Maximilian Ranneberg Mathematician viiflow Jessnerstr. 33 10247 Berlin Germany m.ranneberg@viiflow.com www.viiflow.com
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Fast Aero-Elastic Analysis for Airborne Wind Energy Wings
using Viscous-Inviscid Interaction
Maximilian Ranneberg viiflow Lightweight or semi-rigid wings as well as textile kites commonly used in Airborne Wind Energy applications have strong aero-elastic deformations during flight. These effects have been investigated in a number of works. Due to the computational complexity of compu-tational fluid dynamics, fast methods rely on simple in-viscid methods or pcomputed assumed functional re-lations for the aerodynamic pressure distribution. These approaches lack the ability to accurately model changes in drag, change in lift slope and separation. Ongoing re-search into methods that use Navier-Stokes equations improve these predictions, but are not be feasible for fast design iterations and even less feasible for dynamic sim-ulation besides singular validation runs.
Viscous-inviscid interaction methods allow for fast aero-elastic simulations that are similar to inviscid methods in complexity and runtime, but can predict drag and ef-fects of separation. Viiflow is such a method and dif-fers from other viscid-inviscid interaction methods in its unique coupling solver that enables parabolic boundary layer marching together with a fast and reliable global newton method. This method is presented as well as a structural model and the coupling mechanism, which fa-cilitates viiflow to combine the aerodynamic and struc-tural model into a single newton method.
The elastic deformations are modeled using the same mechanics that are used to model the viscous displace-ment thickness as well as some geometry peculiarities. This allows to keep the inviscid panel operators constant ś and the solver runtime short.
0 0.2 0.4 0.6 0.8 1 x/c -1 -0.5 0 0.5 1 1.5 2 2.5 3 -C p Panel Airfoil Virtual Airfoil w/o Deformation Virt. Airfoil + Boundary Layer Stagnation Point
Transition Points Virtual Airfoil w/ Deformation Virt. Airfoil + Boundary Layer Pressure Coefficient w/ Deformation
Leading-Edge inflatable kite case provided by the FSI group at TU Delft. The thick leading edge and thin canopy are modelled using virtual displacements (blue and red lines) from the actual panel ge-ometry (grey line). The boundary layer adds thickness to this virtual airfoil (dashed lines). Here, the canopy is assumed to be a simple beam fixed to the leading edge with a free end, which under load deforms from its original shape (red) to its final shape (blue).
