A Wake Model for Crosswind Kite Systems

Mojtaba Kheiri Assistant Professor Concordia University

Department of Mechanical, Industrial and Aerospace Engineering 1455 de Maisonneuve Blvd. W., EV-4.217 Montreal, Quebec H3G 1M8 Canada mkheiri@encs.concordia.ca mojtaba@newleaf.co explore.concordia.ca/mojtaba-kheiri

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A Wake Model for Crosswind Kite Systems

Mojtaba Kheiri1,2_{, Frédéric Bourgault}2_{, Samson Victor}1_{, Vahid Saberi Nasrabad}2 1_{Concordia University}

2_{New Leaf Management Ltd.}

A general perception is that the induction factor of a crosswind kite system is always negligible. For example, Loyd [1], in his seminal paper, neglects “the induced ef-fects of the kite slowing the wind.ž

In a recent study [2], Kheiri et al. showed that unless the ratio of the kite planform area Akto the swept area As(i.e.

the solidity factor σ = Ak/As) is very small (practically

vi-able only for small-scale systems), the induction factor for a crosswind kite may not be imperceptible. For example, for a 2MW system with σ = 0.005 flying a circular pattern straight downwind on a plane perpendicular to the wind flow, the induction factor is estimated to be 0.18. Therefore, one may expect presence of a low-speed, highly-turbulent wake flow behind a crosswind kite, sim-ilarly to the conventional wind turbines, which may influ-ence performance and power generation of neighbouring kites.

For a small-scale crosswind kite (e.g. 100 kW, σ = 0.003) in a simplified straight downwind configuration, the in-duction factor is calculated analytically as a ≃ 0.05. Our CFD simulations performed on a super-computer at Con-cordia University agree well with the predicted value. For this system, the wake flow profile at different axial dis-tances x from the rotor plane is shown in Figure 1. These results are obtained after the kite has completed 20 revo-lutions from its position at rest.

The present paper studies the wake flow downstream of a crosswind kite system. A theoretical wake model is de-veloped based on existing models for conventional wind turbines. Moreover, CFD simulations are made for

differ-ent scales of crosswind kite systems, which are used for both calibration and comparison purposes.

U/U_∞ r/ R 0.98 1 0 0.5 1 1.5 2 2.5 3 3.5 U/U_∞ 0.98 1 0 0.5 1 1.5 2 2.5 3 3.5 x=5R U/U_∞ 0.98 1 0 0.5 1 1.5 2 2.5 3 3.5 x=4R U/U_∞ 0.98 1 0 0.5 1 1.5 2 2.5 3 3.5 x=3R U/U_∞ 0.98 1 0 0.5 1 1.5 2 2.5 3 3.5 x=2R x=R

Wake flow velocity profiles for a 100 kW crosswind kite (σ = 0.003, a = 0.05) at different distances (i.e. x = R, 2R, .., 5R) downwind from the kite, wherer and R are, respectively, the radial distances of any point in the flow, and the centroid of the kite to the rotation axis.

References:

[1] Loyd, M. L.: Crosswind Kite Power. Journal of Energy 4(3), 106-111 (1980)

[2] Kheiri, M., Bourgault, F., Saberi Nasrabad, V.: Power Limit for Crosswind Kite Systems. In Proceedings of ISWTP 2017, Montreal, Canada, May 2017.