Optimization design of low specific speed shield pump based on orthogonal experiment

Low specific speed pump is characterized by generally low efficiency, easy to appear hump and optimization difficulties. In order to improve the hydraulic performance of the pump at the shut-off point (0.2Q d) and reduce the hump phenomenon, the influence of impeller geometric parameters on the hydraulic performance of the pump is analyzed without changing the volute structure, the orthogonal experimental design of impeller parameters is carried out. Six geometric parameters, including impeller outlet diameter, impeller outlet width, blade inlet angle, blade outlet angle, wrap angle and blade thickness, are selected as design factors. Each parameter factor is taken to 3 levels, and a total of 18 schemes are designed. 3D impeller design is carried out based on CFturbo, numerical simulation is carried out with CFX. The results show that increasing the impeller outlet diameter can increase the head within a certain range. The impeller efficiency can be improved by reducing the outlet width of the impeller, increasing the blade inlet angle and increasing the wrap angle. The pump performance parameters before and after optimization are analyzed and compared, it is verified that the orthogonal experimental design method combined with numerical simulation can optimize the design of low specific speed shield pump.


Introduction Low specific speed pump ( 20 80
s n  ) has the characteristics of low flow rate and high head, and is widely used in agricultural drainage and irrigation, urban water supply, boiler water supply, mining, petroleum and chemical industry.At the same time, in the design process of the low specific speed centrifugal pump, in order to ensure higher efficiency, the characteristics of the low specific speed pump with low flow rate and high head determine that it has different hydraulic performances from the general centrifugal pump: (1) the efficiency is relatively low.(2) it is easy to produce instability flow under low flow rate conditions.(3) it is easy to overload the supporting motor in the high flow rate area.(4) the cavitation characteristic curve is rapidly declining.Because there is no special theory and design method for hydraulic design of low specific speed centrifugal pump, only the hydraulic design method of ordinary centrifugal pump can be used, which leads to the above problems.In recent years, in order to solve the special problems of low specific speed pump, many scholars and technicians at home and abroad have done a lot of research.
Quan et al. [1] and others designed four groups of impeller models according to three factors and two levels orthogonal table, and carried out internal flow analysis, energy dissipation distribution, etc., so as to design a group of optimal impeller models, which effectively broadened the high-efficiency zone of the pump operation.Zhao [2] and others selected impeller outlet diameter, impeller outlet width, etc. as the design parameters, and designed nine groups of impeller models according to four factors and three levels orthogonal table, after optimization, the pump performance have been significantly improved.Long et al. [3] used orthogonal experiment to optimize the design of stationary components and selected a group of optimal models through numerical simulation, and the efficiency and the pump head under the design condition were improved.Yang et al. [4] used a combination of numerical simulation and orthogonal experiment to optimize the design of the drain tank of a centrifugal pump with a low specific speed, and through the significance analysis to study the degree of influence of each design parameter on the experimental results.Fan et al. [5] used the efficiency and pressure of the fan as the optimization objective, and orthogonal experiment to carry out a multi-parameter and multiobjective optimization design of the fan impeller, and the results showed that the optimal fan efficiency increased by 11.71%.
In order to meet the design requirements of the project, the optimization was carried out under the condition that the volute structure was unchanged, and the orthogonal experimental design method was adopted to optimize the design of the low specific speed shield pump.Considering the design requirements of the shut-off head greater than or equal to 6m, the efficiency was as high as possible.Therefore, geometric parameters that have an impact on the efficiency and head were selected as the design factors.Six geometric parameters, including impeller outlet diameter, impeller outlet width, blade inlet angle, blade outlet angle, blade wrap angle and blade thickness, were taken as design factors.Three levels were selected for each factor, and 18 schemes were designed.CFX software was used for numerical simulation analysis, and the predicted values of head and efficiency of each scheme were obtained respectively.Then, the sequence of each factor's influence on the efficiency is obtained by the method of range analysis, and the optimal scheme is finally obtained.Compared with the initial impeller scheme, the flow changes in the impeller channel and the reasons for the efficiency improvement are analyzed.

governing equation
The medium in the pump is regarded as a three-dimensional viscous, incompressible instability flow, and the mass is determined when the model is computed by CFD, the governing equation of momentum conservation is: Where:  = 1,2,3 respectively represent the x , y and directions of the space coordinate system, and   is the velocity vector in the  direction;  is the mean static pressure,  is the time,   is the external source term, and   and   represent the Reynolds mean velocity in the direction .

