Analysis of Secondary Sound Emission in an Acoustic Analogy with a Propagation Operator Containing Vortex Modes

In this paper, we analyze the acoustic analogy method in relation to the sound radiation of a turbulent subsonic jet. This method of describing aerodynamic sound generation by turbulent flows is based on the use of a linear propagation operator with a random source on the right side. The main problem here is the choice of an effective way to separate the left side of the equation, which is responsible for the propagation of sound waves, and the right part, which is responsible for sound generation, so that the noise calculation result corresponds to experimental data and physical ideas about noise generation by turbulence. One of the unsolved problems of the approach, which is common in most acoustic analogies, is the problem of the so-called “shear noise” associated with the excitation of shear flow disturbances by sources and the additional contribution of these disturbances to sound radiation. It is still unclear whether the shear component of the noise is a reflection of real physical processes or is associated with the transformation of equations and inaccurate modeling of sources. Here, within the framework of the problem formulated above, we consider an acoustic analogy, in which the linearized Euler equations are used as the propagation operator. In this description, the propagation operator contains vortex modes, which leads to the appearance of a shear noise component that arises due to the pumping of vortex disturbances by the sources. When modeling sound sources, hypotheses about the quadrupole nature isotropy of sound sources, as well as the spatial uncorrelation of sound source production, are used. To validate the model, the measurement data of the sound emission of the jet using the azimuthal decomposition method are used. The comparison of the model and experiment indicates the absence of a shear component in the jet noise. This makes it possible to conclude that the idea of pumping linear vortex perturbations of the mean flow by nonlinear turbulent pulsations that is used in the considered acoustic analogy does not correspond to the real mechanism of noise generation by a turbulent jet. Possible causes of the discrepancy between the model and the data of acoustic measurements are analyzed. Possible ways of solving this problem, which make it possible to effectively separate the left side of the equation that is responsible for the propagation of sound waves and the right nonlinear part that is responsible for sound generation are considered.