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Dynamical separation of spherical bodies in supersonic flow

Published online by Cambridge University Press:  26 October 2012

S. J. Laurence ,
N. J. Parziale  and
R. Deiterding
S. J. Laurence*
Affiliation:
Institute of Aerodynamics and Flow Technology, Spacecraft Department, German Aerospace Center, Bunsenstraße 10, 37073 Göttingen, Germany
N. J. Parziale
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
R. Deiterding
Affiliation:
Oak Ridge National Laboratory, PO Box 2008 MS6367, Oak Ridge, TN 37831, USA
*
†Email address for correspondence: stuart.laurence@dlr.de
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Abstract

An experimental and computational investigation of the unsteady separation behaviour of two spheres in Mach-4 flow is carried out. The spherical bodies, initially contiguous, are released with negligible relative velocity and thereafter fly freely according to the aerodynamic forces experienced. In experiments performed in a supersonic Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads which are detached by the arrival of the flow. The subsequent sphere motions and unsteady flow structures are recorded using high-speed (13 kHz) focused shadowgraphy. The qualitative separation behaviour and the final lateral velocity of the smaller sphere are found to vary strongly with both the radius ratio and the initial alignment angle of the two spheres. More disparate radii and initial configurations in which the smaller sphere centre lies downstream of the larger sphere centre each increases the tendency for the smaller sphere to be entrained within the flow region bounded by the bow shock of the larger body, rather than expelled from this region. At a critical angle for a given radius ratio (or a critical radius ratio for a given angle), transition from entrainment to expulsion occurs; at this critical value, the final lateral velocity is close to maximum due to the same ‘surfing’ effect noted by Laurence & Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396–431) at hypersonic Mach numbers. A visualization-based tracking algorithm is used to provide quantitative comparisons between the experiments and high-resolution inviscid numerical simulations, with generally favourable agreement.

JFM classification

Aerodynamics: Aerodynamics Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 159 - 182
Copyright
©2012 Cambridge University Press

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Supplementary material: PDF

Laurence Supplementary Material

Supplementary Material.pdf

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PDF 192.6 KB

Laurence et al. supplementary movie

Experimental shadowgraph and numerical pseudo-Schlieren image sequence of the separation of two spheres with a radius ratio of 0.625 and an initial alignment angle of -0.7 degrees (cf. setup 5, section 3.2 and figures 9c and 11). The nondimensional times have been matched in the two sequences.

Download Laurence et al. supplementary movie(Video)
Video 5.7 MB

Laurence et al. supplementary movie

Experimental shadowgraph and numerical pseudo-Schlieren image sequence of the separation of two spheres with a radius ratio of 0.625 and an initial alignment angle of -0.7 degrees (cf. setup 5, section 3.2 and figures 9c and 11). The nondimensional times have been matched in the two sequences.

Download Laurence et al. supplementary movie(Video)
Video 2.1 MB

Laurence et al. supplementary movie

Domains of two additional levels of mesh refinement and Schlieren plots of fluid density gradient, visualised in planes through the sphere centres, depicting the dynamically evolving mesh (setup 5, section 3.2).

Download Laurence et al. supplementary movie(Video)
Video 28.8 MB

Laurence et al. supplementary movie

Domains of two additional levels of mesh refinement and Schlieren plots of fluid density gradient, visualised in planes through the sphere centres, depicting the dynamically evolving mesh (setup 5, section 3.2).

Download Laurence et al. supplementary movie(Video)
Video 9.7 MB

Laurence et al. supplementary movie

Schlieren plots of fluid density gradient, displayed in planes through the centres of two spheres with a radius ratio of 0.625, visualising the surfing of the secondary body on the bow shock generated by the primary sphere, cf. setup 5, section 3.2.

Download Laurence et al. supplementary movie(Video)
Video 25 MB

Laurence et al. supplementary movie

Schlieren plots of fluid density gradient, displayed in planes through the centres of two spheres with a radius ratio of 0.625, visualising the surfing of the secondary body on the bow shock generated by the primary sphere, cf. setup 5, section 3.2.

Download Laurence et al. supplementary movie(Video)
Video 7.1 MB