In order to determine the optimal structural parameters of a plastic centrifugal pump in the framework of an orthogonal-experiment approach, a numerical study of the related flow field has been performed using CFX. The thickness S, outlet angle β2, inlet angle β1, wrap angle, and inlet diameter D1 of the splitter blades have been considered as the variable factors, using the shaft power and efficiency of the pump as evaluation indices. Through a parametric analysis, the relative importance of the influence of each structural parameter on each evaluation index has been obtained, leading to the following combinations: β1 19°, β2 35°, S 2 mm, wrap angle 154°, and D1 85 mm (corresponding to the maximum efficiency of 75.48%); β1 19°, β2 20°, S 6 mm, wrap angle 158°, and D1 81 mm (corresponding to the minimum shaft power of 75.48%). Moreover, the grey correlation method has been applied to re-optimize the shaft power and efficiency of the pump, leading to the following optimal combination: β1 19°, β2 15°, S 4 mm, D1 81 mm, and wrap angle 152° (corresponding to the maximum efficiency of 71.81% and minimum shaft power of 2.187 kW).

In recent years, pumps have been used in various industries, becoming the second most popular machinery [

Geng et al. [

Korkmaz et al. [

Kergourlay et al. [_{9} (3^{4}) experimental table, calculated the lift and efficiency of the 9 design schemes under the rated flow, and adopted the range The analysis method is used to process and an optimized model is obtained.

In this study, CFX was employed to numerically simulate the flow field of a plastic centrifugal pump. An orthogonal experiment was conducted with such structural parameters as the thickness S, outlet angle β_{2}, inlet angle β_{1}, wrap angle, and inlet diameter D_{1} of the splitter blades as five factors, taking the shaft power and efficiency as evaluation indices. Through range analysis of the orthogonal experiment, the ranking of the influence of each structural parameter on each evaluation index was obtained. Moreover, the grey correlation method was used to achieve the multi-objective optimization of the shaft power and efficiency.

It is a low specific speed centrifugal pump, whose main parameters are listed in

Parameter | Flow rate ^{3} ⋅ ^{−1} |
Head |
Rotational speed |
---|---|---|---|

Value | 50 | 10 | 1450 |

The hydraulic design of the pump was the first step in this study, and the structural parameters of the design would significantly affect the pump’s performance [

Inlet diameter and inlet velocity of the pump

_{s} − Inlet diameter (m);

^{3}/h);

_{s} − Inlet velocity (m/s);

Then, the inlet velocity _{s} = 2.76 m/s [_{s} = 80 mm.

Outlet diameter and outlet velocity of the pump

The outlet diameter of the pump is calculated according to

_{d} − Outlet diameter (mm).

The connection coefficient is 0.9; then, the outlet diameter _{d} = 72 mm.

The outlet velocity is calculated according to

_{d}–Outlet velocity (m/s).

Then, _{d} = 3.41 m/s.

Specific speed

_{s}−Specific speed;

Then,

Hydraulic efficiency of the pump

The hydraulic efficiency of the pump is calculated according to

Then, _{h} = 0.86.

Volumetric efficiency of the pump

The volumetric efficiency of the pump is calculated according to

Then, _{v} = 0.97.

Mechanical efficiency of the pump

The mechanical efficiency of the disc friction loss is calculated according to

Then, _{m} = 0.88.

Total efficiency of the pump

The total efficiency of the pump is calculated according to

Then, η = 0.74.

Shaft power and motor power

The power of the pump is calculated according to

^{3});

^{2}).

where, ^{3}, and g = 9.81 m/s^{2}. Then, P = 1.774 kW.

Motor Power

_{t}−Transmission efficiency, with a direct drive motor;

Then, P_{c }=_{ }2.148 kW.

