# Blade-Tip Vortex Noise Mitigation Traded-Off against Aerodynamic Design for Propellers of Future Electric Aircraft

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Methodology

#### 2.1. Genetic Algorithm-Based Optimization Platform

#### 2.2. Hybrid Computational Aeroacoustics

## 3. Design and Optimization of Propellers

## 4. Transient Flow Simulation

#### 4.1. Computational Setup

#### 4.2. Mesh Independence Study and Aerodynamics Validation

## 5. Tip-Vortex Noise Simulations

#### 5.1. Noise Source Identification

#### 5.2. Aeroacoustic Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AOA | Angle of attack |

BPF | Blade passing frequency |

BVI | Blade votex interaction |

CAA | Computaional aeroacoustics |

CFD | Computational fluid dynamics |

FW-H | Ffowcs Williams and Hawkings |

IDDES | Improved delayed detached eddy simulation |

MRF | Multiple reference frame |

OASPL | Overall sound pressure level |

RPM | Revolutions per minute |

SMM | Sliding Mesh Method |

SPL | Sound pressure level |

RANS | Reynolds-averaged Navier–Stokes equations |

## References

- Follen, G.J.; Del Rosario, R.; Wahls, R.; Madavan, N. NASA’s Fundamental Aeronautics Subsonic Fixed Wing Project: Generation N+3 Technology Portfolio. In Proceedings of the Aerospace Technology Conference and Exposition, Toulouse, France, 18–20 September 2011. [Google Scholar] [CrossRef]
- Krein, A.; Williams, G. FlightPath 2050: Europe Vision 2020 for Aviation. In Innovation for Sustainable Aviation in a Global Environment, Proceedings of the Sixth European Aeronautics Days, Madrid, Spain, 30 March–1 April 2011; IOS Press: Amsterdam, The Netherlands, 2012. [Google Scholar]
- Pornet, C.; Isikveren, A.T. Conceptual Design of Hybrid-Electric Transport Aircraft. Prog. Aerosp. Sci.
**2015**, 79, 114–135. [Google Scholar] [CrossRef] - Huang, Z.J.; Yao, H.D.; Sjögren, O.; Lundbladh, A.; Davidson, L. Aeroacoustic analysis of aerodynamically optimized joined-blade propeller for future electric aircraft at cruise and take-off. Aerosp. Sci. Technol.
**2020**, 107, 106336. [Google Scholar] [CrossRef] - Ffowcs Williams, J.E.; Hawkings, D.L. Sound generation by turbulence and surfaces in arbitrary motion. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1969**, 264, 321–342. [Google Scholar] - Farassat, F.; Succi, G. A review of propeller discrete frequency noise prediction technology with emphasis on two current methods for time domain calculations. J. Sound Vib.
**1980**, 71, 399–419. [Google Scholar] [CrossRef] - Zhao, Y.; Shi, Y.; Xu, G. Helicopter Blade-Vortex Interaction Airload and Noise Prediction Using Coupling CFD/VWM Method. Appl. Sci.
**2017**, 7, 381. [Google Scholar] [CrossRef] [Green Version] - Ottersten, M.; Yao, H.D.; Davidson, L. Tonal noise of voluteless centrifugal fan generated by turbulence stemming from upstream inlet gap. Phys. Fluids
**2021**, 33, 075110. [Google Scholar] [CrossRef] - Richard, A.; Lundbladh, A. Air Propeller Arrangement and Aircraft. U.S. Patent 2012/0288374, 15 November 2012. [Google Scholar]
- Marte, J.E.; Kurtz, D.W. A Review of Aerodyanmic Noise from Propellers, Rotors and Lift Fans; Technical Report; California Institute of Technology: Pasadena, CA, USA, 1970. [Google Scholar]
- Kingan, M.; Self, R. Counter-Rotation Propeller Tip Vortex Interaction Noise. In Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Miami, FL, USA, 11–13 May 2009; AIAA: Miami, FL, USA, 2009. AIAA 2009-3135. [Google Scholar]
- Elson, T. Computational Aerodynamics for Open Rotor Tip Vortex Interaction Noise Prediction. Ph.D. Thesis, Cranfield University, Cranfield, UK, 2015. [Google Scholar]
- Farassat, F. Derivation of Formulations 1 and 1A of Farassat; Technical Report; NASA Technical Reports Server (NTRS): Hampton, VA, USA, 2007.
- Černý, M.; Herzog, N.; Faust, J.; Stuhlpfarrer, M.; Breitsamter, C. Systematic Investigation of a Fixed-Pitch Small-Scale Propeller Under Non-Axial Inflow Conditions. In Proceedings of the Deutscher Luft- und Raumfahrtkongress, Friedrichshafen, Germany, 4–6 September 2018. [Google Scholar] [CrossRef]
