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

Authors: Yuqin Wang; Xinwang Huo; Hailong Ji
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

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. The 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). The optimal mathematical model with the highest efficiency and the lowest pump net positive suction headNPSHr as the objective function was established under the condition of no curve hump. The immune particle swarm optimization algorithm was used to optimize the multiobjective function, and the optimal combination of the main parameters was obtained. The 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 IH model 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%. The 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.


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## Body

## 1. 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. The 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 [2–8]. 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 NPSHr 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.


## 2. Calculation of Mathematical Model for Desulfurization Dust Removal Centrifugal Pump

### 2.1. Hydraulic Design

The hydraulic design of desulfurization dust removal centrifugal pump is carried out by the velocity coefficient method [9], in which rotational speed n=1450r/min, flow rate Q=50m3/h, and head H=20m.The design of desulfurization dust removal centrifugal pump is a single suction impeller: pump specific speedns=3.65nQ/H3/4=65.95, hydraulic efficiency ηh=1+0.0835lgQ/n1/3=0.860, volumetric efficiency ηv=1/1+0.68ns−2/3=0.960, and mechanical efficiency ηm=1−0.071/ns/1007/6=0.886.


### 2.2. 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.(1)
Calculation of the suction port and outlet diameter of centrifugal pumpPump inlet flow rateVS=2.76m/s, pump suction port diameter DS=4Q/πVS=80mm, and pump outlet diameter Dd=1−0.7DS=80–56mm.(2)
Determination of impeller inlet diameterD1Impeller equivalent diameter is(1)D0=k0Qn1/3=84.9mm,where k0 is the impeller inlet coefficient, taking into account the cavitation and efficiency of centrifugal pump, and k0 takes 4.0.Hub diameter is(2)dh=1.4d=28mm,in which pump shaft diameter d=20mm.Impeller inlet diameterD1=D02+dh2=89.4mm.(3)
Determination of impeller outlet diameterD2Impeller outlet diameter is(3)D2=KD2Qn1/3=256.7mm,where KD2=12.09.(4)
Determination of impeller outlet widthb2The calculation formula of impeller outlet width is [9](4)b2=Kb2Qn1/3=12.1mm,where Kb2=0.7ns/1005/6=0.57.(5)
Determination of impeller inlet widthb1First, the impeller inlet velocityv0 is determined, and then the impeller inlet width b1 is calculated:(5)v0=k02gH=2.06m/s,where k0=0.026542+0.001247ns−0.000001ns2=0.104.Impeller inlet width isb1=ηvQ/πDjv0=22.9mm.(6)
Determination of blade inlet and outlet angleThe recommended blade inlet angle isβ′1=20∘–25∘, and the impact angle is Δβ=3∘–15∘.Due toβ1=β′1+Δβ=23∘–40∘, the selected inlet angle is β1=30∘.Considering that the value ofβ2 is usually within the range of 16∘–40∘, the outlet angle β1=30∘ for this design is selected.(7)
Determination of the number of bladesZ(6)Z=6.5D2+D1D2−D1sinβ1+β22=5.2.(8)
Calculation of blade thickness and selection of blade packing angleCalculation of blade thickness is(7)S=AD2HZ=2.13mm,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 angleφ is 90∘–120∘ because the specific speed of the pump is lower, and φ takes 120∘.(9)
Determination of impeller structure parametersIn summary, the main structural parameters of impeller are shown in Table1.Table 1
The main structural parameters of impeller.
Parameters
Calculation results
Final results
D
S (mm)
80
80
D
d (mm)
56–80
65
D
1 (mm)
89.4
90
D
2 (mm)
256.6
260
b
1 (mm)
12.1
12.5
b
2 (mm)
22.9
23
β
1 (°)
23–40
30
β
2 (°)
16–40
30
Z
5.2
6
S (mm)
2.13
3
φ (°)
90–120
120