The motor output torque is calculated according to

Then, _{n} = 14.147(

The impeller of a centrifugal pump usually takes a semi-open or closed structure. A semi-open impeller has high strength and is easy to shape. Hence, it became the first choice in this study. Its structure is shown in

There are plenty of design methods for the impeller, but the parameters in them do not vary significantly. In this study, the speed coefficient method was applied to calculate the structural parameters of the impeller [

Inlet diameter of the impeller

The equivalent diameter of the impeller inlet is calculated according to

_{0}-Coefficient,

Then, _{0} = 95.568

The inlet diameter of the impeller is calculated according to

_{h}−Hub diameter (mm);

_{h} is valid only for structural design. For hydraulic design, _{h} = 0; then,

The blade inlet diameter is estimated as follows:

_{1}-Coefficient, generally _{1} = 0.7 ∼ 1.0;

The coefficient _{1} is determined by the specific speed. It takes a larger value for a low specific speed and a smaller value for a high specific speed. According to the specific speed in this study, _{1} = 0.85; then, _{1} = 85

Inlet width of the impeller

The inlet width of the impeller is calculated according to

_{1}−Ratio of the impeller inlet velocity to the inlet diameter.

Generally, _{1} = 0.9∼1.0; then, substiute D_{1 }=_{ }80 mm, k_{1 }=_{ }0.85 into _{1 }=_{ }25 mm.

Outlet diameter of the impeller

The outlet diameter of the impeller is estimated according to

_{D}–_{2} Correction coefficient.

_{D} is related to the type and specific speed of the pump. This study’s subject is a single-stage pump, and its specific speed _{s} = 89.56. Then, substitute _{2 }=_{ }210 mm.

Outlet width of the impeller

The outlet width of the impeller is calculated according to

_{b}−_{2} Correction coefficient.

_{b} is related to the type and specific speed of the pump. This study’s subject is a single-stage pump, and its specific speed _{s} = 89.56. Then, substitute _{2 }=_{ }15 mm.

Number of blades

The number of blades according to

The values of _{1}, _{2}, _{1}, _{2} are substituted into

Inlet and outlet mounting angle of the impeller

In this study, the inlet mounting angle β_{1} is 19°, outlet mounting angle 33°, and wrap angle 123° [

Blade thickness design

The blade is a three-dimensional irregular curved surface, whose accurate thickness was difficult to obtain. For convenience, approximate calculations were used to obtain the blade thickness, then proved by the approximate relationship between geometric figures.

_{u}). _{m}. The relationship of these parameters is as follows [

_{r}–Radial thickness;

ε–Angle between the axial streamline and the horizontal plane.

In this study, the inlet mounting angle β_{1}, outlet mounting angle β_{2}, and wrap angle

It can be seen from

The thinner the blades are, the wider the flow channel is. Then, the slip coefficient is reduced, and the efficiency of the pump is increased. The blades cannot be too thick; otherwise, their strength will be insufficient, and the impeller will deform. Similarly, the thicker the blades are, the narrower the flow channel is. Then, the relative velocity of the fluid in the flow channel becomes larger, and the hydraulic loss is increased. Therefore, in this study, the blade thickness was taken as 2 mm.

The flow parts of a pump include an impeller and a volute. The volute is an energy converter. In this study, its main dimensions were designed as follows [

Diameter of the base circle D_{3}

The diameter of the base circle affects the pump’s performance. With D_{3} to represent the base circle, usually take

For a smaller pump with a high specific speed, take a larger coefficient; similarly, for a larger pump with a low specific speed, take a smaller coefficient. In this study, The diameter of the base circle D_{3 }=_{ }210 mm.

Inlet width of the volute b_{3}

The inlet width b_{3} of the volute should be determined considering the 8th cross-section, whose shape approaches to be round or square.

Then, b_{3 }=_{ }25 mm.

Mounting angle of the volute tongue

The mounting angle of the volute tongue is represented by _{0}. According to [_{0} = 22°.

Area of each section

The velocity coefficient method to was applied to calculate the area of each section:

_{3}−Average velocity of the volute section;

_{3}−Velocity coefficient, the value of which is 0.38 according to [

Then, _{3} = 6.52 m/s.

