Computational Study of a High-Expansion Ratio Radial Organic Rankine Cycle Turbine Stator

There is a growing interest in organic Rankine cycle (ORC) turbogenerators because they are suitable as sustainable energy converters. ORC turbogenerators can efficiently utilize external heat sources at low to medium temperature in the small to medium power range. ORC turbines typically operate at very high pressure ratio and expand the organic working fluid in the dense-gas thermodynamic region, thus requiring computational fluid dynamics (CFD) solvers coupled with accurate thermodynamic models for their performance assessment and design. This article presents a comparative numerical study on the simulated flow field generated by a stator nozzle of an existing high-expansion ratio radial ORC turbine with toluene as working fluid. The analysis covers the influence on the simulated flow fields of the real-gas flow solvers: FLUENT, FINFLO, and ZFLOW, of two turbulence models and of two accurate thermodynamic models of the fluid. The results show that FLUENT is by far the most dissipative flow solver, resulting in large differences in all flow quantities and appreciably lower predictions of the isentropic nozzle efficiency. If the combination of the $k−ω$ turbulence model and FINFLO solver is adopted, a shock-induced separation bubble appears in the calculated results. The bubble affects, in particular, the variation in the flow velocity and angle along the stator outlet. The accurate thermodynamic models by Lemmon and Span (2006, “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3), pp. 785–850) and Goodwin (1989, “Toluene Thermophysical Properties From 178 to 800 K at Pressures to 1000 Bar,” J. Phys. Chem. Ref. Data, 18(4), pp. 1565–1636) lead to small differences in the flow field, especially if compared with the large deviations that would be present if the flow were simulated based on the ideal gas law. However, the older and less accurate thermodynamic model by Goodwin does differ significantly from the more accurate Lemmon–Span thermodynamic model in its prediction of the specific enthalpy difference, which leads to a considerably different value for the specific work and stator isentropic efficiency. The above differences point to a need for experimental validation of flow solvers in real-gas conditions, if CFD tools are to be applied for performance improvements of high-expansion ratio turbines operating partly in the real-gas regime.