Multiobjective Optimization Design and Experimental Study of Desulfurization Dust Removal Centrifugal Pump Based on Immune Particle Swarm Algorithm

In view of the problems of low efficiency, poor anticavitation performance, and curve hump for current centrifugal pump in the process of desulfurization and dust removal, the desulfurization dust removal centrifugal pump was designed. -e velocity coefficient method was used for hydraulic design of centrifugal pump, and the three-dimensional modeling and numerical simulation of flow field of centrifugal pump were carried out by using computational fluid dynamics technology (CFD). -e optimal mathematical model with the highest efficiency and the lowest pump net positive suction head (NPSHr) as the objective function was established under the condition of no curve hump. -e immune particle swarm optimization algorithm was used to optimize the multiobjective function, and the optimal combination of the main parameters was obtained. -e simulation results showed that, compared with the traditional centrifugal pump, the performance of the optimized centrifugal pump had been greatly improved, which eliminated the phenomenon of curve hump. Based on IHmodel chemical pump to build a prototype test platform, the experimental results of the external characteristics of the prototype pump and the optimization pump under different working conditions were obtained. At the rated flow rate, the optimization pump efficiency was increased by 13.30%, the head was increased by 11.52%, and NPSHr was decreased by 10.14%. -e experimental results showed that the optimized indexes met the design requirements and improved the performance of centrifugal pump. At the same time, the accuracy of the immune particle swarm control method was verified, which provided some reference for the design of desulfurization dust removal centrifugal pump.


Introduction
Centrifugal pump is a widely used general machinery, mainly used in petrochemical, urban water supply and drainage, aerospace, and other fields [1].At present, there are some problems in centrifugal pumps, such as low efficiency, poor anticavitation performance, and curve hump, especially in low speed centrifugal pumps.e early centrifugal pump development is mainly based on the Euler theory, univariate theory, binary theory, and flow similarity theory and other methods for hydraulic design and model conversion, whether the designer has a wealth of engineering experience is the key to determine the success of centrifugal pump design [2][3][4][5][6][7][8].Industries, in order to achieve the function of desulfurization, usually to improve the chemical pump, but the improved efficiency of the chemical pump was low, could not meet the requirements of energy saving and environmental protection, and the operating conditions were not suitable for the desulfurization dust removal pump requirements.Aiming at the shortage of traditional centrifugal pump in this aspect, the structure design of desulfurization dust removal centrifugal pump was carried out by CFD technology, with the highest efficiency, the NPSH r as the objective function, and the no curve hump as the constraint conditions for multiobjective optimization, and the immune particle swarm control algorithm was used to optimize the calculation, so as to get a centrifugal pump with good performance.

Calculation of Mathematical Model for Desulfurization Dust Removal Centrifugal Pump
2.1.Hydraulic Design.e hydraulic design of desulfurization dust removal centrifugal pump is carried out by the velocity coefficient method [9], in which rotational speed n � 1450 r/min, flow rate Q � 50 m 3 /h, and head H � 20 m. e design of desulfurization dust removal centrifugal pump is a single suction impeller: pump specific speed s ) � 0.960, and mechanical efficiency η m � 1 − 0.07(1/ (n s /100) 7/6 ) � 0.886.

Impeller Design.
Considering that the fluid in the desulfurization dust removal centrifugal pump is alkaline medium, the rigid polyvinyl chloride with good corrosion resistance and high mechanical strength is selected as the material of impeller.
where k 0 is the impeller inlet coefficient, taking into account the cavitation and efficiency of centrifugal pump, and k 0 takes 4.0.Hub diameter is in which pump shaft diameter d � 20 mm.
(3) Determination of impeller outlet diameter D 2 Impeller outlet diameter is where K D 2 � 12.09.
(5) Determination of impeller inlet width b 1 First, the impeller inlet velocity v 0 is determined, and then the impeller inlet width b 1 is calculated: where k 0 � 0.026542 + 0.001247n s − 0.000001n 2 s � 0.104.Impeller inlet width is b 1 � η v Q/πD j v 0 � 22.9 mm. 1 � 20 ∘ -25 ∘ , and the impact angle is Considering that the value of β 2 is usually within the range of 16 ∘ -40 ∘ , the outlet angle β 1 � 30 ∘ for this design is selected.
(7) Determination of the number of blades Z Z � 6.5 (8) Calculation of blade thickness and selection of blade packing angle Calculation of blade thickness is where the coefficient A is related to specific speed and material, and A � 4.5 is desirable by look-up table [9].Generally, the value range of the blade angle φ is 90 ∘ -120 ∘ because the specific speed of the pump is lower, and φ takes 120 ∘ .(9) Determination of impeller structure parameters In summary, the main structural parameters of impeller are shown in Table 1.

