Prediction of critical mass rate of flashing carbon dioxide flow in convergent-divergent nozzle

Abstract

The prediction of a critical mass flow rate of flashing flow is of crucial importance for many applications in chemical and processing apparatus. One of the most prosperous application is the two-phase ejector as a device with flashing liquid phase as a motive fluid and vapour phase as a secondary fluid. In that case the prediction of critical flashing flow mass flow rate is necessary. A new generalised procedure of the transonic trajectory determination that uses enhanced Possible-Impossible Flow algorithm is proposed. The procedure is much faster than the commonly used Newton Critical Point (NCP) approach. The approach was applied in modelling of carbon dioxide transonic two-phase flow through the convergent-divergent nozzle by means of Homogeneous Equilibrium Model (HEM) and Delayed Equilibrium Model (DEM). These models were used to simulate flows that were experimentally and theoretically investigated in literature. The application of DEM model for determination of the supersonic trajectory part for CO2 flow is a novel contribution provided in the paper. The comparison with literature experimental data revealed that the original closure equations developed for water are improper for CO2 transonic flows, thus the adjusting attempts were demonstrated. It was revealed that the applied Darcy friction factor determination approach significantly influences on the results. Moreover, an effective DEM adjustment is impossible until Lockhart–Martinelli approach is utilised. It was shown that for CO2 case Darcy friction factor calculated by means of Friedel approach is more appropriate than the one calculated by means of the commonly used Lockhart–Martinelli approach. Nevertheless, it was demonstrated that using a frictionless approach would still give better results while adjusting DEM to better approximate the experimental pressure distributions.