# Analysis of Wind Turbine Wake Dynamics by a Gaussian-Core Vortex Lattice Technique

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## Abstract

**:**

## 1. Introduction

#### Focus of this Study

## 2. The Common ODE Framework (CODEF)

#### Dynamic Rotor Deformation—Blade Element Momentum (DRD-BEM)

## 3. The Gaussian-Core Vortex Lattice Model

- The Gaussian distribution of vorticity enables the representation of the natural viscous decay of the vortex filaments. This allows the freeing up of the memory from vortices that have significantly “dissipated” or “aged”.
- The Guassian distribution also avoids the mutual high-speed satellization of vortex filaments in close proximity, thereby avoiding unrealistically high tangential velocities. This ensures the stability of the vortex lattice, which enables it to be extended to a large distance downstream from the rotor.

#### 3.1. Core Radius at the Formation of Real Vortices

#### 3.2. Turbulent Diffusivity Coefficient

#### 3.3. Vortex Transport and Stretching

#### 3.4. Computation of the Circulation of Vortex Filaments and Vortex Lattice Creation

#### 3.5. Lattice Wake Growth

## 4. Numerical Experiments and Analysis of Results

#### 4.1. Validation Simulations with the NREL N5M-Reference Wind Turbine

#### 4.2. Numerical Experiments on SNL’s SWiFT Facility Scenarios

#### 4.3. SWiFT Facility Overview

- The cup anemometers at three different heights on the met tower;
- The 3D sonic anemometers at five different heights of the met tower;
- The yaw measurement sensor on the turbines;
- The DTU Spinner LiDAR located in the nacelle of turbine WTGa1.

## 5. Conclusions and Outlook for Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Radial distribution of vorticity for a generic Gaussian vortex filament. The progression of curves shows, qualitatively, how the vorticity evolves with time.

**Figure 4.**Radial distributions of swirling velocity induced by the generic Gaussian filament shown in Figure 3, at the same progressive instances in time.

**Figure 5.**A schematic showing the Bound, Trailing, and Shed vortex filaments in the construction of a lattice assembly of a generic wind turbine blade.

**Figure 6.**The complete, stable vortex lattice of the N5M-RWT extending more than 15D downstream of the turbine in steady-state flow, at its nominal operational conditions.

**Figure 8.**Perspective view of the GVLM vortex lattice wake for Scenario 1. The color scheme used in all vortex lattice images is intended to provide a better appreciation of the lattice shape development and is not attached to a specific physical quantity.

**Figure 9.**Rear views of the lattice cross-cut sections at six different locations downstream of the turbine for Scenario 1.

**Figure 11.**GVLM results for the ${\mathrm{v}}_{\mathrm{los}}$ patterns in Scenario 1 at the same downstream locations shown in Figure 10.

**Figure 13.**Rear views of the lattice cross-cut sections at five different locations downstream of the turbine for Scenario 2.

**Figure 15.**GVLM results for the ${\mathrm{v}}_{\mathrm{los}}$ patterns in Scenario 2 at the same downstream locations shown in Figure 14.

**Figure 17.**Rear views of the lattice cross-cut sections at five different locations downstream of the turbine for Scenario 3.

**Figure 19.**GVLM results for the ${\mathrm{v}}_{\mathrm{los}}$ patterns in Scenario 3 at the same downstream locations shown in Figure 18.

Scenario | Wind Speed | Alpha | Veer | Yaw Offset |
---|---|---|---|---|

(Fig. No in [38]) | [m/s] | [deg] | [deg] | |

Scenario 1 (Fig. 7) | 8.2 | 0.12 | 1.3° | 5.9° |

Scenario 2 (Fig. 9) | 6.9 | 0.37 | 14.6° | −0.12° |

Scenario 3 (Fig. 11) | 4.8 | 0.15 | −5.0° | 10.9° |

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**MDPI and ACS Style**

Baruah, A.; Ponta, F.
Analysis of Wind Turbine Wake Dynamics by a Gaussian-Core Vortex Lattice Technique. *Dynamics* **2024**, *4*, 97-118.
https://doi.org/10.3390/dynamics4010006

**AMA Style**

Baruah A, Ponta F.
Analysis of Wind Turbine Wake Dynamics by a Gaussian-Core Vortex Lattice Technique. *Dynamics*. 2024; 4(1):97-118.
https://doi.org/10.3390/dynamics4010006

**Chicago/Turabian Style**

Baruah, Apurva, and Fernando Ponta.
2024. "Analysis of Wind Turbine Wake Dynamics by a Gaussian-Core Vortex Lattice Technique" *Dynamics* 4, no. 1: 97-118.
https://doi.org/10.3390/dynamics4010006