Addition of Heated Solid Particles to a Gas Flowing in a Pipe

A number of processes, such as pneumatic conveying of powdered materials through ducts, feed lines for powdered rocket fuels, or certain flow processes in air-augmented solid-propellant rockets, involve addition of a stream of solid particles to a gas flow. The present study deals with the analysis of gas flows from a constant-pressure and temperature reservoir through a pipe into which the particles are injected at some point, and the pipe is assumed long enough to allow equilibrium between the gas and the particles to be established. Ultimately, the mixture is discharged into another reservoir of constant pressure. The temperature of the injected particles may be different from the reservoir temperature of the gas, so that the effects of simultaneous particle and heat addition must be considered. Allowance is made in the flow equations for the volume fraction occupied by the particles, and the analysis may therefore be applied to arbitrarily high particle loadings. To demonstrate the influence of the various parameters involved, the flow equations are solved numerically with the aid of a digital computer. With increasing particle loading the gas flow is markedly reduced, and the temperature of the discharge closely approaches that of the injected particles as a result of the high heat capacity of the particle stream. If this temperature behavior is assumed to hold, simple relationships can be derived which yield results in good agreement with data obtained from the complete equations if the loading ratio equals about ten or more for typical gas-particle mixtures. Of special interest is the finding that the gas flow needed to transport particles at a prescribed rate can be significantly reduced by heating of the particles before injection. It is demonstrated that equivalent direct heating of the gas would not be practicable unless the particle loading is quite low.