Parametric optimization of split reaction turbine using Box-Behnken design of response surface methodology

This study provides an exhaustive investigation into the performance optimization of a Cone-Enhanced Split Reaction Turbine (CESRT), specifically focusing on a novel geometric configuration characterized by an increased cylindrical housing height of 10.0 inches. The primary objective is to elucidate the complex, non-linear interdependencies between critical operational variables and the resultant energy conversion efficiency. To achieve this, the research employs Response Surface Methodology (RSM) through a Box-Behnken Design (BBD) framework, facilitating a rigorous statistical evaluation of three independent parameters: applied mechanical torque, bypass valve angle (governing volumetric flow rate), and internal cone modifier size. The resulting empirical data was utilized to formulate a highly significant quadratic predictive model, demonstrating exceptional statistical validity with a coefficient of determination ( R 2 ) of 0.9963 and an adjusted R 2 of 0.9916. Analysis of Variance (ANOVA) unequivocally established that applied torque and bypass angle serve as the predominant drivers of system efficiency, further highlighting a critical synergistic interaction between these two factors. The structural integration of the internal conical flow modifier proved paramount in mitigating internal stagnation and managing fluid trajectories, with the 2.75-inch cone identified as the absolute geometric optimum for the extended 10.0-inch turbine casing. Optimization algorithms derived from the RSM model indicate that peak thermodynamic and mechanical efficiency is realized at an applied torque of 60 N-m, a bypass angle of 22.5°, and a cone size of 2.75 inches, yielding a maximum experimental efficiency of 70.1123%. The findings validate the robustness of the BBD-RSM model in predicting complex turbomachinery behavior and provide highly scalable, data-driven geometric and operational guidelines for the deployment of cost-effective, high-performance pico-hydro technologies in remote and off-grid applications.