Theoretical Study of Slightly Underexpanded Jets from Elliptical Nozzles

Abstract

The flow features of shock-containing jets from elliptical convergent nozzles operating under slightly off-design conditions have been studied analytically, where the jet mixing layer is approximated by a vortex sheet and the shock-cell structure is confined to the interior of the vortex sheet. Perturbation conservation equations are solved using eigenfunction expansion, and shock-cell structures for the elliptical jets are obtained explicitly. Only the first Fourier mode of the eigenvalue problem is considered for simplicity. The effects of flow parameters such as the nozzle pressure ratio, aspect ratio, and design Mach number on the shock-cell structure and shock-cell spacings are investigated.