Acoustic-entropy coupling behavior and acoustic scattering properties of a Laval nozzle

Combustion noise of stationary gas turbines or aero engines is associated with unsteady heat release that creates temperature uctuations or so-called entropy waves (hot-spots). When accelerated in the turbine located downstream of the combustor, these temperature uctuations radiate sound, the indirect noise. This gives reason to investigate the acoustic-entropy coupling in a generic convergent-divergent nozzle configuration as a simplified model of the turbine flow and its corresponding entropy sound generation. A two-step approach is applied for that purpose: First, the mean flow is computed by performing a stationary Reynolds-averaged Navier-Stokes (RANS) simulation. Then, the propagation of acoustic and entropy waves is superimposed to the mean flow and modeled by linearized Navier-Stokes equations (LNSEs). These equations are solved numerically in frequency space by a stabilized finite-element approach. The acoustic pressure responses to the excited entropy waves correlate well with experimental measurements indicating that the RANS/LNSEs method includes all physical transport and coupling mechanisms relevant to entropy noise. Furthermore, the acoustic scattering properties of the nozzle are determined. The comparison with analytical models and numerical solutions show good quantitative agreement.