On modeling and physical laws of isentropic speed of sound in dense gas-particle two-phase compressible flows

Abstract

Study of isentropic sound speed of two-phase or multiphase flow has theoretical significance and wide application background. As is well known, the speed of sound in fluid containing particles in suspension differs from that in the pure fluid. In the particular case of bubbly liquids (gas liquid two-phase flow), the researches find that the differences can be drastic. Up to now, the isentropic speed of sound in the flow field with a small volume fraction of bubbles (less than 1%), has been investigated fully both experimentally and theoretically. In this paper, we consider another situation, as the case with solid particles in gas, which is the so-called gas particle two-phase flow. Although many results have been obtained in gas liquid two-phase flow, there is still a lot of basic work to do due to the large differences in the flow structure and flow pattern between gas particle two-phase flow and gas liquid two-phase flow. Treating the gas particle suspension as the relaxed equilibrium, thermodynamic arguments are used to obtain the isentropic speed of sound. Unlike the existing work, we are dedicated to developing the computational model under dense condition. The space volume occupied by particle phase and the interaction between particles are overall considered, then a new formula of isentropic sound speed is derived. The new formula includes formulae of the pure gas flow and the already existing dilute gas particle two-phase flow as a special case. On the one hand, the correctness of our formula is verified. On the other hand, the new formula is more general. The variations of sound speed with different mass fractions of particle phase are analyzed. The theoretical calculation results show that the overall physical law of sound speed change is that with the increase of the particle mass fraction, the sound speed first decreases and then increases. The velocity of sound propagation in gas particle two-phase flow is far smaller than in pure gas in a wide range, so it is easy to reach the supersonic condition. When the particle volume fraction is below 10%, the result is consistent with Prandtl theoretical analysis. In this range, the influences of the particle phase pressure modeling parameters can be neglected. When the particle volume fraction is more than 10%, the particle phase pressure modeling parameters produce influences. Furthermore the corresponding physical principles and the mechanisms are discussed and revealed. The new formula and physical understandings obtained in this paper will provide a theoretical support for the researches of dense gas particle two-phase compressible flow and related engineering applications.