Synchronisation Behaviours Of Steady And Oscillatory Flows Past Multiple Cylinders

The study on bluff-body flow is an eternal problem in both scientific and practical viewpoint.It has been more than a century since the discovery of von Kármán vortex street.Despite its geometric simplicity,there remains many unsolved problems in this fields,such as,the synchronisations and wake interferences among multiple cylinders,the bifurcation of the flow from laminar to turbulence,from two-dimensional(2-D)to three-dimensional(3-D),the correlations between the flow characteristics and hydrodynamic loadings,etc.A sound understanding of those problems not only benefits to the fundamental physics,but it also provides valuable information to the safe design and on-going maintenance of the structures in civil,ocean and wind engineering.The structure(s)with circular cross section is one of the most common structures in the marine environment,such as the columns in fixed and floating platforms,the risers and cables in deep sea.Owing to the functional requirements,multiple cylindrical structures are commonly arranged in groups in real environments.The hydrodynamics around an isolated cylinder change significantly when the other cylinder(s)is in close proximity.A deep understanding of bluff-body flows will provide a strong connection between fluid mechanics and civil engineering.The present study focuses on the bluff-body flows in the laminar regime or in the transition route to turbulence(at low Reynolds number,Re).The objective of the thesis is to gain a comprehensive understanding of the underlying physics of the research topic,fulfilling the bluff-body "jig-saw puzzle" in the fluid mechanics community.It is also hoped that the topics uncovered in the thesis will enhance and inspire the design and maintenance processes in engineering fields.To this end,the thesis numerically studies the(high-order)synchronisations,bifurcation behaviours and hydrodynamic forces of a cylinder or a cylinder array under forcing conditions such as,uniform steady flow and oscillatory flow.A set of 2-D and 3-D direct numerical simulations(DNS),Floquet analyses have been employed.In addition,the thesis pioneers the use of phase dynamics concept to the bluff-body flows.The major findings in this thesis are summarised below.The thesis first focuses on the wake interference of two parallel Kármán vortex streets in the scenario of steady around two side-by-side cylinders.The bistability between in-phase and anti-phase states,the wake interactions and flow state transitions are explored in chapter 3 and 4,respectively.A good understanding of bistability is pivotal to the flow control applications and the interpretation of chaotic flow features observed at high Re.The knowledges of synchronisations and the origins of flip-flop(FF)flows,where the gap flow flaps laterally at a low frequency than the vortex shedding frequency,are important for the design and maintenance of cylindrical structures.It is demonstrated that the irreversible bistability can be observed in other interacting wakes around multiple cylinders.With those understandings gained from 2-D flow,a set of Floquet stability analyses are carried out in chapter 5 to close the knowledge gap of the effect of wake interference on 3-D wake transition of two parallel Kármán vortex streets.Compared with the isolated cylinder case,the 3-D instabilities in the two side-by-side cylinders show fruitful features and are sensitive to the g*and the baseflow states.The information gained from this topic can be used as guides in the careful assessment of the flow interference affects that are necessary prior to scientific or engineering work on flows around multiple bodies.The other topic of this thesis focuses on a circular cylinder or a four cylinder in a diamond arrangement under the oscillatory flow condition,which is abundant in ocean engineering.The oscillatory flow is dependent on both Keulegan-Carpenter(K)and the Stokes(β=Re/K)numbers.In engineering fields,the prediction of hydrodynamic forces exerted on long cylindrical elements in offshore structures requires a clear understanding of the flow in the range of K from 0.001 to 10 over a wide range of β.To this end,chapter 6 is highlighted by providing a possible approach of estimating the hydrodynamic damping on a single circular cylinder at β<～0.8 and,β=1-106.It has been demonstrated the conventional Morison equation,which has been widely used in engineering applications and academic research over the last half century,with the quadratic drag component is fundamentally incorrect at small K as the drag component is linearly proportional to incoming velocity with a phase difference of π/4.A general form of the Morison equation is proposed by considering both viscous and form drag components and demonstrated to be superior to the conventional equation for K<～2.0.In chapter 7,the wake interference effects for oscillatory flow past an array of four cylinders in a diamond arrangement are investigated.Comprehensive regime maps over the(K,Re,g*)parameter spaces are first provided,and corresponding flow characteristics are explained.Compared with the flow around a single cylinder and four cylinders in a square arrangement,the diamond arrangement has more quasi-periodic flow regimes and unique flow features(e.g.,"holes" in the regime maps).The mode competition between the cluster-scale and cylinder-scale flows is identified as the key flow mechanism responsible for those unique flow features,with the support of evidence derived from quantitative analysis,such as phase dynamics.It has also been validated that the interferences of flow around the cylinder array has little effect on the hydrodynamic damping forces at K<～0.8 and g*≥ 1.0,suggesting that the newly proposed applicable range of Stokes-Wang solution and a general form of Morison equation in chapter 6 can be directly applied to estimate the damping forces on a cylinder array.