Axisymmetric turbulent wake behind a sphere in an incompressible fluid has been experimentally investigated from 50 to 300 diam downstream from the sphere at Reynolds numbers from 4000 to 150 000. Mean and turbulent velocity measurements show that the region of self-preservation starts 50 sphere diam downstream, and the virtual origin of the wake is 12 sphere diam downstream. Detailed measurements were made in the self-preserving region of the wake. The three components of the turbulent velocity, turbulent shear, and the mean velocity defect were measured across the wake using the hot-wire anemometer. From the measurements the turbulent energy production, dissipation, convection, and diffusion across the wake were determined. The one-dimensional energy spectra of the three components of the turbulent velocity, their dependence on distance along and across the wake and on Reynolds number have been measured. The large scale motion (low wavenumbers) is dynamically similar and the small scale motion (large wavenumbers) exhibits Kolmogoroff's universal equilibrium. The present spectral measurements are compared with other published measurements of the universal equilibrium spectra in various turbulent flows.
The effect of wind-tunnel contraction on free-stream turbulence is determined by passing a well-defined turbulence through three contractions of ratios 4:1, 9:1, and 16:1. Turbulent velocity measurements show that, in absolute magnitudes, the longitudinal component decreases and the lateral component increases as the flow accelerates through the contraction. Post-and precontraction spectra are measured to get an idea about the distortion of turbulence structure.Corresponding to the test section of a wind tunnel, a uniform section was placed after the contraction. The turbulence is fairly homogeneous and axisymmetric at the end of the contraction, and the turbulent energy in three velocity components slowly equalizes as the flow goes through the uniform section. Measurements show that the lateral (larger) component is losing more energy due to viscosity than by transfer to the longitudinal (smaller) component. The longitudinal component is receiving enough energy to compensate for its decay, and, in fact, it is slowly increasing.For supersonic nozzles, elementary considerations show that the effects of increase in the mean speed and decrease in the density are both beneficial in reducing the flow irregularities.The relation of this investigation to the general problem of turbulent flows is discussed, particularly in connection with local isotropy and the concept of a cascade process in shear flows. SYMBOLS c E F k M n RM U U, V, W Ut Us ^ r p V = = = = = = = = = = = = = =
Energy transfer from large to small eddies at three stations in turbulence behind a square mesh is determined by measuring the rates of change and viscous dissipation of the spectrum and the results are compared with a theoretical prediction. Large eddies for which viscous dissipation is negligible satisfy a similarity relation which agrees with the fact that the total energy decays as some negative power of time. Small eddies which are in approximate statistical equilibrium satisfy local similarity according to Kolmogoroff. Various terms in the vorticity equation are also determined and the quantities representative of small scale motion are universal constants when expressed in terms of Kolmogoroff parameters.
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