Preliminary design and optimization ideas
According to the requirements, without changing the three-dimension of the volute structure, without considering the head, the efficiency reaches 70% in CFX simulation, and the shut-off head (0.2Qd) reaches 6m.First of all, according to the main parameters, the hub diameter is determined Dh=12mm.In CFturbo, the default three-dimensional water model of the impeller is automatically generated first, and this scheme is used as the initial scheme.Then, three-dimensional model and numerical calculation were carried out with the import and export pipeline and volute water body, CFD technology is used to predict the performance of the scheme, the loss of each component is analyzed and appropriate optimization variables are selected, and orthogonal experimental design is further carried out to seek the design goal that could ensure high-efficiency under multiple operating conditions.Design parameters as shown Table 1.

Pump model and mesh generation
Workbench platform is established on which a whole process was built.All geometry were meshed into unstructured grids, which could be divided into four parts: inlet pipe, impeller, volute and outlet pipe.
The calculation domain of pump model is shown in Figure 1.The pump calculation domain uses straight pipe, in which the inlet and outlet sections are appropriately extended to ensure that the flow can be fully developed and the numerical simulation calculation is more accurate. clear water, the reference pressure is 0 atm, the inlet boundary is set as 1 atm total pressure inlet, and the outlet boundary condition is selected as the mass flow outlet, the wall condition is set to No Slip Wall, Smooth Wall; and the accuracy of convergence residual is 5  10 − .

Numerical simulation results
Using the original scheme, the performance curves of different flow rate conditions are simulated.
Analyzing performance parameters and internal flow, it is found that the hump curve appears in the low flow rate, and the head efficiency not meet the requirements.As shown in the Figure 2.

The selection and analysis scheme of orthogonal combination factors
According to the design experience and design requirements, the design selected 6 geometric parameters of the impeller.The geometrical parameters selected for the impeller are impeller outlet diameter (A), impeller outlet width (B), blade inlet angle (C), blade outlet angle (D), wrap angle (E) and blade thickness (F).The corresponding combination factor levels of the impeller are shown in the table, and 18 groups of orthogonal combination analysis schemes are obtained.

Analysis of orthogonal combination results
According to the specified combination analysis scheme, head and efficiency are selected as the evaluation indexes of combination analysis.The numerical simulation analysis of model pumps of 18 combination schemes of impeller is carried out respectively at the condition of shut-off head, and the head and efficiency of corresponding schemes are obtained.
The head and efficiency values of the orthogonal combination scheme are processed to obtain the corresponding range values.The range analysis is used to judge the influence degree of each factor on the optimization objective, and the optimal combination is obtained.The range analysis of impeller combination efficiency is shown in Table 3.As the calculated head can meet the design requirements, efficiency is selected as the optimization objective.Through range analysis, it can be seen that the main and secondary order of influence of each factor rate in impeller orthogonal experimental is B>C>A>D>E>F.The best combination is A3B1C3D1E2F3.Since the optimal combination of the impeller does not appear in the orthogonal combination scheme, the 19th experimental scheme is added, and the values of each factor of the impeller are 73, 3, 35, 28, 95, 2.5.The scheme of group 19 is numerically calculated.The calculation results show that the efficiency and the head of the experimental scheme of group 19 are respectively higher than that of all schemes.
Through numerical calculation, the efficiency and the head of the 19th group of pumps are obtained as follows: 72.7% and 5.94m.After optimization, the efficiency of predicting the impeller under working conditions is improved.For the low specific speed pump, the efficiency is significantly improved, and the shut-off head also meets the design requirements.

Optimization scheme
The original impeller of the pump was replaced by the optimized impeller for numerical simulation, and the optimization results were compared with Figure 3.It can be clearly seen that the efficiency of the optimized pump has been significantly improved, and the head has also been significantly improved, which meets the design requirements.

