Entropy-Patch Choked-Nozzle Interaction: Quasi-Steady and Inertial Modeling Regimes Mapped and Limits of Linearization Established

Abstract

The effects of entropy-patch shape, size, and strength on the upstream acoustic response generated by entropy-patch choked-nozzle interactions are investigated. Numerical-simulation-based investigations, using a two-dimensional planar Euler code, reveal the existence of two distinct modeling regimes: the quasi-steady (matching-condition) regime and the inertial regime, respectively. The ratio of the entropy-patch streamwise length scale to the nozzle throat height was found to be an order parameter, which allows one to determine which of the two modeling regimes applies. Indeed, for entropy patches with a streamwise length scale smaller or equal to the nozzle throat height, the inertial model provides a satisfactory prediction of the upstream acoustic response. For entropy patches with a streamwise length scale larger than the nozzle throat height, the matching condition model has superior predictive accuracy. The entropy patch's shape was judged to have only a slight impact on the applicable modeling regime. Additionally, the study examined entropy-patch strength using the ratio of area-specific perturbation energy to area-specific upstream energy as an order parameter, establishing that both above-mentioned linear models are only valid for weak entropy patches. These findings provide a framework for furthering the fundamental understanding of indirect noise-driven combustion instability.