### 2.3. Calculation of Main Structural Parameters of Vortex Chamber

(1)
Calculation of base circle diameter and vortex chamber inlet widthSince the base circle diameter calculation formula is:D3=1.03–1.08D2=267.8–280.8mm, the selected base circle diameter D3 = 270 mm.Vortex chamber inlet width isb3=b2+0.05D2=25.5mm.(2)
Calculation of each section area of vortex chamberFor convenience of calculation and drawing, circular vortex chamber and 8 equal parts are selected. The average velocityv3 of the vortex chamber is(8)v3=k32gH=9.11m/s,in which the velocity coefficient k3=0.46.The calculation formula of each section area is(9)Fi=i8⋅Qv3,where i takes 1 to 8, respectively.The calculation results of each section area of vortex chamber are shown in Table2.Table 2
Vortex section area.
Section
1
2
3
4
5
6
7
8
Area
cm
2
1.91
3.81
5.72
7.63
9.53
11.44
13.34
15.25


## 2.1. Hydraulic Design

The hydraulic design of desulfurization dust removal centrifugal pump is carried out by the velocity coefficient method [9], in which rotational speed n=1450r/min, flow rate Q=50m3/h, and head H=20m.The design of desulfurization dust removal centrifugal pump is a single suction impeller: pump specific speedns=3.65nQ/H3/4=65.95, hydraulic efficiency ηh=1+0.0835lgQ/n1/3=0.860, volumetric efficiency ηv=1/1+0.68ns−2/3=0.960, and mechanical efficiency ηm=1−0.071/ns/1007/6=0.886.


## 2.2. 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.(1)
Calculation of the suction port and outlet diameter of centrifugal pumpPump inlet flow rateVS=2.76m/s, pump suction port diameter DS=4Q/πVS=80mm, and pump outlet diameter Dd=1−0.7DS=80–56mm.(2)
Determination of impeller inlet diameterD1Impeller equivalent diameter is(1)D0=k0Qn1/3=84.9mm,where k0 is the impeller inlet coefficient, taking into account the cavitation and efficiency of centrifugal pump, and k0 takes 4.0.Hub diameter is(2)dh=1.4d=28mm,in which pump shaft diameter d=20mm.Impeller inlet diameterD1=D02+dh2=89.4mm.(3)
Determination of impeller outlet diameterD2Impeller outlet diameter is(3)D2=KD2Qn1/3=256.7mm,where KD2=12.09.(4)
Determination of impeller outlet widthb2The calculation formula of impeller outlet width is [9](4)b2=Kb2Qn1/3=12.1mm,where Kb2=0.7ns/1005/6=0.57.(5)
Determination of impeller inlet widthb1First, the impeller inlet velocityv0 is determined, and then the impeller inlet width b1 is calculated:(5)v0=k02gH=2.06m/s,where k0=0.026542+0.001247ns−0.000001ns2=0.104.Impeller inlet width isb1=ηvQ/πDjv0=22.9mm.(6)
Determination of blade inlet and outlet angleThe recommended blade inlet angle isβ′1=20∘–25∘, and the impact angle is Δβ=3∘–15∘.Due toβ1=β′1+Δβ=23∘–40∘, the selected inlet angle is β1=30∘.Considering that the value ofβ2 is usually within the range of 16∘–40∘, the outlet angle β1=30∘ for this design is selected.(7)
Determination of the number of bladesZ(6)Z=6.5D2+D1D2−D1sinβ1+β22=5.2.(8)
Calculation of blade thickness and selection of blade packing angleCalculation of blade thickness is(7)S=AD2HZ=2.13mm,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 angleφ is 90∘–120∘ because the specific speed of the pump is lower, and φ takes 120∘.(9)
Determination of impeller structure parametersIn summary, the main structural parameters of impeller are shown in Table1.Table 1
The main structural parameters of impeller.
Parameters
Calculation results
Final results
D
S (mm)
80
80
D
d (mm)
56–80
65
D
1 (mm)
89.4
90
D
2 (mm)
256.6
260
b
1 (mm)
12.1
12.5
b
2 (mm)
22.9
23
β
1 (°)
23–40
30
β
2 (°)
16–40
30
Z
5.2
6
S (mm)
2.13
3
φ (°)
90–120
120


