# Investigation of Rotor Efficiency with Varying Rotor Pitch Angle for a Coaxial Drone

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## Abstract

**:**

## 1. Introduction

## 2. Computational Methods

#### 2.1. Blade Element Momentum Theory

`SciPy`library [22].

`SciPy`library are used for this purpose.

#### 2.2. Computational Fluid Dynamics

`linearUpwind`scheme is used for the convective terms.

`cyclicAMI`boundary condition. At each time step, each face at the AMI boundary identifies overlapping faces from the neighboring patch and the contribution from these faces is weighted according to the intersecting area [35].

## 3. Numerical Setup

#### 3.1. Rotor Geometry

#### 3.2. Mesh

^{®}(Cadence Design Systems, San Jose, CA, USA) [43], a mesh-generation software specifically developed for CFD applications. Particular attention is paid to the rotor surface mesh, which is shown in Figure 6a. Stretched anisotropic quadrilaterals have been extruded from the leading edge and the trailing edge using the 2D T-Rex algorithm. T-Rex allows us to grow layers of rectangular cells given the first cell thickness and a growth factor, and the inflation is stopped once a smooth dimensional transition with the rest of the surface mesh is achieved. The rest of the upper and lower surface domains consist of triangles and quads generated by the “advancing front ortho” algorithm, and are automatically shaped to comply with high-quality criteria, whilst fulfilling a specified maximum cell dimension. The grid at the blunt trailing edge and at the wingtip has been designed to transition smoothly to the T-Rex-extruded upper and lower surface cells using a structured-dominant approach.

## 4. Experimental Setup

## 5. Validation

#### 5.1. Mesh Sensitivity Study

#### 5.2. Single-Rotor Validation

#### 5.3. Coaxial Rotor Validation

## 6. Results

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of parameters and forces for blade element momentum theory. (

**a**) Momentum theory control volume. (

**b**) Blade element.

**Figure 3.**Comparison of A18 airfoil against airfoils along the commercial T-MOTOR G28x9.2” blade at four radial stations. From the bottom: $0.3R$, $0.5R$, $0.7R$, $0.9R$.

**Figure 4.**Top view (

**top**) and front view (

**bottom**) of the computational 3D rotor geometry for a pitch of 9.2”.

**Figure 5.**Aerodynamic drag and lift coefficients for the A18 airfoil, calculated using XFOIL at Re = 175,000.

**Figure 6.**Illustration of mesh arrangements. (

**a**) Rotor surface mesh. (

**b**) Close-up of mesh near rotor with layers generated using 3D T-Rex extrusion. (

**c**) Mesh around rotors. The yellow rectangles indicate the AMI blocks.

**Figure 8.**Picture of experimental setup showing the thrust stand in coaxial configuration and a close-up view of the load cell and motor. (

**a**) Thrust stand. (

**b**) Load cell and motor.

**Figure 9.**Comparison between experiments, BEMT simulations and CFD simulations for a single rotor. (

**a**) Thrust. (

**b**) Efficiency.

**Figure 10.**Magnitude of velocity vector for single-rotor setup at varying RPM. The grey line indicated in (

**a**) shows the position of the second rotor for the coaxial setup. (

**a**) RPM = 1600. (

**b**) RPM = 1900. (

**c**) RPM = 2200. (

**d**) RPM = 2500.

**Figure 11.**Vertical velocity at a vertical distance 0.115 m from the rotor (indicated by the grey line in Figure 10), estimating inflow velocity for the lower rotor in the coaxial setup. The dashed lines are the values predicted from the coaxial BEMT model.

**Figure 12.**Comparison between experiments, BEMT simulations and CFD simulations for the coaxial rotor setup. (

**a**) Thrust. (

**b**) Efficiency.

**Figure 13.**Magnitude of velocity vector for coaxial rotor setup at varying RPM. (

**a**) RPM = 1600. (

**b**) RPM = 1900. (

**c**) RPM = 2200. (

**d**) RPM = 2500.

**Figure 14.**Total efficiency relative to total efficiency at pitch 9.2″ for the coaxial rotor system as a function of lower rotor pitch.

**Figure 16.**BEMT results along the blade for the lower rotor for three different pitches. (

**a**) Thrust along blade. (

**b**) Aerodynamic efficiency along blade.

**Figure 17.**Pressure coefficient and flow pattern (as seen from the rotor) for the lower rotor at radius $r=0.3R$ for two different pitches. (

**a**) Pitch 9.2″. (

**b**) Pitch 14.2″.

**Figure 18.**Pressure coefficient over the lower rotor blade at radius $r=0.3R$ for two different pitches.

Quantity | Unit | Value |
---|---|---|

Rotor diameter, D | cm | 71.12 |

Number of blades | - | 2 |

Hub diameter | cm | 5.4 |

Pitch at 0.75R | in | 9.2 |

Chord at 0.75R | cm | 4.4 |

Object | Base Diameter | Height | Ratio to D |
---|---|---|---|

Upper AMI block | 84.0 cm | 5.50 cm | |

Lower AMI block | 84.0 cm | 6.95 cm | |

Cylindrical source | 1.00 m | 3.00 m | $\sim 4\phantom{\rule{3.33333pt}{0ex}}D$ |

Far-field block | 10.0 m | 10.0 m | $\sim 14\phantom{\rule{3.33333pt}{0ex}}D$ |

Quantity | Unit | Value | Ratio to D |
---|---|---|---|

Rotor surface maximum cell size | mm | 2.00 | $\sim D/350$ |

3D T-Rex 1st layer thickness | m | 1 × 10^{−5} | |

3D T-Rex inflation growth factor | - | 1.2 | |

AMI block maximum cell size | mm | 5.00 | $\sim D/140$ |

Source delimited region max. cell size | cm | 2.00 | $\sim D/35$ |

Far-field block maximum cell size | cm | 20.0 | $\sim D/4$ |

Total number of cells | - | 14.1 × 10^{6} |

Number of Cells | Thrust | Efficiency |
---|---|---|

(×10^{6}) | (N) | (N W^{−1}) |

5.50 | 25.5 | 0.124 |

8.78 | 25.9 | 0.127 |

13.2 | 26.0 | 0.127 |

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**MDPI and ACS Style**

Giljarhus, K.E.T.; Porcarelli, A.; Apeland, J.
Investigation of Rotor Efficiency with Varying Rotor Pitch Angle for a Coaxial Drone. *Drones* **2022**, *6*, 91.
https://doi.org/10.3390/drones6040091

**AMA Style**

Giljarhus KET, Porcarelli A, Apeland J.
Investigation of Rotor Efficiency with Varying Rotor Pitch Angle for a Coaxial Drone. *Drones*. 2022; 6(4):91.
https://doi.org/10.3390/drones6040091

**Chicago/Turabian Style**

Giljarhus, Knut Erik Teigen, Alessandro Porcarelli, and Jørgen Apeland.
2022. "Investigation of Rotor Efficiency with Varying Rotor Pitch Angle for a Coaxial Drone" *Drones* 6, no. 4: 91.
https://doi.org/10.3390/drones6040091