- Sanchez, R.D. Aerodynamic and Aeroacoustic Design of Small Unmanned Aircraft System Propellers at Low Reynolds Numbers. Ph.D. Thesis, Baylor University, Waco, TX, USA, 2020. [Google Scholar]
- Wilson, C.E. Noise Control: Measurement, Analysis and Control of Sound and Vibration; Krieger Publishing Company: Malabar, FL, USA, 2005. [Google Scholar]
- Mellin, R.C.; Sovran, G. Controlling the tonal characteristics of the aerodynamic noise generated by fan rotors. J. Basic Eng.
**1970**, 92, 143–154. [Google Scholar] [CrossRef] - Kim, T. Reduction of Tonal Propeller Noise by Means of Uneven Blade Spacing. Ph.D. Thesis, University of California, Irvine, CA, USA, 2016. [Google Scholar]
- Dobrzynski, W. Propeller noise reduction by means of unsymmetrical blade-spacing. J. Sound Vib.
**1993**, 163, 123–136. [Google Scholar] [CrossRef] - Noda, R.; Ikeda, T.; Nakata, T.; Liu, H. Characterization of the low-noise drone propeller with serrated Gurney flap. Front. Aerosp. Eng.
**2022**, 1, 1004828. [Google Scholar] [CrossRef] - Callender, M. UAS Propeller/Rotor Sound Pressure Level Reduction through Leading Edge Modification. J. Appl. Mech. Eng.
**2017**, 6, 254. [Google Scholar] - Wei, Y.; Xu, F.; Bian, S.; Kong, D. Noise Reduction of UAV Using Biomimetic Propellers with Varied Morphologies Leading-Edge Serration. J. Bionic Eng.
**2020**, 17, 767–779. [Google Scholar] [CrossRef] - Patrao, A.C.; Villar, G.M.; Tomita, J.T.; Bringhenti, C.; Avellan, R.; Lundbladh, A.; Grönstedt, T. An Optimization Platform for High Speed Propellers. In Proceedings of the Aerospace Technology Congress, Toyama, Japan, 25–27 October 2016. [Google Scholar]
- Ghorbaniasl, G.; Lacor, C. A Moving Medium Formulation for Prediction of Propeller Noise at Incidence. J. Sound Vib.
**2012**, 331, 117–137. [Google Scholar] [CrossRef] - Yao, H.D.; Davidson, L.; Eriksson, L.E.; Grundestam, O.; Peng, S.H.; Eliasson, P.E. Surface integral analogy approaches to computing noise generated by a 3D high-lift wing configuration. In Proceedings of the 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA, 9–12 January 2012. AIAA 2012-0386. [Google Scholar]
- Haller, G. An objective definition of a vortex. J. Fluid Mech.
**2005**, 525, 1–26. [Google Scholar] [CrossRef] [Green Version] - Li, Q.; Wang, Y.; Eitelberg, G. An investigation of tip vortices unsteady interaction for Fokker 29 propeller with swirl recovery vane. Chin. J. Aeronaut.
**2016**, 29, 117–128. [Google Scholar] [CrossRef] [Green Version] - Joulain, A.; Desvigne, D.; Alfano, D.; Leweke, T. Numerical investigation of the vortex roll-up from a helicopter blade tip using a novel fixed-wing adaptation method. CEAS Aeronaut. J.
**2017**, 8, 245–260. [Google Scholar] [CrossRef] - Arakawa, C.; Fleig, O.; Iida, M.; Shimooka, M. Numerical approach for noise reduction of wind turbine blade tip with earth simulator. J. Earth Simulator
**2005**, 2, 11–33. [Google Scholar] - Yao, H.D.; Davidson, L.; Peng, S.H.; Eriksson, L.E. Assessment of flap side-edge fence noise using SNGR method. In Proceedings of the 21st AIAA/CEAS Aeroacoustics Conference, Dallas, TX, USA, 22–26 June 2015. [Google Scholar]
- Zhou, B.Y.; Gauger, N.R.; Yao, H.D.; Peng, S.H.; Davidson, L. Towards Adjoint-Based Broadband Noise Minimization Using Stochastic Noise Generation; AIAA 2019-0002; AIAA: Reston, VI, USA, 2019. [Google Scholar]

**Figure 1.**Sources of the aerodynamic noise from a rotating blade, reproduced from [10]. The sources in the colorful boxes are usually predominant, and the one in the red box is the focus in this paper. Note that the loading and thickness noise can also be related to part of the broadband noise if flow separation or turbulence near the blade exists. Moreover, tip vortices can generate tonal noise under certain conditions, e.g., BVI.

