To study the influence of blade profiles of the plastic centrifugal pump on pump performance, the impeller blade profiles were designed and drawn by the single arc method, double arc method, logarithmic spiral method, and B-spline curve method, respectively, with the known structural parameters.The shape and size of four profiles were drawn, and two-dimensional models and three-dimensional models of four impellers and volute were completed, respectively. The impeller models were printed by 3D printing technology, and the performance experiments of the plastic centrifugal pump were carried out. The numerical simulation of the internal flow field was performed. From the contours of the velocity and pressure, the vapor volume fraction distribution, and fluid-structure interaction analysis of impellers, the impeller drawn by the logarithmic spiral method was better than others. The optimization of the logarithmic spiral method was completed. The impeller inlet and outlet diameters (
As a type of general machinery, centrifugal pumps are widely used such as in mechanical engineering, aerospace, and petrochemical industries [
The impeller is the core part of the centrifugal pump, and the impeller blade profile plays a vital role in the fluid flow which will directly impact the performance of centrifugal pumps. At present, there have been many studies on the influence of the impeller parameters on the flow characteristics of centrifugal pumps [
The blade profile directly affects the bending of the blade and has an important impact on the fluid flow in the impeller channel. Studying the impact of the blade profile on the performance of the centrifugal pumps is beneficial to improve the performance and efficiency of the centrifugal pumps. Hu et al. [
In existing research studies, the studies on blade profile are mainly focused on metal pumps and a single profile, while only a few pieces of research are on the performance of plastic centrifugal pumps. Moreover, there is no regularity between the various blade profiles and the performance parameters of centrifugal pumps. In this paper, four design methods of blade profiles, which are the single arc method, double arc method, logarithmic spiral method, and B-spline curve method, are proposed and the influence of four kinds of blade profile on plastic centrifugal pump performance is studied. The flow field simulation of pumps with various impellers is analyzed in detail.
Figure
Blade profile of single arc method.
Take a random point (point
The radius of curvature of the single arc:
The principle of the double arc method is to find the radius of rotation according to the drawing method to determine the first arc and then calculate the value of the radius of rotation to determine the second arc according to the formula.
In Figure
Blade profile of double arc method.
The value of
After the position of point
After determining the impeller inlet and outlet installation angles and the impeller inlet and out diameters, the blade wrap angle has a larger value range. Therefore, the advantage of the logarithmic spiral method in the shape of the cylindrical impeller’s blade is also more prominent. Design and draw the impeller blade profile according to the equivariant angle spiral, and its design principle of the profile is shown in Figure
Blade profile of logarithmic spiral method.
In Figure
When
Profile equation:
Wrap angle:
Substitute
Blade profiles drawn by MATLAB software. (a) Logarithmic spiral method. (b) B-spline curve method.
Use 5-point (or 4-point) Bezier curve to fit the studied impeller profile, which eliminates the inconvenience of curve adjustment caused by traditional cubic polynomial fitting and makes the design of blade profile simpler, smoother, and easier to control. Determine the coordinates of the control points first. According to the Bezier equation,
The coordinate of any point
Figure
Blade profile of B-spline curve method.
Substitute
Take the plastic centrifugal pump designed by a certain unit as an example, and its main design parameters are shown in Table
Design parameters of plastic centrifugal pump.
Performance parameters | Geometrical dimension | ||
---|---|---|---|
Q (m3/h) | 20 | Impeller inlet diameter (mm) | 58 |
H (m) | 30 | Impeller outlet diameter (mm) | 162 |
2900 | Impeller inlet width (mm) | 23 | |
60.871 | Impeller outlet width (mm) | 10 | |
5.5 | Impeller inlet installation angle (°) | 20 | |
NPSHa (m) | 4 | Impeller outlet installation angle (°) | 30 |
Volute width (mm) | 33 | Base circle diameter of volute (mm) | 175 |
Figure
Two-dimensional diagram of the impeller.
Models of impellers drawn by four profile design methods. (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
Figure
Two-dimensional diagram of the volute.
Model of volute.
According to the above completed three-dimensional models, ANSYS-ICEM software is employed to utilized to mesh the computational domains. When we mesh the models, the actual grid cannot reach the ideal shape. If the grid deforms or deformation exceeds a certain limit, the accuracy of the calculation results will change accordingly. Therefore, in the initial division of the grid, it is necessary to use appropriate measures to control or measure the quality of the grid and try to achieve the best grid. The final determination of the number of grid cells in each part of the computational domains is shown in Table
The number of grid cells.
