Heat transfer simulation with low-Re modelling blowing up
 

Hi,

I am simulating atmospheric boundary layer flow over an inclined plate with application to solar panels. I am looking into the heat transfer from the panel. At the domain inlet, I am using mean profiles of velocity, turbulent kinetic energy and specific dissipation rate of turbulence using SST k-omega turbulence model. At the outlet of the domain I am using fixed pressure of 0 Pa. Without low-Re mesh (y+ around 200), for getting pressures on the panel (for wind load estimation), simulations runs fine. However for the heat transfer simulations with y+<1, simulation is blowing up as the courant number gets bigger and bigger (even with time step size of 10^-9 s) although wind speed is low for the heat transfer case (5 m/s at 10m height whereas for the wind loading simulation I have used 25 m/s without no problem). I am using buoyantBoussinesqPimpleFoam solver for the heat transfer simulation. My fvSchemes for heat transfer looks like the following:

ddtSchemes
{
default Euler;
}

gradSchemes
{
default cellLimited leastSquares 1.0;
}

divSchemes
{
default none;
div(phi,U) Gauss vanLeer;
div(phi,T) Gauss vanLeer;
div(phi,k) Gauss vanLeer;
div(phi,omega) Gauss vanLeer ;
div(phi,R) Gauss vanLeer ;
div(R) Gauss limitedLinear 1 ;
div((nuEff*dev(T(grad(U))))) Gauss linear limited 0.5 ;
}

laplacianSchemes
{
default none;
laplacian(nuEff,U) Gauss linear limited 0.5;
laplacian((1|A(U)),p_rgh) Gauss linear limited 0.5 ;
laplacian(kappaEff,T) Gauss linear limited 0.5;
laplacian(DkEff,k) Gauss linear limited 0.5;
laplacian(DomegaEff,omega) Gauss linear limited 0.5;
laplacian(DREff,R) Gauss linear limited 0.5;
}

interpolationSchemes
{
default linear;
}

snGradSchemes
{
default limited 0.5;
}

fluxRequired
{
default no;
p_rgh ;
}

Below is a glimpse when simulation is blowing up

---------------------------------------------------------------------
Time = 0.00010097

Courant Number mean: 4.7345636e-07 max: 1233.7809
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 1.2870124e-06, Final residual = 7.1891992e-09, No Iterations 2
DICPCG: Solving for p_rgh, Initial residual = 0.76361335, Final residual = 0.00097027484, No Iterations 120
time step continuity errors : sum local = 1.4489948e-10, global = 9.5209982e-12, cumulative = -6.5187104e-12
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 2.5226717e-06, Final residual = 8.3556918e-09, No Iterations 101
DICPCG: Solving for p_rgh, Initial residual = 0.69872336, Final residual = 0.00098344698, No Iterations 419
time step continuity errors : sum local = 4.5798547e-10, global = 1.8186047e-11, cumulative = 1.1667336e-11
DILUPBiCG: Solving for omega, Initial residual = 0.00050378054, Final residual = 5.0894516e-09, No Iterations 109
bounding omega, min: -1.6530455e+12 max: 3.8839584e+12 average: 59305422
DILUPBiCG: Solving for k, Initial residual = 0.00035940466, Final residual = 5.3762244e-09, No Iterations 99
bounding k, min: -8.6846115e+11 max: 2.7713031e+12 average: 1585310.7
ExecutionTime = 13894.57 s ClockTime = 13905 s

