Analysis of Velocity and Temperature Fluctuations in Turbulent Shear Flows.
Abstract
Turbulent velocity and temperature fluctuations in the jet-burner mixing-layer were measured. Particular attention was focused on the small scale, high wave number turbulence which strongly affects the optical propagation. Commercial hot-wire sensors involving a newly developed temperature measuring scheme were employed. The velocity and temperature structure functions up to order 18 were measured in the inertial range to establish the power-law relationships, <(Delta u)^{n }> ~ <epsilon> ^{n/3} r ^{zeta_ {n}} and <( Deltatheta)^{n} > ~ <epsilon> ^{rm -n/6} <chi >^{rm n/2} rm r ^{zeta_rm n}, where zeta_{n} is the exponent due to intermittency. In contrast to Kolmogorov's theory (1941), both viscous dissipation rate epsilon and thermal dissipation rate chi were assumed as random quantities. Measured values of zeta_{n} from velocity structure functions were compared with those predicted by lognormal, beta -model and a new theory based on gamma statistics for the local dissipation rate epsilon_ {r}. The present data and past measurements agree more closely with the predictions of gamma model rather than those of the lognormal model. Similarly, the measured values of zeta _{rm n} from temperature structure functions compared more favorably with the predictions of a new theory based on the bivariate gamma distribution for the joint density function of local dissipations ( epsilon_{r} and chi_{r}) than results predicted by bivariate lognormal distribution. Unlike velocity spectra, the measured temperature spectra revealed that at high wave numbers it decreases less rapidly than the k_sp{1} {-5/3} law and has the appearance of a spectral "bump" just prior to the dissipation ranges. A corresponding bump was also observed in the temperature structure function. By considering the joint fluctuations in the dissipations epsilon_ {r} and chi_ {r}, the new analytical spectrum and structure function models based on the bivariate gamma distribution were found to agree well with the present and past experimental data.
- Publication:
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Ph.D. Thesis
- Pub Date:
- March 1989
- Bibcode:
- 1989PhDT........39J
- Keywords:
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- Engineering: Mechanical; Physics: Atmospheric Science; Physics: Fluid and Plasma