Virtual Spring–Damping System for Flow Induced Motion Experiments

Abstract

Flowinduced motion (FIM) experiments of a single circular cylinder or multiple cylinders in an array involve several configuration and hydrodynamic parameters, such as diameter, mass, damping, stiffness, spacing, Reynolds number, and flow regime, and deviation from circular cross section. Due to the importance of the FIM both in suppression for structural robustness and in enhancement for hydrokinetic energy conversion, systematic experiments are being conducted since the early 1960s and several more decades of experimentation are required. Change of springs and dampers is time consuming and requires frequent recalibration. Emulating springs and dampers with a controller makes parameter change efficient and accurate. There are two approaches to this problem: The first involves the hydrodynamic force in the closedloop and is easier to implement. The second called virtual damping and spring (Vck) does not involve the hydrodynamic force in the closedloop but requires an elaborate system identification (SI) process. Vck was developed in the Marine Renewable Energy Laboratory (MRELab) of the University of Michigan for the first time in 2009 and resulted in extensive data generation. In this paper, the second generation of Vck is developed and validated by comparison of the FIM experiments between a Vck emulated oscillator and an oscillator with physical springs and dampers. The main findings are: (a) the Vck system developed keeps the hydrodynamic force out of the controlloop and, thus, does not bias the FIM, (b) The controllerinduced lag is minimal and significantly reduced compared to the first generation of Vck built in the MRELab due to use of an Arduino embedded board to control a servomotor instead of Labview, (c) The SI process revealed a static, thirdorder, nonlinear viscous model but no need for dynamic terms with memory, and (d) The agreement between real and virtual springs and dampers is excellent in FIM including vortexinduced vibrations (VIVs) and galloping measurements over the entire range of spring constants and velocities tested (16,000 < Re < 140,000).