Pressure Waves Through a Gas-Solid Suspension

Equation (6.54) accounts for the change of state in the isentropic processes of a gas-solid mixture in which the effect of a finite particle volume is considered. An example using this equation to obtain the speed of sound in a gas-solid mixture is introduced in the next section. 

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The minus sign indicates that the force is in the opposite direction of the pressure gradient [Tchen, 1947]. The significance of this force is evident, for example, when a shock wave propagates through a gas-solid suspension. 

The propagation of pressure waves such as acoustic wave, shock wave, and Prandtl-Meyer expansion through a gas-solid suspension is a phenomenon associated primarily with the transfer of momentum although certain processes of energy transfer such as kinetic energy dissipation and heat transfer between gas and solids almost always occur. Typical applications of the pressure wave propagation include the measurements of the solids concentration and flow rate by use of acoustic devices as well as detonation combustion such as in a rocket propellant combustor or in the barrel of a gun. 

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