Evaluation of Quadrupole Correction Techniques in Spectral FW-H Analogy for Complex Flow Configurations

The Ffowcs–Williams and Hawkings formulation used to compute far-field noise radiated by turbulent flows employs a permeable integration surface, whereby the volume integral containing the quadrupole source term is omitted from the integral solution. This omission introduces spurious noise effects and therefore necessitates the use of quadrupole correction. The primary objective of this study is to validate a quadrupole correction technique from literature which is formulated in the frequency domain. To test this technique, a high-speed unsteady jet flow, both with and without a heated core, was considered. The flow solution for this is obtained using the Lattice Boltzmann solver SIMULIA PowerFLOW. The acoustic predictions made by the proposed quadrupole correction technique showed good agreement with experimental measurements. When compared with the widely used end-cap averaging technique, the quadrupole correction technique showed comparable results. However, it was demonstrated that end-cap averaging was highly sensitive to the FWH geometry and required application-specific optimization, indicating that the pure quadrupole correction technique was more robust and consistent for predicting noise in highly turbulent flows.