Effect of throat heating on critical roughness and the stability of nozzle wall boundary layer

Abstract

The effect of wall heating in the throat region on the performance of a Mach 3.5 and a Mach 2.4 axisymmetric nozzle is investigated. Owing to the boundary-layer thickening effect of heating, the critical roughness height to trigger laminar-turbulent transition is larger in the heated cases. Therefore, for a given surface finish, the adverse effect of roughness on transition can be minimized by sufficient wall heating. However, the combined effect of heating and pressure gradients is to introduce an overshoot in the streamwise velocity profile, as earlier predicted by Cohen and Reshotko.1 Associated with this overshoot is a new generalized inflection point near the edge of the boundary layer. As a consequence, the nozzle wall boundary layer supports high frequency two-dimensional inviscid disturbances. N-factor results indicate that, with sufficient throat heating, these disturbances could cause premature transition downstream of the throat and hence jeopardize quiet performance. Therefore, favorable (on critical roughness height) and adverse (boundary-layer instability) effects of heating have to be carefully evaluated. In this study, mean flows are computed by using both a boundary-layer code and a full Navier-Stokes solver; the critical roughness heights are calculated based on an empirical formula; and the destabilizing effect of heating is evaluated by using compressible linear stability theory. At the end, the maximum acceptable heat levels and the critical roughness heights are established for the two nozzles.