Hello!

I'm working with external car aerodynamics.

The case I'm working on now is a bit tricky since it does not have a well defined separation point - I'm not able to predict the rear-body separation correctly. Until now all computations I've done have been with wall-functions. I'm thinking about trying a low-Re model instead. That will, however, demand a much better grid resolution of the boundary layers. Does anyone have any experience from this kind of problems? Can I expect improved separation predictions with a low-Re model? I have a feeling I might be creating more problems than I solve with this low-Re approach.

In relation to this I also have another question. Is it possible to combine a wall-function / low-Re model so that I could use wall-funcuntions in one region and then switch to low-Re in the critical region? It must be difficult to get the interface between the two models to work. How critical is this if I switch well upstream of the critical region. Any references?

Thanks in advance!

I like your question. I am glad that you are not working with aircraft aerodynamics. For handling of turbulent wall layers, some people use the so-called wall function treatment where the thin layer next to the wall ( is not solved directly ) is replaced by a parametric wall function treatment. This approach is usually related to the high Reynolds number turbulence modeling. To include the complete turbulent wall layer in the computation, you need to use either algebraic mixing length model ( where you can specify the mixing lenth distribution ), or the so-called low Reynolds number models ( where the turbulent kinetic energy and the length scale equations are modelled through this thin layer ). Both high and low Reynolds number models have been used in the calculation of turbulent flows with separation. You can easily find review papers on the low Reynolds number modelling, such as the AIAA Journal paper by W. Rodi. You can easily find a couple dozen such models on technical journals. These are PhD level topics. So, it is not a yes or no answer. If you are a user of a commerical code, the best place to find an answer is to call the support engineer. If you are writing your code, then try to solve (1) the fully developed 2-D turbulent channel flow ( it's actually 1-D ), and (2) a separated 2-D diffuser problem with a fully developed inlet condition.(that is the item-1) You should be able to learn a lot through this exercise. I like your question, because I had the same question 25 years ago. I can't tell you too much here until you have done what I have just suggested. Feel free to experiment with your own ideas.

John, thanks for your reply!

I'm well aware of the differences between low-Re models and high-Re models. That was not my questions. The question is if anyone has tried to combine the two approaches, using a wall-function approach upstream and then switching to a low-Re model downstream in order to better model separation in the downstream region. I see several problems associated with this. You need an interface between the two models and the high-Re model is not capapable of providing the low-Re model with all the starting profiles of for example k and epsilon (or omega or whatever). But it shouldn't be impossible to do. Perhaps there already exists this kind of models that has this "switch" buildt in based on a sensor of grid y+ or something? Using a low-Re model everywhere, considering the boundary layer resolution it demands, would be too expensive (this is already a > 1 million nodes case).

I think you are dealing with the most challenging problem in real CFD simulation. The zonal approach is practical, that is you divide the computational flow domain into several connecting zones, each with its own characteristics. For example, in the region where the external flow is well defined and the boundary layers remain attached, you can use high Reynolds number model. You could even go a step further by solving the inviscid external flow first, then solve the boundary layer problem separately with the pressure distribution at the edge of the boundary layer provided by inviscid solution just obtained. In this way, you have two smaller problems to solve. In the separated flow region, ( naturally, you must include a section of non-separated region as the inlet conditon, otherwise, the problem will not be properly defined. That is posing a reverse flow at the inlet. This inlet is just a zonal boundary interface. You don't want to place it inside the separated region anyway.) a low Reynolds number model will be able to handle the flow separation without worrying about the validity of the Law of the Wall treatment. ( warning: last year, I was fooling around with a commerical code, I could not even get the flow to separate, even at 60 degree angle of attack for flow over a 2-D cascade. The other code I used with algebraic mixing length model did produce flow separation at around 35 degree angle of attack.) As long as the interface location is well ahead of separation, you can always fit the thin layer region with some regular profiles for u, tke, eps. The boundary layer will be able to re-adjust itself . If you are trying to solve both zones in one formulation, the near wall mesh can be a problem because the first off-the-wall mesh point must be in the Law of the Wall region using high Reynolds number approach ( normally in the region Y+ greater than 100 to be on the safe side ), on the other hand, in the low Reynolds number modeling zone, the first off-the-wall point must be positioned at Y+ less than one in order to have good resolution. At least 20 points are required just in this thin layer region. My suggestion is you can solve the whole computational domain with a Law of the Wall model in the first pass. Then cut out a smaller region where flow separation exists. The inlet ( or inflow ) condition will be copied from the interior solution of the first pass plus some regular ( assumed) profile through the thin layer region.( since you didn't compute this thin layer region in the first pass, you will have to provide the information yourself. ) In the last two years, I have been running problems on workstation with one giga bytes of Ram , this is because I was using a commerical code. If you are writing your own code, a 3-D problem with (100x100x100= 1 mega mesh points) size using 20 stored variables per mesh point ( to store u,v,w,...etc ) will take ( 20x4 mega bytes) of ram. A PC workstation can easily handle 80 mega ram. ( in old days, Cray-xmp has only one mega words fast ram.) The flow separation problem is the core of CFD problem, being able to compute flow separation is one thing, being able to accurately predict separtion is another thing, being able to model turbulent flow consistently with high Re and low Re models will be a big challenge ahead.( currently, solutions from Law of the Wall model and a Low Re model are not consistent. Wall skin friction and velocity distribution are not consistent from two models. Using a low Re model in a non-separated region does not mean that you will get better results.) You are helping a lot of people out there because only less than one percent of CFD experts actually know how to implement the Law of the Wall and Low Re models in a working code. By the way, I am getting the feeling that " Experimental Computational Fluid Dynamics " is a more realistic name than CFD. You are trying to get an answer by trying different approaches, meshes, turbulence models, solution algorithms on computer.

