During computation, I found that the equation of dissipation rate very difficult to converge. Can anybody tell me how to difinite the boundary condition of this eqation to get good convergence?

(1). I am not writing the program right now. So, I don't have the exact definition for you. (2). There are two kinds of definition for the turbulence kinetic energy dissipation function (epsilon). They require different wall boundary conditions for the low Reynolds number model. You have to dig out some papers on low Reynolds number modeling. The review paper by W. Rodi in AIAA Journal is a good place to start. (3). Then, there is also high Reynolds number model with wall function treatment. This is based on the equilibrium boundary layer assumptions. So, there is a simple relationship between the wall skin friction and the turbulence kinetic energy dissipation function (epsilon). There are also several forms available. For this, you also need to check out some papers on the two-equation k-epsilon models. (4). The convergence issue depends on several factors,: the governing equations, the numerical formulations (FD,FV,FE,...), the solution procedures, the boundary conditions, and the computational mesh used. (5). So, the problem is very specific. And there is no general solution to it. It has to be studied based on above factors.

Vincent,

I use the following for k-e model and external flows.

I set k by

k_inf = 0.5(%turb * U_inf)**2 where

%turb is the percent f.s. turbulence. A value of 1% (0.01) is usually good. I then set the dissipation by assuming the turbulent viscosity is larger (say 4x) than the laminar viscosity yielding

e = Cmu * rho_inf * k_inf**2 / (4* mu_laminar).

A typical value of Cmu is 0.09 and mu_laminar can be had from Sutherland's Law.

For internal flows you can use a length scale to get e. Something similar to

e = Cmu**0.75 * k_inf**1.5/(0.03*L)

where L is a mixing length for the problem.

Stacey

Dear Vincent,

You will have to explain your turbulence model and the boundary condition used for epsilon so that we can give some useful advice. For example, if you are solving for the pseudo energy dissipation (see the low reynolds number model of Launder and Spalding), its value is set to zero at the wall. This specification makes the problem stiff and there is bound to be problems with convergence. One can get over such problems by making the grid very fine close to the wall. Using a high Reynolds number model should not give you such problems although in some cases grid refinement blows up the value of epsilon close to the wall (convergent solutions may still be obtained).

Cheers

Thank all of you for your valuable advice. I did not introduce the detailed computaion case. I mean, I am calculating flowfield inside an experiment funace, using FD and SIMPLE algorithm, and employing full reynolds stress model as the turbulennce model. In fact, the boundary condition that I am using is the latter one for internal flows. But I got very large residual source for the e equation at nodes near wall, and the total residual source for e equation kept at a fixed high value while other equations converged nicely. SO, what do you think is the most applicable reason?

Dear Vincent,

If your other residuals seem to have converged then most probably your final solution might be correct. Since epsilon values tend to blow up near the wall the epsilon residuals may show up as a very high value in some cases. You can check whether your final solution is correct by carrying out a grid refinement study.

Cheers