Numerical Investigation of the Plane-Wave Reflection Coefficient of an Exhaust Pipe at Elevated Temperatures Using Linearized Navier-Stokes Equations

Abstract

When modeling gas turbine sound emissions an important boundary condition is the acoustic reflection coefficient at the engine exhaust. Here, the flow discharges into atmosphere at elevated temperature and high flow velocity. The exit reflection coefficient governs the proportion of engine core noise that is radiated into the far-field as well as the acoustic energy contained inside the engine. In addition to pure jet noise, the core noise transmitted through the exit boundary contributes to the overall acoustic emission of an engine, particularly in the audible low frequency regime. In this paper we investigate the plane-wave reflection coefficient at the jet exhaust for a series of different jet Mach numbers and temperatures by solving the linearized Navier-Stokes equations (LNSEs) in frequency space using a finite element method. This approach accounts for effects of mean flow, i.e. scattering and refraction in shear layers, as well as acoustic interaction with unstable shear layers and entropy fluctuations. Their combined effect may cause amplification or attenuation of incident acoustic waves. Applicability and accuracy of the LNSE approach are validated for a set of ambient flow cases at different Mach numbers where a broad base of experimental data and theoretical models is available from literature. Consecutively, the numerical experiment is extended to significantly higher flow temperatures for which few publications exist. The results for elevated flow temperatures show a considerable decrease in the reflection coefficient magnitude with increasing flow temperature. These computations are compared to results obtained from the theory derived by Munt [1,2] and differences are assessed.