Wind Turbine Modeling for Computational Fluid Dynamics December 2010 — December 2012 L.A. Martinez Tossas and S. Leonardi University of Puerto Rico Mayaguez, Puerto Rico NREL Technical Monitor: Pat Moriarty NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency & Renewable Energy Operated by the Alliance for Sustainable Energy, LLC This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Subcontract Report NREL/SR-5000-55054 July 2013 Contract No. DE-AC36-08GO28308 Wind Turbine Modeling for Computational Fluid Dynamics December 2010 — December 2012 L.A. Martinez Tossas and S. Leonardi University of Puerto Rico Mayaguez, Puerto Rico NREL Technical Monitor: Pat Moriarty Prepared under Subcontract No. AFC-1-11305-01 NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency & Renewable Energy Operated by the Alliance for Sustainable Energy, LLC This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. National Renewable Energy Laboratory Subcontract Report 15013 Denver West Parkway NREL/SR-5000-55054 Golden, CO 80401 July 2013 303-275-3000 • www.nrel.gov Contract No. DE-AC36-08GO28308 NOTICE This report was prepared as an account of work sponsored by an agency of the United States government. 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Abstract With the shortage of fossil fuels and the increase of environmental awareness, wind energy is becoming more impor­ tant than ever. As the market for wind energy grows, wind turbines and wind farms are becoming larger. But, there is still more to learn about this technology. For example, current utility-scale turbines extend a significant distance into the atmospheric boundary layer. Therefore, the interaction between the atmospheric boundary layer and the turbines and their wakes needs to be better understood. The turbulent wakes of upstream turbines affect the flow field of the turbines behind them, thus decreasing power production and increasing mechanical loading. With greater knowledge of this type of flow, wind farm developers could plan better-performing, less maintenance-intensive wind farms. Sim­ ulating this flow using computational fluid dynamics (CFD) is one important way to gain a better understanding of wind farm flows. In this study, we compare the performance of actuator disk and actuator line models in producing wind turbine wakes and the wake-turbine interaction between multiple turbines. We also examine parameters that affect the performance of these models, such as grid resolution, the use of a tip-loss correction, and the way in which the turbine force is projected onto the flow field. We see that as the grid is coarsened, the predicted power decreases. As the width of the Gaussian body force projection function is increased, the predicted power is increased. The ac­ tuator disk and actuator line models produce similar wake profiles and predict power within 1% of one another when subject to uniform inflow. The actuator line model is able to capture flow structures near the blades such as root and tip vortices, which the actuator disk does not capture, but in the far wake, they look similar. The actuator line model was validated using the wind tunnel experiment conducted at the Norwegian University of Science and Technol­ ogy, Trondheim. Agreement between the model and the experiments was obtained, with the maximum percentage difference in power coefficients of 25% and 40% for thrust coefficient. The actuator line and actuator disk models were compared when running large-scale wind farm simulations. Normalized power was similar for both models, but dimensional power differed from 1 to 17%. The actuator disk model was able to run approximately three times faster, though. This work shows that actuator models for wind turbine aerodynamics are a viable alternative to using full blade-resolving simulations. However, care must be taken to use the proper grid resolution and force projection to the CFD grid to obtain accurate predictions of aerodynamic forces and, hence, power. More work is needed to determine the best method of body force projection onto the CFD grid. iii This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. Abbreviations and Nomenclature ABL Atmospheric boundary layer ADM Actuator disk model ALM Actuator line model ASM Actuator surface model BEM Blade Element Momentum CFD Computational fluid dynamics DNS Direct numerical simulation LES Large eddy simulation N-S Navier-Stokes equations RANS Reynolds-averaged Navier-Stokes SGS Subgrid-scale CD Drag coefficient CL Lift coefficient CP Power coefficient CT Thrust coefficient p Pressure t Time U Velocity U¥ Free stream velocity l Tip speed ratio nSGS Subgrid-scale viscosity r Density s Solidity factor tSGS Subgrid-scale stress iv This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. Table of Contents 1 Literature Review ............................................... 1 1.1 Introduction ................................................ 1 1.2 Basics of Wind Turbine Aerodynamics .................................. 1 1.3 Wind Turbine Computational Fluid Dynamics .............................. 2 1.4 Atmospheric Boundary Layer Simulations ................................ 3 1.5 Actuator Disc Model (ADM) ....................................... 4 1.6 Actuator Line Model (ALM) ....................................... 6 1.7 Actuator Surface Model (ASM) ..................................... 7 1.8 Comparison Between ADM and ALM .................................. 8 1.9 Conclusions ................................................ 8 2 Actuator Turbine Model Implementation .................................. 9 2.1 Actuator Line Model ........................................... 9 2.2 Actuator Disk Model ........................................... 10 2.3 Numerical Method ............................................ 12 3 Actuator Disk and Actuator Line Models in Uniform Nonturbulent Inflow . 14 3.1 Five Megawatt Reference Turbine .................................... 14 3.2 Actuator Line Model ........................................... 15 3.3 Actuator Disk Model ........................................... 15 3.4 Actuator Points .............................................. 16 3.5 Tip Loss Correction ............................................ 16 3.6 Time-step ................................................. 17 3.7 Comparison ................................................ 18 3.8 The e Parameter .............................................. 28 4 Wind Tunnel Simulations ........................................... 31 4.1 Turbine Model .............................................. 31 4.2 Mesh ................................................... 31 4.3 Results ................................................... 31 5 Wind Farm Simulation ............................................ 36 5.1 Introduction ................................................ 36 5.2 Results ................................................... 36 6 Conclusion and Future Work ......................................... 46 Bibliography .................................................... 47 (Unless otherwise noted, all figures/tables were created by Luis A. Martínez.) v This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. List of Tables Table 1. Percentage difference between the ADM, ALM, and BEM theory in terms of power production. A Richardson extrapolation is used to approximate the converged solution for the ALM and ADM. 21 List of Figures Figure 1. A