## 2.3. Calculation of Main Structural Parameters of Vortex Chamber

(1)
Calculation of base circle diameter and vortex chamber inlet widthSince the base circle diameter calculation formula is:D3=1.03–1.08D2=267.8–280.8mm, the selected base circle diameter D3 = 270 mm.Vortex chamber inlet width isb3=b2+0.05D2=25.5mm.(2)
Calculation of each section area of vortex chamberFor convenience of calculation and drawing, circular vortex chamber and 8 equal parts are selected. The average velocityv3 of the vortex chamber is(8)v3=k32gH=9.11m/s,in which the velocity coefficient k3=0.46.The calculation formula of each section area is(9)Fi=i8⋅Qv3,where i takes 1 to 8, respectively.The calculation results of each section area of vortex chamber are shown in Table2.Table 2
Vortex section area.
Section
1
2
3
4
5
6
7
8
Area
cm
2
1.91
3.81
5.72
7.63
9.53
11.44
13.34
15.25


## 3. Three-Dimensional Modeling and Flow Field Analysis of Desulfurization Dust Removal Centrifugal Pump

### 3.1. Centrifugal Pump Three-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 [10–12]. The 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.Figure 1
Centrifugal pump three-dimensional model.


### 3.2. Grid Division

Pumplinx is a software developed for the hydraulic simulation and calculation of pump, which provides engineers with fast and accurate calculation results. The three-dimensional model of centrifugal pump is imported into the Pumplinx 3.4 software, and the Cartesian grid is divided, as shown in Figure2; a total of 78668 grids are obtained.Figure 2
Grid division.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 pumpη, H, and NPSHr under the same working conditions. Grid independence analysis is shown in Table 3 [13].Table 3
Grid independence analysis.
Schemes
Grid numbers
η
%
H
m
N
P
S
H
r
m
1
60000
81.63
16.76
1.03912
2
65000
81.75
18.65
1.03961
3
70000
82.23
19.24
1.04022
4
75000
82.25
19.28
1.04026
5
80000
82.27
19.32
1.04033
6
85000
82.29
19.33
1.04035As can be seen from Table3, 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. Therefore, 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.


### 3.3. Boundary Condition Setting

Before the flow field simulation, the boundary conditions are set. The rotating speed of impeller isn=1450r/min, the flow rate of pump is Q=50m3/h, the fluid medium is selected by water, and the turbulence model is selected as the k−ε model. The interface coupling between impeller and volute is coupled with dynamic-static interface. The inlet adopts the speed inlet boundary condition, the outlet boundary adopts the free outlet, and the surface of the solid wall has no slip.


### 3.4. Flow Field Simulation

After setting the parameters, the flow field is simulated by Pumplinx 3.4 software. Figure3 shows the pressure contour diagram, velocity contour diagram, and cavitation contour diagram of desulfurization dust removal centrifugal pump, respectively.Figure 3
Prototype pump flow field simulation. (a) Pressure contour diagram. (b) Velocity contour diagram. (c) Cavitation contour diagram.
(a)
(b)
(c)According to Figure3(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 Figure3(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 wall is uneven, and the vortex phenomenon is easy to appear, which affects the normal flow of fluid.As shown in Figure3(c), there is a large range of cavitation in the blades near the impeller inlet. This is because the impeller inlet pressure is very low, to reach the critical pressure of fluid at room temperature, resulting in cavitation phenomenon.


## 3.1. Centrifugal Pump Three-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 [10–12]. The 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.Figure 1
Centrifugal pump three-dimensional model.


