Vortex-induced vibrations of a confined circular cylinder for efficient flow power extraction

The effects of confinement on vortex-induced vibration (VIV) of a circular cylinder (diameter D) and its flow power extraction capability are presented. A two-dimensional numerical study is performed on VIV of a circular cylinder inside a parallel plate channel of height H at Reynolds numbers 100 and 150. The blockage ratio (b = D/H) is varied from 1/4 to 1/2. The cylinder is elastically mounted with a spring such that it can only vibrate transversely to the flow. It has a fixed non-dimensional mass (m*) of 10. The energy extraction process is modeled as a damper (damping ratio ζ) attached to the cylinder. With increasing blockage, the vibration amplitude of the cylinder decreases, the lock-in happens at a larger non-dimensional natural frequency of the cylinder, and the initial branch of the vibration response of the cylinder shrinks. There is a minimum value of the channel height and Reynolds number for the existence of the initial branch. The extracted power is found to increase rapidly with the blockage. For the maximum blockage (b = 1/2), the flow power extracted by the cylinder is an order of magnitude larger as compared to what it would extract in an open domain with free stream velocity equal to the channel mean velocity. The optimal mass-damping (α = m*ζ) for extracting the maximum power is found to lie between 0.2 and 0.3. An expression is derived to predict the maximum extracted power from the undamped response of a confined/unconfined cylinder.