Design guidelines for high-pressure ratio supersonic radial-inflow turbines of organic rankine cycle systems

The radial-inflow turbine (RIT) is a widely adopted turbo-expander in power and propulsion systems of low-to-medium power capacity due to its high efficiency and compactness. Compared to conventional radial turbines for gas turbines and air cycle machines, the design of expanders for high-temperature organic Rankine cycle power systems involves additional challenges, as these machines operate with very high expansion or volumetric flow ratio and partly or entirely in the nonideal compressible fluid dynamic regime. This study examines the impact of the working fluid, of the volumetric flow ratio, and of the nonideal thermodynamic effects on the design guidelines for RIT. To this purpose, a reduced-order modeling framework for turbine fluid-dynamic design encompassing a loss model based on first principles is developed and verified against results from uRANS. Results highlighted that at the geometrical scale of interest the impact of the working fluid molecular complexity on the efficiency is marginal. Moreover, it is shown that the average isentropic pressure-volume exponent <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mover><mml:mi>γ</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> can be used to predict the magnitude of nonideal thermodynamic effects on the stage efficiency, whose variation depends on the value of the volumetric flow ratio and of the work and flow coefficients. Design guidelines that can be used for preliminary turbine design in system-level calculations are presented in graphical form, and illustrate the relation between the optimal set of stage duty coefficients, i.e., the work and flow coefficients that maximize the efficiency, the stage efficiency, the volumetric flow ratio, and the similarity parameter <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mover><mml:mi>γ</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>P</mml:mi><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>.