J.R. Chaplin

Nonlinear forces on a horizontal cylinder beneath waves

Measurements of forces experienced by a submerged horizontal cylinder with its axis parallel to the crests in deep-water waves reveal nonlinear components with frequencies up to three times the fundamental wave frequency. The dominant nonlinear contribution to the loading is a t the third order in the wave amplitude, and, for Keulegan4arpenter numbers approaching 2, its magnitude was found to be as much as one-half that of the inertia force. It is suggested that the third-order force is associated with circulation generated by steady streaming in the oscillatory boundary layer on the cylinder. At higher Keulegan-Carpenter numbers, form drag becomes increasingly important, and velocity measurements close to the cylinder show the rapid development of the wake. Observations of nonlinear features of the transmitted waves are also discussed.

Void fraction measurements in breaking waves

This paper describes detailed measurements and analysis of the time-varying distribution of void fractions in three different breaking waves under laboratory conditions. The measurements were made with highly sensitive optical fibre phase detection probes and document the rapid spatial and temporal evolutions of both the bubble plume generated beneath the free surface and the splashes above. Integral properties of the measured void fraction fields reveal a remarkable degree of similarity between characteristics of the two-phase flow in different breaker types as they evolve with time. Depending on the breaker type, the energy expended in entraining air and generating splash accounts for a minimum of between 6.5 and 14% of the total energy dissipated during wave breaking.

Measurements and predictions of forces, pressures and cavitation on 2-D sections suitable for marine current turbines:

An investigation has been carried out into the lift, drag and cavitation characteristics of two-dimensional foil sections, which may typically be used as a starting point in the design of blade sections for marine current turbines. Cavitation tunnel experiments and numerical predictions using a panel code were carried out on four representative sections derived from the NACA series 4415, 6615, 63—215 and 63—815. The experimental lift and drag results show reasonable correlation with published wind tunnel data. The sections were modelled numerically using the two-dimensional panel code XFoil. The numerical cavitation predictions in most cases showed satisfactory agreement with the experiments and it is considered that such predictions could be used with reasonable confidence for predicting cavitation at the preliminary design stage. Overall, the results of the investigation provide detailed information that should assist in the design and operation of marine current turbines.

Ringing of a vertical cylinder in waves

This paper analyses the results of two series of experiments concerned with the response of a single vertical cylinder in the inertia regime in steep non-breaking waves. We recorded first the loading on a cylinder when it was held stationary, and secondly, its response in the same waves when it was pivoted just above the floor of the wave flume, and supported at the top by springs in the horizontal plane. Spring stiffnesses were set to achieve natural frequencies (measured in still water) in the range between 3 and 11 times the dominant wave frequency. The experiments were repeated with cylinders of three different diameters. Peak loading on stationary cylinders was found to exceed the predictions of a Morison model (based on kinematics computed from a numerical model of the measured waves), though improvements were achieved through the inclusion of slender-body terms. Measured ringing responses are generally in good agreement with those computed on a quasi-static basis from the measured loading history, but in some conditions, particularly at low frequency ratios, there is clearly some feedback from the motion to the excitation. Peak accelerations in the steepest waves are found to be limited approximately to those that would occur if the maximum loading were applied as a step change. Particular attention is given to a rapid cycle of loading that occurs after the crest has passed the cylinders axis, and to images of the flow around the cylinder at the water surface.

Developments of stream-function wave theory

Recent work on the problem of the periodic wave of permanent form has revealed some unexpected characteristics which are not predicted by any of the wave theories in engineering use. Of these, the stream-function wave theory is the most accurate, and it is shown in this paper by means of a reformulated method of application to be capable of predicting correctly the behaviour of steep and near-breaking waves. Errors in stream-function wave-theory tables are assessed and found to be particularly significant for very steep waves, when crest particle velocities are under-estimated by 25% or more. As a development of the modified method of application, an approximate stream-function wave theory is presented. It permits a solution to be obtained for given wave conditions in any depth of water but requires much more modest computer resources than the full stream-function theory.

