Analysis of the equilibrium Eulerian approximation of particle velocity in a spherical blast

The explosive dispersal of particles is an important multiphase physics of considerable interest in many applications. Calculating the particle velocity within these blasts can be costly, however, since it must be calculated separate from the gas velocity, and the two phases can only be assumed to have the same velocity when particles are sufficiently small. However, by using the equilibrium Eulerian approximation, particle velocity can be approximated as a function of gas velocity, acceleration, and the particle time scale [1]. The appropriateness of the equilibrium Eulerian approximation depends on the Stokes number of the particles, which in the present flows varies over both space and time. Several simulations were performed using the in-house code HyBurn, where an Euler-Euler approach was used to solve the gas and particle phase governing equations [2]. The effect of four different parameters were tested: the particle size, initial particulate volume fraction, initial higher pressure, and initial temperature of the high-pressure region. These parameters were studied to examine in which regime the dusty gas and equilibrium Eulerian assumptions are appropriate as these factors would play a significant part in the calculation of Stokes Number.