# Wind Tunnel Studies on Hover and Forward Flight Performances of a Coaxial Rigid Rotor

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

#### 2.1. Test Apparatus

#### 2.2. Test Model and Procedure

_{up =}θ

_{0.7up}+ A

_{1up}· cos(Ψ

_{up}+ Γ) – B

_{1up}· sin(Ψ

_{up}+ Γ)

_{lo =}θ

_{0.7lo}+ A

_{1lo}· cos(Ψ

_{lo}+ Γ) – B

_{1lo}· sin(Ψ

_{lo}+ Γ)

_{P}, is defined as:

#### 2.3. Experimental Content

## 3. Results and Discussion

#### 3.1. Rotor Hover Performance

#### 3.2. Forward Flight Rotor Performance

#### 3.2.1. Tilt Angle Sweep Rotor Performance

#### 3.2.2. Lift Offset Sweep Rotor Performance

#### 3.2.3. Effect of Interference between Upper and Lower Rotors on Rotor Forward Flight Performance

## 4. Conclusions

- (1)
- The hover test results demonstrate that the FM values of the upper and lower rotors are lower than that of the isolated single rotor and FM of the lower rotor is lower than that of the upper rotor. Moreover, the coaxial rotor configuration can contribute to better hover efficiency under the same blade loading condition.
- (2)
- The effective L/De ratio of the coaxial rigid rotor does not monotonously increase as the advance ratio increases. The increases of the required power and drag in the case with a high advance ratio of 0.6 led to the decreasing L/De ratio of the rotor system with an advance ratio of above 0.4. Moreover, the L/De ratio of the rotor is relatively high when the rotor shaft is tilted backward.
- (3)
- The increase in lift offset will reduce the total pitch whilst maintaining the same rotor lift, resulting in a decrease in the power required by the rotor. Moreover, the rotor drag is increased when there is an increase in the attack angle of the forward edge blade in the high dynamic pressure area of the advancing side. When the effect of the reduced rotor power is greater than that of the increased rotor drag, the L/De ratio increases as the lift offset increases. At a lower advance ratio, forward efficiency does not obviously benefit from the increasing lift offset and it even decreases when the lift offset becomes exceedingly high. At a higher advance ratio of 0.4, the benefit of the decreased rotor power is greater than the effect of the increased rotor drag, and the rotor obtains approximately 20% better overall forward efficiency with increased lift offset.
- (4)
- In the forward flight state, the L/De ratios of the upper and lower rotors are smaller than that of the isolated single rotor and that of the upper rotor is lower than that of the lower rotor. The difference in the forward state’s efficiency of upper and lower rotors is significantly different from the case in the hover flight state.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

