Performance Back-deduction from a Loading to Flow Coefficient Map: Application to Radial Turbine

Radial turbine stages are often used for applications requiring off-design operation, as turbocharging for instance. The off-design ability of such stages is commonly analyzed through the traditional turbine map, plotting the reduced mass-flow against the pressure-ratio, for reduced-speed lines. However, some alternatives are possible, such as the flow-coefficient (Ψ ) to loading-coefficient (φ) diagram where the pressure-ratio lines are actually straight lines, very convenient property to perform prediction. A robust method re-creating this map from a predicted Ψ−φ diagram is needed. Recent work has shown that this back-deduction quality, without the use of any loss models, depends on the knowledge of an intermediate pressure-ratio. A modelization of this parameter is then proposed. The comparison with both experimental and CFD results is presented, with quite good agreement for mass flow rate and rotational speed, and for the intermediate pressure ratio. The last part of the paper is dedicated to the application of the intermediate pressure-ratio knowledge to the improvement of the deduction of the pressure ratio lines in the Ψ−φ diagram. Beside this improvement, the back-deduction method of the classical map is structured, applied and evaluated