Mac Gaunaa
Senior Scientist Technical University of Denmark
Department of Wind Energy Frederiksborgvej 299
4000 Roskilde Denmark macg@dtu.dk www.vindenergi.dtu.dk/english
Investigation of the Effect of Modeling Different Degrees of Detail
in the Key Elements in a Crosswind Kite Wind Energy System
Mac Gaunaa
Technical University of Denmark The present work investigates the effect of modelling
dif-ferent degrees of detail of the key elements of a crosswind kite wind energy system. The key performance parame-ters on which the effect is evaluated are effective lift-to-drag ratio, tether tension force and power production. To some extent there is also a pedagogical/didactic scope of this work, for students and those less experienced with crossflow kite wind energy systems to familiarize them-selves with how important the different key elements are for the key output parameters of the system.
The models used in the study are simple engineer-ing models, modellengineer-ing the main key behaviour without drowning in an unnecessarily large amount of model de-tails and/or tweakable constants. For instance, the aero-dynamic model that is used for relating the aeroaero-dynamic drag to the aspect ratio and the chosen lift coefficient is the classic lifting line theory with the addition of a viscous profile drag part. The line force and power production is evaluated using the expressions from Loyd [1].
As an example of the łfirst part of the storyž, the figures show as function of CLand kite aspect ratio AR the effect
on effective L/D from aspect ratio effects only (Fig. 1), as-pect ratio + viscous drag (Fig. 2), asas-pect ratio + viscous drag + line drag penalty (Fig. 3). The power production capability (Loyd expression) based on aspect ratio + vis-cous drag + line drag penalty is shown in Fig. 4. It is seen that for the given kite area (20 m2), wind speed (12 m/s)
and tether length (500 m) the favored lift coefficient and aspect ratio is as high as possible if a maximization of the power is sought.
The main outcome of the present work is to give a quan-titative understanding of the relative importance of mod-elling different key elements in crosswind kite wind en-ergy systems.References:
[1] Loyd, M. L.: Crosswind Kite Power. Journal of Energy 4(3), 106-111 (1980)
Fig. 1: Aerodynamic lift-to-drag ratio L/D from aspect ratio contribution only.
Fig. 2: L/D from aspect ratio and
viscos-ity contributions = L/D for kite alone. Fig. 3: Circles represent the CL that max-imize (L/D)eff for a given AR.
Fig. 4: Power produced when pulling with a reel out vel. that is 1/3 of the wind vel. Circles represent CL values that maximize power for a given A.