The flow through the 8th section is approximately equal to the actual flow of the pump; hence, the area of the 8th section can be calculated by

The area of other sections are calculated by

The area of each section was obtained as shown in

Section | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Angle/° | 45 | 90 | 135 | 180 | 225 | 270 | 315 | 360 |

Area/cm^{2} |
2.5 | 5 | 7.5 | 10 | 12.5 | 15 | 17.5 | 20 |

The SolidWorks software was used to build the water part of the suction chamber, impeller, and volute of the pump. The inlet and outlet section should be slightly longer to ensure a sufficient flow and reduce the influence of the inlet and outlet section on the water flow so as to improve calculation accuracy. The computational domain model is shown in

In this study, ANSYS ICEM CFD was used to mesh the pump model. In ICEM CFD, the design model of the pump imported from the SolidWorks software was processed, and the minimum mesh size was set for the volute, impeller, inlet section, and outlet section, respectively. Because of the complicated computational domain model which consists of a large number of curved parts, these curved parts were divided into unstructured meshes. The meshing steps are shown in

In order to ensure calculation accuracy, there should be enough meshes in the near-wall area to capture the flow in the boundary layer. y+, as a dimensionless parameter [_{w} is the wall shear stress;

The value of y+ is crucial for the selection of the turbulence model. In the numerical simulation of this study, y+ was around 30. In this study, the k-Epsilon model was chosen as the turbulence model to ensure a high quality of meshes [

In order to reduce the influence of the number of meshes on calculation results, four different numbers of meshes were obtained, and mesh independence analysis was carried out, as shown in

Plan number | Plan 1 | Plan 2 | Plan 3 | Plan 4 |
---|---|---|---|---|

The number of meshes | 894272 | 897732 | 949930 | 955965 |

Head/m | 11.19 | 11.33 | 11.92 | 11.96 |

Efficiency/% | 70.91 | 71.14 | 72.08 | 72.11 |

The inlet boundary condition is usually set to velocity-inlet or pressure-inlet. The velocity inlet boundary condition applies to incompressible flow issues, and the magnitude and direction of the velocity need to be specified. The pressure inlet boundary condition applies to both compressible and incompressible issues. The relationship between the total pressure P_{0}, static pressure Ps, and fluid velocity u of an incompressible flow are as follows:

The average velocity at the inlet was estimated, and then the static pressure was estimated by

In this study, the k-ε turbulence model was adopted. It was necessary to set the turbulent kinetic energy k and dissipation rate because a reasonable initial value of each one is beneficial to the convergence of calculations. The following empirical formulas were used to determine the initial values of k and ε:

where, I is the intensity of the turbulence, u is the average velocity at the inlet, L is the characteristic length (in this study, the value is the diameter of the inlet pipe),

The outlet boundary condition is usually set to outflow or pressure-outlet. The outflow boundary condition is applied when the pressure or velocity at the outlet is unknown. In this study, the outlet boundary condition was calculated internally by FLUENT.

Because the Re number of the flow in the near-wall region is low, and the turbulence is not fully developed, such unique ways as the wall function method and low Re number k-ε model are required. In this study, the wall function method was used to solve this problem. The solid wall satisfied the non-slip condition, which indicates the relative velocity W = 0; the pressure was taken as the second boundary condition, namely _{p} be the distance from the near-wall point P to the wall; then, the values of velocity u_{p} and turbulent energy consumption ε_{p} at P were determined by these following wall functions [_{w} is the wall shear stress; the constants E and k are taken as 9.011 and 0.419, respectively.

The CFX software was applied to read the mesh file as shown in

In the simulation software CFX, turbulence models include k-Omega, SST, RNGK-Epsilon, and k-Epsilon. In the k-Epsilon model, the equations are characterized by dissipative scales. Studies have shown that the model can well predict the flow field within fluid machinery. The RNG k-Epsilon model is an improved version of the standard k-Epsilon turbulence model, applying to the turbulence induced by shear motion. Therefore, the k-Epsilon model was chosen for this numerical simulation to predict the flow field.

The turbulent kinetic energy k and dissipation rate ε were used to construct the transport equations as follows:

where, _{k} is the generation term of the turbulent kinetic energy

Continuity equation:

Under normal circumstances:

Assuming that the fluid is not compressible:

Momentum equation (Navier-Stokes equation):

The sum of the various forces acting on the cell from the outside is equal to the rate of change of the momentum of the fluid cell with respect to time.

