# Improving the Design of a Multi-Gear Pump Switchgear Using CFD Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Designs of Objects

#### 2.2. Material Properties

#### 2.3. Grid Construction and Setting of Boundary Conditions in the Distribution System

^{3}/s; in the pressure line, these included the total outlet pressure from 6 to 24 MPa and the volume flow rate at the input from 0.00182 to 0.0055 m

^{3}/s (Figure 4).

## 3. Results

#### 3.1. Input Data to Estimate Hydraulic Parameters in the Suction and Pressure Lines of the Distribution System

- (1)
- The calculation of the suction line of the collector at changes in performance and speed, dynamic viscosity coefficient, and pressure at the inlet of the suction pipe;
- (2)
- The calculation of the collector pressure line at changes in productivity and speed, the coefficient of dynamic viscosity, and pressure at the outlet of the discharge pipe.

^{3}.

^{2}⋅ b ⋅ z,

^{3}.

#### 3.2. Investigation of Changes in the Main Hydraulic Parameters of a Pump System in Suction and Pressure Lines

^{3}/s. At the inlet to the suction line, the pressure value is maximum and equal to 0.8 MPa; then, upon entering the four suction openings, the pressure gradually decreases. The fluid loses energy to overcome the resistance at the inlet of the orifices. Here, the pressure value changes to 0.62 MPa. In the orifices themselves, the pressure decreases to 88 kPa as the fluid moves. Such pressure losses are related to the internal friction of the liquid. Figure 7 shows the change in the fluid flow velocity. At the inlet to the suction connections, the velocity values are minimal and are 6–7 m/s. In the general cavity of the suction line, the presence of low velocities up to 2 m/s and vortex formation zones can be observed. With further movement of liquid into the working chamber of the pump through the holes with a diameter of 10 mm, the speed increases to 17 m/s. According to the velocity distribution diagram, it can be observed that in the center of the cross-sections of the holes, the velocity is maximum and, as it moves away from the center to the walls, the velocity decreases, which is caused by friction between the liquid layers.

^{3}/s. In the pressure line, at the displacement of liquid through four holes from the working chamber, the pressure has the highest values: 10 MPa. Moving along the orifices, the pressure decreases due to the internal resistance in the orifices and reaches the value of 9.99 MPa.

^{3}/s, pressure in suction lines Ps (from 0.3 MPa to 1 MPa) and pressure lines P

_{p}(from 6 MPa to 24 MPa), and the dynamic viscosity coefficient µ in the range from 0.00861 to 8.2 Pa·s.

#### 3.3. Investigation of Manifold Geometry Variation in Fluid Velocity and Pressure Drop

_{1}) and the speed n (X

_{2}) can be described using the multiple regression equation [33].

_{1}+ 0.00436X

_{2}

_{1}indicates that as X

_{1}increases by 1, Y decreases by 6.6682. The coefficient b

_{2}indicates that as X

_{2}increases by 1, Y increases by 0.00436.

## 4. Conclusions

- (1)
- Cavitations were observed in the upper cover of the manifold with a transition radius of 3 mm.
- (2)
- Reducing the transition radius in the manifold from 3 to 15 mm in the suction line of the system reduces the pressure drop by 13%.
- (3)
- The liquid flow velocity in the top cover of a multiple gear pump decreases slightly (3%) as a function of changing the radius in the manifold from 3 to 15 mm.
- (4)
- The minimum pressure on the suction line is 500 kPa or more. Smaller pressures contribute to the interruption of the continuity of the liquid flow and the occurrence of cavitation.
- (5)
- Fluid viscosity and drive shaft speed also influence the performance of the multiple gear pump design.
- (6)
- It is established that with this distribution system, taking into account the variable temperature of the liquid in the hydraulic circuits, the multiple gear pump can operate with liquids belonging to a viscosity class of 5–10.
- (7)
- The rotational speed is not greater than 1200 rpm with a kinematic viscosity coefficient of 10 cSt.
- (8)
- The pressure drop depends on the number of revolutions and the radius of the rounding of the manifold.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**A design of a multi-gear pump: 1—front cover; 2—housing; 3—bearings; 4—driven pinions; 5—driving pinion; 6—flange; 7—retaining ring; 8—back cover.

