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Aeroelastic Stability of Combined Plunge-Pitch Mode Shapes in a Linear Compressor Cascade^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Test Case

## 3. Test Rig

## 4. Numerical Method

#### 4.1. Flow Solver

#### 4.2. Computational Implementation

## 5. Aero-Damping Evaluation Method

## 6. Validation of CFD

#### 6.1. Steady State Flow

#### 6.2. Unsteady Flow

## 7. Stability Analysis

#### 7.1. Influence of Inter-Blade Phase Angle

#### 7.2. Influence of Reduced Frequency

#### 7.3. Influence of Torsion Axis Location

#### 7.4. Stability Map

#### 7.5. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

1F | First Flap Blade Mode |

AIC | Aerodynamic Influence Coefficient |

IBPA | Inter Blade Phase Angle |

ND | Nodal Diameter |

RANS | Reynolds Averaged Navier-Stokes |

SDOF | Single Degree of Freedom |

PS | Pressure Side |

SS | Suction Side |

VBM | Vibrating Blade Module |

$\zeta $ | Aerodynamic Damping Ratio |

${\theta}_{plunge}$ | Plunge Incidence Amplitude |

${\theta}_{pitch}$ | Pitch Incidence Amplitude |

$\xi $ | Stagger Angle |

$\varphi $ | Plunge-to-Pitch Incidence Ratio |

c | Chord |

f | Vibration Frequency |

k | Reduced frequency, $k=2\pi fc/u$ |

M | Mach Number |

s | Pitch |

u | Inlet Flow Velocity |

x | Pitch Axis Location |

z | Lever Length |

## References

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**Figure 10.**Validation of the unsteady mid-span blade surface pressure coefficient—$k=0.4$, $x/c=1$, $\varphi =0.2$.

**Figure 18.**Stability map for an infinite cascade of flat plates with $\xi =45$°, $s/c=1.0$, $\eta =x/c$. (Whitehead, 1974).

Mach number (-) | 0.087 |

Reynolds number (-) | 300,000 |

Incidence angle (deg) | 2 |

Reduced frequency range (-) | 0.2–0.7 |

Normalised torsion axis location (-) | 0.5–3 |

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## Share and Cite

**MDPI and ACS Style**

Hill, G.; Gambel, J.; Schneider, S.; Peitsch, D.; Stapelfeldt, S.
Aeroelastic Stability of Combined Plunge-Pitch Mode Shapes in a Linear Compressor Cascade. *Int. J. Turbomach. Propuls. Power* **2022**, *7*, 7.
https://doi.org/10.3390/ijtpp7010007

**AMA Style**

Hill G, Gambel J, Schneider S, Peitsch D, Stapelfeldt S.
Aeroelastic Stability of Combined Plunge-Pitch Mode Shapes in a Linear Compressor Cascade. *International Journal of Turbomachinery, Propulsion and Power*. 2022; 7(1):7.
https://doi.org/10.3390/ijtpp7010007

**Chicago/Turabian Style**

Hill, George, Julian Gambel, Sabine Schneider, Dieter Peitsch, and Sina Stapelfeldt.
2022. "Aeroelastic Stability of Combined Plunge-Pitch Mode Shapes in a Linear Compressor Cascade" *International Journal of Turbomachinery, Propulsion and Power* 7, no. 1: 7.
https://doi.org/10.3390/ijtpp7010007