Nigel Barltrop

Investigation into wave—current interactions in marine current turbines

Abstract The paper looks at the use of blade element-momentum theory for predicting the torque and thrust on a marine current turbine and the results of wave tank tests using a 400 mm-diameter rotor model. To include the effects of waves, linear wave theory particle velocities and accelerations were integrated into the mathematical model. Comparison with test data shows a good agreement which implies that the theory can be effective in analysing the wave-current interactions in marine current turbines. The paper also carried out parametric studies into related parameters, which include wave height, wave frequency, and tip-speed ratio. The interaction of waves with the current may increase or decrease the torque and hence power output of the turbine. The paper also explains the selection and manufacture of the rotor and the experimental setup.

Three-dimensional Lump-Mass formulation of a catenary riser with bending, torsion and irregular seabed interaction effect

A three-dimensional Lump-Mass formulation of a catenary riser, capable of handling irregular seabed interaction, with bending and torsional stiffness is presented in this paper. This formulation uses only three degrees of translational freedom and one independent torque variable for each computational node. The generality of the present formulation permits static and dynamic analyses of a wide range of offshore-related slender structure systems such as mooring cables, rigid and flexible risers as well as submarine pipelines. Four sets of results are presented for (i) a hanging catenary, (ii) as (i) but subjected to end torsion, (iii) a wire, chain and spring buoy mooring and (iv) a steel catenary riser on an irregular seabed.

Wave-current interactions in marine current turbines

The influence of waves on the dynamic properties of bending moments at the root of blades of tidal stream vertical-axis rotors is reported. Blade element-momentum theory for wind turbines is combined with linear wave theory and used to analyze this influence. Experiments were carried out with a 350 mm diameter rotor to validate the simulation and the comparison shows the ability of the theoretical approach to predict the blade root bending moments. It can be concluded that, in steep waves, linear theory underestimates the dynamic behaviour of bending moments. However, in long waves, linear theory works well. Bending moments at roots of rotor blades fluctuate with significant amplitudes (as much as 50 per cent of mean value for out-of-plane bending moment and 100 per cent of mean value for in-plane bending moment), which will be important for design of tidal stream rotors.

Wave enhancement due to blockage in semi-submersible and TLP structures

An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yues exact algebraic method is utilised (Kagemoto, H., Yue, D.K.P., 1986. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech, 46, 129-139). The isolated cylinder diffraction potential is obtained using Garrets solution and evanescent mode solutions are derived in a similar manner (Garret, C.J.R., 1971. Wave forces on a circular dock. J Fluid Mech, 46, 129-139). Free surface elevations are calculated for an array of four cylinders and compared with experiments. Comparisons show good agreement.

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.

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

Abstract The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections. This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum. The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.

Analysis on the hull girder ultimate strength of a bulk carrier using simplified method based on an incremental-iterative approach

The hull girder ultimate strength of a typical bulk carrier is analyzed using a simplified method based on an incremental-iterative approach. First, vertical bending moment is examined by seven different methods. The moment versus curvature curves and the values of the ultimate longitudinal moments at collapse states are determined for both hogging and sagging cases. Second, the ultimate strength under coupled vertical and horizontal bending moment is accounted. An interaction curve is obtained, which corresponds to the results of series of calculation for the ship hull subject to bending conditions with different angles of curvature. It is found that the interaction curve is asymmetrical because the hull cross section is not symmetrical with respect to the horizontal axis and the structural response of the elements under compression is different from that under tension due to nonlinearity caused by buckling. The angles of the resultant bending moment vector and that of the curvature vector are different in investigated cases. The interaction design equations proposed by other researches are also addressed to discuss the results presented by this study.

Semi-analytical quasi-static formulation for three-dimensional partially grounded mooring system problems

A semi-analytical quasi-static formulation based on the catenary approach capable of solving three-dimensional partially grounded and fully suspended multi-leg mooring-system problems is presented in this paper. The advantage of the present formulation is that only a compact governing vector equation, derived in terms of grounded cable length and anchor tension vector, need to be solved for each mooring cable to determine its grounded and suspended body response, and only a small number of discrete segments are needed to predict its behaviour accurately due to its inherent slope continuity. In addition, it is capable of handling arbitrarily inclined seabed interaction effects, varying cross-sectional and material properties as well as external attachment objects. The generality of the present formulation allows quick parametric analysis of different forms of multi-leg mooring system configurations as well as different types of flexible riser systems to be carried out.

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