Analysis of Gas-Solid Particle Flows in Shock Tubes

Theme T use of shock tubes for experimental investigations of high-speed suspension flows has motivated the development of a corresponding numerical calculation procedure. The Particle-In-Cell (PIC) method has been adapted to handle suspension flows by treating each phase as a set of discrete mass points. As in the single-phase PIC calculation the flowfield is divided into small regions fixed in space (cells), but in the modified procedure phase interactions are incorporated into the equations for the changes in the properties of the materials occupying the cells. Details of the calculation are given in Ref. 2. The purpose of this study was to investigate the dependence of the calculated results on the assumed phase interaction (drag and heat transfer). The behavior of suspension flows in shock tubes also was investigated for the limiting case of problem times that are large compared with the characteristic velocity and thermal equilibration times. In this case, there exists a zone behind the shock within which the phases are in velocity and thermal equilibrium. These equilibrium properties, as well as the equilibrium shock speed, can be calculated by applying the shock tube equations to an equivalent gas defined in terms of the properties of the suspension, thereby providing a check on the calculated flow properties.