Numerical solutions of the sediment conservation law: A review and improved formulation for coastal morphological modelling

Numerical solutions of the sediment conservation law are reviewed in terms of their application to bed update schemes in coastal morphological models. It is demonstrated that inadequately formulated numerical techniques lead to the introduction of diffusion, dispersion and the bed elevation oscillations previously reported in the literature. Four different bed update schemes are then reviewed and tested against benchmark analytical solutions. These include a first order upwind scheme, two Lax-Wendroff schemes and a non-oscillating centred scheme (NOCS) recently applied to morphological modelling by Saint-Cast [Saint-Cast, F., 2002. Modelisation de la morphodynamique des corps sableux en milieu littoral (Modelling of coastal sand banks morphodynamics), University Bordeaux 1, Bordeaux, 245 pp.]. It is shown that NOCS limits and controls numerical errors while including all the sediment flux gradients that control morphological change. Further, no post solution filtering is required, which avoids difficulties with selecting filter strength. Finally, NOCS is compared to a recent Lax-Wendroff scheme with post-solution filtering for a longer term simulation of the morphological evolution around a trained river entrance. (C) 2006 Elsevier B.V. All rights reserved.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

Sheet flow sediment transport under waves with acceleration skewness and boundary layer streaming

The effect of acceleration skewness on sheet flow sediment transport rates (q) over bar (s) is analysed using new data which have acceleration skewness and superimposed currents but no boundary layer streaming. Sediment mobilizing forces due to drag and to acceleration (similar to pressure gradients) are weighted by cosine and sine, respectively, of the angle phi(.)(tau)phi(tau) = 0 thus corresponds to drag dominated sediment transport, (q) over bar (s)similar to vertical bar u(infinity)vertical bar u(infinity), while phi(tau) = 90 degrees corresponds to total domination by the pressure gradients, (q) over bar similar to du(infinity)/dt. Using the optimal angle, phi = 51 degrees based on that data, good agreement is subsequently found with data that have strong influence from boundary layer streaming. Good agreement is also maintained with the large body of U-tube data simulating sine waves with superimposed currents and second-order Stokes waves, all of which have zero acceleration skewness. The recommended model can be applied to irregular waves with arbitrary shape as long as the assumption negligible time lag between forcing and sediment transport rate is valid. With respect to irregular waves, the model is much easier to apply than the competing wave-by-wave models. Issues for further model developments are identified through a comprehensive data review.

Large scale experiments on gravel and mixed beaches: Experimental procedure, data documentation and initial results

This paper provides information on the experimental set-up, data collection methods and results to date for the project Large scale modelling of coarse grained beaches, undertaken at the Large Wave Channel (GWK) of FZK in Hannover by an international group of researchers in Spring 2002. The main objective of the experiments was to provide full scale measurements of cross-shore processes on gravel and mixed beaches for the verification and further development of cross-shore numerical models of gravel and mixed sediment beaches. Identical random and regular wave tests were undertaken for a gravel beach and a mixed sand/gravel beach set up in the flume. Measurements included profile development, water surface elevation along the flume, internal pressures in the swash zone, piezometric head levels within the beach, run-up, flow velocities in the surf-zone and sediment size distributions. The purpose of the paper is to present to the scientific community the experimental procedure, a summary of the data collected, some initial results, as well as a brief outline of the on-going research being carried out with the data by different research groups. The experimental data is available to all the scientific community following submission of a statement of objectives, specification of data requirements and an agreement to abide with the GWK and EU protocols. (C) 2005 Elsevier B.V. All rights reserved.

Hydraulics of skimming flows on stepped chutes: The effects of inflow conditions?

Modern stepped spillways are typically designed for large discharge capacities corresponding to a skimming flow regime for which flow resistance is predominantly form drag. The writer demonstrates that the inflow conditions have some effect on the skimming flow properties. Boundary layer calculations show that the flow properties at inception of free-surface aeration are substantially different with pressurized intake. The re-analysis of experimental results highlights that the equivalent Darcy friction factor is f similar to 0.2 in average on uncontrolled stepped Chute and f similar to 0.1 on stepped chute with pressurized intake. A simple design chart is presented to estimate the residual flow velocity, and the agreement of the calculations with experimental results is deemed satisfactory for preliminary design.

