Modeling of turbulence kinetic energy added by wind-turbine wakes in the atmospheric boundary layer

TL;DR

This paper introduces a new model for predicting the three-dimensional distribution of turbulence kinetic energy added by wind-turbine wakes, using basic input conditions, validated against LES and experimental data, with high accuracy.

Contribution

The study develops a novel, end-to-end wake-added TKE prediction model based on analytical solutions and LES calibration, suitable for direct engineering applications.

Findings

Accurately predicts spatial wake-added TKE distribution

Captures vertical asymmetry and streamwise evolution of TKE

Achieves an average normalized MAE of 8.13% across datasets

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.