Flow-induced vibration of small elastic cylinders mounted in the shear flow of a two-dimensional jet is investigated experimentally. There has been a great deal of work concerned with different vibrating conditions and practical dynamic responses by way of mass ratios and diameters of various different cylinders. In such cases, the amplitude of the cylinder oscillation changed along with the variation of the jet velocity is due to the influence of fluid elastic instability. The experiment is based on the method of the magnetic field induction to measure the motion of the small cylinder, and it involves measurements of the varying velocity in a jet through the hot- wire anemometer. The critical velocity of the cylinder vibration in the shear flow with different diameters, mass ratios and damping factors are examined. Moreover, the oscillation traces of the cylinder by fluid elastic instability were observed when the jet velocity was increased, and then decreased for examination of hysteresis phenomena. The results show that the bifurcation of the cylinder vibration traces is remarkable especially for cylinders with high mass ratios. By the amplitude diagrams of the cylinder vibration, the critical velocity for onset of fluid elastic vibration was determined. The dependence of the critical velocity and hysteresis phenomena on the mass ratio and damping factor are discussed.

Vibrations of small cylinder in a jet flow are investigated experimentally. Because of the flow field in shear layers of jet flow is very complex and filled with vortex structures, so the flow induced vibration phenomena in jet flow is different from the flow induced vibration in uniform flow. The major subject in this experiment is to discuss the major cause of small cylinder vibrations, and the flow field influenced by the cylinder vibration. About flow measurement, velocity measurement by hot-wire is applied. As for the vibration measurement, by using the principle of electromagnetic, a new measurement technology was successfully developed. This new vibration measurement can measure the vibrations in two axial, so as to describe the orbit of vibrations. To find the interrelation of flow field and cylinder vibrations, flow measurement and vibration measurement was carry on at the same time. It is shown that when the jet velocity is increased constantly, small cylinder will vibration intensely. The fixed velocity is called critical velocity. If add a perturb, the vibration will occur in advance. The dominant frequency of cylinder vibration, fr, will be the same with it's nature frequency, fn, in the critical velocity, but when the flow velocity keep on increasing, the dominant frequency, fr, will also increase. Besides, the relation of reduced velocity and mass damping was found in this case. The orbits of vibrations are all like ellipse, and the orbit is different with different reduced velocity. The vibration amplitude be changed into three sections that have different reduced velocity, and different orbit. About the flow field, the velocity profile in potential core is not influenced by vibrations of small cylinder, but the velocity fluctuations in shear layer indeed be inflected. At the fixed velocity region, the dominant frequency of flow is the same with dominant frequency of vibrations when the flow at downstream of small cylinder in shear layer. This phenomena only exist when the vibration amplitude under the fixed range.

Abstract The experiment was performed to measure the flow-induced vibration of tubes in cross flow and to study the effect of different experimental parameters, natural frequency, tube patterns and positions of the missing tube, on the tube vibration. The vibration mode of structures was investigated by root-mean-square values of tube displacements, dominant response frequencies, power spectral densities and orbits. The vibration signals in various velocities were used to analyze the mode and mechanism of the tube vibration by examining the interrelations between power spectral densities and orbits of the tube vibration. It was found that the stability thresholds were higher at the higher natural frequencies of the tubes and approach angles of the flow. Missing tube would affect the stability of local flow field, so that the surrounding tubes became more unstable. For each array pattern, the dominant response frequency of tube was changed with the flow velocity. It should be associated with the flow field, the mode and mechanism of vibration. As the tube frequency jumped, it should be the change of vibrating mode and mechanism. From the spectra and orbits of the tube vibrations, it can be found that the dominant frequencies are more complex at the high flow velocity.

Flow induced vibration of flow around a flexible tube array in cross flow are investigated experimentally. The different parameter including velocity, turbulent intensity, and nature frequency of tube. The flow structure and stability between flow and tube are analyzed by flow visualization and flow measurement. Further more, missing tube to find the change of the flow and the influenced of nearby tube, to get the way decreasing the vibration of tube.

