If you have an reference solution of the $u_{\tau}$, you can use this distribtuion for your apriori calculation.

However, the application of $y^{+}$ for test cases with separation points is challenging. Due to the definition of $y^{+}$ you must use the absolute value of $u_{\tau}$. This absolute value does not capture the correct physics (attached flows: $u_{\tau}$ > 0, detached flows: $u_{\tau}$ < 0).

Furthermore, for flows with laminar-turbulent transition it is meaningful to apply turbulence models which use an intermittency factor. (as starting point: http://www.ansys.com/staticassets/ANSYS/Conference/Confidence/San%20Jose/Downloads/turbulence-transition-modeling-5.pdf)

Regards

Stephan

In general you cannot determine the y+ a priori since it is dependent on the wall shear stress, and therefore on the solution. For k-epsilon you need wall functions, for k-omega you can also resove upto the wall (y+ < 1 everywhere). Wall functions for flows that separate is generally not advised.

The use of transition models, as suggested by Stephan Schmidt, is certainly advised since turbulence models usually 'kick inn' an order of magniture too early. So the transition from laminar to turbulent in your boundary layer is much too early.

Having said all that, to solve a flow past a cylinder with RANS is very difficult, see for example "URANS CALCULATIONS FOR SMOOTH CIRCULAR CYLINDER FLOW IN A WIDE RANGE OF REYNOLDS NUMBERS: SOLUTION VERIFICATION AND VALIDATION" by Rosetti, Vaz and Fujarra (OMAE, 2012).

Thank you for your response. I got  y+ value from this website "http://geolab.larc.nasa.gov/APPS/YPlus/". Although this is only for turbulent flow over a flat plate, I got some estimate for this value. I computed flow past a cylinder case with kOmegaSST RANS model for Re=3900 and got very good results like drag coefficient=0.99 (experimental Cd=1), separation angle=85.87 degrees (experimental=85-86 degrees) and velocity profiles are in very good agreement with experimental data in wake region. But, I am not getting any good result for the same case with transitional models. I have 50% higher drag coefficient, underpredicted wake length and delayed boundary layer separation point. I used k-kL and kkLOmega models for validation of transitional models. Any idea why this might happen!

References

k-kL Models:-Menter, F. R., and Y. Egorov. "The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1: theory and model description." Flow, Turbulence and Combustion 85.1 (2010): 113-138.

kkLOmega Model:-Walters, D. Keith, and Davor Cokljat. "A three-equation eddy-viscosity model for Reynolds-averaged Navier–Stokes simulations of transitional flow." Journal of Fluids Engineering 130.12 (2008): 121401.

Compute y+ as the product of friction velocity times distance from the wall divided by kinematic viscosity. Compute it as in www.cfd-online.com. Ensure that you place your first grid line such that y+ is less than 11.5. Your software will then fit a linear profile (laminar sublayer) no matter what the flow is . When turbulent your software will create the log law further from the laminar sublayer, so do not worry!  Transitional wall functions cannot work in your case because they are in conflict with    your transitional flow ( unless you know where transition occurs which I guess you do not) .

An interesting reference , Karabelas S.J. et al ,High Re no turbulent flow past a rotating Cylinder , Applied Mathematical Modelling,36(1), pp379-398 , 2012

You can have your answer from the article: Compound wall treatment with low‐Re turbulence model by  MM Rahman, T Siikonen

International Journal for Numerical Methods in Fluids 68 (6), 706-723, 2012

You can code this formulation.

Thank you Mr. Rahman, 

      Sorry for the late response. I think this will be useful. I would try to implement it in my code.

Hello Gaurav, did you manage to validate your model? What values of k and omega did you use in your kOmegaSST?

Hi Barreira,

I had no success with with high Re k-epsilon or k-omega model due to the wall function problem. So, I used kOmegaSST model. In kOmegaSST, I used fixed value for k with a very small value of k like 1e-10 and omegaWallFunction for omega and fixed value (value uniform 0) for nut at the wall. I always resolve y+ close to one in case of kOmegaSST.

Thank you very much for your answer, Gaurav. I don't access Research Gate very often, so I just saw your reply now.

I've been working flow past cylinders using several RANS models, but it's indeed more complex and harder than I expected. I've been using low-Re and high-Re when Reynolds is too high (1e6).After reading a lot of papers, I realized that the problem is still not well solved for RANS models.

I also used the kOmegaSST, but got an overprediction for drag and lift for Reynolds equal 1000, 3900 and 10000; and then an underprediction for Reynold 1e5. I have played around a lot with kOmegaSST, but even with various different values of omega and k at the inlet I cant get the same 0.99 for Cd as you did... I used the same boundary condition at the wall, and still. The values I got are actually close to what other papers have reported. Would you have any ideas?

Also, you said you used the kklOmega models, did you get any good results? I tried them, but they were very sensitive to turbulent parameters and to the grid, so I couldn't pin point the values for Drag Coefficient and Lift.