# Flocking Bird Strikes on Engine Fan Blades and Their Effect on Rotor System: A Numerical Simulation

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## Abstract

**:**

## 1. Introduction

## 2. Bird-Strike and Rotor Dynamics System Modeling

#### 2.1. Bird SPH Model and Validation

_{s}− v

_{p}curve’s intercept; S

_{1}, S

_{2}, and S

_{3}are the v

_{s}− v

_{p}curve’s slope coefficients; ${\gamma}_{0}$ is the Gruneisen constant; a is the Gruneisen gamma’s first-order correction; and $\mu =\frac{\rho}{{\rho}_{0}}-1$ where $\rho $ is the material’s density and ${\rho}_{0}$ is the reference density. E is the elastic modulus of the material. For the bird substitute model, $C=1480m/s$, ${S}_{1}=1.29$ and ${\gamma}_{0}=0.1$; all other parameters were set to 0.

#### 2.2. Fan Modeling

#### 2.3. Bird-Strike Settings

#### 2.4. Prestress Analysis

#### 2.5. Aero-Engine Rotor System and Validation

- Consider the fan hub and blades as a disk, and add the bird impact force to this disk;
- The eccentricity of the rotor system existed only on the two simplified rotor disks;
- The connection between blades and disk was ignored, and the shaft and disks were considered to be rigidly connected;
- Gyroscopic effects of the rotor system were not considered due to the low speed of 3772 r/min.

#### 2.6. Dynamic Calculation Settings

## 3. Results and Discussion

#### 3.1. Bird Strike Simulation

#### 3.2. Rotor System Dynamics Calculation

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Nomenclature | |

Abbreviation | Definition |

3D | Three-Dimensional |

CT | Computed Tomography |

EOS | Equation Of State |

FAA | Federal Aviation Administration |

FE | Finite Element |

FEM | Finite Element Method |

IBRG | International Bird-strike Research Group |

SPH | Smoothed Particle Hydrodynamics |

US | United States |

List of symbols | |

Symbol | Definition |

$A$ | Yield stress |

a | First-order volume correction to γ_{0} |

$B$ | Strain hardening modulus |

${B}_{x}{,B}_{y}$ | Bird impact forces in the x and y directions |

C | The intercept of the velocity curve |

${C}_{B}$ | Damping coefficients of ball bearings |

${C}_{R}$ | Damping coefficients of the disk |

$c$ | Strain rate dependence coefficient |

D | Damage parameter |

${D}_{1},{D}_{2},{D}_{3},{D}_{4},{D}_{5}$ | Failure parameters |

E | Elastic modulus of material |

${e}_{R1}$ | The eccentricity of Disk 1 |

${e}_{R2}$ | The eccentricity of Disk 2 |

${\dot{e}}_{ij}$ | Rate-of-deformation tensor |

$G$ | Shear modulus |

$g$ | Gravitational acceleration |

${K}_{r}$ | Stiffness of the shaft |

${M}_{R1}$ | Mass of Disk 1 |

${M}_{R2}$ | Mass of Disk 2 |

${M}_{B1}$ | Mass of Bearing 1 |

${M}_{B2}$ | Mass of Bearing 2 |

${M}_{B3}$ | Mass of Bearing 3 |

$m$ | Softening exponent |

$n$ | Strain hardening exponent |

p | Pressure |

S_{1}, S_{2}, S_{3} | Slope coefficients of the velocity curve |

$T$ | Current temperature |

${T}_{m}$ | The melt temperature of the material |

${T}_{r}$ | Room temperature |

${T}^{*}$ | Homologous temperature |

$x,y$ | Displacement in the x and y directions |

$\stackrel{.}{x},\stackrel{.}{y}$ | Velocity in the x and y directions |

$\stackrel{..}{x}$, $\stackrel{..}{y}$ | Acceleration in the x and y directions |

$\gamma $ | Dynamic viscosity coefficient |

${\gamma}_{0}$ | Gruneisen constant |

${\mu}_{B}$ | Clearance of the ball bearing |

$\rho $ | The density of the material |

${\rho}_{0}$ | Reference density |

$\omega $ | Rotational speed |

List of Markings | |

Symbol | Definition |

A1 | Small flocking bird strike on the root and middle of blades |

A2 | Small flocking bird strike on the root and tip of blades |

A3 | Small flocking bird strike on the middle and tip of blades |

B1 | Medium flocking bird strike on the root of blades |

B2 | Medium flocking bird strike on the middle of blades |

B3 | Medium flocking bird strike on the tip of blades |

C1 | Large single bird strikes on the root of blades |

C2 | Large single bird strikes on the middle of blades |

C3 | Large single bird strikes on the tip of blades |

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**Figure 3.**The different bird-strike cases: (