Computational domains | Inlet extension | Impeller | Volute | Outlet extension |
---|---|---|---|---|
The number of grid cells | 581102 | 397526 | 393266 | 1502055 |
The final meshing is shown in Figure
Meshing.
Numerical calculations were performed in FLUENT software. The turbulence model was a k-epsilon (equation (
The boundary conditions were set to velocity inlet and outflow. The relevant setting parameters were set by default. The reference pressure was set to standard atmospheric pressure. The wall surface was placed under a non-slip boundary condition, and a standard wall surface function was applied. The calculation method was SIMPLEC. The convergence accuracy was set to 10−4.
UTR9000 material was used for 3D printing of impellers, which was an ABS-like stereo light modeling resin with accurate and durable characteristics. The durability of components made of UTR9000 resin was more than 6.5 months. According to the three-dimensional models of the impellers drawn by four profile design methods (Figure
3D printing of impellers. (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
Figure
Pump performance test bench.
The pump test system (electrical measurement method) V8.97 software on the data acquisition platform was used to collect data at each operating point by adjusting the flow control valve. The pump performance experiments were performed on the impellers of the four types of profiles. The parameter settings before the experiment are shown in Table
Parameter settings of pump performance experiment.
Product number | Fluid density (kg/m3) | Fluid viscosity (CST) | Meter factor ( | Inlet diameter (m) | Outlet diameter (m) |
---|---|---|---|---|---|
50UHB15-32 | Water | Water | 79.89 | 0.05 | 0.032 |
Performance experiment of single arc method.
Measured value | |||||||||
---|---|---|---|---|---|---|---|---|---|
Inlet pressure | Outlet pressure | ||||||||
(kPa) | (kPa) | (m3/h) | (r/min) | (kW) | (m3/h) | (m) | (kW) | (%) | |
1 | −70.00 | 170.00 | 20.95 | 2998.60 | 5.85 | 20.26 | 25.72 | 5.29 | 26.83 |
2 | −80.00 | 220.00 | 19.93 | 3001.44 | 5.83 | 19.26 | 31.19 | 5.26 | 31.11 |
3 | −70.00 | 240.00 | 18.92 | 3002.21 | 5.81 | 18.28 | 31.94 | 5.24 | 30.37 |
4 | −60.00 | 260.00 | 16.35 | 3001.81 | 5.56 | 15.80 | 32.47 | 5.01 | 27.87 |
5 | −50.00 | 280.00 | 14.86 | 3001.81 | 5.37 | 14.36 | 33.21 | 4.84 | 26.82 |
6 | −40.00 | 300.00 | 12.93 | 3002.06 | 5.12 | 12.49 | 33.90 | 4.62 | 24.99 |
7 | −30.00 | 310.00 | 10.91 | 3002.36 | 4.96 | 10.54 | 33.66 | 4.47 | 21.62 |
8 | −20.00 | 330.00 | 8.28 | 3001.63 | 4.68 | 8.00 | 34.39 | 4.22 | 17.76 |
9 | −20.00 | 340.00 | 6.33 | 3001.54 | 4.53 | 6.12 | 35.21 | 4.09 | 14.36 |
10 | −10.00 | 350.00 | 2.44 | 3001.34 | 4.26 | 2.36 | 35.06 | 3.84 | 5.86 |
11 | −10.00 | 360.00 | 1.49 | 3001.16 | 4.22 | 1.44 | 36.00 | 3.81 | 3.71 |
12 | −10.00 | 360.00 | 0.21 | 3000.81 | 4.15 | 0.20 | 35.99 | 3.75 | 0.53 |
13 | 0.00 | 380.00 | 0.00 | 3000.90 | 4.03 | 0.00 | 36.94 | 3.64 | 0.00 |
Performance experiment of double arc method.
