Mesh and initial conditions for k-omega model
 

I wish to simulate the Re 100 flow around a sphere using Menter's SST k-omega model. This is my first turbulence calculation ever, and I have some beginners questions I hope you can help me with:

1) The model uses wall functions, and I am not sure if those wall functions require me to put the first off-the-wall grid point in the viscous sublayer or above. But let's assume I figure out a y+ for the first grid point off the wall. Then how do I figure out what that y+ corresponds to in real wall distance?

With y+ = u_tau*y/nu, I need the friction velocity to get y. If all I have is the Reynolds number and the kinematic viscosity, then how can I calculate u_tau - I would need the wall shear stress for this, which I don't have - neither directly nor indirectly via a skin friction coefficient.

2) Assuming I solve (1), nect problem is: how do I mesh the boundary layer? Should cell size increase in some non-heuristic manner away from the wall (i.e. in proportion to how u+ grows according to the law of the wall) ? And how can I know a priori what the thickness of the boundary layer will be; I only want a fine mesh in the BL, not in the core flow.

3) About initial conditions for k and omega. I don't know how to specify them intelligently. My own thoughts went like this:

Initially I just assume isotropic turbulence (u_x)' = (u_y)' = (u_z)' at 5% of the free stream velocity. Then I get k from k = 0.5*((u_x)'² + (u_y)'² + (u_z)'²).

For omega I went through a lot of anguish. I used the fact that w = e/k to change the problem into specifying an initial value for e. Then, assuming we are not near the wall, ie. for example in the log-law region, I know the dissipation rate e scales like u²/l where u and l are velocity and length scales of the energy containing motions. Hence, it is reasonable to model e as e = C*k^1.5/l_m where C is a constant and l_m is the mixing length. I also know that in the log-law, l_m = kappa*y and that turbulence production and dissipation are about equal. From that I found that

e = c³k^1.5/l_m

and worked out c at about 0.55. For the mixing length I would then just replace it by, say, the diameter of the sphere.

But all this assumes I am in the log-law region and it also appears very heuristic to me.

Please, can someone explain how to solve these three issues.

Thanks, Martin

Re: Mesh and initial conditions for k-omega model
 

I am not an expert but can give you some ideas based on my exposure.

1. You need to know for sure if the BC are defined on the wall or the first grid point as the boundary conditions would be very different. You can approximately have some approximate estimation of utau=sqrt(tau_wall/rho) to being with and you can estimate yplus as the computations progress based on new values of utau.

2. Use a hyperbolic tangent function to cluster the grid near the wall. You need to run few computations to really check if the grid is fine enough.

3. For initial conditions you may start with an uniform value for k and w and a perturbed velocity field.

Hope it helps.

Re: Mesh and initial conditions for k-omega model *NM*
 

Hi Martin;
I recommend you to read FLUENT and CFX user's manual specifically for grid generation you can read FLUENT user's manual, section 12.22 " Solution Strategies for Turbulent Flow Simulations" and for initial value, CFX user's manual, chapter three. I hope it can help you.