Reynolds-averaged and large-eddy simulations of turbulent non-equilibrium flows

Abstract

Three non-equilibrium wall-bounded flows have been computed by wall-modeled large-eddy simulations (WMLES) and by the solution of the Reynolds-averaged Navier–Stokes (RANS) equation with various urbulence models. The LES use a wall model based on the detached Eddy simulation (DES) technique. Unlike the standard DES, in which the boundary layer is entirely modeled using RANS and only the separated-flow regions are solved using LES, here a substantial part of the boundary layer is computed using LES, as he RANS/LES interface occurs at less than 5% of the boundary layer hickness. First, we studied the flow over a contoured ramp, which has a mild separation followed by a recovery region. RANS models under-predict the size of the separation region and the back-flow magnitude and show a slow recovery downstream of he separation; the velocity field predicted by the LES is more accurate with the error always less than 10%. Second, we studied he flow past a two-dimensional bump, in which curvature and pressure-gradient effects are important. The mean velocity is predicted reasonably well by all the models, except in the adverse pressure gradient-region where the LES and the shear stress ransport (SST) model predict the mean velocity better than the other models tested. In the adverse pressure-gradient region and in he recovery region of the flow, however, the SST model under-predicts the shear stress by 30%, while the LES over-predicts it in the recovery region by 15%. Finally, we studied the flow past a swept bump in which the initially two-dimensional flow becomes three-dimensional and then relaxes back to a two-dimensional state. In the prediction of the mean horizontal velocity, all the models showed the same trend exhibited in the two-dimensional bump problem. The mean spanwise velocity was under-predicted by all the models in the recovery region. We found that the RANS models performance is dependent on the flow conditions, whereas the WMLES performs as well as or better than the best RANS model in all flow configurations. We also find that the WMLES has maximum errors in equilibrium regions of the flow, due to the well-known limitations of this technique. In non-equilibrium regions the accuracy of the method is found to improve, as additional production terms cause more rapid generation of eddies in the RANS/LES transition region.

Acknowledgment

Support for this work was provided by the Office of Naval Research under grant no. N00014-03-1-0491, monitored by Dr. R. D. Joslin.

Notes

^¶In the experiments, the separation and re-attachment points were determined from the sign of the velocity at a distance of 60 μm from the wall. This distance corresponds o 8.6×10⁻⁴ L _R , which, in the present calculations, occurs 6–7 grid points away from the wall. For consistency with the experiments, the separation and re-attachment points reported in the able are obtained using the experimental criterion, and not the location where the shear stress changes the sign.