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Transition scenario in hypersonic axisymmetrical compression ramp flow

Published online by Cambridge University Press:  17 November 2020

Mathieu Lugrin Open the ORCID record for Mathieu Lugrin [Opens in a new window] ,
Samir Beneddine Open the ORCID record for Samir Beneddine [Opens in a new window] ,
Colin Leclercq ,
Eric Garnier  and
Reynald Bur
Mathieu Lugrin*
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190Meudon, France
Samir Beneddine
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190Meudon, France
Colin Leclercq
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190Meudon, France
Eric Garnier
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190Meudon, France
Reynald Bur
Affiliation:
DAAA, ONERA, Paris Saclay University, F-92190Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

A high-fidelity simulation of the shock/transitional boundary layer interaction caused by a $15^\circ$ axisymmetrical compression ramp is performed at a free stream Mach number of 5 and a transitional Reynolds number. The inlet of the computational domain is perturbed with a white noise in order to excite convective instabilities. Coherent structures are extracted using spectral proper orthogonal decomposition (SPOD), which gives a mathematically optimal decomposition of spatio-temporally correlated structures within the flow. The mean flow is used to perform a resolvent analysis in order to study non-normal linear amplification mechanisms. The comparison between the resolvent analysis and the SPOD results provides insight on both the linear and nonlinear mechanisms at play in the flow. To carry out the analysis, the flow is separated into three main regions of interest: the attached boundary layer, the mixing layer and the reattachment region. The observed transition process is dependent on the linear amplification of oblique modes in the boundary layer over a broad range of frequencies. These modes interact nonlinearly to create elongated streamwise structures which are then amplified by a linear mechanism in the rest of the domain until they break down in the reattachment region. The early nonlinear interaction is found to be essential for the transition process.