Time = 0.00010098

Courant Number mean: 6.9096584e-07 max: 2692.3661
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 3.1575455e-06, Final residual = 9.7394175e-09, No Iterations 2
DICPCG: Solving for p_rgh, Initial residual = 0.74447529, Final residual = 0.00097299859, No Iterations 97
time step continuity errors : sum local = 2.4875275e-10, global = 1.7993474e-11, cumulative = 2.9660811e-11
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 3.7889403e-06, Final residual = 5.7741675e-09, No Iterations 153
DICPCG: Solving for p_rgh, Initial residual = 0.7661894, Final residual = 0.00099395397, No Iterations 444
time step continuity errors : sum local = 2.5940091e-09, global = 8.240833e-11, cumulative = 1.1206914e-10
DILUPBiCG: Solving for omega, Initial residual = 0.00087259239, Final residual = 8.3974792e-09, No Iterations 79
bounding omega, min: -7.5412548e+11 max: 1.9226682e+12 average: 94265063
DILUPBiCG: Solving for k, Initial residual = 0.0015909616, Final residual = 8.3691303e-09, No Iterations 68
bounding k, min: -3.2118556e+11 max: 2.0770441e+12 average: 4234488.5
ExecutionTime = 14445.9 s ClockTime = 14456 s

Time = 0.00010099

Courant Number mean: 1.9504303e-06 max: 5747.6202
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 1.6991088e-05, Final residual = 2.6964904e-09, No Iterations 4
DICPCG: Solving for p_rgh, Initial residual = 0.75607356, Final residual = 0.00099111414, No Iterations 201
time step continuity errors : sum local = 8.4048694e-10, global = 3.4520769e-10, cumulative = 4.5727683e-10
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 2.9118025e-05, Final residual = 7.2186118e-09, No Iterations 419
DICPCG: Solving for p_rgh, Initial residual = 0.84296989, Final residual = 0.00095307524, No Iterations 706
time step continuity errors : sum local = 4.7938114e-09, global = 1.1318495e-09, cumulative = 1.5891263e-09
DILUPBiCG: Solving for omega, Initial residual = 0.0067051264, Final residual = 7.1001411e-09, No Iterations 328
bounding omega, min: -1.4353841e+14 max: 1.3961573e+14 average: 1.7683567e+09
DILUPBiCG: Solving for k, Initial residual = 0.0091318156, Final residual = 9.0899654e-09, No Iterations 214
bounding k, min: -6.8698845e+11 max: 1.075334e+13 average: 19477433
ExecutionTime = 15914.84 s ClockTime = 15926 s

Time = 0.000101

Courant Number mean: 9.2903545e-06 max: 33446.887
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 3.5918305e-05, Final residual = 7.4009402e-09, No Iterations 3
DICPCG: Solving for p_rgh, Initial residual = 0.51530912, Final residual = 0.00098150633, No Iterations 87
time step continuity errors : sum local = 5.6978294e-09, global = 1.1952208e-09, cumulative = 2.7843471e-09
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 9.5350344e-05, Final residual = 6.6825388e-07, No Iterations 1001
DICPCG: Solving for p_rgh, Initial residual = 0.64166418, Final residual = 0.026321393, No Iterations 1001
time step continuity errors : sum local = 1.7760159e-06, global = 1.8077374e-09, cumulative = 4.5920845e-09
DILUPBiCG: Solving for omega, Initial residual = 0.02237984, Final residual = 6.0043179e-09, No Iterations 420
bounding omega, min: -4.1960305e+14 max: 2.2858488e+14 average: 7.0990082e+08
DILUPBiCG: Solving for k, Initial residual = 0.009506604, Final residual = 0.0018439062, No Iterations 1001
bounding k, min: -1.7533181e+15 max: 8.382294e+14 average: -3.8906711e+08
ExecutionTime = 19251.27 s ClockTime = 19265 s