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Bluff bodies immersed in a fluid stream are susceptible to flow-induced vibrations. Depending on the body dynamic characteristics and flow conditions, different types of flow-induced vibrations may occur. The failure of a blade in a large mixing vessel in a chemical plant raised the question of the response of a parabolic cross-section bluff body to the flow excitation. Experiments were conducted in a wind tunnel using two- dimensional “sectional” models. Models with parabolic, semi-elliptic and semi-circular cross-section were investigated. In the dynamic experiments, flow velocity was increased from 0 to 22 m\s, and the oscillating amplitude and wake response were monitored. Vortex-induced vibrations were observed with Strouhal numbers for parabolic and semi-circular cross-sections of 0.13 and 0.12, respectively. Steady lift force and fluid moment for different angles of attack were monitored in the static experiments. From these results, lift and moment coefficients were calculated. For the closed semi-circular cross-section, Reynolds number had a strong influence on the lift coefficient. With an increase in Reynolds number, the lift coefficient decreased. The largest difference was noted at an angle of attack a = 45°. In contrast, the open semi-circular model lift coefficient was independent of Reynolds number. In the experiments where the elastic axis of the model coincided with the model centre of gravity, galloping was not observed in the plunge mode. When the model elastic axis was moved to a position 90 mm behind the test model centre of gravity, galloping was observed for the semi-elliptic and parabolic models. The onset of galloping coincided with the vortex-induced resonance. Changing the model elastic axis position introduced a combination of plunge and torsional motion, and latter is believed to be responsible for the existence of galloping. The parabolic model was modified in an attempt to eliminate galloping instability. Fins were added at the separation points to widen the wake and prevent the reattachment of the flow to the afterbody. With these changes, galloping was not observed, although the oscillation amplitudes remained unacceptably high. The present investigation revealed previously unknown characteristics of semi-elliptical and parabolic cross-section bluff body behaviour in fluid flow. At the same time, it laid a foundation for the solution to the practical problem encountered when a parabolic cross-section bluff body was used as a mixing blade. / Thesis / Master of Engineering (ME)

The wake of a bluff body is a representative issue in vortex dynamics that plays a central role in civil engineering, ocean engineering and thermal engineering. In this work, a flowing soap film was used to investigate the wakes of multiple stationary circular cylinders and of a single oscillating cylinder. Corresponding computer simulations were also conducted. Vortex formation of a stationary circular cylinder was analyzed by proper orthogonal decomposition (POD). The POD analysis was used to define an unsteady vortex formation length, which suggests a relationship between the vortex formation length of a single cylinder and the critical spacing of two cylinders in a tandem arrangement. A systematic parametric study of the wake structure was conducted for a controlled transversely oscillating cylinder. Neural network and support vector machine codes assisted the wake classification procedure and the identification of boundaries between different wake regimes. The phase map of the vortex shedding regimes for the (quasi) two-dimensional experiment qualitatively agrees with previous three-dimensional experiments. The critical spacings of two identical tandem circular cylinders in a flowing soap film system were determined using visual inspections of the wake patterns and calculations of the Strouhal frequencies. The dimensionless spacing was both increased and decreased quasi-statically. Hysteresis was observed in the flow patterns and Strouhal numbers. This study appears to provide the first experimental evidence of critical spacing values that agree with published computational results. The wake interaction between a stationary upstream circular disk and a free downstream circular disk was also investigated. With the ability to tie together the wake structure and the object motion, the relationship between energy generation and flow structure in the simplified reduced order model system was studied. The research results find the optimal efficiency of the energy harvesting system by a parametric study. / PHD / The wake of a bluff body is a classic issue in vortex dynamics that has been the subject of much research in civil engineering, ocean engineering and thermal engineering. Bluff bodies, especially circular cylinders, can be found extensively in heat exchangers, cooling systems and offshore structures. Flow-induced vibration of a bluff body due to the formation of a wake is an important problem in many fields of engineering. Flow-induced vibration determines the oscillation of flexible pipes that transfer oil from the seabed to the surface of the ocean, for example [71]. In civil engineering, flow-induced vibration affects the design of bluff structures in wind such as bridges, chimneys and buildings [62]. Flow-induced vibration caused by vortices being shed from a bluff body is also a promising way to extract energy from geophysical flows [10]. FIV energy harvesting systems are especially suitable for slow flow speeds in the range 0.5-1.5m/s which cannot be efficiently harvested by traditional hydroelectric power technologies. When a pair of tandem cylinders is immersed in a flow, the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. In this work, a flowing soap film was used to investigate the flow-induced vibration of the downstream cylinder of a tandem pair. With the ability to tie together the wake structure and the object motion, we investigate the relationship between energy generation and flow structure in the reduced order model system. The research results find the optimal efficiency of the energy harvesting system by a parametric study. To get deep physical understanding of the flow-induced vibration, wake structures of a circular cylinder undergoing controlled motion and the critical spacing of two identical tandem circular cylinders were also investigated in this research. These research results can help not only the optimization of energy harvesting systems based on flow-induced vibration of the circular-cylinder system, but also will benefit the understanding of wake interactions between multiple bluff bodies such as schooling fish, natural draft cooling towers and wind turbine farms.

