Simulating stall in 2D

Hello everyone,

I and some colleagues of mine are actually studying the cl, cd, and cm coefficients for a public geometry of a helicopter’s rotorcraft blade profile (the so-called SC1095 - the geometry can be downloaded from the website UIUC Airfoil Data Site). In view of testing the capabilities of the PyFR code, we are trying to reproduce the experimental results of the paper AIAA Aerospace Research Central, studying the lift, drag, and moment coefficients at several angles of attack, adopting a 2D O-grid of our production (the mesh has a wall-spacing of 4.08e-5, 40 points per side of the airfoil and 2 points only in the tab – those choices were made in order to adopt polynomial order 4 of the PyFR solver).

In particular, if you consider Fig. 3 of the reference above, we are actually able to catch the values of the coefficients for all the angles of attack between the negative and positive stall points (i.e. in the range [-11°; 15°]) but we cannot do that for angles outside this range (stall points included).

We have some questions regarding the described issue:

  1. Could it be related to the fact that we are using one too-coarse resolution in the airfoil profile direction for the O-grid? To be honest, I personally doubt that because I verified that repeating the simulations with 80 points per airfoil side (instead of 40), the results do not vary significantly;
  2. Is some refinement of the mesh required behind the airfoil with respect to the flow direction? Actually, we decided to use an O-grid in order to avoid re-meshing for different angles but doing that via the far-field condition (basically, modeling the inlet direction at the far-field via the angles); this approach works pretty well with RANS modeling but I am not completely sure that this can be done straightforwardly with DNS;
  3. Does the PyFR code rely on the realistic effects in 3D in order to get a correct estimation of the stall?
  4. To be more precise, does the code inherit any of the key aspects of 2D turbulence phenomena (namely the inverse energy cascade) when simulating on such a topology, therefore making it necessary to perform a 3D simulation of a finite wing?

Thank you for every hint or comment that you could share.

Federico Cipolletta.

Looking briefly at that paper, the Reynolds number range considered fairly quite high at least at the point where 3D effects are important.

I would’ve thought that in order to correctly capture the stall characteristics you would need a 3D mesh. It is probably worth checking out the NACA 0021 in deep stall paper. Now I would’ve thought that there will be features like separation, reattachment and potentially separation induced turbulent transition, all of which will likely not be correct in 2D.

If you are wedded to the idea of 2D wing simulations then, in my view, you might be better off using a tool designed for the task that has a number of models for these regimes.

In terms of answering the last two point, PyFR just approximates solutions to the equation system you ask it to solve. So if a phenomena is effect by 2D vs. 3D then this will be reflected in the solution you get. So if you solve a 2D case that exhibits turbulence, the turbulence will be reflective of the 2D system, ie it should have an inverse energy cascade which is clearly different from the 3D forwards cascade.

You also might like to read this post on the deep stall case: Cuda backend error ‘CudaOutOfMemory’ ‘CudaInvaildDevice’ - #10 by WillT

Thank you @WillT, your answers look reasonable to me.

Federico Cipolletta.