Modeling of wall pressure fluctuations for finite element structural analysis

This paper investigates a modeling technique of wall pressure fluctuations (WPF) due to turbulent boundary layer flows on a surface for finite element structural analysis. This study is motivated by critical issues of structural vibrations due to turbulent WPF over the surface of a body. The WPFs are characterized with random behavior in time and space. The temporal and spatial random behavior of the WPFs is mathematically expressed in the form of the auto- and cross-power spectral density functions (PSDF) in the frequency domain (e.g., Corcos Model). For finite element modeling of the random distributed fluctuations, the cross-PSDF is properly modeled over the finite element structural mesh. The quality of modeling of the cross-PSDF is directly affected by the structural mesh size. We first examine the maximum mesh size required for reliable finite element analysis. The reliability of the FEA results is confirmed by the theoretical results. It is found that the maximum mesh size should be determined under consideration of the spatial distribution of the cross-PSDF in addition to the representation of dynamic behavior of the structure in the frequency range of interest. It is also recognized that the requirement of the maximum mesh size is unrealistic in many practical cases. We then investigate practical modeling schemes under a realistic mesh size condition. We found that the WPF can be modeled without the exact consideration of cross-correlation if the power due to the wall pressure fluctuation can be properly compensated. This is owing to the feature of decreasing the cross-correlation of WPFs at high frequencies and the fact that the WPF does weakly couple into the structural modes at high wavenumbers such that 2 π f / U c < k max . The wall pressure fluctuations can therefore be modeled as uncorrelated loadings with power compensations.