Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream

TLDR: In this paper, a finite difference model is presented for viscous two-dimensional flow of a uniform stream past an oscillating cylinder, where a noninertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder.

Abstract: A finite difference model is presented for viscous two dimensional flow of a uniform stream past an oscillating cylinder. A noninertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Three types of cylinder motion are considered: oscillation in a still fluid, oscillation parallel to a moving stream, and oscillation transverse to a moving stream. Computations are made for Reynolds numbers between 1 and 100 and amplitude-to-diameter ratios from 0.1 to 2.0. The computed results correctly predict the lock-in or wake-capture phenomenon which occurs when cylinder oscillation is near the natural vortex shedding frequency. Drag, lift, and inertia effects are extracted from the numerical results. Detailed computations at a Reynolds number of 80 are shown to be in quantitative agreement with available experimental data for oscillating cylinders.