JFM classification

Instability: Transition to turbulence Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A6
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Adams, N. & Kleiser, L. 1993 Numerical simulation of fundamental breakdown of a laminar boundary-layer at Mach 4.5. In 5th International Aerospace Planes and Hypersonics Technologies Conference, p. 5027. AIAA.CrossRefGoogle Scholar
Adams, N. A. 2000 Direct simulation of the turbulent boundary layer along a compression ramp at $M = 3$ and $Re_\theta = 1685$. J. Fluid Mech. 420, 47–83.CrossRefGoogle Scholar
Amestoy, P. R., Duff, I. S., L'Excellent, J.-Y. & Koster, J. 2001 A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23 (1), 15–41.CrossRefGoogle Scholar
Arnal, D. 1989 Laminar-turbulent transition problems in supersonic and hypersonic flows. AGARD, Special Course on Aerothermodynamics of Hypersonic Vehicles 45 p (SEE N 89-29306 24-02).Google Scholar
Arnal, D. & Juillen, J.-C. 1977 Etude de l'intermittence dans une région de transition de la couche limite. La Recherche Aérospatiale 3, 147–166.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
Beneddine, S. 2017 Characterization of unsteady flow behavior by linear stability analysis. PhD thesis, ONERA.Google Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Bonne, N., Brion, V., Garnier, E., Bur, R., Molton, P., Sipp, D. & Jacquin, L. 2019 Analysis of the two-dimensional dynamics of a Mach 1.6 shock wave/transitional boundary layer interaction using a RANS based resolvent approach. J. Fluid Mech. 862, 1166–1202.CrossRefGoogle Scholar
Brandt, L., Sipp, D., Pralits, J. O. & Marquet, O. 2011 Effect of base-flow variation in noise amplifiers: the flat-plate boundary layer. J. Fluid Mech. 687, 503–528.CrossRefGoogle Scholar
Bugeat, B. 2017 Stabilité et perturbations optimales globales d’écoulements compressibles pariétaux. PhD thesis, Paris 6.Google Scholar
Bugeat, B., Chassaing, J.-C., Robinet, J.-C. & Sagaut, P. 2019 3d global optimal forcing and response of the supersonic boundary layer. J. Comput. Phys. 398, 108888.CrossRefGoogle Scholar
Bur, R. & Chanetz, B. 2009 Experimental study on the PRE-X vehicle focusing on the transitional shock-wave/boundary-layer interactions. Aerosp. Sci. Technol. 13 (7), 393–401.CrossRefGoogle Scholar
Chang, C.-L. & Malik, M. R. 1994 Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273, 323–360.CrossRefGoogle Scholar
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mechanica 1 (3), 215–234.CrossRefGoogle Scholar
Clemens, N. T. & Narayanaswamy, V. 2014 Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu. Rev. Fluid Mech. 46 (1), 469–492.CrossRefGoogle 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
Fasel, H. & Thumm, A. 1991 Direct numerical simulation of three-dimensional breakdown in supersonic boundary layer transition. Bull. Am. Phys. Soc. 36, 2701.Google Scholar
Fasel, H. F., Sivasubramanian, J. & Laible, A. 2015 Numerical investigation of transition in a flared cone boundary layer at mach 6. Proc. IUTAM 14, 26–35.CrossRefGoogle Scholar
Fasel, H. F., Thumm, A. & Bestek, H. 1993 Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown. In Fluids Engineering Conference, pp. 77–92. ASME.Google Scholar
Franko, K. J. & Lele, S. 2014 Effect of adverse pressure gradient on high speed boundary layer transition. Phys. Fluids 26 (2), 024106.CrossRefGoogle Scholar
Franko, K. J. & Lele, S. K. 2013 Breakdown mechanisms and heat transfer overshoot in hypersonic zero pressure gradient boundary layers. J. Fluid Mech. 730, 491–532.CrossRefGoogle Scholar
Gallaire, F., Marquillie, M. & Ehrenstein, U. 2007 Three-dimensional transverse instabilities in detached boundary layers. J. Fluid Mech. 571, 221–233.CrossRefGoogle Scholar
Garnier, E., Adams, N. & Sagaut, P. 2009 Large Eddy Simulation for Compressible Flows. Springer Science & Business Media.CrossRefGoogle Scholar
Garnier, E., Sagaut, P. & Deville, M. 2002 Large eddy simulation of shock/boundary-layer interaction. AIAA J. 40 (10), 1935–1944.CrossRefGoogle Scholar
George, K. J. & Sujith, R. I. 2011 On Chu's disturbance energy. J. Sound Vib. 330 (22), 5280–5291.CrossRefGoogle Scholar
Georgiadis, N. J., Rizzetta, D. P. & Fureby, C. 2010 Large-eddy simulation: current capabilities, recommended practices, and future research. AIAA J. 48 (8), 1772–1784.CrossRefGoogle Scholar
Görtler, H. 1940 Instabilität laminarer grenzschichten an konkaven wänden gegenüber gewissen dreidimensionalen störungen. Z. Angew. Math. Mech. 21 (4), 250–252.CrossRefGoogle Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.CrossRefGoogle Scholar
Hader, C. & Fasel, H. F. 2018 Towards simulating natural transition in hypersonic boundary layers via random inflow disturbances. J. Fluid Mech. 847, R3.CrossRefGoogle Scholar
Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids 8 (3), 826–837.CrossRefGoogle 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.CrossRefGoogle Scholar
