I am a Ph.D. student working on 3D Compressor flows in Jet engines. But I think my problem is of general nature anyway.

Think of a cylinder of medium radius of curvature, which is normal to a flat plate.

The incoming flow is fully turbulent with a Re number of 12.e6. Boundary layers are building up on both solid surfaces and separation occurs in the corner region farther downmstream of the l.e region. I am using a 3d solver for compressible flow with the Wilcox k-omega turbulence model.

My question is : how sensitive is the separation region to the grid refinement ?( On a single surface, the grid should be refined in the direction normal to the surface; there is no such normal direction in the case of a corner flow). Is it sufficient that the grid is such that my first y+ is below one on both orthogonal surfaces ? Is that so critical? A H-mesh type of grid around a blade is very expensive in terms of nodes; Furthermore, my code being explicit, the cell size in the corner is very small and therefore slows down the convergence of my computation.

Did anyone run into that problem and made an investigation of grid dependency in the separated region ?

Stephane.

You have a very good reason to ask these questions, but I am reading 3D game programming with C++ right now. I like your questions, but I can only give you a very brief answer right now. Before you design something, you need to take a look at the real thing, a real compressor blade or a turbine blade first. Look at the real shape closely. After a while, you will realize that in real world people don't design compressor blade or turbine blade with sharp corner. The stress concentration alone will kill the design. Then why are people still talking about the sharp corner flow ? Because they ( engineers doing analysis ) don't know how to model the 3D geometry in their CFD code or input. So in reality, there is no such thing as a sharp corner flow in the compressor blade or turbine blade design. The surface is always smooth and continuous. The use of Y+ in this region ( borrowed from flat plate boundary layer theory ) is not going to create real difficulties. ( There are maybe models where you don't have to use Y+ at all. ....) If you insists on solving the sharp corner problem, it is still useful to solve an identical one with rounded corner first. Then compare the two results to see how they differ in the separation patterns. If you have a turbulent boundary layer approaching the sharp corner, the chances are that the flow is not going to see the sharp corner as a sharp corner. Grid refinement is a standard practice to obtain the grid-independent solution. It's the method your learning ,which is important after your graduation, not the grid-independent solution you are trying to obtain. My short answer here is: try to model and solve a real problem first.

"What you see is what you get", in order to see the separated flow structure you need the fine mesh to resolve the near wall region. You will be able to see the need when you plot the velocity profile in semi-log chart. (Ref. Boundary Layer Theory by H. Schlichting) If you don't have enough points in this region, you are not going to get the right profile and the slope at the wall. When that happens the skin friction will not be correct. So, the first guidline is that you must have enough mesh points in the right places ( places with high gradients ). As for the computing time required for the explicit method, you can use the maximum local time stepping method ( set local time step to maximum allowable CFL condition ). This is a simple method to speed up computation for steady-state solution. Along this line, you can dynamic zonal iteration method to spend more time in the areas where the convergence rate is low.( notice that some areas of the flow field converge faster than other regions). The explicit method is ideal for parallel processing, if you have a net work of PC's or workstations, you may want to look into it. If you are interested in steady-state solution, maybe it is easier to deal directly with steady-state equations right from the begining. In this way, you can eliminate the " wave chasing " associated with the time-dependent compressible flow formulation. Along this line, it is easier to convert the formulation into the imcompressible flow type formulation, if the flow is basically subsonic. If you are interested in the corner flow separation behavior, an incompressible flow formulation would be the first step, unless you are studying the supersonic corner flow problem. As for the Y+ value and the wall normal distance, you can model the turbulene in terms of other turbulence variable so that the normal distance does not explicitly appear in the formulation. You can also use a converged solution as the initial solution for a new case to speed up the convergence. Once you have gained some insight into your problem, you can also easily come up with a parametric representation of the flow field, and then apply it for any new cases as the initial condition. So, you see, there are many ways to speed up the computation. By the way, even the normal distance at a corner can be defined in terms of its neighboring points.