Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

Modelling trickle irrigation: Comparison of analytical and numerical models for estimation of wetting front position with time

Irrigation practices that are profligate in their use of water have come under closer scrutiny by water managers and the public. Trickle irrigation has the propensity to increase water use efficiency but only if the system is designed to meet the soil and plant conditions. Recently we have provided a software tool, WetUp (http://www.clw.csiro.au/products/wetup/), to calculate the wetting patterns from trickle irrigation emitters. WetUp uses an analytical solution to calculate the wetted perimeter for both buried and surface emitters. This analytical solution has a number of assumptions, two of which are that the wetting front is defined by water content at which the hydraulic conductivity (K) is I mm day(-1) and that the flow occurs from a point source. Here we compare the wetting patterns calculated with a 2-dimensional numerical model, HYDRUS2D, for solving the water flow into typical soils with the analytical solution. The results show that the wetting patterns are similar, except when the soil properties result in the assumption of a point source no longer being a good description of the flow regime. Difficulties were also experienced with getting stable solutions with HYDRUS2D for soils with low hydraulic conductivities. (c) 2005 Elsevier Ltd. All rights reserved.

Modelling of different measures for improving removal in a stormwater pond

The effect of retrofitting an existing pond on removal efficiency and hydraulic performance was modelled using the commercial software Mike21 and compartmental modelling. The Mike21 model had previously been calibrated on the studied pond. Installation of baffles, the addition of culverts under a causeway and removal of an existing island were all studied as possible improvement measures in the pond. The subsequent effect on hydraulic performance and removal of. suspended solids was then evaluated. Copper, cadmium, BOD, nitrogen and phosphorus removal were,also investigated for that specific improvement measure showing the best results. Outcomes of this study reveal that all measures increase the removal efficiency of suspended solids. The hydraulic efficiency is improved for all cases, except for the case where the island is removed. Compartmental modelling was also used to evaluate hydraulic performance and facilitated a better understanding of the way each of the different measures affected the flow pattern and performance. It was concluded that the installation of baffles is the best of the studied measures resulting in a reduction in the annual load on the receiving lake by approximately 8,000 kg of suspended solids (25% reduction of the annual load), 2 kg of copper (10% reduction of the annual load) and 600 kg of BOD (10% reduction of the annual load).

Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications

Soft tissue engineering presents significant challenges compared to other tissue engineering disciplines such as bone, cartilage or skin engineering. The very high cell density in most soft tissues, often combined with large implant dimensions, means that the supply of oxygen is a critical factor in the success or failure of a soft tissue scaffold. A model is presented for oxygen diffusion in a 15-60 mm diameter dome-shaped scaffold fed by a blood vessel loop at its base. This model incorporates simple models for vascular growth, cell migration and the effect of cell density on the effective oxygen diffusivity. The model shows that the dynamic, homogeneous cell seeding method often employed in small-scale applications is not applicable in the case of larger scale scaffolds such as these. Instead, we propose the implantation of a small biopsy of tissue close to a blood supply within the scaffold as a technique more likely to be successful. Crown Copyright (c) 2005 Published by Elsevier Ltd. All rights reserved.

Swash overtopping and sediment overwash on a truncated beach

New experimental laboratory data are presented on swash overtopping and sediment overwash on a truncated beach, approximating the conditions at the crest of a beach berm or inter-tidal ridge-runnel. The experiments provide a measure of the uprush sediment transport rate in the swash zone that is unaffected by the difficulties inherent in deploying instrumentation or sediment trapping techniques at laboratory scale. Overtopping flow volumes are compared with an analytical solution for swash flows as well as a simple numerical model, both of which are restricted to individual swash events. The analytical solution underestimates the overtopping volume by an order of magnitude while the model provides good overall agreement with the data and the reason for this difference is discussed. Modelled flow velocities are input to simple sediment transport formulae appropriate to the swash zone in order to predict the overwash sediment transport rates. Calculations performed with traditional expressions for the wave friction factor tend to underestimate the measured transport. Additional sediment transport calculations using standard total load equations are used to derive an optimum constant wave friction factor of f(w)=0.024. This is in good agreement with a broad range of published field and laboratory data. However, the influence of long waves and irregular wave run-up on the overtopping and overwash remains to be assessed. The good agreement between modelled and measured sediment transport rates suggests that the model provides accurate predictions of the uprush sediment transport rates in the swash zone, which has application in predicting the growth and height of beach berms. (c) 2005 Elsevier B.V. All rights reserved.

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

Dynamic rupture in a 3-D particle-based simulation of a rough planar fault

An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particle-based numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.

Measurement and modelling of controlled beach groundwater levels under wave action

New laboratory scale experimental data are presented on the forcing of beach groundwater levels by wave run-up. The experimental setup simulates a coastal barrier dividing the ocean from a relatively constant back beach water level, conditions approximating a closed off lagoon system or beach aquifer. The data are critically compared to an advanced numerical model for simulating wave and beach groundwater interaction in the coastal zone, and provide the first experimental verification of such a model. Overall model-data comparisons are good, but some systematic discrepancies are apparent, and reasons for these are discussed.

Numerical simulation of abrupt contraction flows using the Double Convected Pom-Pom model

The Double Convected Pom-Pom model was recently introduced to circumvent some numerical and theological defects found in other formulations of the Pom-Pom concept. It is used here for the simulation of a benchmark problem: the flow in an abrupt planar contraction. The predictions are compared with birefringence measurements and show reasonable quantitative agreement with experimental data. A parametric study is also carried out with the aim of analysing the effect of the branching parameter on vortex dynamics and extrudate swell. The results show that the Double Convected Pom-Pom model (DCPP) model is able to discriminate between branched and linear macromolecular structures in accordance with experimental observations. In that respect, the role of the extensional properties in determining complex flow behaviour is stressed. Also, the ratio of the first normal stress difference to the shear stress appears to play a major role in die swell observation. For the time being, the role of the second normal stress difference appears to be less obvious to evaluate in this complex flow. (C) 2004 Elsevier B.V. All rights reserved.