Numerical simulations of a three‐dimensional nozzle, from inviscid to turbulent flows

Two numerical methods, based on high order finite volume formulations and upwind schemes, are used to compute the two‐ and three‐dimensional flow field in a transonic nozzle. The influence of numerical diffusivity, boundary treatment and mesh structure is explored for inviscid and turbulent configurations. First order computations provide significantly different inviscid results. However, high order methods lead to similar solutions. An explanation of the error generated through the shockwave is proposed in this case. The two‐dimensional interaction of the shock with the thin turbulent boundary layer developing on the bump wall is also presented. Good agreement between both approaches is obtained considering the rapid thickening of the boundary layer due to the shock. Furthermore, the downstream velocity recovery is almost identical. Only slight discrepancies occur in the main flow, near the outer edge of the boundary layer. These seem to be related to the way the turbulence model deals with the free stream turbulence. Finally,preliminary three‐dimensional unstructured turbulent results are presented and discussed.