# Multiple-Wake Vortex Method for Leading Edge Inflatable Tube Kites used in Airborne Wind Energy Systems

Roland Schmehl, Manoj Mandru, Rachel Leuthold, Carlos Ferreira

Research output: Contribution to conferenceAbstractScientific

## Abstract

In this study we propose a robust vortex model for timedependent vortex shedding at separation locations and trailing edge. The model, which is able to capture flow separation and reattachment phenomena, aims at improving a previously developed a multiple-wake vortex lattice model [1], which could not describe flow reattachment phenomena on suction and pressure surfaces. Starting frompotential theory the two-dimensional Leading Edge Inflatable (LEI) kite airfoil is discretized by several straight panels with point vortices at quarter chord point of each panel. A constant-strength vortex panel is shed at each separation location and is convected in the next time step as vortex blob without change in its strength for further time steps. The circulation is defined as a closed line integral of the tangential velocity component around the fluid element. &#x100000; ≡ ∮C V · ds Considering a closed line integral around the separation panel, as described in Katz [2], applying the above equation, we get d&#x100000;S dt = D Dt ∮ Vds = d dt (Vids − Vi+1ds) ∼= 1 2 (Vi 2 − Vi+1 2), and &#x100000;Ss, &#x100000;Sp are separated wake strengths defined using above formulation on suction and pressure sides respectively. U∞ 2D LEI kite airfoil discretized into straight panels with vorticity placed at quarter chord point. Together, the Np bound vortex strengths &#x100000;Sp, as well as &#x100000;Ss and &#x100000;W, give Np + 3 unknowns. The boundary conditions are no flow penetration through the surface (applied at three-quarter chord point on each panel) and the vorticity shed during the time step at separation locations, along with Kelvin-Helmholtz theorem, form Np + 3 boundary conditions. Circulations obtained from iterative solution scheme are post processed using timedependent Bernoulli’s equation for momentary pressure distribution.
Original language English 27-28 2 https://doi.org/10.4233/uuid:4c361ef1-d2d2-4d14-9868-16541f60edc7 Published - 2017 7th international Airborne Wind Energy Conference (AWEC 2017) - Freiburg, GermanyDuration: 5 Oct 2017 → 6 Oct 2017Conference number: 7https://www.awec2017.com

### Conference

Conference 7th international Airborne Wind Energy Conference (AWEC 2017) AWEC 2017 Germany Freiburg 5/10/17 → 6/10/17 https://www.awec2017.com

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