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Unsteady effects in a hypersonic compression ramp flow with laminar separation

Published online by Cambridge University Press:  04 February 2021

Shibin Cao Open the ORCID record for Shibin Cao [Opens in a new window] ,
Jiaao Hao Open the ORCID record for Jiaao Hao [Opens in a new window] ,
Igor Klioutchnikov ,
Herbert Olivier  and
Chih-Yung Wen Open the ORCID record for Chih-Yung Wen [Opens in a new window]
Shibin Cao*
Affiliation:
Shock Wave Laboratory, RWTH Aachen University, 52056Aachen, Germany
Jiaao Hao
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Igor Klioutchnikov
Affiliation:
Shock Wave Laboratory, RWTH Aachen University, 52056Aachen, Germany
Herbert Olivier
Affiliation:
Shock Wave Laboratory, RWTH Aachen University, 52056Aachen, Germany
Chih-Yung Wen
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Interdisciplinary Division of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations (DNS) are performed to investigate a hypersonic flow over a compression ramp with a free stream Mach number of 7.7 and a free stream Reynolds number of $4.2\times 10^{5}$ based on the flat plate length. The DNS results are validated by comparison with experimental data and theoretical predictions. It is shown that even in the absence of external disturbances, streamwise heat flux streaks form on the ramp surface downstream of reattachment, and that they are non-uniformly distributed in the spanwise direction. The surface heat flux exhibits a low-frequency unsteadiness, which propagates in the streamwise direction. Additionally, the unsteadiness of the heat flux streaks downstream of reattachment is coupled with a pulsation of the reattachment position. By conducting a dynamic mode decomposition (DMD) analysis, several oscillatory modes, characterised by streamwise low-frequency periodicity, are revealed in the separation bubble flow. The DNS results are further explained by a global stability analysis (GSA). Particularly, the flow structure of the leading DMD modes is consistent with that of the oscillatory unstable modes identified by the GSA. It is therefore concluded that the global instabilities are responsible for the unsteadiness of the considered compression ramp flow.

