Transition in convective flows heated internally

The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.

Mechanics of longitudinal rolling of tube through three-grooved rolls

This investigation examined the process of the longitudinal rolling of tubes through a set of three driven grooved rolls. Tubes were rolled with or without internal support i.e. under mandrel rolling or sinking conditions. Knowledge was required of the way in which the roll separating force and rolling torque vary for different conditions of rolling. The objective of this work being to obtain a better understanding and optimization of the mechanics of the process. The design and instrumentation of a complete experimental three-roll mill for the rolling of lead tube as an analogue material for hot steel, with the measurement of the individual roll force and torque is described. A novel type of roll load cell was incorporated and its design and testing discussed. Employing three roll sizes of 170 mm, 255 mm and 340 mm shroud diameter, precise tube specimens of various tube diameter to thickness ratios were rolled under sinking and mandrel rolling conditions. To obtain an indication of the tube-roll contact areas some of the specimens were partially rolled. For comparative purposes the remaining tubes were completely rolled as a single pass. The roll forces, torques and tube parameters e.g. reduction of area, D/t ratio, were collated and compared for each of the three roll diameters considered. The influence of friction, particularly in the mandrel rolling process, was commented upon. Theoretical studies utilising the equilibrium and energy methods were applied to both the sinking and mandrel rolling processes. In general, the energy approach gave better comparison with experiment, especially for mandrel rolling. The influence of the tube deformation zones on the two processes was observed and on the subsequent modification of the tube-roll arc contact length. A rudimentary attempt was made in the theoretical sinking analysis to allow for the deformation zone prior to roll contact; some success was noted. A general survey of the available tube rolling literature, for both the sinking and mandrel processes has been carried out.

Computer aided design and manufacture of form-rolls

Cold roll forming of thin-walled sections is a very useful process in the sheet metal industry. However, the conventional method for the design and manufacture of form-rolls, the special tooling used in the cold roll forming process, is a very time consuming and skill demanding exercise. This thesis describes the establishment of a stand-alone minicomputer based CAD/CAM system for assisting the design and manufacture of form-rolls. The work was undertaken in collaboration with a leading manufacturer of thin-walled sections. A package of computer programs have been developed to provide computer aids for every aspect of work in form-roll design and manufacture. The programs have been successfully implemented, as an integrated CAD/CAM software system, on the ICL PERQ minicomputer with graphics facilities. Thus, the developed CAD/CAM system is a single-user workstation, with software facilities to help the user to perform the conventional roll design activities including the design of the finished section, the flower pattern, and the form-rolls. A roll editor program can then be used to modify, if required, the computer generated roll profiles. As far as manufacturing is concerned, a special-purpose roll machining program and postprocessor can be used in conjunction to generate the NC control part-programs for the production of form-rolls by NC turning. Graphics facilities have been incorporated into the CAD/CAM software programs to display drawings interactively on the computer screen throughout all stages of execution of the CAD/CAM software. It has been found that computerisation can shorten the lead time in all activities dealing with the design and manufacture of form-rolls, and small or medium size manufacturing companies can gain benefits from the CAD/CM! technology by developing, according to its own specification, a tailor-made CAD/CAM software system on a low cost minicomputer.

Computer aided geometric design of form-rolls for NC manufacture

Conventional methods of form-roll design and manufacture for Cold Roll-Forming of thin-walled metal sections have been entirely manual, time consuming and prone to errors, resulting in inefficiency and high production costs. With the use of computers, lead time can be significantly improved, particularly for those aspects involving routine but tedious human decisions and actions. This thesis describes the development of computer aided tools for producing form-roll designs for NC manufacture in the CAD/CAM environment. The work was undertaken to modernise the existing activity of a company manufacturing thin-walled sections. The investigated areas of the activity, including the design and drafting of the finished section, the flower patterns, the 10 to 1 templates, and the rolls complete with pinch-difference surfaces, side-rolls and extension-contours, have been successfully computerised by software development . Data generated by the developed software can be further processed for roll manufacturing using NC lathes. The software has been specially designed for portability to facilitate its implementation on different computers. The Opening-Radii method of forming was introduced as a subsitute to the conventional method for better forming. Most of the essential aspects in roll design have been successfully incorporated in the software. With computerisation, extensive standardisation in existing roll design practices and the use of more reliable and scientifically-based methods have been achieved. Satisfactory and beneficial results have also been obtained by the company in using the software through a terminal linked to the University by a GPO line. Both lead time and productivity in roll design and manufacture have been significantly improved. It is therefore concluded that computerisation in the design of form-rolls for automation by software development is viable. The work also demonstrated the promising nature of the CAD/CAM approach.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Complementary methods to investigate the development of clogging within a horizontal sub-surface flow tertiary treatment wetland