Measured value | |||||||||
---|---|---|---|---|---|---|---|---|---|
Inlet pressure | Outlet pressure | ||||||||
(kPa) | (kPa) | (m3/h) | (r/min) | (kW) | (m3/h) | (m) | (kW) | (%) | |
1 | −80.00 | 190.00 | 21.19 | 3000.59 | 5.47 | 20.48 | 28.60 | 4.94 | 32.31 |
2 | −80.00 | 220.00 | 19.98 | 2998.58 | 5.33 | 19.32 | 31.26 | 4.82 | 34.13 |
3 | −70.00 | 240.00 | 18.09 | 2997.92 | 5.21 | 17.50 | 31.89 | 4.72 | 32.23 |
4 | −70.00 | 250.00 | 16.89 | 2998.15 | 5.18 | 16.34 | 32.64 | 4.69 | 30.98 |
5 | −50.00 | 280.00 | 14.25 | 2998.20 | 5.01 | 13.78 | 33.20 | 4.53 | 27.50 |
6 | −40.00 | 290.00 | 12.63 | 2998.18 | 4.82 | 12.22 | 33.00 | 4.36 | 25.17 |
7 | −30.00 | 310.00 | 10.85 | 2997.94 | 4.60 | 10.50 | 33.76 | 4.16 | 23.18 |
8 | −20.00 | 330.00 | 8.56 | 2998.14 | 4.44 | 8.28 | 34.50 | 4.02 | 19.36 |
9 | −20.00 | 340.00 | 6.70 | 2998.48 | 4.32 | 6.48 | 35.31 | 3.91 | 15.95 |
10 | −10.00 | 350.00 | 4.83 | 2998.58 | 4.20 | 4.67 | 35.20 | 3.80 | 11.79 |
11 | −10.00 | 360.00 | 2.06 | 2998.72 | 3.99 | 1.99 | 36.06 | 3.61 | 5.42 |
12 | −10.00 | 370.00 | 0.24 | 2999.02 | 3.82 | 0.23 | 36.99 | 3.45 | 0.68 |
13 | −10.00 | 380.00 | 0.00 | 2999.52 | 3.71 | 0.00 | 37.93 | 3.35 | 0.00 |
Performance experiment of logarithmic spiral method.
Measured value | |||||||||
---|---|---|---|---|---|---|---|---|---|
Inlet pressure | Outlet pressure | ||||||||
(kPa) | (kPa) | (m3/h) | (r/min) | (kW) | (m3/h) | (m) | (kW) | (%) | |
1 | −70.00 | 180.00 | 21.33 | 2998.60 | 5.58 | 20.63 | 26.75 | 5.05 | 29.79 |
2 | −80.00 | 190.00 | 21.08 | 2998.07 | 5.36 | 20.39 | 28.62 | 4.85 | 32.77 |
3 | −80.00 | 210.00 | 20.24 | 3001.45 | 5.21 | 19.56 | 30.30 | 4.70 | 34.35 |
4 | −80.00 | 230.00 | 18.98 | 3002.29 | 5.20 | 18.33 | 31.95 | 4.69 | 34.05 |
5 | −60.00 | 250.00 | 16.50 | 3001.64 | 5.01 | 15.94 | 31.55 | 4.52 | 33.32 |
6 | −50.00 | 280.00 | 14.65 | 3001.62 | 4.80 | 14.15 | 33.18 | 4.33 | 29.55 |
7 | −30.00 | 310.00 | 11.30 | 3001.65 | 4.48 | 10.92 | 33.72 | 4.04 | 24.82 |
8 | −30.00 | 320.00 | 1.54 | 3001.62 | 4.42 | 10.18 | 34.59 | 3.99 | 24.08 |
9 | −20.00 | 330.00 | 8.46 | 3001.77 | 4.20 | 8.17 | 34.40 | 3.79 | 20.23 |
10 | −20.00 | 340.00 | 7.35 | 3001.72 | 4.11 | 7.10 | 35.27 | 3.71 | 18.41 |
11 | −20.00 | 340.00 | 5.93 | 3001.50 | 3.98 | 5.73 | 35.19 | 3.59 | 15.30 |
12 | −10.00 | 350.00 | 2.63 | 3001.25 | 3.74 | 2.54 | 35.06 | 3.37 | 7.19 |
13 | −10.00 | 370.00 | 0.00 | 3001.34 | 3.43 | 0.00 | 36.93 | 3.09 | 0.00 |
Performance experiment of B-spline curve method.
