# Numerical Study on Aerodynamic and Noise Responses of Rotor with Ramp Increase in Collective Pitch Based on Time-Accurate Free-Wake Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Calculation Methods

#### 2.1. Time-Accurate Free-Wake Model

#### 2.2. Noise Prediction Method

^{.}) above a variable denotes the rate of variation with respect to source time. The subscript ret indicates that the integrals are evaluated at a retarded time; S is the integral surface.

## 3. Validation for Proposed Methods

#### 3.1. Hover Tests by the University of Maryland

#### 3.2. The Langley 2MRTS Rotor Test

#### 3.3. NACA Rotor with a Ramp Increase in Collective Pitch

#### 3.4. Aeroacoustic Experiment with AH-1/OLS

## 4. Aerodynamic and Noise Responses of the Rotor with a Ramp Increase in Collective Pitch

#### 4.1. Ramp Increase in Collective Pitch in Hover

#### 4.2. Ramp Increase in Collective Pitch in Forward Flight

## 5. Conclusions

- (1)
- The numerical cases verify that the modified TAFW scheme proposed has good numerical stability and simulation accuracy for the wake shape and induced velocity distribution of the rotor in steady hover and forward flight, and good consistency with the test for the aerodynamic load simulation of ramp increase in collective pitch. The rotor aerodynamic noise analysis method established also has good effectiveness in predicting rotor aerodynamic noise.
- (2)
- The ramp increase in collective pitch in hover leads to a rapid increase, overshoot, oscillation, and convergence variation in the aerodynamic force of the rotor. The time derivative of aerodynamic load suddenly increases at the initiation of the ramp increase in collective pitch, and the amplitude is large but gradually decreases during the ramp change until it suddenly decreases at the termination. The amplitude of the load derivative after the ramp change is much smaller than that during the ramp change.
- (3)
- The ramp increase in collective pitch has a relatively smaller impact on thickness noise but significantly affects loading noise, resulting in a clear directionality in hover loading noise. However, this phenomenon mainly exists during the ramp change. After the ramp change stops, the loading noise quickly converges to a new steady state.
- (4)
- When the collective pitch experiences a ramp increase in forward flight, there are mainly three timescales of variation in rotor load and loading noise: short-term, medium-term, and long-term, among which the short-term and medium-term variations show significant aperiodicity. In cases with BVI, the BVI noise shows a non-periodic variation in the mid-term timescale.
- (5)
- The influences of pitch rate and the start and stop azimuth angles are mainly reflected in short-term variations, where a higher pitch rate leads to higher loading noise, while the start and end azimuth angles can significantly affect the directionality of loading noise by influencing the azimuth angle of sudden changes in load derivatives and the subsequent evolution of the flow field. A reasonable selection of various ramp change start and end azimuth angles in maneuvering flight has the prospect of becoming an active control method for maneuvering flight noise.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${a}_{0}$ | sound speed |

$M$ | Mach number |

$n$ | outer normal |

$p$ | pressure |

r | distance to the center of the rotor |

$\mathit{r}$ | position vector |

R | rotor radius |

$\mathit{V}$ | velocity |

$\mathsf{\u0413}$ | vorticity magnitude |

$\zeta $ | the age angle of the wake vortex |

$\mu $ | advance ratio |

$\rho $ | density |

$\psi $ | the azimuth angle of the blade |

$\mathsf{\Omega}$ | the rotation speed of the rotor |

$\tau $ | sound source time |

$t$ | observation time |

3 upwind BDF | third-order upwind backward differentiation formulas |

BVI | blade vortex interaction |

CB2D | Center difference and backward difference second-order scheme with numerical dissipation |

CFD | computational fluid dynamics |

F1A | Farassat 1A |

FW H | Fowcs Williams–Hawkings |

PC2B | Predictor-Corrector second-order backward difference |

TAFW | time-accurate free-wake |

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**Figure 2.**Comparison between predicted and measured results in experimental hover tests by the University of Maryland. (

**a**) Tip vortex geometry; (

**b**) Time-averaged induced inflow distribution.

**Figure 3.**Comparison of the tip vortex geometry of Rotor 2 as predicted by the original and modified schemes. (

**a**) Original 3-upwind BDF; (

**b**) modified scheme in present work.

**Figure 4.**Comparison of tip vortex trajectories between predicted and measured results of the Langley 2MRTS rotor for the first blade. (

**a**) $\mu $ = 0.15, $\psi =0\xb0$, top-view; (

**b**) $\mu $ = 0.15, $\psi =0\xb0$, side-view; (

**c**) $\mu $ = 0.25, $\psi =180\xb0$, top-view; (

**d**) $\mu $ = 0.23, $\psi =180\xb0$, side-view.

**Figure 5.**Comparison of time-averaged induced inflow distribution between predicted and measured results of the Langley 2MRTS rotor for the first blade. (

**a**) $\mu $ = 0.15, longitudinal inflow; (

**b**) $\mu $ = 0.23, lateral inflow.

**Figure 6.**Comparison between predicted and measured results of NACA rotor with ramp increase in collective pitch in hover condition. (

**a**) Instantaneous thrust coefficient; (

**b**) the ratio of instantaneous induced velocity to steady-state induced velocity.

**Figure 7.**The aeroacoustics test of the AH-1/OLS rotor and sound pressure time history of Case 10014. (

**a**) the aeroacoustics test; (

**b**) Mic #3; (

**c**) Mic #9.

**Figure 9.**Variation of aerodynamic forces of cases in hover at r = 0.8 R. (

**a**) Nondimensional normal force; (

**b**) time derivative of normal force.

**Figure 10.**Variation of sound pressure level distribution in case 1. (

**a**) Thickness noise: (

**a.1**) 1 rev; (

**a.2**) 2 rev; (

**a.3**) 3 rev; (

**b**) loading noise: (

**b.1**) 1 rev; (

**b.2**) 2 rev; (

**b.3**) 3 rev.

**Figure 12.**Variation of loading noise sound pressure time history of case 1 at different observers with different azimuth angles.

