Theoretical values for the propagation speed of small pressure disturbances through two-phase fluid have been derived by a method analogous to the well-known method for single-phase fluids and using the well-known separated-flow model of two-phase flow. Since the liquid and vapor phases in general flow at different mean speeds, it is appropriate to compute the propagation speed relative to the laboratory frame of reference, not relative to the fluid as is usually done in single phase. With the extra degree of freedom in two-phase flow, two distinct speeds are found for propagation both upstream and downstream, each representing compatible thermodynamic behavior of both phases. Comparisons between calculations based on the model, and several published sets of experimental values of the speed of sound, tend to confirm the theory at low and at high void fractions. Both propagation speeds have been observed in experiments. Also by analogy with the single-phase case, critical flow is predicted to occur when the upstream propagation speed relative to the laboratory is zero, i.e., when pressure waves cannot travel into the opening from which the flow issues. Flow calculations based on the model under these conditions show agreement with published experimental critical-flow measurements in the regions of low and high void fractions. Thus, a satisfactory explanation of the critical-flow phenomenon in two-phase fluids is obtained in these regions. From the analytical–experimental comparisons it appears that of the two propagation speeds and critical flows, one is observed at low void fraction, and the other at high void fraction. In the intermediate range, the theory and experiment differ and it is probable that the separated-flow model does not adequately represent the flow regimes occurring in this range.
Study of Critical Flow : Completely Separated Gas-Liquid Two-Phase Flow
