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.

Gas distribution in shallow packed beds

Packed beds have many industrial applications and are increasingly used in the process industries due to their low pressure drop. With the introduction of more efficient packings, novel packing materials (i.e. adsorbents) and new applications (i.e. flue gas desulphurisation); the aspect ratio (height to diameter) of such beds is decreasing. Obtaining uniform gas distribution in such beds is of crucial importance in minimising operating costs and optimising plant performance. Since to some extent a packed bed acts as its own distributor the importance of obtaining uniform gas distribution has increased as aspect ratios (bed height to diameter) decrease. There is no rigorous design method for distributors due to a limited understanding of the fluid flow phenomena and in particular of the effect of the bed base / free fluid interface. This study is based on a combined theoretical and modelling approach. The starting point is the Ergun Equation which is used to determine the pressure drop over a bed where the flow is uni-directional. This equation has been applied in a vectorial form so it can be applied to maldistributed and multi-directional flows and has been realised in the Computational Fluid Dynamics code PHOENICS. The use of this equation and its application has been verified by modelling experimental measurements of maldistributed gas flows, where there is no free fluid / bed base interface. A novel, two-dimensional experiment has been designed to investigate the fluid mechanics of maldistributed gas flows in shallow packed beds. The flow through the outlet of the duct below the bed can be controlled, permitting a rigorous investigation. The results from this apparatus provide useful insights into the fluid mechanics of flow in and around a shallow packed bed and show the critical effect of the bed base. The PHOENICS/vectorial Ergun Equation model has been adapted to model this situation. The model has been improved by the inclusion of spatial voidage variations in the bed and the prescription of a novel bed base boundary condition. This boundary condition is based on the logarithmic law for velocities near walls without restricting the velocity at the bed base to zero and is applied within a turbulence model. The flow in a curved bed section, which is three-dimensional in nature, is examined experimentally. The effect of the walls and the changes in gas direction on the gas flow are shown to be particularly significant. As before, the relative amounts of gas flowing through the bed and duct outlet can be controlled. The model and improved understanding of the underlying physical phenomena form the basis for the development of new distributors and rigorous design methods for them.

A study on the flow characteristics of an industrial radiant tube burner

The thesis presents an experimentally validated modelling study of the flow of combustion air in an industrial radiant tube burner (RTB). The RTB is used typically in industrial heat treating furnaces. The work has been initiated because of the need for improvements in burner lifetime and performance which are related to the fluid mechanics of the com busting flow, and a fundamental understanding of this is therefore necessary. To achieve this, a detailed three-dimensional Computational Fluid Dynamics (CFD) model has been used, validated with experimental air flow, temperature and flue gas measurements. Initially, the work programme is presented and the theory behind RTB design and operation in addition to the theory behind swirling flows and methane combustion. NOx reduction techniques are discussed and numerical modelling of combusting flows is detailed in this section. The importance of turbulence, radiation and combustion modelling is highlighted, as well as the numerical schemes that incorporate discretization, finite volume theory and convergence. The study first focuses on the combustion air flow and its delivery to the combustion zone. An isothermal computational model was developed to allow the examination of the flow characteristics as it enters the burner and progresses through the various sections prior to the discharge face in the combustion area. Important features identified include the air recuperator swirler coil, the step ring, the primary/secondary air splitting flame tube and the fuel nozzle. It was revealed that the effectiveness of the air recuperator swirler is significantly compromised by the need for a generous assembly tolerance. Also, there is a substantial circumferential flow maldistribution introduced by the swirier, but that this is effectively removed by the positioning of a ring constriction in the downstream passage. Computations using the k-ε turbulence model show good agreement with experimentally measured velocity profiles in the combustion zone and proved the use of the modelling strategy prior to the combustion study. Reasonable mesh independence was obtained with 200,000 nodes. Agreement was poorer with the RNG  k-ε and Reynolds Stress models. The study continues to address the combustion process itself and the heat transfer process internal to the RTB. A series of combustion and radiation model configurations were developed and the optimum combination of the Eddy Dissipation (ED) combustion model and the Discrete Transfer (DT) radiation model was used successfully to validate a burner experimental test. The previously cold flow validated k-ε turbulence model was used and reasonable mesh independence was obtained with 300,000 nodes. The combination showed good agreement with temperature measurements in the inner and outer walls of the burner, as well as with flue gas composition measured at the exhaust. The inner tube wall temperature predictions validated the experimental measurements in the largest portion of the thermocouple locations, highlighting a small flame bias to one side, although the model slightly over predicts the temperatures towards the downstream end of the inner tube. NOx emissions were initially over predicted, however, the use of a combustion flame temperature limiting subroutine allowed convergence to the experimental value of 451 ppmv. With the validated model, the effectiveness of certain RTB features identified previously is analysed, and an analysis of the energy transfers throughout the burner is presented, to identify the dominant mechanisms in each region. The optimum turbulence-combustion-radiation model selection was then the baseline for further model development. One of these models, an eccentrically positioned flame tube model highlights the failure mode of the RTB during long term operation. Other models were developed to address NOx reduction and improvement of the flame profile in the burner combustion zone. These included a modified fuel nozzle design, with 12 circular section fuel ports, which demonstrates a longer and more symmetric flame, although with limited success in NOx reduction. In addition, a zero bypass swirler coil model was developed that highlights the effect of the stronger swirling combustion flow. A reduced diameter and a 20 mm forward displaced flame tube model shows limited success in NOx reduction; although the latter demonstrated improvements in the discharge face heat distribution and improvements in the flame symmetry. Finally, Flue Gas Recirculation (FGR) modelling attempts indicate the difficulty of the application of this NOx reduction technique in the Wellman RTB. Recommendations for further work are made that include design mitigations for the fuel nozzle and further burner modelling is suggested to improve computational validation. The introduction of fuel staging is proposed, as well as a modification in the inner tube to enhance the effect of FGR.

