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.
Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream
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Hurlbut, S. E., Spaulding, M. L., and White, F. M. (June 1, 1982). "Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream." ASME. J. Fluids Eng. June 1982; 104(2): 214–220. https://doi.org/10.1115/1.3241810
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