Limit Cycle Oscillation of a Typical Airfoil in Transonic Flow

Abstract

Using an inviscid flow computational-fluid-dynamic model and a harmonic balance flow solver, a parametric investigation of how structural-inertial parameters and freestream Mach number of a transonic flow affect the limitcycle oscillation characteristics of a typical two-degree-of-freedom transonic airfoil configuration is presented. The computational efficiency of the harmonic balance aerodynamic model allows a much more thorough exploration of the parameter range than has been possible previously. Nomenclature a = nondimensional location of airfoil elastic axis, a = e/b b, c = semichord and chord, respectively ¯ cl, ¯ cm = nondimensional coefficients of lift and moment about elastic axis for simple harmonic motion e = location of airfoil elastic axis, measured positive aft of airfoil midchord h, ¯ h = airfoil plunge degree of freedom and its nondimensional amplitude, respectively; ¯ h is identical to h/b Iα = second moment of inertia about elastic axis L = aerodynamic lift Kh, Kα = airfoil plunge stiffness and torsional stiffness about elastic axis, respectively M = freestream Mach number Me.a. = aerodynamic moment about elastic axis m = airfoil sectional mass rα = radius of gyration of airfoil about elastic axis, r 2 α is identical to Iα/mb 2