In order to improve the hydraulic performance of the centrifugal pump, based on the original model, the optimization mathematical model with the four indexes head, efficiency, shaft power, and pump net positive suction head as objective function was established, and the multiobjective optimization design of the centrifugal pump was carried out by orthogonal test. Based on the
Centrifugal pumps are widely used in various fields of national economy and play an important role in the fields of petroleum, chemical industry, national defense, and aerospace [
In this paper, the orthogonal test is used to optimize the structural parameters of the centrifugal pump; combined with CFD numerical simulation, the influence of the main structural parameters of the impeller on the pump head, efficiency, shaft power, and
The basic parameters of the centrifugal pump are flow rate
The main structural parameters of the impeller.
Parameters  Calculation results  Final results 

Impeller inlet diameter, 
59.5  60 
Impeller outlet diameter, 
182.6–187.6  190 
Impeller inlet width, 
13.5  14 
Impeller outlet width, 
4.5–5  5 
Blade inlet angle, 
23–40  30 
Blade outlet angle, 
16–40  30 
Blade thickness, 
2.4  3 
Blade number, 
6.25  6 
Cape angle, 
90–130  120 
According to the initial results in Table
Impeller threedimensional model.
Orthogonal test is a design method of using the orthogonal table to arrange and analyze the multifactor test [
Considering the influence of impeller geometry parameters on the centrifugal pump head, efficiency, shaft power, and
Level table of orthogonal test factors.
Levels  Factors  









 
1  7  23  20  95 
2  4  28  26  105 
3  5  33  32  115 
4  6  38  38  125 
In accordance with the
Orthogonal test schemes.
Test serial numbers  Factors  Corresponding parameters  








 
1 




7  23  20  95  
2 




7  28  26  105  
3 




7  33  32  115  
4 




7  38  38  125  
5 




4  23  26  115  
6 




4  28  20  125  
7 




4  33  38  95  
8 




4  38  32  105  
9 




5  23  32  125  
10 




5  28  38  115  
11 




5  33  20  105  
12 




5  38  26  95  
13 




6  23  38  105  
14 




6  28  32  95  
15 




6  33  26  125  
16 




6  38  20  115 
PumpLinx is a simulation software for hydraulic simulation of pump research, which can accurately predict pressure, power, cavitation, heat transfer, flow, and other conditions. The impeller threedimensional model is imported into PumpLinx software, and the unstructured grid can be divided, as shown in Figure
Impeller grid division.
As shown in Figure
Distribution of centrifugal pump outlet pressure.
As can be seen from Figure
Before numerical simulation, the boundary conditions of the centrifugal pump are set. Centrifugal pump boundary conditions are pump rotational speed, pump outlet flow rate, inlet pressure, turbulence model, and basic properties of fluid media. Among them, the pump rotational speed is
The basic properties of the fluid medium include density of the medium, reference temperature, kinematic viscosity, saturated vapor pressure, and volume elastic modulus. The basic parameters of fluid medium are set, as shown in Table
Basic parameters of fluid media.
Parameters  Parameter values 

Fluid medium  Water 
Density  998.2 
Reference temperature 

Kinematic viscosity  1 × 10^{−6} 
Saturated vapor pressure  2338.8 
Volume elastic modulus  2.18 × 10^{9} 
The control equations of the pump numerical calculation include the continuous equation, momentum equation (Navier–Stokes), and Reynolds equation. The numerical simulation medium of the centrifugal pump is water, which belongs to incompressible fluid, and its motion law is in accordance with the momentum equation.
The incompressible Navier–Stokes equation is the mathematical expression of momentum conservation law, and the tensor form of its differential equation is [
In (
The 16 sets of experimental data in Table
Orthogonal test results.
Test serial numbers 





1  45.05  74.75  4094  1.297851 
2  44.65  74.56  4068  1.286662 
3  44.26  73.86  4071  1.275654 
4  43.03  70.30  4158  1.240883 
5  36.25  80.59  3056  1.049084 
6  33.10  82.45  2727  0.959460 
7  39.01  77.96  3399  1.127119 
8  36.34  77.20  3198  1.051548 
9  40.41  76.79  3575  1.166883 
10  41.61  75.63  3738  1.200818 
11  39.17  77.56  3431  1.131733 
12  39.80  75.23  3594  1.149505 
13  45.25  76.35  4026  1.303545 
14  44.32  75.80  3972  1.277401 
15  40.43  74.89  3668  1.167473 
16  39.02  73.64  3600  1.127533 
where
Equation (
Equation (
Influence analysis of parameters on the head.
Parameters 






176.99  166.96  156.34  168.18 

144.70  163.68  161.14  165.41 

161.00  162.87  165.34  161.15 

169.03  158.19  168.90  156.97 

44.25  41.74  39.08  42.04 

36.18  40.92  40.28  41.35 

40.25  40.72  41.33  40.29 

42.26  39.55  42.22  39.24 

8.07  2.19  3.14  2.80 
Sorting  1  4  2  3 
Influence analysis of parameters on the efficiency.
Parameters 






293.47  308.48  308.39  303.74 

318.20  308.44  305.27  305.67 

305.21  304.27  303.65  303.71 

300.68  296.36  300.24  304.43 

73.37  77.12  77.10  75.94 

79.55  77.11  76.32  76.42 

76.30  76.07  75.91  75.93 

75.17  74.09  75.06  76.11 

6.18  3.03  2.04  0.49 
Sorting  1  2  3  4 
Influence analysis of parameters on the shaft power.
Parameters 






