Numerical Investigation of the Actual Volumetric Flow Rate and Volumetric Efficiency and Optimization of the Geometric Parameters of a Three-Rotor Pump with Lantern Meshing—Part I

The present Part I of the comprehensive study is dedicated to establishing the fundamental mathematical and experimental apparatus required for the multi-criteria optimization of the geometric parameters of an innovative three-rotor hydraulic pump with bilateral lantern meshing, subjected to the actual volumetric flow rate Q and the volumetric efficiency ηv. A complex approach integrating similarity theory, dimensional analysis, and mathematical modeling is employed to define and refine the two objective functions subject to optimization. Based on the area of geometric existence of the gearing and additionally imposed geometric and operational constraints, the exact domain for seeking the optima of Q and ηv is defined. Based on the statistical processing of experimental data, empirical dependencies of the objective functions are derived, accounting for the influence of the pump’s geometric parameters, the operational conditions and the physical properties of the fluid. The criterion equation of the volumetric efficiency, approximated using all experimental data, was obtained with a very high coefficient of determination R2=0.9898. The rest of the study, related to parameter optimization, is contained in Part II. In it, through numerical investigation and analytical proof, the universal optimal parametric values of the dimensionless geometric coefficients (the relative lantern radius rc,opt* and the shortening coefficient λopt) are identified to achieve maximum flow rate and volumetric efficiency. Furthermore, in Part II, a multi-criteria Pareto optimization (MINLP) is conducted to resolve the engineering conflict regarding the number of teeth z, and a direct simple algebraic dependency z=fp,n. The generalized results from both parts provide a methodological toolkit and recommendations for the optimal selection of the geometric parameters in the design of pumps of this type with respect to the actual flow rate and volumetric efficiency, in accordance with the operating conditions and regimes.