Particle and fluid time scales in a spherical multiphase blast flow

The explosive dispersal of particles is an important problem in multiphase physics and is of considerable interest due to its many applications. Simulations that examine particulate dispersal in such flows have employed a variety of methods, including Euler–Lagrange, Euler–Euler, and dusty gas. The appropriate choice of methodology depends on the balance between accuracy and computational cost. In general, if the particles are very small and tracer-like, a cheaper dusty gas approach will be sufficient. In this paper, we present a series of two-dimensional numerical simulations investigating particle and fluid time scales in the context of the explosive dispersal of particles within a spherical shock-tube problem. Using the timescales, the appropriateness of the equilibrium Eulerian approach in calculating the particle velocity is investigated. With increasing particle inertia, the equilibrium Eulerian approximation offers a good compromise between accuracy and computational efficiency, where the particle velocity becomes an algebraic function of the fluid velocity, acceleration, and particle time scale. Different blast parameters, for which the calculation of particle velocity based solely on the flow acceleration and particle time scale is valid, were studied and presented. Initial particle size, volume fraction, blast pressure, and temperature ratio were varied, and the resulting effects on the particle time scale, fluid time scale, and the Stokes number are presented. It was found that the Stokes number is a valid predictor of the viability of the equilibrium Eulerian approximation. For values of the Stokes number below unity, there was good agreement between the equilibrium Eulerian and the Euler–Euler methods. It was observed that the most significant factor impacting the Stokes number, and consequently, the accuracy of the equilibrium Eulerian approximation, is the particle size.