Relevant Turbulent Time Scale for Broadband Sound and the Prediction of the Grid Cut-Off Frequency for LES Based Aeroacoustic Simulations

In this work, we establish a relation between the generation of broadband sound for the inertial subrange in turbulent flows and the turbulence cascade mechanism. A dimensional analysis of the perturbed convective wave equation (PCWE) source term is used to obtain the time scale of the aeroacoustic source term and its relation to the turbulent length scales. Based on these findings, a new method to estimate the grid cut-off frequency ( \(f_{GCO}\) ) is proposed. The frequency \(f_{GCO}\) determines the maximum frequency up to which the turbulent structures are fully resolved by the grid of the flow simulation. For hybrid aeroacoustic simulations, this maximum resolvable frequency of the flow simulation also determines the maximum frequency content of the aeroacoustic sources and therefore the highest frequency that can be resolved in the subsequent acoustic simulation of broadband sound. The ability of the new method to estimate the \(f_{GCO}\) is tested against two common methods frequently used in literature. The test case of a forward-facing step is chosen which is a common aeroacoustic benchmark case and known to generate broadband sound. The new method shows promising results when the estimated grid cut-off frequency is compared against the estimations from the two reference methods.