**Figure 2.**The flow chart of the optimization platform [4].

**Figure 4.**The sectional distributions of the classical propellers, Conprop-3 and Conprop-6: (

**a**) the stacking line, (

**b**) the chord and thickness, (

**c**) the ideal lift coefficient and (

**d**) the pitch angle.

**Figure 5.**The sectional distributions of the parameters of the Boxprop dual-blade consisting of the leading and trailing sub-blades: (

**a**) the stacking line, (

**b**) the chord and thickness, (

**c**) the ideal lift coefficient and (

**d**) AOA as the sum of the pitch and helix angles.

**Figure 6.**The computational domain in the simulation of the configuration samples in the optimization, where R stands for the radius of the propeller.

**Figure 7.**Surface cells of the meshes for (

**a**) Conprop-6 and (

**b**) Boxprop. Volume and surface cells near the blade tip for (

**c**) Conprop-6 and (

**d**) Boxprop.

**Figure 8.**The Pareto Fronts obtained from the optimization of (

**a**) Conprop-3, (

**b**) Conprop-6 and (

**c**) Boxprop. Here the blue stars mark the points where the optimal configurations are extracted.

**Figure 10.**The transient thrust coefficients with respect to the normalized physical time in revolutions.

**Figure 11.**Iso-surfaces of the Q-criterion, colored by the velocity magnitude. From left to right: Boxprop, Conprop-3 and Conprop-6.

**Figure 12.**Contours of the instantaneous vorticity magnitudes at the radial position of $r=0.95\phantom{\rule{0.166667em}{0ex}}R$, where R is the propeller radius. The snapshots from left to right: $t=T/3$, $2T/3$ and T. T denotes the propeller revolution period. Note that the contour levels outside the range between 100 and 2000 are clipped off here.

**Figure 13.**Contours of the transient vorticity magnitudes in the cutting planes arranged along the propeller axial direction. From left to right: Boxprop, Conprop-3 and Conprop-6.

**Figure 14.**The placement of the permeable surfaces and the observers in the CAA computation. Boxprop is shown as an example.

**Figure 16.**The SPL spectra of the noise from the blade-tip vortices, compared at the far-field microphone positions located at $\theta ={60}^{\circ}$ (

**left**) and ${90}^{\circ}$ (

**right**).

Rotation speed | 1550 RPM |

Diameter | 2.794 m |

Flight altitude | 5151 m |

Cruise Mach number | $0.35$ |

Thrust coefficient | $0.106$ |

Mach number at blade tip | 0.79 |

**Table 2.**The aerodynamic performance of the down-selected optimal propellers, obtained from the preliminary prediction using RANS in the optimization.

Thrust Coefficient | Propeller Efficiency | |
---|---|---|

Conprop-3 | $0.1059$ | $0.845$ |

Conprop-6 | $0.1061$ | $0.873$ |

Boxprop | $0.1061$ | $0.858$ |

**Table 3.**The total number of nodes in Zone 1 and the aerodynamic parameters in the mesh independence study.

Coarse Mesh | Medium Mesh | Fine Mesh | ||
---|---|---|---|---|

Conprop-3 | Number of nodes | 3.6 M | 6.1 | 9.5 |

Thrust coefficient | 0.1056 | 0.1054 | 0.1053 | |

Conprop-6 | Number of nodes | 7.0 M | 11.7 M | 17.3 M |

Thrust coefficient | 0.1022 | 0.1017 | 0.1016 | |

Boxprop | Number of nodes | 7.9 M | 10.9 M | 14.4 M |

Thrust coefficient | 0.1103 | 0.1097 | 0.1095 |

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**MDPI and ACS Style**

Yao, H.-D.; Huang, Z.; Davidson, L.; Niu, J.; Chen, Z.-W.
Blade-Tip Vortex Noise Mitigation Traded-Off against Aerodynamic Design for Propellers of Future Electric Aircraft. *Aerospace* **2022**, *9*, 825.
https://doi.org/10.3390/aerospace9120825

**AMA Style**

Yao H-D, Huang Z, Davidson L, Niu J, Chen Z-W.
Blade-Tip Vortex Noise Mitigation Traded-Off against Aerodynamic Design for Propellers of Future Electric Aircraft. *Aerospace*. 2022; 9(12):825.
https://doi.org/10.3390/aerospace9120825

**Chicago/Turabian Style**

Yao, Hua-Dong, Zhongjie Huang, Lars Davidson, Jiqiang Niu, and Zheng-Wei Chen.
2022. "Blade-Tip Vortex Noise Mitigation Traded-Off against Aerodynamic Design for Propellers of Future Electric Aircraft" *Aerospace* 9, no. 12: 825.
https://doi.org/10.3390/aerospace9120825