Investigating the Validity of the Fundamental Derivative in the Equilibrium and Non-equilibrium Two-Phase Expansion of MM

The aim of the work presented in this paper is to explore the validity and possible extent to which non-ideal compressible-fluid dynamic (NICFD) effects may have a role in the expansion of a two-phase mixture of the siloxane MM by expanding the concept of the fundamental derivative to two-phase flows. For the assumption of a homogeneous two-phase mixture under the two limiting cases of thermal equilibrium and frozen thermal states, expressions for the speed of sound are defined. Using these definitions, the fundamental derivative is evaluated within the saturation dome of MM under the assumption of thermal equilibrium. Following this, the variation in the fundamental derivative under thermal equilibrium and frozen thermal states are compared for expansion processes from different reservoir pressures (5, 10 and 15 bar) and vapour qualities (0.1, 0.5 and 0.9). These preliminary results suggest that the fundamental derivative remains below unity throughout the two-phase dome under both limiting cases, with the lowest values obtained in close proximity to the critical point and saturated liquid line. The results also suggest that the deviation between the equilibrium and frozen models increases as the reservoir vapour quality increases. Ultimately, this implies that NICFD effects are likely to be present during the a two-phase expansion of MM within novel turbomachinery. However, further research is necessary to investigate these effects under more realistic assumptions that are relevant to turbomachinery applications (i.e., in-homogeneous and non-equilibrium flow).