Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-02T19:52:31.333Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer

Published online by Cambridge University Press:  25 March 2021

Iván Padilla Montero Open the ORCID record for Iván Padilla Montero [Opens in a new window]  and
Fabio Pinna Open the ORCID record for Fabio Pinna [Opens in a new window]
Iván Padilla Montero*
Affiliation:
Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640Rhode-Saint-Genèse, Belgium
Fabio Pinna
Affiliation:
Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640Rhode-Saint-Genèse, Belgium
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The disturbances evolving in the wake induced by an isolated roughness element are investigated on a flat plate inside a cold Mach 6 flow. Different instability modes are characterized by means of two-dimensional local linear stability computations for a cuboid and a ramp-shaped roughness element. A single pair of sinuous and varicose disturbances dominates the wake instability in the vicinity of each roughness geometry. A temporal growth-rate decomposition, extended to base flows depending on two spatial inhomogeneous directions, reveals that the roughness-induced wake modes extract most of their potential energy from the transport of disturbance entropy across the base-flow temperature gradients and most of their kinetic energy from the work of the disturbance Reynolds stresses against the base-flow velocity gradients. The growth rate of such instabilities is found to be influenced by the presence of Mack-mode disturbances developing on the flat plate. Evidence is observed of a continuous synchronization between the wake instabilities and the Mack-mode perturbations which resembles the second mechanism hypothesized by De Tullio & Sandham (J. Fluid Mech., vol. 763, 2015, pp. 136–145) for the excitation of wake disturbances. The evolution of the relevant production and dissipation terms of the temporal growth-rate decomposition shows that under this continuous synchronization process, the energy signature of the wake instabilities progressively shifts towards that of Mack-mode instabilities. This leads to an enhancement of the amplification rate of the wake instabilities far downstream of the roughness element, ultimately increasing the associated N-factors for some of the investigated conditions.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A90
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bernardini, M., Pirozzoli, S., Orlandi, P. & Lele, S.K. 2014 Parameterization of boundary-layer transition induced by isolated roughness elements. AIAA J. 52, 2261–2269.Google Scholar
Bridges, T.J. & Morris, P.J. 1984 Differential eigenvalue problems in which the parameter appears nonlinearly. J. Comput. Phys. 55 (3), 437–460.Google Scholar
Candler, G.V. & Campbell, C.H. 2010 Hypersonic Navier–Stokes comparisons to orbiter flight data. AIAA Paper 2010-455.Google Scholar
Chakravarthy, S., Peroomian, O., Goldberg, U. & Palaniswamy, S. 1998 The CFD++ computational fluid dynamics software suite. AIAA Paper 1998-5564.Google Scholar
Choudhari, M.M., Li, F., Chang, C.-L., Edwards, J., Kegerise, M. & King, R.A. 2010 Laminar-turbulent transition behind discrete roughness elements in a high-speed boundary layer. AIAA Paper 2010-1575.Google Scholar
Choudhari, M.M., Li, F., Chang, C.-L., Norris, A. & Edwards, J. 2013 Wake instabilities behind discrete roughness elements in high speed boundary layers. AIAA Paper 2013-0081.CrossRefGoogle Scholar
Chu, B.T. 1965 On the energy transfer to small disturbances in fluid flow (Part I). Acta Mech. 1 (3), 215–234.CrossRefGoogle Scholar
Corke, T.C., Bar-Sever, A. & Morkovin, M.V. 1986 Experiments on transition enhancement by distributed roughness. Phys. Fluids 29 (10), 3199–3213.Google Scholar
