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Multiresolution analysis of density fluctuation in supersonic mixing layer

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Abstract

Due to the difficulties in measuring supersonic density field, the multiresolution analysis of supersonic mixing layer based on experimental images is still a formidable challenge. By utilizing the recently developed nanoparticle based planar laser scattering method, the density field of a supersonic mixing layer was measured at high spatiotemporal resolution. According to the dynamic behavior of coherent structures, the multiresolution characteristics of density fluctuation signals and density field images were studied based on Taylor’s hypothesis of space-time conversion and wavelet analysis. The wavelet coefficients reflect the characteristics of density fluctuation signals at different scales, and the detailed coefficients reflect the differences of approximation at adjacent levels. The density fluctuation signals of supersonic mixing layer differ from the periodic sine signal and exhibit similarity to the fractal Koch signal. The similarity at different scales reveals the fractal characteristic of mixing layer flowfield. The two-dimensional wavelet decomposition and reconstruction of density field images extract the approximate and detailed signals at different scales, which effectively resolve the characteristic structures of the flowfield at different scales.

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References

  1. Michalke A. On spatially growing disturbances in an inviscid shear Layer. J Fluid Mech, 1965, 23: 71–404

    Article  MathSciNet  Google Scholar 

  2. Monkewitz P A, Heurre P. Influence of the velocity ratio on the spatial instability of mixing layers. Phys Fluids, 1982, 25: 1137–1143

    Article  Google Scholar 

  3. Corcos G M, Sherman F S. Vorticity concentration and the dynamics of unstable free shear layers. J Fluid Mech, 1976, 73: 241–264

    Article  MATH  Google Scholar 

  4. Brown G, Roshko L A. On density effects and large structures in turbulent mixing layers. J Fluid Mech, 1974, 64: 775–816

    Article  Google Scholar 

  5. Rogers M M, Moser R D, The three-dimensional evolution of the plane mixing layer: the Kelvin-Helmholtz rollup. J Fluid Mech, 1992, 243: 183–226

    Article  MATH  Google Scholar 

  6. Sreenivasan K R, Meneveau C. The fractal facets of turbulence. J Fluid Mech, 1986, 173: 357–386

    Article  MathSciNet  Google Scholar 

  7. Sreenivasan K R. Fractals and multifractals in fluid turbulence. Annu Rev Fluid Mech, 1991, 23: 539–500

    Article  MathSciNet  Google Scholar 

  8. Turcotte D L. Fractals in fluid mechanics. Annu Rev Fluid Mech, 1988, 20: 5–16

    Article  Google Scholar 

  9. Lane-Serff G F. Investigation of fractal structure of jet and plumes. J Fluid Mech, 1993, 249: 521–534

    Article  Google Scholar 

  10. Frederiksen R D, Dahm W J A, Dowling D R. Experiment assessment of fractal scale-similarity in turbulent flows. Part 1: one-dimensional intersections. J Fluid Mech, 1996, 327: 35–72

    Article  Google Scholar 

  11. Frederiksen R D, Dahm W J A, Dowling D R. Experiment assessment of fractal scale-similarity in turbulent flows. Part 2: higher-dimensional intersections and non-fractal inclusions. J Fluid Mech, 1997, 338: 89–126

    Article  Google Scholar 

  12. Frederiksen R D, Dahm W J A, Dowling D R. Experiment assessment of fractal scale-similarity in turbulent flows. Part 3: multi-fractal scaling. J Fluid Mech, 1997, 338: 127–155

    Article  Google Scholar 

  13. Frederiksen R D, Dahm W J A, Dowling D R. Experiment assessment of fractal scale-similarity in turbulent flows. Part 4: effects of Reynolds and Schmidt numbers. J Fluid Mech, 1998, 377: 169–187

    Article  MATH  Google Scholar 

  14. Zhao Y X, Yi S H, He L, et al. The fractal measurement of experimental images of supersonic turbulent mixing layer. Sci China Ser E-Tech Sci, 2008, 51: 1134–1143

