Two-dimensional indirect entropy noise in a thermally choked-flow nozzle

Dual-mode ramjets with thermally choked flow are a potential solution for a seamless transition between subsonic and supersonic combustion, but the associated indirect combustion noise remains poorly understood. This study investigates the acoustic response induced by two-dimensional entropy inhomogeneities convected through a thermally choked nozzle. Entropy perturbations are modelled as circular spots and rectangular slugs and are injected at the inlet of a two-dimensional flow. The thermal throat is generated using a quasi-one-dimensional model prescribing a non-uniform volumetric heat-release profile. As a reference case, an isentropic convergent-divergent-nozzle flow with a choked (geometric) throat is used. Care is taken to ensure that the base flows of both the thermally choked and geometrically choked reference cases have the same steady Mach-number distribution to facilitate a direct comparison of the aeroacoustic response. The numerically obtained acoustic fields are analysed as a function of the entropy-perturbation size and compared with two one-dimensional reference models: a quasi-steady model and an inertial point-mass model for large- and small-size perturbations, respectively. In the case of the isentropic nozzle, both asymptotic regimes are recovered, although at larger perturbation sizes than previously reported. The latter indicates that the particular geometric features of the convergent part of nozzle have an influence on the acoustic response engendered by entropy-patch choked-geometric-nozzle interaction. For thermally choked flows, all configurations tend towards a quasi-steady regime for large spots, with systematically higher acoustic levels due to the heated region. In contrast, for very small spots, the inertial regime generally breaks down and the acoustic response approaches a finite minimum amplitude.