# Effects of Inflow Parameters and Disk Thickness on an Actuator Disk inside the Neutral Atmospheric Boundary Layer

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Governing Equations

#### 2.2. Actuator Disk Model

#### 2.3. Validation Data

#### 2.4. Computational Settings

#### 2.4.1. Inflow Conditions

#### 2.4.2. Horizontal Homogeneity

## 3. Results and Discussion

#### 3.1. A Study of Inflow Parameters

#### 3.2. Actuator Disk Thickness

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AD | Actuator Disk |

DRM | Direct Rotor Modelling |

IRM | Indirect Rotor Modelling |

BEM | Blade Element Momentum |

AL | Actuator Line |

AS | Actuator Surface |

LES | Large Eddy Simulation |

RANS | Reynolds Averaged Navier-Stokes |

R & H | Richard & Hoxey |

TI | Turbulence Intensity |

${c}_{t}$ | Thrust Coefficient |

${f}_{t}$ | Turbine Thrust |

${u}_{*}$ | Friction Velocity |

${y}_{0}$ | Aerodynamic Surface Roughness Lengths |

$\alpha $ | Terrain Roughness Coefficient |

${u}_{abl}^{*}$ | Boundary Layer Friction Velocity |

${r}^{*}$ | Non-dimensionalized distance from the actuator disk center |

$T/r$ | Thickness Ratio |

$\Delta x$ | Mesh size |

GSCR | Global Scaled Continuity Residuals |

${R}^{c}$ | Continuity Residual |

${R}_{iterationN}^{c}$ | Continuity Residual At The Current Iteration |

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**Figure 2.**Power law and logarithmic profiles at the inlet, velocity profile (

**left**) and turbulence kinetic energy (${\mathrm{m}}^{2}/{\mathrm{s}}^{2}$) (

**right**).

**Figure 3.**Development of power law (

**left**) and logarithmic velocity profile (

**right**) in the absence of the actuator disk.

**Figure 5.**Power law and logarithmic velocity deficit profile in the near wake at $3D$ (

**left**) $5D$ (

**right**).

**Figure 7.**Power law and logarithmic velocity deficit profile in the far wake at $10D$ (

**left**) $15D$ (

**right**).

**Figure 9.**The velocity counter at (

**a**) $xy$ plane at $z=-0.5$ m (

**b**) $xy$ plane at $z=0.075$ (

**c**) at $yz$ plane.

**Figure 10.**Turbulence kinetic energy (${\mathrm{m}}^{2}/{\mathrm{s}}^{2}$) at $1D$ (

**left**) and $2D$ (

**right**).

Author | Method | Inflow Condition |
---|---|---|

Santo et al. [15] | Direct rotor Modelling | Richard & Hoxey |

Fazil et al. [16] | Direct rotor Modelling | Richard & Hoxey |

Cabezón et al. [17] | Actuator Disk | Richard & Hoxey |

Pichandi et al. [18] | Actuator Disk | Richard & Hoxey |

Tian et al. [19] | Actuator Disk—BEM | Richard & Hoxey |

Song et al. [20] | Actuator Disk | Richard & Hoxey |

Ichenial et al. [21] | Direct rotor Modelling | Richard & Hoxey |

Naderi et al. [22] | Actuator Disk—BEM | Richard & Hoxey |

Sedaghatizadeh. [23] | Direct rotor Modelling | Power Law |

Tian et al. [24] | Actuator Disk | Power Law |

Uchida et al. [25] | Direct rotor Modelling | Power Law |

**Table 2.**The friction velocity (${u}_{\ast r}$) and the aerodynamic surface roughness lengths (${y}_{0r}$) of the wind tunnel data.

Surface Type | ${\mathit{y}}_{0\mathit{r}}$ | ${\mathit{u}}_{*\mathit{r}}$ |
---|---|---|

Rough | 1.2 mm | 0.16 m/s |

Smooth | 0.05 mm | 0.11 m/s |

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**MDPI and ACS Style**

RahnamayBahambary, K.; Fleck, B.A.
Effects of Inflow Parameters and Disk Thickness on an Actuator Disk inside the Neutral Atmospheric Boundary Layer. *Wind* **2022**, *2*, 733-746.
https://doi.org/10.3390/wind2040038

**AMA Style**

RahnamayBahambary K, Fleck BA.
Effects of Inflow Parameters and Disk Thickness on an Actuator Disk inside the Neutral Atmospheric Boundary Layer. *Wind*. 2022; 2(4):733-746.
https://doi.org/10.3390/wind2040038

**Chicago/Turabian Style**

RahnamayBahambary, Khashayar, and Brian A. Fleck.
2022. "Effects of Inflow Parameters and Disk Thickness on an Actuator Disk inside the Neutral Atmospheric Boundary Layer" *Wind* 2, no. 4: 733-746.
https://doi.org/10.3390/wind2040038