De Tullio, N., Paredes, P., Sandham, N.D. & Theofilis, V. 2013 Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer. J. Fluid Mech. 735, 613–646.Google Scholar
De Tullio, N. & Sandham, N.D. 2012 Direct numerical simulations of roughness receptivity and transitional shock-wave/boundary-layer interactions. Tech. Rep. RTO-MP-AVT-200, 22, NATO.Google Scholar
De Tullio, N. & Sandham, N.D. 2015 Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer. J. Fluid Mech. 763, 136–145.CrossRefGoogle Scholar
Di Giovanni, A. & Stemmer, C. 2018 Cross-flow-type breakdown induced by distributed roughness in the boundary layer of a hypersonic capsule configuration. J. Fluid Mech. 856, 470–503.CrossRefGoogle Scholar
van Driest, E.R. 1956 The problem of aerodynamic heating. Aeronaut. Engng Rev. 15 (10), 26–41.Google Scholar
Esposito, A. 2016 Development and analysis of mapping and domain decomposition techniques for compressible shear flow stability calculations. Tech. Rep. VKI SR 2016-16. von Karman Institute for Fluid Dynamics.Google Scholar
Estruch-Samper, D., Hillier, R., Vanstone, L. & Ganapathisubramani, B. 2017 Effect of isolated roughness element height on high-speed laminar-turbulent transition. J. Fluid Mech. 818, 1–14.CrossRefGoogle Scholar
Freitag, M.A. & Spence, A. 2007 Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem. Electron. Trans. Numer. Anal. 28, 40–64.Google Scholar
Fujii, K. 2006 Experiment of the two-dimensional roughness effect on hypersonic boundary-layer transition. J. Spacecr. Rockets 43 (4), 731–738.CrossRefGoogle Scholar
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14 (2), 222–224.CrossRefGoogle Scholar
Groot, K.J., Serpieri, J., Pinna, F. & Kotsonis, M. 2018 Secondary crossflow instability through global analysis of measured base flows. J. Fluid Mech. 846, 605–653.CrossRefGoogle Scholar
Groskopf, G. & Kloker, M.J. 2016 Instability and transition mechanisms induced by skewed roughness elements in a high-speed laminar boundary layer. J. Fluid Mech. 805, 262–302.CrossRefGoogle Scholar
Groskopf, G., Kloker, M.J. & Marxen, O. 2010 a Bi-global crossplane stability analysis of high-speed boundary-layer flows with discrete roughness. IUTAM Bookseries, vol. 18, pp. 171–176. Springer.Google Scholar
Groskopf, G., Kloker, M.J., Stephani, K.A., Marxen, O. & Iaccarino, G. 2010 b Hypersonic flows with discrete oblique surface roughness and their stability properties. In Center of Turbulence Research, Proceedings of the Summer Program, pp. 405–422.Google Scholar
Hanifi, A., Schmid, P.J. & Henningson, D.S. 1996 Transient growth in compressible boundary laver flow. Phys. Fluids 8 (3), 826–837.CrossRefGoogle Scholar
Hermanns, M. & Hernández, J.A. 2008 Stable high-order finite-difference methods based on non-uniform grid point distributions. Intl J. Numer. Meth. Fluids 56, 233–255.CrossRefGoogle Scholar
Horvath, T., Tomek, D., Berger, K., Splinter, S., Zalameda, J., Krasa, P., Tack, S., Schwartz, R., Gibson, D. & Tietjen, A. 2010 The HYTHIRM project: flight thermography of the space shuttle during hypersonic re-entry. AIAA Paper 2010-241.CrossRefGoogle Scholar
Horvath, T.J., Zalameda, J.N., Wood, W.A., Berry, S.A., Schwartz, R.J., Dantowitz, R.F., Spisz, T.S. & Taylor, J.C. 2012 Global infrared observations of roughness induced transition on the space shuttle orbiter. Tech. Rep. RTO-MP-AVT-200, 27, NATO.Google Scholar
Iyer, P.S. & Mahesh, K. 2013 High-speed boundary-layer transition induced by a discrete roughness element. J. Fluid Mech. 729, 524–562.CrossRefGoogle Scholar
Joslin, R.D. & Grosch, C.E. 1995 Growth characteristics downstream of a shallow bump: computation and experiment. Phys. Fluids 7 (12), 3042–3047.CrossRefGoogle Scholar
Kegerise, M.A., King, R.A., Owens, L., Choudhari, M., Norris, A., Li, F. & Chang, C.-L. 2012 An experimental and numerical study of roughness-induced instabilities in a Mach 3.5 boundary layer. Tech. Rep. RTO AVT-200/RSM-030, 29, NATO.Google Scholar