16,391  14,751  13,852  15,059 

12,380  14,505  14,386  14,723 

14,338  14,569  14,816  14,465 

15,266  14,550  15,321  14,128 

4098  3688  3463  3765 

3095  3626  3597  3681 

3585  3642  3704  3616 

3817  3638  3830  3532 

1003  62  367  233 
Sorting  1  4  2  3 
Influence analysis of parameters on the
Parameters 






5.101050  4.817363  4.516576  4.851875 

4.187211  4.724340  4.652724  4.773488 

4.648938  4.701979  4.771485  4.653088 

4.875952  4.569469  4.872365  4.534699 

1.275263  1.204341  1.129144  1.212969 

1.046803  1.181085  1.163181  1.193372 

1.162234  1.175495  1.192871  1.163272 

1.218988  1.142367  1.218091  1.133675 

0.228460  0.061973  0.088947  0.079294 
Sorting  1  4  2  3 
From the range analysis of Table
From the range analysis of Table
From the range analysis of Table
From the range analysis of Table
According to the above orthogonal test, the optimal scheme of the four indexes head, efficiency, shaft power, and
According to the orthogonal test results of each factor, the matrices are established as shown in the following equation:
In (
In (
In (
Thus, the weight matrix that affects the test index value is obtained as
According to the orthogonal test results, the weight matrix is calculated by calculating the weight matrix of each index, and the weight matrix
From the weight matrix
In order to verify the feasibility of the optimization scheme, the external characteristics test bench is set up by the IH 6560190 chemical centrifugal pump, as shown in Figures
Test pump.
External characteristics test bench. (1) Water tank. (2) Vacuum control valve. (3) Inlet control valve. (4) Vacuum table. (5) Pressure gauge. (6) Flow meter. (7) Flow control valve. (8) Test pump. (9) Motor. (10) Water tank.
Based on the optimal scheme, the impeller is made of polyvinyl chloride (PVC), as shown in Figure
Test impeller.
Comparison of external characteristics of optimization pump and prototype pump. (a)
As shown in Figure
The experimental results before and after optimization of each index under different conditions are extracted from Figure
Experimental results before and after optimization of each index.
Indexes 
 

5  10  15  20  25  30  
Before optimization, 
45.26  43.67  42.83  41.79  37.77  30.44 
After optimization, 
39.58  38.12  38.06  36.74  31.35  22.56 

12.55  12.71  11.14  12.08  17.00  25.89 
Before optimization, 
30.96  50.77  63.34  69.22  69.69  62.25 
After optimization, 
40.34  60.74  70.65  75.43  76.06  68.27 

30.30  19.64  11.54  8.97  9.14  9.67 
Before optimization, 
2137  2464  2786  3285  3712  4037 
After optimization, 
1444  1885  2339  2717  2914  3026 

32.43  23.50  16.04  17.29  21.50  25.04 
Before optimization, 
1.303873  1.258968  1.235231  1.205830  1.092041  0.883916 
After optimization, 
1.143303  1.101958  1.100258  1.062849  0.909804  0.659033 

12.31  12.47  10.93  11.86  16.69  25.44 
As shown in Table
The changes of external characteristics of the centrifugal pump and
PIV system test platform.
At fixed speed (
Prototype pump relative speed velocity (a) vector diagram and (b) cloud diagram.
Optimization pump relative speed velocity (a) vector diagram and (b) cloud diagram.
From Figures
The velocity coefficient method was used to design the hydraulic design of the centrifugal pump, the main structure parameters of the impeller were obtained, and the threedimensional model of the impeller was established by CFturbo software.
The 16 sets of experimental schemes were designed by orthogonal test, the internal flow field of centrifugal pump was simulated by PumpLinx software, the weight matrix was used to optimize the head, efficiency, shaft power, and
To build the external characteristics test of the centrifugal pump, the simulation values and experimental values before and after optimization under different working conditions were obtained. The simulation values and experimental values of each index are consistent with the law of flow variation, the relative error of simulation value and experimental value was relatively small, the optimization of pump indexes except head had significant improvement, the curve hump was eliminated, and the feasibility of the weight matrix optimization method was verified.
Based on the PIV test system, the experimental results show that there was no obvious “jetwake” flow structure in the optimization pump, its maximum velocity was less than the prototype pump, the area of lowspeed zone was larger than the prototype pump, the efficiency and anticavitation performance of centrifugal pump were improved, the head and shaft power were reduced, and the accuracy of the optimization design process was proved.
Taking the centrifugal pump as the research object, the hydraulic performance of the centrifugal pump was improved by orthogonal test, which laid a foundation for the research of hydraulic design and external characteristics of the centrifugal pump. However, due to the limitations of the research conditions, there were still some deficiencies that need to be improved. In this paper, the weight matrix method was used to optimize the orthogonal test results, the influence of the impeller geometric parameters on the comprehensive performance of centrifugal pump was obtained by calculating the weight, and a set of optimal scheme was obtained. In the experimental results, although the performance of other indicators was significantly improved, the head was greatly reduced, which had a greater impact on the efficiency of pump. Therefore, in the followup work, the influence of the main geometric parameters of the impeller and shell on the hydraulic performance of the centrifugal pump will be comprehensively considered, in order to improve the overall performance of the centrifugal pump.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This project is supported by Key Project of Natural Science Research in Colleges and Universities of Anhui Province, China (KJ2017A450), Anhui Province University Outstanding Young Talent Support Program Project, China (gxyq2017071), and Natural Science Foundation of Chaohu University, China (XLZ201503).