A boundary element extension of Curle's analogy for non-compact geometries at low-Mach numbers

Abstract

The aeroacoustic analogy derived by Curle for the prediction of the sound resulting from turbulence/body interactions has proved quite powerful for low Helmholtz numbers, i.e. when the interaction region is acoustically compact. In such case, incompressible flow modeling can be used to obtain the source field used as the input of the analogy. It was, however, shown in a previous paper that Curle's analogy can yield erroneous results for non-compact cases, when an incompressible flow model is adopted. Yet, at low-Mach numbers, incompressible flow modeling can be substantially more efficient than compressible simulations, due to the stiffness issues faced by the latter. The present work focuses on the derivation of a method combining Curle's analogy with a boundary element method (BEM), in order to compensate for the weaknesses of the traditional approach at high Helmholtz numbers. The validation of this method is performed by application to a generic test case: the spinning of two vortex filaments in an infinite two-dimensional duct. This flow model is amenable to a nearly exact derivation by an incompressible vortex model. Moreover, the acoustic field can also be obtained very accurately using the tailored Green's function based on the duct modes, providing a reference solution to validate our numerical approach. The sound field predicted using the BEM/Curle approach shows excellent agreement with the reference solution based on the tailored Green's function, thereby validating the general principle of BEM/Curle method and its numerical implementation.