**Figure 13.**Variation of loading noise sound pressure level distribution of the various cases in hover. (

**a**) case 1 (+4°, 25°/s): (

**a.1**) 1 rev; (

**a.2**) 2 rev; (

**a.3**) 3 rev; (

**b**) case 2 (+4°, 50°/s): (

**b.1**) 1 rev; (

**b.2**) 2 rev; (

**b.3**) 3 rev; (

**c**) case 3 (+2°, 50°/s): (

**c.1**) 1 rev; (

**c.2**) 2 rev; (

**c.3**) 3 rev.

**Figure 14.**Variation of loading noise sound pressure time history of cases 1 and 2 to the observer with an elevation angle of 30° and an azimuth angle of 130°.

**Figure 16.**Variation of the nondimensional normal force of the two blades of cases in forward flight at r = 0.85 R during t = 0.15–0.5 s. (

**a**) Overall; (

**b**) case 1 (+4°, 25°/s); (

**c**) case 2 (+4°, 50°/s); (

**d**) case 3 (+2°, 50°/s); (

**e**) case 4 (+4°, 50°/s, delayed).

**Figure 17.**Variation of the nondimensional normal force of the two blades of cases in forward flight at r = 0.85 R during t = 0.5–1.0 s. (

**a**) Overall; (

**b**) case 1 (+4°, 25°/s); (

**c**) case 2 (+4°, 50°/s); (

**d**) case 3 (+2°, 50°/s); (

**e**) case 4 (+4°, 50°/s, delayed).

**Figure 18.**Variation of loading noise sound pressure level distribution of the various cases with the same start azimuth angle in forward fight. (

**a**) Case 1 (+4°, 25°/s): (

**a.1**) 1 rev; (

**a.2**) 2 rev; (

**a.3**) 3 rev; (

**a.4**) 4 rev; (

**b**) case 2 (+4°, 50°/s): (

**b.1**) 1 rev; (

**b.2**) 2 rev; (

**b.3**) 3 rev; (

**b.4**) 4 rev; (

**c**) case 3 (+2°, 50°/s): (

**c.1**) 1 rev; (

**c.2**) 2 rev; (

**c.3**) 3 rev; (

**c.4**) 4 rev.

**Figure 19.**Variation of loading noise sound pressure time history of the various cases with the same start time at different observers. (

**a**) Observer with elevation angle of 40° and azimuth angle of 40°; (

**b**) observer with elevation angle of 40° and azimuth angle of 130°; (

**c**) observer with elevation angle of 40° and azimuth angle of 260°.

**Figure 20.**Variation of loading noise sound pressure time history of the various cases with the same start azimuth angle at the observer with an elevation angle of 40° and an azimuth angle of 130°. (

**a**) 0.2–0.4 s; (

**b**) 0.4–0.6 s; (

**c**) 0.6–0.8 s; (

**d**) 0.8–1.0 s.

**Figure 21.**Variation of loading noise sound pressure level distribution of the various cases with different start times of ramp change in forward fight. (

**a**) Case 2 (start time at t = 0.16 s): (

**a.1**) 1 rev; (

**a.2**) 2 rev; (

**b**) case 4 (start time at t = 0.2 s): (

**b.1**) 1 rev; (

**b.2**) 2 rev.

**Figure 22.**Variation of loading noise sound pressure time history of the various cases with different start times at different observers. (

**a**) observer with elevation angle of 40° and azimuth angle of 40°; (

**b**) observer with elevation angle of 40° and azimuth angle of 130°; (

**c**) observer with elevation angle of 40° and azimuth angle of 260°.

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## Share and Cite

**MDPI and ACS Style**

Hu, Z.; Xia, R.; Shi, Y.; Xu, G.
Numerical Study on Aerodynamic and Noise Responses of Rotor with Ramp Increase in Collective Pitch Based on Time-Accurate Free-Wake Method. *Machines* **2023**, *11*, 1007.
https://doi.org/10.3390/machines11111007

**AMA Style**

Hu Z, Xia R, Shi Y, Xu G.
Numerical Study on Aerodynamic and Noise Responses of Rotor with Ramp Increase in Collective Pitch Based on Time-Accurate Free-Wake Method. *Machines*. 2023; 11(11):1007.
https://doi.org/10.3390/machines11111007

**Chicago/Turabian Style**

Hu, Zhiyuan, Runze Xia, Yongjie Shi, and Guohua Xu.
2023. "Numerical Study on Aerodynamic and Noise Responses of Rotor with Ramp Increase in Collective Pitch Based on Time-Accurate Free-Wake Method" *Machines* 11, no. 11: 1007.
https://doi.org/10.3390/machines11111007