# About the Influence of Eco-Friendly Fluids on the Performance of an External Gear Pump

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

_{v}, the face width, b, and the number of teeth, z. Meanwhile, in Equation (9), the formula for the computation of the ideal delivered flow rate is shown.

#### 3.1. Physics Comparison

#### 3.2. Influence of Eco-Friendly Fluids on the Thermo-Fluid-Dynamic Performance of the Pump

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

µ | Dynamic viscosity |

µ_{B} | Dynamic viscosity of Total BIOHYDRAN TMP 46 |

µ_{M} | Dynamic viscosity of mineral oil |

µ_{O} | Dynamic viscosity of olive oil |

ρ | Density |

ρ_{0} | Density at the atmospheric pressure |

ρ_{0,B} | Density of the Total BIOHYDRAN TMP 46 at the atmospheric pressure |

ρ_{0,M} | Density of the mineral oil at the atmospheric pressure |

ρ_{0,O} | Density of the olive oil at the atmospheric pressure |

A_{v} | Area of the displacement chamber |

b | Face width of the gears |

c | Speed of sound of the fluid |

CAD | Computer-aided design |

CFD | Computational fluid dynamics |

EGP | External gear pump |

FEM | Finite element method |

n | Pump rotation speed rate |

Q_{th} | Theoretical supply flow rate |

T | Temperature |

V | Displacement of the pump |

z | Teeth of the gears |

## References

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**Figure 2.**Layout of the pump: (

**a**) Three-dimensional transparent view of the case test EGP and its main mechanical components; (

**b**) driving gear and driven gear.

**Figure 5.**Overset mesh approach: (

**a**) Quadrilateral mesh of the background and overset regions; (

**b**) initialized overset interfaces; (

**c**) zoomed view of the gears’ meshing region; (

**d**) zoomed view of the mesh in the 10-μm radial gap.

**Figure 6.**Mesh of the axial leakages: (

**a**) Surface mesh; (

**b**) zoomed view of the mesh in the 30-μm axial gap. In the top left corner, a 3D view of the entire EGP highlights the position of the axial leakages.

**Figure 9.**Eco-friendly fluids properties: (

**a**) BIOHYDRAN TMP 46: density vs. temperature; (

**b**) BIOHYDRAN TMP 46: viscosity vs. temperature; (

**c**) olive oil: density vs. temperature; (

**d**) olive oil: viscosity vs. temperature.

**Figure 11.**Experimental volumetric efficiency of the pump (blue) and CFD result in Case #2 (orange).

**Figure 13.**Pressure within a displacement chamber of the pump during an entire revolution of the driving shaft. On the top left corner, the initial position of the monitoring point is reported.

**Figure 14.**Pressure colored maps: (

**a**) Pressure distribution within the entire 3D fluid domain of the pump; (

**b**) section view of the pressure field in the gears’ region.

**Figure 15.**Pressure signal within the axial gap of the pump during an entire revolution of the driving shaft. On the top left corner, the initial position of the monitoring point is reported.

**Figure 16.**Intermittency colored maps: (

**a**) Intermittency along the flow transfer section; (

**b**) intermittency within the axial leakage. The background and overset regions are highlighted in beige.

**Figure 17.**Pressure-intermittency correlation: (

**a**) Isobaric curves on a zoomed view of the axial leakage; (

**b**) intermittency on a zoomed view of the axial leakage. The background and overset regions are highlighted in beige.

**Figure 18.**Temperature within a displacement chamber of the pump (green) and in the 30-µm axial gap (purple).

**Figure 19.**Delivered flow rate: (

**a**) Case #2 and Case #3; (

**b**) Case #2 and Case #4. Both graphs are illustrated with respect to the angular position of the pump driving shaft.

**Figure 22.**Pressure within a displacement chamber of the pump during an entire revolution of the driving shaft for Case #2, Case #3, and Case #4.

**Figure 23.**Pressure within the axial gap of the pump during an entire revolution of the driving shaft for Case #2, Case #3, and Case #4.

