Author Contributions
M.H.S., Conceptualization, methodology, validation and writing original draft; B.K., software, formal analysis, resources, project administration; A.S., Validation, review and editing; G.H., review and editing; D.-E.L., supervision. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Computational flow domain of centrifugal pump.
Figure 1.
Computational flow domain of centrifugal pump.
Figure 2.
Impeller flow domain with splitter blades (Ref1).
Figure 2.
Impeller flow domain with splitter blades (Ref1).
Figure 3.
Flow domain mesh.
Figure 3.
Flow domain mesh.
Figure 4.
Grid independence test at the design flowrate.
Figure 4.
Grid independence test at the design flowrate.
Figure 5.
Centrifugal pump test rig.
Figure 5.
Centrifugal pump test rig.
Figure 6.
Rheometer MCR301.
Figure 6.
Rheometer MCR301.
Figure 7.
Rheological fluid properties: (a) dynamic viscosity versus shear rate and (b) shear stress versus shear rate.
Figure 7.
Rheological fluid properties: (a) dynamic viscosity versus shear rate and (b) shear stress versus shear rate.
Figure 8.
Flowcharts for simulation and optimization processes.
Figure 8.
Flowcharts for simulation and optimization processes.
Figure 9.
Architecture of ANN.
Figure 9.
Architecture of ANN.
Figure 10.
Validation of numerical results for all cases: (a) H versus Q/Qd and (b) Ψ versus Q/Qd.
Figure 10.
Validation of numerical results for all cases: (a) H versus Q/Qd and (b) Ψ versus Q/Qd.
Figure 11.
Pareto optimal front for the case using water.
Figure 11.
Pareto optimal front for the case using water.
Figure 12.
Pareto optimal front for case C1.
Figure 12.
Pareto optimal front for case C1.
Figure 13.
Pareto optimal front for case C2.
Figure 13.
Pareto optimal front for case C2.
Figure 14.
Pareto optimal front for case C3.
Figure 14.
Pareto optimal front for case C3.
Figure 15.
Pump performance comparison for water: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 15.
Pump performance comparison for water: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 16.
Pump performance comparison for oil C1: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 16.
Pump performance comparison for oil C1: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 17.
Pump performance comparison for oil C2: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 17.
Pump performance comparison for oil C2: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 18.
Pump performance comparison for oil C3: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 18.
Pump performance comparison for oil C3: (a) Ψ versus Q/Qd and (b) H versus Q/Qd.
Figure 19.
Streamline at the midspan of reference and optimized impeller for all cases: (a) water, (b) C1, (c) C2, and (d) C3.
Figure 19.
Streamline at the midspan of reference and optimized impeller for all cases: (a) water, (b) C1, (c) C2, and (d) C3.
Figure 20.
Static pressure contours at the midspan of the reference and optimized impeller for all cases: (a) water, (b) C1, (c) C2, and (d) C3.
Figure 20.
Static pressure contours at the midspan of the reference and optimized impeller for all cases: (a) water, (b) C1, (c) C2, and (d) C3.
Figure 21.
Pressure distribution at the axial central plane: (a) Ref2 design and (b) Opt2a design.
Figure 21.
Pressure distribution at the axial central plane: (a) Ref2 design and (b) Opt2a design.
Figure 22.
Velocity at the vortex core region of the reference and optimized impeller: (a) C1 and (b) C4.
Figure 22.
Velocity at the vortex core region of the reference and optimized impeller: (a) C1 and (b) C4.
Figure 23.
Turbulent kinetic energy of the reference and optimized impeller: (a) C1 and (b) C3.
Figure 23.
Turbulent kinetic energy of the reference and optimized impeller: (a) C1 and (b) C3.
Figure 24.
Relationship X1 and X2 with µ for (a) minimizing input power (Ψ), (b) maximizing head (H).
Figure 24.
Relationship X1 and X2 with µ for (a) minimizing input power (Ψ), (b) maximizing head (H).
Figure 25.
Effect of oil viscosity on pump performance for reference design: (a) head rise (H) vs. Q/Qd and (b) input power (Ψ).
Figure 25.
Effect of oil viscosity on pump performance for reference design: (a) head rise (H) vs. Q/Qd and (b) input power (Ψ).
Figure 26.
Effect of oil viscosity on pump performance curves for optimized design of maximized head rise: (a) head rise (H) vs. Q/Qd and (b) input power (Ψ).
Figure 26.
Effect of oil viscosity on pump performance curves for optimized design of maximized head rise: (a) head rise (H) vs. Q/Qd and (b) input power (Ψ).
Figure 27.
Effect of oil viscosity on the performance curves for optimized design of minimized input power: (a) head rise (H) vs. Q/Qd and (b) input power (Ψ).
Figure 27.
Effect of oil viscosity on the performance curves for optimized design of minimized input power: (a) head rise (H) vs. Q/Qd and (b) input power (Ψ).
Table 1.
Study of splitter blades in a centrifugal pump.
Table 1.
Study of splitter blades in a centrifugal pump.
