Momentum deficit and wake-added turbulence kinetic energy budgets in the stratified atmospheric boundary layer

TL;DR

This study investigates how atmospheric stability affects wind turbine wake dynamics, focusing on momentum deficit and turbulence kinetic energy, revealing limitations in current empirical wake models under different stability conditions.

Contribution

It provides a detailed analysis of the physical mechanisms influencing wake behavior in stratified ABL using large eddy simulation, highlighting the impact of stability on turbulence and momentum.

Findings

Stable conditions increase shear and affect wake turbulence.

Neutral conditions lead to higher total TKE in wakes.

Existing empirical models do not account for ABL stability effects.

Abstract

To achieve decarbonization targets, wind turbines are growing in hub height, rotor diameter, and are being deployed in new locations with diverse atmospheric conditions not previously seen, such as offshore. Physics-based analytical wake models commonly used for design and control of wind farms simplify atmospheric boundary layer (ABL) and wake physics to achieve computational efficiency. This is done primarily through a simplified model form that neglects certain flow processes and through parameterization of ABL and wake turbulence through a wake spreading rate. In this study, we analyze the physical mechanisms that govern momentum and turbulence within a wind turbine wake in the stratified ABL. We use large eddy simulation and analysis of the streamwise momentum deficit and wake-added turbulence kinetic energy (TKE) budgets to study wind turbine wakes under neutral and stable conditions. To parse the wake from the turbulent, incident ABL flow, we decompose the flow into the base ABL flow and the deficit flow produced by the presence of a turbine. We analyze the decomposed flow field budgets to study the effects of changing stability on the streamwise momentum deficit and wake-added TKE. The results demonstrate that stability changes the importance of physical mechanisms for both quantities primarily through the nonlinear interactions of the base and deficit flows, with the stable case most affected by higher shear in the base flow and the neutral case by higher base flow TKE. Buoyancy forcing terms in the momentum deficit and wake-added TKE budgets are relatively less important compared to the aforementioned effects. While total TKE is higher in wakes in neutral ABL flows, the wake-added TKE is higher downwind of turbines in stable ABL conditions. The dependence of wake-added TKE on ABL stability is not represented in existing empirical models widely used for mean wake flow modeling.