A boundary integral formulation of the kinetic field in aerodynamics. Part II: Applications to unsteady 2-D flows.

The new boundary integral formulation for the velocity field in Aerodynamics, proposed in Part I, is investigated in detail in the 2D case. The formulation is purely kinematical and includes rotational flows and potential flows with or without circulation. A scalar boundary integral equation, derived from the appropriate version of the Poincare identity for exterior domains, is analyzed and a stability estimate for the (weak) solution is proved. A model for the generation of vorticity for unsteady flows past airfoils is derived from the Euler equations and its relation with the Kutta condition for steady flows is discussed. Numerical results are obtained using collocation and Galeerkin techniques for unsteady 2D flows of interest in Aerodynamics. Namely, flows past airfoils starting from rest, where the circulation and vorticity are determined from the wake model, and steady flows with circulation determined from the Kutta condition. The present approach compares favourably with classical formulations in terms of the velocity potential in the irrotational case.