_{i} and _{j} are the velocity components, _{t} are the dynamic viscosity and turbulent viscosity of the mixed medium, _{ij} is the Kronecker number, and

In the calculation, the SIMPLEC algorithm was used for the pressure-velocity coupling; the momentum equation, turbulent kinetic energy, and dissipative transport equation were in the second-order windward scheme. In the steady calculation, it converged when the total outlet pressure fluctuated steadily; the unsteady calculation converged when the monitoring results displayed a periodically stable distribution.

In the steady calculation, the “Frozen Rotor” model was used for the two interfaces between the inlet pipe and the impeller and between the impeller and the volute; the General Connection model was used for the interface between the volute and the outlet pipe for they were both stationary. In the unsteady calculation, the “Transient Rotor Stator” model was used for the two interfaces between the inlet pipe and the impeller and between the impeller and the volute, which can capture the interaction between the transient and the stationary state of the rotor in relative motion and take the steady calculation results as the initial conditions for the unsteady calculation [

The non-steady time step size Δt is defined as the impeller’s rotational angle at each computational step:

n--impeller’s rotational speed (r/min);

x--the rotational angle of the impeller in each time step.

After setting the boundary conditions, the number of iterations was set to obtain the residual dynamic monitoring process of the internal flow field of the pump. The number of iterations was set to 1000.

An orthogonal experiment is a method designed through an orthogonal table standardized by mathematical statistics. It is frequently used to handle multi-factor issues. Its basic steps are as follows:

Determine experimental objectives and indices

When designing an orthogonal experiment for selected parameters, it is necessary to determine its experimental objectives and quality evaluation indices.

Select factors and their levels

In an orthogonal experiment, priority should be given to factors that have more pronounced effects on the quality evaluation indices. The number of levels is usually between 2 to 4 for higher experimental efficiency, and the interval of level values should be reasonable.

It is impossible to include all factors affecting the efficiency and shaft power of the pump into the orthogonal experiment table. According to relevant theoretical and practical information, the thickness, outlet angle, inlet angle, wrap angle, inlet diameter of the splitter blades were selected as the five factors of the orthogonal experiment. The selected factors and their level values are shown in _{1}, outlet angle β_{2}, thickness S, inlet diameter D_{1}, and wrap angle, respectively.

Level | Factor | ||||
---|---|---|---|---|---|

β_{1} |
β_{2} |
S | D_{1} |
Wrap angle | |

1 | 15° | 15° | 2 | 81 | 152° |

2 | 17° | 20° | 3 | 83 | 154° |

3 | 19° | 25° | 4 | 85 | 156° |

4 | 21° | 30° | 5 | 87 | 158° |

5 | 23° | 35° | 6 | 89 | 160° |

For the five-factor and five-level orthogonal experiment, the orthogonal table was L_{25} (25^{5}). The 25 groups of the orthogonal experiment parameters were numerically simulated separately through the CFX simulation software. The results of the orthogonal experiment are shown in

Experiment number | β1 (A) | β2 (B) | S (C) | D_{1} (D) |
Wrap angle (E) | Shaft power (kW) | Efficiency (%) |
---|---|---|---|---|---|---|---|

