Some Properties of Shock Relaxation in Gas Flows Carrying Small Particles

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Abstract
Shock waves passing through uniform suspensions of droplets or solid particles in a gas upset the velocity and temperature equilibrium between the two phases, and a relaxation zone is created in which the equilibrium is gradually re-established. The effects of varying the shock strength or the properties of the mixture are investigated theoretically, and it is noted that some flow variables do not always change monotonically throughout the relaxation zone but may go through a maximum or minimum. The behavior of individual variables is discussed in some detail. A particularly interesting finding is that, for weak shock waves, the maximum particle drag and heat transfer may appear at some distance from, rather than immediately behind, the shock front. The behavior of the variables changes at critical conditions which depend on the thermodynamic properties of the materials involved, on the shock strength, and sometimes also on the assumptions made for the drag coefficient or the Nusselt number. For the gas velocity, these critical conditions can be expressed in simple analytical forms. In all calculations some assumptions must be made for particle drag and heat transfer. Calculations based on plausible variations of the customarily used formulas show that the results are significantly affected by the assumption made for particle drag, but only to a minor extent by that for heat transfer. It is concluded that experimental determination of the drag coefficient by shock-tube techniques appears feasible.

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