Dam break wave of thixotropic fluid

Thixotropy is the characteristic of a fluid to form a gelled structure over time when it is not subjected to shearing, and to liquefy when agitated. Thixotropic fluids are commonly used in the construction industry (e.g., liquid concrete and drilling fluids), and related applications include some forms of mud flows and debris flows. This paper describes a basic study of dam break wave with thixotropic fluid. Theoretical considerations were developed based upon a kinematic wave approximation of the Saint-Venant equations down a prismatic sloping channel. A very simple thixotropic model, which predicts the basic theological trends of such fluids, was used. It describes the instantaneous state of fluid structure by a single parameter. The analytical solution of the basic flow motion and theology equations predicts three basic flow regimes depending upon the fluid properties and flow conditions, including the initial degree of jamming of the fluid (related to its time of restructuration at rest). These findings were successfully compared with systematic bentonite suspension experiments. The present work is the first theoretical analysis combining the basic principles of unsteady flow motion with a thixotropic fluid model and systematic laboratory experiments.

Estimation of water retention curve from mercury intrusion porosimetry and van Genuchten model

The water retention curve (WRC) is a hydraulic characteristic of concrete required for advanced modeling of water (and thus solute) transport in variably saturated, heterogeneous concrete. Unfortunately, determination by a direct experimental method (for example, measuring equilibrium moisture levels of large samples stored in constant humidity cells) is a lengthy process, taking over 2 years for large samples. A surrogate approach is presented in which the WRC is conveniently estimated from mercury intrusion porosimetry (MIP) and validated by water sorption isotherms: The well-known Barrett, Joyner and Halenda (BJH) method of estimating the pore size distribution (PSD) from the water sorption isotherm is shown to complement the PSD derived from conventional MIP. This provides a basis for predicting the complete WRC from MIP data alone. The van Genuchten equation is used to model the combined water sorption and MIP results. It is a convenient tool for describing water retention characteristics over the full moisture content range. The van Genuchten parameter estimation based solely on MIP is shown to give a satisfactory approximation to the WRC, with a simple restriction on one. of the parameters.

Simulation study of ammonia adsorption on graphitized carbon black

GCMC simulations are applied to the adsorption of sub-critical ammonia on graphitized carbon black at 240 K. The carbon black was modelled both with and without carbonyl functional groups. Large differences are seen between the amount adsorbed for different carbonyl configurations at low pressure (P < 10kPa). Once a single layer is formed on the carbon black, the adsorption behaviour is similar between the model surfaces with and without functional groups. Simulation isotherms are qualitatively similar to the few experimental isotherms available in the literature for ammonia on highly graphitized carbon black. The mode of adsorption up to monolayer coverage is exhaustively shown to be two-dimensional clustering using various techniques. A comparison between experiment and simulation isosteric heats shows that a surface without functional groups cannot reproduce the experimental isosteric heats of adsorption, even comparing with the experimental results of carbon black heat treated at 3373 K. The addition of carbonyls produces isosteric heats with similar features to those in the literature if the separation between the carbonyls is small.

Effect of pore constriction on adsorption behaviour in nanoporous carbon slit pore: a computer simulation

A Grand Canonical Monte Carlo simulation (GCMC) method is used to study the effects of pore constriction on the adsorption of argon at 87.3 K in carbon slit pores of infinite and finite lengths. It is shown that the pore constriction affects the pattern of adsorption isotherm. First, the isotherm of the composite pore is greater than that of the uniform pore having the same width as the larger cavity of the composite pore. Secondly, the hysteresis loop of the composite pore is smaller than and falls between those of uniform pores. Two types of hysteresis loops have been observed, irrespective of the absence or presence of constriction and their presence depend on pore width. One hysteresis loop is associated with the compression of adsorbed particles and this phenomenon occurs after pore has been filled with particles. The second hysteresis loop is the classical condensation-evaporation loop. The hysteresis loop of a composite pore depends on the sizes of the larger cavity and the constriction. Generally, it is found that the pore blocking effect is not manifested in composite slit pores, and this result does not support the traditional irkbottle pore hypothesis.

Modeling of adsorption on nongraphitized carbon surface: GCMC simulation studies and comparison with experimental data

We model nongraphitized carbon black surfaces and investigate adsorption of argon on these surfaces by using the grand canonical Monte Carlo simulation. In this model, the nongraphitized surface is modeled as a stack of graphene layers with some carbon atoms of the top graphene layer being randomly removed. The percentage of the surface carbon atoms being removed and the effective size of the defect ( created by the removal) are the key parameters to characterize the nongraphitized surface. The patterns of adsorption isotherm and isosteric heat are particularly studied, as a function of these surface parameters as well as pressure and temperature. It is shown that the adsorption isotherm shows a steplike behavior on a perfect graphite surface and becomes smoother on nongraphitized surfaces. Regarding the isosteric heat versus loading, we observe for the case of graphitized thermal carbon black the increase of heat in the submonolayer coverage and then a sharp decline in the heat when the second layer is starting to form, beyond which it increases slightly. On the other hand, the isosteric heat versus loading for a highly nongraphitized surface shows a general decline with respect to loading, which is due to the energetic heterogeneity of the surface. It is only when the fluid-fluid interaction is greater than the surface energetic factor that we see a minimum-maximum in the isosteric heat versus loading. These simulation results of isosteric heat agree well with the experimental results of graphitization of Spheron 6 (Polley, M. H.; Schaeffer, W. D.; Smith, W. R. J. Phys. Chem. 1953, 57, 469; Beebe, R. A.; Young, D. M. J. Phys. Chem. 1954, 58, 93). Adsorption isotherms and isosteric heat in pores whose walls have defects are also studied from the simulation, and the pattern of isotherm and isosteric heat could be used to identify the fingerprint of the surface.

