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

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Two assumptions commonly made in predictions based on Lighthill's formalism are investigated: a constant density in the quadrupole expression, and the evaluation of the source quantity from incompressible simulations. Numerical predictions of the acoustic field are conducted in the case of a subsonic spatially evolving two-dimensional mixing layer at Re = 400. Published results of the direct noise computation (DNC) of the flow are use as reference and input for hybrid approaches before the assumptions on density are progressively introduced. Divergence free velocity fields are obtained from an incompressible simulation of the same flow case, exhibiting the same hydrodynamic field as the DNC. Fair comparisons of the hybrid predictions with the reference acoustic field valid both assumptions in the source region for the tested values of the Mach number. However, in the observer region, the inclusion of flow effects in the Lighthill source term is not preserved, which is illustrated through a comparison with the Kirchhoff wave-extrapolation formalism, and with the use of a convected Green function in the integration process.

Aeroacoustic wave equation based on Pierce's operator applied to the sound generated by a mixing layer

“…The upstream deviation is larger for the results of the AWE-PO, which has an extinction line at 12 degrees. A similar extinction line was found in [7] and associated with insufficient integration over the source region regarding the 𝑥-direction. The insufficient integration over the source region was examined but not found to be the case for AWE-PO.…”

“…Figure 2 visualizes the sources of Lighthill's equation ( 1) and shows the merging of two consecutive vortices at the time 𝑡 ≈ 𝑡 0 + 𝑇 p /3 and location 𝑥/𝛿 𝜔 ≈ 110. Lighthill's equation's source characteristics were previously investigated in [7,8,20,21,40] and the authors obtained similar source distributions. Between the moving vortices (red dots), steady source regions of relatively high magnitude are visible.…”

“…Lighthill started to quantify the proportion of flow energy converted into sound by reformulating the conservation equations. In doing so, a nonlinear right-hand side term was obtained, which can be simplified for dominant vortical sound sources [6] (e.g., for an isothermal subsonic mixing layer [7,8]). The Lighthill wave equation reads as…”

“…The sound sources are plotted at three frames over one vortex pairing period 𝑇 p , to analyze the temporal evolution of the individual sources of the respective equations (reported in section III). All source illustrations are given in a rectangular cutout of −15 < 𝑦/𝛿 𝜔 < 15, where the instability waves grow and consequently the most dominant source terms occur [7,33]. Figure 2 visualizes the sources of Lighthill's equation ( 1) and shows the merging of two consecutive vortices at the time 𝑡 ≈ 𝑡 0 + 𝑇 p /3 and location 𝑥/𝛿 𝜔 ≈ 110.…”

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

“…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.…”