Relation at the Fluid-Structure Interface and Residuary Force in Flow Induced Oscillations with Experimental Validation (VIV & Galloping)

Fluid-Structure Interaction (FSI) is a frequently occurring physical phenomenon in many applications and across various engineering disciplines including structural, offshore, aerospace, civil, mechanical and biomedical engineering. Suspension bridges, smoke-stacks, wind turbines, mooring lines, pipelines, heat exchangers, marine risers, and offshore platforms, are examples. The problem for Flow Induced Oscillation (FIO) is studied using experimental data and a novel analytical method revealing an eigen-relation at the fluid-structure interface. That is a relation between excitation and a dynamical system that has to be satisfied for a non-trivial solution to exist. Consistent rather than heuristic nondimensionalization of the fluid and oscillator dynamics in fluid-structure interaction, leads to decoupling of amplitude from frequency response. Further, recognizing that the number of governing dimensionless parameters should decrease, rather than increase, due to the fluid-structure synergy at the interface, an eigen-relation is revealed for a cylinder in Flow Induced Oscillations (FIO). It shows that, for a given dimensionless oscillation frequency f*, the ratio of real added-mass to oscillating-mass is fully defined. The primary assumption of this approach is that for the eigen-relation to hold, the FIO has to be monochromatic. This is a common assumption in VIV and galloping. For very low natural frequencies of the oscillator in vacuum this assumption does not hold. Amplitude decoupling and the eigen-relation, lead to explicit expressions for coefficients, phases, and magnitudes of the total hydrodynamic force, the force in phase with the acceleration of the oscillator (added-mass), and the force in phase with the velocity of the oscillator. Those reveal their dependence on the generic Strouhal number, damping, and Reynolds. Heuristic dimensionless parameters, used in VIV data presentation are not needed. Theoretical derivations and force reconstruction match nearly perfectly with extensive experimental data collected over a decade in the Marine Renewable Energy Laboratory (MRELab) at the University of Michigan using four different oscillator test-models. Further, based on the above derivations the following analyses are presented: (a) Single-cylinder experimental data in FIO are analyzed using the eigen-relation and derived force expressions. The ranges of parameters are: mass ratio m* ∈ [1.007 to 2.0], spring stiffness k ∈ [400N/m to 1200N/m] and total system damping ratio ∈ [0.02 to 0.26] (b) Beyond the single frequency response model, the residuary force is derived by comparison to experiments. Using the theory, established facts regarding VIV and galloping and new important observations are readily explained: • The effects of Strouhal, damping-ratio, mass-ratio, Reynolds, reduced velocity, and stagnation pressure. • The cause of expansion/contraction of the VIV range of synchronization. • The corresponding slope-change in oscillation frequency with respect to the Strouhal frequency of a stationary-cylinder. • The critical mass-ratio implying perpetual VIV. • The significance of the natural frequency of the oscillator in vacuum. • The effect of vortices in VIV and galloping. • The magnitude of vortex forces divided into direct and indirect forces. (c) The derived eigen-relation is a first order solution to the VIV and galloping problems. The developed equations for the forces in-phase with the velocity and acceleration, when subtracted from the total force measured experimentally, yield a residuary force. (d) Data obtained from the MRELab experimentally and with CFD are analyzed further to identify other force components likely related to vortex shedding directly. This is a step towards higher order theories for VIV and galloping beyond the eigen-relation.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168107/1/ofuegbej_1.pd