Modeling of turbulence kinetic energy added by wind-turbine wakes in the atmospheric boundary layer
Bowen Du, Jingshan Zhu, Baoliang Li, Mingwei Ge, Xintao Li, Yongqian Liu
TL;DR
The paper tackles predicting wake-added turbulence kinetic energy ($k_w$) in wind-turbine wakes within the atmospheric boundary layer by proposing a physics-based two-submodule framework that yields a closed-form azimuthally-averaged $k_w$ and a ground-effect correction $\delta_{k_w}$, enabling end-to-end three-dimensional predictions from basic inflow and turbine operating conditions. The azimuthally averaged module is derived from a simplified $k$-budget in cylindrical coordinates and solved analytically via a Green's-function approach, with parameters ($U_\rho$, $\nu_t$, $\Psi$) determined from LES data and a near-wake Super-Gaussian velocity deficit for $U_\rho$. The ground-effect term is modeled with a unified, self-similar form that is Gaussian in radius and sinusoidal in azimuth, with parameters ($r_{\delta}$, $\sigma_{\delta}$, $B$, $C$) calibrated from LES. Validation against LES calibrations and public wind-tunnel/LES datasets yields $\text{NMAE}$ below 12% (average ~8.13%), demonstrating robustness and practical potential for engineering assessments of wake recovery and downstream fatigue loads.
Abstract
Accurate prediction of turbulence kinetic energy (TKE) added by wind-turbine wakes is of significant scientific value for understanding the wake recovery mechanisms. Furthermore, this physical quantity is a critical input for engineering applications. In this study, we propose a novel wake-added TKE prediction model capable of accurately predict the three-dimensional spatial distribution of wake-added TKE using only basic inflow and wind turbine operation conditions as inputs. The model consists of two sub-modules: one for calculating the azimuthally-averaged wake-added TKE and the other for determining the ground effect correction function. The calculation of the azimuthally-averaged wake-added TKE is based on the analytical solution derived from the corresponding wake-added TKE budget, while the ground effect correction function is determined using a unified functional form, owing to its self-similarity. To ensure the closure of these two sub-modules, we develop methods for determining all free parameters based on the large-eddy simulation (LES) cases. This results in an end-to-end prediction framework, enabling direct engineering applications of the proposed model. We compared the proposed model with LES calibration data and publicly available validation datasets from the literature, which include LES and wind tunnel experiments under various inflow and turbine operating conditions. The comparison results show that the proposed model can accurately predict the spatial distribution of wake-added TKE, particularly capturing the vertical asymmetry of wake-added TKE and the streamwise evolution of the hub-height wake-added TKE profile. The averaged normalized mean absolute error of the proposed model across all validation datasets is only 8.13%, demonstrating its robustness and broad applicability.