Search for: All records

Analytical wake models provide a computationally efficient means to predict velocity distributions in wind turbine wakes in the atmospheric boundary layer (ABL). Most existing models are developed for neutral atmospheric conditions and correspondingly neglect the effects of buoyancy and Coriolis forces that lead to veer, i.e., changes in the wind direction with height. Both veer and changes in thermal stratification lead to lateral shearing of the wake behind a wind turbine, which affects the power output of downstream turbines. Here we develop an analytical engineering wake model for a wind turbine in yaw in ABL flows including Coriolis and thermal stratification effects. The model combines the new analytical representation of ABL vertical structure based on coupling Ekman and surface layer descriptions developed in Narasimhan et al. [Boundary Layer Meteorol. 190, 16 (2024)] with the vortex sheet-based wake model for yawed turbines proposed in Bastankhah et al. [J. Fluid Mech. 933, A2 (2022)], as well as a new method to predict the wake expansion rate based on the Townsend-Perry logarithmic scaling of streamwise velocity variance. The proposed wake model's predictions show good agreement with large-eddy simulation results, capturing the effects of wind veer and yawing, including the curled and sheared wake structures across various states of the ABL, ranging from neutrally to strongly stably stratified atmospheric conditions. The model significantly improves power loss predictions from wake interactions, especially in strongly stably stratified conditions where wind veer effects dominate. 

Abstract Reliable characterization of wind turbine wakes in the presence of Atmospheric Boundary Layer (ABL) flows is crucial to accurately predict wind farm performance. Wind veering in the ABL shears the wake in the lateral direction, and wind veer strength depends on the thermal stability of the ABL. Analytical wake modeling approaches must capture these ABL effects to ensure correct prediction of the wake structure under varied atmospheric conditions. To this end, a new physics-based analytical wake model is developed in this study that is capable of predicting the shape of wakes influenced by wind veer and thermal stratification effects. This model combines a novel ABL wind field model with the Gaussian wake model. The new ABL wind model is capable of predicting both the streamwise and spanwise velocity components in conventionally neutral (CNBL) and stable (SBL) ABL flows. The analytical expressions for both of these horizontal velocity components adhere to Monin-Obukhov Similarity Theory (MOST) in the surface layer, while capturing wind veering in the outer layer of the ABL. Incorporating this ABL model with the Gaussian wake model predicts laterally deflected wake shapes in a fully predictive and self-consistent fashion for a wide range of atmospheric conditions. The results also demonstrate that the enhanced wake model gives improved predictions relative to Large Eddy Simulations of power losses due to wake interactions under strongly stably stratified atmospheric conditions, where wind veer effects are dominant. 

We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer repre- sentation, which is valid for conventionally neutral (CNBL) and stable (SBL) atmospheric conditions. The model is based on a self-similar profile of horizontal stress for both CNBL and SBL flows that merges the classic 3/2 power law profile with a MOST-consistent stress profile in the surface layer. The velocity profiles are then obtained from the Ekman momentum balance equation. The same stress model is used to derive a new self-consistent Geostrophic Drag Law (GDL). We determine the ABL height (h) using an equilibrium boundary layer height model and parameterize the surface heat flux for quasi-steady SBL flows as a function of a prescribed surface temperature cooling rate. The ABL height and GDL equations can then be solved together to obtain the friction velocity (u∗) and the cross-isobaric angle (α0) as a function of known input parameters such as the Geostrophic wind speed and surface roughness (z0). We show that the model predictions agree well with simulation data from the literature and newly generated Large Eddy Simulations (LES). These results indicate that the proposed model provides an efficient and relatively accurate self-consistent approach for predicting the mean wind velocity distribution in CNBL and SBL flows.