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The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow

Published online by Cambridge University Press:  28 June 2019

Guoliang Xu Open the ORCID record for Guoliang Xu [Opens in a new window] ,
Jianqiang Chen ,
Gang Liu ,
Siwei Dong  and
Song Fu Open the ORCID record for Song Fu [Opens in a new window]
Guoliang Xu
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Jianqiang Chen
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Gang Liu
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Siwei Dong
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Song Fu*
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: [email protected]
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Abstract

The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow are studied using Floquet theory. High-frequency secondary instability modes of ‘y’ mode on top of stationary cross-flow vortices, and ‘z’ mode concentrating on the shoulder of the stationary cross-flow vortex are found. The most unstable secondary instability mode is always the ‘z’ mode as in incompressible swept wing flows. A new secondary instability mode concentrating on the trough of the stationary cross-flow vortex is found. The balance analysis of disturbance kinetic energy shows that the new mode belongs to the class of ‘y’ mode. The growth rate of the new ‘y’ mode located on the trough of the stationary cross-flow vortex is significantly larger than that of the ‘y’ mode on top of the stationary cross-flow vortex, and is comparable with the growth rate of the ‘z’ mode. It is also found that the new ‘y’ mode with higher frequency can evolve into the ‘z’ mode further downstream. The role of the pressure fluctuation term, including the pressure diffusion and pressure dilatation, in the energy production of secondary instability modes, is also investigated. It is shown that the pressure diffusion will only enhance the growth rate of the ‘z’ mode with higher frequency, but has little influence on other types of secondary instability mode. However, the pressure dilatation term arising from non-vanishing velocity divergence will reduce the growth rates of all secondary instability modes.

JFM classification

Boundary Layers: Boundary layer stability Aerodynamics: High-speed flow Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 914 - 941
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Copyright
© 2019 Cambridge University Press 

