I'm attaching my model so you can check if I am in the right path.
In the attached model, I mapped out 1D graphs of mass flow rate vs x and bulk temperature vs x.
Thanks!
Best,
Tae Jin Kim
Thank you for the response. I thought I attached the file but just noticed it wasn't there.
I didn't know that the mass flux may not be identical between the inlet and outlet (I guess I need to understand FEM better). I think this is indeed the main issue here, but I'm attaching my model so you can check if I am in the right path.
In the attached model, I mapped out 1D graphs of mass flow rate vs x and bulk temperature vs x.
Thanks!
Best,
Tae Jin Kim
Attachments:
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Posted:
1 decade ago
Hi,
I had a look at your model... the "werid" peak of mass flux is due to your "wrong" inlet boundary condition. You can understand much more if you keep things easy, at least at the beginning.
I you are willing to inspect simple test case of this type look at the model "cylinder_flow". it's 2D isotermal flow. try to understand the boundary conditions, have a look to the mesh and afterwards add the 'heat transfer' module.
Regarding mass flux.. the problem must be sought within the FEM formulation and the numerical approximation of NavierStokes equation. You can read about this in any book about FEM with applications to CFD. A practical advice to improve this is using a finer mesh and higher order elements.
Mattia
I had a look at your model... the "werid" peak of mass flux is due to your "wrong" inlet boundary condition. You can understand much more if you keep things easy, at least at the beginning.
I you are willing to inspect simple test case of this type look at the model "cylinder_flow". it's 2D isotermal flow. try to understand the boundary conditions, have a look to the mesh and afterwards add the 'heat transfer' module.
Regarding mass flux.. the problem must be sought within the FEM formulation and the numerical approximation of NavierStokes equation. You can read about this in any book about FEM with applications to CFD. A practical advice to improve this is using a finer mesh and higher order elements.
Mattia
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Posted:
1 decade ago
Hi Mattia,
Once again thanks for your response.
I noticed that the average velocity was incorrect.
I thought I used 0.0001m/s but I must have forgot to save it before rerunning the model (the 1m/s it made it turbulent but the module was laminar!)
The Reynolds number is now Re=11 and the entrance length should be around 0.1m, so the water should be coming into the mesh as fully developed and laminar.
Also, I updated the heat transfer portion as uniform heat flux on one wall and adiabatic on all other walls. The inlet temperature is 293K.
I am still seeing a bump in the inlet mass flux. At least now I'm seeing the bulk temperature rise as it should, but it drops from 293K from the inlet to 287K (x>0). Comparing the heated wall temperature to bulk temperature, the reason seems clearer to me. My take is that they both start at the same temperature (which should be the case) but in order to match the constant heat flux boundary condition, the mass flux drops down in order to keep the gap between the wall temperature and the bulk fluid temperature.
I think I need to add a constraint to keep the mass flux constant instead (this will probably increase the wall temperature to keep the heat flux consistent), but do you have any suggestions on how to do this? It might be a simple solution but one problem is leading to another, and I'm concerned that I might start off at a wrong direction.
Thanks.
TJ
Once again thanks for your response.
I noticed that the average velocity was incorrect.
I thought I used 0.0001m/s but I must have forgot to save it before rerunning the model (the 1m/s it made it turbulent but the module was laminar!)
The Reynolds number is now Re=11 and the entrance length should be around 0.1m, so the water should be coming into the mesh as fully developed and laminar.
Also, I updated the heat transfer portion as uniform heat flux on one wall and adiabatic on all other walls. The inlet temperature is 293K.
I am still seeing a bump in the inlet mass flux. At least now I'm seeing the bulk temperature rise as it should, but it drops from 293K from the inlet to 287K (x>0). Comparing the heated wall temperature to bulk temperature, the reason seems clearer to me. My take is that they both start at the same temperature (which should be the case) but in order to match the constant heat flux boundary condition, the mass flux drops down in order to keep the gap between the wall temperature and the bulk fluid temperature.
I think I need to add a constraint to keep the mass flux constant instead (this will probably increase the wall temperature to keep the heat flux consistent), but do you have any suggestions on how to do this? It might be a simple solution but one problem is leading to another, and I'm concerned that I might start off at a wrong direction.
Thanks.
TJ
Attachments:
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Posted:
1 decade ago
Solved the problem: I had the Laminar flow model as 'incompressible'.
I just took it for granted that water is incompressible, which implies that the density is fixated.
Basically, with 'incompressible' flow assumption, the density is decoupled from the mass flux equation and hence is just a surface integral of the normal velocity field. For this case, I confirmed that the average velocity was constant over the entire channel distance, but the average density dropped with distance. Basically, by multiplying these two, the mass flow rate drops by the ratio of the density drop with increased temperature.
Solving the Laminar flow model as compressible (Ma<0.3) definitely made the mass flux constant over the entire channel length. So my take is: if working with fluids without any particular heating (or at least to the point that it is negligible) you can select the 'incompressible' option, but when you couple with heat transfer or anything that may affect the density, select the 'compressible' option. It was a very simple, yet devastating mistake for me.
Now the bulk temperature and the wall temperature acts the way they should, while there is a kink in the mass flow rate at the inlet. I'd say this is just a meshing issue and should reduce with refined meshing. I've attached the final version of my model, so if there is yet again a different mistake, please let me know!
TJ
I just took it for granted that water is incompressible, which implies that the density is fixated.
Basically, with 'incompressible' flow assumption, the density is decoupled from the mass flux equation and hence is just a surface integral of the normal velocity field. For this case, I confirmed that the average velocity was constant over the entire channel distance, but the average density dropped with distance. Basically, by multiplying these two, the mass flow rate drops by the ratio of the density drop with increased temperature.
Solving the Laminar flow model as compressible (Ma<0.3) definitely made the mass flux constant over the entire channel length. So my take is: if working with fluids without any particular heating (or at least to the point that it is negligible) you can select the 'incompressible' option, but when you couple with heat transfer or anything that may affect the density, select the 'compressible' option. It was a very simple, yet devastating mistake for me.
Now the bulk temperature and the wall temperature acts the way they should, while there is a kink in the mass flow rate at the inlet. I'd say this is just a meshing issue and should reduce with refined meshing. I've attached the final version of my model, so if there is yet again a different mistake, please let me know!
TJ
Attachments: