# Leading-Edge Erosion and Floating Particles: Stagnation Point Simulation in Particle-Laden Turbulent Flow via Lagrangian Particle Tracking

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Theory

#### 2.2. Turbulent Flow Characterizations

#### 2.3. Stokes Number

#### 2.4. Stagnation Plane Definition

- In the Lagrangian particle tracking method (LPT), the path line of each particle can be followed from the time it entered the study area to the time it left.
- When particles encircle the streamlined body, two-particle states can be observed; the particles either pass the stagnation plane or continue their path without crossing the stagnation plane.

## 3. Apparatus

## 4. Results and Discussion

#### 4.1. Particle Characterization

#### 4.2. Particle Leading to Erosion and Stagnation Plane

#### 4.3. Erosion Caused by Turbulence and Flow Strain

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LPT | Lagrangian Particle Tracking |

PTV | Particle Tracking Velocimetry |

PIV | Particle Image Velocimetry |

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**Figure 1.**A sketch of the straining turbulent flow simulation [21].

**Figure 2.**A photo of the facility used in the experiment. A tank containing water seeded with tracer and inertial particles separately; impellers generate turbulence flow, while two circular plates cause strain deformation with a particular mean strain rate. The laser sheet has been synchronized with a high-speed camera to record the frames.

**Figure 3.**A side-view sketch of the facility illustrates the measurement area location, size, and coordinate system [21].

**Figure 4.**In view of the assumed stagnation plane, the location crosses the stagnation point on the airfoil. Particles have two scenarios, some pass the stagnation plane, and others do not. Image used courtesy of ANSYS, Inc. Canonsburg, PA, USA [49].

**Figure 5.**Flow cases with two different $R{e}_{\lambda}$ are affected by the strain rate, and both variables make the erosion ratio vary.

**Figure 6.**Flow cases with two different mean strain rates are affected by the turbulence intensity, and both variables vary the erosion ratio.

Particle Type | Diameter [mm] | Density [kg/m${}^{3}$] | ${\mathit{\tau}}_{\mathit{p}}$ [ms] | Strain Rate on a Prototype Airfoil S809 [s${}^{-1}$] | Non-Dimensional Time Scale |
---|---|---|---|---|---|

Hail | 5.00 | 8.2 × 10${}^{-2}$ | 6.3 × 10${}^{0}$ | 14 | 8.8 × 10${}^{-2}$ |

Raindrop | 1.00 | 1.0 × 10${}^{3}$ | 3.0 × 10${}^{-1}$ | 14 | 4.3 × 10${}^{-3}$ |

Sand | 0.67 | 1.4 × 10${}^{3}$ | 7.1 × 10${}^{-1}$ | 14 | 9.9 × 10${}^{-2}$ |

Insects | 5.00 | 2.4 × 10${}^{-1}$ | 3.5 × 10${}^{-4}$ | 14 | 4.7 × 10${}^{-6}$ |

Tracer | 0.01 | 1.1 × 10${}^{3}$ | 1.6 × 10${}^{-3}$ | 14 | 2.3 × 10${}^{-5}$ |

Inertial | 0.25 | 2.5 × 10${}^{3}$ | 2.8 × 10${}^{-2}$ | 14 | 3.9 × 10${}^{-4}$ |

**Table 2.**The coordinates of the stagnation plane were measured in 2D for each flow case and where the particles have velocity ≈ 0. Tracer particles were used to seed the flow and both the turbulence intensity and strain rate were varied.

Flow Case | Mean Strain Rate [s${}^{-1}$] | x-Coordinate [mm] | y-Coordinate [mm] |
---|---|---|---|

$R{e}_{\lambda}=100$ | 4 | −4.6 | 7.3 |

$R{e}_{\lambda}=100$ | 8 | −2.3 | 7.0 |

$R{e}_{\lambda}=160$ | 4 | 1.9 | 1.6 |

$R{e}_{\lambda}=160$ | 8 | 2.8 | −3.1 |

**Table 3.**The erosion ratio of two types of particles has been varied and is affected by the mean strain rate (deformation/shear of the flow) and the turbulence intensity.

Turbulence Intensity | Mean Strain Rate [s${}^{-1}$] | Particle Type | Erosion Ratio (ER) |
---|---|---|---|

$R{e}_{\lambda}=100$ | 4 | Tracer | 26% |

4 | Inertial | 28% | |

8 | Tracer | 36% | |

8 | Inertial | 32% | |

$R{e}_{\lambda}=160$ | 4 | Tracer | 49% |

4 | Inertial | 47% | |

8 | Tracer | 46% | |

8 | Inertial | 42% |

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**MDPI and ACS Style**

Hassanian, R.; Riedel, M.
Leading-Edge Erosion and Floating Particles: Stagnation Point Simulation in Particle-Laden Turbulent Flow via Lagrangian Particle Tracking. *Machines* **2023**, *11*, 566.
https://doi.org/10.3390/machines11050566

**AMA Style**

Hassanian R, Riedel M.
Leading-Edge Erosion and Floating Particles: Stagnation Point Simulation in Particle-Laden Turbulent Flow via Lagrangian Particle Tracking. *Machines*. 2023; 11(5):566.
https://doi.org/10.3390/machines11050566

**Chicago/Turabian Style**

Hassanian, Reza, and Morris Riedel.
2023. "Leading-Edge Erosion and Floating Particles: Stagnation Point Simulation in Particle-Laden Turbulent Flow via Lagrangian Particle Tracking" *Machines* 11, no. 5: 566.
https://doi.org/10.3390/machines11050566