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References

Balakumar, P. & King, R. A.2011 Receptivity to roughness, acoustic and vortical disturbances in supersonic boundary layers over swept wings. AIAA Paper 2011-1314.Google Scholar
Balakumar, P. & Owens, L. R.2010 Stability of hypersonic boundary layer on a cone at an angle of attack. AIAA Paper 2010-4718.Google Scholar
Bertolotti, F. P., Herbert, T. & Spalart, P. R. 1992 Linear and nonlinear stability of the blasius boundary layer. J. Fluid Mech. 242, 441–474.10.1017/S0022112092002453Google Scholar
Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aero. Sci. 35, 363–412.Google Scholar
Borg, M. P., Kimmel, R. L. & Stanfield, S. 2015 Travelling crossflow instability for the HiFiRE-5 elliptic cone. J. Spacecr. Rocket. 52 (3), 664–674.10.2514/1.A33145Google Scholar
Chang, C.-L., Malik, M. R., Erlebacher, G. & Hussaini, M. Y.1991 Compressible stability of growing boundary layers using parabolized stability equations. AIAA Paper 91-1636.10.2514/6.1991-1636Google Scholar
Choudhari, M. M., Li, F., Duan, L., Chang, C.-L., Carpenter, M. H., Streett, C. L. & Malik, M. R.2013 Towards bridging the gaps in holistic transition prediction via numerical simulations. AIAA Paper 2013-2718.10.2514/6.2013-2718Google Scholar
Choudhari, M. M., Li, F., Paredes, P. & Duan, L.2017 Computations of crossflow instability in hypersonic boundary layers. AIAA Paper 2017-4300.Google Scholar
Craig, A. S. & Saric, W. S.2015 Experimental study of crossflow instability on a Mach 6 yawed cone. AIAA Paper 2015-2774.Google Scholar
Craig, A. S. & Saric, W. S. 2016 Crossflow instability in a hypersonic boundary layer. J. Fluid Mech. 808, 224–244.Google Scholar
Dinzl, D. J. & Candler, G. V. 2017 Direct simulation of hypersonic crossflow instability on an elliptic cone. AIAA J. 55 (6), 1769–1782.10.2514/1.J055130Google Scholar
Duan, L., Beekman, I. & Martin, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.Google Scholar
Gray, W. E. 1952 The nature of the boundary layer flow at the rose of a swept wing. In Royal Aircraft Estabilishment, Rae Tm Aero 256. UK: Farnborough, England.Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 254–283.10.1146/annurev.fluid.29.1.245Google Scholar
King, R. A. 1992 Three-dimensional boundary-layer transition on a cone at Mach 3.5. Exp. Fluids 13 (5), 305–314.10.1007/BF00209502Google Scholar
Koch, W., Bertolotti, F. P., Stolte, A. & Hein, S. 2000 Nonlinear equilibrium solutions in a three-dimensional boundary layer and their secondary instability. J. Fluid Mech. 406, 131–174.Google Scholar
Kohama, Y., Onodera, T. & Egami, Y. 1996 Design and control of crossflow instability field. In Proceedings IUTAM Symposium On Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, Manchester, UK, pp. 147–156.Google Scholar
Kohama, Y., Saric, W. S. & Hoos, J. A. 1991 A high frequency secondary instability of crossflow vortices that leads to transition. In Proceedings of the Royal Aeronautical Society Conference on Boundary-Layer Transition and Control, Cambridge. UK.Google Scholar
Li, F. & Choudhari, M. M. 2011 Spatially developing secondary instabilities in compressible swept airfoil boundary layers. Theor. Comput. Fluid Dyn. 25, 65–85.10.1007/s00162-010-0190-xGoogle Scholar
Li, F., Choudhari, M. M., Paredes, P. & Duan, L. 2016 High-frequency instabilities of stationary crossflow vortices in a hypersonic boundary layer. Phys. Rev. Fluids 1, 053603.Google Scholar
Mack, C. J. & Schmid, P. J. 2011 Global stability of swept flow around a parabolic body: the neutral curve. J. Fluid Mech. 678, 589–603.Google Scholar
Malik, M. R. & Balakumar, P.1992 Instability and transition in three-dimensional supersonic boundary layers. AIAA Paper 1992-5049.10.2514/6.1992-5049Google Scholar
Malik, M. R., Li, F. & Chang, C.-L. 1994 Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability. J. Fluid Mech. 268, 1–36.Google Scholar
Malik, M. R., Li, F., Choudhari, M. M. & Chang, C.-L. 1999 Secondary instability of crossflow vortices and swept-wing boundary layer transition. J. Fluid Mech. 399, 85–115.Google Scholar
Moyes, A. J., Paredes, P., Kocian, T. S. & Reed, H. L.2016 Secondary instability analysis of crossflow on a hypersonic yawed straight circular cone. AIAA Paper 2016-0848.Google Scholar
Moyes, A. J., Paredes, P., Kocian, T. S. & Reed, H. L. 2017 Secondary instability analysis of crossflow on a hypersonic yawed straight circular cone. J. Fluid Mech. 812, 370–397.Google Scholar
Owens, L. R., Beeler, G. B., Balakumar, P. & McGuire, P. J.2014 Flow disturbance and surface roughness effects on crossflow boundary-layer transition in supersonic flows. AIAA Paper 2014-2638.Google Scholar
Poll, D. I. A. 1985 Some observations of the transition process on the windward face of a long yawed cylinders. J. Fluid Mech. 150, 329–356.Google Scholar
Pruett, C. D. & Streett, C. L. 1991 A spectral collocation method for compressible, non-similar boundary layers. Intl J. Numer. Meth. Fluids 13 (6), 713–737.Google Scholar
Ren, J. & Fu, S. 2015 Secondary instabilities of Görtler vortices in high-speed boundary layer flow. J. Fluid Mech. 781, 388–421.10.1017/jfm.2015.490Google Scholar
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.10.1146/annurev.fluid.35.101101.161045Google Scholar
Schuele, C. Y., Corke, T. C. & Matlis, E. 2013 Control of stationary crossflow modes in a Mach 3.5 boundary layer using patterned passive and active roughness. J. Fluid Mech. 718, 5–38.Google Scholar
Stetson, K. F., Thompson, E. R., Donaldson, J. C. & Siler, L. G.1984 Laminar boundary layer stability experiments on a cone at Mach 8, part 2: Blunt cone. AIAA Paper 84-0006.Google Scholar
Vreman, A. W., Sandham, N. D. & Luo, K. H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258.10.1017/S0022112096007525Google Scholar
Ward, C. A. C., Henderson, R. O. & Schneider, S. P.2015 Possible secondary instability of stationary crossflow vortices on an inclined cone at Mach 6. AIAA Paper 2015-2773.Google Scholar
Wassermann, P. & Kloker, M. 2002 Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer. J. Fluid Mech. 456, 49–84.10.1017/S0022112001007418Google Scholar
White, E. B. & Saric, W. S. 2005 Secondary instability of crossflow vortices. J. Fluid Mech. 525, 275–308.Google Scholar
Xu, G. L., Jiang, X. & Liu, G. 2016 Delayed detached eddy simulations of fighter aircraft at high angle of attack. Acta Mechanica Sin. 32 (4), 588–603.10.1007/s10409-016-0565-3Google Scholar
Xu, G. L., Liu, G., Chen, J. Q. & Fu, S. 2018a Role of freestream slow acoustic waves in a hypersonic three-dimensional boundary layer flow. AIAA J. 56 (9), 3570–3584.Google Scholar
Xu, G. L., Liu, G., Jiang, X. & Qian, W. Q. 2018b Effect of pitch down motion on the vortex reformation over fighter aircraft. Aerosp. Sci. Technol. 73, 278–288.Google Scholar
Xu, G. L., Xiao, Z. X. & Fu, S. 2011 Analysis of the secondary instability of the incompressible flows over a swept wing. Sci. China G 54 (4), 724–736.Google Scholar