Design and off-design optimisation of an organic Rankine cycle (ORC) system with an integrated radial turbine model

This paper investigates the design and thermodynamic optimisation of both sub- and transcritical organic Rankine cycle (ORC) power systems featuring radial turbines via performance calculations using mean-line models. The emphasis is on rapid performance predictions for a given turbine geometry, as well as geometric optimisation for a given heat source. From three specified quantities, which are the turbine inlet temperature, inlet pressure and mass flow rate, the other flow properties (e.g., outlet pressure and temperature) are computed, together with derived quantities which are required for cycle- or system-level assessments, such as the isentropic efficiency of the turbine. Experimental investigations from the open literature suitable for validation purposes are summarised and analysed with respect to their strengths and weaknesses. Similar computational fluid dynamic (CFD) simulations are also used to complement the available experimental data. The main contributions of this paper are that it provides a comprehensive overview of radial turbine performance modelling, and that it proposes a detailed framework that can be used for the improved development of efficient thermodynamic power systems based on a unified mean-line model that is validated against experimental data and supported by CFD results. Specifically, predictions from the mean-line model show good accuracy over a wide range of operating conditions for different turbine designs and fluids with compressibility factors from 0.6 to 1.0. Finally, in order to demonstrate its efficacy, the integrated radial turbine and ORC system design framework is used in a case study of a nominally 400-kW power system with propane as the working fluid in low-grade waste-heat application, where the turbine inlet temperature is fixed at 150 °C and the condenser temperature is fixed at 15 °C. The novelty of this work arises from the optimisation of the turbine nozzle vane position at off-design conditions. This feature, along with multi-stage radial turbine designs are shown to allow high-performance operation over a wide range of off-design conditions. Specifically, good efficiencies are demonstrated over a wide range of heat-source fluid flow rates when employing an adjustable nozzle geometry, as is the ability of radial turbines to achieve efficiencies that are not constrained by the pressure ratio across them by replacing single-stage designs with multi-stage designs