# Small-Scale Rotor Aeroacoustics for Drone Propulsion: A Review of Noise Sources and Control Strategies

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Noise Modelling: Tonal and Broad-Band

- a is the speed of sound;
- ${p}^{\prime}$ is the perturbation on the static pressure;
- t is the observer time;
- ${x}_{i}$ are the components of the position vector;
- ${T}_{ij}$ are the components of the Lighthill stress tensor;
- ${\rho}_{a}$ is the air density;
- ${v}_{i}$ is the components of the source velocity vector;
- $\delta $ is Kronecker’s delta function;
- f is a function that defines the surface of the body producing the pressure wave;
- ${p}_{ij}$ are the components of the generalized stress tensor.

- ${\widehat{\mathbf{r}}}_{\mathbf{k}}$ is the position vector of an observer relative to the k-point noise source $\left(\widehat{\left|r\right|}=1\right)$,;
- ${\mathbf{F}}_{\mathbf{k}}$ is the aerodynamic force on the k-point blade element of volume ${\mathsf{\Phi}}_{k}$;
- ${M}_{{r}_{k}}$ is a scalar magnitude that represents the component of the Mach vector ${\mathbf{M}}_{\mathbf{k}}=\frac{\mathbf{v}}{a}$ on ${\mathbf{r}}_{\mathbf{k}}$.

**Figure 2.**Representation of the reference coordinate system considered for the definition of the aeroacoustic model.

#### 2.2. Noise Reduction Strategies

#### 2.2.1. Optimized Geometry

#### 2.2.2. Serrated Trailing Edge

- The non-dimensional tooth height, defined as the ratio between the tooth half-height and the boundary layer thickness ${h}^{*}=h/2\delta $;
- The aspect ratio of the tooth, defined as the ratio between the width and the half-height $A{R}_{t}=2b/h$;
- The boundary layer thickness-based Strouhal number $S{t}_{\delta}=f\delta /U$.

#### 2.2.3. Leading Edge Serration

#### 2.2.4. Boundary Layer Tripping System

#### 2.2.5. Porous Material Inserts

#### 2.2.6. Metamaterials

#### 2.2.7. Bio-Inspired Blade Shape

#### 2.2.8. Active Control Strategy: Synchrophaser

## 3. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MAV | Micro Aerial Vehicles |

UAV | Unmanned Aerial Vehicle |

UAS | Unmanned Aerial System |

MDO | Multi Disciplinary optimization |

STE | Serrated Trailing Edge |

TE | Trailing Edge |

LE | Leading Edge |

TBL | Turbulent Boundary Layer |

LBL | Laminar Boundary Layer |

UOM | Ultra-Open Metamaterial |

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**Figure 3.**3D rendering of the propeller blade: (

**a**) baseline; (

**b**) serrated trailing edge; (

**c**) boundary layer tripping system.

**Figure 4.**Schematic of the sawtooth and the combed-sawtooth TE geometry [70].

**Figure 5.**Sketch of the serrated trailing edge. In the enlargement of figure, the main geometrical parameters of the tooth are reported: tooth basis b, height h and the serration angle $\alpha $.

**Figure 9.**Representation of the considered baseline blade (

**a**) and of the new bio-inspired blade (

**b**).

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Candeloro, P.; Ragni, D.; Pagliaroli, T.
Small-Scale Rotor Aeroacoustics for Drone Propulsion: A Review of Noise Sources and Control Strategies. *Fluids* **2022**, *7*, 279.
https://doi.org/10.3390/fluids7080279

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Candeloro P, Ragni D, Pagliaroli T.
Small-Scale Rotor Aeroacoustics for Drone Propulsion: A Review of Noise Sources and Control Strategies. *Fluids*. 2022; 7(8):279.
https://doi.org/10.3390/fluids7080279

**Chicago/Turabian Style**

Candeloro, Paolo, Daniele Ragni, and Tiziano Pagliaroli.
2022. "Small-Scale Rotor Aeroacoustics for Drone Propulsion: A Review of Noise Sources and Control Strategies" *Fluids* 7, no. 8: 279.
https://doi.org/10.3390/fluids7080279