A nonlinear model of vortex-induced forces on an oscillating cylinder in a fluid flow

A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and synchronisation, is studied both for swept sine and multisine excitation. A nonparametric nonlinear distortion analysis (FAST) is used to distinguish odd from even nonlinear behaviour. The information which is obtained from the nonlinear analysis is explicitly used in constructing a nonlinear model of the polynomial nonlinear state-space (PNLSS) type. The latter results in a reduction of the number of parameters and an increased accuracy compared to the generic modelling approach where typically no such information of the nonlinearity is used. The obtained model is able to accurately simulate time series of the transverse force coefficient over a wide range of the frequency-amplitude plane of imposed cylinder motion.Comment: Accepted for publication in Journal of Fluids and Structure

Nonlinear forcing, response and damping of oscillating water columns

This thesis improves the physical understanding of a dynamically responding offshore OscillatingWater Column (OWC) of a fixed and cylindrical type. The study concerns the analytical models of the linear potential flows and the numerical simulations of the fully nonlinear viscous flows of OWCs undergoing different excitation mechanisms and conditions. Of particular interest in this research are the physical origin and the significance of nonlinearities in the forces acting on a water column. The vortex shedding at the lowermost end of an OWC has a marked influence on the forcing caused by wave excitation at the resonant and a higher frequency. On the other hand, the free-surface nonlinearity has a negligible effect on this force. Furthermore, an evaluation of the hydrodynamic and the air forces demonstrates the diminishing role of the vortex shedding as the amplitude of the response (or motion) of a water column increases. The vortex shedding and the nonlinear inertial forcing are responsible for any nonlinear characteristics of the internal water surface elevation within an OWC. The former causes the progressively decreasing response amplitude operator and progressively varying phase difference of the water elevation, while the latter provokes the response asymmetry. The hydrodynamic coefficients crucially depend on the amplitude of the water column motion, the mouth shape, and the dimensions of an OWC. When flow separation occurs, the added-mass coefficient progressively increases with the amplitude. It is consistent with the departures from linear radiation theory when considering the radiated wave elevation near an OWC with a sharp-edged mouth. Formation of the vortex that primarily contributes to the nonlinear damping coefficient most significantly reduces the response at the resonant frequency. This role of vortex formation is more pronounced under a high- than a low-frequency excitation. These insights and the dominance of the flow driven by the water column (in relative comparison to the wave flow) explain the applicability of the hydrodynamic coefficients evaluated from a forced oscillation test to predict a wave-induced response.Open Acces

New developments in rain–wind-induced vibrations of cables

On wet and windy days, the inclined cables of cable stayed bridges can experience large amplitude, potentially damaging oscillations known as rain-wind-induced vibration (RWIV). RWIV is believed to be the result of a complicated non-linear interaction between rivulets of rain water that run down the cables and the wind loading on the cables from the unsteady aerodynamics; however, despite a considerable international research effort, the underlying physical mechanism that governs this oscillation is still not satisfactorily understood. An international workshop on RWIV was held in April 2008, hosted at the University of Strathclyde. The main outcomes of this workshop are summarised in the paper. A numerical method to investigate aspects of the RWIV phenomenon has recently been developed by the authors, which couples an unsteady aerodynamic solver to a thin-film model based on lubrication theory for the flow of the rain water to ascertain the motion of the rivulets owing to the unsteady aerodynamic field. This novel numerical technique, which is still in the relatively early stages of development, has already provided useful information on the coupling between the external aerodynamic flow and the rivulet, and a summary of some of the key results to date is presented

Influence of Beam Rotation on the Response of Cantilevered Flow Energy Harvesters Exploiting the Galloping Instability

