The law of the wake and the law of the wall in incompressible turbulent boundary layers formulated by Coles (1956) and their use by Mathews et al. (1970) in the development of a wall-wake representation of the velocity profile in a form applicable for isoenergetic compressible boundary layers are extended to a modified wall-wake velocity profile for turbulent compressible boundary layers. The modified wall-wake profile is shown to provide good representations of experimental velocity distributions.

A modified wall wake velocity profile for turbulent compressible boundary layers.

The self-similar evolution to turbulence of a multi-mode miscible Rayleigh-Taylor (RT) mixing layer has been investigated for Atwood numbers 0.03-0.6, using an air-helium gas channel experiment. Two co-flowing gas streams, one containing air (on top) and the other a helium-air mixture (at the bottom), initially flowed parallel to each other at the same velocity separated by a thin splitter plate. The streams met at the end of the splitter plate, with the downstream formation of a buoyancy unstable interface, and thereafter buoyancy-driven mixing. This buoyancy-driven mixing layer experiment permitted long data collection times, short transients and was statistically steady. Several significant designs and operating characteristics of the gas channel experiment are described that enabled the facility to be successfully run for A t ~ 0.6. We report, and discuss, statistically converged measurements using digital image analysis and hot-wire anemometry. In particular, two hot-wire techniques were developed for measuring the various turbulence and mixing statistics in this air-helium RT experiment. Data collected and discussed include: mean density profiles, growth rate parameters, various turbulence and mixing statistics, and spectra of velocity, density and mass flux over a wide range of Atwood numbers (0.03 ≤ A t ≤ 0.6). In particular, the measured data at the small Atwood number (0.03-0.04) were used to evaluate several turbulence-model constants. Measurements of the root mean square (r.m.s.) velocity and density fluctuations at the mixing layer centreline for the large A t case showed a strong similarity to lower A t behaviours when properly normalized. A novel conditional averaging technique provided new statistics for RT mixing layers by separating the bubble (light fluid) and spike (heavy fluid) dynamics. The conditional sampling highlighted differences in the vertical turbulent mass flux, and vertical velocity fluctuations, for the bubbles and spikes, which were not otherwise observable. Larger values of the vertical turbulent mass flux and vertical velocity fluctuations were found in the downward-falling spikes, consistent with larger growth rates and momentum of spikes compared with the bubbles.

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Detailed Measurements of a Statistically Steady Rayleigh-Taylor Mixing Layer from Small to High Atwood Numbers

Laser Velocimeter and Hot-wire Anemometer Comparison in a Supersonic Boundary Layer

This paper presents an overview of some of the recent developments that have taken place in the understanding, prediction and control of two-dimensional shock-wave-turbulent-boundary-layer interaction at high speeds. Following a brief description of the upstream influence phenomena, detailed discussions of incipient and fully separated flows at supersonic and transonic speeds are presented. A brief account of certain gross unsteady features of shock-separated flows is given next. Typical examples demonstrating the current ability to predict these complex flows are also included. Finally, a review of techniques using suction and tangential blowing for controlling shock-separated flows is presented.

Shock-wave-turbulent-boundary-layer interaction and its control - A survey of recent developments

Direct measurements of the Reynolds normal and shear stresses have been made upstream and downstream of a two-dimensional, adiabatic, shock-wave boundary-layer interaction at M-2.9. The measurements were obtained independently with a laser velocimeter and a constant-temperature, hot-wire anemometer. In addition to these turbulence data, mean velocity data were obtained with the laser velocimeter and compared with data obtained from pitot-static probe. Obtained from the two independent systems, the turbulence data are compared with each other and with previous turbulence measurements. These data are examined in light of modeling the Reynolds stresses appearing in the streamwise momentum equation.

Turbulence in a Shock-Wave Boundary-Layer Interaction

The rms intensities of fluctuating mass flux and total temperature and their correlation coefficients are given for the case of an adiabatic, Mach 4, axisymmetric shock-wave boundary-layer interaction. Data were obtained upstream, within, and downstream of the interaction by the use of constant temperature hot-wire anemometer. Turbulence spectra and quantitative behavior from oscilloscope traces are shown at selected locations. The measurements indicate that certain frequencies of the turbulence are increased as a result of the interaction and that the mass flux and total temperature fluctuations remain highly correlated over most of the boundary layer throughout the interaction. The present data are also transformed to rms intensities of fluctuating static temperature and velocity and compared with existing data obtained in adiabatic flows.

W. C. Rose

Papers

Turbulence measurements in a compressible boundary layer subjected to a shock-wave-induced adverse pressure gradient.