#
Effect of Geometry Variability on Transonic Fan Blade Untwist ^{†}

^{1}

^{2}

^{*}

^{†}

^{‡}

## Abstract

**:**

## 1. Introduction

## 2. Test Cases and Computational Approach

#### 2.1. Test Cases

#### 2.2. Aeroelastic Solver

#### 2.3. APD Computations

#### 2.4. Computational Domain

## 3. APD Mechanism

## 4. Results and Discussion

#### 4.1. APD Intensity Map

#### 4.2. Reduced Order Approach

## 5. APD and Mistuning

## 6. Conclusions and Future Work

- Through the APD contour map and the loci of peak shock displacement sensitivity, it can be concluded that APD is closely related to the discontinuity/non-linearity in the untwist behaviour of the fan blades.
- Comparison of the two blades’ geometry and the corresponding difference in their APD behaviour reveals that a discontinuous/abrupt transition in the passage shock position exacerbates the APD behaviour. A spin-off idea from this observation is the convergent section of the covered passage (where the passage shock cannot be stabilised) on fan 2 can introduce unsteadiness in the annulus because it prompts shock displacement and further aeromechanical change. In fact, it is previously observed that under certain conditions, APD can be accompanied by a travelling disturbance around the annulus. It is important to investigate the unsteady effect of APD because it can influence the fan blades’ high cycle fatigue life.
- From the results comparison between the reduced order model and the full annulus coupled computation, it is evident that the peak APD conditions at each constant speed line can be located by the reduced order model. This will result in the reduction in computation cost. Therefore, it would be interesting to investigate whether reduced order model can be used to quantify APD intensity such that it can be incorporated into fan blade design approach.
- As demonstrated, APD occurs in close proximity to design point which sets it apart from other types of aeromechanical instabilities (such as flutter) which usually occur at off-design conditions and thus of relatively less concern to the engine manufacturers. This makes it paramount for the manufacturers to comprehend this phenomenon.
- Given that intentional mistuning which is usually used to prevent flutter behaviour (i.e., at off-design conditions) can introduce APD behaviour (close to design condition), it is crucial for engine manufacturers to investigate the APD behaviour.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

APD | Alternate passage divergence |

ESS | Engine section stator |

FE | Finite element |

FFT | Fast Fourier transform |

MPT | Multiple pure tone |

OGV | Outlet guide vane |

RANS | Reynolds-averaged Navier–Stokes |

SLS | Sea level static |

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**Figure 1.**Typical alternate passage divergence (APD) behaviour illustrated through relative tip stagger pattern.

**Figure 2.**Normalised deflection contour plots for blade from fan 1. (

**a**) First flapwise bending modes. (

**b**) Second flapwise bending mode. (

**c**) First torsional mode. (

**d**) Untwist deflection contour at peak efficiency condition.

**Figure 4.**Three types of flow regimes on a constant speed line. Aeromechanical data from fan 1 are presented.

**Figure 5.**Schematic diagram illustrating the passage shock displacement at blade tip under APD condition.

**Figure 9.**Pressure distribution at blade tips after a full annulus calculation (the worst APD case on the design speed line). (

**a**) Pressure distribution changes on Fan 1. (

**b**) Pressure distribution changes on Fan 2. Direction of rotation is represented by descending blade numbers. Blade 4 is initially mis-staggered.

**Figure 10.**Relative shock displacement and its second derivative. The data are from fan 1’s design speed cases.

**Figure 11.**Effect of mistuning on running geometry. (a) Initial mistuning pattern. (b) Resulting tip stagger pattern. (c) Fourier decomposition of the patterns. A mistuned system (frequency mistuning on mode 1) could results in alternating tip stagger from a perfectly symmetrical initial geometry.

Fan 1 | Fan 2 | |
---|---|---|

Aspect Ratio (Blade Height/Mid-Span Chord) | 2.0 | 2.3 |

By-Pass Ratio | 8–12 | 5–7 |

Number of Blades | 18 | 26 |

Tip Stagger Angle | 63–68${}^{\xb0}$ | 65–70${}^{\xb0}$ |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lu, Y.; Lad, B.; Green, J.; Stapelfeldt, S.; Vahdati, M.
Effect of Geometry Variability on Transonic Fan Blade Untwist ^{†}. *Int. J. Turbomach. Propuls. Power* **2019**, *4*, 24.
https://doi.org/10.3390/ijtpp4030024

**AMA Style**

Lu Y, Lad B, Green J, Stapelfeldt S, Vahdati M.
Effect of Geometry Variability on Transonic Fan Blade Untwist ^{†}. *International Journal of Turbomachinery, Propulsion and Power*. 2019; 4(3):24.
https://doi.org/10.3390/ijtpp4030024

**Chicago/Turabian Style**

Lu, Yaozhi, Bharat Lad, Jeff Green, Sina Stapelfeldt, and Mehdi Vahdati.
2019. "Effect of Geometry Variability on Transonic Fan Blade Untwist ^{†}" *International Journal of Turbomachinery, Propulsion and Power* 4, no. 3: 24.
https://doi.org/10.3390/ijtpp4030024