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Viscous terms in rhoCentralFoam

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Old   September 20, 2010, 10:50
Default Viscous terms in rhoCentralFoam
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Florian Ettner
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Dear Foamers,
I have a few questions on the viscous terms in rhoCentralFoam. In the source code, the energy equation looks like this:

Quote:
00176 solve
00177 (
00178 fvm::ddt(rhoE)
00179 + fvc::div(phiEp)
00180 - fvc::div(sigmaDotU)
00181 );
00182
00183 e = rhoE/rho - 0.5*magSqr(U);
00184 e.correctBoundaryConditions();
00185 thermo.correct();
00186 rhoE.boundaryField() =
00187 rho.boundaryField()*
00188 (
00189 e.boundaryField() + 0.5*magSqr(U.boundaryField())
00190 );
00191
00192 if (!inviscid)
00193 {
00194 volScalarField k("k", thermo.Cp()*mu/Pr);
00195 solve
00196 (
00197 fvm::ddt(rho, e) - fvc::ddt(rho, e)
00198 - fvm::laplacian(thermo.alpha(), e)
00199 + fvc::laplacian(thermo.alpha(), e)
00200 - fvc::laplacian(k, T)
00201 );
00202 thermo.correct();
00203 rhoE = rho*(e + 0.5*magSqr(U));
00204 }
1. Why is the viscous term "sigmaDotU" included in the inviscid equation?
2. I think I understand the heat conduction in line 200. What kind of conduction of internal energy is in lines 198-199 ?
3. What is the use of the repeated use of fvm and fvc discretisation of the same expressions in lines 197-199? Why is it not applied to the heat conduction in line 200?

I'd be glad if anybody could help me understanding this issue. It would be quite important to me, as I currently work on extending the solver to reactive flows.

Thank you in advance!
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Old   March 14, 2012, 05:47
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Alexander
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Good day to everyone!

I also use rhoCentralFoam and I am interesting in questions about viscous dissipation.
And about your questions:
2. "I think I understand the heat conduction in line 200. What kind of conduction of internal energy is in lines 198-199 ?" I want to know answer too =) Probably, it is turbulent heat transfer. In new version of rhoCentralFoam it is written as
Code:
- fvm::laplacian(turbulence->alphaEff(), e)
+ fvc::laplacian(turbulence->alpha(), e)
3. "What is the use of the repeated use of fvm and fvc discretisation of the same expressions in lines 197-199?"
Answer is simple: there is solving of "corrector" step, because "fvm" means that for this term the matrix is prepared and the system wil be solved ("m" for "matrix"). Term with "fvc" means that term will be calculated in explicit way (the right part of matrix equation; "c" for "calculate"). So, lines 197-200 is the corrector which include the influence of thermal conductivity part in energy equation. Why turbulence is there? I do not know. I hope, alpha is zero for laminar flow =)

But the main question: is the dissipation correctly taken into account? Because in my laminar trans-sonic tests (with low Reynolds number about 100) heating due to dissipation is absent (although it should be meaningful) =(
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Old   March 21, 2012, 04:05
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Alexander
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I've just found that Prandtl number in rhoCentralFoam is always 1 (independent of what you have set in constant/thermophysicalProperties).
See bug http://www.openfoam.org/mantisbt/view.php?id=475
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