Wind Energy

48
Numerical Computations of Wind Turbine
Wakes
Stefan Ivanell, Jens N. Sørensen and Dan Henningson
48.1 Numerical Method
Numerical simulations using CFD are performed for wind turbine applications.
The aim of the project is to get a better understanding of wake behaviour
that cannot be obtained by standard industrial design codes for wind
power applications. Such codes are based on the Blade Element Momentum
(BEM) technique, extended with a number of empirical corrections that are
not entirely based on physical flow features. The importance of accurate design
models also increases as the turbines become larger. Therefore, the research
is today undergoing a shift toward more fundamental approaches, aiming at
understanding basic aerodynamic mechanisms.
Theoretically, the bound circulation on the blades is equal to the circulation
behind the rotor, i.e. in the wake. For inviscid flows, the sum of the
circulation of the tip and the root vortex should ideally be zero. However, this
is not entirely correct for viscous flow. The tip and root vortex do, however,
both for inviscid and viscous flows, have different sense of rotation, i.e. different
signs of the circulation. A steep decline of circulation toward the tip will
lead to a rapid concentration of the vortex at the tip (occurring a few chord
lengths behind the tip). The sign of the circulation gradient along the blade
will also determine the sense of rotation of the vortex behind the blade.
The simulations are performed using the CFD program “EllipSys3D” developed
at DTU (The Technical University of Denmark) and Risø. The socalled
Actuator Line Method is used, where the blade is represented by a line
instead of a large number of panels. The forces on that line are introduced
by using tabulated aerodynamic coefficients. In this way, computer resources
are used more efficiently since the number of node points locally around the
blade is decreased, and they are instead concentrated in the wake behind the
blades. The actuator line method was introduced by Sørensen and Shen [1]
and later implemented into the EllipSys3D code by Mikkelsen [2]. EllipSys3D
is a general purpose 3D solver developed by Sørensen [3] and Michelsen [4,5].