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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, MD 20742, USA
T. J. Whalen
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
C. E. Sousa
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
S. J. Laurence*
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, 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

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Type
JFM Papers
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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

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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