An aeroacoustic hybrid approach for non‐isothermal flows at low Mach number

Abstract

SUMMARYThis paper presents an aeroacoustic hybrid technique for the study of non-isothermal ows at low Mach number. The ow dynamics and the acoustic production and propagation are computed separately. The fully compressible Navier-Stokes equations are modiÿed through an expansion of the physical quantities using a low Mach number approximation. Compressibility e ects are thus removed in the CFD while inhomogeneities of the ow related to heat transfer are preserved. One advantage is a reduction of the time step constraint. Another advantage is that the Mach number does not appear explicitly and a simple rescaling allows a study over a relatively wide band of subsonic Mach number ows with a single dynamic simulation.Compatible acoustic source terms for LEE based propagation have been deÿned and the procedure is implemented in the case of a temporal mixing layer. Compressible simulations for Mach numbers of 0.2, 0.3 and 0.4 are compared with the numerical results obtained using the proposed method. Very good agreement is obtained even at relatively high subsonic Mach number demonstrating the e ciency of the proposed technique.

Control of the vorticity mode in the linearized Euler equations for hybrid aeroacoustic prediction

“…This allows to use S i as well as S q i to define acoustic source terms on the solution obtained with an incompressible Navier-Stokes solver. We recall that S q i solutions have been validated with direct acoustic computation in situations where vorticity generation was not critical [24]. Some numerical simulations have been carried out to illustrate the response of LEE in density and vorticity.…”

“…As a consequence, driving the LEE with S i instead of S q i should limit the presence of vorticity mode. Given that S i could be evaluated by (24), or by (25) when neglecting viscous terms, and given that the divergence of S t i is null (if the density is constant), the divergences of S i andS q i are precisely the same. According to what was written in this section, it is clear that driving the LEE with S i instead of S q i can reduce one of the major difficulty inherent to the LEE linked to the presence of the vorticity mode.…”

A hybrid adaptive low-Mach number/compressible method: Euler equations

“…While being a canonical test case with a well-controlled physics of the flow, this test case is representative of the phenomena that appear in the context of noise generated by jets in practical industrial applications. Therefore, this test case has been widely computed in the aeroacoustic community to understand the sources of vortex sound generation, as well as to evaluate the performances of computational aeroacoustic techniques as mentioned in the introduction part of the present paper (see [28,29,30,31], among others). Indeed, the main issue here is that the mixing interface must be well enough resolved in order to capture accurately the vortex formation, which is critical to capture as well the proper aeroacoustic phenomena, especially in terms of frequency and pressure amplitudes.…”

“…The configuration of the test case is inspired by the temporal representation of the instability as proposed by Golanski et al [30], which features a controlled excitation to generate several pairs of vortices that eventually merge together and generate noise. The computational domain is a rectangle of dimension L x × L y , with L x = 2λ a and L y = 64λ a .…”

“…A review of aeroacoustic methods is beyond the scope of this paper, but a comparison of EIF, MPV and LEEs is given in Roller et al [27]. More recently, many groups [28,29,30,31] have investigated the coupling between a low-Mach-number detailed simulation of noise sources from a small scale turbulent flow, and the aeroacoustic propagation within a larger domain with the LEEs. It will be shown in the results section that the novel hybrid method developed in the present paper is able to tackle the same kind of problem while solving the purely compressible equations instead of the LEEs and allowing feedback of the acoustics into the low-Mach-number solution.…”