Highlights of two-phase critical flow: On the links between maximum flow rates, sonic velocities, propagation and transfer phenomena in single and two-phase flows

Abstract

To improve the understanding of two-phase critical flow phenomena, both single- and two-phase flows are studied in parallel. This can be done only if compatible mathematical models are used for both flows. In particular, since the evolution of the fluid or of the mixture is, in fact, a consequence of the transfers at the wall and at the interface, it is more rational to postulate transfer laws than to assume fluid, or mixture, evolutions. It is shown that the mathematical form of the above transfer laws is of primary importance, and it is proposed to allow for the presence, in the transfer terms, of partial derivatives of dependent variables. The critical flow condition is discussed within the above framework. A necessary critical flow criterion is obtained by equating to zero the determinant of the set of equations describing the steady-state flow. This criterion must be complemented by the study of the compatibility conditions of the set. It is verified that a flow is critical when disturbances, initiated downstream of some “critical” section, cannot propagate upstream of this section. A decrease of the outlet pressure has therefore no effect on the flow parameters upstream of the critical section, and the flow rate is maximum. Examples are given to demonstrate the potentialities of the method. It is shown that appropriate assumptions on the transfer laws enable existing models to be discussed.