Authors | Description | Outcome |
---|
Golcu et al., 2007 [16] | Experimental study for centrifugal pump for water application; modified number of blades and splitter length | Splitter blade improves pump performance for a small number of blades |
Shigemitsu et al., 2013 [19] | Numerical and experimental investigation of mini semi-open impeller; addition of splitter blades at high outlet angle of impeller blades | Back-flow region suppressed, vortex loss at volute casing decreased |
Cavazzini et al., 2015 [21] | Numerical and experimental testing of centrifugal pump for water; addition of splitter blades | Improved cavitation performance at high flowrate |
An et al., 2016 [22] | Numerical simulation and optimization of centrifugal pump impeller; modified main blade and splitter profile using Bezier curves | Pump performance improved by reducing secondary flow |
Korkmaz, et al., 2017 [23] | Experimental analysis of centrifugal pump impeller; modified of number of blades, outlet blade angle, and splitter length | Modifying outlet blade angle and at particular splitter length give high pump performance while pumping water |
Namazizadeh et al., 2020 [20] | Numerical simulation and experimental testing of centrifugal pump for water; modified splitter length and position from main blade varied | Adding splitter blades improves pump head with negligible efficiency change |
Xie et al., 2021 [24] | experimental testing of centrifugal pump impeller; optimization of splitter blade length | Optimized location of splitter blade, nonuniformity, maximum equivalent stress of the blade decreased |
Siddique et al., 2021 [17] | Numerical and experimental testing of centrifugal pump for water; number of blades, splitter length, wrap angle modified | Through optimization shape and length of splitter blade presented, which improved pump performance |
Table 2.
Reference pump dimensions.
Table 2.
Reference pump dimensions.
Parameters | Dimensions |
---|
Suction pipe diameter, ds | 50 mm |
Delivery pipe diameter, dd | 32 mm |
Shaft diameter, ds | 24 mm |
Impeller outlet diameter, Do | 142 mm |
Number of blades, z | 5 |
Inlet blade angle at hub, β1sh | 40 |
Inlet blade angle at shroud, β1h | 10 |
Outlet blade angle, β2 | 36 |
Blade thickness, t | 3 mm |
Base circle diameter of volute casing, Db | 147 mm |
Table 3.
Uncertainty analysis of instruments used in testing.
Table 3.
Uncertainty analysis of instruments used in testing.
Instruments | Range |
---|
Pressure gauge | 0.1–2.0 bar ± 0.5% |
Flowmeter | 10–380 L/min ± 1% |
Tachometer | 0–10,000 rpm ± 0.25% |
Power meter | 0–1000 watt ± 0.25% |
Table 4.
Pumping fluid properties.
Table 4.
Pumping fluid properties.
Pumping Fluids | Density (kg/m3) | ⁰API | Dynamic Viscosity (mPaS) |
---|
Water | 1000 | 10 | 1 |
C1 | 805 | 44.3 | 4.5 |
C2 | 814 | 42.3 | 14 |
C3 | 827 | 39.6 | 26 |
C4 | 855 | 33.8 | 65 |
Table 5.
RMSD for the optimal design point in each case.
Table 5.
RMSD for the optimal design point in each case.
Cases | H-PRED | Ψ-PRED | H-CFD | Ψ-CFD | RMSD |
---|
Opt1a | 5.603 | 178.0 | 5.582 | 178.1 | 0.07 |
Opt1e | 5.652 | 179.7 | 5.643 | 179.9 | 0.14 |
Opt2a | 5.351 | 167.5 | 5.351 | 168.2 | 0.49 |
Opt2e | 5.495 | 169.5 | 5.453 | 169.4 | 0.08 |
Opt3a | 5.356 | 169.1 | 5.318 | 168.7 | 0.28 |
Opt3e | 5.36 | 169.3 | 5.354 | 170.3 | 0.71 |
Opt4a | 4.896 | 166.4 | 4.918 | 166.3 | 0.07 |
Opt4e | 5.140 | 170.4 | 5.128 | 170.1 | 0.21 |
Table 6.
Final optimal designs for maximum head and minimum input power.
Table 6.
Final optimal designs for maximum head and minimum input power.
Optimal Designs | X1 | X2 | H | Ψ |
---|
Ref1 | - | - | 5.22 | 171.4 |
Opt1a | 0.57 | 170 | 5.58 | 178.1 |
Opt1e | 0.49 | 174 | 5.64 | 179.9 |
Ref2 | 0.57 | 170 | 5.13 | 150.2 |
Opt2a | 0.21 | 175 | 5.35 | 169.4 |
Opt2e | 0.89 | 145 | 5.57 | 176.4 |
Ref3 | 0.57 | 170 | 4.86 | 159.9 |
Opt3a | 0.33 | 168 | 5.32 | 168.7 |
Opt3e | 0.85 | 128 | 5.35 | 170.3 |
Ref4 | 0.57 | 170 | 4.54 | 161.1 |
Opt4a | 0.89 | 161 | 4.90 | 166.3 |
Opt4e | 0.90 | 102 | 5.13 | 170.1 |