1 | 20 | 3 | 23 | 152 | 83 | 2.2 | 72.02 |

2 | 35 | 6 | 17 | 152 | 89 | 2.252 | 69.65 |

3 | 25 | 5 | 23 | 154 | 81 | 2.214 | 70.88 |

4 | 35 | 3 | 21 | 156 | 81 | 2.292 | 71.85 |

5 | 15 | 6 | 23 | 160 | 85 | 2.162 | 71.15 |

6 | 35 | 4 | 23 | 158 | 87 | 2.284 | 71.01 |

7 | 20 | 2 | 21 | 160 | 87 | 2.221 | 72.56 |

8 | 25 | 3 | 19 | 160 | 89 | 2.247 | 72.08 |

9 | 25 | 2 | 17 | 158 | 83 | 2.254 | 72.39 |

10 | 15 | 2 | 15 | 152 | 81 | 2.219 | 72.57 |

11 | 30 | 2 | 23 | 156 | 89 | 2.278 | 72.53 |

12 | 30 | 3 | 15 | 158 | 85 | 2.26 | 72.32 |

13 | 20 | 6 | 19 | 158 | 81 | 2.127 | 69.95 |

14 | 15 | 5 | 21 | 158 | 89 | 2.171 | 71.33 |

15 | 35 | 2 | 19 | 154 | 85 | 2.217 | 75.48 |

16 | 25 | 4 | 21 | 152 | 85 | 2.219 | 71.7 |

17 | 30 | 5 | 19 | 152 | 87 | 2.256 | 71.47 |

18 | 15 | 4 | 19 | 156 | 83 | 2.187 | 71.79 |

19 | 25 | 6 | 15 | 156 | 87 | 2.173 | 69.97 |

20 | 15 | 3 | 17 | 154 | 87 | 2.196 | 71.97 |

21 | 20 | 5 | 17 | 156 | 85 | 2.165 | 71.03 |

22 | 30 | 4 | 17 | 160 | 81 | 2.255 | 71.87 |

23 | 20 | 4 | 15 | 154 | 89 | 2.186 | 71.5 |

24 | 35 | 5 | 15 | 160 | 83 | 2.275 | 70.69 |

25 | 30 | 6 | 21 | 154 | 83 | 2.232 | 70.82 |

The R value of each parameter was calculated according to the experimental results in

With the efficiency as the evaluation index, the analysis results are shown in

With the shaft power as the evaluation index, the analysis results are shown in

A | B | C | D | E | |
---|---|---|---|---|---|

K1 | 71.410 | 71.762 | 73.106 | 71.424 | 71.482 |

K2 | 71.382 | 71.412 | 72.048 | 71.542 | 72.130 |

K3 | 72.154 | 71.404 | 71.574 | 72.336 | 71.434 |

K4 | 71.652 | 71.802 | 71.080 | 71.396 | 71.400 |

K5 | 71.518 | 71.736 | 70.308 | 71.418 | 71.670 |

R | 0.77 | 0.40 | 2.798 | 0.94 | 0.73 |

Ranking | 3 | 5 | 1 | 2 | 4 |

A | B | C | D | E | |
---|---|---|---|---|---|

K1 | 2.223 | 2.187 | 2.238 | 2.221 | 2.229 |

K2 | 2.224 | 2.180 | 2.239 | 2.230 | 2.209 |

K3 | 2.207 | 2.221 | 2.226 | 2.205 | 2.219 |

K4 | 2.227 | 2.256 | 2.216 | 2.226 | 2.219 |

K5 | 2.228 | 2.264 | 2.189 | 2.227 | 2.232 |

R | 0.021 | 0.084 | 0.050 | 0.025 | 0.023 |

Ranking | 5 | 1 | 2 | 3 | 4 |

For the efficiency

In _{3}B_{5}C_{1}D_{3}E_{2}, where the maximum efficiency was obtained when the inlet angle blade was 19°, outlet angle 35°, thickness 2 mm, wrap angle 154°, and inlet diameter 85 mm.

The orthogonal experiment results were processed by range analysis, and then the ranking of the influence of each factor on the efficiency was obtained as follows: thickness > inlet diameter > inlet angle > wrap angle > outlet angle.

For the shaft power

In _{4}B_{2}C_{5}D_{4}E_{1}, where the minimum shaft power was obtained when the inlet angle was 21°, outlet angle 20°, thickness 6 mm, wrap angle 158°, and inlet diameter 81 mm.

The ranking of the influence of each factor on the shaft power was obtained as follows: outlet angle > thickness > inlet diameter > wrap angle > inlet angle.

The orthogonal experiment revealed that when the combination of the structural parameters is A_{3}B_{5}C_{1}D_{3}E_{2}, the efficiency is optimal and that when the combination is A_{4}B_{2}C_{5}D_{4}E_{1}, the shaft power is optimal. However, the range and variance processing only reached the optimum of a single index, and it failed to achieve the simultaneous optimization of multiple goals. Therefore, it was necessary to find a set of structural parameter combinations to optimize the shaft power and efficiency simultaneously. Grey correlation analysis is often used to process data in orthogonal experiments, transforming a multi-objective issue into a single-objective issue that is easier to be analyzed.