Calculation of Main Structural Parameters of Vortex Chamber.
(1) Calculation of base circle diameter and vortex chamber inlet width Since the base circle diameter calculation formula is: D 3 � (1.03-1.08)D 2 � 267.8-280.8mm, the selected base circle diameter D 3 � 270 mm.(2) Calculation of each section area of vortex chamber For convenience of calculation and drawing, circular vortex chamber and 8 equal parts are selected.e average velocity v 3 of the vortex chamber is in which the velocity coefficient k 3 � 0.46.e calculation formula of each section area is where i takes 1 to 8, respectively.e calculation results of each section area of vortex chamber are shown in Table 2.

Three-Dimensional Modeling and Flow Field Analysis of Desulfurization Dust Removal Centrifugal Pump
3.1.Centrifugal Pump ree-Dimensional Model.CFturbo is a professional impeller and volute design software, easy to operate, widely used in centrifugal pumps, centrifugal fans, turbines, and other rotating machinery designs [10][11][12].e above design parameters are introduced into the CFturbo 10.0 software, and the three-dimensional model of centrifugal pump is shown in Figure 1 through the parameter setting.

Grid Division.
Pumplinx is a software developed for the hydraulic simulation and calculation of pump, which provides engineers with fast and accurate calculation results.e three-dimensional model of centrifugal pump is imported into the Pumplinx 3.4 software, and the Cartesian grid is divided, as shown in Figure 2; a total of 78668 grids are obtained.
In order to further verify the effect of grid number on the numerical simulation performance of centrifugal pump, six groups of grid numbers are selected to simulate the changes of centrifugal pump η, H, and NPSH r under the same working conditions.Grid independence analysis is shown in Table 3 [13].
As can be seen from Table 3, when the number of grids is between 60000 and 70000, the number of grids has a great influence on each index of centrifugal pump.When the number of grids is between 70000 and 85000, the variation range of each index is small.erefore, when the number of grids is more than 70000, the sensitivity of the external characteristics of centrifugal pump to the number of grids is small, and each index value tends to be stable.Visible, the number of selected impeller grids is reasonable.

Boundary Condition Setting.
Before the flow field simulation, the boundary conditions are set.e rotating speed of impeller is n � 1450 r/min, the flow rate of pump is Q � 50 m 3 /h, the fluid medium is selected by water, and the turbulence model is selected as the k − ε model.e interface coupling between impeller and volute is coupled with dynamic-static interface.
e inlet adopts the speed inlet boundary condition, the outlet boundary adopts the free outlet, and the surface of the solid wall has no slip.

Flow Field Simulation.
After setting the parameters, the flow field is simulated by Pumplinx 3.4 software.Figure 3 shows the pressure contour diagram, velocity contour diagram, and cavitation contour diagram of desulfurization dust removal centrifugal pump, respectively.
According to Figure 3(a), the pressure from the center of the impeller to the volute is gradually increased, reaching the maximum at the volute outlet, so that the fluid has enough energy to reach the specified head.However, the uneven pressure distribution on the volute and the reaction to the impeller may cause the vortex phenomenon among the blades.
As shown in Figure 3(b), the velocity from the center of the impeller to the outlet of the impeller is gradually increasing, the velocity distribution of impeller near the volute    Advances in Materials Science and Engineering wall is uneven, and the vortex phenomenon is easy to appear, which a ects the normal ow of uid.As shown in Figure 3(c), there is a large range of cavitation in the blades near the impeller inlet. is is because the impeller inlet pressure is very low, to reach the critical pressure of uid at room temperature, resulting in cavitation phenomenon.

Centrifugal Pump Optimization Mathematical Model Establishment
In view of the above ow eld simulation, with the highest e ciency and the lowest NPSH r as the objective function, the centrifugal pump was optimized with the constraint conditions of no curve hump.

Maximum E ciency Model of Centrifugal Pump.
According to the Stodola formula, when the inlet has no prerotating, the theoretical head of the centrifugal pump is [14] where σ 1 − π/Z sin β 2 , σ denotes the slip coe cient, and ψ 2 denotes the impeller outlet exclusion coe cient.e total e ciency of centrifugal pump is expressed as where P m is the centrifugal pump mechanical loss and S 1 is the hydraulic loss.When η is the largest, 1/η is the smallest, and the highest e ciency objective function is where λ is the inlet pressure drop coe cient of the blade, and k 1 and k 2 are the coe cients.Centrifugal pump NPSH r objective function is min In summary, the total objective function is where ω i is the weight coe cient and f * i is the ideal value of corresponding subobjective function.4 Advances in Materials Science and Engineering

Constraint Conditions.
In order to avoid the problem of curve hump in centrifugal pump, according to empirical function, the following should be satisfied [16]: According to the requirements of optimization design, the scope of design variables is adjusted appropriately, and other constraints can be obtained:

