Vortex-induced Vibrations of a Confined Circular Cylinder for Efficient Flow Power Extraction

A simple method to increase the flow power extraction efficiency of a circular cylinder, undergoing vortex-induced vibration (VIV), by confining it between two parallel plates is proposed. A two-dimensional numerical study was performed on VIV of a circular cylinder inside a parallel plate channel of height H at Reynolds number 150 to quantify the improvement. The cylinder is elastically mounted with a spring such that it is only free to vibrate in the direction transverse to the channel flow and has a fixed mass ratio (m*) of 10. The energy extraction process is modelled as a damper, with spatially constant damping ration ((), attached to the cylinder. The simulations are performed by varying the reduced velocity for a set of fixed mass-damping ({\alpha} = m*() values ranging between 0 to 1. The blockage ratio (b = D/H) is varied from 0.25 to 0.5 by changing the channel height. The quasi-periodic initial branch found for the unconfined cylinder shrinks with the increasing blockage. The extracted power is found to increase rapidly with the blockage. For maximum blockage (b = 0.2), the maximum 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 ({\alpha}c ) for extracting maximum power is found to lie between 0.2 to 0.3. An expression is derived to predict the maximum extracted power from the undamped response of a confined/unconfined cylinder. With the assumption {\alpha}c = 0.25, the derived expression can predict the maximum power extraction within +-20% of the actual values obtained from present and previous numerical and experimental studies.