Development of a Generalized Corcos Model for the Prediction of Turbulent Boundary Layer-Induced Noise

Abstract

The characterization of the wall pressure field generated by a turbulent boundary layer $\mathrm {\left( TBL\right) }$ is a challenging problem in different fields. Its description is strictly dependent on the prediction of the noise and vibration induced by the flow-excited structure. $\mathrm {TBL}$ characterization often requires specific experimental setups and huge facilities, like wind tunnels, which are quite expensive. Usually, for simple configurations, semi-empirical or empirical models fit to experimental data are used to model the wall pressure characteristics. Many $\mathrm {TBL}$ models have been developed since the 1950s. Among others, the Corcos model has been widely used, especially because of its advantageous mathematical features that allow significantly reduced computational effort. However, an obvious problem with the Corcos model is its behaviour for wavenumbers below the convective peak. Within this paper, a Generalized Corcos model is considered for the prediction of $\mathrm {TBL}$-induced noise. Being built on a two-dimensional Butterworth filter, such a model is characterized by two more parameters than Corcos, which are the order of the filters along the streamwise and spanwise direction. The applicability of such a model is here investigated considering two representative flow conditions: (1) low-speed flow; (2) high-speed flow. Particular attention is drawn to the effect of the order of the filters. In this way, it will be shown how an accurate description of the wavenumber-frequency spectrum at and below the convective peak can be given by using the Generalized Corcos model.