A Numerical Model to Predict the Nonlinear Response of External Flow Over Vibrating Bodies (Planar Flow)

A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a portion of which is subjected to time varying harmonic motion. The model is tested by comparison to previous numerical simulations for flow over a square cavity, oscillatory flow through a wavy channel and boundary layer flow along a flat plate. The model is applied to predict the flow over a flat plate with a section forced in simple sinusoidal motion. The dimensionless vibration amplitude, H₀, and the Reynolds number, Re are maintained at 0.1 and 1000, respectively. The Strouhal number, St, defined as the ratio of the flow advective time scale to the plate oscillation period, is varied in the range 0.0 ≦ St ≦ 1.0. The friction and pressure coefficients over the vibrating portion of the body are analyzed using Fast Fourier Transform techniques. For low frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady state results for flow over a fixed sinusoidal bump. A small amplitude pressure wave generated by the oscillating plate propagates downstream with the flow. For high frequency vibrations (high Strouhal number) the pressure and friction coefficients over the vibrating portion of the body deviate from the steady state results and a high amplitude pressure wave propagates downstream. The pressure at one chord length upstream is also affected. As St increases the flow becomes highly nonlinear and harmonics appear in the downstream velocity and pressure fields. The nonlinearity is controlled by the convective acceleration term near the vibrating plate surface.