I think using a two-layer turbulence model such as the one developed by Rodi et al., 1993 might be good alternative to the wall-function and Low-Res. The basic idea of the two-layer model is to divide the flow region into near-wall and outer-wall regions. In the near-wall region, one can employ one-equaiton models and in the outer-wall region the standard k-e model can be used. The two regions can be matched by some prescribed condition, e.g. Ret=60. The two-layer models can effectively reduce the computational cost needed by Low-Res and retain resonable accuracy. I recently developed a two-layer model that can also deal with the non-isothermal boundary layers and found it quite accurate and cost-effective. But for your external car aerodynamics problem, I think Rodi's model will be enough. His paper was published on J. Fluid Eng.,1993.

Yes, a two-layer model could be an alternative. However, I'm not convinced that you save that much time compared to a common low-Re two-equation model. Doesn't the two-layer model you refer to (Rodi, 1993) require approximately the same boundary layer resoultion as a 2-eqn low-Re model? If that is the case it will definitely be very much more expensive than useing a wall-function approach in all regions except the critical separation region. It is my impression that the main advantage with the two-layer models is that they are more stable and easier to use numerically than the 2-eqn models since you avoid the notorious epsilon equation in the inner parts of the boundary layer, or do you disagree? How much computational time would you estimate that you save with a two-layer model compared to a common low-Re 2-eqn model?

John, thanks for that very complete answer! You pointed out several of the difficulties I were worried about and also the fact that using a low-Re 2-eqn model will not necessarily improve the code's ability to predict separation. I think I will first try to do what you suggested, that is run the whole case with a high-Re model and wall functions (I already did this) and then cut out the critical separation region and re-mesh and re-run only that region with a low-Re model. If things look promising (that is separation predictions seem to improve) I will then consider developing some kind of interface between the two models so that I can run everything together. I'm also worried about the meshing problem that you mentioned in that case. Either I could gradually expand my mesh and switch models at a certain y+ (say 10 or something) or I could make a local refinement with non 1-1 matching of grid points so that the low-Re region can have more nodes. I already have this in the code but I'm not sure it will work perfectly if I also switch models at the interface. Thanks again for your input, it was very valuable! I hope that you are correct in that a low-Re model will adjust itself and behave well if you switch well upstream. This is what I hoped and also belive myself.

Thank you for your response and questions. In my experiences of applying and developing two-layer models, I found that in a typical boundary layer, 5-7 grids are enough to arrive a good result, comparing 20~30 grids needed by a Low-Re model. Your impression about two-layer models are also correct, it indeed avoids solving epsilon equation in boundary layers. Applying a two-layer model is little more expensive than using the wall function, but it gives more accurate results especially when you have seperations, reverse pressure, etc. I am not sure if there are some researches developing wall functions that can handle seperation. If there is, it might be interesting to take a look.