Nonlinear Response of Planar Laminar Flow Over a Flat Plate Vibrating in Different Modes

Abstract

A computer model developed by Venkat and Spaulding (1991a) for unsteady flows over vibrating bodies is used to investigate the nonlinear characteristics of external flow over a flat plate, a section of which is subjected to time varying motion of various mode shapes (n). The Reynolds number, Re is fixed at 1000. For the first case, the Strouhal number, St and the vibration amplitude ratio, H0 are fixed at 0.25 and 0.025, respectively while for the second case, St and H0 are increased to 1.0 and 0.1, respectively. Simulations are performed for modes varying in the range 1<n<4. For n=1, upstream and downstream pressure wave propagation is very high compared to higher modes. The transfer of energy from the input frequency to the first harmonic is pronounced for higher modes. A source-sink pair exists over the vibrating section for even modes. For high St and H0 the pressure spectral amplitude of higher harmonics far downstream is quite large for n=4 compared to n=2 thus indicating more nonlinear interaction between the vibrating body and the external flow for large even modes. The pressure coefficient on either side of the vibrating section is controlled by the gradient of vorticity for odd modes and by the convective acceleration terms for even modes.