# Frequency Response of RC Propellers to Streamwise Gusts in Forward Flight

^{*}

## Abstract

**:**

## 1. Introduction and Background

#### 1.1. Gust Types and Unsteady Wind Tunnels

#### 1.2. Propeller Performance in Unsteady Flows

## 2. Experimental Setup

#### 2.1. Propeller Test Setup

#### 2.2. Propeller Geometry

#### 2.3. Shuttering System

## 3. Shuttering System Characterization

## 4. Results

#### 4.1. Propeller Performance in Steady Freestream

#### 4.2. Propeller Performance under Time-Varying Sinusoidal Freestream

#### 4.2.1. KDE 12.5 × 4.3 Propeller

#### 4.2.2. APC 11 × 7 Propeller

#### 4.3. Effect of the Propeller Incidence Angle

#### 4.3.1. KDE 12.5 × 4.3 Propeller

#### 4.3.2. APC 11 × 7 Propeller

#### 4.4. Phase Response of Propellers

## 5. Conclusions

- An increment in propeller thrust, power, pitching moment, and rolling moment was found with the increment of incidence angle at the same advance ratio, which is consistent with the helicopter literature [9].
- Using the normalized advance ratio, ${J}_{{z}_{0}}$ and ${J}_{{z}_{90}}$, the propeller performance under various incidence angles collapses, except for thrust and power coefficient in near edgewise flight conditions.

- A good fit between the steady-state model and measurement is found for both coefficients up to a reduced frequency of 0.2.
- A reduction in both coefficients is found at a higher reduced frequency under 90${}^{\circ}$ and 75${}^{\circ}$ incidence angles for the lower $\gamma /D$ propeller. For the higher $\gamma /D$ propeller, an increment in both coefficients is observed at $\theta ={75}^{\circ}$.
- A phase lag in the propeller response is also observed at a higher reduced frequency range. The phase lag for the pitching moment overlaps for all cases. While the phase lag for the propeller thrust depends on the incidence angle.
- A reduction in the incidence angle leads to a phase lead in the thrust coefficient at a small reduce frequency range and a smaller phase lag at a higher reduced frequency range.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

c | Propeller local chord length, (m) |

${C}_{T}$ | Propeller thrust coefficient; ${C}_{T}=T/\left(\rho {n}^{2}{D}^{4}\right)$ |

${C}_{P}$ | Propeller Power coefficient; ${C}_{P}=P/\left(\rho {n}^{3}{D}^{5}\right)$ |

${C}_{Q}$ | Propeller torque coefficient; ${C}_{Q}=Q/\left(\rho {n}^{2}{D}^{5}\right)$ |

D | Propeller diameter, (m) |

J | Advance ratio; $J={V}_{\infty}/\left(nD\right)$ |

${J}_{z}$ | Normalized advance ratio |

${k}_{\omega}$ | Normalized shuttering system frequency |

n | Propeller rotational speed per second |

P | Power, (W) |

Q | Torque, ($N.m$) |

T | Thrust, (N) |

$\theta $ | Propeller incidence angle, ($deg$) |

$\gamma $ | Propeller pitch, (m) |

$\varphi $ | Propeller local blade pitch angle, ($deg$) |

$\omega $ | Shuttering system frequency, ($Hz$) |

$\Omega $ | Wind tunnel fan rotational speed, ($RPM$) |

$\Delta \lambda $ | Phase lag, ($rad$) |

## References

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**Figure 2.**(

**a**) Local blade pitch distribution and (

**b**) local chord distribution for APC 11 × 7 and KDE 12.5 × 4.3 Propellers.

**Figure 5.**Measured freestream velocity vs sinusoidal model at 0.1 Hz louver frequency for (

**a**) full and (

**b**) limited louver rotation angle.

**Figure 6.**Measured freestream velocity compared with the sinusoidal model for (

**a**) 1.75 Hz louver frequency and (

**b**) 2.25 Hz louver frequency.

**Figure 7.**Mean, the lower and the upper bound of freestream vs. shuttering system frequency at fan RPM of (

**a**) 200, (

**b**) 300 and (

**c**) 400.

**Figure 8.**(

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{P}$ vs J for APC 11 × 7 under different $\theta $ at 100 RPS along with experimental results from Simmons [18].

**Figure 9.**(

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{P}$ vs J for KDE 12.5 × 4.3 propeller under different $\theta $ at 100 RPS.

**Figure 10.**(

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{P}$ vs ${J}_{z0}$ for APC 11 × 7 under different $\theta $ at 100 RPS.