Time = 0.00010101

Courant Number mean: 2.9411928e-05 max: 42822.926
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 0.011547178, Final residual = 4.2007322e-09, No Iterations 7
DICPCG: Solving for p_rgh, Initial residual = 0.5517749, Final residual = 0.00098472085, No Iterations 87
time step continuity errors : sum local = 1.9706388e-08, global = 1.9126112e-09, cumulative = 6.5046957e-09
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 0.00045584686, Final residual = 5.7580162e-07, No Iterations 1001
DICPCG: Solving for p_rgh, Initial residual = 0.79932465, Final residual = 0.21947454, No Iterations 1001
time step continuity errors : sum local = 4.5888733e-05, global = 2.4650819e-09, cumulative = 8.9697776e-09
DILUPBiCG: Solving for omega, Initial residual = 0.046824604, Final residual = 0.42651976, No Iterations 1001
bounding omega, min: -2.9120631e+16 max: 7.5610454e+15 average: -1.7510987e+10
DILUPBiCG: Solving for k, Initial residual = 0.10073936, Final residual = 0.053489969, No Iterations 1001
bounding k, min: -6.1933141e+14 max: 5.4698344e+14 average: -1.1146877e+09
ExecutionTime = 23333.7 s ClockTime = 23350 s

Time = 0.00010102

Courant Number mean: 0.00057248341 max: 283410.74
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 0.84933889, Final residual = 2.0178504e-09, No Iterations 9
DICPCG: Solving for p_rgh, Initial residual = 0.91110456, Final residual = 0.00098260631, No Iterations 202
time step continuity errors : sum local = 2.6226461e-07, global = -4.8494379e-08, cumulative = -3.9524602e-08
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 0.033386681, Final residual = 0.014155016, No Iterations 1001
DICPCG: Solving for p_rgh, Initial residual = 0.80383648, Final residual = 5.7958476, No Iterations 1001
time step continuity errors : sum local = 0.020399066, global = -9.6567685e-09, cumulative = -4.918137e-08
DILUPBiCG: Solving for omega, Initial residual = 0.98880096, Final residual = 11962.323, No Iterations 1001
bounding omega, min: -6.4680894e+24 max: 3.2921399e+25 average: 5.2212511e+19
DILUPBiCG: Solving for k, Initial residual = 0.014781795, Final residual = 3.0990057e-08, No Iterations 1001
bounding k, min: -4.8263648e+14 max: 5.4072665e+14 average: 1.0635891e+09
ExecutionTime = 27448.32 s ClockTime = 27467 s

Time = 0.00010103

Courant Number mean: 0.045544987 max: 5.2721582e+08
PIMPLE: iteration 1
DILUPBiCG: Solving for T, Initial residual = 0.49369191, Final residual = 7.5375708e-09, No Iterations 7
DICPCG: Solving for p_rgh, Initial residual = 0.96557631, Final residual = 0.00099907484, No Iterations 238
time step continuity errors : sum local = 3.3753698e-05, global = 7.2331754e-06, cumulative = 7.183994e-06
PIMPLE: iteration 2
DILUPBiCG: Solving for T, Initial residual = 0.88776239, Final residual = 50.198586, No Iterations 1001
DICPCG: Solving for p_rgh, Initial residual = 0.0023242099, Final residual = 1.4577883, No Iterations 1001
time step continuity errors : sum local = 171.529, global = 1.7893858e-06, cumulative = 8.9733799e-06

------------------------------------------------------------------

I'll be really glad if someone helps me dealing with this problem and getting my simulation running. Thanks.


Jubayer

Have you tried using different input for the divergence and laplacian schemes?

divergence as "Gauss upwind" and laplacian as "Gauss linear corrected", especially for the parts where you use k and omega. These schemes have worked for me with different simulations. If you really need to use the schemes that you have as an input now, I would start from these easier schemes and switch over to more advanced schemes step by step.

hello,
Your time step seems too big, since your Co number is getting higer and higer ...
Try to lower your time step, or use adaptative time stepping.

regards,
olivier

Hi Roman,

Thanks for your advice. I'll try those schemes. However, I used simpler schemes before, but did not work. Lets hope this time it works.

Jubayer

Hi Olivier,

I thought of the time step size at first. But as you can see, I have even used 10^-09 s for this full scale simulation, lowering time step size more than that does not make sense. This made me belief that the problem is somewhere else. Thanks for your input.

Jubayer