Air-water interface dynamic and free surface features in hydraulic jumps

Following previous experimental works (Mouaze et al., J. Fulids Engng. ASME 127(6) (2005) 1191–1193; Murzyn et al., Int. J. Multiphase Flow, 31(1) (2005) 141–154) on gas fraction characterisation in hydraulic jumps, the present paper aims to investigate free surface properties developing in these flows. Indeed, air–water interface exhibits a wide range of frequencies that free surface probes are not always enough accurate to follow. As a solution, two new free surface wire gauges (thin wires, φ = 0.05 mm, 1mm apart) have been built and calibrated. Accurate measurements of free surface fluctuations have been obtained with frequency resolution up to 12 Hz. Two sets of experiments have been made depending on Froude (Fr) and Weber (We) numbers. Experimental results showthat free surface mean and turbulent profiles exhibit discontinuities at the front of the toe characterized by a sudden high level of turbulence downstream followed by a zone of dissipation. Furthermore, free surface length scales have been estimated from correlation measurements. Similar features are found according to Fr andWe. Good agreement is shown with results deduced from a video analysis technique (Mouaze et al., J. Fulids Engng. ASME 127(6) (2005) 1191–1193). Lastly, comparison is made with Brocchini and Peregrine (Brocchini and Peregrine, J. Fluid Mech. 449 (2001a) 225–254; 449 (2001b) 255–290) depicting similar shapes for behaviour of vertical velocity fluctuations (w ′) as a function of longitudinal free surface length scale.

Mass transport around a horizontal cylinder beneath waves

Around a horizontal cylinder submerged beneath waves with its axis parallel to the wave crests there exists, owing to streaming flow in the boundary layer, circulation with the same sense of rotation as that of the orbital motion in the waves. Experimental results, for conditions in which the effects of separation are not important, confirm theoretical predictions of the mass-transport velocity at the outer edge of the oscillatory boundary layer. Pressure measurements on the cylinder reveal a nonlinear component which is interpreted as a consequence of circulation induced by steady streaming.

Level-Set Computations of Free Surface Rotational Flows

A numerical method is developed for modelling the violent motion and fragmentation of an interface between two fluids. The flow field is described through the solution of the Navier-Stokes equations for both fluids (in this case water and air), and the interface is captured by a Level-Set function. Particular attention is given to modelling the interface, where most of the numerical approximations are made. Novel features are that the reintialization procedure has been redefined in cells crossed by the interface; the mass across the interface has been smoothed using an exponential function to obtain an equally stiff variation of the density and of its inverse; and we have used an Essentially Non-Oscillatory scheme with a limiter whose coefficients depend on the distance function at the interface. The results of the refined scheme have been compared with those of the basic scheme and with other numerical solvers, with favourable results. Besides the case of the vertical surface-piercing plate (for which new laboratory measurements were carried out) the numerical method is applied to problems involving a dam-break and wall-impact, the interaction of a vortex with a free surface, and the deformation of a cylindrical bubble. Promising agreement with other sources of data is found in every case.

Rubber tubes in the sea

A long tube with elastic walls containing water is immersed in the sea aligned in the direction of wave travel. The waves generate bulges that propagate at a speed determined by the distensibility of the tube. If the bulge speed is close to the phase velocity of the waves, there is a resonant transfer of energy from the sea wave to the bulge. At the end of the tube, useful energy can be extracted. This paper sets out the theory of bulge tubes in the sea, and describes some experiments on the model scale and practical problems. The potential of a full-scale device is assessed.

Orbital flow around a circular cylinder. Part 2. Attached flow at larger amplitudes

A time-stepping numerical model of uniform circular orbital flow around a cylinder provides results which are compared with the steady-state predictions of a boundary-layer solution by Riley. At small amplitudes of motion excellent agreement is found in most respects, but in the numerical model the outer recirculating flow and related components of loading do not reach a steady state after any finite time. At a Stokes parameter ? of 500, the boundary-layer approach remains reasonably accurate for amplitudes of motion up to about 8 % of the cylinder diameter; for amplitudes up to twice this at the same value of ? the flow remains largely attached. The strength of the outer recirculating flow is enhanced by nonlinear interactions, but the computed nonlinear loading exceeds that observed in experiments. Flow visualization shows a three-dimensional structure in the flow, and it is argued that this has an important effect on the loading that cannot yet be predicted. A computed force component at a frequency of about 30 % of that of the ambient flow is related to the retrogressive motion of vortex structures around the cylinder.