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Adding a source term in k-epsilon model

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Old   November 17, 2018, 03:14
Unhappy Adding a source term in k-epsilon model
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Chen Sihe
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Hi all,
I am testing out a model raised by S.B. Pope, which modified the epsilon equation with a source term. I tried to implement it with udf in the FLUENT, but the convergence seems to be a problem. The modified epsilon-equation looks like the following:
{\displaystyle {\frac {\partial (\rho \epsilon )}{\partial t}}+{\frac {\partial (\rho \epsilon u_{i})}{\partial x_{i}}}={\frac {\partial }{\partial x_{j}}}\left[{\frac {\mu _{t}}{\sigma _{\epsilon }}}{\frac {\partial \epsilon }{\partial x_{j}}}\right]+C_{1\epsilon }{\frac {\epsilon }{k}}2{\mu _{t}}{E_{ij}}{E_{ij}}-(C_{2\epsilon }-C_{3\epsilon}\chi)\rho {\frac {\epsilon ^{2}}{k}}}
The added source term is related to the C_{3\epsilon}\chi term, which is a measure of the vortex stretching. Here, \chi=\frac{1}{4}(\frac{k}{\epsilon})^3(\frac{\partial U}{\partial r}-\frac{\partial V}{\partial x})^2\frac{V}{r}.
The case I am simulating is basically a turbulent round jet. I firstly calculated the case until convergence, and then implemented the source term to the epsilon equation as the following code:
Code:
#include "udf.h"
DEFINE_SOURCE(epsilon_Pope_source, cell, thread, dS, eqn)
{
real source;
real time_scale = C_K(cell,thread) / C_D(cell,thread);
real omega = 0.5 * time_scale * (C_DUDY(cell,thread)-C_DVDX(cell,thread));
real x_c[ND_ND];
real kai;
C_CENTROID(x_c,cell,thread);
kai = time_scale * omega * omega * C_V(cell,thread)/x_c[1];// Use DVDY instead of V/r?

source = 0.79 * kai / time_scale * C_D(cell,thread);
dS[eqn] = source * (-1) / C_D(cell,thread);
return source;
}
However, the convergence is not possible. The plot of residual is as follows:

Clearly the white line (continuity) is driven to a very high level. Also other variables would not converge. Interestingly if I do not initiate with the calculation of the standard model, the residual stabilizes at a even higher value. Cannot figure out what is going wrong.
I tried to observe the flow field, and find out that the v,k,epsilon fields are all making no sense. I think the problem comes with the udf and I might have not done it properly. What I am doing is simply to add the C_{\epsilon3}\chi\frac{\epsilon^2}{k} term as the source term directly. What is the issue with that?
Thanks so much for your help!
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k-epsilon model, turbulence, udf code

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