How does low Reynolds k-e model work?
 

I'm working on low Reynolds k-e model recently, but I found the model didn't work for 2d incompressible backstep benchmark( although it works very well for turbulence flate ), including Shih's realizable, Lam Bremhost, etc. I found it related to the damping funtion near walls, but I don't know how to limit the action range of the damping function.
Can anyone help me on this? Thanks a lot.

Have a look at the turbulence modeling by wilcox ? One option is to try a k-omega model by wilcox or davidson or menter. Another option would be to apply recent k-epsilon models. With Lam Bremost model the performance can depend on the boundary condition employed. With backward-facing step case, the definition of yplus for damping might be problematic and you might want to try y^+=y * sqrt(k)/nu

Try to find some information about the SST model (Menter); is an hybrid between k-e and k-w models. In the particular case of backstep benchmark, some results show that this model predict very well the retouch point in the wall. good luck

http://www.cfd-online.com/Wiki/SST_k-omega_model
http://www.ansys.com/assets/tech-briefs/cfx-sst.pdf

Thanks a lot.
I have tried SST and get good result, and I am testing the k-e model now. I find it may be related with y+, but I think y+ not good, and I find Shih get good result with his realizable model(better than SST), but I found it not so good, hehe. Maybe this is CFD.
Maybe nonlinear model may work.

The problem with RANS modeling is you do not have THE model for any applications. The constants and damping for the models are computed from benchmark problems and they may or may not work for other cases. The non linear models may help in resolving the anisotropy of the Re stress tensor but not may not know better results for other parameters.