T | Rotor thrust force, N |

D | Rotor drag force, N |

L | Rotor lift force, N |

P | Rotor power, W |

${\mathrm{M}}_{\mathrm{x}}$ | Rotor rolling moment, N·m |

ρ | Air density, kg/m^{3} |

R | Rotor radius, m |

α | Rotor shaft tilt angle, deg. |

σ | Rotor solidity |

${\mathrm{C}}_{\mathrm{T}}$ | Rotor thrust coefficient |

${\mathrm{C}}_{\mathrm{P}}$ | Rotor power coefficient |

${\mathrm{C}}_{\mathrm{L}}$ | Rotor lift force coefficient |

${\mathrm{C}}_{\mathrm{D}}$ | Rotor drag force coefficient |

${\mathrm{C}}_{\mathrm{Mx}}$ | Rotor rolling moment coefficient |

LOS | Lateral lift offset |

L/De | Effective lift-to-drag ratio |

FM | Figure of merit |

${\mathrm{C}}_{\mathrm{T}}$/σ | Blade loading coefficient |

μ | Advance ratio |

ρ | Air density, kg/m^{3} |

ω | Rotor angular velocity, rad/s |

Ψ | Blade azimuthal angle, deg. |

${\mathsf{\theta}}_{\mathrm{up}}$ | Blade pitch angle of upper rotor, deg. |

${\mathsf{\theta}}_{\mathrm{lo}}$ | Blade pitch angle of lower rotor, deg. |

${\mathsf{\theta}}_{0.7}$ | Coupled collective pitch, deg. |

${\mathrm{A}}_{1}$ | Coupled longitudinal cyclic pitch, deg. |

${\mathrm{B}}_{1}$ | Coupled lateral cyclic pitch, deg. |

${\mathsf{\theta}}_{0.7}^{\prime}$ | Differential collective pitch, deg. |

${\mathrm{A}}_{1}^{\prime}$ | Differential longitudinal cyclic pitch, deg. |

${\mathrm{B}}_{1}^{\prime}$ | Differential lateral cyclic pitch, deg. |

${\mathsf{\theta}}_{0.7\mathrm{up}}$ | Collective pitch of upper rotor, deg. |

${\mathrm{A}}_{1\mathrm{up}}$ | Longitudinal cyclic pitch of upper rotor, deg. |

${\mathrm{B}}_{1\mathrm{up}}$ | Lateral cyclic pitch of upper rotor, deg. |

${\mathsf{\theta}}_{0.7\mathrm{lo}}$ | Collective pitch of lower rotor, deg. |

${\mathrm{A}}_{1\mathrm{lo}}$ | Longitudinal cyclic pitch of lower rotor, deg. |

${\mathrm{B}}_{1\mathrm{lo}}$ | Lateral cyclic pitch of lower rotor, deg. |

$\text{\Gamma}$ | Rotor phase lag angle, deg. |

Φ | Diameter |

Subscripts | |

up | Upper rotor |

lo | Lower rotor |

hub | Rotor hub |

∞ | Free-stream conditions |

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**Figure 3.**Counter-rotating coaxial rotor system installed on the test rig in the wind tunnel test section.

**Figure 6.**Relationships between power coefficient (C

_{P}) and thrust coefficient (C

_{T}) of upper, lower, and isolated single rotors.

**Figure 7.**Variations of figure of merit (FM) values for the coaxial and isolated single rotors with blade loading coefficient (${\mathrm{C}}_{\mathrm{T}}$/σ).

**Figure 14.**Rolling moment coefficient (${\mathrm{C}}_{\mathrm{Mx}}$) of each rotor as a function of the lift offset (LOS).

**Figure 15.**Coupled collective pitch (${\mathsf{\theta}}_{0.7}$) as a function of the lift offset (LOS).

**Figure 16.**Lateral cyclic pitch of upper and lower rotors (${\mathrm{B}}_{1\mathrm{up}}$ and ${\mathrm{B}}_{1\mathrm{lo}}$) as a function of the lift offset (LOS).

**Figure 20.**Variations of L/De ratio with rotor shaft tilt angles (a) for coaxial and isolated single rotors.

**Figure 21.**Variations of thrust coefficients (C

_{T}) with rotor shaft tilt angles (a) for coaxial and isolated single rotors.

**Figure 22.**Variations of power coefficients (C

_{P}) with rotor shaft tilt angles (a) for coaxial and isolated single rotors.

Measurement Parameters | Maximum Capacity | Measured Standard Deviation of Error | |
---|---|---|---|

Value | % Capacity | ||

Normal force or lift, N | 2200 | 0.66 | 0.03 |

Side force, N | 500 | 0.3 | 0.06 |

Axial force or drag, N | 500 | 0.25 | 0.05 |

Pitching moment, N·m | 200 | 0.08 | 0.04 |

Rolling moment, N·m | 250 | 0.05 | 0.02 |

Torque, N·m | 340 | 0.27 | 0.08 |

Rotor Parameters | Value |
---|---|

Rotor radius, R (m) | 1 |

Root cut out (m) | 0.18 |

Number of blades | 8 (4 for the upper rotor and 4 for the lower rotor) |

Chord (m) | 0.07 |

Twist angle (°) | −12 |

Plan form | Untapered |

Precone angle (°) | 2 |

Rotational direction | Counterclockwise for the upper rotor, clockwise for the lower rotor. |

Solidity, σ | 0.178 (coaxial rotor) |

Airfoil | NACA0026, NACA0020, and NACA0012 |

Nominal rotation speed | 1860 RPM |

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**MDPI and ACS Style**

Wang, C.; Huang, M.; Peng, X.; Zhang, G.; Tang, M.; Wang, H.
Wind Tunnel Studies on Hover and Forward Flight Performances of a Coaxial Rigid Rotor. *Aerospace* **2021**, *8*, 205.
https://doi.org/10.3390/aerospace8080205

**AMA Style**

Wang C, Huang M, Peng X, Zhang G, Tang M, Wang H.
Wind Tunnel Studies on Hover and Forward Flight Performances of a Coaxial Rigid Rotor. *Aerospace*. 2021; 8(8):205.
https://doi.org/10.3390/aerospace8080205

**Chicago/Turabian Style**

Wang, Chang, Minqi Huang, Xianmin Peng, Guichuan Zhang, Min Tang, and Haowen Wang.
2021. "Wind Tunnel Studies on Hover and Forward Flight Performances of a Coaxial Rigid Rotor" *Aerospace* 8, no. 8: 205.
https://doi.org/10.3390/aerospace8080205