Validation of an Actuator-Line Tower Model for Upwind and...
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International Conference on Future Technologies for Wind Energy October 24-26, 2017, Boulder, Colorado, USA Validation of an Actuator-Line Tower Model for Upwind and Downwind Turbine Configurations and Wind Farms Adam W. Lavely*, Matthew Churchfield**, Scott Larwood*** Sven Schmitz**** *Pennsylvania State University, University Park, PA, USA, [email protected] **NREL, Boulder, CO, USA, [email protected] *** University of the Pacific, Stockton, CA, USA, [email protected] ****Pennsylvania State University, University Park, PA, USA, [email protected] Abstract The tower of a wind turbine causes velocity fluctuations affecting blade loads and and wakes of upwind turbines and the blade loading for downstream turbines. We continue the development of an actuator-line based tower model[11,12] and validate azimuthally varying blade loads against upwind and downwind NREL Phase VI campaigns. We further show how the tower model affects turbine loads and power in a wind farm using both actuator line and actuator disk methods to resolve the turbines, with particular attention to non-torque variations on the low-speed shaft loading. Keywords: Actuator line model, Tower model, ABL, NREL Phase VI Introduction Wind turbine modelling has become important for the understanding of non-steady turbine blade loading due to atmospheric turbulence and wind farm power output for advanced control of local and regional power grids. Prediction of blade load distributions, in general, have improved with recent advances in actuator line models. Little attention, however, has been given to tower modelling, which not only has an effect on azimuthally varying blade loads, and hence blade fatigue, but also on the downstream flow, including wake meandering and variation in the wake swirl [2]. Furthermore, several of the next-generation concept turbines have downwind configurations to increase the blade length beyond the current limitations of upwind turbines [3,15]. Therefore, an accurate representation of the turbine tower within actuator line models is an important area of research towards accurate prediction of turbine fatigue and wake flow physics altered due to the presence of a tower. Methods In this work, we continue to develop a C p based actuator-line model for wind turbine towers within NREL’s SOWFA tool, built within OpenFOAM. OpenFOAM is an open-source finite-volume toolbox for solving differential equations [5-7]. In actuator line models, sectional blade loads are calculated based on local flow properties and added back as body forces into the momentum equation of the underlying flow solver [8,9,10]. A two-way coupling of wind turbines represented as actuator lines and an ABL solver allows for wind farm applications and is necessary for accurate prediction of non-steady atmospheric loading on wind turbine blades [4]. Tower models have been developed using a single actuator drag line [13,14], multiple actuator lines to add drag and side forces [11,12], and an advanced actuator line with a C p -based force distribution. The Cp based model uses a function , , = !( !!! ! ! ) ! !( !!! ! ! ! ) ! where R is the local tower radius and C is given by = [ ! ! ! ! ! + ! ! ! (1 + erf ( ! ! ! ))] !! . The azimuthal variation can be found by fitting a correction to the potential solution to align with experimental data [11]. Preliminary Results
Transcript of Validation of an Actuator-Line Tower Model for Upwind and...
International Conference on Future Technologies for Wind Energy October 24-26, 2017, Boulder, Colorado, USA
Validation of an Actuator-Line Tower Model for Upwind and Downwind Turbine Configurations and Wind Farms
Adam W. Lavely*, Matthew Churchfield**, Scott Larwood*** Sven Schmitz****
*Pennsylvania State University, University Park, PA, USA, [email protected] **NREL, Boulder, CO, USA, [email protected]
*** University of the Pacific, Stockton, CA, USA, [email protected] ****Pennsylvania State University, University Park, PA, USA, [email protected]
Abstract The tower of a wind turbine causes velocity fluctuations affecting blade loads and and wakes of upwind turbines and the blade loading for downstream turbines. We continue the development of an actuator-line based tower model[11,12] and validate azimuthally varying blade loads against upwind and downwind NREL Phase VI campaigns. We further show how the tower model affects turbine loads and power in a wind farm using both actuator line and actuator disk methods to resolve the turbines, with particular attention to non-torque variations on the low-speed shaft loading. Keywords: Actuator line model, Tower model, ABL, NREL Phase VI Introduction
Wind turbine modelling has become important for the understanding of non-steady turbine blade loading due to atmospheric turbulence and wind farm power output for advanced control of local and regional power grids. Prediction of blade load distributions, in general, have improved with recent advances in actuator line models. Little attention, however, has been given to tower modelling, which not only has an effect on azimuthally varying blade loads, and hence blade fatigue, but also on the downstream flow, including wake meandering and variation in the wake swirl [2]. Furthermore, several of the next-generation concept turbines have downwind configurations to increase the blade length beyond the current limitations of upwind turbines [3,15]. Therefore, an accurate representation of the turbine tower within actuator line models is an important area of research towards accurate prediction of turbine fatigue and wake flow physics altered due to the presence of a tower. Methods
In this work, we continue to develop a Cp based actuator-line model for wind turbine towers within NREL’s SOWFA tool, built within OpenFOAM. OpenFOAM is an open-source finite-volume toolbox for solving differential equations [5-7]. In actuator line models, sectional blade loads are calculated based on local flow properties and added back as body forces into the momentum equation of the underlying flow solver [8,9,10]. A two-way coupling of wind turbines represented as actuator lines and an ABL solver allows for wind farm applications and is necessary for accurate prediction of non-steady atmospheric loading on wind turbine blades [4]. Tower models have been developed using a single actuator drag line [13,14], multiple actuator lines to add drag and side forces [11,12], and an advanced actuator line with a Cp-based force distribution. The Cp based model uses a function
𝑔 𝑟, 𝜃, 𝑧 = 𝐶𝑒!(!!!!!
