A control algorithm for attaining stationary statistics in LES of thermally stratified wind-turbine array boundary layers Adrian Sescu * and Charles Meneveau Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD * present affiliation: Department of Aerospace Engineering, Mississippi State University, Starkville, MS Background Objectives Issue # 1 Solution to issue # 2 LES Results Conclusions Funding from ”NSF-Physical Meteorology program, Grant NSF-AGS ” is gratefully acknowledged Issue # 2 Recent LES studies of the interaction between neutral atmospheric boundary layer (ABL) and infinitely large arrays of wind turbines have led to derivations of new similarity relations within the surface layer, based on observations of stationary averaged vertical profiles of mean flow and turbulent fluxes. A similar analysis in non-neutral conditions is not trivial, since achieving statistically stationary conditions in LES is challenging. For example, the heat flux at the ground forces vertical profiles of mean temperature to vary significantly over time. -Stratified ABL is highly non-stationary: e.g., mean temperature profiles evolve in time; -Stationarity is desirable to understand the interaction between ABL and wind farms The focus of this work is on using an artificial heat source or sink, in a region located above ABL, that provides the amount of heat necessary to maintain the overall temperature field inside the ABL stationary. This is achieved by using a PI control algorithm, designed to keep constant the initial horizontally averaged temperature at a specified height and above. Another controller is used to drive the flow within the ABL, causing the mean velocity to achieve a prescribed direction at a specified height. This is done by controlling a source term (in the form of an additional Coriolis force) in the momentum equations. This term is deactivated once the flow becomes statistically stationary and the geostrophic wind aligns with the desired direction at a given height. A suite of large eddy simulations at various resolutions, with and without wind turbines, and with different levels of thermal stratification are presented. -use of a source term in the momentum equation: -A controlling algorithm has been applied to keep the scalar field stationary. -A source term was used inside the momentum equations to rotate the flow to the desired direction. -The results show that the control scheme is successful -LES of a fully-developed wind farm have been carried out in stratified conditions. Future work: -A model for the effective roughness length for stratified ABL in the presence of wind farms will be derived. -Mean wind velocity is not perpendicular to the rotor disk as required by the actuator disk or line method. Solution to issue # 1 Unstabl e Stable Mean temperature profiles -An artificial heat source/sink term is added to the heat equation: -A PI controller is used to update the source: Governing equations -Momentum equation: -Continuity equation: -Heat equation: Mean flow angle - Update : Unstabl e Stable interval of rotation, and wher e is the time x-component velocity; 4x6 rotors; unstable conditions x-component velocity; 4x6 rotors; stable conditions A13G-0274