Numerical Simulation of Unsteady Laminar Flow Over Vibrating Bodies (Planar Flow)
Date of Original Version
A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a part of which is subjected to simple harmonic motion. The vibration amplitude ratio, H0, and the Reynolds number, Re, are maintained at 0.1 and 1000, respectively. The Strouhal number, St, is varied in the range 0.0 ≤ St ≤ 1.0. The computer code is tested for the flow in a square cavity and also over a flat plate. The friction and pressure coefficients over the vibrating portion of the body are determined. Fast Fourier Transforms are performed on the time series data of these coefficients. For low-frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady-state results for flow over a 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 higher harmonics appear in the downstream flow. Subsequent analysis indicates that the nonlinearity is controlled by the term v(∂u/∂y).
Journal of Ship Research
Venkat, N. K., and Malcolm Spaulding. "Numerical Simulation of Unsteady Laminar Flow Over Vibrating Bodies (Planar Flow)." Journal of Ship Research 35, 3 (1991): 230-249. doi:10.5957/jsr.19126.96.36.199.