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Dynamical separation of spherical bodies in supersonic flow

  • S. J. Laurence (a1), N. J. Parziale (a2) and R. Deiterding (a3)

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.

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Corresponding author

Email address for correspondence: stuart.laurence@dlr.de

References

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Artem’eva, N. A. & Shuvalov, V. V. 1996 Interaction of shock waves during the passage of a disrupted meteoroid through the atmosphere. Shock Waves 5, 359367.
Artemieva, N. A. & Shuvalov, V. V. 2001 Motion of a fragmented meteoroid through the planetary atmosphere. J. Geophys. Res. 106 (E2), 32973309.
Berger, M. & Colella, P. 1988 Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 6484.
Billig, F. S. 1967 Shock-wave shapes around spherical- and cylindrical-nosed bodies. J. Spacecr. Rockets 4 (6), 822823.
Borovic˘ka, J. & Kalenda, P. 2003 The Morávka meteorite fall: 4 Meteoroid dynamics and fragmentation in the atmosphere. Meteorit. Planet. Sci. 38 (7), 10231043.
Canny, J. 1986 A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 (6), 679698.
Deiterding, R. 2003 Parallel adaptive simulation of multi-dimensional detonation structures. PhD thesis, Brandenburgische Technische Universität Cottbus.
Deiterding, R. 2005a Construction and application of an AMR algorithm for distributed memory computers. In Adaptive Mesh Refinement – Theory and Applications (ed. Plewa, T., Linde, T. & Weirs, V. G.). Lecture Notes in Computational Science and Engineering, vol. 41 , pp. 361372.
Deiterding, R. 2005b Detonation structure simulation with AMROC. In High Performance Computing and Communications 2005 (ed. Dongarra, J., Yang, L. T., Rana, O. F. & Di Martino, B.). Lecture Notes in Computer Science, vol. 3726 , pp. 916927.
Deiterding, R. 2009 A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains. Comput. Struct. 87, 769783.
Deiterding, R. 2011a Block-structured adaptive mesh refinement – theory, implementation and application. ESAIM Proc. 34, 97150.
Deiterding, R. 2011b High-resolution numerical simulation and analysis of Mach reflection structures in detonation waves in low-pressure ${\mathrm{H} }_{2} : {\mathrm{O} }_{2} : \mathrm{Ar} $ mixtures: a summary of results obtained with the adaptive mesh refinement framework AMROC. J. Combust. 2011, Article ID 738969, 18 pages.
Deiterding, R., Cirak, F., Mauch, S. P. & Meiron, D. I. 2007 A virtual test facility for simulating detonation- and shock-induced deformation and fracture of thin flexible shells. Intl J. Multiscale Comput. Engng 5 (1), 4763.
Deiterding, R., Radovitzky, R., Mauch, S. P., Noels, L., Cummings, J. C. & Meiron, D. I. 2005 A virtual test facility for the efficient simulation of solid materials under high energy shock-wave loading. Engng Comput. 22 (3–4), 325347.
Fedkiw, R. P., Aslam, T., Merriman, B. & Osher, S. 1999 A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152, 457492.
Hoerner, S. F. 1965 Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance. Hoerner Fluid Dynamics.
Laurence, S. J. 2012 On the tracking of rigid bodies through edge-detection and least-squares fitting. Exp. Fluids 52 (2), 387401.
Laurence, S. J. & Deiterding, R. 2011 Shock-wave surfing. J. Fluid Mech. 676, 396431.
Laurence, S. J., Deiterding, R. & Hornung, H. G. 2007 Proximal bodies in hypersonic flow. J. Fluid Mech. 590, 209237.
Laurence, S. J. & Karl, S. 2010 An improved visualization-based force-measurement technique for short-duration hypersonic facilities. Exp. Fluids 48 (6), 949965.
Moffat, R. J. 1982 Contributions to the theory of single-sample uncertainity analysis. Trans. ASME: J. Fluids Engng 104 (2), 250260.
Mouton, C. A. & Hornung, H. G. 2008 Experiments on the mechanism of inducing transition between regular and Mach reflection. Phys. Fluids 20, 126103.
Passey, Q. R. & Melosh, H. J. 1980 Effects of atmospheric breakup on crater field formation. Icarus 42, 211233.
Settles, G. S. 2006 Schlieren and Shadowgraph Techniques. Springer.
Ziegler, J. L., Deiterding, R., Shepherd, J. E. & Pullin, D. I. 2011 An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry. J. Comput. Phys. 230 (20), 75987630.
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Supplementary materials

Laurence Supplementary Material
Supplementary Material.pdf

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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.

 Video (5.7 MB)
5.7 MB
VIDEO
Movies

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.

 Video (2.1 MB)
2.1 MB
VIDEO
Movies

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).

 Video (28.8 MB)
28.8 MB
VIDEO
Movies

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).

 Video (9.7 MB)
9.7 MB
VIDEO
Movies

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.

 Video (25.0 MB)
25.0 MB
VIDEO
Movies

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.

 Video (7.1 MB)
7.1 MB

Dynamical separation of spherical bodies in supersonic flow

  • S. J. Laurence (a1), N. J. Parziale (a2) and R. Deiterding (a3)

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