Laurence, Stuart J | Engineering Papers

DOE OSTI2012

Dynamical separation of spherical bodies in supersonic flow

An experimental and computational investigation of the unsteady separation behaviour of two spheres in a highly supersonic flow is carried out. The spherical bodies, initially touching, are released with negligible relative velocity, an arrangement representing the idealized binary fragmentation of a meteoritic body in the atmosphere. In experiments performed in a Mach-4 Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads and, following detachment of the threads by the arrival of the flow, fly freely according to the aerodynamic forces experienced. The resulting sphere motions and unsteady flow structures are recorded using high-speed 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 that of the larger sphere both increase 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 surfing effect noted by Laurence & Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396-431) at hypersonic Mach numbers. A high-precision tracking algorithm is used to provide quantitative comparisons between experiments and high-resolution inviscid numerical simulations, with generally favourable agreement.

Laurence, Stuart J↗

DOE OSTI2011

Shock-wave surfing

A phenomenon referred to as shock-wave surfing , in which a body moves in such a way as to follow the shock wave generated by another upstream body, is investigated numerically and theoretically. This process can lead to the downstream body accumulating a significantly higher lateral velocity than would otherwise be possible, and thus is of importance in situations such as meteoroid fragmentation, in which the fragment separation behaviour following disruption is determined to a large extent by aerodynamic effects. The surfing effect is first investigated in the context of interactions between a sphere and a planar oblique shock. Numerical simulations are performed and a simple theoretical model is developed to determine the forces acting on the sphere. A phase-plane description is employed to elucidate features of the system dynamics. The theoretical model is then generalised to the more complex situation of aerodynamic interactions between two spheres, and, through comparisons with further computations, is shown to adequately predict, in particular, the final separation velocity of the surfing sphere in initially touching configurations. Both numerical simulations and theory indicate a strong influence of the body radius ratio on the separation process and predict a critical radius ratio for initially touching fragments that delineates entrainment of the smaller fragment within the larger fragment s shock from expulsion; this critical ratio also results in the most extended surfing. Further, these results show that an earlier prediction for the separation velocity to scale with the square root of the radius ratio does not accurately describe the separation behaviour. The theoretical model is then employed to investigate initial configurations with varying relative sphere positions and initial velocities. A phase-space description is also shown to be useful in elucidating the dynamics of the sphere-sphere system. With regard to meteoroid fragmentation, it is shown that a large fraction of the variation in the separation behaviour deduced by previous authors from an analysis of terrestrial crater fields can be explained by a combination of surfing and a modest rotation rate of the parent body. Finally, a selection effect for multiple fragments travelling together, e.g., immediately following atmospheric disruption, is predicted, whereby larger fragments repel one another whereas smaller fragments are entrained within the shocks of larger bodies.

59 BASIC BIOLOGICAL SCIENCES↗