A combination of experimental methods was applied at a clogged, horizontal subsurface flow (HSSF) municipal wastewater tertiary treatment wetland (TW) in the UK, to quantify the extent of surface and subsurface clogging which had resulted in undesirable surface flow. The three dimensional hydraulic conductivity profile was determined, using a purpose made device which recreates the constant head permeameter test in-situ. The hydrodynamic pathways were investigated by performing dye tracing tests with Rhodamine WT and a novel multi-channel, data-logging, flow through Fluorimeter which allows synchronous measurements to be taken from a matrix of sampling points. Hydraulic conductivity varied in all planes, with the lowest measurement of 0.1 md1 corresponding to the surface layer at the inlet, and the maximum measurement of 1550 md1 located at a 0.4m depth at the outlet. According to dye tracing results, the region where the overland flow ceased received five times the average flow, which then vertically short-circuited below the rhizosphere. The tracer break-through curve obtained from the outlet showed that this preferential flow-path accounted for approximately 80% of the flow overall and arrived 8 h before a distinctly separate secondary flow-path. The overall volumetric efficiencyof the clogged system was 71% and the hydrology was simulated using a dual-path, dead-zone storage model. It is concluded that uneven inlet distribution, continuous surface loading and high rhizosphere resistance is responsible for the clog formation observed in this system. The average inlet hydraulic conductivity was 2 md1, suggesting that current European design guidelines, which predict that the system will reach an equilibrium hydraulic conductivity of 86 md1, do not adequately describe the hydrology of mature systems.

Clogging in horizontal subsurface flow constructed wetlands

Horizontal Subsurface Flow Treatment Wetlands (HSSF TWs) are used by Severn Trent Water as a low-cost tertiary wastewater treatment for rural locations. Experience has shown that clogging is a major operational problem that reduces HSSF TW lifetime. Clogging is caused by an accumulation of secondary wastewater solids from upstream processes and decomposing leaf litter. Clogging occurs as a sludge layer where wastewater is loaded on the surface of the bed at the inlet. Severn Trent systems receive relatively high hydraulic loading rates, which causes overland flow and reduces the ability to mineralise surface sludge accumulations. A novel apparatus and method, the Aston Permeameter, was created to measure hydraulic conductivity in situ. Accuracy is ±30 %, which was considered adequate given that conductivity in clogged systems varies by several orders of magnitude. The Aston Permeameter was used to perform 20 separate tests on 13 different HSSF TWs in the UK and the US. The minimum conductivity measured was 0.03 m/d at Fenny Compton (compared with 5,000 m/d clean conductivity), which was caused by an accumulation of construction fines in one part of the bed. Most systems displayed a 2 to 3 order of magnitude variation in conductivity in each dimension. Statistically significant transverse variations in conductivity were found in 70% of the systems. Clogging at the inlet and outlet was generally highest where flow enters the influent distribution and exits the effluent collection system, respectively. Surface conductivity was lower in systems with dense vegetation because plant canopies reduce surface evapotranspiration and decelerate sludge mineralisation. An equation was derived to describe how the water table profile is influenced by overland flow, spatial variations in conductivity and clogging. The equation is calibrated using a single parameter, the Clog Factor (CF), which represents the equivalent loss of porosity that would reproduce measured conductivity according to the Kozeny-Carman Equation. The CF varies from 0 for ideal conditions to 1 for completely clogged conditions. Minimum CF was 0.54 for a system that had recently been refurbished, which represents the deviation from ideal conditions due to characteristics of non-ideal media such as particle size distribution and morphology. Maximum CF was 0.90 for a 15 year old system that exhibited sludge accumulation and overland flow across the majority of the bed. A Finite Element Model of a 15 m long HSSF TW was used to indicate how hydraulics and hydrodynamics vary as CF increases. It was found that as CF increases from 0.55 to 0.65 the subsurface wetted area increases, which causes mean hydraulic residence time to increase from 0.16 days to 0.18 days. As CF increases from 0.65 to 0.90, the extent of overland flow increases from 1.8 m to 13.1 m, which reduces hydraulic efficiency from 37 % to 12 % and reduces mean residence time to 0.08 days.

