Efficient Implementation of Equivalent Sources from CFD Data in Curle's Analogy

Abstract

Two aspects related to the synthesis of equivalent sources from CFD data for their use in Curle’s analogy are investigated in this work. On the one hand, the number of equivalent sources that describe a quadrupolar field can be significantly reduced with respect to the original size of the CFD data, provided that every equivalent quadrupole accounts for a compact subdomain; in order to assess the limits of this procedure, we apply a systematic coarsening starting from the initial CFD mesh. On the other hand, the truncation of the quadrupolar field due to the finiteness of the CFD domain is also addressed. Several correction methods proposed in the literature are compared. These methods are typically combined with the use of a reference framework that moves with a constant convection velocity, and with respect to which the sources are defined; we study the application of these methodologies in the case of a fixed framework, within which the sources may be moving at spatially varying convection speeds. The computation of flow generated sound through the hybrid method is based on the acoustic analogies pioneered by Lighthill in the 1950s. 1 The analogies interprete certain terms of the flow equations as source terms of an acoustic propagation equation, allowing a sequencial computation of flow field and acoustic propagation. This provides an efficient approach for the computation of flow generated sound for practical applications, where very often a direct computation of the acoustic field through the flow equations would be unaffordable. Curle’s variant of Lighthill’s analogy provides a general framework when the interaction between turbulence and solid boundaries plays a role in the mechanism of sound production. 2 A fundamental step in the application of Curle’s analogy is the synthesis of equivalent sources from CFD data. In this study, we address the reduction of the number of equivalent sources as a way of decreasing the computational requirements in the numerical evaluation of sound at low Mach numbers through Curle’s analogy. In a recent work, Gloerfelt et al. 4 illustrate for the case of the sound generated by a cylinder the equivalence of the dipole contribution in Curle’s analogy with the scattered part of the quadrupolar field; furthermore, they recover the diffraction properties in the cylinder by placing a single equivalent quadrupole near its surface, yielding a good agreement with the field computed by considering all the sources synthesized from a CFD computation. The use of a single equivalent source involves assuming that the source field is compact; while this hypothesis is not generally applicable for the turbulent wake, these results show that the number of equivalent sources can be drastically reduced and still preserve the most relevant features of the acoustic field.