## 3.2. Grid Division

Pumplinx is a software developed for the hydraulic simulation and calculation of pump, which provides engineers with fast and accurate calculation results. The three-dimensional model of centrifugal pump is imported into the Pumplinx 3.4 software, and the Cartesian grid is divided, as shown in Figure2; a total of 78668 grids are obtained.Figure 2
Grid division.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 pumpη, H, and NPSHr under the same working conditions. Grid independence analysis is shown in Table 3 [13].Table 3
Grid independence analysis.
Schemes
Grid numbers
η
%
H
m
N
P
S
H
r
m
1
60000
81.63
16.76
1.03912
2
65000
81.75
18.65
1.03961
3
70000
82.23
19.24
1.04022
4
75000
82.25
19.28
1.04026
5
80000
82.27
19.32
1.04033
6
85000
82.29
19.33
1.04035As can be seen from Table3, 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. Therefore, 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.


## 3.3. Boundary Condition Setting

Before the flow field simulation, the boundary conditions are set. The rotating speed of impeller isn=1450r/min, the flow rate of pump is Q=50m3/h, the fluid medium is selected by water, and the turbulence model is selected as the k−ε model. The interface coupling between impeller and volute is coupled with dynamic-static interface. The inlet adopts the speed inlet boundary condition, the outlet boundary adopts the free outlet, and the surface of the solid wall has no slip.


## 3.4. Flow Field Simulation

After setting the parameters, the flow field is simulated by Pumplinx 3.4 software. Figure3 shows the pressure contour diagram, velocity contour diagram, and cavitation contour diagram of desulfurization dust removal centrifugal pump, respectively.Figure 3
Prototype pump flow field simulation. (a) Pressure contour diagram. (b) Velocity contour diagram. (c) Cavitation contour diagram.
(a)
(b)
(c)According to Figure3(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 Figure3(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 wall is uneven, and the vortex phenomenon is easy to appear, which affects the normal flow of fluid.As shown in Figure3(c), there is a large range of cavitation in the blades near the impeller inlet. This is because the impeller inlet pressure is very low, to reach the critical pressure of fluid at room temperature, resulting in cavitation phenomenon.


## 4. Centrifugal Pump Optimization Mathematical Model Establishment

In view of the above flow field simulation, with the highest efficiency and the lowestNPSHr as the objective function, the centrifugal pump was optimized with the constraint conditions of no curve hump.


### 4.1. Maximum Efficiency Model of Centrifugal Pump

According to the Stodola formula, when the inlet has no prerotating, the theoretical head of the centrifugal pump is [14](10)HT=1gσπnD2602−Qn60ηvb2ψ2tanβ2,where σ=1−π/Zsinβ2, σ denotes the slip coefficient, and ψ2 denotes the impeller outlet exclusion coefficient.The total efficiency of centrifugal pump is expressed as(11)1η=PmρgQH+HTAHT−S1,where Pm is the centrifugal pump mechanical loss and S1 is the hydraulic loss.Whenη is the largest, 1/η is the smallest, and the highest efficiency objective function is(12)minf1x=1η=PmρgQH+HTAHT−S1.


### 4.2. Centrifugal Pump MinimumNPSHr Model

The expression of centrifugal pumpNPSHr is [15](13)NPSHr=12g1+λk2242Q2D04π2ηv2+λk12π2n2D02602×2g,where λ is the inlet pressure drop coefficient of the blade, and k1 and k2 are the coefficients.Centrifugal pumpNPSHr objective function is(14)minf2x=NPSHr.In summary, the total objective function is(15)minfx=∑i=12ωifix−fi∗fi∗,where ωi is the weight coefficient and fi∗ is the ideal value of corresponding subobjective function.


### 4.3. Constraint Conditions

In order to avoid the problem of curve hump in centrifugal pump, according to empirical function, the following should be satisfied [16]:(16)β2Z0.773<90.According to the requirements of optimization design, the scope of design variables is adjusted appropriately, and other constraints can be obtained:(17)3Qn3<D1<4.5Qn3,Q4.5Q/n3Km12gH<b1<Q3Q/n3Km12gH,9ns100−1/2Qn3<D2<10.5ns100−1/2Qn3,0.6ns1005/6Qn3<b2<0.9ns1005/6Qn3,23°<β1<40°,10°<β2<40°,90°<φ<130°,4<Z<9.