Grey correlation analysis is used to obtain the correlation grades between some factors, and the correlation grades reveal the effects and contribution rates of the factors to a system [

Construction of the evaluation index matrix

The values of the evaluation indices formed the following evaluation index matrix.

n–Experiment number;

m–Evaluation index number;

_{i}(

Normalization of the evaluation index data

The dimensions of the raw data were different, and the numerical difference between the factors was large, affecting the model’s accuracy. In order to ensure the equivalence between the indices, it is necessary to normalize the raw data to eliminate their dimensions. The formula of normalization processing is shown in

_{i}(

Construction of the grey correlation coefficient matrix

Take the maximum value of each index as the reference sequence:

The formula for calculating the grey correlation coefficient is shown in _{0j}(_{j} − _{i}(_{j} − _{i}(_{j} − _{i}(_{i} is the correlation coefficient of each evaluation index;

The grey correlation coefficient matrix was obtained as follows:

Calculation of the grey correlation grades

According to

Experiment number | Evaluation index matrix | Normalized matrix | Correlation coefficient matrix | Grey correlation grade | |||
---|---|---|---|---|---|---|---|

_{i}(1) |
|||||||

1 | 2.2 | 72.02 | 0.558 | 0.593 | 0.969 | 0.457 | 0.713 |

2 | 2.252 | 69.65 | 0.242 | 1 | 0.986 | 0.333 | 0.660 |

3 | 2.214 | 70.88 | 0.473 | 0.789 | 0.974 | 0.388 | 0.681 |

4 | 2.292 | 71.85 | 0 | 0.623 | 1 | 0.445 | 0.723 |

5 | 2.162 | 71.15 | 0.788 | 0.743 | 0.957 | 0.402 | 0.680 |

6 | 2.284 | 71.01 | 0.048 | 0.767 | 0.997 | 0.395 | 0.696 |

7 | 2.221 | 72.56 | 0.430 | 0.501 | 0.976 | 0.500 | 0.738 |

8 | 2.247 | 72.08 | 0.273 | 0.583 | 0.985 | 0.462 | 0.723 |

9 | 2.254 | 72.39 | 0.230 | 0.530 | 0.987 | 0.485 | 0.736 |

10 | 2.219 | 72.57 | 0.442 | 0.499 | 0.976 | 0.500 | 0.738 |

11 | 2.278 | 72.53 | 0.085 | 0.506 | 0.995 | 0.497 | 0.746 |

12 | 2.26 | 72.32 | 0.194 | 0.542 | 0.989 | 0.480 | 0.735 |

13 | 2.127 | 69.95 | 1 | 0.949 | 0.946 | 0.345 | 0.646 |

14 | 2.171 | 71.33 | 0.733 | 0.712 | 0.960 | 0.413 | 0.687 |

15 | 2.217 | 75.48 | 0.455 | 0 | 0.975 | 1 | 0.987 |

16 | 2.219 | 71.7 | 0.442 | 0.648 | 0.976 | 0.435 | 0.705 |

17 | 2.256 | 71.47 | 0.218 | 0.688 | 0.988 | 0.420 | 0.704 |

18 | 2.187 | 71.79 | 0.636 | 0.633 | 0.965 | 0.441 | 0.703 |

19 | 2.173 | 69.97 | 0.721 | 0.945 | 0.961 | 0.346 | 0.653 |

20 | 2.196 | 71.97 | 0.582 | 0.602 | 0.968 | 0.454 | 0.711 |

21 | 2.165 | 71.03 | 0.770 | 0.763 | 0.958 | 0.396 | 0.677 |

22 | 2.255 | 71.87 | 0.224 | 0.619 | 0.987 | 0.447 | 0.717 |

23 | 2.186 | 71.5 | 0.642 | 0.683 | 0.965 | 0.423 | 0.694 |

24 | 2.275 | 70.69 | 0.103 | 0.822 | 0.994 | 0.378 | 0.686 |

25 | 2.232 | 70.82 | 0.364 | 0.799 | 0.980 | 0.385 | 0.682 |

Through range analysis of the grey correlation grades, the mean values and range values were obtained. The larger the value of a factor, the larger the grey correlation grade and the higher the influence on the evaluation indices, as shown in

Level | A | B | C | D | E |
---|---|---|---|---|---|

1 | 0.333 | 0.714 | 0.556 | 0.553 | 0.561 |

2 | 0.400 | 0.769 | 0.625 | 0.625 | 0.625 |

3 | 0.500 | 0.833 | 0.714 | 0.724 | 0.716 |

4 | 0.667 | 0.909 | 0.833 | 0.831 | 0.835 |

5 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |

Range | 0.667 | 0.286 | 0.444 | 0.447 | 0.439 |

Ranking | 1 | 5 | 3 | 2 | 4 |

Note: A-inlet angle, B-outlet angle, C-thickness, D-inlet diameter, E-wrap angle.

