Shan Huang

A NUMERICAL METHOD FOR PREDICTING SNAP LOADING OF MARINE CABLES

A numerical approach for predicting the snap loading of marine cables operating in alternating taut-slack conditions is presented. The modelling is based upon the lumped-mass-and-spring method with modifications to take into account the bilinear axial stiffness of the cable. The resulting governing equations are integrated in the time domain using the modified Euler method. Numerical examples are given and comparisons of the numerical results and the experimental results available are made which demonstrate the validity of the present method.

Dynamics of small-sagged taut-slack marine cables

The snap tension of small-sagged marine cables operating in alternating taut-slack conditions is considered in this paper. The marine cable is suspended at the two ends on the same level. One of the two ends is fixed, while the other is subjected to horizontal excitation. A single non-linear equation of vertical motion of the cable is derived and solved by the Galerkin method. It is found that only the symmetric modes with respect to the mid-span need to be considered. Numerical examples are given and comparisons are made between numerical and experimental results which help to demonstrate the validity of the present method.

Multiple Stable/Unstable Equilibria of a Cylinder in the Wake of an Upstream Cylinder

The static equilibrium position and its associated dynamic stability of a cylinder situated in the wake of an upstream cylinder is investigated in this paper. Both the upstream and downstream cylinders are elastically mounted on springs to allow for streamwise and transverse displacements. Due to the wake effect the downstream cylinder is subject to a lift force as well as a drag. It is shown that under certain flow conditions there exist multiple stable and unstable equilibria for the downstream cylinder. There also exist a critical flow velocity and once this velocity is exceeded no equilibrium positions of the downstream cylinder can be found, which suggests a likely occurrence of clashing between the two cylinders.

Some observations of two interfering VIV circular cylinders of unequal diameters in tandem

Analysis of model test results was carried out to investigate the hydrodynamic interaction between a pair of elastically-supported rigid cylinders of dissimilar diameters in a water flume. The two cylinders are placed in tandem with one situated in the wake of the other. The diameter of the upstream cylinder is twice as large as that of the downstream cylinder. The spacing between the two cylinders ranges from 1 to 10 times the larger cylinder diameter. The Reynolds numbers are within the sub-critical range. The cylinders are free to oscillate in both the in-line and the cross-flow directions. The reduced velocity ranges from 1 to 10 and the low damping ratio of the model test set-up at 0.006 gives a combined mass-damping parameter of 0.02. It is found that the lift on and the cross-flow motion of the downstream cylinder have the frequency components derived from the upstream cylinder’s vortex shedding as well as from its own vortex shedding, and the relative importance of the two sources of excitation is influenced by the spacing between the two cylinders. The downstream cylinder’s VIV response appears to be largely dependent upon the actual reduced velocity of the cylinder.

Current induced instability of two circular cylinders

The mean lift and drag forces on a cylinder placed in the wake of another upstream cylinder are investigated in the paper as well as the influence of these forces on the stability of the downstream cylinder. It is assumed that the two cylinders have the same diameter with the upstream cylinder always fixed. The forces are predicted based upon a free streamline model and the utilisation of some available experimental data. The stability of the downstream cylinders equilibrium position is then analysed by finding eigenvalues of the linearised equation of motion. Numerical results of the lift and drag forces on the downstream cylinder are presented which are in a good agreement with the experimental data. It is found that under the influence of these forces the equilibrium position can become unstable through either the Hopf or stationary bifurcation depending upon the value of the mass parameter. For marine applications, the stationary bifurcation is the more likely scenario. The effect of the reduced velocity is identified in the paper.

Wake-Induced Large-Amplitude Low-Frequency Motions of a Vertical Riser in the Wake of an Upstream Riser

It is concluded from our previous work that a vertical riser situated in the wake of an upstream riser can lose its stability when the current velocity exceeds a critical value. The ensuing irregular motion of the downstream riser is characterised by its large amplitude and low frequency. A numerical method is further developed in this paper to simulate the wake-induced large-amplitude low-frequency motions of the downstream riser as it wanders about in the wake. While an accurate structural model for riser clashing is still yet to be developed, the preliminary results presented here do indicate that in considering the riser impact velocity it is inadequate to use the VIV velocity alone as the wake-induced motion can have a significant contribution to the riser impact velocity.Copyright

Interference between two stationary or elastically supported rigid circular cylinders of unequal diameters in tandem and staggered arrangements

Analysis of model test results was carried out to investigate the hydrodynamic interaction between pairs of fixed or elastically supported rigid cylinders of dissimilar diameters in a water flume. The two cylinders are placed with one situated in the wake of the other. The spacing between the cylinders ranges from 1 to 15 times the larger cylinder diameter. The Reynolds numbers are within the subcritical range. For the vibrating cylinders which are free to oscillate in both the in-line and the cross-flow directions, the reduced velocity ranges from 1 to 13 and the low damping ratio of the test setup at 0.006 gives a combined mass-damping parameter of 0.02. For the fixed cylinders, the downstream cylinder experiences a drag reduction and it was found that this drag reduction also depends upon the diameter ratio. The lift on the fixed downstream cylinder has the frequency components derived from the upstream cylinders vortex shedding as well as from its own vortex shedding, and the relative importance of the two sources is influenced by the spacing between the two cylinders. This is reflected in the downstream cylinders vortex induced vibration (VIV) response which appears to be dependent upon the actual reduced velocities of both the cylinders.

Long term extreme analysis of FPSO mooring systems based on Kriging metamodel

Establishing statistical distributions of the response extremes is of particular importance for the design of FPSO mooring systems and the related riser design. Long term time domain simulation is the most accurate design approach to determine the extreme responses. It involves, however, coupled dynamic analysis of FPSO mooring system for a large number of sea states and consequently the task is often prohibitively time consuming. To solve this problem, an approach for the long term extreme analysis based on a metamodel in conjunction with the design of experiment methodology is proposed in the paper. In this approach, Latin Hypercube Sampling (LHS) based on the design of experiment method, is performed to select a sub-set of sea states from all sea states. Short term distributions for this sub-set of sea states are simulated and estimated. Kriging metamodel, which can map the relations between the sea states characteristics and the short term distribution parameters, is then applied. The accuracy of the metamodel is investigated. The long term response distribution of moored FPSO systems for all sea states can be predicted based on the metamodel. This approach for the long term extreme analysis of FPSO mooring systems avoids the response analysis over all sea states and can greatly improve the computational efficiency of the long term extreme analysis of FPSO mooring systems.