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Vortex Induced Vibrations experiments have been carried out with a clamped, lightly damped and long, flexible, circular cylinder suspended from a towing tank carriage. The lock-in phenomenon has been observed through bending strain measurements taken along the tube span, within a range of speeds — Reynolds number varying from 6×10 to 4×10 — fully exciting the first flexural eigenmode. Experimental results clearly show 2 resonance branches, in accordance with similar experiments performed in water with rigid cylinders mounted in linearly elastic supports (Khalak and Williamson, 1996; Parra, 1996), or in air (Feng, 1968). But now, an upper overlapping branch of oscillation appears at higher reduced velocities than in the case of rigid models. For the first natural mode of flexural vibration the nondimensional mass-damping parameter in water, (m*+Ca) ζain Khalak's and Williamson's 1996 work, takes the value 0.016 if only the structural damping in water is considered. This value has the same low order of magnitude observed by those authors. As could be expected, a jump phenomenon, from the lower to the upper branch, has been experimentally observed. This jump takes place at a reduced velocity value close to Vr ≡ 8.30, giving further evidences of a nonlinear scenario, as discussed, e.g., by Bearman (1984), Brika and Laneville (1993), Khalak and Williamson (1996) and first addressed by Feng (1968). INTRODUCTION The self-exciting vibration phenomenon of elastically mounted rigid cylinders, or else flexible cylinders, acted on by a steady current, although being one of the most important examples of the general Vortex Induced Vibrations (VIV) problems in fluid mechanics, is far from being fully understood. A considerable amount of research work has been done, either experimental or theoretically, the latter through nonlinear-oscillator modelling approaches and, recently, also through Computational Fluid Dynamics (CFD) techniques.
Dynamic Curvature In Catenary Risers At the Touch Down Point Region: An Experimental Study And the Analytical Boundary-Layer Solution
Pesce, C.P. (Escola Politécnica, University of São Paulo, Brazil) | Aranha, J.A.P. (Escola Politécnica, University of São Paulo, Brazil) | Martins, C.A. (Escola Politécnica, University of São Paulo, Brazil) | Ricardo, O.G.S. (São Paulo State Research Technological Institute (IPT), São Paulo, Brazil) | Silva, S. (São Paulo State Research Technological Institute (IPT), São Paulo, Brazil)
ABSTRACT Recently, the dynamics of catenary risers, in the absence of shock conditions against the soil, has been studied in the vicinity of the touch down point (TDP) by means of asymptotic methods and boundary-layer theory (Aranha, Martins and Pesce, 1997). The major outcome of this previous study is a simple mathematical expression that enables one to relate, in time and space, the dynamic curvature and TDP excursion when an oscillatory tension is applied to the riser. Such a dynamic asymptotic boundary-layer solution, though simple, contains all the nonlinear features that result from the nonlinear geometric boundary condition at the soil, of the one-side type. In order to validate the boundary-layer solution, an experimental study has been conducted with a structural model, at the IPT laboratory facilities. The riser model was instrumented along its length by an array of strain-gages, of the resistive type, with static and periodic dynamic problems being investigated in detail. Comparison with the analytical asymptotic solution has been carried out showing outstanding agreement. Not only time-average, rms and maximum amplitude variation of curvature over the riser length are recovered, but also the corresponding curvature time-histories along the riser's span, within the boundary layer, fully validating the analytical approximate solution. INTRODUCTION Recent research on the technical feasibility of the steel catenary riser alternative applied to the oil industry (Phifer et al., 1994) gave rise to a number of questions concerning the local dynamics in the touch down point (TDP) region. The precise evaluation of dynamic curvature in this region is mandatory, as fatigue life calculation is a crucial point in design. In a purely two-dimensional problem, we can think of an instantaneous TDP position in close analogy to the instantaneous center of rotation in the kinematics of a rolling cylinder.
- South America > Brazil (0.48)
- North America (0.46)
- Research Report > New Finding (0.85)
- Research Report > Experimental Study (0.85)
Analytical Approximation For the Dynamic Bending Moment At the Touchdown Point of a Catenary Riser
Aranha, J.A.P. (Department of Naval Architecture and Ocean Engineering) | Martins, C.A. (Department of Mechanical Engineering Escola Politécnica, University of São Paulo, São Paulo, Brazil) | Pesce, C.P. (Department of Mechanical Engineering Escola Politécnica, University of São Paulo, São Paulo, Brazil)
ABSTRACT This paper introduces an analytical approximation, of a boundary layer type, for the dynamic bending moment at the touchdown point of a catenary riser. The approximation is based on a quasi-linear frequency domain solution of a cable (EJ = 0), the only source of nonlinearity being the viscous drag on the riser, and it takes care of the motion of the touchdown point, a specially important phenomenon in the fatigue analysis. In spite of the fact that this motion is predicted from a quasi-linear frequency domain model, the final expression for the moment is strongly nonlinear and compares very well, for the low sea states used in the fatigue analysis, with results obtained from nonlinear time domain simulation; as a matter of fact, even for the extreme sea condition in Campos Basin the comparison between the analytical approximation and numerical results is reasonable. The expression for the moment depends nonlinearly, although in an explicit way, on two quasi-linear dynamic variables of the cable: the displacement x0(t) of the touchdown point and the dynamic tension τ(t). In this way, the obtained expression can also become useful in the study of the complex nonlinear statistical behavior of the riser's bending moment in the vicinity of the touchdown point. INTRODUCTION The oil industry has lately become interested in the study of the technical feasibility of a steel catenary riser anchored in a deepwater floating production system (Phifer et al., 1994). Besides some aspects related to their installation, the troublesome spots of the steel catenary riser are located at the suspended end, where a flexible joint has to be used, and at the touchdown point, where the bending moment, both static and dynamic, must be evaluated. The problem is essentially nonlinear, the main sources of nonlinearity being the fluid drag along the suspended length.
- North America > United States (0.68)
- South America > Brazil (0.66)