AEROELASTIC STABILITY AND TIME RESPONSE ANALYSIS OF CONVENTIONAL AND SUPERCRITICAL AIRFOILS IN TRANSONIC FLOW BY TIME INTEGRATION METHOD
Computer based numerical procedures have been developed for aero-elastic stability (flutter) and response analysis of conventional and supercritical airfoils in transonic flow by time integration method. Airfoils are assumed to be oscillating in two dimensional, small disturbance and inviscid flows with low frequencies. Aerodynamic computations are carried out by finite difference methods with the use of transonic computer code LTRAN2. Both indicial and time integration methods are employed for obtaining unsteady coefficients. Aeroelastic equations of motion for the flutter and response analysis are formulated by using the strip theory. Equations are derived for two degrees of freedom system of airfoil, plunging and pitching. Four aeroelastic parameters considered are: airfoil-air mass ratio; plunge to pitch frequency ratio; position of mass center; and position of elastic axis. The flutter solution is obtained by U-g method by solving an eigen value equation. Time response solution is obtained by simultaneously integrating aerodynamic and structural equations of motion by time marching direct integration method. Flutter results are presented in the form of plots of flutter speed and corresponding reduced frequency versus aeroelastic parameters and Mach number. Response results are presented in the form of plots of aerodynamic force and the corresponding structural displacement versus time for various values of airfoil-air mass ratios. For a NACA 64A006 conventional airfoil, pitching and plunging aerodynamic and flutter results are obtained at zero angle of attack for various Mach numbers ranging from 0.7 to 0.87. Effects of four aeroelastic parameters on flutter speeds are studied. Effect of Mach number on flutter speed is also studied. Thus the 'transonic dip' phenomenon is investigated. For a MBB A-3 supercritical airfoil, pitching and plunging, aerodynamic and flutter results are obtained at design conditions. Effects of aeroelastic parameters on flutter speed are studied. At design conditions, effects of camber and supercritical thickness distribution on flutter speed are also studied. At zero angle of attack, the effect of Mach number on flutter speed is studied for various values of aeroelastic parameters. Thus, the 'transonic dip' phenomenon is investigated. At design Mach number 0.765, effect of angle of attack on flutter speed is also studied. For a CAST-7 supercritical airfoil, pitching and plunging, aerodynamic and flutter results are obtained at zero angle of attack for various Mach numbers ranging from 0.6 to 0.72. Effect of Mach number on flutter speed for various values of four aeroelastic parameters are studied. Thus the 'transonic dip' phenomenon is investigated. In response analysis, force and displacement time responses are obtained for both single- and two-degree of freedom systems. At subsonic Mach number 0.7, the response results obtained by LTRAN2 are compared with those obtained by subsonic method based on quasi-steady state theory. The comparison is good. At M = 0.88, the present results obtained for a single pitching degree of freedom NACA 64A006 airfoil compare well with the corresponding results available in literature. For the NACA 64A006 airfoil, pitching and plunging at M = 0.85, converging, diverging and neutrally stable response results are obtained by varying the airfoil-air mass density ratio. These response results are compared with those obtained by U-g method based on time integration, indicial and harmonic methods. The effect of airfoil-air mass ratio on response results are studied.
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