Prediction of transonic flutter for a supercritical wing by modifiedstrip analysis

Abstract

The experiments of Farmer, Hanson, and Wynne showed that use of a supercritical airfoil can adversely affect wing flutter speeds in the transonic range. Inasmuch as adequate theories for three-dimensional unsteady transonic flow are not yet available, the modified strip analysis published by Yates in 1958 has been used to predict the transonic flutter boundary for the supercritical wing tested by Farmer, Hanson, and Wynne. The steady-state spanwise distributions of the section lift-curve slope and aerodynamic center, required as input for the flutter calculations, were obtained from pressure distributions measured by Harris. The calculated flutter boundary is in excellent agreement with experiment in the subsonic range. In the transonic range, a ''transonic bucket" is calculated which closely resembles the experimental one with regard to both shape and depth; however, it occurs at about 0.04 Mach number lower than that found experimentally. Nomenclaturea Ctn = nondimensional distance from midchord to section aerodynamic center measured perpendicular to elastic axis, positive rearward, fraction of semichord b b r -semichord of wing measured perpendicular to elastic axis at spanwise reference station 77 = 0.75 (b r = 0.14948m) C, = section lift-curve slope for a section perpendicular to elastic axis C p = pressure coefficient H =translational displacement of wing at elastic axis, positive downward, fraction of reference semichord b r k nr -reduced frequency based on spanwise reference station (77 = 0.75) and on velocity component normal to elastic axis, b r ul VcosA. ea M = freestream Mach number m r =mass of wing per unit span at spanwise reference station (r? = 0.75) (m r = 2.57 kg/m) q -freestream dynamic pressure V -freestream speed X =streamwise distance from local leading edge, fraction of local chord Y = spanwise station, fraction of semispan a. =angle of attack r] = nondimensional coordinate measured from wing root along elastic axis, fraction of elastic axis length 6 =torsional displacement of wing about elastic axis, positive leading edge up A efl = sweep angle of elastic axis (A ea = 40.03 deg) \i r =mass ratio based on spanwise reference station -freestream density = circular frequency of vibration