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The one-dimensional implementation of the Delayed Equilibrium Model (DEM) is known as a relatively simple yet accurate approach for prediction of critical mass flow rate, pressure and void fraction distributions for two-phase water transonic flows in ducts of variable geometry. However, the direct application of DEM equipped with original saturation index evolution law and Lockhart-Martinelli approach (the original setup) is incapable of accurate prediction of CO2 transonic flow. Moreover, the Darcy friction factor approach has a significant impact on the simulation results. Consequently, this paper presents a new law of the saturation index evolution and a new frictional pressure gradient approach for CO2 transonic two-phase flows together with experimental validation and discussion of obtained data. A comparative analysis of the developed DEM setup and the referential Homogeneous Equilibrium Model revealed that application of the proposed approaches decreases the mean maximal discrepancy between experimental and calculated static pressure values by a factor of app. 2, with simultaneous decrease of the standard deviation by a factor of app. 4. That proves that both the frictional pressure gradient approach and the proper introduction of the thermal non-equilibrium effects are substantial for accurate modelling of the flashing process in CO2 flows.

In this research, the n-hexane jets discharged from a straight channel were studied numerically to reveal the development and characteristics of under-expanded flashing jets. Firstly, the development of flash boiling jets was investigated and compared to that of two-phase jets without phase transition. It was shown that the two-phase jets without phase transition can be under-expanded only if the flow is choked. In contrast, flash boiling jets can be under-expanded whether or not the choked conditions are verified. Secondly, the factors affecting the flashing jet behaviors were discussed. The relaxation time in phase transition, the expansion ratio, and the injection pressure have been identified as three key factors determining the jet characteristics. With high enough expansion ratio and low enough relaxation time, the expansion was so strong that the flow became transonic and shock structures similar to those of under-expanded gaseous jets appeared near the orifice exit. Finally, two types of choking have been identified for flash boiling jets, i.e., vaporization-induced choking and expansion-induced choking. The former one is mainly ascribed to the vapor formation in the orifice which reduces the local speed of sound, while the latter one is due to the expansion of under-expanded two-phase flow and the resultant flow acceleration.

The instability of circular liquid jet immersed in a coflowing high velocity air stream is studied assuming that the flow of the viscous gas and liquid is irrotational. The basic velocity profiles are uniform and different. The instabilities are driven by Kelvin–Helmholtz instability due to a velocity difference and neckdown due to capillary instability. Capillary instabilities dominate for large Weber numbers. Kelvin– Helmholtz instability dominates for small Weber numbers. The wavelength for the most unstable wave decreases strongly with the Mach number and attains a very small minimum when the Mach number is somewhat larger than one. The peak growth rates are attained for axisymmetric disturbances (n = 0) when the viscosity of the liquid is not too large. The peak growth rates for the first asymmetric mode (n = 1) and the associated wavelength are very close to the n = 0 mode; the peak growth rate for n = 1 modes exceeds n = 0 when the viscosity of the liquid jet is large. The effects of viscosity on the irrotational instabilities are very strong. The analysis predicts that breakup fragments of liquids in high speed air streams may be exceedingly small, especially in the transonic range of Mach numbers. � 2005 Elsevier Ltd. All rights reserved.

Submerged gas injection into liquids is a widely applied processing technique. At low gas flow rates, a bubble plume forms in the liquid. With increasing gas flow rates, the gas bubbles in the plume coalesce and a gas jet is formed. Transition from bubbling to jetting occurs in the transonic region. To date, there is no sufficient theoretical explanation for this transition. In this paper, a basic theory is developed to explain the transition from bubbling to jetting. The instability of a circular compressible gas jet in a liquid was studied. For the axisymmetric mode, it was found that there is a peak growth rate for both the temporal and spatial instabilities when the Mach number approaches unity. The instability quickly reduces to vanishing values at supersonic gas velocities. However, in the supersonic region, it was shown that the helical instability mode may become important. Gas pressure perturbations have a destabilizing effect in the subsonic region but a stabilizing effect in the supersonic region. The problem of absolute instability was studied in order to explain the physical phenomenon of the transition from bubbling to jetting. Absolute instability was found in the subsonic region and a gas jet always breaks up into bubbles in the subsonic region. No absolute instability was found in the supersonic region, and the gas jet may remain stable. This transition from absolute to non-absolute instability occurs in the transonic region which was observed to be the transition from bubbling to jetting.