Circulation and Rear Stagnation Point Dynamics in Airfoils with Rounded Trailing Edges

The Kutta condition does not apply when the airfoil trailing edge is rounded, leaving circulation and the location of the rear stagnation point undefined by conventional aerodynamic theory. We study unsteady, impulsively started flow past a family of airfoils with a constant leading-edge radius and varying trailing edge radii, at fixed pre-stall angles of attack. Euler, DNS (Re = 10k–50k), and LES (Re = 1M–6M) simulations are used to analyze how the rear stagnation point and airfoil circulation vary with Reynolds number. We assess whether the high-Re flow approaches the inviscid Euler limit, and whether the Euler solution agrees with the analytical result derived from Hertz's principle of least curvature. We examine how the ratio of leading to trailing edge radii influences suction and stagnation point behavior at both edges. Results show that rounded trailing edges shift the rear stagnation point, reduce adverse pressure gradients, and delay stall onset—though at the cost of reduced circulation and lift. These findings offer new insights for circulation and separation control on airfoils, with applications in reverse flow conditions on rotorcraft and other unsteady aerodynamic flows.