# Three-Dimensional Unsteady Aerodynamic Analysis of a Rigid-Framed Delta Kite Applied to Airborne Wind Energy

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Flight Test Campaign

#### 2.2. In-House Three-Dimensional Unsteady Panel Method (UnPaM)

#### 2.2.1. Aerodynamic Mesh

#### 2.2.2. Kinematic Module of UnPaM

#### 2.2.3. Force and Moment Coefficients Computation with UnPaM

## 3. Comparison of Numerical and Experimental Results

## 4. Analysis of the Potential Flow

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

AWE | Airborne Wind |

CM | Kite Center of Mass |

GNSS | Global Navigation Satellite System |

IMU | Inertial Measurement Unit |

LE | Leading Edge |

LEI | Leading Edge Inflatable |

RANS | Reynolds-Averaged Navier-Stokes |

RFD | Rigid-Framed Delta |

TE | Trailing Edge |

UnPaM | Unsteady Panel Method |

VLM | Vortex Lattice Method |

## Appendix A. UnPaM High-Level Flowchart

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**Figure 1.**(

**a**) shows the RFD kite (HQ Fazer XXL) during the experimental campaign. (

**b**) displays the aerodynamic mesh of the VLM model. The color bar represents the aspect ratio of the mesh panels.

**Figure 2.**Trajectory of the kite in the selected maneuver. The color in (

**a**–

**d**) correspond to the true airspeed, the total tension on the two tethers, the angle of attack and the sideslip angle, respectively. The upward red triangle and the downward blue triangle are the starting and final points and the arrows in (

**a**) show the direction of the kite motion.

**Figure 3.**Mesh convergence analysis for steady conditions with $\alpha ={20}^{\circ}$ and $\beta ={0}^{\circ}$.

**Figure 4.**Reference frames and wake in an UnPaM unsteady simulation at the 20th (

**a**) and 30th (

**b**) times steps. Left image in (

**a**) represents the B and W frames orientation (their origins are at the kite CM) on the ${x}_{G}-{z}_{G}$ plane at the 20th time step, center and right [left and right] images of (

**a**,

**b**) show the ${x}_{G}-{z}_{G}$ plane and the ${y}_{G}-{z}_{G}$ plane, respectively.

**Figure 5.**Force (

**a**–

**c**) for lift, lateral force and drag) and moment (

**d**–

**f**) for roll, pitch and yaw) coefficients comparison between UnPaM and experimental aerodynamic results.

**Figure 6.**Lift coefficient (crosses and points for experimental and UnPaM data, respectively) versus the sideslip angle with colormap for $\alpha $ values.

**Figure 7.**Kite trajectory with color map representing the force coefficients coming from experimental data (

**left figures**) and UnPaM simulations (

**right figures**).

**Figure 8.**UnPaM aerodynamic simulation (20th time step) at a fixed $\alpha $ of 20º and $\beta $ of 0º. (

**a**) shows the $\Delta {C}_{p}$ across the kite and the wake roll-up while (

**b**) shows the central spine $\Delta {C}_{p}$ distribution for the 3D case (UnPaM) and 2D theory of a flat plate.

**Figure 9.**Lift coefficient for unsteady, quasi-steady and steady UnPaM simulations for the kinematics resulting from the figure-of-eight maneuver under study. (

**a**,

**b**) give the full trajectory and and a zoom-in, respectively.

Property | Value |
---|---|

Mass | 2 kg |

${I}_{{x}_{B}}$ | 0.72 kg m${}^{2}$ |

${I}_{{y}_{B}}$ | 0.09 kg m${}^{2}$ |

${I}_{{z}_{B}}$ | 0.81 kg m${}^{2}$ |

Surface (S) | 1.86 m${}^{2}$ |

Span (b) | 3.60 m |

Chord (c) | 0.59 m |

${x}_{{A}^{\pm}}$ | $-0.07$ m |

${y}_{{A}^{\pm}}$ | $\pm 0.73$ m |

${z}_{{A}^{\pm}}$ | 1 m |

Tether length | 39.28 m |

Tether frontal surface (${S}_{t}$) | 0.08 m${}^{2}$ |

Tether drag coeff. (${C}_{{d}_{t}}$) | 1 |

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**MDPI and ACS Style**

Castro-Fernández, I.; Borobia-Moreno, R.; Cavallaro, R.; Sánchez-Arriaga, G. Three-Dimensional Unsteady Aerodynamic Analysis of a Rigid-Framed Delta Kite Applied to Airborne Wind Energy. *Energies* **2021**, *14*, 8080.
https://doi.org/10.3390/en14238080

**AMA Style**

Castro-Fernández I, Borobia-Moreno R, Cavallaro R, Sánchez-Arriaga G. Three-Dimensional Unsteady Aerodynamic Analysis of a Rigid-Framed Delta Kite Applied to Airborne Wind Energy. *Energies*. 2021; 14(23):8080.
https://doi.org/10.3390/en14238080

**Chicago/Turabian Style**

Castro-Fernández, Iván, Ricardo Borobia-Moreno, Rauno Cavallaro, and Gonzalo Sánchez-Arriaga. 2021. "Three-Dimensional Unsteady Aerodynamic Analysis of a Rigid-Framed Delta Kite Applied to Airborne Wind Energy" *Energies* 14, no. 23: 8080.
https://doi.org/10.3390/en14238080