Fluid dynamics of cavitating sonic two-phase flow in a converging-diverging nozzle

Abstract

Both cavitating and flashing flows are important phenomena in fluid flow. Cavitating flow, a common consideration in valves, orifices, and metering devices, is also a concern in loss of coolant accidents for liquid water in power plants when saturation pressures are below atmospheric pressure. Flashing flow is a common consideration for devices such as relief and expansion valves and fluid injectors as well as for loss of coolant accidents in which the coolant’s saturation pressure is above atmospheric. Of the two phenomena, flashing flow has received greater interest due to its applicability to safety concerns, though cavitating flow is perhaps of greater interest in terms of energy efficiency. It is possible for cavitating and flashing flow to actually become sonic. That is, the local velocity of a fluid can exceed the local speed of sound due to the unique properties of two-phase mixtures. When a flow becomes sonic, it is possible for the flow to accelerate and impose additional energy losses that would not otherwise occur. Models of this aspect of two-phase flow are not well developed, typically only being presented for the case of constant area ducts. In this paper two models for cavitating sonic flow are developed and described by applying the integral forms of the mass, momentum, and energy equations to a control volume of variable cross-sectional area. These models, based on the homogeneous equilibrium model (HEM) and separated flow model, are then applied to experimental data taken by the author with R-134a as the fluid of interest. Experimental data were taken with four instrumented converging-diverging nozzles of various geometries using a custom testing rig that allowed for precise control and measurement of flow parameters such as mass flow, temperature, and pressure. The resultant data from the models are then examined, focusing on the resultant velocities, Mach numbers, quality, and shear stresses.