It can be seen from _{3}B_{1}C_{3}D_{1}E_{1} (inlet angle 19°, outlet angle 15°, thickness 4 mm, inlet diameter 81 mm, and wrap angle 152°). This combination has the most significant impact on the shaft power and efficiency, and it is the optimal combination of the structural parameters. The CFX software was used to simulate and analyze the combination of the structural parameters, as shown in

It can be seen from

The structural parameters of the pump were optimized through the orthogonal experiment and grey correlation analysis, and the results are shown in

Index | Ranking | Structural parameter combination | Shaft power (kW) | Efficiency (%) |
---|---|---|---|---|

Shaft power analysis based on the orthogonal experiment | A > C > D > E > B | A_{4}B_{2}C_{5}D_{4}E_{1} |
2.127 | 69.95 |

Efficiency analysis based on the orthogonal experiment | C > D > A > E > B | A_{3}B_{5}C_{1}D_{3}E_{2} |
2.217 | 75.48 |

Comprehensive analysis based on the grey correlation analysis | A > D > C > E > B | A_{3}B_{1}C_{3}D_{1}E_{1} |
2.187 | 71.81 |

Note: A-inlet angle, B-outlet angle, C-thickness, D-inlet diameter, E-wrap angle.

It can be seen from

The efficiency of plastic centrifugal pumps has become the focus in recent studies, while there has been little research on the shaft power of pumps. In this paper, the structural parameters of a plastic centrifugal pump were calculated and modeled, and numerical simulation analysis of the flow field of the model was performed using CFX, in the framework of an orthogonal experiment. The experiment took such structural parameters as the thickness S, outlet angle β_{2}, inlet angle β_{1}, wrap angle, and inlet diameter D_{1} of the splitter blades as five factors, using the shaft power of the pump as the primary evaluation index. Through range analysis, the ranking of the influence of each structural parameter on each evaluation index was obtained. Moreover, the grey correlation method was applied to re-optimize the shaft power and efficiency. The conclusions are as follows:

The order of the influence of the five factors on the efficiency is as follows: the splitter blades’ thickness > inlet diameter > inlet angle > wrap angle > outlet angle. When the splitter blades’ inlet angle is 19°, outlet angle 35°, thickness 2 mm, wrap angle 154°, and inlet diameter 85 mm, the maximum efficiency of 75.48% can be obtained;

The order of the influence of the five factors on the shaft power is as follows: the splitter blades’ outlet angle > thickness > inlet diameter > wrap angle > inlet angle. When the splitter blades’ inlet angle is 19°, outlet angle 20°, thickness 6 mm, wrap angle 158°, and inlet diameter 81 mm, the minimum shaft power of 2.127 kW can be obtained;

The grey correlation method was applied to conduct the multi-objective optimization, leading to the following optimal combination of the structural parameters (A_{3}B_{1}C_{3}D_{1}E_{1}): inlet angle 19°, outlet angle 15°, thickness 4 mm, inlet diameter 81 mm, and wrap angle 152°;

Through CFX analysis of the re-optimized model, its shaft power and efficiency were found to be 2.187 kW and 71.81%, respectively. Neither the shaft power nor the efficiency was optimal among the three groups of the evaluation indices, but they were improved simultaneously. Therefore, it can be concluded that grey correlation analysis is conducive to optimizing the structural parameters of plastic centrifugal pumps.

Based on the above conclusions, further research may be conducted from the following aspects:

The shape of splitter blades should be designed based on the impeller of a pump;

The design of splitter blades involves plenty of structural parameters. However, this paper only analyzed the influence of the thickness, inlet diameter, inlet angle, outlet angle, and wrap angle. In the future, more parameters such as the chord length may also be studied.