Unexpected Outcomes: Propagating Light Rays in the Atmosphere, a New Technique for Solving Partial Differential Equations

Problems that arise out of an industrial context normally have clear cut objectives, and the results are usually important in context but of limited general interest. Sometimes, however, the investigations lead to results that are both unexpected and of much broader interest. Two such investigations are described here. In the first problem an investigation of the propagation of light rays across the ocean leads to new results concerning optical distortion. In the second problem a surface tension investigation leads to an entirely new technique for solving partial differential equations

Analysis of coil slumping

Steel strip is usually stored as a coil, which will slump to some degree after the removal of the mandrel. More often than not, the amount of slumping is so minor that it is assumed not to have occurred. Occasionally, the amount, though minor, is sufficient to compromise the integrity of the cylindrical bore which compromises subsequent handling of the coil. In extreme situations, the slumping progresses to a complete collapse of the coil. Such a collapse is rare. It occurs when a coil cannot hold up its own mass and loses its circular cross-section. It is thought to be principally associated with the size and weight of the coil, inappropriate coiling tensions and/or poor re-coiler equipment design. Strip properties, especially inter-strip contact characteristics, have been demonstrated experimentally to be crucial determinants of whether or not coil collapse is likely to occur. The particular kind of slumping/collapse of interest to BlueScope Steel, who proposed this Study Group problem, is the minor slumping that compromises cylindrical bore integrity. It is referred to as coil slump. The Study Group was asked to investigate and model the phenomenon of coil slumping, and, if possible, to quantify the effect of critical parameters, especially coil mass, strip thickness and inter-strip friction. In particular, it was suggested that deliberations should aim to characterize the geometry of slumping and to predict the deformation profile at the innermost and outermost wraps. For BlueScope Steel, the long term objectives are: (1) the formulation of the governing equations for the stresses in a coil under self-weight, (2) the identification of analytical solutions and/or numerical schemes for the final coil shape after slumping, and (3) the formulation of exclusion rules-of-thumb which predict when a particular form of slump (oval or triangular) is likely to occur. The Study Group made some progress with (1), limited progress with (2) and most progress with (3). Though various computer programs were written to explore different force and energy balance scenarios, they only scratched the surface with regards to (2). Success with it is heavily dependent in substantial progress being made with (1). As explained in detail in the sequel, the Study Group’s deliberations resulted in an improved understanding of the coil slumping/collapse problem by identifying a number of specific issues that should be of direct assistance to BlueScope Steel’s future management of coil slumping/collapse. In particular, such issues included the need, from a modelling perspective, to draw a clear distinction between minor slumping and major slumping which can subsequently lead to collapse; the formulation of a heuristic hypothesis about the dynamics of coil slumping/collapse which can be compared with historical data and act act as a conceptualization guide for further investigations; the identification of a “tension-weight ratio” (R) as the relevant dimensionless group which represents an indicative rule-of-thumb which can be applied in practice; and proposed, on the basis of the hypothesis, an efficient procedure for recording collapse events and statistically identifying possible collapse situations

Extraction of Molasses from Sugar Crystals in a Centrifuge

Massecuite is a mixture of sugar crystals and molasses produced during the manufacture of sugar. A centrifuge, which is a rotating cylindrical basket, is used to separate the sugar crystals from the molasses. Water and steam are introduced into the centrifuge during the latter part of the process to further facilitate drainage. Models developed indicate that a fifty percent increase in molasses drainage can result from the addition of steam, whereas water does not significantly affect drainage

Global Vascular Guidelines on the Management of Chronic Limb-Threatening Ischemia

Chronic limb-threatening ischemia (CLTI)is associated with mortality, amputation, and impaired quality of life. These Global Vascular Guidelines (GVG)are focused on definition, evaluation, and management of CLTI with the goals of improving evidence-based care and highlighting critical research needs. The term CLTI is preferred over critical limb ischemia, as the latter implies threshold values of impaired perfusion rather than a continuum. CLTI is a clinical syndrome defined by the presence of peripheral artery disease (PAD)in combination with rest pain, gangrene, or a lower limb ulceration >2 weeks duration. Venous, traumatic, embolic, and nonatherosclerotic etiologies are excluded. All patients with suspected CLTI should be referred urgently to a vascular specialist. Accurately staging the severity of limb threat is fundamental, and the Society for Vascular Surgery Threatened Limb Classification system, based on grading of Wounds, Ischemia, and foot Infection (WIfI)is endorsed. Objective hemodynamic testing, including toe pressures as the preferred measure, is required to assess CLTI. Evidence-based revascularization (EBR)hinges on three independent axes: Patient risk, Limb severity, and ANatomic complexity (PLAN). Average-risk and high-risk patients are defined by estimated procedural and 2-year all-cause mortality. The GVG proposes a new Global Anatomic Staging System (GLASS), which involves defining a preferred target artery path (TAP)and then estimating limb-based patency (LBP), resulting in three stages of complexity for intervention. The optimal revascularization strategy is also influenced by the availability of autogenous vein for open bypass surgery. Recommendations for EBR are based on best available data, pending level 1 evidence from ongoing trials. Vein bypass may be preferred for average-risk patients with advanced limb threat and high complexity disease, while those with less complex anatomy, intermediate severity limb threat, or high patient risk may be favored for endovascular intervention. All patients with CLTI should be afforded best medical therapy including the use of antithrombotic, lipid-lowering, antihypertensive, and glycemic control agents, as well as counseling on smoking cessation, diet, exercise, and preventive foot care. Following EBR, long-term limb surveillance is advised. The effectiveness of nonrevascularization therapies (eg, spinal stimulation, pneumatic compression, prostanoids, and hyperbaric oxygen)has not been established. Regenerative medicine approaches (eg, cell, gene therapies)for CLTI should be restricted to rigorously conducted randomizsed clinical trials. The GVG promotes standardization of study designs and end points for clinical trials in CLTI. The importance of multidisciplinary teams and centers of excellence for amputation prevention is stressed as a key health system initiative. © 2019 Society for Vascular Surgery and European Society for Vascular Surger

