Nonlinear state-space modelling of the kinematics of an oscillating cylinder in a fluid flow

What happens when a fluid flows around a bluff (i.e. a not-streamlined) body? This question has been addressed in various fields: by civil engineers designing tall towers, chimneys or bridges that should withstand the wind loads, by marine engineers that develop offshore oil rigs or underwater pipelines to withstand the ocean currents, and by mechanical engineers building heat exchangers. Sometimes heuristic models are employed to study such complicated problems in practice, but due to their simplified nature, these methods require large safety factors and thus over-dimensioned structures. Another option is the use of high-fidelity computational fluid dynamics (CFD) simulations. These simulations are very valuable and can offer a great deal of insight, but they require an enormous amount of computational power: a calculation time of several days or weeks is not exceptional for such coupled fluid-structure problems. Therefore, CFD simulations have been reserved for some very specific applications, and are typically not used in the design stages or for control purposes. In this dissertation, we develop a new method to tackle the question of interacting fluids and structures. This method should offer accurate yet fast solutions, so as to allow the active control of the fluid loads on the structures.

Fluid-structure interaction in general has been a hot research topic in both academia and industry for over a century. One specific instance of fluid-structure interaction is the so-called vortex-induced vibration of elastic structures in a fluid flow. It is well known that over a wide range of flow conditions, alternating vortex shedding occurs in the wake of bluff bodies. These vortices cause fluctuating forces on the body and can so induce vibrations. These vibrations are generally undesirable; in some cases high amplitudes result which may harm or even destroy the structure. To guarantee robustness against the occurring fluid forces, accurate predictions are vital during the design phase of a structure. An analytical solution however remains unfound. Since CFD requires a lot of computing power and experiments a dedicated lab, these approaches are unfit for those applications where only limited time and resources are available.

System identification offers the possibility to build (reduced-order) mathematical models based on input-output data. Until recently only linear models could reliably be identified, and thus this approach was not applicable to the obviously nonlinear case of vortex-induced vibrations. In this dissertation, we have used novel nonlinear system identification techniques to build a fully nonlinear state-space model of a 2D circular cylinder transversely oscillating in a fluid flow. The model is constructed using time series obtained from a set of CFD simulations. To be able to excite the wake as richly as possible, we fully controlled (imposed) the motion of the cylinder. Different excitation signals have been used: simple harmonic motion (at various frequencies), sine sweeps, and multisines, to study the oscillating cylinder at different frequencies and amplitudes (in and around the lock-in region). All these data have then been used to train the nonlinear model. Comparison of this identified model with a different set of CFD simulation data show that it is in good agreement. We now have a model that can represent the oscillating cylinder over a set of frequencies and amplitudes at only a fraction of the computational time required by CFD.