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Shock wave–boundary layer interactions in rectangular inlets: three-dimensional separation topology and critical points

Published online by Cambridge University Press:  02 September 2014

W. Ethan Eagle  and
James F. Driscoll
W. Ethan Eagle*
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA
James F. Driscoll
Affiliation:
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
†Email address for correspondence: [email protected]
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Abstract

The interaction between two separated flow regions was studied for the fundamental problem of a shock wave–boundary layer interaction (SBLI) within a rectangular inlet. One motivation is that the inlet of an engine on a supersonic aircraft may contain separation zones on the sidewalls and the bottom wall; if one region separates first it can alter the flow on the other wall and lead to engine unstart. In our work an oblique shock wave was generated by a wedge suspended from the upper wall of a Mach 2.75 wind tunnel. Stereo particle image velocimetry (PIV) measurements were recorded in 25 planes that include all three possible orthogonal orientations. The lateral velocity and vorticity measurements help to explain the underlying flow structure and these quantities were not measured previously for this problem. It is concluded that the sidewall and bottom wall separation zones interact due to an underlying flow structure that is similar to the two types of 3-D separation patterns previously described by Tobak & Peake (Annu. Rev. Fluid Mech., vol. 14, 1982, pp. 61–85). Separation first occurs at an upstream location where the shock interacts with the sidewall. Lateral velocities direct flow toward the centreline to cause separation on the bottom wall. This causes significant curvature of the shock wave, so that even the region near the tunnel centreline cannot be explained by conventional 2-D concepts. A number of critical points (saddle points, nodes, focus points) were identified. Results are consistent with the general ideas of Burton & Babinsky (J. Fluid Mech., vol. 707, 2012, pp. 287–306) and help to provide details of how the sidewalls redistribute the adverse pressure gradient in space.

JFM classification

Boundary Layers: Boundary layer separation Aerodynamics: High-speed flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 328 - 353
Copyright
© 2014 Cambridge University Press 