Batch processing in a glass furnace

In a glass furnace solid batches of material are fed into a chamber and radiation heating applied. An individual batch is melted over the course of several minutes to form molten glass. A travelling front within the batch designates the progress of the melting, a process characterized by multiple radiation reflections. This results in an effective conductivity within the melting zone that is significantly larger than that in the unmelted batch. Approximations based on these disparate conductivities enable accurate explicit expressions for the almost constant melting front speed and the associated temperature profile to be derived. Our results compare favourably with existing numerical simulations of the process, with the advantage of being both analytic and relatively simple. These predictions may be useful in suggesting how a furnace might be most effectively controlled under varying batch conditions, as well as ensuring the quality of the glass sheets produced. doi:10.1017/S144618111500020

Truck safety barriers for mining sites

Safescape is a Western Australian company that has recently developed a device for improved safety in open-pit mines. Serious accidents can occur when large trucks veer off the roads running around the edge of the mine. The conventional technique to mitigate the risk is to pile waste rock to form a so-called bund on the edge of the road. This method is not fail safe though as vehicles can, and do, drive completely over the bund. In this paper, we describe a new device that consists of a row of filled polyethylene shell units which are linked together and sit on the road side of the rock bund. The vertical front face of the edge protector prevents out of control dump trucks from climbing over the bund and into the pit, so that they push against the barriers and heave the broken rock behind the bund. The models developed here suggest that the primary resistance to an impacting truck is provided by the large heaving force with the barrier simply facilitating this process. The theory indicates that the total resistance is independent of truck speed, meaning that simple barrier pushing experiments are sufficient to validate the analysis. The conclusions of the theory and field tests suggest that in a worst-case scenario involving the normal impact of a 500 tonne filled dump truck, the barriers and bund move a few metres before coming to rest. doi:10.1017/S144618111700028

Geothermal data analysis and optimization

The possibility of convective upwelling in the sedimentary Perth Basin, based on available data and simple models, was examined and its relative contribution to heat transport in a geothermal context assessed. The presence of such upwelling could greatly increase the viability of geothermal power extraction from the Basin. The onset of convection is determined by the Rayleigh number, which provides a measure for the balance between buoyancy driven upwelling and viscous resistance to flow. Being sedimentary, the porous aquifer system is layered and fractured so that the effects of anisotropy, especially that in permeability, need to be accounted for when determining the critical Rayleigh number. Variations in viscosity and the coefficient of thermal expansion also occur within the convection zone. Estimates were made for the relative size of the convective contribution to heat transport. The possibility of the surface detection of cellular convection and the effects of horizontal inflow into the convection zone were examined. References D. N. Smith, ``Cockburn No. 1 Well, Western Australia, Well Completion Report'', Western Australian Petroleum, Pty. Limited, October 1967. O. Kvernvold and P. A. Tyvand, ``Nonlinear thermal convection in anisotropic porous media'', J. Fluid Mech., 90, pp.609--624, 1979. E. R. Lapwood, ``Convection of a fluid in a porous medium'', Proc. Camb. Phil. Soc., 44, pp.508--521, 1948. R. McKibbin, ``Convection in an aquifer above a layer of heated impermeable bedrock'', NZ J. Sci., 26, pp.49--64, 1983. R. McKibbin, ``Thermal convection in layered and anisotropic porous media: a review'', In: Wooding, R. A. and I. White, (eds) ``Convective Flows in Porous Media'', Dept. Sci. Indust. Res., Wellington, New Zealand, pp.113--127, 1985. R. McKibbin, N. Hale, R. W. Style, and N. Walters, ``Convection and heat transport in layered sloping warm-water aquifers'', Journal of Porous Media, In press. D. A. Nield and A. Bejan, Convection in porous media, 3rd Edition, Springer, 2006. R. C. Ransom, Practical formation evaluation, Wiley, 1995. K. Regenauer-Lieb, H. T. Chua, X. Wang, F. G. Horowitz and J. Wellman, ``Direct heat geothermal applications in the Perth Basin of Western Australia'', Proc. 34th Annual Stanford Workshop on Geothermal Engineering, Chapter 14, Stanford University, California, 2009