Compressible, turbulent mixing layers have been investigated experimentally using pressure mesurements, Schlieren photographs, and velocity measurements with a two-component laser Doppler velocimeter system. Seven mixing-layer cases were examined, with relative Mach numbers ranging from 0.40 to 1.97 which spans the region of significant compressibility effects. Both the spatial development and similarty of the mixing layers were considered.

Experimental study of compressible turbulent mixing layers

A high Reynolds number two-dimensional constant pressure compressible shear layer was formed at the trailing edge of an 0.5 mm-thick splitter plate. Convective Mach numbers of 0.51 and 0.64 were investigated using a two-component coincident LDV for the measurements. For the lower convective Mach number case, the nondimensionalized shear-layer and vorticity thickness growth rates were over 20 percent higher and the momentum thickness growth rate was over 30 percent higher than those of the higher convective Mach number case. The results seen to indicate that both small scale and large scale mixing are reduced with increasing convective Mach number.

Effects of compressibility on the characteristics of free shear layers

A new shear-layer growth-rate compressibility-scaling parameter is proposed as an alternative to the total convective Mach number, Mc. This parameter derives from considerations of compressibility as a means of kinetic-to-thermal-energy conversion and can be significantly different from Mc for flows with far-from-unity free-stream-density and speed-of-sound ratios. Experimentally observed growth rates are well-represented by the new scaling.

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Turbulent shear-layer mixing: growth-rate compressibility scaling

For over a quarter of a century it has been recognized that turbulent shear flows are dominated by large-scale structures. Yet the majority of models for turbulent mixing fail to include the properties of the structures either explicitly or implicitly. The results obtained using these models may appear to be satisfactory, when compared with experimental observations, but in general these models require the inclusion of empirical constants, which render the predictions only as good as the empirical database used in the determination of such constants. Existing models of turbulence also fail to provide, apart from its stochastic properties, a description of the time-dependent properties of a turbulent shear flow and its development. In this paper we introduce a model for the large-scale structures in a turbulent shear layer. Although, with certain reservations, the model is applicable to most turbulent shear flows, we restrict ourselves here to the consideration of turbulent mixing in a two-stream compressible shear layer. Two models are developed for this case that describe the influence of the large-scale motions on the turbulent mixing process. The first model simulates the average behaviour by calculating the development of the part of the turbulence spectrum related to the large-scale structures in the flow. The second model simulates the passage of a single train of large-scale structures, thereby modelling a significant part of the time-dependent features of the turbulent flow. In both these treatments the large-scale structures are described by a superposition of instability waves. The local properties of these waves are determined from linear, inviscid, stability analysis. The streamwise development of the mean flow, which includes the amplitude distribution of these instability waves, is determined from an energy integral analysis. The models contain no empirical constants. Predictions are made for the effects of freestream velocity and density ratio as well as freestream Mach number on the growth of the mixing layer. The predictions agree very well with experimental observations. Calculations are also made for the time-dependent motion of the turbulent shear layer in the form of streaklines that agree qualitatively with observation. For some other turbulent shear flows the dominant structure of the large eddies can be obtained similarly using linear stability analysis and a partial justification for this procedure is given in the Appendix. In wall-bounded flows a preliminary analysis indicates that a linear, viscous, stability analysis must be extended to second order to derive the most unstable waves and their subsequent development. The extension of the present model to such cases and the inclusion of the effects of chemical reactions in the models are also discussed.

On the turbulent mixing of compressible free shear layers

Research progress on active thermal protection for hypersonic vehicles

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity (σu/ΔU).

Mean and turbulent velocity measurements of supersonic mixing layers

Experimental and analytical investigations of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity (σ
 u
 /ΔU).

A constructed, dual-stream, supersonic wind tunnel has been designed to provide comparatively long run times for investigations of reactive and nonreactive, two-dimensional supersonic mixing layers. Control of the stagnation temperatures enables the velocity ratio, density ratio, and convective Mach number of the two streams to be varied. Laser Doppler velocimetry has been employed to measure the incoming boundary layers, the subsequent compressible mixinglayer growth rate, and the mean and turbulent velocity field development for two density ratios of 0.76 and 1.56, corresponding to velocity ratios of 0.79 and 0.58 and convective Mach numbers of 0.20 and 0.45, respectively. For a given density and velocity ratio, the convective Mach number has been found to correlate the ratio of compressible to incompressible mixing layer growth rate, as suggested by other workers.

J. P. Renie

Papers

Mean and turbulent velocity measurements of supersonic mixing layers

Experimental and analytical investigations of supersonic mixing layers

Mean and turbulent velocity measurements of supersonic mixing layers

Investigation of supersonic mixing layers