Hydraulic structure optimization of centrifugal pump based on orthogonal test

To reduce global carbon emissions and reduce the energy consumption of pumps, it is necessary to continuously improve the performance efficiency of pumps. In this paper, the blade wrapping angle, inlet mounting angle and outlet mounting angle are selected as the design variables, and the hydraulic structure of the pump is orthogonally optimized. Through experiments and simulations, the internal flow bonding and external energy characteristics of the centrifugal pump under different orthogonal test combinations were compared, and finally the impeller wrapping angle was 130 degrees, the outlet installation angle was 20 degrees, and the inlet installation angle was 40 degrees. It is found that compared with the original design scheme, the efficiency of the optimized scheme under the design flow rate is increased by 2.775%, and the hydraulic loss in the impeller is reduced by 1.18%. The main and secondary orders of influence of parameter factors on lift and efficiency are impeller wrapping angle, impeller outlet mounting angle, and impeller inlet mounting angle. The internal flow of the optimized impeller is significantly improved, and the flow loss is reduced. The research results provide a design basis for further improving the hydraulic performance of centrifugal pumps.


Introduction
Because of its high efficiency and high lift characteristics, centrifugal pumps are widely used in construction, mining, aviation, ships and other important fields.However, as applications become more extensive and extreme application environments become more numerous, the performance requirements of pumps become higher and higher [1].In recent years, with the proposal of the dual carbon strategy, countries around the world are making unremitting efforts to reduce carbon.Since the power consumption of the pump accounts for about 20% of the world's total power generation, improving its operating efficiency will save the world tens of thousands of tons of ore energy, which is an important direction for the development of dual carbon.In all respects, the efficiency of a pump is closely related to its hydraulic structure, so the efficiency of the pump can be improved by optimizing the hydraulic structure of the pump.
Through reviewing the relevant literature, it can be seen that the orthogonal optimization method has become the first choice for pump hydraulic optimization methods because of its good robustness and adaptability after years of development.Based on the three parameters of blade outlet width, blade outlet angle and blade wrapping angle, Li et al. [2] optimized the performance of centrifugal pump by orthogonal experimental design method.Under the design conditions, the head and efficiency of the optimized centrifugal pump are appropriately improved, and the increments are 0.74 m and 0.48%, respectively.Chang et al. [3] selected the short blade inlet diameter, inlet offset angle and outlet offset angle for orthogonal tests to optimize the long and short vane centrifugal pump, so that the hydraulic performance of the pump was significantly improved.Xue et al. [4] optimized the centrifugal pump based on the blade load distribution by using the five-factor four-level orthogonal test method, which effectively improved the pump efficiency, reduced the blade surface pressure, and improved the internal flow instability of the impeller.Xu et al. [5] optimized the impeller wrapping angle, inlet and outlet angle, blade leading edge position and blade trailing edge inclination orthogonally, and obtained that the optimal centrifugal pump efficiency was 3.09% higher than that of the original pump.Yuan et al. [6] used orthogonal tests and GA-PSO algorithms to improve the efficiency of centrifugal pumps with elbow inlets by 4.7%.Yang et al. [7] carried out a three-dimensional reverse design of a low specific speed steam turbine, and then analyzed the suction performance of different load positions, loading slopes and blade inclination angles based on orthogonal experimental design.
It can be seen that orthogonal test optimization has a wide range of applications, because of its good optimization efficiency and robustness.

Basic parameters of the centrifugal pump model
The research object of this paper is a centrifugal pump with a specific rotation number of 133.38, the impeller two-dimensional diagram is shown in Figure 1, the specific structure of the pump is shown in Figure 2, including four parts of the Inlet pipeline, Volute, Impeller and Outlet pipeline.Design the flow Q=100m 3 /h, Design head H=32m, Rated speed n=2950 r/min, Impeller inlet diameter Dj=100mm, Impeller outlet diameter D2=173mm, Impeller outlet width b2=17.5mm,Volute discharges the caliber Dd=80mm, Volute base circle diameter D3=185mm, Volute inlet width b3=35mm, Number of blades Z=6, the main parameters of this pump are shown in Table 1.

Centrifugal pump boundary condition setting
In order to better capture the strong shear characteristics of the boundary layer flow and improve the accuracy of the simulation results, the corresponding conditions are set in the CFD software ANSYS CFX.The boundary condition adopts the mass flow inlet and hydrostatic outlet, setting the impeller area to the rotating domain, the remaining domains to the fixed domain, and the interface between the stationary domain and the rotating domain to the frozen rotor.Set the rotating wall in the rotation domain as the rotating wall, the solid wall as the non-slip boundary, the wall function is set automatically, the convection term is set to high resolution, the turbulence value is set to the high order, and the residual convergence criterion is set to 10 −5 .