Immune Particle Swarm Control Algorithm Design
e immune particle swarm algorithm is a new improved particle swarm algorithm based on the immune mechanism of the biological system.e control effect is obvious, which has the characteristics of fast convergence speed, high convergence precision, and strong adjustment ability.In this paper, Matlab 7.0 software is used to write immune particle swarm optimization algorithm to optimize the multiobjective function.
Determine the optimal solution for the parameter selection: where e(t) is the system error, u(t) is the output of the immune controller, and t is the time.
In order to avoid the overshoot phenomenon, using the penalty function, the optimal solution is if ey(t) < 0, where ey(t) � y(t) − y(t − 1) and y(t) is the system output.
Fitness function f � 1/J, and the greater the fitness, the higher the accuracy of particles.e parameter optimization process is shown in Figure 4 [17,18].

Optimization Design of Desulfurization Dust
Removal Centrifugal Pump

Analysis of Results after Optimization.
e immune particle swarm algorithm is programmed by Matlab 7.0 software, and the iterative result of optimal solution is shown in Figure 5.
e optimized parameters of impeller are shown in Table 4.

Simulation of Flow Field after Optimization.
According to the optimized parameters, the parameters are remodeled, and the CFD analysis is carried out, as shown in Figure 6.
As can be seen from Figure 6(a), the pressure distribution on the volute of the optimization pump is relatively uniform, the energy loss in the volute is small, and the vortex phenomenon between blades is avoided.
As can be seen from Figure 6(b), the velocity of the uid near the volute wall of the optimization pump is relatively uniform, and the vortex phenomenon is avoided.
As can be seen from Figure 6(c), the cavitation near the inlet of the impeller of the optimization pump is obviously reduced, and the cavitation phenomenon is basically eliminated.
From the optimized pressure contour diagram, velocity contour diagram, and cavitation contour diagram, it can be seen that the e ect of the initial design structure of centrifugal pump has been signi cantly improved, and the overall performance of centrifugal pump has a certain promotion.

Simulation of External Characteristics.
In order to verify the feasibility of the optimization scheme, the external characteristics of the prototype pump and the optimization pump under rated operating conditions are simulated respectively (where rated ow Q d 50 m 3 /h), and the simulation results are shown in Table 5.
According to the simulation results of the external characteristics, the optimization pump e ciency is improved by

Experimental Verification
In order to verify the accuracy of immune particle swarm optimization, an external characteristic test bench is built with IH model horizontal stainless steel chemical centrifugal pump, as shown in Figures 7 and 8, respectively.IH model chemical pump is mainly composed of pump body, shaft key, impeller nut, packing ring, brake pad, packing gland, shaft, pump cover, and suspension bearing components.e chemical pump has the advantages of reasonable and reliable layout of water conservancy, small size, light weight, good anticavitation performance, low power consumption, easy maintenance, and high work efficiency.
Based on the optimized impeller structure parameters given in Table 4, the impeller is made as shown in Figure 9, and the impeller material is made of transparent rigid polyvinyl chloride.e internal flow field of centrifugal pump is measured under 6 working conditions of 0.2Q d , 0.4Q d , 0.6Q d , 0.8Q d , 1.0Q d , and 1.2Q d .Figure 10 shows the external characteristic curves of the prototype pump and the optimization pump.
According to the pump characteristic curves, the experimental values of the optimization pump and the prototype pump are in good agreement, which can accurately reflect the change trend of η, H, and NPSH r with the variation of flow rate.

Advances in Materials Science and Engineering
ere is a small error between the simulation value and the experimental value; the main reason is that, in the numerical simulation experiment of centrifugal pump hydraulic design, the leakage of impeller sealing ring, volume loss caused by axial force, and mechanical loss caused by centrifugal pump in the working process is not considered.
e experimental results of each index of prototype pump and optimization pump under di erent working conditions are extracted from Figure 10, as shown in Table 6.
As can be seen from Table 6, under di erent working conditions, the optimization pump e ciency and head are all larger than the prototype pump, and the optimization pump NPSH r is less than the prototype pump.At the rated ow rate, the optimization pump e ciency is increased by 13.30%, the head is increased by 11.52%, and NPSH r is decreased by 10.14%, which achieve the desired optimization goal.
In summary, every index of the optimization pump has been signi cantly improved, and it can be concluded that the immune particle swarm optimization algorithm is feasible; the control strategy is further veri ed by the centrifugal pump external characteristic test.

Conclusion
(1) e hydraulic design of desulfurization dust removal centrifugal pump was carried out by the velocity

( 6 )
Determination of blade inlet and outlet angle e recommended blade inlet angle is β ′

Table 1 :
e main structural parameters of impeller.

Table 5 :
Simulation results of external characteristics.

Table 6 :
Experimental results of prototype pump and optimization pump.