Acoustic and entropy waves in nozzles in combustion noise framework

Abstract

A low-order model is presented to study the propagation and interaction of acoustic and entropic perturbations through a convergent-divergent nozzle. The calculations deal with choked, unchoked, as well as compact and noncompact nozzles. In the choked case, a normal shock exists in the divergent section of the nozzle. First, for circumferential waves and for a compact choked nozzle, it is shown that the pressure, entropy, and vorticity perturbations at the nozzle outlet can be obtained directly from the perturbations at the nozzle inlet. Thus, for the choked case, there is no need to model either the linear waves or the mean flow within the nozzle. Then, to validate the models developed, cylindrical configurations corresponding to the so-called Entropy Wave Generator and Hot Acoustic Testrig are studied. For the Entropy Wave Generator, an entropy wave is generated upstream of a nozzle by an electrical heating device, and for the Hot Acoustic Testrig, a speaker is used to generate pressure waves. In these two configurations and for the choked case, the supersonic region between the nozzle throat and the normal shock is assumed to be acoustically compact. The results of the low-order model are found to give excellent agreement with the experimental results of the Entropy Wave Generator and Hot Acoustic Testrig. To give insight into the physics, the model is used to undertake a parametric study for a range of nozzle lengths and shock strengths. The low-order model is finally used to calculate the direct to indirect (entropy and vorticity) combustion noise ratio for an idealized thin annular combustor. For this model combustor, the direct acoustic noise is found to dominate within the combustor, whereas the entropy indirect noise is found to be the main source of noise downstream of the choked nozzle. The indirect vorticity noise has a negligible contribution