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Dynamics of a spherical body shedding from a hypersonic ramp. Part 2. Viscous flow

Published online by Cambridge University Press:  16 November 2020

C. S. Butler ,
T. J. Whalen ,
C. E. Sousa  and
S. J. Laurence Open the ORCID record for S. J. Laurence [Opens in a new window]
C. S. Butler
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD20742, USA
T. J. Whalen
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD20742, USA
C. E. Sousa
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD20742, USA
S. J. Laurence*
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD20742, USA
*
†Email address for correspondence: stuartl@umd.edu
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Abstract

The separation dynamics of a sphere released from the surface of a ramp into a hypersonic flow is investigated, focusing on the influence of the ramp boundary layer on the sphere behaviour. First, numerical simulations are conducted of a sphere interacting with an isolated high-speed boundary layer to determine the influence on the sphere force coefficients as the sphere diameter and wall-normal location are varied. It is found that the lift coefficient is strongly affected by the near-wall interactions, becoming increasingly negative as the ratio of the sphere radius to boundary-layer thickness, $r/\delta$, is decreased. These results are combined with force coefficients derived from simulations of the sphere interacting with the ramp-generated oblique shock to enable numerical predictions of the sphere trajectories for a $10^{\circ }$ ramp at Mach 6 (using a similar decoupled approach to Part 1 of this work). It is found that the three trajectory types of the inviscid situation – shock surfing, ejection followed by re-entrainment within the shock layer and direct entrainment – also characterize the sphere behaviour here. Their relative prevalence, however, is influenced by the sphere size: for smaller values of $r/\delta$, direct entrainment dominates because of the wall suction, while shock surfing and then ejection/re-entrainment become increasingly likely at larger values of $r/\delta$. Increasing the ramp angle and/or the free-stream Mach number reduces the relative influence of the boundary-layer interactions. Finally, experiments are conducted using free-flying spheres released from a ramp surface in a hypersonic shock tunnel, confirming the major trends predicted numerically.

