On the scattering of entropy waves at sudden area expansions

Abstract

In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier–Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the quasi-steady model proposed here correctly captures the low-frequency entropy noise generated at sudden area expansions, including at high subsonic Mach numbers.