Hydrodynamics of A Flexible Riser Undergoing the Vortex-Induced Vibration at High Reynolds Number
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Abstract:
This study proposed a method to obtain hydrodynamic forces and coefficients for a flexible riser undergoing the vortex-induced vibration (VIV), based on the measured strains collected from the scale-model testing with the Reynolds numbers ranging from 1.34E5 to 2.35E5. The riser is approximated as a tensioned spatial beam, and an inverse method based on the FEM of spatial beam is adopted for the calculation of hydrodynamic forces in the cross flow (CF) and inline (IL) directions. The drag coefficients and vortex-induced force coefficients are obtained through the Fourier Series Theory. Finally, the hydrodynamic characteristics of a flexible riser model undergoing the VIV in a uniform flow are carefully investigated. The results indicate that the VIV amplifies the drag coefficient, and the drag coefficient does not change with time when the CF VIV is stable. Only when the VIVs in the CF and IL directions are all steady vibrations, the vortex-induced force coefficients keep as a constant with time, and under "lock-in" condition, whether the added-mass coefficient changes with time or not, the oscillation frequency of the VIV keeps unchanged. It further shows that the CF excitation coefficients at high frequency are much smaller than those at the dominant frequency, while, the IL excitation coefficients are in the same range. The axial distributions of the excitation and damping region at the dominant frequency and high frequency are approximately consistent in the CF direction, while, in the IL direction, there exists a great difference.Keywords:
Vortex-induced vibration
Oscillation (cell signaling)
Added mass
Morison equation
Vortex shedding
Morison equation
Added mass
Velocity potential
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Morison equation
Added mass
Earthquake shaking table
Offshore geotechnical engineering
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The drag coefficient and added mass (hydrodynamic mass) are the essential parameters for the dynamics analysis of submerged objects with mobility such as bio-mimicking fish robots or underwater vehicles. The shape dependence of these parameters makes them difficult to have good theoretical approximations and the parameters should be determined either numerically or experimentally. Different experiments have been proposed to obtain either the drag coefficient or added mass. This paper presents a new method to simultaneously determine the drag coefficient and added mass from a simple and economic experiment and a numerical identification procedure. An experiment was carried out to demonstrate the method and the identification error was studied analytically and numerically for some experimental uncertainties.
Added mass
Morison equation
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Experimental results for the drag coefficient and the added hydrodynamic mass coefficient for block bodies, plates, and models of deadweight anchors are presented. A unique method is examined for eliminating noise from an analog signal that relates to the analysis of the recorded forces, and for determining the drag and inertia coefficients in the frequency domain. Results from a regression analysis to determine the drag coefficients and hydrodynamic mass coefficients are presented and compared to the other method employed. The experiments show that both the added mass and the drag coefficients are dependent upon the ratio of the amplitude of the water particle excursion to the major dimension of the body.
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Morison equation
Excursion
Particle (ecology)
Drag equation
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Vortex shedding
Vortex-induced vibration
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Morison equation
Added mass
Mass flow
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Cylinders with various aspect-ratios and spheres, attached axially to a vertical spring, were vibrated longitudinally in still water by a vibrator which provided the top of the spring with a sinusoidal displacement. Then, the drag and added-mass coefficients were analysed by introducing the experimental values of amplitudes and frequency in the resonance into the solution of a spring-mass-damper system. First, to examine the validity of this method, the results on the spheres were compared with those by Sarpkaya, and both results proved to be in fairly good agreement. The results on the cylinders led to the following conclusions. There is a good correlation between those coefficients and Keulegan-Carpenter number Kc(=UmT/D). AS Kc. increases, the added-mass coefficient increases linearly and the drag coefficient decreases exponentially. When Kc exceeds about 10, the drag coefficient approaches the constant value. However, there is no clear correlation between these coefficients and Reynolds number.
Added mass
Morison equation
Vibrator (electronic)
Axial symmetry
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Vortex-induced vibration
Added mass
Vortex shedding
Catenary
Morison equation
Strouhal number
Oscillation (cell signaling)
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Buffers with various shapes and aspect-ratios, attached axially to a vertical spring, were vibrated longitudinally in still water by a vibrator which excited the top of the spring with a sinusoidal displacement. Then, the drag and added mass coefficients were analysed by introducing the experimentally obtained values of buffer's amplitude and frequency in resonance as well as the amplitude of the forcing displacement to the solution of a springmass-damper system.The results obtained are as follows:(1) There is a good correlation between the drag and added mass coefficients of buffers vibrating longitudinally in water and the number of Keulegan-Carpenter, Kc. However, there is no clear correlation between those coefficients and Reynolds number.(2) The drag coefficients decrease exponentially as Kc increases. Then, the drag coefficients approach the constant values when Kc exceeds some values. These constant values are about 1.0 for a cylindrical buffer, about 0.35 for a cylindro-semispherical one and about 0.3 for a cylindro-conical one. Furthermore, these values are independent of aspect ratios.(3) There is a linear relationship between the added mass coefficient and Kc. In case of a cylindrical buffer, the coefficient increases as Kc increases and the rate of increase is greater in smaller aspect-ratio. In cases of cylindro-semispherical and cylindro-conical buffers, however, the coefficients decrease as Kc increases and the rates of decrease are greater in larger aspect-ratio.(4) The absolute values of those added mass coefficients are compared with each other in case that Kc is equal to 10. These values pertaining to the aspect-ratio of 1 are about 1.1 for a cylindrical buffer, about 0.3 for a cylindro-semispherical one and about 0.25 for a cylindro-conical one. On the other hand, the values pertaining to the aspect-ratio of 3 are about 0.2 for all buffers.
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Morison equation
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Added mass
Vortex-induced vibration
Morison equation
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Citations (15)