Abstract
An analytic solution is obtained for one-dimensional adiabatic flow behind converging shock waves propagating through a channel of variable cross section containing a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and small solid particles, in which solid particles are continuously distributed. In order to obtain the analytical solutions, the Whitham's geometrical shock dynamics method is employed and the initial density of the ambient medium is assumed to be constant. The effects of the variation of cross-sectional area of channel on the flow variables immediately behind the shock are investigated. The effects of increase in (i) the mass fraction (concentration) of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables are also discussed in comparison with a non-dusty gas case.
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