The effect of innate compliance on the performance of a counterpulsation device

Cardiovascular disease (CVD) continues to be one of the top causes of mortality in the world. World Heart Organization (WHO) reported that in 2004, CVD contributed to almost 30% of death from estimated worldwide death figures of 58 million[1]. Heart failure treatment varies from lifestyle adjustment to heart transplantation; its aims are to reduce HF symptoms, prolong patient survival and minimize risk [2]. One alternative available in the market for HF treatment is Left Ventricular Assist Device (LVAD). Chronic Intermittent Mechanical Support (CIMS) device is a novel (LVAD) heart failure treatment using counterpulsation similar to Intra Aortic Balloon Pumps (IABP). However, the implantation site of the CIMS balloon is in the ascending aorta just distal to aortic valve contrasted with IABP in the descending aorta. Counterpulsation coupled with implantation close to the aortic valve enables comparable flow augmentation with reduced balloon volume. Two prototypes of the CIMS balloon were constructed using rapid prototyping: the straight-body model is a cylindrical tube with a silicone membrane lining with zero expansive compliance. The compliant-body model had a bulging structure that allowed the membrane to expand under native systolic pressure increasing the device’s static compliance to 1.5 mL/mmHg. This study examined the effect of device compliance and vascular compliance on counterpulsating flow augmentation. Both prototypes were tested on a two-element Windkessel model human mock circulatory loop (MCL). The devices were placed just distal to aortic valve and left coronary artery. The MCL mimicked HF with cardiac output of 3 L/min, left ventricular pressure of 85/15 mmHg, aortic pressure of 70/50 mmHg and left coronary artery flow rate of 66 mL/min. The mean arterial pressure (MAP) was calculated to be 57 mmHg. Arterial compliance was set to be1.25 mL/mmHg and 2.5 mL/mmHg. Inflation of the balloon was triggered at the dicrotic notch while deflation was at minimum aortic pressure prior to systole. Important haemodynamics parameters such as left ventricular pressure (LVP), aortic pressure (AoP), cardiac output (CO), left coronary artery flowrate (QcorMean), and dP (Peak aortic diastolic augmentation pressure – AoPmax ) were simultaneously recorded for both non-assisted mode and assisted mode. ANOVA was used to analyse the effect of both factors (balloon and arterial compliance) to flow augmentation. The results showed that for cardiac output and left coronary artery flowrate, there were significant difference between balloon and arterial compliance at p < 0.001. Cardiac output recorded maximum output at 18% for compliant body and stiff arterial compliance. Left coronary artery flowrate also recorded around 20% increase due to compliant body and stiffer arterial compliance. Resistance to blood ejection recorded highest difference for combination of straight body and stiffer arterial compliance. From these results it is clear that both balloon and arterial compliance are statistically significant factors for flow augmentation on peripheral artery and reduction of resistance. Although the result for resistance reduction was different from flow augmentation, these results serves as an important aspect which will influence the future design of the CIMS balloon and its control strategy. References: 1. Mathers C, Boerma T, Fat DM. The Global Burden of disease:2004 update. Geneva: World Heatlh Organization; 2008. 2. Jessup M, Brozena S. Heart Failure. N Engl J Med 2003;348:2007-18.

The charge effect on the hindrance factors for diffusion and convection of a solute in pores II

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

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.

Effects of electric charge on osmotic flow across periodically arranged circular cylinders

An electrostatic model is developed for osmotic flow across a layer consisting of identical circular cylinders with a fixed surface charge, aligned parallel to each other so as to form an ordered hexagonal arrangement. The expression of the osmotic reflection coefficient is derived for spherical solutes with a fixed surface charge suspended in an electrolyte, based on low-Reynolds-number hydrodynamics and a continuum, point-charge description of the electric double layers. The repulsive electrostatic interaction between the surface charges with the same sign on the solute and the cylinders is shown to increase the exclusion region of solute from the cylinder surface, which enhances the osmotic flow. Applying the present model to the study of osmotic flow across the endothelial surface glycocalyx of capillary walls has revealed that this electrostatic model could account well for the reflection coefficients measured for charged macromolecules, such as albumin, in the physiological range of charge density and ion concentration.

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft

A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity Lp, defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6nm radius and 8nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall.

Mean zonal flows generated by librations of a rotating spherical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid-filled cavity. An analytical theory is developed for the case of a spherical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that longitudinal librations create a steady zonal flow through the nonlinear advection in the Ekman layers. The theory can be applied to laboratory experiments as well as to solid planets and satellites with a liquid core. Copyright © Cambridge University Press 2010.