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Shock Wave Relations in Lunar Ash Flow
Author(s) -
Pai S. I.,
Hsieh T.
Publication year - 1975
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19750550507
Subject(s) - shock wave , mechanics , drag , physics , shock (circulatory) , flow (mathematics) , particle (ecology) , work (physics) , momentum (technical analysis) , classical mechanics , thermodynamics , pressure gradient , geology , medicine , oceanography , finance , economics
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 M 0 , initial particle volume fraction Z 0 and the density ratio G are presented. The thickness of the relaxation zone is found to increase with decreasing Z 0 and almost independent of G for any given values of M 0 . 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.