Influence of Vibration Amplitude on Laminar Flow Over a Plate Vibrating at Low Strouhal Number

Abstract

The spectral and hydrodynamic response of laminar flow over a flat plate with a vibrating section forced in sinusoidal motion with a dimensionless amplitude ratio, H0 (vibration amplitude divided by plate length) varying in the range 0.0 < H0 < 0.1 is analyzed using numerical simulations. The Reynolds number, Re, based on the length of the vibrating plate, is fixed at 1000. The flow is simulated for Strouhal number, St, = 0.25 (low frequency). The spectral characteristics are obtained by performing Fast Fourier Transform (FFT) on the pressure coefficient time series data. The hydrodynamic analysis is performed by plotting stream function contour plot in the vicinity of the vibrating section for one vibration cycle. The model predicted results show that the friction and pressure coefficients over the vibrating body vary with vibration amplitude. For low amplitude ratios, the interaction of the external flow with the vibrating section is linear and there is little up or downstream influence. For high H0 , there is considerable downstream influence of the disturbance. Nonlinear energy transfer, as evidenced by the existence of a significant first harmonic in the pressure wave, takes place between the vibrating plate and the flow field. Energy transfer to the higher harmonics is less significant.