JFM classification

Boundary Layers: Boundary layer separation Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A3
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Anderson, J.D. Jr. 2006 Hypersonic and High-Temperature Gas Dynamics. American Institute of Aeronautics and Astronautics.Google Scholar
Benay, R., Chanetz, B., Mangin, B., Vandomme, L. & Perraud, J. 2006 Shock wave/transitional boundary-layer interactions in hypersonic flow. AIAA J. 44 (6), 1243–1254.CrossRefGoogle Scholar
Cao, S., Klioutchnikov, I. & Olivier, H. 2019 a Görtler vortices in hypersonic flow on compression ramps. AIAA J. 57 (9), 3874–3884.Google Scholar
Cao, S., Klioutchnikov, I. & Olivier, H. 2019 b Influence of the separation bubble flow at a compression ramp on Görtler-type vortices. In Proceedings of the 32nd International Symposium on Shock Waves, pp. 899–909. Research Publishing.Google Scholar
Cao, S., Klioutchnikov, I. & Olivier, H. 2020 Görtler number evaluation for laminar separated hypersonic compression ramp flow. AIAA J. 58 (8), 3706–3710.Google Scholar
Chuvakhov, P.V., Borovoy, V.Y., Egorov, I.V., Radchenko, V.N., Olivier, H. & Roghelia, A. 2017 Effect of small bluntness on formation of Görtler vortices in a supersonic compression corner flow. J. Appl. Mech. Tech. Phys. 58 (6), 975–989.CrossRefGoogle Scholar
Clemens, N.T. & Narayanaswamy, V. 2014 Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu. Rev. Fluid Mech. 46, 469–492.Google Scholar
Dwivedi, A., Sidharth, G.S., Nichols, J.W., Candler, G.V. & Jovanović, M.R. 2019 Reattachment streaks in hypersonic compression ramp flow: an input–output analysis. J. Fluid Mech. 880, 113–135.CrossRefGoogle Scholar
Gageik, M., Klioutchnikov, I. & Olivier, H. 2015 Comprehensive mesh study for a direct numerical simulation of the transonic flow at ${R}e_c= 500\ 000$ around a NACA 0012 airfoil. Comput. Fluids 122, 153–164.CrossRefGoogle Scholar
Ginoux, J.J. 1971 Streamwise vortices in reattaching high-speed flows – a suggested approach. AIAA J. 9 (4), 759–760.CrossRefGoogle Scholar
Hendrickson, T.R., Kartha, A. & Candler, G.V. 2018 An improved Ducros sensor for the simulation of compressible flows with shocks. AIAA Paper 2018-3710.CrossRefGoogle Scholar
Hermes, V., Klioutchnikov, I. & Olivier, H. 2012 Linear stability of WENO schemes coupled with explicit Runge–Kutta schemes. Intl J. Numer. Meth. Fluids 69 (6), 1065–1095.Google Scholar
Hildebrand, N., Dwivedi, A., Nichols, J.W., Jovanović, M.R. & Candler, G.V. 2018 Simulation and stability analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92. Phys. Rev. Fluids 3 (1), 013906.Google Scholar
Inger, G.R. 1977 Three-dimensional heat-and mass-transfer effects across high-speed reattaching flows. AIAA J. 15 (3), 383–389.CrossRefGoogle Scholar
Jiang, G. & Shu, C. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202–228.Google Scholar
Jovanović, M.R., Schmid, P.J. & Nichols, J.W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 024103.CrossRefGoogle Scholar
Kavun, I.N., Lipatov, I.I. & Zapryagaev, V.I. 2019 Flow effects in the reattachment region of supersonic laminar separated flow. Intl J. Heat Mass Transfer 129, 997–1009.Google Scholar
Klioutchnikov, I., Cao, S. & Olivier, H. 2017 DNS of hypersonic ramp flow on a supercomputer. In International Symposium on Shock Waves, pp. 897–903. Springer.Google Scholar
Li, X.S., Demmel, J.W., Gilbert, J.R., Grigori, L., Shao, M. & Yamazaki, I. 1999 SuperLU Users’ Guide. Lawrence Berkeley National Laboratory.Google Scholar
de Luca, L., Cardone, G., de la Chevalerie, D.A. & Fonteneau, A. 1995 Viscous interaction phenomena in hypersonic wedge flow. AIAA J. 33 (12), 2293–2298.CrossRefGoogle Scholar
MacCormack, R.W. 2014 Numerical Computation of Compressible and Viscous Flow. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Mani, A. 2012 Analysis and optimization of numerical sponge layers as a nonreflective boundary treatment. J. Comput. Phys. 231 (2), 704–716.CrossRefGoogle Scholar
Matsumura, S., Schneider, S.P. & Berry, S.A. 2005 Streamwise vortex instability and transition on the Hyper-2000 scramjet forebody. J. Spacecr. Rockets 42 (1), 78–89.CrossRefGoogle Scholar
Navarro-Martinez, S. & Tutty, O.R. 2005 Numerical simulation of Görtler vortices in hypersonic compression ramps. Comput. Fluids 34 (2), 225–247.CrossRefGoogle Scholar
Ohmichi, Y. & Suzuki, K. 2013 Three-dimensional numerical simulation of Görtler vortices in hypersonic compression ramp. AIAA Paper 2013-262.CrossRefGoogle Scholar
Pasquariello, V., Hickel, S. & Adams, N.A. 2017 Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number. J. Fluid Mech. 823, 617–657.CrossRefGoogle Scholar
Priebe, S. & Martín, M.P. 2012 Low-frequency unsteadiness in shock wave–turbulent boundary layer interaction. J. Fluid Mech. 699, 1–49.CrossRefGoogle Scholar
Robinet, J. 2007 Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach. J. Fluid Mech. 579, 85–112.CrossRefGoogle Scholar
Roghelia, A., Chuvakhov, P.V., Olivier, H. & Egorov, I. 2017 a Experimental investigation of Görtler vortices in hypersonic ramp flows behind sharp and blunt leading edges. AIAA Paper 2017-3463.CrossRefGoogle Scholar
Roghelia, A., Olivier, H., Egorov, I. & Chuvakhov, P. 2017 b Experimental investigation of Görtler vortices in hypersonic ramp flows. Exp. Fluids 58 (10), 139.CrossRefGoogle Scholar
Schmid, P.J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Sidharth, G.S., Dwivedi, A., Candler, G.V. & Nichols, J.W. 2017 Global linear stability analysis of high speed flows on compression ramps. AIAA Paper 2017-3455.Google Scholar
Sidharth, G.S., Dwivedi, A., Candler, G.V. & Nichols, J.W. 2018 Onset of three-dimensionality in supersonic flow over a slender double wedge. Phys. Rev. Fluids 3 (9), 093901.Google Scholar
Simeonides, G. & Haase, W. 1995 Experimental and computational investigations of hypersonic flow about compression ramps. J. Fluid Mech. 283, 17–42.CrossRefGoogle Scholar
Sorensen, D., Lehoucq, R., Yang, C. & Maschhoff, K. 1996–2008 ARPACK software.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
Theofilis, V., Hein, S. & Dallmann, U. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358 (1777), 3229–3246.CrossRefGoogle Scholar
Welch, P. 1967 The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.CrossRefGoogle Scholar
Yang, L., Zare-Behtash, H., Erdem, E. & Kontis, K. 2012 Investigation of the double ramp in hypersonic flow using luminescent measurement systems. Exp. Therm. Fluid Sci. 40, 50–56.CrossRefGoogle Scholar
Zapryagaev, V.I., Kavun, I.N. & Lipatov, I.I. 2013 Supersonic laminar separated flow structure at a ramp for a free-stream Mach number of 6. Prog. Flight Phys. 5, 349–362.CrossRefGoogle Scholar

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