Measured value | |||||||||
---|---|---|---|---|---|---|---|---|---|
Inlet pressure | Outlet pressure | ||||||||
(kPa) | (kPa) | (m3/h) | (r/min) | (kW) | (m3/h) | (m) | (kW) | (%) | |
1 | −80.00 | 180.00 | 21.27 | 2998.15 | 5.40 | 20.57 | 27.70 | 4.89 | 31.77 |
2 | −80.00 | 220.00 | 20.05 | 3001.80 | 5.31 | 19.37 | 31.21 | 4.79 | 34.39 |
3 | −80.00 | 240.00 | 17.69 | 3001.60 | 5.13 | 17.09 | 32.69 | 4.63 | 32.90 |
4 | −80.00 | 250.00 | 16.65 | 3001.51 | 5.03 | 16.09 | 33.48 | 4.54 | 32.34 |
5 | −60.00 | 280.00 | 14.91 | 3001.36 | 4.81 | 14.41 | 34.17 | 4.34 | 30.91 |
6 | −40.00 | 300.00 | 12.75 | 3001.13 | 4.60 | 12.32 | 33.90 | 4.15 | 27.41 |
7 | −30.00 | 310.00 | 11.08 | 3000.93 | 4.44 | 10.71 | 33.71 | 4.01 | 24.54 |
8 | −30.00 | 330.00 | 8.29 | 3000.63 | 4.26 | 8.01 | 35.37 | 3.85 | 20.07 |
9 | −20.00 | 340.00 | 7.06 | 3000.61 | 4.17 | 6.82 | 35.28 | 3.76 | 17.42 |
10 | −20.00 | 350.00 | 5.81 | 3000.56 | 4.05 | 5.62 | 36.16 | 3.66 | 15.13 |
11 | −10.00 | 350.00 | 4.75 | 3000.45 | 3.92 | 4.59 | 35.16 | 3.54 | 12.42 |
12 | −10.00 | 360.00 | 3.29 | 3000.55 | 3.82 | 3.18 | 36.05 | 3.45 | 9.05 |
13 | −10.00 | 370.00 | 2.14 | 3000.56 | 3.72 | 2.07 | 36.97 | 3.36 | 6.20 |
Figures
Figure
Contours of the velocity of the four impellers. (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
Figure
Contours of the pressure of the four impellers. (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
Figure
Vapor volume fraction distribution (NPSHr = 1 m). (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
Figure
Vapor volume fraction distribution (NPSHr = 2 m). (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
In summary, when NPSHr = 1 m and 2 m, the impeller drawn by the logarithmic spiral method is significantly better than the other three impellers, which means that the logarithmic spiral method is the best design method.
According to the above conclusion, CFD-Post software was used to calculate the performance parameters of the four profiles, as shown in Table
Performance parameters comparison of four methods.
Method | Single arc | Double arc | Logarithmic spiral | B-spline curve |
---|---|---|---|---|
H (m) | 35.4435 | 35.4653 | 35.541 | 35.3835 |
P (kW) | 3.50485 | 3.3662 | 3.30089 | 3.51129 |
76.99 | 81.53 | 81.98 | 76.72 |
The purpose of fluid-structure interaction was to find how the flow field influenced the impeller, which was mainly reflected in the deformation of the impeller caused by the fluid, and the force on the impeller. ANSYS-CFX software was used to complete the fluid-structure interaction analysis.
Figure
Total deformation of the impellers. (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
The maximum total deformation of the impellers drawn by four profile design methods was 0.61503 mm, 0.58614 mm, 0.57442 mm, and 0.61609 mm, respectively. The following can be concluded for total deformation: B-spline curve method > single arc method > double arc method > logarithmic spiral method.
Figure
Equivalent stress of the impellers. (a) Single arc. (b) Double arc. (c) Logarithmic spiral. (d) B-spline curve.
The maximum equivalent stress of the impellers drawn by four profiles was 41.357 MPa, 41.43 MPa, 40.909 MPa, and 44.891 MPa, respectively. The following can be concluded for equivalent stress: B-spline curve method > double arc method > single arc method > logarithmic spiral method.
Based on the above analysis, it is shown that the logarithmic spiral method has the highest efficiency. To maximize the efficiency, the impeller inlet and outlet diameters (
The basic equation of NPSHr:
Assuming that there is no prerotation at impeller inlet,
Then,
Therefore, the minimum objective function of NPSHr is min [
The centrifugal pump losses mainly include volume, mechanical, and hydraulic losses. The volume loss accounts for a small proportion of the total loss, so the volume loss can be ignored. The optimization model is established with the mechanical loss and hydraulic loss.
