Aeroacoustic formulations for confined flows based on incompressible flow data

The hybrid aeroacoustic approach is an efficient way to address the issue of the disparity of scales in Computational AeroAcoustics (CAA) at low Mach numbers. In the present paper, three wave equations governing propagation of flow-induced sound of low Mach number flows, namely the Perturbed Convective Wave Equation (PCWE), Ribner's Dilatation (RIB) equation, and Lighthill's wave equation, are applied using the Finite Element Method (FEM). An airflow through a circular pipe with a half-moon-shaped orifice at three operating flow speeds is considered, where validation data from measurements on a dedicated test rig is available. An extensive analysis of the flow field is provided based on the results of the incompressible flow simulation. The resulting acoustic source terms are investigated, and the relevant source term contributions are determined. The results of the acoustic propagation simulations revealed that the PCWE and RIB are best suited for the present task. The overall deviation of the predicted pressure spectra from the measured mean values amounted to 2.26 and 2.13 times the standard deviation of the measurement compared to 3.55 for Lighthill's wave equation. Besides reliably predicting the flow-induced sound, the numerical procedure of source term computation is straightforward for PCWE and RIB, where the source term contributions, shown to be relevant, solely consist of time derivatives of the incompressible pressure. In contrast, the Lighthill source term involves spatial derivatives and, thus, is strongly dependent on the spatial resolution and the numerical method actually used for approximating these terms.