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Fractal characteristics of turbulent–non-turbulent interface in supersonic turbulent boundary layers

Published online by Cambridge University Press:  26 March 2018

Yi Zhuang ,
Huijun Tan Open the ORCID record for Huijun Tan [Opens in a new window] ,
Hexia Huang ,
Yazhou Liu  and
Yue Zhang
Yi Zhuang
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China MIIT(Ministry of Industry and Information Technology) Key Laboratory of Aero-Engine Thermal Environment and Structure, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Huijun Tan*
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China MIIT(Ministry of Industry and Information Technology) Key Laboratory of Aero-Engine Thermal Environment and Structure, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Hexia Huang
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China MIIT(Ministry of Industry and Information Technology) Key Laboratory of Aero-Engine Thermal Environment and Structure, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Yazhou Liu
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China MIIT(Ministry of Industry and Information Technology) Key Laboratory of Aero-Engine Thermal Environment and Structure, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Yue Zhang
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China MIIT(Ministry of Industry and Information Technology) Key Laboratory of Aero-Engine Thermal Environment and Structure, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
†Email address for correspondence: [email protected]
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Abstract

The turbulent–non-turbulent interface (TNTI) of supersonic turbulent boundary layers is a fundamental but relatively unexplored physics problem. In this study, we present experimental results from fractal analysis on the TNTI of supersonic turbulent boundary layers, and test the applicability of the additive law for these flows. By applying the nanoparticle-tracer planar laser scattering (NPLS) technique in a supersonic wind tunnel, we obtain data covering nearly three decades in scale. The box-counting results indicate that the TNTI of supersonic turbulent boundary layers is a self-similar fractal with a fractal dimension of 2.31. By comparing data sets acquired from two orthogonal planes, we find that the scaling exponent does not depend on direction, consistent with the validity of the additive law for the TNTI of turbulent boundary layers in a scale range with the large-scale limit not exceeding approximately $0.05\unicode[STIX]{x1D6FF}$.

JFM classification

Boundary Layers: Boundary Layers Nonlinear Dynamical Systems: Fractals Aerodynamics: High-speed flow
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 843 , 25 May 2018 , R2
Copyright
© 2018 Cambridge University Press 

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References

Bo, W., Liu, W. D., Zhao, Y. X., Fan, X. Q. & Chao, W. 2012 Experimental investigation of the micro-ramp based shock wave and turbulent boundary layer interaction control. Phys. Fluids 24 (5), 1166–1175.Google Scholar
Borrell, G. & Jiménez, J. 2016 Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 801 (1), 554–596.Google Scholar
Catrakis, H. J. 2000 Distribution of scales in turbulence. Phys. Rev. E 62 (1 Pt A), 564–577.Google Scholar
Constantin, P., Procaccia, I. & Sreenivasan, K. R. 1991 Fractal geometry of isoscalar surfaces in turbulence: theory and experiments. Phys. Rev. Lett. 67 (13), 1739–1742.Google Scholar
Corrsin, S. & Kistler, A. L.1955 The free-stream boundaries of turbulent flows. Naca Tech. Rep. TN-1244.Google Scholar
Gang, D. D., Yi, S. H., Wu, Y. & Zhu, Y. Z. 2014 Supersonic flow over circular protuberances on a flat plate. J. Vis. 17 (4), 307–317.Google Scholar
Gouldin, F. C. 1987 An application of fractals to modeling premixed turbulent flames. Combust. Flame 68 (3), 249–266.Google Scholar
Liebovitch, L. S. & Toth, T. 1989 A fast algorithm to determine fractal dimensions by box counting. Phys. Lett. A 141 (8–9), 386–390.Google Scholar
Lovejoy, S. 1982 Area-perimeter relation for rain and cloud areas. Science 216 (4542), 185–187.Google Scholar
Mandelbrot, B. B. & Pignoni, R. 1983 The Fractal Geometry of Nature, vol. 173. WH Freeman.Google Scholar
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 2065–2072.Google Scholar
Meneveau, C. & Sreenivasan, K. R. 1990 Interface dimension in intermittent turbulence. Phys. Rev. A 41 (4), 2246–2248.Google Scholar
North, G. L. & Santavicca, D. A. 1990 The fractal nature of premixed turbulent flames. Combust. Sci. Technol. 72 (4–6), 215–232.Google Scholar
Prasad, R. R. & Sreenivasan, K. R. 1989 Scalar interfaces in digital images of turbulent flows. Exp. Fluids 7 (4), 259–264.Google Scholar
Prasad, R. R. & Sreenivasan, K. R. 1990 The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows. Phys. Fluids A 2 (5), 792–807.Google Scholar
Praskovsky, A. A., Dabberdt, W. F., Praskovskaya, E. A., Hoydysh, W. G. & Holynskyj, O. 1996 Fractal geometry of isoconcentration surfaces in a smoke plume. J. Atmos. Sci. 53 (1), 5–21.Google Scholar
Rys, F. S. & Waldvogel, A. 1986 Fractal shape of hail clouds. Phys. Rev. Lett. 56 (7), 784–787.Google Scholar
Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. 2012 Nih image to imagej: 25 years of image analysis. Nat. Methods 9 (7), 671–675.Google Scholar
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46 (1), 567–590.Google Scholar
da Silva, C. B. & dos Reis, R. J. N. 2011 The role of coherent vortices near the turbulent/non-turbulent interface in a planar jet. Phil. Trans. R. Soc. Lond. A 369 (1937), 738–753.Google Scholar
da Silva, C. B. & Taveira, R. R. 2010 The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys. Fluids 22 (12), 121702.Google Scholar
de Silva, C. M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent–nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111 (4), 044501.Google Scholar
Sreenivasan, K. R. 1991 Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23 (1), 539–604.Google Scholar
Sreenivasan, K. R. & Meneveau, C. 1986 The fractal facets of turbulence. J. Fluid Mech. 173, 357–386.Google Scholar
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 421, pp. 79–108. The Royal Society.Google Scholar
Tao, Y., Fan, X. Q. & Zhao, Y. L. 2014 Viscous effects of shock reflection hysteresis in steady supersonic flows. J. Fluid Mech. 759, 134–148.Google Scholar
Wang, D. P., Xia, Z. X., Zhao, Y. X. & Wang, Q. H. 2013a Vortical structures of supersonic flow over a delta-wing on a flat plate. Appl. Phys. Lett. 102 (6), 061911.Google Scholar
Wang, Q. C. & Wang, Z. G. 2016 Structural characteristics of the supersonic turbulent boundary layer subjected to concave curvature. Appl. Phys. Lett. 108 (11), 114102.Google Scholar
Wang, Q. C., Wang, Z. G., Lei, J. & Feng, J. H. 2013b Characteristics of mixing enhanced by streamwise vortices in supersonic flow. Appl. Phys. Lett. 103 (14), 453–477.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2005 Mechanics of the turbulent–nonturbulent interface of a jet. Phys. Rev. Lett. 95 (17), 174501.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631 (631), 199–230.Google Scholar
Zhao, Y. X., Yi, S. H., Tian, L. F. & Cheng, Z. Y. 2009 Supersonic flow imaging via nanoparticles. Sci. China Technol. Sci. 52 (12), 3640–3648.Google Scholar
Zhuang, Y., Tan, H. J., Liu, Y. Z., Zhang, Y. C. & Ling, Y. 2017 High resolution visualization of Görtler-like vortices in supersonic compression ramp flow. J. Vis. 20 (3), 505–508.Google Scholar