A numerical method for flexible airfoils in incompressible inviscid flow

Summary The paper deals with the aerodynamic analysis of flexible airfoils, based on a quasi-lattice vortex method (QVLM). The analysis is formulated in matrix form and leads, as in other similar studies, to a linear algebraic system when the angle of attack is nonzero, and to an eigenvalue problem when the incidence angle is zero. The aerodynamic characteristic curvesC _L -,C _m - are presented. Finally, the airfoil shapes for several values of the tension coefficient and angles of attack are drawn. The results obtained with the present method are in good agreement with those reported in previous studies and evidentiate the flexibility of the QVLM as applied to flexible airfoils.Notation A aerodynamic matrix, defined in QVL method, (8) - B matrix, see Eq. (18) - c chord of airfoil - C matrix defined asAB - C _L lift coefficient, 2L/V ² c) - C _p moment coefficient, 2M/(V ² c ²) - C _p pressure coefficient,C _p =2p/(V ² ) - C _T tension coefficient, 2T/(V ² c) - D matrix, see Eq. (11) - I unit matrix - l curvilinear length of the flexible airfoil - N number of collocation points on the airfoil shape - q dynamic pressure, V ² /2 - T tension force in the sail - V freestream velocity - w downwash - x nondimensional coordinate,x/c - X _i control points, Eq. (9) - X _max dimensionless position of the maximum camber - Y _k source points, Eq. (9) - z coordinate normal tox axis - Z nondimensional coordinate,z/c - Z _s camber equation in dimensionless form,z _s /c - incidence with respect to the upstream flow velocity - column vector of the local curvatures {₁, ₂,..., _N } ^T - nondimensional membrane excess ratio - eigenvalue of the problem (23) - _k zeroes of the Chebyshev polynomia of the first kind, 1kN - column vector of the local slopes, {₀, ₁, ₂,..., _N } ^T - column vector, {₁, ₂,..., _N } ^T - ₀ slope at airfoil leading edge