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.

In §II. Theory, two reduced-order models are proposed, which the authors have termed: the quasi-steady model (§II.A. Quasi-steady one-dimensional model) & the inertial/hybrid model (§II.B. Quasi-one-dimensional pointmass model), respectively. N.b., in both cases time dependence isn’t explicitly modeled, i.e., technically speaking both models are quasi-steady. Ergo, in hindsight, it would have been more apt to call the model proposed in §II.A.: the matching-condition model. With that in mind, the readership is encouraged to substitute “matching-condition model/modeling regime” instead of “quasi-steady model/modeling regime,” when reading this conference paper. Moreover, the following title would have been more suitable: “Entropy-patch chokednozzle interaction: matching-condition and inertial modeling-regimes mapped”.

Indirect combustion noise due to the interaction of flow inhomogeneities with a choked combustion-chamber exit is an important cause of combustion instability in solid rocket motors. Moreover, it is believed to be an issue in electrical-power generation turbines and aero-engines. If these flow inhomogeneities are essentially characterized by the fluid having a locally appreciably-different thermodynamic state, the acoustic response engendered by its interaction with the combustion-chamber exit is commonly referred to as entropy noise. In this paper, dedicated numerical-simulation results of entropy-patch choked-nozzle interactions are presented. Two types of entropy patches were considered: rectangular slugs and circular spots. Moreover, analytical-model-based analysis, of said simulation results, is presented. Based on said analysis, the authors posit the existence of three modeling regimes: the quasi-steady-modeling regime, the blended-physical-effects regime, and the inertial-modeling regime.