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References

Adamson, T. C. & Messiter, A. F. 1980 Analysis of two-dimensional interactions between shock waves and boundary layers. Annu. Rev. Fluid Mech. 12 (1), 103–138.CrossRefGoogle Scholar
Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000 Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29 (3), 275–290.CrossRefGoogle Scholar
Adrian, R. J. & Westerweel, J. 2010 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Akilli, H. & Rockwell, D. 2002 Vortex formation from a cylinder in shallow water. Phys. Fluids 14 (9), 2957–2967.CrossRefGoogle Scholar
Alvi, F. S. & Settles, G. S. 1992 Physical model of the swept shock wave/boundary-layer interaction flowfield. AIAA J. 30 (9), 2252–2258.CrossRefGoogle Scholar
Babinsky, H. & Harvey, J. K. 2011 Shock Wave–Boundary-Layer Interactions. Cambridge University Press.CrossRefGoogle Scholar
Bruce, P. J. K., Burton, D. M. F., Titchener, N. A. & Babinsky, H. 2011 Corner effect and separation in transonic channel flows. J. Fluid Mech. 679, 247–262.CrossRefGoogle Scholar
Burton, D. M. F. & Babinsky, H. 2012 Corner separation effects for normal shock wave/turbulent boundary layer interactions in rectangular channels. J. Fluid Mech. 707, 287–306.CrossRefGoogle Scholar
Burton, D. M. F., Babinsky, H. & Bruce, P. J. K.2011 Experimental investigation of the flow structure for shock wave/boundary layer interactions at an intersecting normal and spanwise plane. In 49th AIAA Aerospace Sciences Meeting, AIAA Paper 2011-0856. Orlando, Florida: American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13 (1), 457–515.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.CrossRefGoogle Scholar
Clemens, N. T. & Mungal, M. G. 1991 A planar Mie scattering technique for visualizing supersonic mixing flows. Exp. Fluids 11, 175–185.CrossRefGoogle Scholar
DeBonis, J. R., Oberkampf, W. L., Wolf, R. T., Orkwis, P. D., Turner, M. G., Babinsky, H. & Benek, J. A. 2012 Assessment of computational fluid dynamics and experimental data for shock boundary-layer interactions. AIAA J. 50 (4), 891–903.CrossRefGoogle Scholar
Délery, J. M. 2001 Robert Legendre and Henri Werlé: toward the elucidation of three-dimensional separation. Annu. Rev. Fluid Mech. 33 (1), 129–154.CrossRefGoogle Scholar
Délery, J. M. 2013 Three-dimensional Separated Flows Topology. Wiley-ISTE.CrossRefGoogle Scholar
Délery, J. M. & Dussauge, J.-P. 2009 Some physical aspects of shock wave/boundary layer interactions. Shock Waves 19 (6), 453–468.CrossRefGoogle Scholar
Doerffer, P. & Dallmann, U. 1989 Reynolds number effect on separation structures at normal shock wave/turbulent boundary-layer interaction. AIAA J. 27 (9), 1206–1212.CrossRefGoogle Scholar
Dupont, P., Haddad, C., Ardissone, J. P. & Debiéve, J.-F. 2005 Space and time organisation of a shock wave/turbulent boundary layer interaction. Aerosp. Sci. Technol. 9 (7), 561–572.CrossRefGoogle Scholar
Dupont, P., Piponniau, S., Sidorenko, A. & Debiève, J.-F. 2008 Investigation by particle image velocimetry measurements of oblique shock reflection with separation. AIAA J. 46 (6), 1365–1370.CrossRefGoogle Scholar
Eagle, W. E.2012 An experimental study of three-dimensional inlet shock-boundary layer interactions. PhD thesis, University of Michigan at Ann Arbor.Google Scholar
Eagle, W. E., Driscoll, J. F. & Benek, J. A.2012 3-D inlet shock-boundary layer interactions – PIV database for the second SBLI workshop. In 30th AIAA Applied Aerodynamics Conference, AIAA Paper 2012-3214. New Orleans, Louisiana: American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2007 Effects of upstream boundary layer on the unsteadiness of shock-induced separation. J. Fluid Mech. 585, 369–394.CrossRefGoogle Scholar
Helmer, D. B., Campo, L. M. & Eaton, J. K. 2012 Three-dimensional features of a Mach 2.1 shock/boundary layer interaction. Exp. Fluids 53 (5), 1347–1368.CrossRefGoogle Scholar
Hill, P. & Peterson, C. 1992 Mechanics and Thermodynamics of Propulsion, 2nd edn. Prentice Hall.Google Scholar
Humble, R. A., Elsinga, G. E., Scarano, F. & van Oudheusden, B. W. 2009 Three-dimensional instantaneous structure of a shock wave/turbulent boundary layer interaction. J. Fluid Mech. 622, 33–62.CrossRefGoogle Scholar
Humble, R. A., Scarano, F. & van Oudheusden, B. W. 2007 Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction. Exp. Fluids 43 (2–3), 173–183.CrossRefGoogle Scholar
Kandasamy, M., Xing, T. & Stern, F. 2009 Unsteady free surface wave-induced separation: vortical structures and instabilities. J. Fluids Struct. 25 (2), 343–363.CrossRefGoogle Scholar
Kubota, H. & Stollery, J. L. 1982 An experimental study of the interaction between a glancing shock wave and a turbulent boundary layer. J. Fluid Mech. 116, 431–458.CrossRefGoogle Scholar
Lapsa, A. P.2009 Experimental study of passive ramps for control of shock-boundary layer interactions. PhD thesis, University of Michigan at Ann Arbor.Google Scholar
Lapsa, A. P. & Dahm, W. J. A. 2011 Stereo particle image velocimetry of nonequilibrium turbulence relaxation in a supersonic boundary layer. Exp. Fluids 50 (1), 89–108.CrossRefGoogle Scholar
van Oudheusden, B. W., Nebbeling, C. & Bannink, W. J. 1996 Topological interpretation of the surface flow visualization of conical viscous/inviscid interactions. J. Fluid Mech. 316, 115–137.CrossRefGoogle Scholar
Palau-Salvador, G., Stoesser, T., Fröhlich, J., Kappler, M. & Rodi, W. 2010 Large eddy simulations and experiments of flow around finite-height cylinders. Flow Turbul. Combust. 84 (2), 239–275.CrossRefGoogle Scholar
Panaras, A. G. 1996 Review of the physics of swept-shock/boundary layer interactions. Prog. Aerosp. Sci. 32 (2–3), 173–244.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19 (1), 125–155.CrossRefGoogle Scholar
Perry, A. E. & Fairlie, B. D. 1974 Critical points in flow patterns. In Turbulent Diffusion in Environmental Pollution (ed. Frenkiel, F. N. & Munn, R. E.), vol. 18B, pp. 299–315. Academic Press.Google Scholar
Priebe, S., Wu, M. & Martín, M. P. 2009 Direct numerical simulation of a reflected-shock-wave/turbulent-boundary-layer interaction. AIAA J. 47 (5), 1173–1185.CrossRefGoogle Scholar
Samimy, M. & Lele, S. K. 1991 Motion of particles with inertia in a compressible free shear layer. Phys. Fluids A 3 (8), 1915–1923.CrossRefGoogle Scholar
Souverein, L. J., Dupont, P., Debiève, J.-F., van Oudheusden, B. W. & Scarano, F. 2010 Effect of interaction strength on unsteadiness in shock-wave-induced separations. AIAA J. 48 (7), 1480–1493.CrossRefGoogle Scholar
Squire, L. C. 1961 The motion of a thin oil sheet under the steady boundary layer on a body. J. Fluid Mech. 11 (02), 161–179.CrossRefGoogle Scholar
Surana, A., Grunberg, O. & Haller, G. 2006 Exact theory of three-dimensional flow separation. Part 1. Steady separation. J. Fluid Mech. 564, 57–103.CrossRefGoogle Scholar
Surana, A., Jacobs, G. B., Grunberg, O. & Haller, G. 2008 An exact theory of three-dimensional fixed separation in unsteady flows. Phys. Fluids 20 (10), 107101.CrossRefGoogle Scholar
Tobak, M. & Peake, D. J. 1982 Topology of three-dimensional separated flows. Annu. Rev. Fluid Mech. 14 (1), 61–85.CrossRefGoogle Scholar
Wang, K. C. 1972 Separation patterns of boundary layer over an inclined body of revolution. AIAA J. 10 (8), 1044–1050.CrossRefGoogle Scholar
Wang, K. C. 1974 Boundary layer over a blunt body at high incidence with an open-type of separation. Proc. R. Soc. A: Math. Phys. Engng Sci. 340 (1620), 33–55.Google Scholar
Wu, J. Z., Tramel, R. W., Zhu, F. L. & Yin, X. Y. 2000 A vorticity dynamics theory of three-dimensional flow separation. Phys. Fluids 12 (8), 1932–1954.CrossRefGoogle Scholar