# Impact of Subgrid-Scale Modeling in Actuator-Line Based Large-Eddy Simulation of Vertical-Axis Wind Turbine Wakes

## Abstract

**:**

## 1. Introduction

## 2. Large-Eddy Simulation Framework

#### 2.1. LES Governing Equations

#### 2.2. Subgrid-Scale Parametrization

#### 2.2.1. Standard Smagorinsky Model

#### 2.2.2. Lagrangian Scale-Dependent Dynamic Smagorinsky Model

#### 2.2.3. Anisotropic Minimum Dissipation Model

#### 2.3. Wind Turbine Parametrization

#### 2.4. Numerical Setup

## 3. Results

## 4. Resolved-Scale Turbulent Kinetic Energy Budget

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Effects of the Smearing Parameter and Grid Resolution

**Figure A1.**Lateral profiles of the normalized streamwise velocity ($U/{U}_{0}$) (

**left**) and streamwise velocity variance ($\overline{{u}^{\prime}{u}^{\prime}}/{U}_{0}^{2}$) (

**right**) through the hub level at $x/D=1,3,7,15,24$ downwind of the turbine obtained from the LSDD model with two different $\u03f5$ values and two different spatial resolutions.

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**Figure 2.**Mean angle of attack (

**left**) and tangential force coefficient (

**right**) versus the azimuthal angle, $\theta $, for different SGS models. The azimuthal angle of the blade at the top is defined to be zero degree.

**Figure 3.**Contours of the normalized mean streamwise velocity ($U/{U}_{0}$) in the central vertical $x-z$ plane (

**left**) and in the central horizontal $x-y$ plane (

**right**) for different SGS models: (from top to the bottom) Lagrangian scale-dependent dynamic (LSDD) model, anisotropic minimum dissipation (AMD) model, standard Smagorinsky model (SMAG) model with ${C}_{S}=0.16$, and SMAG model with ${C}_{S}=0.065$.

**Figure 4.**Vertical (

**left**) and lateral (

**right**) profiles of the normalized mean streamwise velocities ($U/{U}_{0}$) through the turbine equator at $x/D=1,3,7,15,24$ downwind of the turbine for different SGS models.

**Figure 5.**Contours of the normalized streamwise velocity variance ($\overline{{u}^{\prime}{u}^{\prime}}/{U}_{0}^{2}$) in the central vertical $x-z$ plane (

**left**) and in the central horizontal $x-y$ plane (

**right**) for different SGS models: (from top to the bottom) LSDD model, AMD model, SMAG model with ${C}_{S}=0.16$, and SMAG model with ${C}_{S}=0.065$.

**Figure 6.**Vertical (

**left**) and lateral (

**right**) profiles of the normalized streamwise velocity variance ($\overline{{u}^{\prime}{u}^{\prime}}/{U}_{0}^{2}$) through the hub level at $x/D=1,3,7,15,24$ downwind of the turbine for different SGS models.

**Figure 7.**Contours of the normalized subgrid-scale (SGS) dissipation rate (${\u03f5}_{sgs}D/{U}_{0}^{3}$) in the central vertical $x-z$ plane (

**left**) and in the central horizontal $x-y$ plane (

**right**) for different SGS models: (from top to the bottom) LSDD model, AMD model, SMAG model with ${C}_{S}=0.16$, and SMAG model with ${C}_{S}=0.065$.

**Figure 8.**Contours of the normalized turbulent kinetic energy (TKE) ($\overline{\tilde{k}}/{U}_{0}^{2}$) in the central vertical $x-z$ plane (

**left**) and in the central horizontal $x-y$ plane (

**right**) for different SGS models: (from top to the bottom) LSDD model, AMD model, SMAG model with ${C}_{S}=0.16$, and SMAG model with ${C}_{S}=0.065$.

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**MDPI and ACS Style**

Abkar, M.
Impact of Subgrid-Scale Modeling in Actuator-Line Based Large-Eddy Simulation of Vertical-Axis Wind Turbine Wakes. *Atmosphere* **2018**, *9*, 257.
https://doi.org/10.3390/atmos9070257

**AMA Style**

Abkar M.
Impact of Subgrid-Scale Modeling in Actuator-Line Based Large-Eddy Simulation of Vertical-Axis Wind Turbine Wakes. *Atmosphere*. 2018; 9(7):257.
https://doi.org/10.3390/atmos9070257

**Chicago/Turabian Style**

Abkar, Mahdi.
2018. "Impact of Subgrid-Scale Modeling in Actuator-Line Based Large-Eddy Simulation of Vertical-Axis Wind Turbine Wakes" *Atmosphere* 9, no. 7: 257.
https://doi.org/10.3390/atmos9070257