Meshing and Correlation Analysis
In the numerical calculation of centrifugal pumps, high-quality grids can speed up the calculation process and, more importantly, improve the convergence accuracy.Structured grids are more orthogonal than unstructured meshes and have stronger data transfer capabilities [8].The greater the number of meshes, the more accurate the numerical calculation, but the corresponding calculation time is longer [9].When the number of meshes reaches a certain value, the impact on the calculation result is negligible.Therefore, mesh independence verification, while meeting the calculation accuracy, minimizing the number of meshes is an important means to save time and improve efficiency.Seven different sets of grid numbers were used for the calculation, and the comparison results are shown in Figure 3.It can be seen that when the number of grids increases to 1.2 million, the efficiency tends to be stable, so this set of grids is used for calculation.The main components of the impeller and the mesh of the volute are shown in Figure 4.

Experimental setup
As shown in Figure 5, the test bench is mainly composed of a centrifugal pump, a frequency conversion motor, an electromagnetic flow meter, two pressure sensors, two valves, a water tank and pipeline.The pressure transducer is located at the suction and discharge pipes with a diameter of 100 mm and is used to measure the head of the centrifugal pump.The centrifugal pump is driven by a variable frequency motor, and in this experiment the motor speed is set to a constant speed of 2950 r/min.The flow rate is regulated by an outlet valve and measured by an electromagnetic flow meter.First, turn on the power switch of the motor, observe the operation of the motor and centrifugal pump, and cut off the power if there is no abnormality.Before the experiment, a pump is needed to drain the gas inside the pump.After the filling pump is completed, close the regulating valve and the irrigation valve, then start the centrifugal pump and start the experiment.During the experiment, the control valve is gradually opened to increase the flow rate, and the flow value in the pipeline can be observed through the flow meter.Adjusting the control valve to different openings can obtain the hydraulic performance of centrifugal pumps under different flow conditions.A schematic diagram of the overall test bench is shown in Figure 6.

Orthogonal optimization
Compared with other optimization methods, the optimization process of orthogonal experimental optimization is relatively simple, the amount of calculation is small, and it has a good optimization effect.Orthogonal optimization is based on the optimization goal to determine the optimization parameters, select the appropriate parameter level for combination, establish the orthogonal test table, calculate the combination of impeller change design parameters, and compare the calculation results to find the final optimal solution [10].The orthogonal optimization process is shown in Figure 7.

Optimization Purposes
Since the impeller is the most important component for energy conversion, the impeller has the greatest impact on the hydraulic performance of the centrifugal pump, and optimizing the impeller can improve the hydraulic performance of the centrifugal pump to the greatest extent.The optimization variables in this paper are the wrapping angle Ф of the centrifugal pump impeller, the inlet mounting angle β1 and the outlet mounting angle β2.Since the head of the centrifugal pump can be adjusted by changing the speed, efficiency is the most important hydraulic performance of the centrifugal pump.The purpose of this optimization is to achieve the following purposes under the design flow:

max( ) 32
Effciency Head H m Calculation of the hydraulic performance of a centrifugal pump, the head H is： Where Pout is the total pressure at the outlet, Pin is the total pressure at the inlet, ρ is the fluid density, and g is the acceleration due to gravity.
To calculate the efficiency of the centrifugal pump, the shaft power P is first calculated: Where P is the input power of the pump, n is the speed of the pump, and Mn is the torque of the impeller.
The effective power Pe of the centrifugal pump is: Where Pe is the effective power of the pump and Q is the rated flow rate of the pump.The efficiency of the centrifugal pump can be obtained: = / e P P  (5) Where η is the hydraulic efficiency of the pump.

