On the determination of the dissipation rate of turbulence kinetic energy

Autor: Timothy Koster, James M. Lewis, John C. LaRue
Rok vydání: 2021
Předmět:
Zdroj: Experiments in Fluids. 62
ISSN: 1432-1114
0723-4864
DOI: 10.1007/s00348-021-03243-2
Popis: Abstract The paper presents a comparison of the dissipation rate obtained from numerical differentiation of the time-resolved velocity, analog differentiation of the hot-wire signal, integration of the velocity derivative spectra obtained from the velocity spectra, and the application of a power decay law. Hot-wire measurements downstream of an active-grid provide the time-resolved velocity with a Taylor Reynolds number in the range of 200–470, turbulence intensities in the range of 5.8–11%, and nominal mean velocities of 4, 6, and 8 m s$$^{-1}$$ - 1 . The dissipation rate calculated using a ninth-order central-difference scheme differs at most by $${\pm }$$ ± 4% from the value obtained by analog differentiation. For comparison, a 23rd-order central-difference scheme offers negligible (0.02%) difference relative to the ninth-order scheme. Correction for an apparent uncertainty in the calibration of the analog differentiator reduces the difference to $${\pm }$$ ± 2.5%. In contrast, integration of the velocity derivative spectra obtained from the velocity spectra leads to a dissipation rate 14–45% larger than the corresponding values obtained using analog differentiation. Results obtained from the application of a power decay law of turbulence kinetic energy with a nonzero virtual origin to determine the dissipation rate deviate by 1.7%, 1.6%, and 3.6% relative to the corresponding values obtained from the analog differentiator based on the ensemble average of downstream locations with a $${\pm }$$ ± 5.6% scatter about the ensemble average. Graphic abstract
Databáze: OpenAIRE
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