Internal flow analysis
Figure 4 shows the comparison of static pressure distribution in cross-section of the impeller, volute and outlet pipe under four working conditions before and after pump optimization.It can be seen from the figure that the pressure distribution in cross-section of the impeller is evenly distributed from blade inlet to blade outlet, and the pressure decreases with the of flow rate.The section pressure of the volute increases with the flow at the inlet, and there is a pressure increase at the outlet.Due to the special structure of the cut-water, the flow of water into the outlet pipe produces a backflow, and the pressure becomes larger.After optimization, the pressure minimum at the inlet of the blade is obviously increased.Figure 6 shows the comparison of turbulent kinetic energy in the middle section of the impeller under four conditions before and after optimization.It can be seen from the figure that the area with large turbulent kinetic energy of the impeller before optimization is mainly distributed at the blade outlet, and the area is mainly distributed in the volute and outlet pipe with the increase of the flow rate.After optimization, the turbulent kinetic energy of each working condition is significantly reduced, and the turbulent kinetic energy of 0.6Qd and 1.0Qd is almost close to 0, indicating that the flow in the impeller channel after optimization is more stable, and the change of flow rate has almost no effect on the turbulent kinetic energy at the blade inlet, indicating that the internal flow of the optimized impeller is more stable than that before optimization, but larger surface appears in the flow channel under high flow condition.The region with high turbulent kinetic energy indicates that the flow is blocked and the efficiency is not significantly improved, which is more suitable for operation under design conditions and low flow rate.

Conclusions
In this paper, based on the orthogonal experimental design method, different geometric parameters of the impeller were selected as design factors to carry out orthogonal experimental optimization design of 18 schemes.In order to meet the requirements of shut-off head, the efficiency of the design working condition was improved as much as possible.CFX software was used to conduct numerical simulation of the optimized the model pump.The prediction and optimization results were combined with internal flow analysis, and the following conclusions were obtained: (1) Orthogonal experimental design method was adopted to rapidly optimize the impeller.Compared with the original design scheme, the efficiency of the model pump was increased by 11.6% under 1.0Qd, and the head increased by 1.138m under 0.2Qd.(2) According to the range analysis, within the appropriate factor level, increasing the blade inlet angle, reducing the impeller outlet diameter, and increasing the wrap angle appropriately can improve the efficiency, and increasing the impeller outlet diameter can increase the head within a certain range.(3) Through the analysis of the internal flow of the impeller, it can be seen that appropriately increasing the blade wrap angle to make the flow channel length within a certain range can enhance the blade constraint ability on the flow, reduce the velocity gradient from the pressure surface to the suction surface, reduce the fluid energy loss and improve the efficiency of the pump.

Figure 1 .
Figure 1.Pump model calculation domain.2.4.Boundary condition settingsAfter the calculation domain grids are generated, the grids are imported into CFX and appropriate physical models are selected.The control equation of Shear Stress Transfer (SST) turbulence model is

Figure 3 .
Figure 3.Comparison of hydraulic performance of model pump before and after optimization.

Figure 4 .
Figure 4. Static pressure distribution in the middle section of pump.

Figure 5 Figure 5 .
Figure5shows the comparison of cross section velocity distribution between impeller and volute under four conditions before and after pump optimization.It can be seen from the figure that the velocity distribution of impeller decreases with the increase of flow rate.When the flow rate increases, the water flow in the outlet pipe is instability, and the velocity distribution diagram shows an irregular size.When the water is about to go out of the volute, the water loss is greater.After optimization, flow rate is becoming larger.

Figure 6 .
Figure 6.Turbulent kinetic energy distribution in the middle section of pump.

Table 1 .
Design parameters of pump.

Table 2 .
Factor level of orthogonal combination of impellers.

Table 3 .
Range analysis of orthogonal combination efficiency of impeller.

Table 3 .
Range analysis of orthogonal combination efficiency of impeller (Continued).

Table 4 .
Comparison of optimization results of model pump.