**Figure 11.**Propeller efficiency for (

**a**) APC 11 × 7 and (

**b**) KDE 12.5 × 4.3 calculated based on the normalized advance ratio ${J}_{z0}$.

**Figure 12.**(

**a**) ${C}_{Qx}$ and (

**b**) ${C}_{Qy}$ for APC 11 × 7 propeller vs. J at different incidence angles.

**Figure 13.**(

**a**) ${C}_{Qx}$ and (

**b**) ${C}_{Qy}$ for APC 11 × 7 propeller vs. ${J}_{z90}$ at different incidence angles.

**Figure 14.**Measured and predicted ${C}_{Tz}$ at (

**a**) ${k}_{\omega}$ = 0.012 and (

**b**) ${k}_{\omega}$ = 0.294 for KDE 12.5 × 4.3 at 83 RPS, $\theta $ = 90${}^{\circ}$ and $\Omega $ = 300 RPM.

**Figure 15.**Measured and predicted ${C}_{Qx}$ at (

**a**) ${k}_{\omega}$ = 0.012 and (

**b**) ${k}_{\omega}$ = 0.294 for KDE 12.5 × 4.3 at 83 RPS, $\theta $ = 90${}^{\circ}$ and $\Omega $ = 300 RPM.

**Figure 16.**Measured and steady-state ${C}_{Tz}$ vs. J (

**a**–

**c**) and ${C}_{Qx}$ vs. J (

**d**–

**f**) for KDE 12.5 × 4.3 at 83 RPS, $\theta =$ 90${}^{\circ}$ and $\Omega $ = 300 RPM under ${k}_{\omega}$ of 0.012 (

**a**,

**d**), 0.180 (

**b**,

**e**) and 0.294 (

**c**,

**f**).

**Figure 17.**Measured and steady state ${C}_{Tz}$ vs. ${C}_{Qx}$ for KDE 12.5 × 4.3 at 83 RPS, $\theta =$ 90${}^{\circ}$ and $\Omega $ = 300 RPM under ${k}_{\omega}$ of (

**a**) 0.012, (

**b**) 0.180 and (

**c**) 0.294.

**Figure 18.**Measured and Steady State (

**a**,

**b**) ${C}_{Tz}$ and (

**c**,

**d**) ${C}_{Qx}$ mean and variation vs. ${k}_{\omega}$ for KDE 12.5 × 4.3 at 83 RPS, $\theta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{90}^{\circ}$ and (

**a**,

**c**) $\Omega $ = 300 RPM and (

**b**,

**d**) $\Omega $ = 200 RPM.

**Figure 19.**Measured and Steady State (

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{Qx}$ mean and variation vs. ${k}_{\omega}$ for APC 11 × 7 at 83 RPS, $\theta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{90}^{\circ}$ and $\Omega $ = 300 RPM.

**Figure 20.**Measured and Steady State (

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{Qx}$ mean and variation vs. ${k}_{\omega}$ for KDE 12.5 × 4.3 at 83 RPS, $\theta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{75}^{\circ}$ and $\Omega $ = 200 RPM.

**Figure 21.**Measured and Steady State (

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{Qx}$ mean and variation vs. ${k}_{\omega}$ for APC 11 × 7 at 83 RPS, $\theta \phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{75}^{\circ}$ and $\Omega $ = 300 RPM.

**Figure 22.**(

**a**) ${C}_{Tz}$ and (

**b**) ${C}_{Qx}$ phase lag for KDE 12.5 × 4.3 and APC 11 × 7 propeller under different $\theta $ and $\Omega $ at 83 RPS.

Propeller Type | Diameter (m) | Pitch (m) | Blade Twist Angle at 75% Radius (°) |
---|---|---|---|

KDE 12.5 × 4.3 | 0.3175 | 0.1100 | 8.3 |

APC 11 × 7E | 0.2794 | 0.1778 | 15.1 |

Test Conditions | Values |
---|---|

Propeller RPS (n) | 80, 100 RPS |

Freestream Velocity (${V}_{\infty}$) | 0, 22 m/s |

Propeller Incidence Angle ($\theta $) | 75, 90 Degree |

Shuttering System Frequency ($\omega $) | 0–2.0 Hz |

Propeller Reduced Frequency (${k}_{p}$) | 0–0.45 |

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## Share and Cite

**MDPI and ACS Style**

Cai, J.; Gunasekaran, S.
Frequency Response of RC Propellers to Streamwise Gusts in Forward Flight. *Wind* **2023**, *3*, 253-272.
https://doi.org/10.3390/wind3020015

**AMA Style**

Cai J, Gunasekaran S.
Frequency Response of RC Propellers to Streamwise Gusts in Forward Flight. *Wind*. 2023; 3(2):253-272.
https://doi.org/10.3390/wind3020015

**Chicago/Turabian Style**

Cai, Jielong, and Sidaard Gunasekaran.
2023. "Frequency Response of RC Propellers to Streamwise Gusts in Forward Flight" *Wind* 3, no. 2: 253-272.
https://doi.org/10.3390/wind3020015