Assuming that there is no prerotation at impeller inlet,
Then,
Impeller outlet speed triangle:
Then,
Therefore, the minimum objective function of
The weighting coefficient transformation method is used to deal with the two objective functions. According to the actual situation, the power loss of the plastic centrifugal pump has a greater impact on the total efficiency of the pump than NPSHr. Therefore, it is assumed that NPSHr accounts for 30% and the power loss accounts for 70% for optimization and the unified objective function is min [
The constraint ranges of design variables were determined by combining the statistical formula of the velocity coefficient method with the actual excellent model pump. Then, we increased the constraint ranges appropriately.
Constraint formulas:
According to the creation of a multiobjective optimization program, the four parameters of impeller inlet and outlet diameters and impeller inlet and outlet installation angles were optimized. The final optimization results were that the impeller inlet and outlet diameters were 57.778 mm and 161.57 mm and the impeller inlet and outlet installation angles were 16.836° and 30.68°. The optimization results were rounded and compared with those before optimization, and the design variables are shown in Table
Comparison of optimization design variables.
Parameters | ||||
---|---|---|---|---|
Before optimization | 58 | 162 | 20 | 30 |
After optimization | 58 | 162 | 17 | 31 |
The optimized parameters were used to remodel the impeller. Under the same working conditions, the internal flow field simulation was performed. The results after analysis are shown in Figure
Optimization results.
According to the basic parameters of the centrifugal pump and the four different design methods of impeller profile, the shapes and sizes of several profiles were determined. Three-dimensional models were drawn by UG software. ANSYS-ICEM software was utilized to mesh the computational domains. According to the three-dimensional models drawn by four profile design methods, the impeller models were printed by 3D printing technology. The performance experiments of the plastic centrifugal pumps were carried out. The experimental results showed that the logarithm spiral method was the best and the single arc method was the worst. The analysis of numerical simulation was performed by FLUENT software. From the contours of velocity and pressure, the flow field in the impeller drawn by the logarithmic spiral method was significantly better. The maximum pressure values corresponding to the four methods were 437563 Pa, 441628 Pa, 438368 Pa, and 435518 Pa. From the vapor volume fraction distribution, when NPSHr = 1 m and 2 m, the impeller drawn by the logarithmic spiral method was significantly better than the other three impellers. According to the calculation of performance parameters, it can be concluded that the impeller drawn by the logarithmic spiral method was the optimal impeller under the design condition. ANSYS-CFX software was used to complete the fluid-structure interaction analysis. The maximum total deformation of the impellers drawn by the four profile design methods was 0.61503 mm, 0.58614 mm, 0.57442 mm, and 0.61609 mm, respectively. Deformation: B-spline curve method > single arc method > double arc method > logarithmic spiral method. The maximum equivalent stress of the impellers drawn by the four profile design methods was 41.357 MPa, 41.43 MPa, 40.909 MPa, and 44.891 MPa, respectively. Equivalent stress: B-spline curve method > double arc method > single arc method > logarithmic spiral method. Based on the analysis, the impeller drawn by the logarithmic spiral method had the highest efficiency. To maximize the efficiency, the impeller inlet and outlet diameters (
Impeller inlet diameter, mm
Impeller outlet diameter, mm
Impeller inlet installation angle,
Impeller outlet installation angle,
Radius of curvature, mm
Impeller inlet radius, mm
Impeller outlet radius, mm
Radius of rotation of the point
Blade angle of point F,
Number of blades
Impeller installation angle,
Wrap angle,
Variation of wrap angle
Flow rate, m3/
Pump head, m
Rotational speed,
Specific speed
Shaft power, kW
Impeller inlet diameter, m
Impeller hub diameter, m
Blade inlet pressure drop coefficient
Absolute velocity of the slightly forward part of the blade inlet, m/s
Relative velocity of the slightly forward part of the blade inlet, °/s
Total loss power, kW
Hydraulic loss power, kW
Mechanical loss power, kW
Velocity energy loss coefficient in the pressurized water chamber
Dimensionless disc friction coefficient
Absolute velocity of impeller outlet, m/s
Circumferential velocity of inlet, m/s
Circumferential velocity of outlet, m/s
Circumferential absolute velocity of inlet, m/s
Circumferential absolute velocity of outlet, m/s
Theoretical head of the pump, m
Crowding coefficient of impeller outlet
Stodola’s slip coefficient.
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
This work was supported by the University Synergy Innovation Program of Anhui Province (GXXT-2019-004), the Teaching Research Project of Anhui Education Department (2019jyxm0229), and the Natural Science Foundation of Anhui Province Education Department (KJ2017ZD12).