First of all: if you do a steady-state CFD simulation, nothing is guaranteeing it, that the steady-state fluid flow you are heading for is really existing in reality. The real flow might be heavily transient instead, so that no steady-state solution to the Navier-Stokes RANS equations exist. Usually a CFD solver reacts to such a question, where no mathematical correct answer can be found, with divergence or with oscillations in the convergence behavior.

I think that this is exactly the pattern which you are observing. With increasing angle of attack there is flow separation developing on the suction (upper) side of the airfoil. The recirculation zone is by no means steady-state in space and time (at least not necessarily). A frequently observed flow pattern is a periodic detachment of the vortex in the recirculation zone, which moves downstream the airfoil with the main flow. In principle a similar pattern like in a Von-Karman vortex street, but for the airfoil as a single-sided phenomenon on the upper side of the airfoil. The consequence is a periodic oscillation in integral quantities like forces and moments, acting on the airfoil. So my first question would be - have you ever had a look on the velocity vector or pressure field around your studied airfoil at this AoA? If yes, you should have observed this chain of vortices, which are flowing downstream together with the main flow. Creating a movie from a series of intermediate results files helps in this regard as well. Or conducting a transient simulation for a period of the observed oscillations to look at them at detail.

Hopefully this helps.

Regards, Thomas Frank.

Thomas Frank , Thank you so much for the time and effort to write such a comprehensive and clear answer . And yes I am continuously noticing the velocity and pressure contours and I could see the pattern you have mentioned .

So what value of lift coefficient should I use while making a Cl vs Alpha plot, as the values will be changing with time and I will be having multiple values of lift coefficients at the end.

The answer can be best deduced, if you think about an experimentalist and what he would do to provide you with an experimentally measured value for comparison? Effectively from any experiment you are provided with time-averaged or ensemble-averaged measurement data. So the experimentalist attaches his measurement device for a period of time, he is measuring several thousands of measurement values for the quantity of interest, and finally he provides you with a - hopefully - meaningful and comprehensive, statistically reliable average and standard deviation.

In CFD you can do exactly the same. Best it would be to run a transient CFD simulation for a couple of full signal periods (!!! that is essential, partial periods would have influence on the mean and deviation, if the number of periods is small, as almost always too small in CFD for statistical reliability of averaged values). During that simulation you record the oscillation and average it over the number of samples/timesteps. You could do the same for your steady-state simulation, and some people do. From a purely mathematical point of view, this has the taste of an a bit illegal approach. Why?

At the beginning of your steady-state CFD simulation you posed the hypothesis, that a steady-state solution for the solved RANS equations exists. But how the simulation went, it essentially provided the proof, that your hypothesis was wrong. In conclusion, since you made simplifying assumptions for the steady-state iteration/solution approach, you would not be allowed to use the result, since it might be erroneous due to the failed hypothesis and the therefore not justified simplifying assumptions. E.g. in a steady-state, pseudo-transient solution it is not guaranteed, that for any intermediate iteration of the solver the overall mass, momentum and energy conservation is satisfied. Only if the iterative solution approach leads to a converged (really converged) solution, the conservation principles are obeyed for the final steady-state solution. But your solution approach does not converge! At least not in the sense of a steady-state solution. In practice you will be able to observe (potentially small, but existing) differences between the time-averaged transient solution and the iteration-averaged steady-state solution. The time-averaged transient solution result should be the more accurate result (and theoretically justified result), provided that the mesh is fine enough and the timestep is much smaller than the signal period.

Best regards,

Thomas Frank.

Dear researchers,

Have a nice weekend with your family....