Throat Heating Effect on Critical Roughness and Nozzle Wall Boundary-Layer Stability

Abstract

The effect of wall heating in the throat region on the e ow quality in a Mach 3.5 and a Mach 2.4 axisymmetric nozzle is investigated. Because of the boundary-layer thickening effect, the critical roughness height to trigger laminar‐turbulent transition is larger in the heated cases. Therefore, for a given surface e nish, the adverse effect of roughness on transition can be minimized by sufe cient wall heating. However, the combined effect of heating and pressure gradients is to introduce an overshoot in the streamwise velocity proe le, as earlier predicted by Cohen and Reshotko. Associated with this overshoot is a new generalized ine ection point near the edge of the boundary layer, and, as a consequence, the nozzle wall boundary layer supports high-frequency two-dimensional inviscid disturbances. N-factor results indicate that, with excessive throat heating, these disturbances could cause prematuretransitiondownstream ofthethroatand,hence, jeopardizethequiet performance.Therefore, favorable (on critical roughness height ) and adverse (on boundary-layer instability ) effects of heating have to be carefully evaluated. Mean e ows are computed by using both a boundary-layer code and a Navier ‐Stokes solver, the critical roughnessheights are calculated based on an empirical formula, and the destabilizing effect of heating is evaluated by using compressible linear stability theory. The critical roughness heights are established for the two nozzles for given heating strips.