Statistical and Computational Evaluation of Empirical Axial Turbine Correlations in Design of Centrifugal Turbines

Centrifugal turbines have recently regained interest of the engineering community as they could serve as cost-effective alternatives in diverse energy applications. In this device, the working fluid expands in a centrifugal flowpath and entails rotation of concentric rings of airfoil-shaped blades. Yet in their current design paradigm, their meanline performance estimation and optimization have dubiously exploited axial turbine empirical correlations. To the authors knowledge, there are no theoretical nor practical foundation that could justify such practice. Hence, this paper intends to deliver an answer on this matter with application of the biased Kacker and Okapuu (KO) and Aungier (Ag) correlations on 33 pairs of similar axial and centrifugal cascades. The uncovered content is twofold. First, the Ag loss demonstrates a probability of achieving an error within ±15% of 44% whereas that of KO is lessened to 38% in axial cascades. The Ag deviation attains 15% which is thrice that of the KO under same condition. In second, the insensitivity of the Ag profile and secondary losses under drastic change of flow condition in the centrifugal cascades is proven to be practically significant. While the Ag deviation is still able to reach an accuracy of 11%. The coupling effect of the terms intervening in the correlations reveal to be weak. Thereupon, the empirical axial turbine loss correlations are unreliable in performance estimation or optimization of centrifugal turbines.