Experiments in Turbulent Transport and Mixing

[PhD thesis]. Johns Hopkins University

Corrsin, Stanley (supervisor)

1978

- Links
- Abstract and keywords
Part A:

The evolution of experimental turbulence research and some of the instruments connected with it are reviewed briefly; the hot-wire anemometer and the metallic resistance thermometer are examined separately.

Part B:

A reasonably uniform mean temperature gradient has been superimposed upon a nearly homogeneous turbulent shear flow in a wind-tunnel. The overheat is small enough to have negligible effect on the turbulence. Away from the wind-tunnel entrance, the transverse statistical homogeneity is good and the temperature fluctuations and their integral scales grow monotonically like the corresponding velocity fluctuations (Harris, Graham, and Corrsin, J. Fluid Mech. 81, 657 (1977)). Measurements of several moments, one- and two-point correlation functions, spectra, integral scales, microscales, and probability densities of the turbulent velocities, temperature fluctuations, and temperature-velocity products are reported. The heat transport characteristics are much like those of momentum transport, with the turbulent Prandtl number nearly 1. The temperature fluctuation is better correlated to the streamwise than to the transverse velocity component. Some correspondence of directional properties (relative magnitudes of correlation functions, integral scales, microscales) of the temperature with The fine those of the streamwise velocity is also observed. structures of the two fluctuation fields are studied through the statistics of signal derivatives and of band-passed (filtered) signals. Neither field is locally isotropic in the spectral range covered, presumably because of the insufficiently large turbulent Reynolds and Péclet numbers. The flatness factors of the temperature derivatives and of the band-passed high frequency (hence high wavenumber, in view of Taylor's "frozen pattern" approximation) temperature are a bit higher than those of the streamwise velocity. An incidental comparison of the present data to measurements in the inner part of a heated boundary layer shows comparable magnitudes of temperature-velocity correlation coefficients, turbulent Prandtl number, ratio of turbulent diffusivities, and skewness and flatness factors of several velocity and temperature derivatives.

Part C:

In an attempt to learn the dependence of mixing upon the integral scale ratio, velocity and temperature fields behind a turbulence-generating grid with alternate rods heated were compared with prior data behind grids with every rod heated. Contrary to expectation, the system change did not change the ratio of velocity to temperature scale in the region where the fields had become statistically homogeneous. The principal effect of the changed initial conditions was a sizeable increase in relative temperature fluctuations and a slight increase in their decay rate. Some old theoretical estimates were roughly confirmed.

Part D:

Previous measurements in the moderate to small Reynolds number range of isotropic turbulence have all shown the streamwise velocity derivative skewness factor, S= S = (-(∂u/∂x)³/(∂u/∂x)²)

^{3/2}to increase with decreasing Reynolds number. This "paradoxical" trend was found for 150 ≥ R_{λ}≥ 4. New data covering the range 4 ≥ R_{λ}≥ 1 show a maximum S for R_{λ}between 4 and 3, and a rapid decrease for R_{λ}< 2 Some crude theoretical estimates show that S → 0 as R_{λ}→ 0.Keywords: