A mixed-integer non-linear programming optimisation framework is formulated and developed that combines a molecular-based, group-contribution equation of state, SAFT-γγ Mie, with a thermodynamic description of an organic Rankine cycle (ORC) power system. In this framework, a set of working fluids is described by its constituent functional groups (e.g., since we are focussing here on hydrocarbons: single bondCH3, single bondCH2single bond, etc. ), and integer optimisation variables are introduced in the description the working-fluid structure. Molecular feasibility constraints are then defined to ensure all feasible working-fluid candidates can be found. This optimisation framework facilitates combining the computer-aided molecular design of the working fluid with the power-system optimisation into a single framework, thus removing subjective and pre-emptive screening criteria, and simultaneously moving towards the next generation of tailored working fluids and optimised systems for waste-heat recovery applications. SAFT-γγ Mie has not been previously employed in such a framework. The optimisation framework, which is based here on hydrocarbon functional groups, is first validated against an alternative formulation that uses (pseudo-experimental) thermodynamic property predictions from REFPROP, and against an optimisation study taken from the literature. The framework is then applied to three industrial waste-heat recovery applications. It is found that simple molecules, such as propane and propene, are the optimal ORC working fluids for a low-grade (150 °C) heat source, whilst molecules with increasing molecular complexity are favoured at higher temperatures. Specifically, 2-alkenes emerge as the optimal working fluids for medium- and higher-grade heat-sources in the 250–350 °C temperature range. Ultimately, the results demonstrate the potential of this framework to drive the search for the next generation of ORC systems, and to provide meaningful insights into identifying the working fluids that represent the optimal choices for targeted applications. Finally, the effects of the working-fluid structure on the expander and pump are investigated, and the suitability of group-contribution methods for evaluating the transport properties of hydrocarbon working-fluids are considered, in the context of performing complete thermoeconomic evaluations of these systems

The aim of this paper is to conduct a generalised assessment of both optimal working fluids and radial turbine designs for small-scale organic Rankine cycle (ORC) systems across a range of heat-source temperatures. The former has been achieved by coupling a thermodynamic model of subcritical, non-recperated cycles with the Peng–Robinson equation of state, and optimising the working-fluid and cycle parameters for heat-source temperatures ranging between 80 $°\mathrm{C}$ and 360 $°\mathrm{C}$ . The critical temperature of the working fluid is found to be an important parameter governing working-fluid selection. Moreover, a linear correlation between heat-source temperature and the optimal critical temperature that achieves maximum power output has been found for heat-source temperatures below 300 $°\mathrm{C}$ ( $T_{\mathrm{cr}}=0.830T_{\mathrm{hi}}+41.27$ ). This correlation has been validated against cycle calculations completed for nine predefined working fluids using both the Peng–Robinson equation of state and using the REFPROP program. Ultimately, this simple correlation can be used to identify working-fluid candidates for a specific heat-source temperature. In the second half of this paper, the effect of the heat-source temperature on the optimal design of a radial-inflow turbine rotor for a 25 kW subcritical ORC system has been studied. As the heat-source temperature increases, the optimal blade-loading coefficient increases, whilst the optimal flow coefficient reduces. Furthermore, passage losses are dominant in turbines intended for low-temperature applications. However, at higher heat-source temperatures, clearance losses become more dominant owing to the reduced blade heights. This information can be used to identify the most direct route to efficiency improvements in these machines. Finally, it is observed that the transition from a conventional converging stator to a converging-diverging stator occurs at heat-source temperatures of approximately 165 $°\mathrm{C}$ , whilst radially-fibered turbines seem unsuitable as the heat-source temperature exceeds 250 $°\mathrm{C}$ ; these conclusions can be used to inform expander design and selection at an early stage.

Supercritical carbon dioxide (sCO${}_2$) power cycles are promising candidates for concentrated-solar power and waste-heat recovery applications, having advantages of compact turbomachinery and high cycle efficiencies at heat-source temperature in the range of 400 to 800 ${}^{\circ }$C. However, for distributed-scale systems (0.1–1.0 MW) the choice of turbomachinery type is unclear. Radial turbines are known to be an effective machine for micro-scale applications. Alternatively, feasible single-stage axial turbine designs could be achieved allowing for better heat transfer control and improved bearing life. Thus, the aim of this study is to investigate the design of a single-stage 100 kW sCO${}_2$ axial turbine through the identification of optimal turbine design parameters from both mechanical and aerodynamic performance perspectives. For this purpose, a preliminary design tool has been developed and refined by accounting for passage losses using loss models that are widely used for the design of turbomachinery operating with fluids such as air or steam. The designs were assessed for a turbine that runs at inlet conditions of 923 K, 170 bar, expansion ratio of 3 and shaft speeds of 150k, 200k and 250k RPM respectively. It was found that feasible single-stage designs could be achieved if the turbine is designed with a high loading coefficient and low flow coefficient. Moreover, a turbine with the lowest degree of reaction, over a specified range from 0 to 0.5, was found to achieve the highest efficiency and highest inlet rotor angles.

The design of optimal organic Rankine cycle (ORC) systems requires the simultaneous identification of the optimal cycle architecture, operating conditions and working fluid, whilst accounting for the effect of these parameters on expander performance. In this paper, a novel method for predicting the design-point efficiency of a radial turbine is developed, which can predict the achievable efficiency based only on the thermodynamic conditions. This model is integrated into an optimization framework in which the working fluid is modeled using the Peng-Robinson equation of state and the fluid parameters (i.e., critical temperature) are simultaneously optimized alongside the cycle conditions. This framework can evaluate recuperated and transcritical cycles, whilst heat-transfer area requirements are estimated based on representative overall heat-transfer coefficients. For a range of heat sources, a single-objective optimization is first completed in which power output is maximized, which is then followed by a multi-objective optimization in which the trade-off between power output and total heat-transfer area is investigated. It is demonstrated that the optimization framework can simultaneously optimize the working fluid and cycle parameters, and identify whether a subcritical or transcritical cycle, with or without a recuperator, is best suited for a particular application, whilst accounting for the effect of these variables on the expander performance. This information is critical to identify optimal cycle configurations and working fluids that result in the best thermodynamic performance, yet exist in the design space in which feasible turbines can be designed. It is found that the optimal critical temperature does not vary significantly between different cycle architectures, and is not affected by whether a single or multi-objective optimization is completed. However, including the expander performance model results in significantly different cycles to optimal thermodynamic cycles.