A method of calculation of flow around bearing surface undergoing arbitrary deformations (Q2754757)

In the suggested technique of calculation of aerodynamic characteristics of a thin airfoil its middle surface at each time instant is approximated by a double cubic spline. Spline passes through nodal points of the surface. Mathematically, the problem is reduced to a singular integro-differential equation for a function related to the circulation of velocity on the airfoil surface. In this method, all aerodynamic characteristics are obtained as functions of coordinates of nodal points. The problem is reduced to determination of position of extremum of a continuous scalar function of coordinates of nodal points. Thus optimal geometric characteristics of the airfoil can be determined. A numerical example is considered.