Synthesis of wall pressure fields of non-homogeneous turbulent boundary layers for vibroacoustic simulations

Abstract

In this paper, a numerical process is presented for predicting the response of vibrating structures excited by a non-homogeneous turbulent boundary layer. This one is based on the synthesis of different realizations of the random pressure fluctuations that can be introduced as loading of a vibroacoustic model. The vibratory response is finally deduced by averaging together the responses of the different loads. As a first approach, the pressure fluctuations of the non-homogeneous turbulent boundary layer can be generated separately for different sub-areas of the structure by using the uncorrelated wall plane waves technique and mean boundary layer parameters. An extension of this basic approach consists in taking into account the interaction between the sub-areas and a refinement of the sub-area decomposition. Wall pressure fluctuations related to a continuous evolution of the boundary layer can then be generated and introduced in the vibroacoustic model. The accuracy of the proposed approach is studied on a rectangular panel excited on one side by a growing fully turbulent boundary layer triggered at one edge of the plate. Comparisons with the spatial approach and the wavenumber approach using the sub-area decomposition technique are proposed. Interests of the proposed approach in terms of accuracy and computing times are discussed.

Vibroacoustic simulations with non-homogeneous TBL excitations: Synthesis of wall pressure fields with the Continuously-varying Uncorrelated Wall Plane Waves approach

“…A numerical process has been described for predicting the response of vibrating structures excited by a non-homogeneous turbulent boundary layer. The theoretical fundaments of this approach can be found in [14] (based on some works presented in [10]). This process makes it possible to consider the spatial variations of the TBL parameters in vibroacoustic simulations.…”

“…Let us illustrate the application of the C-UWPW approach [14] on a rectangular panel excited by a growing turbulent boundary layer triggered at one edge of the plate as shown in Fig. 1.…”

“…In the case of an inhomegenous TBL, the amplitudes of the wall plane waves should vary continuously to represent the spatial variations of the excitation strength. It is carried out using the Continuouslyvarying Uncorrelated Wall Plane Waves (C-UWPW) method [14]. The blocked pressure of a realization r is then given by:…”

“…Fig 6 shows the response for 30 realizations and the ensemble average. For a validation purpose, the response of the plate to the growing TBL excitation calculated by the present C-UWPW process was compared to the response calculated with the spatial approach (see [14]). An excellent agreement was observed.…”

“…These realizations can then be easily used as loadings of any vibroacoustic model. The theoretical developments of this extension have been recently presented in [14]. We describe and illustrate the different steps of this process in the present paper.…”