## 4.1. Maximum Efficiency Model of Centrifugal Pump

According to the Stodola formula, when the inlet has no prerotating, the theoretical head of the centrifugal pump is [14](10)HT=1gσπnD2602−Qn60ηvb2ψ2tanβ2,where σ=1−π/Zsinβ2, σ denotes the slip coefficient, and ψ2 denotes the impeller outlet exclusion coefficient.The total efficiency of centrifugal pump is expressed as(11)1η=PmρgQH+HTAHT−S1,where Pm is the centrifugal pump mechanical loss and S1 is the hydraulic loss.Whenη is the largest, 1/η is the smallest, and the highest efficiency objective function is(12)minf1x=1η=PmρgQH+HTAHT−S1.


## 4.2. Centrifugal Pump MinimumNPSHr Model

The expression of centrifugal pumpNPSHr is [15](13)NPSHr=12g1+λk2242Q2D04π2ηv2+λk12π2n2D02602×2g,where λ is the inlet pressure drop coefficient of the blade, and k1 and k2 are the coefficients.Centrifugal pumpNPSHr objective function is(14)minf2x=NPSHr.In summary, the total objective function is(15)minfx=∑i=12ωifix−fi∗fi∗,where ωi is the weight coefficient and fi∗ is the ideal value of corresponding subobjective function.


## 4.3. Constraint Conditions

In order to avoid the problem of curve hump in centrifugal pump, according to empirical function, the following should be satisfied [16]:(16)β2Z0.773<90.According to the requirements of optimization design, the scope of design variables is adjusted appropriately, and other constraints can be obtained:(17)3Qn3<D1<4.5Qn3,Q4.5Q/n3Km12gH<b1<Q3Q/n3Km12gH,9ns100−1/2Qn3<D2<10.5ns100−1/2Qn3,0.6ns1005/6Qn3<b2<0.9ns1005/6Qn3,23°<β1<40°,10°<β2<40°,90°<φ<130°,4<Z<9.


## 5. Immune Particle Swarm Control Algorithm Design

The immune particle swarm algorithm is a new improved particle swarm algorithm based on the immune mechanism of the biological system. The 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:(18)J=∫0∞ω1et+ω2u2tdt,where et is the system error, ut 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(19)if⁡eyt<0,J=∫0∞ω1et+ω2u2t+ω3eytdt.where eyt=yt−yt−1 and yt is the system output.Fitness functionf=1/J, and the greater the fitness, the higher the accuracy of particles.The parameter optimization process is shown in Figure4 [17, 18].Figure 4
Parameter optimization process.


## 6. Optimization Design of Desulfurization Dust Removal Centrifugal Pump

### 6.1. Parameter Determination

By calculating, the constraints could be obtained as follows:63.7mm<D1<95.6mm, 21.6mm<b1<32.4mm, 235.4mm<D2<274.6mm, 9.0mm<b2<13.5mm, 23° < β1 < 40°, 10° < β2 < 40°, 90° < φ < 130°, and 4<Z<9.Particle sizeN=60, maximum number of iterations maxDT=200, learning factor c1=c2=1.624, inertia weight coefficient ω=0.628, crossover probability pc=0.576, mutation probability pm=0.01−1:1:N∗0.01/N, and weight ω1=0.003, ω2=0.87, andω3=96.


### 6.2. Analysis of Results after Optimization

The immune particle swarm algorithm is programmed by Matlab 7.0 software, and the iterative result of optimal solution is shown in Figure5.Figure 5
Optimal solution iterative process.The optimized parameters of impeller are shown in Table4.Table 4
Impeller parameter optimization results.
Parameters
D
1 (mm)
b
1 (mm)
D
2 (mm)
b
2 (mm)
β
1 (°)
β
2 (°)
φ (°)
Z
Prototype pump
90
23
260
12.5
30
30
120
6
Optimization pump
94
26
262
11
28
18
110
6


### 6.3. 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 Figure6.Figure 6
Optimization pump flow field simulation. (a) Optimized pressure contour diagram. (b) Optimized velocity contour diagram. (c) Optimized cavitation contour diagram.
(a)
(b)
(c)As can be seen from Figure6(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 Figure6(b), the velocity of the fluid near the volute wall of the optimization pump is relatively uniform, and the vortex phenomenon is avoided.As can be seen from Figure6(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 effect of the initial design structure of centrifugal pump has been significantly improved, and the overall performance of centrifugal pump has a certain promotion.


