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.

Bayesian data assimilation

This thesis addresses data assimilation, which typically refers to the estimation of the state of a physical system given a model and observations, and its application to short-term precipitation forecasting. A general introduction to data assimilation is given, both from a deterministic and' stochastic point of view. Data assimilation algorithms are reviewed, in the static case (when no dynamics are involved), then in the dynamic case. A double experiment on two non-linear models, the Lorenz 63 and the Lorenz 96 models, is run and the comparative performance of the methods is discussed in terms of quality of the assimilation, robustness "in the non-linear regime and computational time. Following the general review and analysis, data assimilation is discussed in the particular context of very short-term rainfall forecasting (nowcasting) using radar images. An extended Bayesian precipitation nowcasting model is introduced. The model is stochastic in nature and relies on the spatial decomposition of the rainfall field into rain "cells". Radar observations are assimilated using a Variational Bayesian method in which the true posterior distribution of the parameters is approximated by a more tractable distribution. The motion of the cells is captured by a 20 Gaussian process. The model is tested on two precipitation events, the first dominated by convective showers, the second by precipitation fronts. Several deterministic and probabilistic validation methods are applied and the model is shown to retain reasonable prediction skill at up to 3 hours lead time. Extensions to the model are discussed.

The modelling of energy efficient drying for DSM (BL)

This thesis investigates the modelling of drying processes for the promotion of market-led Demand Side Management (DSM) as applied to the UK Public Electricity Suppliers. A review of DSM in the electricity supply industry is provided, together with a discussion of the relevant drivers supporting market-led DSM and energy services (ES). The potential opportunities for ES in a fully deregulated energy market are outlined. It is suggested that targeted industrial sector energy efficiency schemes offer significant opportunity for long term customer and supplier benefit. On a process level, industrial drying is highlighted as offering significant scope for the application of energy services. Drying is an energy-intensive process used widely throughout industry. The results of an energy survey suggest that 17.7 per cent of total UK industrial energy use derives from drying processes. Comparison with published work indicates that energy use for drying shows an increasing trend against a background of reducing overall industrial energy use. Airless drying is highlighted as offering potential energy saving and production benefits to industry. To this end, a comprehensive review of the novel airless drying technology and its background theory is made. Advantages and disadvantages of airless operation are defined and the limited market penetration of airless drying is identified, as are the key opportunities for energy saving. Limited literature has been found which details the modelling of energy use for airless drying. A review of drying theory and previous modelling work is made in an attempt to model energy consumption for drying processes. The history of drying models is presented as well as a discussion of the different approaches taken and their relative merits. The viability of deriving energy use from empirical drying data is examined. Adaptive neuro fuzzy inference systems (ANFIS) are successfully applied to the modelling of drying rates for 3 drying technologies, namely convective air, heat pump and airless drying. The ANFIS systems are then integrated into a novel energy services model for the prediction of relative drying times, energy cost and atmospheric carbon dioxide emission levels. The author believes that this work constitutes the first to use fuzzy systems for the modelling of drying performance as an energy services approach to DSM. To gain an insight into the 'real world' use of energy for drying, this thesis presents a unique first-order energy audit of every ceramic sanitaryware manufacturing site in the UK. Previously unknown patterns of energy use are highlighted. Supplementary comments on the timing and use of drying systems are also made. The limitations of such large scope energy surveys are discussed.

Drying processess in the United Kingdom:assessment of industrial energy utilisation and efficiency of drying systems and the modelling of drying characters using neural networks (BL)

Drying is an important unit operation in process industry. Results have suggested that the energy used for drying has increased from 12% in 1978 to 18% of the total energy used in 1990. A literature survey of previous studies regarding overall drying energy consumption has demonstrated that there is little continuity of methods and energy trends could not be established. In the ceramics, timber and paper industrial sectors specific energy consumption and energy trends have been investigated by auditing drying equipment. Ceramic products examined have included tableware, tiles, sanitaryware, electrical ceramics, plasterboard, refractories, bricks and abrasives. Data from industry has shown that drying energy has not varied significantly in the ceramics sector over the last decade, representing about 31% of the total energy consumed. Information from the timber industry has established that radical changes have occurred over the last 20 years, both in terms of equipment and energy utilisation. The energy efficiency of hardwood drying has improved by 15% since the 1970s, although no significant savings have been realised for softwood. A survey estimating the energy efficiency and operating characteristics of 192 paper dryer sections has been conducted. Drying energy was found to increase to nearly 60% of the total energy used in the early 1980s, but has fallen over the last decade, representing 23% of the total in 1993. These results have demonstrated that effective energy saving measures, such as improved pressing and heat recovery, have been successfully implemented since the 1970s. Artificial neural networks have successfully been applied to model process characteristics of microwave and convective drying of paper coated gypsum cove. Parameters modelled have included product moisture loss, core gypsum temperature and quality factors relating to paper burning and bubbling defects. Evaluation of thermal and dielectric properties have highlighted gypsum's heat sensitive characteristics in convective and electromagnetic regimes. Modelling experimental data has shown that the networks were capable of simulating drying process characteristics to a high degree of accuracy. Product weight and temperature were predicted to within 0.5% and 5C of the target data respectively. Furthermore, it was demonstrated that the underlying properties of the data could be predicted through a high level of input noise.

Charge effects on hindrance factors for diffusion and convection of solute in pores I

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

Charge effects on the hindered transport of macromolecules across the endothelial surface glycocalyx layer

A fluid mechanical and electrostatic model for the transport of solute molecules across the vascular endothelial surface glycocalyx layer (EGL) was developed to study the charge effect on the diffusive and convective transport of the solutes. The solute was assumed to be a spherical particle with a constant surface charge density, and the EGL was represented as an array of periodically arranged circular cylinders of like charge, with a constant surface charge density. By combining the fluid mechanical analyses for the flow around a solute suspended in an electrolyte solution and the electrostatic analyses for the free energy of the interaction between the solute and cylinders based on a mean field theory, we estimated the transport coefficients of the solute across the EGL. Both of diffusive and convective transports are reduced compared to those for an uncharged system, due to the stronger exclusion of the solute that results from the repulsive electrostatic interaction. The model prediction for the reflection coefficient for serum albumin agreed well with experimental observations if the charge density in the EGL is ranged from approximately -10 to -30 mEq/l.

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.

Pattern competition in volumetricaly heated fluids

Finite element simulations have been performed along side Galerkin-type calculations 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.

Optical microbubble resonator

We develop a method for fabricating very small silica microbubbles having a micrometer-order wall thickness and demonstrate the first optical microbubble resonator. Our method is based on blowing a microbubble using stable radiative CO2 laser heating rather than unstable convective heating in a flame or furnace. Microbubbles are created along a microcapillary and are naturally opened to the input and output microfluidic or gas channels. The demonstrated microbubble resonator has 370 µm diameter, 2 µm wall thickness, and a Q factor exceeding 10. © 2010 Optical Society of America.

Optical microbubble resonator

We develop a method for fabricating very small silica microbubbles having a micrometer-order wall thickness and demonstrate the first optical microbubble resonator. Our method is based on blowing a microbubble using stable radiative CO2 laser heating rather than unstable convective heating in a flame or furnace. Microbubbles are created along a microcapillary and are naturally opened to the input and output microfluidic or gas channels. The demonstrated microbubble resonator has 370 µm diameter, 2 µm wall thickness, and a Q factor exceeding 10. © 2010 Optical Society of America.

Convection induced by instabilities in the presence of a transverse seepage

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.