New method to determine PSD using supercritical adsorption: Applied to methane adsorption in activated carbon

Adsorption of supercritical fluids is increasingly carried out to determine the micropore size distribution. This is largely motivated by the advances in the use of supercritical adsorption in high energy applications, such as hydrogen and methane storage in porous media. Experimental data are reported as mass excess versus pressure, and when these data are matched against the theoretical mass excess, significant errors could occur if the void volume used in the calculation of the experimental mass excess is incorrectly determined [Malbrunot, P.; Vidal, D.; Vermesse, J.; Chahine, R.; Bose, T. K. Langmuir 1997, 13, 539]. 1 The incorrect value for the void volume leads to a wrong description of the maximum in the plot of mass excess versus pressure as well as the part of the isotherm over the pressure region where the isotherm is decreasing. Because of this uncertainty in the maximum and the decreasing part of the isotherm, we propose a new method in which the problems associated with this are completely avoided. Our method involves only the relationship between the amount that is introduced into the adsorption cell and the equilibrium pressure. This information of direct experimental data has two distinct advantages. The first is that the data is the raw data without any manipulation (i.e., involving further calculations), and the second one is that this relationship always monotonically increases with pressure. We will illustrate this new method with the adsorption data of methane in a commercial sample of activated carbon.

Adsorption in slit pores and pore-size distribution: A molecular layer structure theory

A new approach is developed to analyze the thermodynamic properties of a sub-critical fluid adsorbed in a slit pore of activated carbon. The approach is based on a representation that an adsorbed fluid forms an ordered structure close to a smoothed solid surface. This ordered structure is modelled as a collection of parallel molecular layers. Such a structure allows us to express the Helmholtz free energy of a molecular layer as the sum of the intrinsic Helmholtz free energy specific to that layer and the potential energy of interaction of that layer with all other layers and the solid surface. The intrinsic Helmholtz free energy of a molecular layer is a function (at given temperature) of its two-dimensional density and it can be readily obtained from bulk-phase properties, while the interlayer potential energy interaction is determined by using the 10-4 Lennard-Jones potential. The positions of all layers close to the graphite surface or in a slit pore are considered to correspond to the minimum of the potential energy of the system. This model has led to accurate predictions of nitrogen and argon adsorption on carbon black at their normal boiling points. In the case of adsorption in slit pores, local isotherms are determined from the minimization of the grand potential. The model provides a reasonable description of the 0-1 monolayer transition, phase transition and packing effect. The adsorption of nitrogen at 77.35 K and argon at 87.29 K on activated carbons is analyzed to illustrate the potential of this theory, and the derived pore-size distribution is compared favourably with that obtained by the Density Functional Theory (DFT). The model is less time-consuming than methods such as the DFT and Monte-Carlo simulation, and most importantly it can be readily extended to the adsorption of mixtures and capillary condensation phenomena.

Features of nitrogen adsorption on nonporous carbon and silica surfaces in the framework of classical density functional theory

Equilibrium adsorption data of nitrogen on a series of nongraphitized carbon blacks and nonporous silica at 77 K were analyzed by means of classical density functional theory to determine the solid-fluid potential. The behavior of this potential profile at large distance is particularly considered. The analysis of nitrogen adsorption isotherms seems to indicate that the adsorption in the first molecular layer is localized and controlled mainly by short-range forces due to the surface roughness, crystalline defects, and functional groups. At distances larger than approximately 1.3-1.5 molecular diameters, the adsorption is nonlocalized and appears as a thickening of the adsorbed film with increasing bulk pressure in a relatively weak adsorption potential field. It has been found that the asymptotic decay of the potential obeys the power law with the exponent being -3 for carbon blacks and -4 for silica surface, which signifies that in the latter case the adsorption potential is mainly exerted by surface oxygen atoms. In all cases, the absolute value of the solid-fluid potential is much smaller than that predicted by the Lennard-Jones pair potential with commonly used solid-fluid molecular parameters. The effect of surface heterogeneity on the heat of adsorption is also discussed.