JFM classification

Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A29
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Bailey, A. B. & Hiatt, J. 1971 Free-flight measurements of sphere drag at subsonic, transonic, supersonic, and hypersonic speeds for continuum, transition, and near-free-molecular flow conditions. AEDC-TR-70-291.Google Scholar
Borker, R., Huang, D., Grimberg, S., Farhat, C., Avery, P. & Rabinovitch, J. 2019 Mesh adaptation framework for embedded boundary methods for computational fluid dynamics and fluid-structure interaction. Intl J. Numer. Meth. Fluids 90, 389–424.CrossRefGoogle Scholar
Britan, A., Elperin, T., Igra, O. & Jiang, P. 1995 Acceleration of a sphere behind planar shock waves. Exp. Fluids 20, 84–90.CrossRefGoogle Scholar
Butler, C. & Laurence, S. J. 2019 HyperTERP: a newly commissioned hypersonic shock tunnel at the University of Maryland. AIAA Paper 2019-2860.CrossRefGoogle Scholar
Candler, G. V. 2011 Numerical simulation of hypersonic shock wave-boundary-layer interactions. In Shock Wave-Boundary-Layer Interactions (ed. H. Babinsky & J. K. Harvey), pp. 314–335. Cambridge University Press.CrossRefGoogle Scholar
Farhat, C., Gerbeau, J. & Rallu, A. 2012 Fiver: a finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps. J. Comput. Phys. 231, 6360–6379.CrossRefGoogle Scholar
Hung, F. T. & Clauss, J. M. 1981 Three-dimensional protuberance interference heating in high speed flow. Prog. Aeronaut. Astronaut. 77, 109–136.Google Scholar
Koren, B. 1993 A robust upwind discretization method for advection, diffusion and source terms. In Numerical Methods for Advection–Diffusion Problems (ed. C.B. Vreugdenhil & B. Koren), Notes on Numerical Fluid Mechanics, pp. 117–138. Vieweg.Google Scholar
Lakshmanan, B. & Tiwari, S. N. 1994 Investigation of three-dimensional separation at wing/body junctions in supersonic flows. AIAA J. 31, 64–71.Google Scholar
Laurence, S. J. 2012 On tracking the motion of rigid bodies through edge detection and least-squares fitting. Exp. Fluids 52, 387–401.CrossRefGoogle Scholar
Laurence, S. J. & Deiterding, R. 2011 Shock-wave surfing. J. Fluid Mech. 676, 396–431.CrossRefGoogle Scholar
Laurence, S. J., Deiterding, R. & Hornung, H. G. 2007 Proximal bodies in hypersonic flow. J. Fluid Mech. 590, 209–237.CrossRefGoogle Scholar
Laurence, S. J. & Karl, S. 2010 An improved visualization-based force-measurement technique for short-duration hypersonic facilities. Exp. Fluids 48, 949–965.CrossRefGoogle Scholar
Laurence, S. J., Parziale, N. & Deiterding, R. 2012 Dynamical separation of spherical bodies in supersonic flow. J. Fluid Mech. 713, 159–182.CrossRefGoogle Scholar
Ozawa, H. & Laurence, S. J. 2018 Experimental investigation of the shock-induced flow over a wall-mounted cylinder. J. Fluid Mech. 849, 1009–1042.CrossRefGoogle Scholar
Özkan, O. & Holt, M. 1984 Supersonic separated flow past a cylindrical obstacle on a flat plate. AIAA J. 22, 611–617.CrossRefGoogle Scholar
Sedney, R. & Kitchens, C. W. 1971 Survey of viscous interactions associated with high Mach number flight. AIAA J. 9, 771–784.Google Scholar
Sousa, C. E., Deiterding, R. & Laurence, S. J. 2021 Dynamics of a spherical body shedding from a hypersonic ramp. Part 1. Inviscid flow. J. Fluid Mech. 906, A28.Google Scholar
Sun, M., Saito, T., Takayama, K. & Tanno, H. 2005 Unsteady drag on a sphere by shock wave loading. Shock Waves 14, 3–9.CrossRefGoogle Scholar
Tanno, H., Itoh, K., Saito, T., Abe, A. & Takayama, K. 2003 Interaction of a shock with a sphere suspended in a vertical shock tube. Shock Waves 13, 191–200.CrossRefGoogle Scholar
Tutty, O. R., Roberts, G. T. & Schuricht, P. H. 2013 High-speed laminar flow past a fin-body junction. J. Fluid Mech. 737, 19–55.CrossRefGoogle Scholar
White, F. 1991 Viscous Fluid Flow, 2nd edn. McGraw-Hill.Google Scholar
White, J. A. & Morrison, J. H. 1999 A pseudo-temporal multi-grid relaxation scheme for solving the parabolized navier stokes equations. AIAA Paper 99-3360.CrossRefGoogle Scholar

Butler et al. supplementary movie 1

Experimental shadowgraph movie of a 3.18-mm diameter sphere: x0/r=3.9, r/δ=5.6.

Download Butler et al. supplementary movie 1(Video)
Video 3 MB

Butler et al. supplementary movie 2

Experimental shadowgraph movie of a 3.18-mm diameter sphere: x0/r=7.2, r/δ=3.9.

Download Butler et al. supplementary movie 2(Video)
Video 2.7 MB

Butler et al. supplementary movie 3

Experimental shadowgraph movie of a 3.18-mm diameter sphere: x0/r=7.9, r/δ=3.7.

Download Butler et al. supplementary movie 3(Video)
Video 2.4 MB

Butler et al. supplementary movie 4

Experimental shadowgraph movie of a 3.18-mm diameter sphere: x0/r=9.1, r/δ=3.7.

Download Butler et al. supplementary movie 4(Video)
Video 2.1 MB