    Google Scholar 

  15. Saracco G, Grossmann A, Tchamitchian P. Use of Wavelet Transforms in the Study of Propagator of Transient Acoustic Signals Across a Plane Interface Between Two Homogeneous Media: Wavelets, Time-Frequency Methods and Phase Space. Heidelberg: Springer, 1989. 139–146

  16. Argoul F, Arnrodo A, Grasseau G, et al., Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade. Nature, 1989 338:51–53

    Article  Google Scholar 

  17. Farge M, Holschneider M, Colonna J F. Wavelet analysis of coherent structures in two-dimensional turbulent flows. In: Moffatt H K, ed. Topological Fluid Mechanics. Cambridge: Cambridge Univ. Press, 1990. 765–776

    Google Scholar 

  18. Mallat S. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans Am Math Soc, 1989 315:69–87

    Article  MATH  MathSciNet  Google Scholar 

  19. Yu S T. Modern CFD applications for the design of a reacting shear layer facility. AIAA-91-0577, 1991

  20. Urban W D. A PIV study of compressible shear layers. CA 94035-3032 USA. 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 12–15, 1998

  21. Urban W D. Planar velocity measurements in compressible mixing layers. AIAA 97-0697, 1997

  22. Urban W D. Velocity field of the planar shear layer—compressibility effects. AIAA 98-0697, 1998

  23. Cutler A D. Supersonic coaxial jet experiment for CFD code validation. AIAA-99-3588, 1999

  24. Bogdanoff D W. Compressibility effects in turbulent shear layers. AIAA J, 1983, 21: 926–927

    Article  Google Scholar 

  25. Papamoschou D, Roshko A. The compressible turbulent shear layer: an experimental study. J Fluids Mech, 1988, 197: 453–477

    Article  Google Scholar 

  26. Settles G S, Schlieren and Shadowgraph Techniques. Heidelberg: Springer, 2001

    MATH  Google Scholar 

  27. Brassington G B, Patterson J C, Lee M. A new algorithm for analyzing shadowgraph images. J Flow Vis Image Proc, 2002, 9: 25–51

    Google Scholar 

  28. Settles G S. Colour-coding Schlieren techniques for the optical study of heat and fluid flow. Int J Heat Fluid Flow, 1985, 6: 3–15

    Article  Google Scholar 

  29. Merzkirch W. Density-sensitive whole-field flow measurement by optical speckle photography. Exp Thermal Fluid Sci, 1995, 10: 435–443

    Article  Google Scholar 

  30. Lauterborn W, Vogel A. Modern optical techniques in fluid mechanics. Annu Rev Fluid Mech, 1984, 16: 2 23–244

    Article  Google Scholar 

  31. Gross K P, McKenzie R L, Logan P. Measurement of temperature, density, pressure, and their fluctuations in supersonic turbulence using laser-induced fluorescence. Exp Fluids, 1987, 5: 372–380

    Article  Google Scholar 

  32. Miles R B, Lempert W R. Two-dimensional measurement of density, velocity, and temperature in turbulent high-speed air flows by UV Rayleigh scattering. Appl Phys B, 1990, 51: 1–7

    Article  Google Scholar 

  33. Taylor J T. The spectrum of turbulence. Proc R Soc Lond, 1938, A164: 476–490

    Google Scholar 

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Authors and Affiliations

  1. College of Aerospace and Material Engineering, National University of Defense Technology, Changsha, 410073, China

    YuXin Zhao, ShiHe Yi, LiFeng Tian, Lin He & ZhongYu Cheng

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  1. YuXin Zhao
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  2. ShiHe Yi
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  3. LiFeng Tian
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  4. Lin He
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  5. ZhongYu Cheng
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Correspondence to YuXin Zhao.

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Zhao, Y., Yi, S., Tian, L. et al. Multiresolution analysis of density fluctuation in supersonic mixing layer. Sci. China Technol. Sci. 53, 584–591 (2010). https://doi.org/10.1007/s11431-010-0004-9

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  • DOI: https://doi.org/10.1007/s11431-010-0004-9

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