Gas particle nozzle flows

Abstract

The equations governing the one-dimensional flow of gas-particle mixtures are discussed. It is shown that the sound velocity in the mixture is the frozen sound velocity in the gas alone and is unaffected by the presence of the particles unless the mixture is always in equilibrium. The equilibrium sound velocity in the mixture is derived and is shown to be lower than the frozen sound velocity. Shock waves in gas-particle mixtures are discussed and it is shown that two shock structures are possible. When the flow velocity in front of the shock is supersonic (based on the frozen speed of sound), the shock consists of a discontinuous shock front followed by a relaxation zone. When the flow velocity in front of the shock is greater than the equilibrium sound speed but less than the frozen sound speed, the shock is fully diffuse and consists of a relaxation zone in which both the gas and particle properties vary continuously. The frozen sound velocity is found to occur downstream of the nozzle throat for all gas-particle nozzle flows. It is shown that the throat conditions depend on the nozzle inlet geometry and that the nozzle mass flow and performance are determined by the nozzle inlet geometry. Analytical and numerical solutions to the equations governing the one-dimensional flow of gas-particle mixtures through nozzles are presented. The particle velocity and thermal lags are found to be greatest at the nozzle throat and expressions are given for estimating these lags. The equations governing axially symmetrical flows of gas-particle mixtures are briefly discussed. These equations are of hyperbolic type when the flow is supersonic (based on the frozen speed of sound in the gas) and can be solved by the method of characteristics. A sample nozzle calculation is given and compared with one-dimensional calculations. A summary is given of all gas-particle nozzle experiments and the results are compared to the calculated gas-particle nozzle flows. It is found that the calculations and experiments are in agreement within the accuracy of the experimental measurements. It is concluded that the flow of gas-particle mixtures can be accurately predicted by the present analysis.