Kenneth C. Wilson

Friction of wave-induced sheet flow

Abstract For many years it has been assumed that mobile beds obey a rough-boundary friction law. Recently it was shown analytically, and verified by comparison with experimental results, that this assumption is not correct for sheet flow. For this type of flow, where the bed-load particles travel in a layer much thicker than the grain diameter, the equivalent roughness increases in direct proportion to the shear stress, and may become very large. The analysis is now extended from unidirectional to oscillatory motion, evaluating sheet-flow friction and defining the region where this type of flow occurs.

Effects of wave asymmetry on sheet flow

Abstract In earlier work the concepts of unidirectional sheet flow were extended to sinusoidal oscillatory motion. The analysis is now generalised to deal with asymmetric and irregular waves, obtaining relationships for friction factor and for the transition from bedforms to sheet flow. Comparison is made with experimental results obtained at Queens University, Canada, and with data from Delft Hydraulics in the Netherlands. Asymmetric waves also produce net bed-load transport, which is analysed here and compared with the Delft Hydraulics data. It is found that the net bed-load transport rate is proportional to 〈 U3〉, the third moment of near-bed free-stream velocity.

Operating points for pipelines carrying concentrated heterogeneous slurries

Early studies of slurry pipeline systems were based on moderate volumetric concentrations of solids (say up to 18%), for which the excess pressure gradient caused by solids is proportional to concentration. Much larger concentrations now coming into common use show more complicated behaviour. An algebraic analysis is developed to determine desirable operating points and associated energy consumption for settling slurries. This deals initially with the simple proportional behaviour, and then is extended to other cases. Comparison is made to recent experiments using highly concentrated settling slurries with various particle gradings. It is found that near-uniform gradings tend to have high frictional losses, while very broad gradings can give rise to energy-efficient transport at high concentrations.

BEHAVIOUS OF MOBILE BEDS AT HIGH SHEAR STRESS

Tanah Lot Temple is situated in Tabanan Regency - Bali, on the coast of the Indonesian Ocean. Due to continuous wave attack, wind force, and weathering of the rock bank where the Temple stands, abrasion has occured which is more and more threatening the existence of the Temple. Considering that Tanah Lot Temple is a sacred place for the Hindu Balinese people and a place of high cultural value, and also an important tourism, steps to save the Temple are imperative. The Central as well as the Regional Authorities, and also the Bali nese community are very much interested in the effort to keep the Temple intact. Measures have been undertaken to protect both the seaside and land-side banks of the Temple rock bank. This paper only discusses counter measures of the sea —side bank of the Temple.

Coarse-particle pipeline transport: Effect of particle degradation on friction

Abstract When coarse particles are transported in pipes, mechanical friction occurs near the pipe invert, and hence large pressure gradients are required. This behaviour is described by the sliding-bed model, from which an approximate expression for the solids effect has been derived. Pilot-plant tests were carried out with coarse gravel in a large recirculating pipe loop. Initially, all particles were larger than 10 mm in diameter, and the solids effect was in good accord with the equation derived from the sliding-bed model. However, as the testing continued the particles degraded, and the pressure gradient diminished significantly. It was seen how the solids effect changes with exposure time or, equivalently, with the number of passes through the pump.

Effect of broad particle grading on slurry stratification ratio and scale-up

Abstract Analysis of the two basic mechanisms of particle support (intergranular contact and fluid turbulence) led earlier to a method of predicting slurry stra

ECONOMIC APPROACH TO OPTIMIZING DESIGN PARAMETERS

The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.The calculation of turbulent flow using Naviers equations assumes the introduction of a turbulent viscosity coefficient the value of which is normally constant, conforming with Boussinesqs hypothesis. It was shown that setting aside this hypothesis, a velocity profile quite different to that resulting from the classic theory is obtained in the case of flow induced by wind. This result appears to be confirmed by the tests carried out in the Mediterranean. The advantage of this method is that it gives the vertical turbulent diffusion which is of particular interest to pollution studies.In the numerical method of prediction of wind waves in deep water, Hasselmanns nonlinear interaction theory is applied. This method assumes the energy balance of individual component waves. However, the total energy balance must exist in the transformation of irregular waves in shoaling water. In this investigation, experiments were carried out on the transformations in shoaling water of composite waves having two components and random waves having one or two main peaks. It was found that the elementary component wave height of the composite waves and the elementary peak power of the random waves decrease with decrease in the water depth. This reason can be explained qualitatively by the theory of the elementary component wave height change of finite amplitude waves in shoaling water. The secondary component wave height of the composite waves and the secondary peak power of the random waves increase with decrease in the water depth. This can be explained qualitatively by Hamadas theory of nonlinear interaction in uniform depth.Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. • It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length. INTRODUCTION Many studies have been done on the impulsive pressures acting on a vertical wall, but there has been very little investigation of breaking wave forces on a cell-type structure. The breaking wave forces should be taken into consideration all the same in the design of pile-type or cell-type structures in nearshore area, because breaking waves cause extreme shock pressures on a cell structure asThe air bubble plume induced by the steady release of air into water has been analyzed with an integral technique based on the equations for conservation of mass, momentum and buoyancy. This approach has been widely used to study the behavior of submerged turbulent jets and plumes. The case of air-bubble induced flow, however, includes additional features. In this study the compressibility of the air and the differential velocity between the rising air bubbles ,and the water are introduced as basic propertie s of the air bubble plume in addition to a fundamental coefficient of entrainment and a turbulent Schmidt number characterizing the lateral spreading of the air bubbles. Theoretical solutions for twoand three-dimensional air-bubble systems in homogeneous, stagnant water are presented in both dimensional and normalized form and compared to existing experimental data. The further complication of a stratified environment is briefly discussed since this case is of great practical interest. This paper is to be considered as a progress report, as future experimental verification of various hypotheses is needed.

Net positive suction head requirement for centrifugal slurry pumps

The objective of this chapter is to present controlled performance results for a typical phosphate matrix pump under normal and vacuum-limiting suction conditions. The experiments were carried out at the GIW Hydraulic Testing Laboratory, Georgia U.S.A. In the pit, there are additional entrance losses caused by vertical bars, which prevent oversized roots and other debris from entering the suction pipe. To simulate suction-side conditions in the laboratory, a valve was installed in the suction pipe, which can be closed to induce cavitation. The majority of industrial slurry-transport installations tend to be free of cavitation and related problems with pump suction performance, but in many other applications cavitation is important and must be considered in system design. In disposal pipelines operated by the dredging industry and also in pipeline applications such as those used by the phosphate extraction industry (for example in Florida, U.S.A.), the first (upstream) pump is susceptible to highly sub-atmospheric suction pressures. In these cases, cavitation is a common occurrence, and may be significant in determining the costs of operation. As the pressure on the suction side of a centrifugal pump gradually drops to greater sub-atmospheric values (i.e. the suction-side vacuum increases) there comes a point where cavitation begins, and this is followed by drops in both the efficiency of the pump and the head which it produces. This decrease in head is associated with a drop in the discharge rate (flow), but this effect may be small initially if other pumps along the pipeline are operating without cavitation. Controlling the speed of one or more of the pumps can prevent the dropoff in flow, but the cavitation-induced reduction in efficiency increases the power requirement and hence the cost of operating the pipeline.