A Discrete Model of Turbulence Loading Function for Computation of Flow-Induced Vibration and Noise

Abstract This paper discusses a discrete representation of the spatially homogeneous and temporally stationary turbulence loading on a structure induced by low speed incompressible flow. In the classical random vibration theory involved with continuous structural systems, this forcing function is expressed as the space-time cross correlation function or its Fourier conjugate, the wavevector-frequency spectrum of the turbulent boundary layer (TBL) wall pressure. These functions cannot be applied directly to finite discrete systems, such as most finite-element structural models, because they contain a fine-scale oscillating component which represents the predominant pressure fluctuations convected with the flow. For example, at mid- and moderate high frequencies, this fluctuating length scale may become smaller than the mesh size of a discrete structure model. An approximated discrete forcing function model to ease this numerical difficulty is presented in this paper. The approximate forcing function model is verified by comparing the numerically calculated modal input force spectra to that obtained from exact analytical solutions. The numerical calculated values approach the exact solutions as the finite-element mesh size becomes smaller.