Shock Wave Relations in Lunar Ash Flow

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Abstract
A detailed analysis of steady normal shock waves in a layer of lunar ash by the theory of two phase flow of a mixture of a gas and small solid particles is presented. New terms of pressure gradient and virtual mass forces in the particle momentum equation and the particle kinetic energy and work done in the particle energy equation are included in the fundamental equations and their influences are investigated. It is found that the virtual mass force is only important at low density ratio of the solid particles and the gas in the free stream, hence it may be neglected in ash flow calculations. On the other hand, the rest new terms must not be neglected in the normal shock wave calculation as was done by previous authors. The flow variables as functions of the free stream Much number M0, initial particle volume fraction Z0 and the density ratio G are presented. The thickness of the relaxation zone is found to increase with decreasing Z0 and almost independent of G for any given values of M0. A new empirical relation of the drag coefficient for the spherical particles in the mixture to fit experimental data for Z up to 0.55 and Rep up to 1,000 is proposed in the calculation.