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An aerodynamic performance analysis is essential for nearly all aspects of radial-inflow turbine aerodynamic design and application. The highly complex three-dimensional flow fields in these machines are strongly influenced by viscous effects and passage curvature. In contrast to the axial-flow turbine, the most effective approach to the performance analysis of radial-inflow turbine is the one-dimensional or mean-line method. Indeed, there is a close parallel with compressor performance analysis where the one-dimensional method is the most effective technique for the centrifugal compressor  but the more general hub-to-shroud flow method is the better choice for the axial-flow compressor .
One-dimensional performance analysis relies on analysis of the flow along a mean stream surface through various stage components. This approach is quite effective, but also has definite limitations. There are really an infinite number of ways a component can be designed to produce the specific geometrical parameters used by a one-dimensional performance analysis. The best a one-dimensional analysis can do is to predict the expected performance assuming the detailed geometry is based on “good design practice.” Obviously, good design practice is a relative term. In the case of the diffusing flows in compressors, this can result in significant uncertainty, particularly when analyzing older designs. It is a much less serious issue for turbines, where the accelerating flow results in less sensitivity to local flow behavior.
The literature includes a number of investigations into the performance analysis of radial-inflow turbines [67, 68, 75–83]. But unlike other popular turbomachinery types, the literature really doesn't provide any comprehensive and well-validated performance prediction systems for these machines. The axial-flow turbine performance analysis of chapters 4 and 5 is based on several well-developed and competing systems for modeling the loss and fluid turning. This writer's performance analyses for centrifugal and axial-flow compressors [1, 2] are based on similar well-developed technology from the open literature. In contrast, the empirical models presented in this chapter are largely unique. Some axial-flow turbine and centrifugal compressor models were adaptable to the radial-inflow turbine application, but most models were formulated specifically for this aerodynamic performance analysis. Although the open literature is quite limited, there are a number of proprietary performance analyses for radial-inflow turbines that appear to be well developed and effective. Indeed, some of these are implemented in commercially available software systems.