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Convective term in heat equation for rotating solids 

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October 16, 2015, 17:55 
Convective term in heat equation for rotating solids

#1 
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Hello FOAMers,
I recently created a solver for steadystate, incompressible flow, multiregion conjugate heat transfer in a single rotating frame. The equations that are solved in the fluid and solid regions are listed in one of the attached images (equations.png). The variable V is the velocity in the rotating frame and Vrot in the solid equation is the convective velocity due to relative motion in the rotating frame of reference. A crosssectional view of the geometry can be found in the attached image. Symmetry is applied to the top and bottom walls and cyclic BCs are applied to the side walls. A volumetric heat source is applied. The rotating frame is fixed to the fluid region. The Solid2 rotates with the fluid region. Whereas, "solid1" remains stationary i.e. it rotates in the opposite direction relative to fluid region in the rotating frame. Hence, the convective term in the heat equation for this particular region is nonzero. I ran a couple of test cases to make sure if everything is in order but I noticed some strange temperature profiles in the circumferential direction in "solid1" region near the solid1  heat zone interface (The dotted line in geometry.png shows the line where the temp. profile was plotted). In the case where the solid1 region was rotating with the fluid region I saw a perfectly symmetric temperature profile in the circumferential direction, as expected (rotaing_Tprofile.png). However, when the solid1 region was set to stationary or set to rotate in the opposite direction relative to friction plate in the rotating frame, I am seeing some strange results. Of course, the temp. profile in this case will not be symmetric due to the shear action of the solid1 region at the solid1  fluid interface. However, I would expect the slope at the two ends of cyclic boundaries to be similar. I don't see that (nonrotaing_Tprofile.png). At this point, I am not sure if I missing something or if indeed the slopes won't be same at both ends. I believe this inconsistency arises from the convective term in the heat equation in solid region. I am not sure if the cyclic boundaries is the root cause or if my implementation of the heat equation with convective term is incorrect. The following code reflects the implementation of heat equation in the solid region: Code:
tmp<fvScalarMatrix> TEqn ( fvm::ddt(T) + fvm::div(((linearInterpolate(SRFS.U())) & solidRegions[i].Sf()),T)  fvm::laplacian(DT, T) == HeatSource ); TEqn().relax(); TEqn().solve(); Any suggestions/pointers would really help. Please let me know if you need more information. Thanks, Abishek Last edited by vabishek; October 16, 2015 at 17:58. Reason: typo 

October 24, 2015, 17:29 

#2 
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Bruno Santos
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Hi Abishek,
As I mentioned in the answer I sent you to the PM you sent me, without a test case and access to the source code, I'm not able to diagnose problem. My guess is that the problem is not in the equations, but instead the problem might be in the boundary conditions that relate the static and the rotating regions. The other possibility is that the flux disturbances caused by mesh motion or by the MRF/SRF are not being taken into account for the heat distribution equation. Beyond this, my guess is that you should take a closer look into the tutorial "$FOAM_TUTORIALS/heatTransfer/chtMultiRegionSimpleFoam/heatExchanger" in the latest versions of OpenFOAM. Best regards, Bruno
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November 8, 2015, 06:46 

#3  
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Bruno Santos
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Hi Abishek,
Even though you've sent me the case via PM, I'll answer most of the questions here in public, without disclosing the case itself. Quote:
Quote:
The first problem I noticed is that the plot axis in the images do not match up to the dimensions you stated, namely "0.0050563 to 0.0050563" doesn't match up with the plots that have "0.0 to 0.01xx"... unless you transposed the X axis by "+0.0050563". From what I can figure out, the problem doesn't seem to be in the solver itself, the temperature plot seems to be reflecting the flow being rotated as a result of the Coriolis effect. Since you still defined in the file "constant/S1SRFProperties" that the fluid domain is rotating, even though you defined the other two solids are stationary, but the domain itself is still rotating. In addition, there is nothing stating if the region "HeatSource" is static or not, i.e. "constant/S4SRFProperties" doesn't exist... so I guess it's using the definition that is in "constant/SRFProperties"? Which it is also rotating? In other words, even though the solids are not rotating, the heat source is rotating, so is the fluid domain, therefore the temperature distribution seems legitimate for the stationary solids, because the flow is being pushed against the heat source on one side and pulled away on the other side. By the way, the solver wasn't in the shared folder. But it's for the best, because I hopefully diagnosed this correctly after looking at the mesh, how the parts are connected and how the boundaries and SRF settings were defined. In addition, you might want to doublecheck if the diagnosis about the flow is correct. Use an already existing SRF solver to test the flow for the fluid part, i.e. to confirm if the flow profile with static solids is correct in your solver. Best regards, Bruno
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November 9, 2015, 11:52 

#4  
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Hi Bruno,
Thank you for looking into the issue. Quote:
Quote:
Quote:
If I understand you correctly, we don't see similar slopes at the boundaries because the flow is being pushed against the heat source on one side and pulled away on the other side? Quote:
Quote:
Thanks, Abishek 

November 15, 2015, 16:10 

#5 
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Bruno Santos
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Hi Abishek,
Attached are 2 images that shows the plot at time "10", because I didn't want to run the complete simulation:
The cyclic boundary condition only ensures that the values on each patch are identical. It does not ensure that the gradients near the patches are identical as well. I hope this makes things clearer? Best regards, Bruno 

November 16, 2015, 16:06 

#6  
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Quote:
Thank you for your explanation. Things are much clearer now. If I understand correctly, I need to write my own piece of code that would take care of gradients near the patches as part of the cyclic boundary condition? Any pointers? I know it is not that straightforward but I am trying to get my head around to see if something like that is feasible. Thanks, Abishek 

November 17, 2015, 16:12 

#7  
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Quote:
What I forgot to mention is that from what I could figure out, the results seemed physically correct. Have a look at the temperature profile in the fluid region and you'll also see that it's more intensely transferring heat more to one side than the other. Because if most of the solid regions are stationary and only one solid is rotating, then that means that there is practically a moving wall going over one side of the fluid region, resulting in a swirl effect being induced inside the fluid region. 

November 18, 2015, 15:04 

#8  
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Quote:
Thanks for your help on this, Bruno. I appreciate it. Regards, Abishek 

June 24, 2020, 11:10 

#9  
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Quote:
How you calculated Vrot in your solver? 

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