# Parameter Analysis and Optimization of Annular Jet Pump Based on Kriging Model
The results showed that when \(q>0.2\), the cavitation at the inlet of the throat played an important role in the efficiency of the pump. [PERSON] [11] conducted a large eddy simulation of the annular jet pump flow characteristics and studied the jet pump internal flow field mechanism by time average and instantaneous analysis. The results show that the axial component of turbulence mainly occurs in the near wall area of the mixing layer and diffuser. [PERSON] [12] numerically studied the influence of different installation methods on the jet pump property and concluded that the jet pump was more efficiently installed vertically. CFD techniques were used in most of these studies. They supplemented the deficiencies of experimental research through effective simulation of real flow, and thereby provided more detailed and comprehensive information than experiments, at a lower cost. However, because the CFD model was a large and complex computer program, the analysis of complex flow required a lot of time to obtain a good numerical solution. This usually led to a heavy computation load, requiring hours or even days of calculation. In addition, the traditional method required a continuous trial and error process to reach a good result. This is because using CFD technology to enhance the annular jet pump hydraulic  
Figure 1: Structural schematic drawing of annular jet pump. performance relies on the designer's engineering experience. Further, the results were scattered \"points\" rather than \"lines\" or \"surfaces\", so the design space cannot be comprehensively analyzed. In recent years, various optimization methods [4; 6; 7; 8] were proposed with CFD to improve the performance of hydraulic machinery. Among them, the approximate model was a method of approximating the mapping function of design parameters and objective parameters by constructing a metal model. Compared with other optimization methods, the approximate model-based optimization method took the advantage of low calculation cost and can study properties of the response function more effectively. Furthermore, the value of head ratio, \(h\), needs to meet the special demand of the project in the engineering application of jet pump. However, the traditional design means it is difficult to handle the annular jet pump optimization problem with a given \(h\). [PERSON] [13] reviewed the application of approximate models in structural optimization. In addition, approximate models were widely used in multi-objective optimization as well, such as the response surface method [14; 15], artificial neural network [16; 17] and radial basis function [18; 19]. [PERSON] [20] proposed a multi-objective optimization method combining experiment and Kriging model which had both local and global statistical characteristics and could analyze and predict the trend of the known information. This method was suitable for the optimization of centrifugal pumps. The optimization results were basically consistent with the experimental results. [PERSON] [21] proposed a multi-objective optimization method for centrifugal pumps, using a genetic algorithm based on a neural network to solve Pareto optimal solution. [PERSON] [22] obtained the pareto optimal front of low specific speed centrifugal pump efficiency and cavitation safety margin based on the back-propagating neural network model. In this paper, the optimization method based on the modified method of feasible directions (MMFD) is used to obtain the maximum efficiency of 34.15% which is closer to the global optimal solution based on an approximate model and to solve the constrained optimization problem with a given head ratio by building the functional relationship between efficiency and design parameters, which makes the method more applicable.