Flow-induced structural vibration is experienced in many engineering applications, such as aerospace industry and civil engineering infrastructures. One of the main mechanisms of flow-induced vibration is instability which can be triggered by parametric excitations or fluid-elastic forces. Experiments show that turbulence has a significant impact on the stability of structures. The objective of this research is to bridge the gap between flow-induced vibration and stochastic stability of structures. The flow-induced vibration of a spring-supported circular cylinder is studied in this research. The equations of motion for the cylinder placed in a cross-flow are set up, in which the vortex force is modeled by a bounded noise because of its narrow-band characteristics. Since the vibration in the lift direction is more prominent in the lock-in region, the system is reduced to one degree-of-freedom, i.e., only the vibration of the cylinder in the lift direction is considered. The equation of motion for the cylinder can be generalized as a two-dimensional system excited by a bounded noise. Stochastic analysis is used to determine the moment Lyapunov exponents and Lyapunov exponents for the generalized system. The results are then applied to study the parametric instability of a cylinder in the lock-in region. Fluidelastic instability can occur when the cylinder is placed in a shear flow. The equations of motion are established by using the quasi-steady theory to model the fluid-elastic forces. To study the turbulence effect on the stability of the cylinder, a real noise or an Ornstein-Uhlenbeck process is used to model the grid-generated turbulence. The equations of motion are randomized resulting in a four-dimensional system excited by a real noise. The stability of the stochastic system is studied by determining the moment Lyapunov exponents and Lyapunov exponents. Parameters of the system and the noise are varied to investigate their effects on the stability. It is found that the grid-generated turbulence can stabilize the system when the parameters take certain values, which agrees with the experimental observations. Many flow-induced vibration problems can be modeled by a two degrees-of-freedom system parametically excited by a narrow-band process modeled by a bounded noise. The system can be in subharmonic resonance, combination (additive or differential) resonance, or both if the central frequency of the bounded noise takes an appropriate value. The method for a single degree-of-freedom system is extended to study the stochastic stability of the two degrees-of-freedom system. The moment Lyapunov exponents and Lyapunov exponents for the three cases are obtained using a perturbation method. The effect of noise on various types of parametric resonance, such as subharmonic resonance, combination additive resonance, and combined subharmonic and combination additive resonance, is investigated. The main contributions of this thesis are stochastic stability analysis of one-degree-of-freedom systems and two-degree-of-freedom systems. Stability analysis for systems under the excitation of real noise and bounded noise is carried out by determining the moment Lyapunov exponents and Lyapunov exponents. Good agreement is obtained between analytical results and those obtained from Monte Carlo simulations. In the two degrees-of-freedom case, the effect of free stream turbulence on cylinder vibration and its stability is examined.

Flow-induced structural vibration is experienced in many engineering applications, such as aerospace industry and civil engineering infrastructures. One of the main mechanisms of flow-induced vibration is instability which can be triggered by parametric excitations or fluid-elastic forces. Experiments show that turbulence has a significant impact on the stability of structures. The objective of this research is to bridge the gap between flow-induced vibration and stochastic stability of structures. The flow-induced vibration of a spring-supported circular cylinder is studied in this research. The equations of motion for the cylinder placed in a cross-flow are set up, in which the vortex force is modeled by a bounded noise because of its narrow-band characteristics. Since the vibration in the lift direction is more prominent in the lock-in region, the system is reduced to one degree-of-freedom, i.e., only the vibration of the cylinder in the lift direction is considered. The equation of motion for the cylinder can be generalized as a two-dimensional system excited by a bounded noise. Stochastic analysis is used to determine the moment Lyapunov exponents and Lyapunov exponents for the generalized system. The results are then applied to study the parametric instability of a cylinder in the lock-in region. Fluidelastic instability can occur when the cylinder is placed in a shear flow. The equations of motion are established by using the quasi-steady theory to model the fluid-elastic forces. To study the turbulence effect on the stability of the cylinder, a real noise or an Ornstein-Uhlenbeck process is used to model the grid-generated turbulence. The equations of motion are randomized resulting in a four-dimensional system excited by a real noise. The stability of the stochastic system is studied by determining the moment Lyapunov exponents and Lyapunov exponents. Parameters of the system and the noise are varied to investigate their effects on the stability. It is found that the grid-generated turbulence can stabilize the system when the parameters take certain values, which agrees with the experimental observations. Many flow-induced vibration problems can be modeled by a two degrees-of-freedom system parametically excited by a narrow-band process modeled by a bounded noise. The system can be in subharmonic resonance, combination (additive or differential) resonance, or both if the central frequency of the bounded noise takes an appropriate value. The method for a single degree-of-freedom system is extended to study the stochastic stability of the two degrees-of-freedom system. The moment Lyapunov exponents and Lyapunov exponents for the three cases are obtained using a perturbation method. The effect of noise on various types of parametric resonance, such as subharmonic resonance, combination additive resonance, and combined subharmonic and combination additive resonance, is investigated. The main contributions of this thesis are stochastic stability analysis of one-degree-of-freedom systems and two-degree-of-freedom systems. Stability analysis for systems under the excitation of real noise and bounded noise is carried out by determining the moment Lyapunov exponents and Lyapunov exponents. Good agreement is obtained between analytical results and those obtained from Monte Carlo simulations. In the two degrees-of-freedom case, the effect of free stream turbulence on cylinder vibration and its stability is examined.