**Figure 24.**Temperature within a displacement chamber of the pump: (

**a**) Case #2 and Case #3; (

**b**) Case #2 and Case #4.

Gears’ Geometrical Parameter | Value |
---|---|

Number of teeth | 12 |

Outside diameter | 38.50 mm |

Root diameter | 24.85 mm |

Face width | 6 mm |

Region | Cell Shape | Base Size | Extruded Layers | Wall Prism Layers |
---|---|---|---|---|

Background | Quadrilateral | 0.1 mm | 50 | 5 and PLS |

Oversets | Quadrilateral | 0.06 mm | 50 | 5 and PLS |

Axial Leakages | Quadrilateral | 0.2 mm | 20 | 5 |

Others | Quadrilateral | 0.3 mm | / | 2 |

Port | Boundary | Value |
---|---|---|

Suction | Stagnation Inlet | 0 bar |

Delivery | Pressure Outlet | 20 bar |

Drain | Pressure Outlet | 0 bar |

**Table 4.**Molecular weight, specific heat, speed of sound, and thermal conductivity of the three fluids.

Fluid | Physical Parameter | Value |
---|---|---|

Mineral Oil | Molecular Weight | 480 kg/kmol |

Mineral Oil | Specific Heat | 2000 J/kg-K |

Mineral Oil | Speed of Sound | 1300 m/s |

Mineral Oil | Thermal Conductivity | 0.13 W/m-K |

BIOHYDRAN TMP 46 | Molecular Weight | 900 kg/kmol |

BIOHYDRAN TMP 46 | Specific Heat | 2000 J/kg-K |

BIOHYDRAN TMP 46 | Speed of Sound | 1257 m/s |

BIOHYDRAN TMP 46 | Thermal Conductivity | 0.16 W/m-K |

Olive Oil | Molecular Weight | 1382.2 kg/kmol |

Olive Oil | Specific Heat | 2000 J/kg-K |

Olive Oil | Speed of Sound | 1455 m/s |

Olive Oil | Thermal Conductivity | 0.17 W/m-K |

Solver | Time Step | Turbulence | Wall-Y+ | Residuals |
---|---|---|---|---|

Coupled Implicit | 8.33 × 10^{−5} s | k-ω SST Model and gamma transition | <0.92 | <0.01 |

Case # | Fluid | Density | Viscosity | Energy |
---|---|---|---|---|

1 | Mineral Oil | $\rho ={\rho}_{25\xb0\mathrm{C}}$ | $\mu ={\mu}_{25\xb0\mathrm{C}}$ | Yes |

2 | Mineral Oil | (1), (2) | (3) | Yes |

3 | BIOHYDRAN TMP 46 | (1), (4) | (5) | Yes |

4 | Olive Oil | (1), (6) | (7) | Yes |

**Table 7.**Delivered flow rate and volumetric efficiency of the EGP for both the incompressible and the compressible fluid models. CFD: computational fluid dynamics.

Case # | CFD Flow Rate | Ideal Flow Rate | Volumetric Efficiency |
---|---|---|---|

1 | 8.28 L/min | 8.2 L/min | 101% |

2 | 8.04 L/min | 8.2 L/min | 98% |

**Table 8.**Delivered flow rate and volumetric efficiency of the pump for three different fluids: mineral oil, Total BIOHYDRAN TMP 46, and olive oil.

Case # | CFD Flow Rate | Ideal Flow Rate | Volumetric Efficiency |
---|---|---|---|

2 | 8.04 L/min | 8.2 L/min | 98% |

3 | 8.06 L/min | 8.2 L/min | 98.2% |

4 | 7.68 L/min | 8.2 L/min | 93.7% |

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**MDPI and ACS Style**

Muzzioli, G.; Montorsi, L.; Polito, A.; Lucchi, A.; Sassi, A.; Milani, M.
About the Influence of Eco-Friendly Fluids on the Performance of an External Gear Pump. *Energies* **2021**, *14*, 799.
https://doi.org/10.3390/en14040799

**AMA Style**

Muzzioli G, Montorsi L, Polito A, Lucchi A, Sassi A, Milani M.
About the Influence of Eco-Friendly Fluids on the Performance of an External Gear Pump. *Energies*. 2021; 14(4):799.
https://doi.org/10.3390/en14040799

**Chicago/Turabian Style**

Muzzioli, Gabriele, Luca Montorsi, Andrea Polito, Andrea Lucchi, Alessandro Sassi, and Massimo Milani.
2021. "About the Influence of Eco-Friendly Fluids on the Performance of an External Gear Pump" *Energies* 14, no. 4: 799.
https://doi.org/10.3390/en14040799