Prediction of coherent vortices in an impinging jet with unsteady averaging and a simple turbulent model

The classical problem of a plane jet impinging on a flat surface is used here as a test to show that it is possible to use URANS and steady boundary conditions to predict coherent structures in the flow field from a simple model with the unsteady time and ensemble averaging of the quantities proposed by Ha Minh. The two-equation model of Myong and Kasagi, where the damping functions have the appropriate asymptotic behaviour near the wall, is used to solve the problem in two dimensions, for a jet located at a distance equal to ten times the nozzle width, using control volumes and second order finite-differences in time and space. It is found that the unsteady averaging approach of Ha Minh is able to reproduce the coherent vortices observed experimentally in the jet. Spectral analysis shows that the coherent part of the numerical solution is compatible with the vorticity dynamics near the nozzle. Overall, computational results show that the presence of coherent mean field components in the solution, if they are predicted, will improve the performance of even a simple eddy-viscosity model.