Flow characteristics in the wake of a circular cylinder and those of the flow past an oscillating circular cylinder are computed numerically using Direct Numerical Simulation(DNS) with a higher-order finite-difference scheme. The higher-order finite difference scheme is employed for the spatial distributions along with the second order Adams-Bashforth and the first order Backward-Euler time integration. In x-y plane, the convection term is applied by the fifth or the seventh order upwind scheme, and the pressure and viscosity terms are applied by the fourth order central difference. In spanwise, Navier-Stokes equation is applied using Spectral Method with a period boundary condition. The grid system makes use of the regular grid system and the lattice is generated by an elliptic equation.
Laminar two-dimensional, time-dependent flow past a circular cylinder is numerically investigated using DNS for the low Reynolds number (Re=45~280). And two-dimensional flow past a circular cylinder is also numerically investigated for the comparative high Reynolds number (Re=2000). The calculated results of drag coefficients, lift coefficients, pressure distributions, vorticity contours and other informations are compared with experimental and numerical ones. These results obtained by the present DNS show good agreement with the previous studies.
Three-dimensional time-dependent flow past a circular cylinder is examined using direct numerical simulation for Reynolds number 220, 250, 280 and 300. The secondary instability leads to three-dimensionality with a spanwise wavelength about 4 cylinder diameters at onset (A-mode). At Reynolds number 259, the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength about 1.0 diameters at onset (B-mode). Results of three-dimensional effect in the wake of a circular cylinder are represented with spanwise and streamwise vorticity contours in terms of Reynolds numbers.
The flow past a circular cylinder forced to vibrate transversely is numerically simulated by solving the two-dimensional Navier-Stokes equation modified by the vibration velocity of a circular cylinder at a Reynolds number, 164. The calculated cylinder vibration frequency is between 0.60 and 1.30 times of the natural vortex-shedding frequency. The calculated oscillation amplitude extends to 25% of the cylinder diameter and in the case of the lock-in region, it reaches to 60%. It is made clear that the cylinder oscillation gives influence on the wake pattern, the time histories of the drag and lift forces, power spectral density and phase diagrams and so on. It is found that these results include both the periodic (lock-in) and the quasi-periodic (non-lock-in) state. The vortex shedding frequency equals the driving frequency in the lock-in region but it is independent in the non-lock-in region. The mean drag and the maximum lift coefficient increase with the increase of the forcing amplitude in the lock-in state. The lock-in boundaries are also established from the present direct numerical simulation.