Wall-pressure fluctuations associated with turbulent boundary layer of pump-jet duct and empirical spectrum modeling

Abstract

This study establishes the relationship between the pressure fluctuation on outer wall of the pump-jet duct and the source term of velocity-field in the Turbulent Boundary Layer (TBL) based on the Poisson equation and develops it in frequency-wavenumber domain. The wall-pressure fluctuations caused by source terms of different TBL regions are investigated and the spatial-temporal distribution is compared through the wavenumber-frequency spectrum. The characteristics of turbulent structures are revealed in detail using the vortex scale and intensity. The empirical spectrum model is developed for the estimation of the wall-pressure fluctuations. Besides, the simulation of velocity-field source is carried out by using the Large Eddy Simulation (LES) numerical method. Results show that the logarithmic subrange has a dominant contribution to the wall-pressure fluctuations. The remarkable energy distribution at low-frequency and low-wavenumber domain is mainly reflected in the logarithmic subrange and a low-frequency diffusion exists due to the rotor and pressure gradient. The small-scale vortices corresponding to high-wavenumbers are in the viscous subrange and the contribution of large-scale vortices corresponding to low-wavenumbers are reflected in viscous, buffer and logarithmic subranges. The deformation and rotation forms of vortices migration represent in different subranges of TBL. Moreover, the empirical spectrum model can qualitatively predict the pressure fluctuations at different positions of the duct wall, providing a reference for engineering applications.