Indirect noise prediction in compound, multi-stream nozzle flows

Abstract

An analytical framework to compute the acoustic response of one-dimensional planar waves in a compound-compressible nozzle is presented. Using the steady-state conservation equations, a set of algebraic relations governing compound flow is solved numerically. In each stream, the linearized Euler equations are recast using the invariant formulation and solved with a Magnus expansion following Duran & Moreau (Journal of Fluid Mechanics 723 (2013) 190–231). The modeled acoustic response is compared to the direct solution of the non-linear Euler equations with a maximum error of 5%. A parametric investigation of the acoustic response of a two-stream compound nozzle is presented. The effects of the bypass inflow Mach number and bypass ratio on the magnitude and phase of the transmitted and reflected acoustic waves are studied. It is shown that indirect noise generation is maximum in the peripheral bypass stream, not the core jet and that the initial Mach number of the bypass greatly impacts the phase shift of the resulting acoustic waves. The work provides an insight for acoustic response mitigation of high-speed confined jets.