A general alternate loading technique and its applications in the inverse designs of centrifugal and mixed-flow pump impellers

For the inverse designs of centrifugal and mixed-flow pump impellers,clarifying the generation process of secondary flows and putting forward corresponding suppression measures is an important approach to improve the impeller performance.In this paper,to provide a better qualitative insight into the generation mechanism of secondary flows in the impeller,a simple kinematic equation is derived based on the ideal assumptions,which indicates that the potential rothalpy gradient(PRG)is the most important dynamic source that actively induces secondary vortical flows.Induced by the natural adverse PRG on the S1 and S2 stream surfaces,two typical secondary flows,H-S and P-S secondary flows,are clearly presented.To specially suppress these typical secondary flows,a general alternate loading technique(GALT)is proposed,aiming to adjust the real blade loadingδp to control the PRG features.At the blade fore part,theδp on the hub streamline should be slowly increased to avoid breakneck growth of the potential rothalpy to reduce adverse streamwise PRG on the S2 streamsurface.At the blade middle part,theδp should be moderately decreased to reduce adverse streamwise PRG on the S1 streamsurface.At the blade aft part,the difference in theδp between the shroud and hub streamlines should be decreased faster to control the exit uniformity.By applying the GALT to the impeller designs of three typical pump types in hydraulic engineering,the organizational effect of the PRG on fundamental flow structures is proven.The GALT can effectively control the PRG distributions and suppress the secondary flows,thereby widening the pump’s high-efficiency zone,improving flow uniformity and suppressing pressure fluctuations.Compared with the current Z-G method and the ALT,the GALT can meet the requirements of"de-experience"better,thereby enabling the designers to obtain good products explicitly and quickly.

Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique

A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.