Decomposition of the spatially filtered and ensemble averaged kinetic energy, the associated fluxes and scaling trends in a rotor wake

Abstract

Particle image velocimetry data obtained in the rotor wake of a turbomachine are used for examining elements of the ensemble averaged and spatially filtered kinetic energy. These two distinct averaging processes decompose the kinetic energy into four parts, consisting of the mean-flow resolved, mean-flow subgrid, fluctuating resolved, and fluctuating subgrid parts. Their evolution equations include energy flux terms among these parts. The results elucidate the fundamental difference between the filtered turbulence ͑Reynolds͒ production and the ensemble averaged subgrid scale ͑SGS͒ dissipation rates. Each of these terms consist of three energy fluxes, but only one of them is common to both, the flux from the mean-flow resolved to the fluctuating subgrid kinetic energy parts. The other two elements of the SGS dissipation are the fluxes from the mean-flow resolved to the mean-flow subgrid parts and the fluctuating resolved to the fluctuating subgrid parts. Likewise, the other two contributions to the turbulence production are the fluxes from the mean-flow resolved to the fluctuating resolved parts and the mean-flow subgrid to the fluctuating subgrid parts. In order to examine the decay rates of the kinetic energy parts throughout the rotor wake, a new method for determining the scaling parameters is introduced. The mean-flow resolved and subgrid parts scale with the modified velocity defect squared, but the decay rates of the turbulence parts are slower.

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