Shock Waves (2011) 21:341–355 DOI 10.1007/s00193-011-0311-5 ORIGINAL ARTICLE Numerical modelling of the entrainment of particles in inviscid supersonic flow Z. Zarei · D. L. Frost · E. V. Timofeev Received: 22 June 2010 / Revised: 7 March 2011 / Accepted: 8 March 2011 / Published online: 1 April 2011 © Springer-Verlag 2011 Abstract The interaction between particles situated in close proximity and moving at supersonic speeds is investigated computationally. The simplest case of the motion of a single particle travelling behind a lead particle is used to elucidate the role of aerodynamic forces in the motion of a group of par- ticles. The effect of the following parameters on the drag and lift forces acting on each of two particles of equal diameter in proximity is investigated: the free-stream Mach number, and the axial and lateral displacements of the trailing parti- cle. The two-dimensional flow field is numerically simulated using an unsteady Euler CFD code to find the steady-state drag and lift coefficients for both particles. Three static zones of aerodynamic influence in the wake of the lead particle are identified, which are denoted as the entrainment, lateral attraction, and ejection zones. A non-dimensional represen- tation of the zones of influence is given. It is shown that the dynamic entrainment of particles can occur even when the path of the trailing particle originates outside the entrainment and lateral attraction zones. Keywords Particle entrainment · Supersonic flow · Drag and lift coefficients 1 Introduction Groups or clusters of solid particles traveling at high speed through an ambient gas is a phenomenon that occurs in a wide range of fields, such as the motion of meteorite fragments Communicated by B. W. Skews. Z. Zarei (B ) · D. L. Frost · E. V. Timofeev Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC H3A 2K6, Canada e-mail: zouya.zarei@mail.mcgill.ca when they enter the Earth’s atmosphere [2, 4], the motion of ash plumes from a volcanic eruption [22], and the ballistic motion of shot gun pellets [6, 7]. Understanding the motion of these solid particles is of great interest and under ongoing investigation. The ability to predict their motion can assist in determining, for instance, the area subject to the fallout from a volcanic plume [20] or the type and shape of cratering that could result from the impact of a cluster of meteorite fragments [19]. The application that motivates the current study is the explosive acceleration of solid particles to supersonic speeds into quiescent air [25]. It is a common practice in the explo- sives industry to add metal particles to condensed explosives (thus producing so-called metalized explosives) in order to improve their performance. With inert particles, the momen- tum flux of the flow generated is increased [10]. In the case of reactive metal particles, the combustion of the particles adds energy to the flow and can result in an augmentation of the impulse delivered by the blast [24]. The ability to predict the location of the particles, and hence the location of energy release, is vital in order to more precisely under- stand the dynamics of blast waves generated by metalized explosives. Therefore, it is necessary to gain a better under- standing of the motion of explosively dispersed solid parti- cles. A typical experimental setup consists of a sphere that is filled with metal particles. The bed of particles is saturated with a liquid explosive. A central burster charge initiates the detonation. The solid particles are accelerated by the passage of the detonation wave [25] and the rapidly expanding det- onation products. As a result, they move outwards at high speed into the region surrounding the explosive charge, typ- ically travelling at speeds of Mach 2–Mach 5. Particles of sufficient size and inertia may leave the detonation products and enter the region of shocked air behind the blast wave. In 123