Sensitivity Analysis of Phase Change Modelling for Non-Ideal Fluids in Turbomachinery Applications

Abstract Investigating phase change phenomena with numerical methods reveals a strong dependence of the results on the selected model equations. The phase change from gaseous to liquid, referred to as condensation, is primarily determined by the physical processes of nucleation and droplet growth. A large number of different model equations for both processes can be found in the literature. These are derived based on the law of ideal gases and empirical factors, whose range of definition was determined for the medium water for historical reasons. Despite this fluid-specific adjustment, the results show a strong model sensitivity even for water. This effect is amplified for other fluids, such as CO2, which are additionally characterised by a significant non-ideality of their thermophysical properties. To ensure suitable modelling for these fluids, it seems indispensable to first quantify which model parameters show a dominant influence on the results. The present study contributes to this by systematically varying different model approaches and parameters. For each of the fluids, water, and CO2, a test case of a supersonic flow through a Laval nozzle geometry is chosen. The sensitivity study includes a variation of the calculation approaches for the critical energy barrier, which is decisive for nucleation, the droplet growth rate, and various types of modelling of the droplet size distribution. An additional comparison of two fundamentally different numerical schemes also makes it possible to relate the variation of the results due to different physical model approaches to the general numerical variance. The results for CO2 show a sensitivity comparable to that of water concerning the type of droplet size distribution. For the phase change modelling, however, a broadening of the range of results compared to water is apparent. This also shows a dependence on the non-ideality of the fluid states. The results presented in this paper allow a systematic estimation of the uncertainties associated with modelling the phase change when designing turbomachinery operated with CO2. The analysis also indicates the need for experimental validation of the condensation modelling for non-ideal fluids.