Question

During the formation of starting vortex, for an airfoil starting from rest, which is the correct sequence of events? (TE: Trailing Edge)

(a) Velocity becomes infinite at the TE > Unstable vortex sheet formed due to very high vorticity > High velocity gradient formed at TE which is pushed downstream > Flow starts to curl at the TE > Unstable vortex sheet curls to form point vortex

(b) Velocity becomes infinite at the TE > High velocity gradient formed at TE which is pushed downstream > Unstable vortex sheet formed due to very high vorticity > Flow starts to curl at the TE > Unstable vortex sheet curls to form point vortex

(c) Velocity becomes infinite at the TE > Flow starts to curl at the TE > Unstable vortex sheet formed due to very high vorticity > Unstable vortex sheet curls to form point vortex > High velocity gradient formed at TE which is pushed downstream >

(d) Flow starts to curl at the TE > Velocity becomes infinite at the TE > High velocity gradient formed at TE which is pushed downstream > Unstable vortex sheet formed due to very high vorticity > Unstable vortex sheet curls to form point vortex

I have been asked this question by my school teacher while I was bunking the class.

My question is based upon Kelvin’s Circulation Theorem and the Starting Vortex in section Incompressible Flow over Airfoils of Aerodynamics

Answer 1

Right answer is (d) Flow starts to curl at the TE > Velocity becomes infinite at the TE > High velocity gradient formed at TE which is pushed downstream > Unstable vortex sheet formed due to very high vorticity > Unstable vortex sheet curls to form point vortex

To explain: As the motion starts, the Kutta theorem starts enforcing itself due to which flow starts curling at the trailing edge and the high velocity gradient formed is pushed downwards so that the flow leaves the trailing edge smoothly. Then as the vortex sheet formed due to high velocity and consequently high vorticity is unstable, it curls itself to form what is called the starting vortex.