Publications Details

Approximate analytical models for turbulent boundary layer wall pressure and wall shearfluctuation spectra and coherence functions

DeChant, Lawrence J.; Smith, Justin S.; Barone, Matthew F.

Fluctuating boundary layer wall shear stress can be an important loading component for structures subjected to turbulent boundary layer flows. While normal force loading via wall pressure fluctuation is relatively well described analytically, there is a dearth of information for wall shear behavior. Starting with an approximate acoustic analogy we derive simple approximate expressions for both wall pressure and wall shear fluctuations behavior utilizing a Taylor hypothesis based analogy between streamwise and temporal fluctuations. Analytical results include longitudinal spatial correlation, autocorrelation, frequency spectrum, RMS intensity and longitudinal and lateral coherence expressions. While coefficients in these expressions usually require some empirical input they nonetheless provide useful predictions for functional behavior. Comparison of the models with available literature data sets suggests reasonable agreement. Dedicated high fidelity numerical computations (direct numerical simulations) for a supersonic boundary layer are used to further explore the efficacy of these models. The analytical models for wall pressure fluctuation and wall shear fluctuation spectral density compare well for low frequency with the simulations when Reynolds number effects are included in the pressure fluctuation intensity. The approximate analytical models developed here provide a physics-based connection between classical empirical expressions and more complete experimental and computational descriptions.