Experimental study of the kinetic energy budget in a wind turbine streamtube

Abstract

The classical streamtube analysis for a wind turbine couples the Bernoulli equation with the actuator-disk model to obtain the maximum possible power extraction at the wind turbine based on the difference between inlet and outlet fluxes of kinetic energy. However, the classical analysis neglects turbulence, which can play a crucial role in the various interactions of the streamtube with the turbulent Atmospheric Boundary Layer (ABL). The present study aims at examining the fluxes of kinetic energy on a wind turbine streamtube including the effects of turbulence, based on an existing Particle Image Velocimetry (PIV) data set obtained previously in a wind tunnel study of a model wind farm. The data are used to evaluate the most relevant fluxes of kinetic energy through the various parts of the control surface bounding the stream tube. It is found that the flux due to mean axial velocity, the turbulence-induced flux across the periphery of the streamtube, and the power extracted at the wind turbine are all of the same order of magnitude. The losses due to dissipation of mean kinetic energy inside the streamtube are also considerable, although our measurements cannot capture the dissipation in its entirety. Fluxes due to turbulent normal stresses are found to be negligible, and the flux of angular kinetic energy due to wake rotation is also found to be very small. The analysis results confirm that turbulence plays a central role in the energetics of a wind turbine streamtube, and the measured trends provide guidance for the development of improved models.

Keywords:

• wind turbine
• streamtube
• turbulence

Acknowledgments

Acknowledgements

The authors thank the National Science Foundation’s Energy for Sustainability Program for funding this project (Projects CBET 0730922 and CBET 1133800) and the NSF GK-12 program # 0742436 entitled: “New GK-12: Building Bridges from High School to Grad School: Inspiring Students Through Discovery-Based Activities in Energy and the Environment.” They also thank Andrew Baitinger for assisting in the initial visualizations of the wind turbine streamtube based on the data set.