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Disturbance evolution in a Mach 4.8 boundary layer with two-dimensional roughness-induced separation and shock



A numerical investigation of the disturbance amplification in a Mach 4.8 flat-plate boundary layer with a localized two-dimensional roughness element is presented. The height of the roughness is varied and reaches up to approximately 70% of the boundary-layer thickness. Simulations are based on a time-accurate integration of the compressible Navier–Stokes equations, with a small disturbance of fixed frequency being triggered via blowing and suction upstream of the roughness element. The roughness element considerably alters the instability of the boundary layer, leading to increased amplification or damping of a modal wave depending on the frequency range. The roughness is also the source of an additional perturbation. Even though this additional mode is stable, the interaction with the unstable mode in the form of constructive and destructive interference behind the roughness element leads to a beating and therefore transiently increased disturbance amplitude. Far downstream of the roughness, the amplification rate of a flat-plate boundary layer is recovered. Overall, the two-dimensional roughness element behaves as disturbance amplifier with a limited bandwidth capable of filtering a range of frequencies and strongly amplifying only a selected range.


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Anderson, J. D. 2000 Hypersonic and High Temperature Gas Dynamics. AIAA.
Balakumar, P. 2003 Transition in a supersonic boundary-layer due to roughness and acoustic disturbances. Paper, 2003-3589. AIAA.
Balakumar, P. & Malik, M. R. 1992 Discrete modes and continuous spectra in supersonic boundary layers. J. Fluid Mech. 239, 631656.
Eissler, W. & Bestek, H. 1996 Spatial numerical simulations of linear and weakly nonlinear wave instabilities in supersonic boundary layers. Theoret. Comput. Fluid Dyn. 8 (3), 219235.
Fedorov, A. V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101129.
Fedorov, A. V. & Khokhlov, A. P. 1993 Excitation and evolution of unstable disturbances in supersonic boundary layer. In Transitional and Turbulent Compressible Flows (ed. Kral, L. D. & Zang, T. A.), vol. 151, pp. 113. ASME.
Fedorov, A. V. & Khokhlov, A. P. 2001 Prehistory of instability in a hypersonic boundary layer. Theor. Comp. Fluid Dyn. 14, 359375.
Fezer, A. & Kloker, M. 2002 DNS of transition mechanisms at Mach 6.8—flat plate vs. sharp cone. In West East High Speed Flow Fields 2002 (ed. Zeitoun, D. E., Periaux, J., Désidéri, J. A. & Marini, M.), pp. 18. CIMNE.
Herbert, T. 1997 Parabolized stability equations. Ann. Rev. Fluid Mech. 29, 245283.
Ma, Y. & Zhong, X. 2003 a Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions. J. Fluid Mech. 488, 3178.
Ma, Y. & Zhong, X. 2003 b Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound. J. Fluid Mech. 488, 79121.
Mack, L. M. 1969 Boundary layer stability theory. Tech. Rep. JPL-900-277-REV-A; NASA-CR-131501. Jet Propulsion Laboratory, NASA.
Mack, L. M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13 (3), 2782285.
Malik, M. R. 1989 Prediction and control of transition in supersonic and hypersonic boundary layers. AIAA J. 27 (11), 14871493.
Malik, M. R. 2003 Hypersonic flight transition data analysis using parabolized stability equations with chemistry effects. J. Spacecraft Rockets 40 (3), 332344.
Malik, M. R. & Anderson, E. C. 1991 Real gas effects on hypersonic boundary-layer stability. Phys. Fluids A 3 (5), 803821.
Marxen, O. & Iaccarino, G. 2008 a An immersed boundary method for numerical simulations of high-speed boundary layers with two- and three-dimensional roughness. In Annual Research Briefs 2008, pp. 89100. Center for Turbulence Research, Stanford University.
Marxen, O. & Iaccarino, G. 2008 b Numerical simulation of the effect of a roughness element on high-speed boundary-layer instability. Paper 2008-4400. AIAA.
Marxen, O., Iaccarino, G. & Shaqfeh, E. S. G. 2007 Numerical simulation of hypersonic instability using different gas models. In Annual Research Briefs 2007, pp. 1527. Center for Turbulence Research, Stanford University.
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order method for large eddy simulation. J. Comput. Phys. 191, 392419.
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471504.
Pagella, A., Babucke, A. & Rist, U. 2004 Two-dimensional numerical investigations of small-amplitude disturbances in a boundary layer at Ma = 4.8: compression corner versus impinging shock wave. Phys. Fluids 16 (7), 22722281.
Pagella, A., Rist, U. & Wagner, S. 2002 Numerical investigations of small-amplitude disturbances in a boundary layer with impinging shock wave at Ma = 4.8. Phys. Fluids 14 (7), 20882100.
Robinet, J. C. 2007 Bifurcations in shock-wave/laminar–boundary-layer interaction: global instability approach. J. Fluid Mech. 579, 85112.
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows, 1st ed. Springer.
Sipp, D. & Lebedev, A. 2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. J. Fluid Mech. 593, 333358.
Tumin, A. 2006 Receptivity of compressible boundary layers to three-dimensional wall perturbations. Paper 2006-1110. AIAA.
Tumin, A. 2007 Three-dimensional spatial normal modes in compressible boundary layers. J. Fluid Mech. 586, 295322.
Tumin, A. & Reshotko, E. 2005 Receptivity of a boundary-layer flow to a three-dimensional hump at finite Reynolds numbers. Phys. Fluids 17, 094101.
Tumin, A., Wang, X. & Zhong, X. 2007 Direct numerical simulation and the theory of receptivity in a hypersonic boundary layer. Phys. Fluids 19, 014101.
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