Interpolation-Based Evaluation and Prediction of Vortex Efficiency in Torque-Flow Pumps

The article presents the results of a study on the energy efficiency of torque-flow pumps with a particular focus on isolating the efficiency of the vortex operating process. The relevance of the topic is determined by the complexity of describing the combined operating process, which includes both blade and vortex components, the latter of which has remained insufficiently studied until now. The research aimed to improve the accuracy of predicting the efficiency of torque-flow pumps by analytically determining the effectiveness of the vortex operating process over the full range of specific speed coefficients. The study employed empirical data from bench tests of prototype pumps, supplemented by well-known empirical methodologies. To construct analytical dependencies, a Lagrange interpolation polynomial with equally spaced nodes in the range ns = 10–220 was applied. This made it possible to obtain generalized functions for the efficiency of torque-flow pumps, centrifugal (blade) pumps, and, for the first time, to determine the complete characteristic of the vortex operating process efficiency. The proposed interpolation method reproduces the empirical efficiency characteristics with an accuracy better than 1.1–1.2%, enabling reliable prediction of the intrinsic vortex process efficiency across the entire range of specific speeds. It was established that the maximum value of the vortex operating process efficiency is 66.6% at ns, while the optimal operating range of the pumps corresponds to ns = 70–140. The practical significance of the obtained results lies in their applicability for pump design and optimization for the transportation of liquids containing inclusions, as well as in ensuring higher accuracy of engineering calculations without the need for extensive experimental testing. The importance of the study is further emphasized by its contribution to achieving the United Nations Sustainable Development Goals, particularly in the areas of energy efficiency, industrial innovation, and resilient infrastructure.