Exact Tuning of Von Karman - Pao Energy Spectrum for Stochastic Noise Generation in Turbulent Flows

Stochastic Noise Generation and Radiation (SNGR) is a high-fidelity numerical method for the estimation of broadband noise generated by turbulent velocity fluctuations. Its generation part (simply referred to as SNG) consists in the synthesis of a stochastic turbulent velocity field, reconstructed from the results provided by a Reynolds-Averaged Navier-Stokes (RANS) simulation. Within this framework, the present work introduces a new strategy for performing an exact tuning of the parameters governing the Von Karman-Pao isotropic energy spectrum, whose closed-form expression is used in the generation process. The proposed approach is analytically derived and stands in contrast to the approach adopted in current applications of SNGR method. In this latter, spectrum parameters are calculated under an assumption not always locally valid and therefore potentially leading to an inconsistency between the inputs and the output of SNG. The new approach ensures such consistency at all points in the domain, as demonstrated by a verification procedure which is formulated and then applied to a reference case.