Energy harvesters are scalable devices that generate microwatt to milliwatt power levels by scavenging energy from their ambient natural environment. Applications of such devices are numerous, ranging from wireless sensing to biomedical implants. A particular type of energy harvester is a device which converts the momentum of an incident fluid flow into electrical output by using flow-induced instabilities such as galloping, flutter, vortex shedding and wake galloping. Galloping flow energy harvesters (GFEHs), which represent the core of this thesis, consist of a prismatic tip body mounted on a long, thin cantilever beam fixed on a rigid base. When the bluff body is placed such that its leading edge faces a moving fluid, the flow separates at the edges of the leading face causing shear layers to develop behind the bluff face. The shear layer interacts with the surface area of the afterbody. An asymmetric condition in the shear layers causes a net lift which incites motion. This causes the beam to oscillate periodically at or near the natural frequency of the system. The periodic strain developed near the base of the oscillating beam is then transformed into electricity by attaching a piezoelectric layer to either side of the beam surface. This thesis focuses on characterizing the influence of the rotation of the beam tip on the response and output power of GFEHs. Previous modeling efforts of GFEHs usually adopt two simplifying assumptions. First, it is assumed that the tip rotation of the beam is arbitrarily small and hence can be neglected. Second, it is assumed that the quasi-steady assumption of the aerodynamic force can be adopted even in the presence of tip rotation. Although the validity of these two assumptions becomes debatable in the presence of finite tip rotations, which are common to occur in GFEHs, none the previous research studies have systematically addressed the influence of finite tip rotations on the validity of the quasi-steady assumption and the response of cantilevered flow energy harvesters. To this end, the first objective of this thesis is to investigate the influence of the tip rotation on the output power of energy harvesters under the quasi-steady assumption. It is shown that neglecting the tip rotation will cause significant over-prediction of the output power even for small tip rotations. This thesis further assesses the validity of the quasi-steady assumption of the aerodynamic force in the presence of tip rotations using extensive experiments. It is shown that the quasi-steady model fails to accurately predict the behavior of square and trapezoidal prisms mounted on a cantilever beam and undergoing galloping oscillations. In particular, it is shown that the quasi-steady model under-predicts the amplitude of oscillation because it fails to consider the effect of body rotation. Careful analysis of the experimental data indicates that, unlike the quasi-steady aerodynamic lift force which depends only on the angle of attack, the effective aerodynamic curve is a function of both the angle of attack and the upstream flow velocity when the effects of body rotation are included. Nonetheless, although the quasi-steady assumption fails, the remarkable result is that the overall structure of the aerodynamic model remains intact, permitting the use of aerodynamic force surfaces to capture the influence of tip rotation. The second objective of this thesis is to present an approach to optimize the geometry of the bluff body to improve the performance of flow energy harvesters. It is shown that attaching a splitter plate to the afterbody of the prism can improve the output power of the device by as much as 60\% for some cases. By increasing the reattachment angle of the shear layer and producing additional flow recirculation bubbles, the extension of the body using the splitter plate increases the useful range of the galloping instability for energy harvesting

Physics-based Machine Learning Methods for Control and Sensing in Fish-like Robots

Underwater robots are important for the construction and maintenance of underwater infrastructure, underwater resource extraction, and defense. However, they currently fall far behind biological swimmers such as fish in agility, efficiency, and sensing capabilities. As a result, mimicking the capabilities of biological swimmers has become an area of significant research interest. In this work, we focus specifically on improving the control and sensing capabilities of fish-like robots. Our control work focuses on using the Chaplygin sleigh, a two-dimensional nonholonomic system which has been used to model fish-like swimming, as part of a curriculum to train a reinforcement learning agent to control a fish-like robot to track a prescribed path. The agent is first trained on the Chaplygin sleigh model, which is not an accurate model of the swimming robot but crucially has similar physics; having learned these physics, the agent is then trained on a simulated swimming robot, resulting in faster convergence compared to only training on the simulated swimming robot. Our sensing work separately considers using kinematic data (proprioceptive sensing) and using surface pressure sensors. The effect of a swimming body\u27s internal dynamics on proprioceptive sensing is investigated by collecting time series of kinematic data of both a flexible and rigid body in a water tunnel behind a moving obstacle performing different motions, and using machine learning to classify the motion of the upstream obstacle. This revealed that the flexible body could more effectively classify the motion of the obstacle, even if only one if its internal states is used. We also consider the problem of using time series data from a `lateral line\u27 of pressure sensors on a fish-like body to estimate the position of an upstream obstacle. Feature extraction from the pressure data is attempted with a state-of-the-art convolutional neural network (CNN), and this is compared with using the dominant modes of a Koopman operator constructed on the data as features. It is found that both sets of features achieve similar estimation performance using a dense neural network to perform the estimation. This highlights the potential of the Koopman modes as an interpretable alternative to CNNs for high-dimensional time series. This problem is also extended to inferring the time evolution of the flow field surrounding the body using the same surface measurements, which is performed by first estimating the dominant Koopman modes of the surrounding flow, and using those modes to perform a flow reconstruction. This strategy of mapping from surface to field modes is more interpretable than directly constructing a mapping of unsteady fluid states, and is found to be effective at reconstructing the flow. The sensing frameworks developed as a result of this work allow better awareness of obstacles and flow patterns, knowledge which can inform the generation of paths through the fluid that the developed controller can track, contributing to the autonomy of swimming robots in challenging environments

