A Framework for Modeling Two-Point Statistics of Coherence from a Database for Airwake with Helicopter Downwash

Abstract

Airwake-downwash turbulence is nonhomogeneous and rapidly distorting, impacting on pilot workload and such critical aspects of helicopter shipboard operations. It requires both the one-point statistics of auto spectrum and the two-point statistics of coherence for a relatively complete description. While major strides have been made in generating databases of flow velocity points through computational fluid dynamics (CFD) and experimental investigations, in numerically computing auto spectra and coherences and in developing a framework for extracting auto spectral models from a database, relatively little is known about such a development for coherence models. Accordingly, this study presents a framework for extracting coherence models from a database using a perturbation series expansion of coherence; therein, the basis function or the first term on the right hand side of the series is represented by the corresponding coherence for HIT: homeogeneous isotropic turbulence for which the frozen turbulence hypothesis is applicable. The perturbation series coefficients are evaluated by satisfying the theoretical constraints and fitting a curve in a least squares sense on a set of numerically generated coherence points in the low-frequency bandwidth (0≤ω≤10 rad/s). These models are interpretive and in closed form. Compared to voluminous, numerically generated points, they bring better understanding and complement the experimental and CFD investigations as surrogate models. As for the basis functions, the literature on coherence for HIT is scattered and piecemeal, and the expressions for coherences vary from one study to the other. Therefore, this work presents a unified account of these coherences for all three velocity components from first principles. Although, the framework has not been tested against a database, it is formulated with a mathematical basis of perturbation theory. Finally, for the assumed values of perturbation series constants, this work describes how coherences of airwake-downwash turbulence and such flow-fields that weakly deviate from HIT compare to coherences of HIT.