The method of fundamental solutions for free surface Stefan problems

In this paper, free surface problems of Stefan-type for the parabolic heat equation are investigated using the method of fundamental solutions. The additional measurement necessary to determine the free surface could be a boundary temperature, a heat flux or an energy measurement. Both one- and two-phase flows are investigated. Numerical results are presented and discussed.

Deflection of jets discharged into a reservoir with a free surface

Deflections of jets discharged into a reservoir with a free surface are investigated numerically. The jets are known to deflect towards either side of the free surface or the bottom, whose direction is not determined uniquely in some experimental conditions, i.e. there are multiple stable states realizable in the same condition. The origin of the multiple stable states is explored by utilizing homotopy transformations in which the top boundary of the reservoir is transformed from a rigid to a free boundary and also the location of the outlet throat is continuously moved from mid-height to the top. We depicted bifurcation diagrams of the flow compiling the data of numerical simulations, from which we identified the origin as an imperfect pitchfork bifurcation, and obtained an insight into the mechanism for the direction to be determined. The parameter region where such multiple stable states are possible is also delimited. © 2011 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

The performance of stabilized and unstabilized minestone in an aqueous environment with emphasis on its erosion resistance

Britain's sea and flood defences are becoming increasingly aged and as a consequence, more fragile and vulnerable. As the government's philosophy on resources shifts against the use of prime quarried and dredged geo-materials, the need to find alternative bulk materials to bolster Britain's prone defences becomes more pressing. One conceivable source for such a material is colliery waste or minestone. Although a plethora of erosion-abrasion studies have been carried out on soils and soil-cements, very little research has been undertaken to determine the resistance of minestone and its cement stabilized form to the effects of water erosion. The thesis reviews the current extent to which soil-cements, minestone and cement stabilized minestone (CSM) have been employed for hydraulic construction projects. A synopsis is also given on the effects of immersion on shales, mudstones and minestone, especially with regard to the phenomena of slaking. A laboratory study was undertaken featuring a selection of minestones from several British coalfields. The stability of minestone and CSM in sea water and distilled water was assessed using slaking tests and immersion monitoring and the bearing on the use of these materials for hydraulic construction is discussed. Following a review of current erosion apparatus, the erosion/abrasion test and rotating cylinder device were chosen and employed to assess the erosion resistance of minestone and CSM. Comparison was made with a sand mix designed to represent a dredged sand, the more traditional, bulk hydraulic construction material. The results of the erosion study suggest that both minestone and CSM were more resistant to erosion and abrasion than equivalently treated sand mixes. The greater resistance of minestone to the agents of erosion and abrasion is attributed to several factors including the size of the particles, a greater degree of cement bonding and the ability of the minestone aggregate to absorb, rather than transmit shock waves produced by impacting abrasive particles. Although minestone is shown to be highly unstable when subjected to cyclic changes in its moisture content, the study suggests that even in an intertidal regime where cyclic immersion does takes place, minestone will retain sufficient moisture within its fabric to prevent slaking from taking place. The slaking study reveals a close relationship between slaking susceptibility and total pore surface area as revealed by porosimetry. The immersion study shows that although the fabric of CSM is rapidly attacked in sea water, a high degree of the disruption is associated with the edges and corners of samples (ie. free surface) while the integrity of the internal fabric remains relatively intact. CSM samples were shown to be resilient when subjected to immersion in distilled water. An overall assessment of minestone and CSM would suggest that with the implementation of judicious selection and appropriate quality control they could be used as alternative materials for flood and sea defences. It is believed, that even in the harsh regime of a marine environment, CSM could be employed for temporary and sacrificial schemes.

Discrete element modelling of a rotating drum and drum granulation

This thesis reports the results of DEM (Discrete Element Method) simulations of rotating drums operated in a number of different flow regimes. DEM simulations of drum granulation have also been conducted. The aim was to demonstrate that a realistic simulation is possible, and further understanding of the particle motion and granulation processes in a rotating drum. The simulation model has shown good qualitative and quantitative agreement with other published experimental results. A two-dimensional bed of 5000 disc particles, with properties similar to glass has been simulated in the rolling mode (Froude number 0.0076) with a fractional drum fill of approximately 30%. Particle velocity fields in the cascading layer, bed cross-section, and at the drum wall have shown good agreement with experimental PEPT data. Particle avalanches in the cascading layer have been shown to be consistent with single layers of particles cascading down the free surface towards the drum wall. Particle slip at the drum wall has been shown to depend on angular position, and ranged from 20% at the toe and shoulder, to less than 1% at the mid-point. Three-dimensional DEM simulations of a moderately cascading bed of 50,000 spherical elastic particles (Froude number 0.83) with a fractional fill of approximately 30% have also been performed. The drum axis was inclined by 50 to the horizontal with periodic boundaries at the ends of the drum. The mean period of bed circulation was found to be 0.28s. A liquid binder was added to the system using a spray model based on the concept of a wet surface energy. Granule formation and breakage processes have been demonstrated in the system.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.