Fluid-structure interaction modeling on a 3D ray-strengthened caudal fin

In this paper, we present a numerical model capable of solving the fluid-structure interaction problems involved in the dynamics of skeleton-reinforced fish fins. In this model, the fluid dynamics is simulated by solving the Navier-Stokes equations using a finite-volume method based on an overset, multi-block structured grid system. The bony rays embedded in the fin are modeled as nonlinear Euler-Bernoulli beams. To demonstrate the capability of this model, we numerically investigate the effect of various ray stiffness distributions on the deformation and propulsion performance of a 3D caudal fin. Our numerical results show that with specific ray stiffness distributions, certain caudal fin deformation patterns observed in real fish (e.g. the cupping deformation) can be reproduced through passive structural deformations. Among the four different stiffness distributions (uniform, cupping, W-shape and heterocercal) considered here, we find that the cupping distribution requires the least power expenditure. The uniform distribution, on the other hand, performs the best in terms of thrust generation and efficiency. The uniform stiffness distribution, per se, also leads to 'cupping' deformation patterns with relatively smaller phase differences between various rays. The present model paves the way for future work on dynamics of skeleton-reinforced membranes

A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact

A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-alpha scheme are used for the spatial and temporal discretization. The membrane discretization is based on curvilinear surface elements that can describe large deformations and rotations, and also provide a straightforward description for contact. The fluid is described by the incompressible Navier-Stokes equations, and its discretization is based on stabilized Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming sharp interface discretization, and the resulting non-linear FE equations are solved monolithically within the Newton-Raphson scheme. An arbitrary Lagrangian-Eulerian formulation is used for the fluid in order to account for the mesh motion around the structure. The formulation is very general and admits diverse applications that include contact at free surfaces. This is demonstrated by two analytical and three numerical examples exhibiting strong coupling between fluid and structure. The examples include balloon inflation, droplet rolling and flapping flags. They span a Reynolds-number range from 0.001 to 2000. One of the examples considers the extension to rotation-free shells using isogeometric FE.Comment: 38 pages, 17 figure

Rising and settling 2D cylinders with centre-of-mass offset

Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in situations when mass eccentricity, and thereby a new pendulum timescale, is introduced to the system. We employ two-dimensional simulations to study the motion of a single cylinder in a quiescent unbounded incompressible Newtonian fluid. This allows us to vary the Galileo number, density ratio, relative moment of inertia, and Centre-Of-Mass offset (COM) systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibit a resonance mode, during which the coupling via the Magnus lift force causes a positive feedback between translational and rotational motions. This mode results in vastly different trajectories with significantly larger rotational and translational amplitudes and an increase of the drag coefficient easily exceeding a factor two. We propose a simple model that captures how the occurrence of the COM offset induced resonance regime varies, depending on the other input parameters, specifically the density ratio, the Galileo number, and the relative moment of inertia. Remarkably, depending on the input parameters, resonance can be observed for centre-of-mass offsets as small as a few percent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter.Comment: 32 pages, 13 figure