Optimization of Reaction Turbine via Central Composite Design: A Parametric Analysis

Abstract

The study comprehensively investigates hydrodynamic performance, parameter optimization, and scaling implications of a 10-inch-high Cone-Enhanced Split Reaction Turbine (CESRT). By employing a rigorously structured Central Composite Design (CCD), the analysis evaluates the independent, quadratic, and interactive effects of three critical operational parameters: applied torque, system bypass angle, and internal cone size. The statistical model demonstrated exceptional predictive reliability, characterized by an F-value of 319.59 and a coefficient of determination (R²) of 0.9976. The empirical findings reveal that while applied torque serves as the primary driver of operational efficiency, complex, non-linear interactions exist between the torque, the bypass angle governing the inlet flow, and the geometric influence of the internal cone modifier. Maximum hydraulic efficiency for the 10-inch architecture is achieved at an applied torque of 60 N-m, a bypass angle of 22.5°, and a cone size of 2.5 inches, yielding a peak predicted efficiency of 64.5803%. Crucially, a comparative scaling analysis against preceding 8-inch CESRT configurations reveals a significant degradation in isentropic efficiency associated with the increased aspect ratio of the 10-inch model. These findings demonstrate mathematically that radial expansion, rather than vertical elongation, is hydrodynamically optimal for simple reaction turbomachinery.