Density and Compressibility Effects on the Structure of Supersonic Mixing Layer: Experimental Results and Similarity Analysis

Fluids Engineering ◽

10.1115/imece2003-42509 ◽

2003 ◽

Author(s):

M. Menaa ◽

J. P. Dussauge

Keyword(s):

Mach Number ◽

Velocity Profile ◽

Mixing Layer ◽

Variable Density ◽

Turbulent Shear ◽

Turbulent Friction ◽

Low Speed ◽

Rate Of Spread ◽

Supersonic Mixing ◽

Supersonic Mixing Layer

Self-similar solutions for mixing layers in supersonic flow and in subsonic flow with variable density are examined. The equation for the velocity profile is derived for a unity turbulent Prandtl number and/or prescribed density distributions. It is found that the shape of the velocity profile is not sensitive to Mach number and is nearly the same for supersonic layers with moderate convective Mach numbers and in low speed flows with variable density: in such conditions, the only compressibility effect is found on the rate of spread. It is also found that turbulent friction is a function of Mach number and of velocity and density ratios. The effect of these last parameters on turbulent friction in low speed layers is proposed. Finally the scaling for turbulent shear stress last parameters on turbulent friction in low speed layers is proposed. Finally the scaling for turbulent shear strees in supersonic mixing layer is discussed. A simple formulation is proposed, in which the effects of density ratio and convective Mach number can be sepearated, as it is usually done for the rate of spread.

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A numerical study of a variable-density low-speed turbulent mixing layer

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.583 ◽

2017 ◽

Vol 830 ◽

pp. 569-601 ◽

Cited By ~ 16

Author(s):

Antonio Almagro ◽

Manuel García-Villalba ◽

Oscar Flores

Keyword(s):

Growth Rate ◽

Mach Number ◽

Incompressible Flows ◽

Numerical Study ◽

Density Ratio ◽

Mixing Layer ◽

Variable Density ◽

The Self ◽

Low Speed ◽

Self Similar

Direct numerical simulations of a temporally developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier–Stokes equations in the low-Mach-number approximation are solved using a novel algorithm based on an extended version of the velocity–vorticity formulation used by Kim et al. (J. Fluid Mech., vol 177, 1987, 133–166) for incompressible flows. Four cases with density ratios $s=1,2,4$ and 8 are considered. The simulations are run with a Prandtl number of 0.7, and achieve a $Re_{\unicode[STIX]{x1D706}}$ up to 150 during the self-similar evolution of the mixing layer. It is found that the growth rate of the mixing layer decreases with increasing density ratio, in agreement with theoretical models of this phenomenon. Comparison with high-speed data shows that the reduction of the growth rates with increasing density ratio has a weak dependence with the Mach number. In addition, the shifting of the mixing layer to the low-density stream has been characterized by analysing one-point statistics within the self-similar interval. This shifting has been quantified, and related to the growth rate of the mixing layer under the assumption that the shape of the mean velocity and density profiles do not change with the density ratio. This leads to a predictive model for the reduction of the growth rate of the momentum thickness, which agrees reasonably well with the available data. Finally, the effect of the density ratio on the turbulent structure has been analysed using flow visualizations and spectra. It is found that with increasing density ratio the longest scales in the high-density side are gradually inhibited. A gradual reduction of the energy in small scales with increasing density ratio is also observed.

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Balance of Kinetic Energy in a Supersonic Mixing Layer Compared to Subsonic Mixing Layer and Subsonic Jets with Variable Density

Fluid Mechanics and Its Applications - IUTAM Symposium on Variable Density Low-Speed Turbulent Flows ◽

10.1007/978-94-011-5474-1_37 ◽

1997 ◽

pp. 303-308 ◽

Cited By ~ 4

Author(s):

O. Chambres ◽

S. Barre ◽

J. P. Bonnet

Keyword(s):

Kinetic Energy ◽

Mixing Layer ◽

Variable Density ◽

Supersonic Mixing ◽

Supersonic Mixing Layer

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Compressibility effects on the structure of supersonic mixing layers: experimental results

Journal of Fluid Mechanics ◽

10.1017/s0022112094000030 ◽

1994 ◽

Vol 259 ◽

pp. 47-78 ◽

Cited By ~ 88

Author(s):

S. Barre ◽

C. Quine ◽

J. P. Dussauge

Keyword(s):

Mixing Layer ◽

Spreading Rate ◽

Turbulent Friction ◽

Radiated Noise ◽

Supersonic Mixing ◽

Diffusion Scheme ◽

Supersonic Mixing Layer ◽

Compressibility Effects ◽

Supersonic Mixing Layers ◽

Convective Mach Number

An experiment in a supersonic mixing layer at convective Mach number Mc = 0.62 was performed to study the evolution of a flow from a turbulent boundary layer to a fully developed mixing layer. Turbulence measurements were taken and are interpreted with a diffusion model, which is well adapted to these flows. These measurements show that the level of turbulent friction varies with Mc proportionally to the spread rate. Our measurements appear to be consistent with the spreading rate of the layer and suggest that compressibility does not significantly alter the diffusion scheme at Mc = 0.62. This is also confirmed by a review of the existing data. Moreover, in the present flow, the anisotropy of the turbulent stresses seems to be affected by compressibility. The evolution of the radiated noise shows an increase corresponding to the developed part of the layer. Quantitative assessments of compressibility effects on turbulent quantities are given and are related to modifications in the structure of the flow.

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