# Optimal design of multistage centrifugal pump based on the combined energy loss model and computational fluid dynamics

### Significance Statement

Pumps are the most popular general machinery with a wide range of applications. Nearly 22% of the total world’s energy by electric motors is consumed pumps. Therefore, pumps appear to have an enormous energy consumption and a significant energy saving potential. End-users and the quest for more energy saving methods have pushed researchers to focus on enhancing the pump efficiency. In addition, multistage centrifugal pumps that are fundamental in providing high energy liquid have received more attention in the recent years.

Currently, there are several methods that have been proposed for improving the efficiency of the pump. They include coefficient optimization, Computational Fluid Dynamics, and energy loss model. Test optimization plays and important role in the pump design because test optimization is semi theoretical and semi-empirical.

Velocity coefficient optimization is a conversion method that is based on hydraulic models. A suitable velocity coefficient must be chosen as the basis of pump size consistent with the specific speed. The method appears to be straightforward, but it is quite challenging to design new hydraulic systems in view of the limitation of the current models as well as experience.

Researchers led by Professor Ling Zhou at Jiangsu University in China proposed a method to combine the Computational Fluid Dynamics optimization and energy loss models. By implementing numerical simulations, the authors were able to compute all types of energy losses in the conventional multistage centrifugal pump. This was in a bid to evaluate their individual or combined effects on the pump’s performance. They obtained an optimal design by combining energy loss model and computational fluid dynamics and confirmed by testing a prototype. Their research work is published in Applied Energy.

The authors established four different calculation models in order to analyze the various kinds of energy losses in the pump. They conducted numerous numerical computations with varying grid numbers, convergence precisions, turbulence models and surface roughness. This was in a bid to get appropriate numerical settings and ensure dependence on the results. All forms of energy losses in the typical multistage centrifugal pump were computed to evaluate their combined or individual effects on the pump performance.

It was observed that setting methods of numerical calculation for multi-stage centrifugal pump rendered the numerical results more credible. The accuracy of the computation domain was an important contributor to the precision of the Computational Fluid dynamics results. When the precision of the computation domain increased, the efficiency decreased constantly. The greatest deviation exceeded 50% and the head initially increased and then reduced.

A combination method of the computational fluid dynamics and energy loss model was developed for the optimal design, which entailed the numerous kinds of energy losses in the pump, for instance, disk friction loss, inter-stage leakage loss, volumetric leakage loss, and hydraulic loss. These occurred at the inlet section, impeller, outlet section, and pump cavity, respectively.

The inter-stage leakage loss was converted by the disk friction loss, and the volumetric leakage loss was negatively correlated with the disk friction loss. The increase of the volumetric leakage loss was higher than the decrement of the disk friction loss for typical centrifugal pumps. For this reason, reducing both inter-stage leakage and volumetric leakage losses was more efficient to enhance the efficiency of the pump.

Fig. 1 Real front rings of the above three pump models

Fig. 2 Experimental results of three kinds of pump models

Fig. 3 Schematic diagram of the test rig 1. Pool　2. Inlet control valve　3. Inlet pressure transmitter　4. Pump　5. Outlet pressure transmitters　 6. Turbine flowmeter　7. Flow control valve　8. Motor

### About The Author

Dr. Chuan Wang is an Assistant Professor of National Research Center of Pumps at Jiangsu University, China. He received his Ph. D. in 2016 in fluids engineering from Jiangsu University, and published more than 20 journal papers in the past 5 years.

### About The Author

Dr. Ling Zhou, is an Assistant Professor of National Research Center of Pumps at Jiangsu University, China. He received his M. S. degree in 2011, and his Ph. D. in 2014 both in fluids engineering from Jiangsu University. He completed one year joint Ph.D. research program at Washington University in St. Louis. He is a member of American Society of Mechanical Engineers.

His research interests are in the area of hydraulic design, optimization, and multiphase flow of multistage centrifugal pump. He has published over 20 peer-reviewed journal papers and conference articles, co-edited three books in Chinese, and one in English.

### Reference

Chuan Wang, Weidong Shi, Xikun Wang, Xiaoping Jiang, Yang Yang, Wei Li, Ling Zhou. Optimal design of multistage centrifugal pump based on the combined energy loss model and computational fluid dynamics. Applied Energy, volume 187 (2017), pages 10–26.