# Experimental and Numerical Investigation of Tip Leakage Flows in a Roots Blower

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Experimental Setup and Data Processing

#### 2.2. Experimental Findings

## 3. CFD Model for Roots Blower

#### 3.1. CFD Settings and Boundary Conditions

#### 3.2. Grid Generation and Grip Independence Study

## 4. Analysis of the Tip Leakage Flow

#### 4.1. Comparison between the Experimental and Simulation Results

#### 4.2. Analysis of the Overall Flow Field

## 5. Discussion

## 6. Conclusions

- (1)
- A series of factors deteriorating the results of the PIV test were observed as follows: the surface flaws of the transparent window, the reflection of the surface, the jitter in the phase-locking due to uncertainties in the transmission of the synchronized gear, the accumulation of the liquid particles and the pressure fluctuations. These factors caused an increase in erroneous vectors and limited the quality of measured velocity fields. The solutions to these problems were discussed and will be implemented in future measurements in our lab.
- (2)
- The CFD flow field agrees with experimental results in the flow pattern and velocity magnitude at certain areas but overestimates the leakage flow velocity.
- (3)
- The vortex induced by the leakage flow through the tip gap results in the separation of high and low-velocity areas in the downstream region of the leakage flow. The main flow field changes significantly with the increased pressure ratio.
- (4)
- The leakage flow in the tip gap is laminar under the pressure ratios in this paper. The main flow losses occur upstream at the entrance of the tip gap. The total pressure changes moderately along the gap since the leakage flow does not diffuse much. The step at the rotor tip can be redesigned to increase pressure losses and reduce the leakage flow.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Roots blower test rig and diagram of visualizing test: (

**a**) Layout of the test rig, (

**b**) The laser plane on the Roots blower, (

**c**) Diagram of visualizing test. A—inverter, B—electromotor, C—pulleys, D—shaft encoder, E—torque meter, F—Roots blower, G—smoke tank, H—smoke machine, I—orifice plate, J—valve, K—Light source, L—surface mirror, M—double shutter camera, N—Position of Laser plane, T1—suction temperature transducer, P1—suction pressure transducer, T2—discharge temperature transducer, P2—discharge pressure transducer, T3—upstream temperature transducer, ΔP—differential pressure across an orifice plate.

**Figure 11.**Comparison between the flow fields in gaps obtained by experimental PIV and numerical CFD under the pressure ratio of 1.072 at two different angles of rotation (30

^{o}and 43

^{o}).

**Figure 12.**The overall flow field on the laser plane at 43° under pressure ratio 1.015 (

**a**) and 1.072 (

**b**).

**Figure 13.**The velocity and pressure distribution in the tip gap at the crank angle of 43° under the pressure ratio of 1.015: (

**a**) velocity field, (

**b**) Total pressure, (

**c**) Static pressure.

**Figure 14.**The velocity and pressure distribution in the tip gap at the crank angle of 43° under the pressure ratio of 1.072: (

**a**) velocity field, (

**b**) Total pressure, (

**c**) Static pressure.

Items | Specification | Items | Specification |
---|---|---|---|

Diameter of the rotor (mm) | 101.3 | Tip gap (mm) | 0.4 |

Axis distance (mm) | 63.12 | Lobe gap (mm) | 0.17 |

Rotor length (mm) | 50.5 | Axial gap (mm) | 0.15 |

Displacement volume (L/rev) | 0.4618 | Width of tip step (mm) | 6.4 |

Inlet Pressure (Bar) | Inlet Temperature (K) | Outlet Pressure (Bar) | Outlet Temperature (K) | Pressure Ratio (-) | Speed (rpm) | Mass Flow Rate (g/s) |
---|---|---|---|---|---|---|

0.990 | 300.1 | 1.005 | 301.2 | 1.015 | 464 | 1.71 |

0.990 | 300.6 | 1.061 | 306.9 | 1.072 | 464 | 1.18 |

Setting | Specification | Setting | Specification |
---|---|---|---|

Advection scheme | High-resolution | Turbulence numeric | 1st order |

Transient scheme | 2nd order backward Euler | Wall model | No-slip with adiabatic walls |

Turbulence model | SST k-w with automatic wall functions | Iteration per time step | 20 |

Heat transfer model | Total energy including viscous terms | Inlet/Outlet condition | Opening with static pressure & temperature |

Working fluid | Air as Ideal gas | Inlet turbulence intensity | 5% |

Domain initialization | Standard atmospheric conditions | Convergence criteria | RMS 1E-4 |

Time step at 464 rpm | 3.592 × 10^{−4} |

Level | Circumference | Radial | Angular | Axial | Number of Grid Cells in Rotors |
---|---|---|---|---|---|

Grid-1 | 200 | 15 | 180 | 18 | 216,000 |

Grid-2 | 285 | 21 | 180 | 25 | 600,600 |

Grid-3 | 400 | 30 | 180 | 35 | 1,680,000 |

Grid-4 | 500 | 38 | 180 | 44 | 3,344,000 |

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**MDPI and ACS Style**

Sun, S.; Singh, G.; Kovacevic, A.; Bruecker, C.
Experimental and Numerical Investigation of Tip Leakage Flows in a Roots Blower. *Designs* **2020**, *4*, 3.
https://doi.org/10.3390/designs4010003

**AMA Style**

Sun S, Singh G, Kovacevic A, Bruecker C.
Experimental and Numerical Investigation of Tip Leakage Flows in a Roots Blower. *Designs*. 2020; 4(1):3.
https://doi.org/10.3390/designs4010003

**Chicago/Turabian Style**

Sun, Shuaihui, Gursharanjit Singh, Ahmed Kovacevic, and Christoph Bruecker.
2020. "Experimental and Numerical Investigation of Tip Leakage Flows in a Roots Blower" *Designs* 4, no. 1: 3.
https://doi.org/10.3390/designs4010003