scholarly journals Absolute/convective instabilities and the convective Mach number in a compressible mixing layer

1990 ◽  
Vol 2 (6) ◽  
pp. 949-954 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Mach Number ◽  
Mixing Layer ◽  
Compressible Mixing Layer ◽  
Convective Instabilities ◽  
Convective Mach Number

Large-scale structure and entrainment in the supersonic mixing layer

1995 ◽  
Vol 284 ◽  
pp. 171-216 ◽  
Author(s):  
N. T. Clemens ◽  
M. G. Mungal
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Large Scale ◽  
Mixture Fraction ◽  
Mixing Layer ◽  
Mie Scattering ◽  
Planar Laser ◽  
The Cross ◽  
Convective Mach Number ◽  
Stream Direction

Experiments were conducted in a two-stream planar mixing layer at convective Mach numbers,Mc, of 0.28, 0.42, 0.50, 0.62 and 0.79. Planar laser Mie scattering (PLMS) from a condensed alcohol fog and planar laser-induced fluorescence (PLIF) of nitric oxide were used for flow visualization in the side, plan and end views. The PLIF signals were also used to characterize the turbulent mixture fraction fluctuations.Visualizations using PLMS indicate a transition in the turbulent structure from quasi-two-dimensionality at low convective Mach number, to more random three-dimensionality for$M_c\geqslant 0.62$. A transition is also observed in the core and braid regions of the spanwise rollers as the convective Mach number increases from 0.28 to 0.62. A change in the entrainment mechanism with increasing compressibility is also indicated by signal intensity profiles and perspective views of the PLMS and PLIF images. These show that atMc= 0.28 the instantaneous mixture fraction field typically exhibits a gradient in the streamwise direction, but is more uniform in the cross-stream direction. AtMc= 0.62 and 0.79, however, the mixture fraction field is more streamwise uniform and with a gradient in the cross-stream direction. This change in the composition of the structures is indicative of different entrainment motions at the different compressibility conditions. The statistical results are consistent with the qualitative observations and suggest that compressibility acts to reduce the magnitude of the mixture fraction fluctuations, particularly on the high-speed edge of the layer.

Numerical Simulation of the Supersonic Planar Mixing Layer

2011 ◽  
Vol 347-353 ◽  
pp. 922-926
Author(s):  
Jin Liang Gu ◽  
Huan Hao Zhang ◽  
Zhi Hua Chen ◽  
Xiao Hai Jiang
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Large Eddy Simulation ◽  
Engineering Design ◽  
Mixing Layer ◽  
Eddy Simulation ◽  
Layer Structures ◽  
Eddy Characteristics ◽  
Large Eddy ◽  
Convective Mach Number

Large eddy simulation (LES) has been used to simulate both non-reacting and reacting supersonic planar mixing layers at convective Mach number Mc=0.3. The different eddy characteristics of two cases have been visualized and discussed based on our calculated results, and the differences of mixing layer structures have also been shown, which can provide some important guide for future relative engineering design.

Inviscid spatial stability of a compressible mixing layer

1989 ◽  
Vol 208 ◽  
pp. 609-637 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Mach Number ◽  
Growth Rates ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Value ◽  
Propagation Direction ◽  
General Behaviour ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Wave Stability

We present the results of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency, and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than ½ and is supersonic with respect to the stationary stream. The other is slow with phase speeds less than ½ and supersonic with respect to the moving stream. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. Finally, we show that three-dimensional modes have the same general behaviour as the two-dimensional modes but with higher growth rates over some range of propagation direction.

Three-dimensional simulations of large eddies in the compressible mixing layer

1991 ◽  
Vol 224 ◽  
pp. 133-158 ◽  
Author(s):  
N. D. Sandham ◽  
W. C. Reynolds
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Large Scale Structure ◽  
Two Dimensional ◽  
Instability Waves ◽  
Compressible Mixing Layer ◽  
Mach Numbers ◽  
High Mach

The effect of Mach number on the evolution of instabilities in the compressible mixing layer is investigated. The full time-dependent compressible Navier–Stokes equations are solved numerically for a temporally evolving mixing layer using a mixed spectral and high-order finite difference method. The convective Mach number Mc (the ratio of the velocity difference to the sum of the free-stream sound speeds) is used as the compressibility parameter. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers (Mc > 0.6) oblique waves grow more rapidly than two-dimensional waves. Simulations are then presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves. A change in the developed large-scale structure is observed as the Mach number is increased, with vortical regions oriented in a more oblique manner at the higher Mach numbers. At convective Mach numbers above unity the two-dimensional instability is found to have little effect on the flow development, which is dominated by the oblique instability waves. The nonlinear structure which develops from a pair of equal and opposite oblique instability waves is found to resemble a pair of inclined A-vortices which are staggered in the streamwise direction. A fully nonlinear computation with a random initial condition shows the development of large-scale structure similar to the simulations with forcing. It is concluded that there are strong compressibility effects on the structure of the mixing layer and that highly three-dimensional structures develop from the primary inflexional instability of the flow at high Mach numbers.

Direct numerical simulation of a spatially developing compressible plane mixing layer: flow structures and mean flow properties

2012 ◽  
Vol 711 ◽  
pp. 437-468 ◽  
Author(s):  
Qiang Zhou ◽  
Feng He ◽  
M. Y. Shen
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Mixing Layer ◽  
The Self ◽  
Streamwise Vortices ◽  
Hairpin Vortices ◽  
Self Similar ◽  
Flower Structures ◽  
Convective Mach Number

AbstractThe spatially developing compressible plane mixing layer with a convective Mach number of 0.7 is investigated by direct numerical simulation. A pair of equal and opposite oblique instability waves is introduced to perturb the mixing layer at the inlet. The full evolution process of instability, including formation of $ \mrm{\Lambda} $-vortices and hairpin vortices, breakdown of large structures and establishment of self-similar turbulence, is presented clearly in the simulation. In the transition process, the flow fields are populated sequentially by $ \mrm{\Lambda} $-vortices, hairpin vortices and ‘flower’ structures. This is the first direct evidence showing the dominance of these structures in the spatially developing mixing layer. Hairpin vortices are found to play an important role in the breakdown of the flow. The legs of hairpin vortices first evolve into sheaths with intense vorticity then break up into small slender vortices. The later flower structures are produced by the instability of the heads of the hairpin vortices. They prevail for a long distance in the mixing layer until the flow starts to settle down into its self-similar state. The preponderance of slender inclined streamwise vortices is observed in the transversal middle zone of the transition region after the breakup of the hairpin legs. This predominance of streamwise vortices also persists in the self-similar turbulent region, though the vortices there are found to be relatively very weak. The evolution of both the mean streamwise velocity profile and the Reynolds stresses is found to have close connection to the behaviour of the large vortex structures. High growth rates of the momentum and vorticity thicknesses are observed in the transition region of the flow. The growth rates in the self-similar turbulence region decay to a value that agrees well with previous experimental and numerical studies. Shocklets occur in the simulation, and their formation mechanisms are elaborated and categorized. This is the first three-dimensional simulation that captures shocklets at this low convective Mach number.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

Sign in / Sign up

Export Citation Format

Share Document