### 6.4. 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 flowQd=50m3/h), and the simulation results are shown in Table 5.Table 5
Simulation results of external characteristics.
Optimization index
Prototype pump
Optimization pump
Optimization rate (%)
η
%
82.28
92.23
12.09
H
m
19.31
21.43
10.98
N
P
S
H
r
m
1.04030
0.94876
8.80According to the simulation results of the external characteristics, the optimization pump efficiency is improved by 12.09%, the head is increased by 10.98%, andNPSHr is reduced by 8.80%. At the same time, β2Z0.773 before and after optimization are 119.85 and 71.91, respectively, and the curve hump is eliminated.


## 6.1. Parameter Determination

By calculating, the constraints could be obtained as follows:63.7mm<D1<95.6mm, 21.6mm<b1<32.4mm, 235.4mm<D2<274.6mm, 9.0mm<b2<13.5mm, 23° < β1 < 40°, 10° < β2 < 40°, 90° < φ < 130°, and 4<Z<9.Particle sizeN=60, maximum number of iterations maxDT=200, learning factor c1=c2=1.624, inertia weight coefficient ω=0.628, crossover probability pc=0.576, mutation probability pm=0.01−1:1:N∗0.01/N, and weight ω1=0.003, ω2=0.87, andω3=96.


## 6.2. Analysis of Results after Optimization

The immune particle swarm algorithm is programmed by Matlab 7.0 software, and the iterative result of optimal solution is shown in Figure5.Figure 5
Optimal solution iterative process.The optimized parameters of impeller are shown in Table4.Table 4
Impeller parameter optimization results.
Parameters
D
1 (mm)
b
1 (mm)
D
2 (mm)
b
2 (mm)
β
1 (°)
β
2 (°)
φ (°)
Z
Prototype pump
90
23
260
12.5
30
30
120
6
Optimization pump
94
26
262
11
28
18
110
6


## 6.3. 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 Figure6.Figure 6
Optimization pump flow field simulation. (a) Optimized pressure contour diagram. (b) Optimized velocity contour diagram. (c) Optimized cavitation contour diagram.
(a)
(b)
(c)As can be seen from Figure6(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 Figure6(b), the velocity of the fluid near the volute wall of the optimization pump is relatively uniform, and the vortex phenomenon is avoided.As can be seen from Figure6(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 effect of the initial design structure of centrifugal pump has been significantly improved, and the overall performance of centrifugal pump has a certain promotion.


## 6.4. 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 flowQd=50m3/h), and the simulation results are shown in Table 5.Table 5
Simulation results of external characteristics.
Optimization index
Prototype pump
Optimization pump
Optimization rate (%)
η
%
82.28
92.23
12.09
H
m
19.31
21.43
10.98
N
P
S
H
r
m
1.04030
0.94876
8.80According to the simulation results of the external characteristics, the optimization pump efficiency is improved by 12.09%, the head is increased by 10.98%, andNPSHr is reduced by 8.80%. At the same time, β2Z0.773 before and after optimization are 119.85 and 71.91, respectively, and the curve hump is eliminated.


