Publications Details

Consistent turbulent boundary layer wall pressure spectra and coherence functions

DeChant, Lawrence J.; Smith, Justin S.

Fluctuating boundary layer pressure fluctuations are an important loading component for high speed reentry vehicles. Characterization of the unsteady time series requires access to longitudinal and lateral coherence expressions as well spatial correlation and frequency power-spectral density models. Coherence, spatial correlation and frequency power spectral density are related as through their cross-spectral density definitions. However the frequency PSD and the spatial correlation are often based upon measurements or approximate models which may introduce bias in the associated derived coherence function. Here, we examine the effect of measurement and model form associated with frequency spectrum and correlation on the longitudinal and lateral coherence for supersonic pressure fluctuation flow fields. The widely utilized Corcos separable coherence model functional form has been employed in this study. The associated integral equations which relate coherence and correlation are solved using a simple iterative approach. To minimize distortion in results due to computational issues a high accuracy numerical integration procedure is utilized. Despite a more robust computational approach, solution accuracy is limited for some problems by the functional form of the longitudinal coherence model. These limitations are discussed in detail. This overall approach is applied to Mach 5 and Mach 8 seven degree sharp cone pressure fluctuation measurements. Estimates for the parameters associated with the Corcos coherence expressions are typically larger than more traditional values especially for the longitudinal coherence. These larger values suggest that fluctuations streamwise correlation length is small. Limited longitudinal correlation can be associated with shock influence and is explored as a possible cause.