Numerical Study of Mach Number and Thermal Effects on Sound Radiation by a Mixing Layer

Abstract

Mach number and thermal effects on the mechanisms of sound generation and propagation are investigated in spatially evolving two-dimensional isothermal and non-isothermal mixing layers at Mach number ranging from 0.2 to 0.4 and Reynolds number of 400. A characteristic-based formulation is used to solve by direct numerical simulation the compressible Navier-Stokes equations using high-order schemes. The radiated sound is directly computed in a domain that includes both the near-field aerodynamic source region and the far-field sound propagation. In the isothermal mixing layer, Mach number effects may be identified in the acoustic field through an increase of the directivity associated with the non-compactness of the acoustic sources. Baroclinic instability effects may be recognized in the non-isothermal mixing layer, as the presence of counter-rotating vorticity layers, the resulting acoustic sources being found less efficient. An analysis based on the acoustic analogy shows that the directivity increase with the Mach number can be associated with the emergence of density fluctuations of weak amplitude but very efficient in terms of noise generation at shallow angle. This influence, combined with convection and refraction effects, is found to shape the acoustic wavefront pattern depending on the Mach number.

The influence of a pressure wavepacket's characteristics on its acoustic radiation

“…Note also that for short wavepackets, the plateau is reached for lower values of M c and lasts longer. The behavior at low M c is consistent with observations of Moser et al 3 who reported such an effect of the convective Mach number on the noise directivity for subsonic mixing-layers. At a given phase velocity, the maximum of efficiency is reached around rk h ¼ 1, which does not deviate from the conclusions of the analytical study.…”

“…However, for a plane Kirchhoff surface and no other sources, the contributions of each of the two terms in Eq. (3) to the resulting integral are identical. 25 For other (relatively simple) geometries, designing a tailored Green function can fix that issue out.…”

“…The hydrodynamic pressure fluctuation associated with the vortices then has the form of such a wavepacket along the mixing layer. 3,4 Such radiation by amplified hydrodynamic fluctuations also occurs at the trailing edge of a sharp-edged flat plate. 5 A solution of this problem is critical to the efficient design of control strategies, because the latter may be different whether the acoustic power output is due to a high amount of energy brought by the hydrodynamic flow or a high efficiency through the conversion process into acoustics.…”

On compressibility assumptions in aeroacoustic integrals: A numerical study with subsonic mixing layers

“…As shown by Moser et al 14 there are almost no observable differences between the vorticity field of the simulation at M = 0.25 and that of the simulation at M = 0.40. No more differences appear when the comparison includes the incompressible simulation.…”

“…As investigated by Moser et al 14 , increasing the Mach number of mixing layers with U 1 = 2U 2 leads to a reinforcement of the directivity peak around θ = 50 o especially for the radiation towards the high-speed flow. This is illustrated in figure 11a) and figure 11c) with the instantaneous acoustic pressure field as given by the DNC for M = 0.25 and M = 0.4 respectively.…”