The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction
<p>This study introduces the actuator farm model (AFM), a novel parameterization for simulating wind turbines within large eddy simulations (LESs) of wind farms. Unlike conventional models like the actuator disk (AD) or actuator line (AL), the AFM utilizes a single actuator point at the rotor...
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Copernicus Publications
2024-12-01
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| Series: | Wind Energy Science |
| Online Access: | https://wes.copernicus.org/articles/9/2301/2024/wes-9-2301-2024.pdf |
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| author | S. Stipa A. Ajay J. Brinkerhoff |
| author_facet | S. Stipa A. Ajay J. Brinkerhoff |
| author_sort | S. Stipa |
| collection | DOAJ |
| description | <p>This study introduces the actuator farm model (AFM), a novel parameterization for simulating wind turbines within large eddy simulations (LESs) of wind farms. Unlike conventional models like the actuator disk (AD) or actuator line (AL), the AFM utilizes a single actuator point at the rotor center and only requires two to three mesh cells across the rotor diameter. Turbine force is distributed to the surrounding cells using a new projection function characterized by an axisymmetric spatial support in the rotor plane and Gaussian decay in the streamwise direction. The spatial support's size is controlled by three parameters: the half-decay radius <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>r</mi><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="27f1caa887926dd8dce18530ebf900c8"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00001.svg" width="20pt" height="12pt" src="wes-9-2301-2024-ie00001.png"/></svg:svg></span></span>, smoothness <span class="inline-formula"><i>s</i></span>, and streamwise standard deviation <span class="inline-formula"><i>σ</i></span>. Numerical experiments on an isolated National Renewable Energy Laboratory (NREL) 5MW wind turbine demonstrate that selecting <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>r</mi><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mi>R</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="40pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="4f7e0481fb859c228ed057d5eb4a8cc5"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00002.svg" width="40pt" height="14pt" src="wes-9-2301-2024-ie00002.png"/></svg:svg></span></span> (where <span class="inline-formula"><i>R</i></span> is the turbine radius), <span class="inline-formula"><i>s</i></span> between 6 and 10, and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi mathvariant="italic">σ</mi><mo>≈</mo><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>/</mo><mn mathvariant="normal">1.6</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="58pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="513419cf9f56555a3167718d25d80d91"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00003.svg" width="58pt" height="14pt" src="wes-9-2301-2024-ie00003.png"/></svg:svg></span></span> (where <span class="inline-formula">Δ<i>x</i></span> is the grid size in the streamwise direction) yields wake deficit profiles, turbine thrust, and power predictions similar to those obtained using the actuator disk model (ADM), irrespective of horizontal grid spacing down to the order of the rotor radius.</p>
<p>Using these parameters, LESs of a small cluster of 25 turbines in both staggered and aligned layouts are conducted at different horizontal grid resolutions using the AFM. Results are compared against ADM simulations employing a spatial resolution that places at least <span class="inline-formula">10</span> grid points across the rotor diameter. The wind farm is placed in a neutral atmospheric boundary layer (ABL) with turbulent inflow conditions interpolated from a previous simulation without turbines. At horizontal resolutions finer than or equal to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M10" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>R</mi><mo>/</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="23pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="4d9eeacd57a6767478330158ce905f4c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00004.svg" width="23pt" height="14pt" src="wes-9-2301-2024-ie00004.png"/></svg:svg></span></span>, the AFM yields similar velocity, shear stress, turbine thrust, and power as the ADM. Coarser resolutions reveal the AFM's ability to accurately capture power at the non-waked wind farm rows, although it underestimates the power of waked turbines. However, the far wake of the cluster can be predicted well even when the cell size is of the order of the turbine radius.</p>
<p>Finally, combining the AFM with a domain nesting method allows us to conduct simulations of two aligned wind farms in a fully neutral ABL and of wind-farm-induced atmospheric gravity waves under a conventionally neutral ABL, obtaining excellent agreement with ADM simulations but with much lower computational cost. The simulations highlight the AFM's ability to investigate the mutual interactions between large turbine arrays and the thermally stratified atmosphere.</p> |
| format | Article |
| id | doaj-art-81a575295d2042ee8678c8d5110c27cd |
| institution | Kabale University |
| issn | 2366-7443 2366-7451 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Wind Energy Science |
