Variation of Acoustic Energy Across Sudden Area Expansions Sustaining a Subsonic Flow

The acoustic energy balance of a sudden area expansion is known to be altered in the presence of a mean flow. In this work, Ronneberger's quasi-steady model describing the acoustic response of a sudden area expansion sustaining a subsonic mean flow of arbitrary Mach number is revisited using the acoustic absorption coefficient, shown to be a function of the inlet Mach number Mu, cross-sectional area ratio theta, and upstream acoustic reflection coefficient Ru. These analytical predictions are tested using a two-step numerical strategy, whereby the mean flow variables are obtained using Reynolds-averaged Navier-Stokes simulations and the fluctuating variables are computed using in-house linearized Navier-Stokes equations solvers. The agreement between the analytical model and the numerical results is found to be excellent for all geometries, mean flows, and acoustic boundary conditions investigated. The generation of acoustic energy by the flow expansion is observed analytically and numerically for high-Mach-number flows undergoing a slight sudden area increase for given acoustic boundary conditions. Conversely, it is found that substantial acoustic energy damping occurs across sudden area expansions characterized by a wide range of parameters (Mu,theta,Ru). Moreover, entropy and vorticity fluctuations are found to be generated at the sudden area expansion, but entropy fluctuations are shown to have a negligible impact on the acoustic response of the area expansion at low and intermediate Mach numbers. Finally, the analytical model is found to be reasonably accurate up to Helmholtz numbers He & SIM;0.05-0.1, corresponding to the frequency range of many industrial applications.