Optimisation of a converging-diverging nozzle for the wet-to-dry expansion of the siloxane MM

Abstract

Wet-to-dry expansion within the nozzle guide vane of an ORC turbine has been proposed as a means to improve the power output of ORC systems for waste-heat recovery (< 250 °$C$). However, given the rapid fluid acceleration in the stator, the phases can develop significant velocity and temperature disparity due to density difference and finite rate of interphase heat transfer. Since these factors can significantly affect the phase-change process, wet-to-dry nozzle design techniques must account for non-equilibrium effects. The first part of this paper aims to further verify a previously developed quasi-1D inviscid non-equilibrium nozzle design tool by comparing it to non-equilibrium CFD simulations, which, unlike the design model, account for lateral flow variations, viscous and turbulence effects, along with secondary momentum forces. Within the CFD model, the interphase mass, momentum, and energy exchange models have been updated using correlations better tailored to evaporating droplet flows and a corrected drag equation. Moreover, the definition of the vapour mass fraction has been modified, while a simplified droplet breakup model has been used to predict the droplet size. The results from the CFD simulations indicate that the outlet vapour mass fraction is approximately 10 to 15% lower than that predicted by the quasi-1D tool. However, the overall flow behaviour and phase-change pattern were in satisfactory agreement, justifying the use of the design tool for 1D optimisation. As such, the quasi-1D tool is coupled to a gradient-based optimiser to optimise the nozzle pressure profile and enhance evaporation of siloxane MM for expansions with an inlet pressure ranging from 450 to 650 kPa, and inlet vapour quality of 0.3. CFD simulations of the optimised geometries indicate an increase of 3.3 to 5.7% in the outlet vapour mass fraction, which was raised from 84.9, 87.7 and 90.5% to 88.2, 93.4 and 95.7% for 450, 550 and 650 kPa inlet pressures respectively. However, a more abrupt expansion in the optimised nozzles resulted in the development of a shock and led to deterioration in nozzle efficiency compared to the baseline nozzles. Finally, a CFD-based shape optimisation was conducted, which demonstrated that it may be difficult to further enhance the vapourisation rate. However, the optimised geometry did mitigate the effect of the oblique shock that appears in the diverging section of the nozzle, raising the expansion efficiency by around 3%.