Orthogonal test table
Using ANSYS Workbench as a platform, CFturbo is used to model parametric 3D models of impellers, volutes, inlet and outlet lines and sets optimization variables as "input parameters.".Turbogrid is used to directly generate the structural mesh of the impeller, ICEM generates the structural mesh of the remaining parts, numerical calculations are performed in CFX, efficiency and head calculation formulas are set in expression in CFX, and monitors are set to set efficiency and head as "output parameters" in CFX-POST.
Compared with other parameters of the impeller, the impeller wrapping angle and the inlet and outlet mounting angle have a greater impact on the impeller performance, so three influencing factors are selected to optimize the centrifugal pump, namely the impeller wrapping angle Ф, the inlet mounting angle β1 and the outlet mounting angle β2.According to the single-factor calculation analysis, the influence of impeller wrapping angle Ф on efficiency is greater than that of the other two, and the impeller wrapping angle Ф is first optimized by single factor, and then the orthogonal test is carried out in combination with the inlet mounting angle β1 and the outlet mounting angle β2.For the impeller wrapping angle Ф, seven levels were selected, and four levels were selected each for the inlet mounting angle β1 and the outlet mounting angle β2 for optimization.Table 2 shows the horizontal values of each factor.
Among them, A1 means that the impeller wrapping angle is 80 degrees, A2 means that the impeller wrapping angle is 90 degrees, A3 means that the impeller wrapping angle is 100 degrees, A4 means that the impeller wrapping angle is 110 degrees, A5 means that the impeller wrapping angle is 120 degrees, A6 means that the impeller wrapping angle is 130 degrees (initial wrapping angle angle), and A7 means that the impeller wrapping angle is 140 degrees.B1 means that the impeller inlet mounting angle is 40 degrees (initial inlet mounting angle), B2 means that the impeller inlet mounting angle is 30 degrees, B3 means that the impeller inlet mounting angle is 50 degrees.C1 means that the impeller outlet mounting angle is 20 degrees (initial outlet mounting angle angle), C2 means that the impeller outlet mounting angle is 30 degrees, and C3 means that the impeller outlet mounting angle is 40 degrees.
According to the single-factor optimization of the packet angle Ф, and the orthogonal test of the joint inlet mounting angle β1 and the outlet mounting angle β2, the experimental scheme was designed, and the 15 model configuration schemes designed were shown in Table 3.

Analysis of optimization results
According to the optimization design scheme (Table 3), the hydraulic model was modified, and CFX was used to numerically simulate 16 model configuration schemes under design conditions, so as to obtain the heads and efficiency of 15 schemes, and the performance numerical calculation results are shown in Table 4.

Visual analysis
From Table 4, it can be seen that the heads of the 15 schemes meet the design requirements under the design conditions, and all of them are greater than 32m.Compared with other schemes, the efficiency of scheme 1, scheme 2 and scheme 3 is relatively low, and these solutions do not achieve the purpose of optimization, so these design solutions are directly not considered.The efficiency of scheme 6 and scheme 7 is higher, and the efficiency value of scheme 6 is greater than the efficiency value of scheme 7, and the head of scheme 6 is obviously much higher than that of scheme 7, so the package angle design degree of scheme 6 is selected for subsequent optimization.Based on scheme 6, according to the basic knowledge of impeller, the inlet and outlet mounting angles that have a great influence on the efficiency of the centrifugal pump are orthogonal tests, obviously, the efficiency of the subsequent scheme is lower than that of scheme 6, so scheme 6 is the best scheme for this optimization.

Range analysis
After reviewing the relevant literature, it can be understood that the range value calculated by the formula is not the same value, so the size of the selected impeller wrapping angle, inlet mounting angle and outlet mounting angle can be judged in the selection range by the size of the range value.
The range value can also be used to determine the degree to which the selected impeller parameters affect the head and efficiency, and the larger the difference, the greater the target is affected by this factor.At the same time, according to the size of the range value to sort, correspondingly, the size of the three factors of the selected impeller can be obtained to influence the pump performance.
The range calculation formula is as follows: Where Ki is the sum of j levels, Ej is the value of a factor, ki is the average of each factor, s is the range, and n is the number of values of a factor.
After corresponding calculations, the range results are shown in Table 5: Obviously, it can be seen from Table 4 and Table 5 that the order of the degree of influence of the package angle, inlet mounting angle and outlet mounting angle on the lift is: wrapping angle> outlet mounting angle > inlet mounting angle.For head, the best combination order with the largest k value is A3B3C3, and the order of influence on efficiency is: wrapping angle> outlet mounting angle> inlet mounting angle.For efficiency, the best combination order with the largest k value is A7B2C1.After comparison, the result of the sixth scheme is taken as the final result of optimization.

Conclusion
In order to meet the design head under the design conditions and improve the hydraulic efficiency of the centrifugal pump, the impeller of the core component of the centrifugal pump was optimized by the orthogonal experimental design method, and the hydraulic performance of 15 optimization schemes was calculated using ANSYS CFX 2021, and the following conclusions were obtained: (1) The range difference method was used to analyze and determine the primary and secondary order of the three optimization parameters of the impeller on the efficiency of the centrifugal pump, which were wrapping angle, outlet mounting angle and inlet mounting angle, and the orthogonal experimental design method greatly shortened the optimization cycle and saved time cost.
(2) Through the optimization of orthogonal experimental design, the optimization time is greatly saved, the work efficiency is improved, and the efficiency of the optimized scheme is increased by

Figure 1 .
Figure 1.Schematic diagram of the two-dimensional structure of the impeller.

Figure 2 .
Figure 2. Schematic diagram of centrifugal pump calculation domain.

Figure 6 .
Figure 6.Schematic diagram of the test bench.

Table 1 .
Design working conditions and design parameters of centrifugal pump.

Table 4 .
Performance numerical calculation results.

Table 5 .
Range analysis of head and efficiency under design conditions.