Decomposition of the Spatially Filtered and Ensemble Averaged Kinetic Energy, the Associated Fluxes and Scaling Trends in a Rotor Wake

Y-C Chow, O. Uzol, J. Katz & C. Meneveau
Department of Mechanical Engineering
Johns Hopkins University
Baltimore, MD 21218

ABSTRACT: PIV data obtained in the rotor wake of a turbomachine is 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 (Reynolds) production and the ensemble averaged subgrid scale (SGS) 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.

(2005), Phys. Fluids 17, 085102.

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(Reused with permission from Yi-Chih Chow, Physics of Fluids, 17, 085102 (2005). Copyright 2005, American Institute of Physics.)

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