SNS COLLEGE OF TECHNOLOGY (An Autonomous Institution) COIMBATORE–35 DEPARTMENT OF AERONAUTICAL ENGINEERING BOUND VORTEX AND HORSESHOE VORTEX 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 1 Bound Vortex a vortex that is considered to be tightly associated with the body around which a liquid or gas flows, and equivalent with respect to the magnitude of speed circulation to the real vorticity that forms in the boundary layer owing to viscosity. In calculations of the lift of a wing of infinite span, the wing can be replaced by a bound vortex that has a rectilinear axis and generates in the surrounding medium the same circulation as that generated by the real wing. In the case of a wing of finite span, the bound vortex continues into the surrounding medium in the form of free vortices. Knowledge of the vortex system of a wing permits calculation of the aerodynamic forces acting upon the wing. In particular, the interaction between bound and free vortices gives rise to the induced drag of the wing. The idea of the bound vortex was made use of by N. E. Zhukovskii in the theory of the wing and the screw propeller. 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 2 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 3 WHAT IS HORSE SHOE VORTEX? The horseshoe vortex model is a simplified representation of the vortex system of a wing. In this model the wing vorticity is modelled by a bound vortex of constant circulation, travelling with the wing, and two trailing wingtip vortices, therefore having a shape vaguely reminiscent of a horseshoe 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 4 STARTING VORTEX • A starting vortex is shed as the wing begins to move through the fluid, which dissipates under the action of viscosity, as do the trailing vortices far behind the aircraft 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 5 WING TIP VORTEX •The trailing wingtip vortices are responsible for the component of the downwash which creates induced drag 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 6 HORSE SHOE VORTEX MODEL • The horseshoe vortex model is unrealistic in that it implies uniform circulation (and hence, according to the Kutta–Joukowski theorem, uniform lift) at all sections on the wingspan. 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 7 HORSE SHOE VORTEX MODEL Aviation Lighting 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 8 HORSE SHOE VORTEX MODEL PREPARED BY MS.X.BERNADETTE EVANGELINE 02-04-2020 9 AP/AERO HORSE SHOE VORTEX MODEL 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 10 HORSE SHOE VORTEX-REALISTIC MODEL • In a more realistic model, the lifting-line theory, the vortex strength varies along the wingspan, and the loss in vortex strength is shed as a vortex sheet all along the trailing edge, rather than as a single trail at the wing-tips. Nevertheless, the simpler horseshoe vortex model used with a reduced effective wingspan but same mid-plane circulation provides an adequate model for the flows induced far from the aircraft PREPARED BY MS.X.BERNADETTE EVANGELINE 02-04-2020 11 AP/AERO HS-VORTEX FLOW VISUALISATION PREPARED BY MS.X.BERNADETTE EVANGELINE 02-04-2020 12 AP/AERO .