| spelling | doaj-art-81a575295d2042ee8678c8d5110c27cd2024-12-18T10:48:04ZengCopernicus PublicationsWind Energy Science2366-74432366-74512024-12-0192301233210.5194/wes-9-2301-2024The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interactionS. Stipa0A. Ajay1J. Brinkerhoff2School of Engineering, University of British Columbia – Okanagan, Kelowna, CanadaSchool of Engineering, University of British Columbia – Okanagan, Kelowna, CanadaSchool of Engineering, University of British Columbia – Okanagan, Kelowna, Canada<p>This study introduces the actuator farm model (AFM), a novel parameterization for simulating wind turbines within large eddy simulations (LESs) of wind farms. Unlike conventional models like the actuator disk (AD) or actuator line (AL), the AFM utilizes a single actuator point at the rotor center and only requires two to three mesh cells across the rotor diameter. Turbine force is distributed to the surrounding cells using a new projection function characterized by an axisymmetric spatial support in the rotor plane and Gaussian decay in the streamwise direction. The spatial support's size is controlled by three parameters: the half-decay radius <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M1" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>r</mi><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="12pt" class="svg-formula" dspmath="mathimg" md5hash="27f1caa887926dd8dce18530ebf900c8"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00001.svg" width="20pt" height="12pt" src="wes-9-2301-2024-ie00001.png"/></svg:svg></span></span>, smoothness <span class="inline-formula"><i>s</i></span>, and streamwise standard deviation <span class="inline-formula"><i>σ</i></span>. Numerical experiments on an isolated National Renewable Energy Laboratory (NREL) 5MW wind turbine demonstrate that selecting <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi>r</mi><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mi>R</mi></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="40pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="4f7e0481fb859c228ed057d5eb4a8cc5"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00002.svg" width="40pt" height="14pt" src="wes-9-2301-2024-ie00002.png"/></svg:svg></span></span> (where <span class="inline-formula"><i>R</i></span> is the turbine radius), <span class="inline-formula"><i>s</i></span> between 6 and 10, and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi mathvariant="italic">σ</mi><mo>≈</mo><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>/</mo><mn mathvariant="normal">1.6</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="58pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="513419cf9f56555a3167718d25d80d91"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00003.svg" width="58pt" height="14pt" src="wes-9-2301-2024-ie00003.png"/></svg:svg></span></span> (where <span class="inline-formula">Δ<i>x</i></span> is the grid size in the streamwise direction) yields wake deficit profiles, turbine thrust, and power predictions similar to those obtained using the actuator disk model (ADM), irrespective of horizontal grid spacing down to the order of the rotor radius.</p> <p>Using these parameters, LESs of a small cluster of 25 turbines in both staggered and aligned layouts are conducted at different horizontal grid resolutions using the AFM. Results are compared against ADM simulations employing a spatial resolution that places at least <span class="inline-formula">10</span> grid points across the rotor diameter. The wind farm is placed in a neutral atmospheric boundary layer (ABL) with turbulent inflow conditions interpolated from a previous simulation without turbines. At horizontal resolutions finer than or equal to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M10" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>R</mi><mo>/</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="23pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="4d9eeacd57a6767478330158ce905f4c"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="wes-9-2301-2024-ie00004.svg" width="23pt" height="14pt" src="wes-9-2301-2024-ie00004.png"/></svg:svg></span></span>, the AFM yields similar velocity, shear stress, turbine thrust, and power as the ADM. Coarser resolutions reveal the AFM's ability to accurately capture power at the non-waked wind farm rows, although it underestimates the power of waked turbines. However, the far wake of the cluster can be predicted well even when the cell size is of the order of the turbine radius.</p> <p>Finally, combining the AFM with a domain nesting method allows us to conduct simulations of two aligned wind farms in a fully neutral ABL and of wind-farm-induced atmospheric gravity waves under a conventionally neutral ABL, obtaining excellent agreement with ADM simulations but with much lower computational cost. The simulations highlight the AFM's ability to investigate the mutual interactions between large turbine arrays and the thermally stratified atmosphere.</p>https://wes.copernicus.org/articles/9/2301/2024/wes-9-2301-2024.pdf |
| spellingShingle | S. Stipa A. Ajay J. Brinkerhoff The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction Wind Energy Science |
| title | The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction |
| title_full | The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction |
| title_fullStr | The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction |
| title_full_unstemmed | The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction |
| title_short | The actuator farm model for large eddy simulation (LES) of wind-farm-induced atmospheric gravity waves and farm–farm interaction |
| title_sort | actuator farm model for large eddy simulation les of wind farm induced atmospheric gravity waves and farm farm interaction |
| url | https://wes.copernicus.org/articles/9/2301/2024/wes-9-2301-2024.pdf |
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