# Transient Thrust Analysis of Rigid Rotors in Forward Flight

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Testing

#### 2.1.1. Description of Experimental Setup and Conventions

#### 2.1.2. Verification of the Rotor-Test Stand

#### 2.1.3. T-MOTOR 18x6.1 Rotor Testing

#### 2.2. Computational Modeling

#### 2.2.1. Overview of the Method

#### 2.2.2. Unsteady Aerodynamic Predictions

#### 2.2.3. Rotor Performance Predictions

#### 2.2.4. Validation of the DDE Method

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

${C}_{T}$ | Thrust coefficient |

${\overline{C}}_{T}$ | Mean thrust coefficient |

${\widehat{C}}_{T}$ | Normalized thrust coefficient |

c | Chord length |

D | Diameter |

$DDE$ | Distributed doublet element |

J | Propeller advance ratio |

M | Number of chordwise elements |

n | Revolutions per second |

V | Velocity |

${V}_{\infty}$ | Freestream velocity |

${\alpha}_{tpp}$ | Rotor tip-path plane angle of attack |

$\mathsf{\Gamma}$ | Circulation |

$\Delta {x}_{c}$ | Chord length of a DDE element |

$\Delta {x}_{w}$ | Distance traveled by lifting surface in one timestep |

$\widehat{\lambda}$ | Normalized thrust oscillation amplitude |

$\mu $ | Rotor advance ratio |

${\mu}_{\infty}$ | Normalized freestream velocity |

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**Figure 1.**Ryerson University’s subsonic wind-tunnel [3].

**Figure 2.**The rotor-test stand configuration and angle of attack convention. (

**a**) The rotor-test stand. (

**b**) Definition of tip-path plane angle of attack [3].

**Figure 3.**Comparison between UIUC and RU wind-tunnel test data for the Master Airscrew 11x7E propeller.

**Figure 4.**T-MOTOR 18x6.1 rotor geometry [3].

**Figure 9.**Comparison of time-averaged thrust forces for various advance ratios and angles of attack.

**Figure 10.**Sectional thrust coefficient $\mathrm{d}{C}_{T}/\mathrm{d}(r/R)$ predictions for ${\alpha}_{tpp}={5}^{\circ}$, $\mu =0.162$. (

**a**) CFD predictions [5]. (

**b**) DDE metond predictions.

**Figure 13.**Rotor and wake visualization of the APC 12x5.5MR (${\alpha}_{tpp}={0}^{\circ}$, ${\mu}_{\infty}=0.25$) as modeled in the DDE method.

**Figure 14.**Normalized thrust oscillation amplitude vs. normalized freestream velocity as predicted with the DDE method.

**Figure 16.**Normalized single blade thrust oscillation amplitude vs. normalized freestream velocity as predicted with the DDE method.

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**MDPI and ACS Style**

Krebs, T.; Bramesfeld, G.; Cole, J. Transient Thrust Analysis of Rigid Rotors in Forward Flight. *Aerospace* **2022**, *9*, 28.
https://doi.org/10.3390/aerospace9010028

**AMA Style**

Krebs T, Bramesfeld G, Cole J. Transient Thrust Analysis of Rigid Rotors in Forward Flight. *Aerospace*. 2022; 9(1):28.
https://doi.org/10.3390/aerospace9010028

**Chicago/Turabian Style**

Krebs, Travis, Goetz Bramesfeld, and Julia Cole. 2022. "Transient Thrust Analysis of Rigid Rotors in Forward Flight" *Aerospace* 9, no. 1: 28.
https://doi.org/10.3390/aerospace9010028