#
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 |

## References

- Schuff, M.; Lengyel-Kampmann, T.; Forsthofer, N. Influence of the Steady Deformation on Numerical Flutter Prediction for Highly Loaded and Flexible Fan Blades. In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition; American Society of Mechanical Engineers: New York, NY, USA, 2017; p. V07BT36A011. [Google Scholar]
- Rugg, D. Trends and Issues—Titanium Alloy use in Gas Turbines. 2010. Available online: https://goo.gl/Hxzj6j (accessed on 2 July 2018).
- Wilson, M.J.; Imregun, M.; Sayma, A.I. The Effect of Stagger Variability in Gas Turbine Fan Assemblies. J. Turbomach.
**2007**, 129, 404–411. [Google Scholar] [CrossRef] - Stratford, B.; Newby, D. A New Look at the Generation of Buzz-Saw Noise. In Proceedings of the AIAA 4th Aeroacoustics Conference, Atlanta, GA, USA, 3–5 October 1977; AIAA: Reston, VA, USA, 1977. AIAA Paper 77-1343. [Google Scholar]
- Han, F.; Sharma, A.; Paliath, U.; Shieh, C. Multiple Pure Tone Noise Prediction. J. Sound Vib.
**2014**, 333, 6942–6959. [Google Scholar] [CrossRef] - McAlpine, A.; Fisher, M.; Tester, B. ‘Buzz-Saw’ noise: A Comparison of Measurement with Prediction. J. Sound Vib.
**2006**, 290, 1202–1233. [Google Scholar] [CrossRef] - Lu, Y.; Green, J.; Vahdati, M.; Stapelfeldt, S.C. Effect of Geometry Variability on Fan Performance and Aeromechanical Characteristics. In Proceedings of the 15th International Symposium on Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, Oxford, UK, 24–27 September 2018; pp. 24–27. [Google Scholar]
- Stapelfeldt, S.C.; Vahdati, M. On the Importance of Engine-Representative Models for Fan Flutter Predictions. J. Turbomach.
**2018**, 140, 081005. [Google Scholar] [CrossRef] - Vahdati, M.; Simpson, G.; Imregun, M. Mechanisms for Wide-Chord Fan Blade Flutter. J. Turbomach.
**2011**, 133, 041029. [Google Scholar] [CrossRef] - Choi, M.; Smith, N.H.; Vahdati, M. Validation of Numerical Simulation for Rotating Stall in A Transonic Fan. J. Turbomach.
**2013**, 135, 021004. [Google Scholar] [CrossRef] - Stapelfeldt, S.C.; Parry, A.B.; Vahdati, M. Investigation of Flutter Mechanisms of A Contra-Rotating Open Rotor. J. Turbomach.
**2016**, 138, 051009. [Google Scholar] [CrossRef] - Sayma, A.I.; Vahdati, M.; Sbardella, L.; Imregun, M. Modeling of Three-Dimensional Viscous Compressible Turbomachinery Flows using Unstructured Hybrid Grids. AIAA J.
**2000**, 38, 945–954. [Google Scholar] [CrossRef] - Spalart, P.; Allmaras, S. A One-Equation Turbulence Model for Aerodynamic Flows. In Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 6–9 January 1992; p. 439. [Google Scholar]
- Lee, K.; Wilson, M.; Vahdati, M. Numerical Study on Aeroelastic Instability for a Low Speed Fan. In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition; American Society of Mechanical Engineers: New York, NY, USA, 2016; p. V07BT34A006. [Google Scholar]
- Sayma, A.; Vahdati, M.; Imregun, M. An Integrated Nonlinear Approach for Turbomachinery Forced Response Prediction. Part I: Formulation. J. Fluids Struct.
**2000**, 14, 7–101. [Google Scholar] [CrossRef] - Mayorca, M.A. Numerical Methods for Turbomachinery Aeromechanical Predictions. Ph.D. Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2011. [Google Scholar]
- Calvert, W.; Ginder, R. Transonic Fan and Compressor Design. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**1999**, 213, 419–436. [Google Scholar] [CrossRef] - Denton, J.D.; Xu, L. The Effects of Lean and Sweep on Transonic Fan Performance. In ASME Turbo Expo 2002: Power for Land, Sea, and Air; American Society of Mechanical Engineers: New York, NY, USA, 2002; pp. 23–32. [Google Scholar][Green Version]
- V. Kaza, K.R.; Kielb, R.E. Flutter and Response of a Mistuned Cascade in Incompressible Flow. AIAA J.
**1982**, 20, 1120–1127. [Google Scholar] [CrossRef] - Salles, L.; Vahdati, M. Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter. In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition; American Society of Mechanical Engineers: New York, NY, USA, 2016; p. V07BT34A0188. [Google Scholar]
- Figaschewsky, F.; Kühhorn, A.; Beirow, B.; Nipkau, J.; Giersch, T.; Power, B. Design and Analysis of an Intentional Mistuning Experiment Reducing Flutter Susceptibility and Minimizing Forced Response of a Jet Engine Fan. In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition; American Society of Mechanical Engineers: New York, NY, USA, 2017; p. V07BT36A020. [Google Scholar]

**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