**a**) small flocking birds, (

**b**) medium flocking birds, (

**c**) single large bird.

**Figure 7.**Distribution of Von Mises stress after impact by: (

**a**) small flocking birds; (

**b**) medium flocking birds; (

**c**) large single bird.

**Figure 8.**Contact force vs. time: (

**a**) small flocking birds; (

**b**) medium flocking birds; (

**c**) large single bird. The bearing force vs. time: (

**d**) small flocking birds; (

**e**) medium flocking birds; (

**f**) large single bird.

**Figure 9.**Kinetic energy vs. time: (

**a**) small flocking birds; (

**b**) medium flocking birds; (

**c**) large single bird.

**Figure 10.**The dynamic response of the fan before and after bird strike: displacement vs. time in the X direction (

**a**) before bird strike; (

**b**) after small flocking bird strike; (

**c**) after medium flocking bird strike; (

**d**) after large single bird strike; axis orbit: (

**e**) before bird strike; (

**f**) after small flocking bird strike; (

**g**) after medium flocking bird strike; (

**h**) after large single bird strike.

**Figure 11.**The dynamic response of the fan before and after bird strike: frequency spectrum of (

**a**) small flocking bird strike; (

**b**) medium flocking bird strike; (

**c**) large single bird strike; time-frequency graph of (

**d**) no bird strike; (

**e**) small flocking bird strike; (

**f**) medium flocking bird strike; (

**g**) large single bird strike.

Categories | Bird Quantity | Bird Weight (kg) | d (mm) | SPH Particles |
---|---|---|---|---|

Large bird | 1 | 2.75 | 130.8 | 36,755 |

Medium bird | 1 | 1.15 | 97.8 | 15,215 |

+5 | 0.7 | 82.9 | 9404 | |

Small bird | 16 | 0.085 | 41 | 1111 |

Parameter | Symbol |
---|---|

Density | $\mathsf{\rho}=4420\mathrm{kg}/\mathrm{m}3$ |

Shear modulus | $\mathrm{G}=41.9\mathrm{GPa}$ |

Yield stress | $\mathrm{A}=1098\mathrm{MPa}$ |

Strain hardening modulus | $\mathrm{B}=1092\mathrm{MPa}$ |

Strain hardening exponent | $\mathrm{n}=0.93$ |

Strain rate dependence coefficient | $\mathrm{c}=0.014$ |

Softening exponent | $\mathrm{m}=1.1$ |

Melting temperature | ${\mathrm{T}}_{\mathrm{M}}=1878\mathrm{K}$ |

Room temperature | ${\mathrm{T}}_{\mathrm{R}}=293\mathrm{K}$ |

Specific heat | ${\mathrm{C}}_{\mathrm{P}}=612\mathrm{J}/\mathrm{kg}\xb7\mathrm{K}$ |

Failure parameters | ${\mathrm{D}}_{1}=0.112$ |

${\mathrm{D}}_{2}=0.123$ | |

${\mathrm{D}}_{3}=0.48$ | |

${\mathrm{D}}_{4}=0.014$ | |

${\mathrm{D}}_{5}=3.87$ |

Symbol | Definition | Value |
---|---|---|

${B}_{x}{,B}_{y}$ | Bird impact forces in the x and y directions | / |

${C}_{B}$ | Damping coefficients of ball bearings | $4200N\cdot s/m$ |

${C}_{R}$ | Damping coefficients of the disk | $2050N\cdot s/m$ |

${e}_{R1}$ | The eccentricity of Disk 1 | ${5\times 10}^{-5}m$ |

${e}_{R2}$ | The eccentricity of Disk 2 | ${5\times 10}^{-5}m$ |

$g$ | Gravitational acceleration | $9{.8m/s}^{2}$ |

${K}_{r}$ | Stiffness of the shaft | ${3\times 10}^{7}N/m$ |

${M}_{R1}$ | Mass of Disk 1 | $294.75\mathrm{kg}$ |

${M}_{R2}$ | Mass of Disk 2 | $101.2\mathrm{kg}$ |

${M}_{B1}$ | Mass of Bearing 1 | $25.2\mathrm{kg}$ |

${M}_{B2}$ | Mass of Bearing 2 | $25.2\mathrm{kg}$ |

${M}_{B3}$ | Mass of Bearing 3 | $25.2\mathrm{kg}$ |

$x,y$ | Displacement in the x and y directions | / |

$\stackrel{.}{x},\stackrel{.}{y}$ | Velocity in the x and y directions | / |

$\stackrel{..}{x}$, $\stackrel{..}{y}$ | Acceleration in the x and y directions | / |

$\omega $ | Rotational speed | $3772\mathrm{rpm}$ |

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**MDPI and ACS Style**

Wu, B.; Lin, J.; Xie, A.; Wang, N.; Zhang, G.; Zhang, J.; Dai, H.
Flocking Bird Strikes on Engine Fan Blades and Their Effect on Rotor System: A Numerical Simulation. *Aerospace* **2022**, *9*, 90.
https://doi.org/10.3390/aerospace9020090

**AMA Style**

Wu B, Lin J, Xie A, Wang N, Zhang G, Zhang J, Dai H.
Flocking Bird Strikes on Engine Fan Blades and Their Effect on Rotor System: A Numerical Simulation. *Aerospace*. 2022; 9(2):90.
https://doi.org/10.3390/aerospace9020090

**Chicago/Turabian Style**

Wu, Bin, Jiewei Lin, Anshun Xie, Ning Wang, Guichang Zhang, Junhong Zhang, and Huwei Dai.
2022. "Flocking Bird Strikes on Engine Fan Blades and Their Effect on Rotor System: A Numerical Simulation" *Aerospace* 9, no. 2: 90.
https://doi.org/10.3390/aerospace9020090