Numerical investigation in chaos characteristics of macro-mixing efficiency of two-dimensional supersonic mixing layer

Abstract

Coherent structures of two-dimensional supersonic turbulent mixing layers with the engineering background have been investigated numerically with large eddy simulation method. The chaos characteristics of transverse sections of mixing layer flowfield have been obtained through the analyses of two chaos characteristic parameters, Lyapunov exponent and correlation dimension. The results show that under the conditions of the present numerical simulations and physical models, the distribution of correlation dimension is roughly consistent with that of streamwise turbulent intensity at transverse sections of mixing layers through analysis of nonlinear time series, as may be used to measure the macro-mixing efficiency of mixing layers quantitatively. The distribution of maximal Lyapunov exponent could be used to validate the quantitative results. Therefore, a potential experimental method measuring the thickness of mixing layers with low costs on the basis of chaos characteristic parameters has been proposed firstly.

Keywords

Supersonic mixing layer large eddy simulation nonlinear time-series analysis chaos

Get full access to this article

View all access options for this article.

References

Yan

Liu

. Hypersonic vehicle with dual-combustor ramjet (in Chinese). Missiles Space Veh 2008; 5: 26–30.

Liu

. Investigation of possibilities in developing dual-mode scramjets (in Chinese). Exp Meas Fluid Mech 2000; 4(1): 1–12.

Zhao

Tian

. The fractal measurement of experimental images of supersonic turbulent mixing layer. Sci China Ser G-Phys Mech Astron 2008; 51: 1134–1143.

Sun

Wang

. Flame stabilization in a supersonic combustor with hydrogen injection upstream of cavity flameholders: experiments and simulations. Proc IMechE, Part G: J Aerospace Engineering 2011; 225: 1351–1365.

Fan

Liu

Sun

. Theoretical analysis of flamelet model for supersonic turbulent combustion. Sci China Tech Sci 2012; 55(1): 193–205.

Wang GR and Fiedler HE. Some flow phenomena in a confined plane wake. In: International conference on flow interaction cum exhibition/lectures on interaction of science & art. TV Berlin, 1997, pp.12–14. Berlin: HF Institute.

Luo

Zhang

Zhou

. An approach to enhance the mixing of a compressible mixing layer. Sci China Ser A 2000; 30(11): 1033–1039.

Cao

Zhou

. Study on mixing enhancement of a two-dimensional supersonic mixing layer. Sci China Ser A 2002; 32(2): 150–157.

Luo

Shen

Zhang

. Analysis to the nonlinear instability of two-dimensional supersonic shear layer (in Chinese). Acta Aerodyn Sin 2002; 20(3): 282–288.

10.

Yan

Liu

. Non-linear time series analysis of evolution status of supersonic mixing layer (in Chinese). J Natl Univ Defense Technol 2009; 31(5): 112–119.

11.

Menon

Yeung

Kim

. Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence. Comput Fluids 1996; 25(2): 165–180.

12.

Goebel

Dutton

. Experimental study of compressible turbulent mixing layers. J AIAA 1991; 29(4): 538–546.

13.

Georgiadis

Alexander

JID

Reshotko

. Hybrid Reynolds-averaged Navier-Stokes/large-eddy simulations of supersonic turbulent mixing. J AIAA 2003; 41(2): 218–229.

14.

Wang

. Nonlinear time series analysis and its application (in Chinese), Beijing: Science Press, 2006.

15.

Wang

Sun

. Nonlinear analysis of combustion oscillations in a cavity-based supersonic combustor. Sci China Tech Sci 2013; 56(5): 1093–1101.

16.

Fraser

Swinney

. Independent coordinates for strange attractors from mutual information. Phys Rev A 1986; 33: 1134–1140.

17.

Grassberger

Procaccia

. Chracterization of strange attractors. Phys Rev Lett 1983; 50: 346–349.

18.

Rosenstein

Collins

Luca

CJD

. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 1993; 65: 117–134.