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Boundary condition of the third kind or Danckwertz boundary condition

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Old   October 2, 2006, 16:56
Default Hi, It seems that nobody ha
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It seems that nobody has read my question. I am posting this to bring it to attention. Can anyone answer it?

Is there any implemented BC in OpenFOAM that can be used to treat implicitly a BC of third kind?

Thanks for any help,

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Old   October 3, 2006, 04:34
Default mixedFvPatchField in the finit
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Mattijs Janssens
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mixedFvPatchField in the finiteVolume library?
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Old   October 3, 2006, 05:08
Default I'll give it a shot. k*nf &
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Eugene de Villiers
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I'll give it a shot.

k*nf & grad(T)_b = Cp*U_b*(T_b-To)

k*nf & grad(T)_b = k*snGrad(T)_b

k*snGrad(T)_b = k*(T_b - T_cell)/(nf & d)

where d = X_boundaryFace - X_cellCentre


T_b = (k*T_cell/(nf & d) - Cp*U_b*To)/(k/(nf & d) -Cp*U_b)

Once you have the correct boundary value of T, snGrad(T) can be found without iteration.

Of course you have to stick all this stuff inside the evaluate function of your custom boundary condition so it can be updated properly. See OpenFOAM-1.3/src/finiteVolume/fields/fvPatchFields/basicFvPatchFields/fixedGradi ent/fixedGradientFvPatchField.C
line 137-140 for details.

Is this what you wanted or am I competely missing the point? If so you will have to do a bit more explaining.

(PS. I probably made some mistakes with the gradient signs)
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Old   October 3, 2006, 11:47
Default Dear Mattijs Janssens, I ha
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Dear Mattijs Janssens,

I had already checked the mixedFvPatchField because of its name. Due to your suggestion, I read the code again more carefully. From it, it seems that mixedFvPatchField should do the job for the BC:

nf & grad(T) = A*(Tref - T)

if I specify:

refGrad = 0
refValue = Tref

and calculate f at each boundary face of the patch by

f = A/(A+1/d), where 1/d = patch().deltaCoeffs() and 0<f<1>0,

as soon as the local A value is available. If it is constant (not my case), this has to be done only once at the beginning of computation.

For a third order boundary condition that comes from flux conservation:

-k (nf & grad(T)) = h*(T - Tref) => A = h/k > 0

For a Danckwertz boundary condition:

(nf & grad(T)) = (Cp/k)*(phi/magSf)*(T-Tref) => A = - (Cp/k)*(phi/magSf) > 0 because phi < 0 at an inlet boundary.

I have not tried yet, but I will post if this solution works after trying.

Does this seem correct to you?

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Old   October 3, 2006, 12:21
Default A small mistake in the line:
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A small mistake in the line:

f = A/(A+1/d), where 1/d = patch().deltaCoeffs() and 0<f<1
for A>0,

in the previous post. The system did not produce correctly the text:
for A>0
both in the same line.
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