Scale and scope economies and the efficient vertical and horizontal configuration of the water industry:a survey of the literature

This paper surveys the literature on scale and scope economies in the water and sewerage industry. The magnitude of scale and scope economies determines the cost efficient configuration of any industry. In the case of a regulated sector, reliable estimates of these economies are relevant to inform reform proposals that promote vertical (un)bundling and mergers. The empirical evidence allows some general conclusions. First, there is considerable evidence for the existence of vertical scope economies between upstream water production and distribution. Second, there is only mixed evidence on the existence of (dis)economies of scope between water and sewerage activities. Third, economies of scale exist up to certain output level, and diseconomies of scale arise if the company increases its size beyond this level. However, the optimal scale of utilities also appears to vary considerably between countries. Finally, we briefly consider the implications of our findings for water pricing and point to several directions for necessary future empirical research on the measurement of these economies, and explaining their cross country variation.

Vertical and horizontal scope economies in the regulated US electricity power industry

This paper investigates vertical economies between generation and distribution of electric power, and horizontal economies between different types of power generation in the U.S. electric utility industry. Our quadratic cost function model includes three generation output measures (hydro, nuclear and fossil fuels), which allows us to analyze the effect that generation mix has on vertical economies. Our results provide (sample mean) estimates of vertical economies of 8.1% and horizontal economies of 5.4%. An extensive sensitivity analysis is used to show how the scope measures vary across alternative model specifications and firm types. © 2012 Blackwell Publishing Ltd and the Editorial Board of The Journal of Industrial Economics.

Measuring economies of horizontal and vertical integration in the US electric power industry:how costly is unbundling?

This research employs econometric analysis on a cross section of American electricity companies in order to study the cost implications associated with unbundling the operations of integrated companies into vertically and/or horizontally separated companies. Focusing on the representative sample average firm, we find that complete horizontal and vertical disintegration resulting in the creation of separate nuclear, conventional, and hydro electric generation companies as well as a separate firm distributing power to final consumers, results in a statistically significant 13.5 percent increase in costs. Maintaining a horizontally integrated generator producing nuclear, conventional, and hydro electric generation while imposing vertical separation by creating a stand alone distribution company, results in a lower but still substantial and statistically significant cost penalty amounting to an 8.1 % increase in costs relative to a fully integrated structure. As these results imply that a vertically separated but horizontally integrated generation firm would need to reduce the costs of generation by 11% just to recoup the cost increases associated with vertical separation, even the costs associated with just vertical unbundling are quite substantial. Our paper is also the first academic paper we are aware of that systematically considers the impact of generation mix on vertical, horizontal, and overall scope economies. As a result, we are able to demonstrate that the estimated cost of unbundling in the electricity sector is substantially influenced by generation mix. Thus, for example, we find evidence of strong vertical integration economies between nuclear and conventional generation, but little evidence for vertical integration benefits between hydro generation and the distribution of power. In contrast, we find strong evidence suggesting the presence of substantial horizontal integration economies associated with the joint production of hydro generation with nuclear and/or conventional fossil fuel generation. These results are significant because they indicate that the cost of unbundling the electricity sector will differ substantially in different systems, meaning that a blanket regulatory policy with regard to the appropriateness of vertical and horizontal unbundling is likely to be inappropriate.

FDI horizontal and vertical effects on local firm technical efficiency

Differencing from previous studies on foreign direct investment (FDI) spillovers to domestic enterprises which mainly focus on productivity, in this paper we take a different perspective by analysing the impacts of FDI to technical efficiency of domestic firms. The paper goes beyond the current literature to shed some light on the spillover effects of FDI to technical efficiency of small and medium enterprises in a developing country. By exploiting a firm-level panel dataset and using SFA models following Battese and Coelli (1995), the paper is able to analyse horizontal spillovers through imitation and competition and labour mobility as well as vertical spillovers through backward and forward linkages on technical efficiency. The paper contributes to the understanding of potential effects on foreign invested enterprises on domestic economy in general and local enterprises performance in particular. Thus it importantly assists policy making by the government of developing countries, where FDI is believed to create technical spillovers on domestic enterprises.

Pattern formation in volumetrically heated fluids

Finite element simulations have been performed along side normal mode analysis on the linear stability that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

Pattern competition in homogeneously heated fluid layers

Simulations examining pattern competition have been performed on a horizontal homogeneously heated layer that is bounded by an isothermal plane above an adiabatic plane. Several different circulation patterns arose as the heating regime applied to the horizontal layer was modified. The sequence of the patterns formed as the Grashof number was increased had the following order: laminar layer, rolls, squares, hexagons and pentagons, and then two square modes of differing orientations. Fourier analysis was used to determine how the key modes interact with each pattern.