A harmonic analysis method for unsteady transonic flow and its application to the flutter of airfoils

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. A study is presented of the shock motion associated with an oscillating airfoil and its representation by the harmonic procedure. The effects of the shock motion and the resulting pressure pulse are shown to be included in the harmonic pressure distributions and the corresponding generalized forces. Analytical and experimental pressure distributions for the NACA 64A010 airfoil are compared for Mach numbers of 0.75, 0.80 and 0.842. A typical section, two-degree-of-freedom flutter analysis of a NACA 64A010 airfoil is performed. The results show a sharp transonic bucket in one case and abrupt changes in instability modes.

[1]  N. Yu,et al.  Unsteady transonic flow computations , 1977 .

[2]  D. Rizzetta,et al.  Numerical Solution of Three-Dimensional Unsteady Transonic Flow over Swept Wings , 1982 .

[3]  K. Isogai,et al.  Transonic dip mechanism of flutter of a sweptback wing. II , 1981 .

[4]  E. B. Klunker,et al.  Contribution to methods for calculating the flow about thin lifting wings at transonic speeds: Analytic expressions for the far field , 1971 .

[5]  R. F. Warming,et al.  Numerical calculations of two dimensional, unsteady transonic flows with circulation , 1974 .

[6]  E. L. Yip,et al.  FORTRAN subroutines for out-of-core solutions of large complex linear systems , 1979 .

[7]  W. Weatherill,et al.  The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings , 1978 .

[8]  J. Cole,et al.  Calculation of plane steady transonic flows , 1970 .

[9]  A. Majda,et al.  Radiation boundary conditions for acoustic and elastic wave calculations , 1979 .

[10]  W. Weatherill,et al.  On the computation of the transonic perturbation flow field around two- and three-dimensional oscillating wings , 1976 .

[11]  Koji Isogai,et al.  Numerical Study of Transonic Flutter of A Two-dimensional Airfoil , 1980 .

[12]  S. S. Stahara.  Operational manual for two-dimensional transonic code TSFOIL , 1978 .

[13]  E. M. Murman,et al.  Computation of Transonic Flows past Lifting Airfogs and Slender Bodies , 1972 .

[14]  T Y Yang,et al.  Flutter analysis of a two-degree-of-freedom MBB A-3 supercritical airfoil in two-dimensional transonic flow , 1980 .

[15]  Effect of Frequency in Unsteady Transonic Flow , 1979 .

[16]  M. H. Williams,et al.  Linearization of unsteady transonic flows containing shocks , 1979 .

[17]  T Y Yang,et al.  Flutter analysis of a NACA 64A006 airfoil in small disturbance transonic flow , 1980 .

[18]  W. H. Weatherill,et al.  Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings , 1980 .

[19]  W. S. Rowe,et al.  Prediction of unsteady aerodynamic loadings caused by trailing-edge control-surface motions in subsonic compressible flow , 1972 .

[20]  P. Goorjian,et al.  Implicit Finite-Difference Computations of Unsteady Transonic Flows about Airfoils , 1977 .

[21]  H. Tijdeman,et al.  Investigations of the transonic flow around oscillating airfoils , 1977 .

[22]  J. A. McGrew,et al.  Supercritical Wing Flutter , 1978 .

[23]  H. Yoshihara,et al.  Calculations of transonic flow over an oscillating airfoil , 1975 .

[24]  D. Kwak,et al.  Nonreflecting far-field boundary conditions for unsteady transonic flow computation , 1980 .

[25]  Holt Ashley,et al.  Role of Shocks in the "Sub-Transonic" Flutter Phenomenon , 1980 .

[26]  R. Traci,et al.  A perturbation method for transonic flows about oscillating airfoils , 1975 .

[27]  Bayesian Rcvr,et al.  I I I I I I I I I , 1972 .

[28]  R. M. Traci,et al.  Small Disturbance Transonic Flows About Oscillating Airfoils and Planar Wings. , 1975 .

[29]  H. Ashley,et al.  On the role of shocks in the 'sub-transonic' flutter phenomenon , 1979 .

[30]  F. E. Ehlers,et al.  A finite difference method for the solution of the transonic flow around harmonically oscillating wings , 1974 .

[31]  G. N. Malcolm,et al.  Experimental unsteady aerodynamics of conventional and supercritical airfoils. [conducted in the Ames 11 foot transonic wind tunnel] , 1980 .

[32]  D. Rizzetta,et al.  Computations of the pitching oscillation of a NACA 64A-010 airfoil in the small disturbance limit , 1980 .