**Figure 2.**Elements of a multi-gear pump created in Solidworks: (

**a**) collector; (

**b**) housing: 1—inlets; 2—low pressure chamber (suction); 3—suction line openings; 4—discharge line holes; 5—high pressure chamber (pressure); 6—pressure pipe.

**Figure 3.**Construction of a global grid in the areas of fluid flows: (

**a**) the creation of a grid in the calculation of inlet channels; (

**b**) the creation of a grid in the calculation of outlet channels: 1—inlets; 2—low pressure chamber (suction); 3—high pressure chamber (pressure); 4—pressure pipe hole.

**Figure 4.**Example of setting the boundary conditions for the suction line: (

**a**) input pressure; (

**b**) outlet volumetric flow rate.

**Figure 5.**Options for the presentation of calculation results: (

**a**) velocity change in the pressure line (cross-sectional picture); (

**b**) velocity change in the suction line (flow path).

**Figure 10.**Velocity υ and pressure drop ∆P in the suction lines (

**a**) and pressure (

**b**) of the distribution system of a multi-gear pump: 1—dependence of pressure drop on fluid flow ∆P = f(Q); 2—dependence of pressure drop on dynamic viscosity coefficient ∆P = f(μ); 3—dependence of pressure drop on suction pressure ∆P = f(P

_{s})/discharge pressure ∆P = f(P

_{p}); 4—dependence of fluid velocity on flow rate υ = f(Q); 5—dependence of fluid velocity on the coefficient of dynamic viscosity υ = f(μ); 6—dependence of fluid speed on suction pressure υ = f(P

_{s})/discharge pressure υ = f(P

_{p}).

**Figure 12.**Fluid velocity (

**a**) and pressure (

**b**) distribution diagrams with a transition radius of 3 mm in the manifold.

**Figure 13.**Fluid velocity (

**a**) and pressure (

**b**) distribution diagrams with a transition radius of 15 mm in the manifold.

**Figure 14.**Distribution of the pressure drop as a function of the radius of the transition in the manifold in the suction line of the distribution system.

Material | Yield Strength, MPa | Tensile Strength, MPa | Modulus of Elasticity, GPa | Poisson’s Ratio | Density, kg/m^{3} |
---|---|---|---|---|---|

Aluminum (Alloy RA6) | 250 | 390 | 72.5 | 0.33 | 2790 |

Density (20 °C), kg/m ^{3} | Dynamic Viscosity Coefficient, Pa·s | ||||||||
---|---|---|---|---|---|---|---|---|---|

−55 °C | −50 °C | −45 °C | −40 °C | −30 °C | −20 °C | 20 °C | 30 °C | 50 °C | |

861 | 8.2 | 4.305 | 2.407 | 1.09 | 0.84 | 0.21 | 0.025 | 0.0173 | 0.00861 |

No. of Experience | Speed, n, rpm | Coefficient of Dynamic Viscosity, µ, Pa·s | Pressure P_{s}, kPa | Pump Capacity Q, m^{3}/s |
---|---|---|---|---|

Series 1 | ||||

1 | 400 | 0.00861 | 0.5 | 0.00182 |

2 | 500 | 0.00227 | ||

3 | 600 | 0.00275 | ||

4 | 700 | 0.00318 | ||

5 | 800 | 0.00367 | ||

6 | 900 | 0.0041 | ||

7 | 1000 | 0.00458 | ||

8 | 1200 | 0.0055 | ||

Series 2 | ||||

9 | 1000 | 8.2 | 0.5 | 0.00458 |

10 | 4.305 | |||

11 | 1.09 | |||

12 | 0.84 | |||

13 | 0.21 | |||

14 | 0.025 | |||

15 | 0.0173 | |||

16 | 0.00861 | |||

Series 3 | ||||

17 | 1000 | 0.00861 | 1 | 0.00458 |

18 | 0.9 | |||

19 | 0.8 | |||

20 | 0.7 | |||

21 | 0.6 | |||

22 | 0.5 | |||

23 | 0.4 | |||

24 | 0.3 |

**Table 4.**Variable parameters in the modeling of fluid flow in the pressure line of the distribution system.

No. of Experience | Speed, n, rpm | Coefficient of Dynamic Viscosity, µ, Pa·s | Pressure Ps, kPa | Pump Capacity Q, m^{3}/s |
---|---|---|---|---|

