Optimization of Parameters of Plastic Lined Pump Structural Based on Fluidsolid Coupling Analysis

: The main objective of the present article was to obtain the optimum structure of the plastic lined pump under the condition of fluid-structure interaction. The structural parameters of the pump were calculated according to the given design parameters. The three-dimensional geometric model was established. The flow field analysis was carried out by CFD. The inlet diameter 𝐷 𝑗 , outlet width 𝑏 2 , vane outlet angle 𝛽 2 and vane number 𝑍 of the impeller were selected as the four factors to design orthogonal experiment. The results were analyzed by range analysis. The efficiency and NPSH were obtained as combined parameters under the evaluation index. The genetic algorithm was used to optimize its structural parameters, and the best structural combination parameters of the plastic-lined pump under the conditions of maximum efficiency and minimum cavitation were obtained. T he efficiency was increased by 2.78% and the NPSH was reduced by 0.249707 after optimization. Finally, the stress distribution and displacement deformation under the condition of the coupling field were obtained by the fluidsolid coupling analysis. The maximum stress was 4.83mpa and the maximum displacement deformation was 3.1547e-5m.


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In the process of scientific and engineering case analysis, there is usually no absolute singlefield problem, and most physical phenomena are coupled with each other [1] . For the plastic lined pump, fluid-structure coupling is the interaction between the flow field and the structure of the pump body. The internal running state of pump is very complex on account of the fluidsolid coupling and the process of conveying medium. Therefore, it is urgent to study the plastic lined pump from the perspective of multi physical field coupling [2] . The method of fluidsolid coupling is closer to the actual operation of the plastic lined pump than the traditional ones. Its novelty stems from the fact it takes into account the turbulence modeling and at the same time the strong-coupling of fluid and structure [3] . The fluid-structure-interaction (FSI) technology makes the coupling analysis of flow field and structure field become a reality, which makes it possible to study the fluid structure interaction of pump.
Researchers mainly focus on the single-stage and multi-stage metal centrifugal pump, but less on plastic lined centrifugal pump. Such as the distribution of the internal flow field of plastic lined pump, the stress of fluid structure coupling during operation, the situation and location of cavitation damage in the plastic lined pump, and the deformation and displacement of the impeller under the action of fluid-solid coupling have not been studied. Therefore, it is necessary to study the internal flow field and fluid structure coupling of plastic lined pump.
In this paper, CFD is used to analyze the flow field of the lining plastic pump. Through orthogonal experiment and range analysis, it can be concluded that the efficiency and NPSH are taken as the combined parameters under the evaluation index. The genetic algorithm is used to optimize the structural parameters of the plastic lined pump, and the optimal parameter combination is obtained. Based on ANSYS Workbench, the structural change of the impeller under the effect of fluidsolid coupling is obtained.
3 corrosion resistance of the plastic and its market ownership is increasing day by day.
The basic parameters of the lining plastic pump are as follows: flow rate Q=100 m 3 /h, head H=80 m, rotate speed n=2900 rpm, inlet diameter of impeller =90 mm, outlet diameter =80 mm, width of impeller inlet b 1 =18 mm, outlet width b 2 =10 mm, impeller inlet angle 1 =20°, outlet angle 2 =30°, and the wrap angle =110°. According to the above parameters, the physical model of impeller and the volute-type discharge passage was established [4] , as shown in

Flow Field Simulation
Build 3D model by CFturbo10.0 and simulate by PumpLinx. After the impeller and volute were imported into PumpLinx, an inlet section needed to be established at the entrance of the impeller. Then the inlet section, impeller and volute were meshed, as shown in Figure 2.
Here, the iterative steps of the plastic lined pump were set as 1000 steps. Figure 3 shows the convergence of the iterative residual curve.  [4] . It shows that the velocity inside the impeller of the plastic lined pump was generally symmetrical. The closer the impeller was to the edge, the higher the velocity was. Besides, the velocity on the working face of the impeller was greater than that on the back of the vane with the same diameter.  Figure 5 shows the pressure distribution of the lining plastic pump. The pressure was increasing gradually from the inlet of the impeller to its outlet [4] . The pressure field inside the impeller was axisymmetric. There was no obvious mutation area between the impeller and the volute channel. In addition, the pressure near the impeller inlet was the lowest. Due to the pressure difference, this area is also most prone to cavitation.  In this paper, the gas mass fraction and gas volume fraction inside the plastic-lined pump are used to express the degree of cavitation. The higher the gas mass fraction and gas volume fraction are, the more serious the cavitation is. Figure 6 shows that the gas mass fraction of the pump was 1.7926×10 -5 after reaching stable convergence and cavitation mainly occurred in the back area of the blade above the tongue, there was slight cavitation at the head of other blades, too. Combined with the analysis of the pressure cloud diagram in Figure 5, the prediction of the cavitation location was also verified. Figure 7 shows that the gas volume fraction of the impeller is as high as 0.999906. Since the fluid medium set by the boundary conditions is water, it means that the medium has reached the critical pressure of vaporization in this operating state. Especially, the medium itself is also a certain gas content, so the fluid medium evaporates rapidly. A large number of vapor bubbles were generated, which results in a relatively high gas volume fraction and brings cavitation damage to the plastic-lined pump.
When the internal flow field of the plastic-lined pump is stable, its internal speed, pressure, etc. also tend to be stable. At this time, the working efficiency of the plastic-lined pump can be calculated according to formulas (1) and (2). It can be seen from Figure 8 that the outlet pressure of the plastic lined pump was 850975pa.
Because the inlet pressure of the boundary condition was set as 101325pa, the pressure difference between the inlet and outlet was: According to the efficiency calculation formula of the pump: Where is the density of fluid medium (kg/m3); is the gravitational acceleration; is the efficiency; is the shaft power; is the pressure difference between pump inlet and outlet. Calculated: = 1000 = 68.79%

