Method of Calculating Flow around Extremely Thin Airfoil with Slotted Leading-edge Slat and Flap

A mathematical model is proposed for the potentional flow around a combination of a thin plate with a leading-edge slotted slat and a flap. The solution of the problem is carried out by a numerical-analytical method proposed earlier by the author. A feature of the method is a combination of the theory of functions of a complex variable (TFCV) and the discrete vortex method (DVM). The idea of the numerical-analytical method is to use a conformal mapping for a thin airfoil and DVM to simulate the flow around slat and flap, which allows us to represent the analytical function of the complex potential as a finite series, the number of members of which is equal to the number of discrete vortices. The statement of the problem is formulated as the Neumann boundary problem. Fulfillment of impermeability conditions at control points only on the surfaces of the slat and flap ultimately leads to solving a system of linear algebraic equations for the unknown circulations of discrete vortices located on the boundary elements of the surfaces of the slat and flap. A good agreement is demonstrated between the calculated results of the proposed method and the Sedov's analytical solution for two plates arranged in the tandem scheme. A good agreement between the changes in the derivative of the lift coefficient for the flap deflection angle depending on the relative flap cord also is demonstrated.