Laible, A. C. & Fasel, H. F. 2016 Continuously forced transient growth in oblique breakdown for supersonic boundary layers. J. Fluid Mech. 804, 323–350.CrossRefGoogle Scholar
Laible, A., Mayer, C. & Fasel, H. 2009 Numerical investigation of transition for a cone at Mach 3.5: oblique breakdown. In 39th AIAA Fluid Dynamics Conference, p. 3557. AIAA.CrossRefGoogle Scholar
Laurence, S. J., Wagner, A. & Hannemann, K. 2016 Experimental study of second-mode instability growth and breakdown in a hypersonic boundary layer using high-speed schlieren visualization. J. Fluid Mech. 797, 471–503.CrossRefGoogle Scholar
Lehoucq, R. B., Sorensen, D. C. & Yang, C. 1998 ARPACK Users’ Guide: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, vol. 6. SIAM.CrossRefGoogle Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic.Google Scholar
Mack, L. M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13 (3), 278–289.CrossRefGoogle Scholar
Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L. 2009 Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech. 622, 1–21.CrossRefGoogle Scholar
Marxen, O., Iaccarino, G. & Shaqfeh, E. S. G. 2010 Disturbance evolution in a Mach 4.8 boundary layer with two-dimensional roughness-induced separation and shock. J. Fluid Mech. 648, 435–469.CrossRefGoogle Scholar
Marxen, O. & Rist, U. 2010 Mean flow deformation in a laminar separation bubble: separation and stability characteristics. J. Fluid Mech. 660, 37–54.CrossRefGoogle Scholar
Mary, I. & Sagaut, P. 2002 Large eddy simulation of flow around an airfoil near stall. AIAA J. 40, 1139–1145.CrossRefGoogle Scholar
Mayer, C. S. J., Von Terzi, D. A. & Fasel, H. F. 2011 Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3. J. Fluid Mech. 674, 5–42.CrossRefGoogle Scholar
Murray, N., Hillier, R. & Williams, S. 2013 Experimental investigation of axisymmetric hypersonic shock-wave/turbulent-boundary-layer interactions. J. Fluid Mech. 714, 152–189.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
Paladini, E., Beneddine, S., Dandois, J., Sipp, D. & Robinet, J.-C. 2019 Transonic buffet instability: from two-dimensional airfoils to three-dimensional swept wings. Phys. Rev. Fluids 4 (10), 103906.CrossRefGoogle Scholar
Péron, S., Renaud, T., Mary, I., Benoit, C. & Terracol, M. 2017 An immersed boundary method for preliminary design aerodynamic studies of complex configurations. In 23rd AIAA Computational Fluid Dynamics Conference, p. 3623. AIAA.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
Renard, N. & Deck, S. 2016 A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer. J. Fluid Mech. 790, 339–367.CrossRefGoogle Scholar
Robinet, J.-Ch. 2007 Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach. J. Fluid Mech. 579, 85–112.CrossRefGoogle Scholar
Sandham, N. D., Adams, N. A. & Kleiser, L. 1995 Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer. Appl. Sci. Res. 54 (3), 223–234.CrossRefGoogle Scholar
Sandham, N. D., Schülein, E., Wagner, A., Willems, S. & Steelant, J. 2014 Transitional shock-wave/boundary-layer interactions in hypersonic flow. J. Fluid Mech. 752, 349–382.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 1992 A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids A 4 (9), 1986–1989.CrossRefGoogle Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.CrossRefGoogle Scholar
Schmid, P. J., de Pando, M. F. & Peake, N. 2017 Stability analysis for $n$-periodic arrays of fluid systems. Phys. Rev. Fluids 2 (11), 113902.CrossRefGoogle Scholar
Schneider, S. P. 2008 Development of hypersonic quiet tunnels. J. Spacecr. Rockets 45 (4), 641–664.CrossRefGoogle 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
Sipp, D. & Marquet, O. 2013 Characterization of noise amplifiers with global singular modes: the case of the leading-edge flat-plate boundary layer. Theor. Comput. Fluid Dyn. 27, 617–635.CrossRefGoogle Scholar
Spalart, P. R. 2000 Strategies for turbulence modelling and simulations. Intl J. Heat Fluid Flow 21 (3), 252–263.CrossRefGoogle Scholar
Teramoto, S. 2005 Large-eddy simulation of transitional boundary layer with impinging shock wave. AIAA J. 43 (11), 2354–2363.CrossRefGoogle Scholar
Thumm, A. 1991 Numerische untersuchungen zum laminar-turbulenten strömungsumschlag in transsonischen grenzschichtströmungen. PhD thesis, University of Stuttgart.Google Scholar
Timme, S. 2018 Global instability of wing shock buffet. arXiv:1806.07299.Google Scholar
Towne, A., Schmidt, O. T. & Colonius, T. 2018 Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. J. Fluid Mech. 847, 821–867.CrossRefGoogle Scholar
Wu, M. & Martin, M. P. 2007 Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp. AIAA J. 45 (4), 879–889.CrossRefGoogle Scholar
Zhuang, Y., Tan, H.-J., Li, X., Sheng, F.-J. & Zhang, Y.-C. 2018 Görtler-like vortices in an impinging shock wave/turbulent boundary layer interaction flow. Phys. Fluids 30 (6), 061702.CrossRefGoogle Scholar