Orthogonal Experiment
In this paper, the efficiency and cavitation of the plastic lined pump were selected as the evaluation indexes of the orthogonal test. The inlet diameter , outlet width 2 , vane outlet angle 2 and vane number were selected as the four factors of the orthogonal test, which were respectively represented by A, B, C and D. Each factor was set with five levels, as shown in Table  1.  [4] . 25 groups of experimental data obtained from orthogonal test were simulated to obtain the gas volume fraction under each group of parameters. The centrifugal pump efficiency of corresponding groups was calculated by equations (1) and (2), as shown in Table 2.

Range analysis
(1)Analysis of the influence trend of various factors on efficiency The larger the value of R is, the greater the influence of this factor on the test evaluation index is. Table 3 shows that the order of the influence of each test factor on the efficiency of the evaluation index is: D>A>B>C, namely: vane number > inlet diameter > outlet width > vane outlet angle. The influence trend of various factors on efficiency is shown in Figure 9. According to the highest efficiency evaluation index, the best combination of structural parameters can be obtained as A5B5C4D3, that is, when the inlet diameter was 98mm, the outlet width 2 was 14mm, the vane outlet angle 2 was 32 ° and the number of vanes Z was 6, the maximum efficiency value can be obtained. Representatively, this group of parameters is included in 25 groups of test data. The new tests results are shown in Figure 10 and Figure 11.   According to the range value R, the order of the influence of each parameter on the cavitation is: B>D>C>A, namely: outlet width > vane number > vane outlet angle > inlet diameter.
The influence trend of various factors on cavitation is shown in Figure 12. It can be seen from Table 4 that according to the evaluation index of the smallest cavitation damage (the smallest gas volume fraction), the best combination of structural parameters can be obtained as A1B2C1D4, that is, when the inlet diameter was 80mm, the outlet width 2 was 8mm, the vane outlet angle 2 was 26 ° and the vane number Z was 7, the gas volume fraction was the minimum. The optimized structural parameters of the plastic lined pump were not in the existing tests [4] . The CFD software was used to remodel and verify the test results [4] , As shown in Figure 13, the minimum gas volume fraction of this group was 0.90108. Significantly, the cavitation damage was reduced.  The optimal individual in the last generation population can be used as the approximate optimal solution of the problem after decoding.

Optimization and calculation of genetic algorithm
Genetic algorithm toolbox was used for objective optimization. Input calculation formula, set population size to 1000, population to 1000, stall generations to 1000 and function tolerance to 1e-3, genetic toolbox began to calculate and solve. Then the iterative optimization diagram and optimization results were obtained, as shown in figure 14 and figure 15.  The parameters of the final optimization results after rounding are shown in Table 5. After optimization 100 14 27 6 Use the optimized parameters to perform three-dimensional modeling of the plastic-lined pump again, and import the new model into PumpLinx for flow field analysis. As shown in Figure   16, the outlet pressure of the plastic lined pump was 885337Pa, the efficiency of the pump can be calculated as 71.57%, 2.78% higher than the previous 68.79%. As shown in Figure 17, the gas volume fraction was increased from the previous 0. 999906 to 0.750199, reduced by 0.249707.
The overall performance of plastic lined pump had been improved. It can be seen from Figure 18 that the equivalent stress under the flow field load of impeller was axisymmetric. There was no obvious abrupt change of the distribution of pressure in each channel. Besides those, the maximum pressure was at the impeller inlet and the pressure at the impeller outlet decreased gradually. At the same radius, the pressure of the working face of vane was larger than that of the back area. Figure 19 shows that the closer the impeller was to the center, the greater the pressure was. Pressure comes mainly from the action of fluid on the impeller surface. The overall distribution of pressure load was also corresponding to the distribution of water pressure in Figure 18.      Table 6.  is the edge of vane. If the clearance between impeller and pump cover is not designed reasonably, wear will occur in the working process. Therefore, according to the deformation and displacement of the impeller, it is significant to reasonably design the clearance between the impeller and the pump cover and the inlet width of the vortex chamber.

Conclusion
This paper focuses on improving the efficiency of plastic lined pump and reducing cavitation damage. The internal flow field of plastic lined pump was simulated and analyzed by CFD. Then the optimal structure parameter combination was found based on genetic algorithm. Combined with the actual working condition of plastic lined pump, the fluidsolid coupling method is adopted to analyze the stress and structure change of impeller. It has guiding significance for the safety and reliability of the plastic lined pump. The main research results are as follows.
(1) The orthogonal experimental table of 25 (5 4 ) was designed and orthogonal experiment was carried out. In this paper, the best combination parameters of efficiency conditions and cavitation conditions are obtained respectively.
(2) This paper uses genetic algorithm to find the best combination of structural parameters.
Based on ANSYS Workbench, the fluidsolid coupling calculation method, which is closer to the essence of impeller operation, was adopted to analyze the stress and structure change.