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Airfoil starting vortex

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Uploaded on Mar 7, 2011

Well here it is, my newly developed unsteady potential flow code in action ;-D. The wake is modelled using linearly varying strength vortex panels that are shed from the trailing edge and advected with the local flow field (i.e. the wake sheet is force-free). The strength of the wake at each time step is set to satisfy Kelvin's circulation theorem - the circulation contained within a contour bounding the same fluid elements (i.e. here the aerofoil + its wake) is constant for all time in the absence of external rotational forces and viscosity.

This video shows the starting vortex, created when a wing is impulsively set into motion. It is left behind and eventually decays due to viscous dissipation (but not here because this is inviscid flow). The wake is responsible for a source of inviscid drag known as induced drag which is caused by the induced downwash of the wake tilting the resultant force vector rearwards a little. Notice also how the resultant force vector actually grows in time - lift is not instantaneously established but takes a while to reach its steady state value. In fact this time is longer for higher aspect ratio wings because of their more intense wake sheet.

In this and all future videos, the blue lines represent suction force (i.e. directed away from the surface) and the red lines represent overpressure force (i.e. directed towards the surface)

The apparent fragmentation of the wake sheet at the end of the video is caused by truncation error inducing an instability on the wake sheet (which, in an inviscid fluid, is unstable to infinitesimal perturbations anyway). I am using only a simple first order time marching scheme for now (backward differencing in time).

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