Performance Prediction for High Pressure-Ratio Radial Inflow Turbines

This paper describes the latest developments in a method for predicting the design and off-design performance of radial inflow turbines, using a one-dimensional analysis. As such, it is suitable for preliminary design purposes and also for turbine map generation as an aid to the modelling of systems including such turbines. Previous development work has resulted in methods of loss correlation allowing the power output and efficiency to be predicted with confidence. The focus of this paper is on extending the calculation method to high-pressure ratios, and the accurate prediction of flow capacity for unchoked and choked conditions. A numerical method provides for the identification of subsonic, transonic, and supersonic flow regimes in the bladed rows of the turbine, and allows their solution in a consistent manner. Numerically stable and validated solutions have been obtained for a cryogenic expander case with the stage pressure ratios as high as 13.6. In this paper, we will report cases with pressure ratio up to 4.0, where the nozzle and rotor are operating at the choked condition. When a blade row is choked, the flow capacity depends on the throat area, and accurate predictions require that this area is known with confidence. Previous meanline methods have typically concentrated on unchoked flow conditions, in which it is not necessary to know the throat area accurately. In turbine design, the method thus enables the necessary throat areas to be established at an early stage in the design process, and this information is required for the subsequent blade design. In analysis, comparison with test data has revealed the importance of throat aerodynamic blockage, which has hitherto largely been overlooked in meanline prediction methods. Estimates of appropriate blockages have been obtained from such comparisons. An unusual feature of radial inflow turbine nozzles is the reduction of annulus area downstream of the blade row. This can lead to situations where it is the flow area at the trailing edge rather than the throat that limits the flow capacity in choking conditions. The method accommodates this by introducing additional deviation at the trailing edge to ensure that the throat remains choked for all blade row pressure ratios greater than the critical pressure ratio, and the flow between the throat and trailing edge develops in a form that is fully consistent with the basic principles of fluid motion.