## 7. 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 Figures7 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. The 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.Figure 7
IH model chemical pump.Figure 8
External characteristic 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, and (10) water tank.Based on the optimized impeller structure parameters given in Table4, the impeller is made as shown in Figure 9, and the impeller material is made of transparent rigid polyvinyl chloride. The internal flow field of centrifugal pump is measured under 6 working conditions of 0.2Qd, 0.4Qd, 0.6Qd, 0.8Qd, 1.0Qd, and 1.2Qd. Figure 10 shows the external characteristic curves of the prototype pump and the optimization pump.Figure 9
Test impeller.Figure 10
External characteristic curves of prototype pump and optimization pump. (a)η‐Q, (b) H‐Q, and (c) NPSHr-Q.
(a)
(b)
(c)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 ofη, H, and NPSHr with the variation of flow rate.There 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.The experimental results of each index of prototype pump and optimization pump under different working conditions are extracted from Figure10, as shown in Table 6.Table 6
Experimental results of prototype pump and optimization pump.
Indexes
Q
m
3
/
h
10
20
30
40
50
60
Prototype pumpη%
32.12
51.77
63.36
72.69
74.43
71.24
Optimization pumpη%
33.46
55.06
69.44
79.17
84.33
79.71
Δ
η
%
4.17
6.36
9.60
8.91
13.30
11.89
Prototype pumpHm
20.36
20.11
19.49
18.53
18.06
15.97
Optimization pumpHm
22.97
22.22
21.55
21.41
20.14
17.64
Δ
H
%
12.82
10.49
10.57
15.54
11.52
10.46
Prototype pumpNPSHrm
1.09198
1.05678
1.02558
1.01914
0.95987
0.84287
Optimization pumpNPSHrm
0.97007
0.9584
0.92943
0.88455
0.86255
0.76461
Δ
N
P
S
H
r
%
11.16
9.31
9.38
13.21
10.14
9.28As can be seen from Table6, under different working conditions, the optimization pump efficiency and head are all larger than the prototype pump, and the optimization pump NPSHr is less than the prototype pump. At the rated flow rate, the optimization pump efficiency is increased by 13.30%, the head is increased by 11.52%, and NPSHr is decreased by 10.14%, which achieve the desired optimization goal.In summary, every index of the optimization pump has been significantly improved, and it can be concluded that the immune particle swarm optimization algorithm is feasible; the control strategy is further verified by the centrifugal pump external characteristic test.


## 8. Conclusion

(1)
The hydraulic design of desulfurization dust removal centrifugal pump was carried out by the velocity coefficient method, and the main structural parameters of impeller and volute were obtained. The three-dimensional model of centrifugal pump was established by CFturbo 10.0 software, and the centrifugal pump was numerically simulated and analyzed by Pumplinx 3.4 software.
(2)
An optimization mathematical model with the highest efficiency and the lowestNPSHr as the objective function was established under the condition of no curve hump. A total of eight indexes of D1, b1, D2, b2, β1, β2, φ, and Z were optimized by the immune particle swarm algorithm.
(3)
Through the simulation and analysis of the optimization results, the optimization pump efficiency was increased from 82.28% to 92.23%, the head was increased from 19.31 m to 21.43 m, andNPSHr was decreased from 1.04030 m to 0.94876 m; the curve hump problem was eliminated. The overall performance of centrifugal pump was improved significantly, and the feasibility of immune particle swarm optimization was verified.
(4)
Based on the IH model chemical pump, the external characteristic test bench was built, and the external characteristic curves of each index parameter of centrifugal pump under different working conditions were obtained. The variation law of experimental values of all index parameters was basically consistent before and after optimization, and compared with the prototype pump, the experimental values of the optimization pump were significantly improved. The accuracy of the immune particle swarm optimization control strategy was verified, which provided some reference value for the structural optimization design of desulfurization dust removal centrifugal pump in the future.
(5)
Taking centrifugal pump as the research object, the main indexes of centrifugal pump were optimized by immune particle swarm optimization algorithm, which improved the hydraulic performance of centrifugal pump. Due to the limitation of research conditions, this paper only studied the optimization of pump efficiency, head, andNPSHr, without considering the optimization of other indicators. In the following research work, based on immune particle swarm optimization control strategy, the influence of the main geometric parameters of centrifugal pump on the pump characteristics will be considered comprehensively, in order to improve the working performance of centrifugal pump.



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*Source: 6294824-2018-03-21.xml*