Series 1 | ||||

1 | 400 | 0.00861 | 10 | 0.00182 |

2 | 500 | 0.00227 | ||

3 | 600 | 0.00275 | ||

4 | 700 | 0.00318 | ||

5 | 800 | 0.00367 | ||

6 | 900 | 0.0041 | ||

7 | 1000 | 0.00458 | ||

8 | 1200 | 0.0055 | ||

Series 2 | ||||

9 | 1000 | 8.2 | 10 | 0.00458 |

10 | 4.305 | |||

11 | 2.407 | |||

12 | 1.09 | |||

13 | 0.84 | |||

14 | 0.21 | |||

15 | 0.0173 | |||

16 | 0.00861 | |||

Series 3 | ||||

17 | 1000 | 0.00861 | 6 | 0.00458 |

18 | 8 | |||

19 | 10 | |||

20 | 16 | |||

21 | 18 | |||

22 | 20 | |||

23 | 22 | |||

24 | 24 |

№ | Collector Transition Radius r, (X_{1}), mm | Speed n, (X_{2}), rpm | Pressure Drop ΔP (Y), kPa |
---|---|---|---|

1 | 15 | 800 | 342.328 |

2 | 14 | 1000 | 351.135 |

3 | 13 | 1200 | 362.234 |

4 | 9 | 1200 | 351.432 |

5 | 8 | 1000 | 361.753 |

6 | 7 | 800 | 371.457 |

7 | 5 | 800 | 412.532 |

8 | 4 | 1000 | 421.384 |

9 | 3 | 1200 | 431.224 |

Criteria | Value | Note |
---|---|---|

Average approximation error | 3.79% | The equation model is well fitted as the average approximation error does not go beyond 5–7% |

Multiple correlation coefficient | 0.877 | Strong influence of factors Xi on the response Y, since the values of the multiple correlation and determination coefficients are in the range from 0.7 to 1 |

Determination coefficient | 0.769 | |

Fisher criterion | 10.03 > 5.14 | The coefficient of determination is statistically significant, and the regression equation is statistically reliable because Fcal > Ftab |

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**MDPI and ACS Style**

Zharkevich, O.; Nikonova, T.; Gierz, Ł.; Reshetnikova, O.; Berg, A.; Warguła, Ł.; Berg, A.; Wieczorek, B.; Łykowski, W.; Nurzhanova, O.
Improving the Design of a Multi-Gear Pump Switchgear Using CFD Analysis. *Appl. Sci.* **2024**, *14*, 5394.
https://doi.org/10.3390/app14135394

**AMA Style**

Zharkevich O, Nikonova T, Gierz Ł, Reshetnikova O, Berg A, Warguła Ł, Berg A, Wieczorek B, Łykowski W, Nurzhanova O.
Improving the Design of a Multi-Gear Pump Switchgear Using CFD Analysis. *Applied Sciences*. 2024; 14(13):5394.
https://doi.org/10.3390/app14135394

**Chicago/Turabian Style**

Zharkevich, Olga, Tatyana Nikonova, Łukasz Gierz, Olga Reshetnikova, Alexandra Berg, Łukasz Warguła, Andrey Berg, Bartosz Wieczorek, Wiktor Łykowski, and Oxana Nurzhanova.
2024. "Improving the Design of a Multi-Gear Pump Switchgear Using CFD Analysis" *Applied Sciences* 14, no. 13: 5394.
https://doi.org/10.3390/app14135394