Klebanoff, P.S. & Tidstrom, K.D. 1972 Mechanism by which a two-dimensional roughness element induces boundary-layer transition. Phys. Fluids 15 (7), 1173–1188.CrossRefGoogle Scholar
Lehoucq, R.B. & Sorensen, D.C. 1996 Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM J. Matrix Anal. Applics. 17 (4), 789–821.CrossRefGoogle Scholar
Malik, M.R. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86 (2), 376–413.CrossRefGoogle Scholar
Marxen, O., Iaccarino, G. & Shaqfeh, E.S. 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
Padilla Montero, I. & Pinna, F. 2020 BiGlobal stability analysis of the wake behind an isolated roughness element in hypersonic flow. Proc. Inst. Mech. Engrs G 234 (1), 5–19.CrossRefGoogle Scholar
Paredes, P., De Tullio, N., Sandham, N.D. & Theofilis, V. 2015 a Instability study of the wake behind a discrete roughness element in a hypersonic boundary-layer. In Instability and Control of Massively Separated Flows, Fluid Mechanics and Its Applications (ed. V. Theofilis & J. Soria), vol. 107, pp. 91–96. Springer.CrossRefGoogle Scholar
Paredes, P., Hanifi, A., Theofilis, V. & Henningson, D.S. 2015 b The nonlinear PSE-3D concept for transition prediction in flows with a single slowly-varying spatial direction. Procedia IUTAM 14, 36–44.CrossRefGoogle Scholar
Pinna, F. 2013 VESTA toolkit: a software to compute transition and stability of boundary layers. AIAA Paper 2013-2616.CrossRefGoogle Scholar
Reda, D.C. 2002 Review and synthesis of roughness-dominated transition correlations for reentry applications. J. Spacecr. Rockets 39 (2), 161–167.CrossRefGoogle Scholar
Redford, J.A., Sandham, N.D. & Roberts, G.T. 2010 Compressibility effects on boundary-layer transition induced by an isolated roughness element. AIAA J. 48 (12), 2818–2830.CrossRefGoogle Scholar
Reshotko, E. & Tumin, A. 2004 Role of transient growth in roughness-induced transition. AIAA J. 42 (4), 766–770.CrossRefGoogle Scholar
Ruban, A.I. & Kravtsova, M.A. 2013 Generation of steady longitudinal vortices in hypersonic boundary layer. J. Fluid Mech. 729, 702–731.CrossRefGoogle Scholar
Schneider, S.P. 2008 Effects of roughness on hypersonic boundary-layer transition. J. Spacecr. Rockets 45 (2), 193–209.CrossRefGoogle Scholar
Stemmer, C., Birrer, M. & Adams, N.A. 2017 Disturbance development in an obstacle wake in a reacting hypersonic boundary layer. J. Spacecr. Rockets 54 (4), 945–960.CrossRefGoogle Scholar
Stouffer, S.D., Baker, N.R., Capriotti, D.P. & Northam, G.B. 1993 Effects of compression and expansion ramp fuel injector configurations on scramjet combustion and heat transfer. AIAA Paper 1993-609.Google Scholar
Theiss, A., Hein, S.J., Ali, S.R.C. & Radespiel, R. 2016 Wake flow instability studies behind discrete roughness elements on a generic re-entry capsule. AIAA Paper 2016-4382.CrossRefGoogle Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39 (4), 249–315.CrossRefGoogle Scholar
Tirtey, S.C. 2009 Characterization of a transitional hypersonic boundary layer in wind tunnel and flight conditions. PhD thesis, Université Libre de Bruxelles and von Karman Institute for Fluid Dynamics.Google Scholar
Trefethen, L.N. 2000 Spectral Methods in MATLAB. SIAM.CrossRefGoogle Scholar
Tumin, A. & Reshotko, E. 2005 Receptivity of a boundary-layer flow to a three-dimensional hump at finite Reynolds numbers. Phys. Fluids 17 (9), 1–8.CrossRefGoogle Scholar
Van Den Eynde, J.P. & Sandham, N.D. 2016 Numerical simulations of transition due to isolated roughness elements at Mach 6. AIAA J. 54 (1), 53–65.CrossRefGoogle Scholar
Weder, M. 2012 Linear stability and acoustics of a subsonic plane jet flow. Master's thesis, Institute of Fluid Dynamics, ETH Zurich.Google Scholar
Weder, M., Gloor, M. & Kleiser, L. 2015 Decomposition of the temporal growth rate in linear instability of compressible gas flows. J. Fluid Mech. 778, 120–132.CrossRefGoogle Scholar