Towards a Simplified Dynamic Wake Model using POD Analysis

TL;DR

This paper explores the use of proper orthogonal decomposition (POD) to develop a simplified dynamic wake model for wind turbines, demonstrating that few modes can capture key wake dynamics despite limited energy content.

Contribution

The study introduces a POD-based approach to model wind turbine wakes, highlighting mode selection based on application-specific measures and providing physical interpretation of modes.

Findings

Few POD modes suffice to capture essential wake dynamics.

Mode importance varies with the physical measure considered.

POD modes relate to specific wake properties like large-scale movement.

Abstract

We apply the proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analyis mainly focuses on the question whether POD could be a useful tool to develop a simplified dynamic wake model. The extracted POD modes are used to obtain approximate descriptions of the velocity field. To assess the quality of these POD reconstructions, we define simple measures which are believed to be relevant for a sequential turbine in the wake such as the energy flux through a disk in the wake. It is shown that only a few modes are necessary to capture basic dynamical aspects of these measures even though only a small part of the turbulent kinetic energy is restored. Furthermore, we show that the importance of the individual modes depends on the measure chosen. Therefore, the optimal choice of modes for a possible model could in principle depend on the application of interest. We additionally present a possible interpretation of the POD modes relating them to specific properties of the wake. For example the first mode is related to the horizontal large scale movement. Besides yielding a deeper understanding, this also enables us to view our results in comparison to existing dynamic wake models.