Hi everyone,

I'm trying to calculate the flow around an airfoil by using a finite volume RANS solver with the standard k-epsilon turbulence model. The size of the grid around the airfoil extends 30 times the chord-length in all directions.

I want to establish a turbulence intensity(Tu) of 1% near the nose. Tu decreases in flow direction, so Tu must be greater at inlet. At inlet I have to specify velocity(v), turbulent kinetic energy k=1.5*(Tu*v)^2 and epsilon.

How Do I estimate the epsilon or Tu at inlet?

Any suggestions are welcome. Thanks, Norman

Hi, Norman,

A suggestion only (I tried k-epsilon only once, long time ago and only briefly; there can be stability issues): take the equations of the standard k-epsilon model and solve them for the case of a uniform flow (no airfoil present, v=const everywhere). If second derivatives are too cumbersome, neglect them at first on the assumption that convection is stronger than diffusion: then the equations can be solved analyticly as far as I can see. This will give you decaying k(x) and epsilon(x). Adjust the inlet condition to get what you want where you want. The airfoil will distort the results but hopefully not too far upstream.

Regards

Sergei

Thank you for your suggestion.

Instead of solving the equations analytically, I did some computations varying k and epsilon at inlet. Because of {epsilon = C_mu * k^2 / nu_t} the values of k and epsilon are strongly coupled, e.g. raising k increases epsilon.

Plotting k and epsilon over flow direction x shows, that k plunges down to the minimum limit of 1e-8 before it reaches the airfoil. Even if I use an inlet-Tu of 10% and a ratio of the kinematic viscosity nu_t/nu=100. Normally a value of 1 for nu_t/nu is recommended in this case.

There are so many pictures of airfoil computations on WWW but information of the correct boundary condition setup seams to be rare. Does anyone know a well documented subsonic (Re=1e6, Ma<0.3) airfoil testcase with appropriate turbulence intensity?

Thank you, Norman

Hi, Norman,

Well, this is how the solution behaves. Increase k and decrease epsilon at the inlet.

Explicit solution would help to understand the problem rather than use trial and error blindly.

Do you actually need to have the grid extended to 30 chords upstream, by the way?

Sergei