)!𝑒!(!!!!!!
)!
where R is the local tower radius and C is given by
𝐶 = [𝜖!!𝜖!𝜋!! + 𝜋!𝜖!𝜖!𝑅(1 + erf (
!!!))]!!.
The azimuthal variation can be found by fitting a correction to the potential solution to align with experimental data [11]. Preliminary Results
International Conference on Future Technologies for Wind Energy October 24-26, 2017, Boulder, Colorado, USA
We compare different methods for a) validation cases for a cylinder in a uniform flow, b) NREL Phase VI upwind configuration, and c) NREL Phase VI downwind configuration. Preliminary results[11] showing the variation in the wake associated with the particular tower model are shown in Figures a and b. Additionally, we are working on a wind farm simulations using atmospheric inflow with and without the tower model to show the effect on downstream loadings due to variations on upstream turbine wakes.
a) NREL Phase VI rotor - Tower modelled as single drag line
b) NREL Phase VI rotor - Tower modelled with Cp-based force distribution
Conclusions
In the present work, we continue the development of tower models using an actuator line approach, including the validation of the models using cylinder and NREL Phase VI flows. The tower model affects the turbine wake in swirl and velocity deficit, having an effect on downstream turbines in wind farms and affecting wind farm power production. Additionally, the specific choice of tower model has a large effect on downwind turbines as the wake causes noteable one-per-rev variations that must be represented in order to accurately predict load variations for power and fatigue prediction. References 1. Larwood, Scott M., and R. Chow. "Comparison of upwind and downwind operation of the NREL Phase VI Experiment." Journal of Physics: Conference Series. Vol. 753. No. 2. IOP Publishing, 2016. 2. Kang, S., Yang, X., and Sotiropoulos, F., “On the Onset of Wake Meandering for an Axial Turbine in a Turbulent Open Channel Flow,” Journal of Fluid Mechanics, Vol. 744, 2014, pp. 376–403. 3. Kress, C., N. Chokani, and R. S. Abhari. "Passive minimization of load fluctuations on downwind turbines." Renewable Energy 89 (2016): 543-551. 4. Lavely, Adam W., “Effects of daytime atmospheric boundary layer turbulence on the generation of nonsteady wind turbine loadings and predictive accuracy of lower order models.“ The Pennsylvania State University, 2017. 5. OpenCFD “OpenFOAM Documentation,” http://www.openfoam.org., 2012. 6. Churchfield, M. J., S. Lee, J. Michalakes, and P. J. Moriarty (2012) “A numerical study of the effects of atmospheric and wake turbulence on wind turbine dynamics,” Journal of turbulence, (13), p. N14. 7. Churchfield, Matthew J., Sang Lee, and Patrick J. Moriarty. "Adding complex terrain and stable atmospheric condition capability to the OpenFOAM-based flow solver of the simulator for on/offshore wind farm applications (SOWFA)." ITM Web of Conferences. Vol. 2. EDP Sciences, 2014. 8. Troldborg, Niels, Jens N. Sørensen, and Robert Mikkelsen. "Actuator line simulation of wake of wind turbine operating in turbulent inflow." Journal of physics: conference series. Vol. 75. No. 1. IOP Publishing, 2007. 9. Nilsson, Karl, et al. "Validation of the actuator line method using near wake measurements of the MEXICO rotor." Wind Energy 18.3 (2015): 499-514. 10. Jha, Pankaj K., et al. "The effect of various actuator-line modeling approaches on turbine-turbine interactions and wake-turbulence statistics in atmospheric boundary-layer flow." Proceedings of the 52th AIAA Aerospace Sciences Meeting, National Harbor, MD, USA. Vol. 1317. 2014. 11. Churchfield, Matthew J., Zhixiang Wang, and Sven Schmitz. "Modeling Wind Turbine Tower and Nacelle Effects within an Actuator Line Model." 33rd Wind Energy Symposium. 2015. 12. Wang, Zhixiang. "Modeling Wind Turbine/Tower Interactions within an Actuator Line Model." (2015). 13. Aitken, M. L., Kosovi ́c, B., Mirocha, J. D., and Lundquist, J. K., “Large Eddy Simulaton of Wind Turbine Wake Dynamics in the Stable Boundary Layer Using the Weather Research adn Forecasting Model,” Journal of Renewable and Sustainable Energy, Vol. 6, 2014, pp. 033137. 14. Wu, Y.-T. and Port ́e-Agel, F., “Large-Eddy Simulation of Wind Turbine Wakes: Evaluation of Turbine Parameterisa- tions,” Boundary-Layer Meteorology, Vol. 138, 2011, pp. 345–366. 15, Loth, Eric, et al. "Downwind pre‐aligned rotors for extreme‐scale wind turbines." Wind Energy (2017).
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