Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.

Numerical study of ultrasound induced non-linear shape and size bubble oscillations in viscoelastic media

The theoretical study of forced bubble oscillations is motivated by the importance of cavitation bubbles and oscillating encapsulated microbubbles (i.e. contrast agents) in medical sciences. In more details,theoretical studies on bubble dynamics addressing the sound-bubble interaction phenomenon provide the basis for understanding the dynamics of contrast agent microbubbles used in medical diagnosis and of non-linearly oscillating cavitation bubbles in the case of high-intensity ultrasound therapy. Moreover, the inclusion of viscoelasticity is of vital importance for an accurate theoretical analysis since most biological tissues and fluids exhibit non-Newtonian behavior.

Two-phase flow measurements with spacer grid in a rod bundle geometry

Heat transfer effectiveness in nuclear rod bundles is of great importance to nuclear reactor safety and economics. An important design parameter is the Critical Heat Flux (CHF), which limits the transferred heat from the fuel to the coolant. The CHF is determined by flow behaviour, especially the turbulence created inside the fuel rod bundle. Adiabatic experiments can be used to characterize the flow behaviour separately from the heat transfer phenomena in diabatic flow. To enhance the turbulence, mixing vanes are attached to spacer grids, which hold the rods in place. The vanes either make the flow swirl around a single sub-channel or induce cross-mixing between adjacent sub-channels. In adiabatic two-phase conditions an important phenomenon that can be investigated is the effect of the spacer on canceling the lift force, which collects the small bubbles to the rod surfaces leading to decreased CHF in diabatic conditions and thus limits the reactor power. Computational Fluid Dynamics (CFD) can be used to simulate the flow numerically and to test how different spacer configurations affect the flow. Experimental data is needed to validate and verify the used CFD models. Especially the modeling of turbulence is challenging even for single-phase flow inside the complex sub-channel geometry. In two-phase flow other factors such as bubble dynamics further complicate the modeling. To investigate the spacer grid effect on two-phase flow, and to provide further experimental data for CFD validation, a series of experiments was run on an adiabatic sub-channel flow loop using a duct-type spacer grid with different configurations. Utilizing the wire-mesh sensor technology, the facility gives high resolution experimental data in both time and space. The experimental results indicate that the duct-type spacer grid is less effective in canceling the lift force effect than the egg-crate type spacer tested earlier.

Usable work of macro-scale cavities in liquids

It is shown that the generation of cavities in a liquid can produce usable work, which is illustrated by the stretching of a string. This work is done during the expansion of the cavity, and not with its collapse. Basic equations are presented for the movement of a device moved by the so called cavity events. A theoretical solution is also proposed, which uses polynomial functions relating the so called "excess of pressure" in the cavity and time. Evaluations of the force generated during the expansion of the cavity showed a mean peak value of about 58 N for the moving container, while measurements with the container fixed to a support showed a peak value of 476 N, considered somewhat overestimated, because high frequency oscillations seem to superpose the mean behavior. Simultaneous phenomena occurring during the cavity events are also described. Series of pictures of the experiments are presented.

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Effect of boiling on deposition of metallic colloids

In this study the relationship between heterogeneous nucleate boiling surfaces and deposition of suspended metallic colloidal particles, popularly known as crud or corrosion products in process industries, on those heterogeneous sites is investigated. Various researchers have reported that hematite is a major constituent of crud which makes it the primary material of interest; however the models developed in this work are irrespective of material choice. Qualitative hypotheses on the deposition process under boiling as proposed by previous researchers have been tested, which fail to provide explanations for several physical mechanisms observed and analyzed. In this study a quantitative model of deposition rate has been developed on the basis of bubble dynamics and colloid-surface interaction potential. Boiling from a heating surface aids in aggregation of the metallic particulates viz. nano-particles, crud particulate, etc. suspended in a liquid, which helps in transporting them to heating surfaces. Consequently, clusters of particles deposit onto the heating surfaces due to various interactive forces, resulting in formation of porous or impervious layers. The deposit layer grows or recedes depending upon variations in interparticle and surface forces, fluid shear, fluid chemistry, etc. This deposit layer in turn affects the rate of bubble generation, formation of porous chimneys, critical heat flux (CHF) of surfaces, activation and deactivation of nucleation sites on the heating surfaces. Several problems are posed due to the effect of boiling on colloidal deposition, which range from research initiatives involving nano-fluids as a heat transfer medium to industrial applications such as light water nuclear reactors. In this study, it is attempted to integrate colloid and surface science with vapor bubble dynamics, boiling heat transfer and evaporation rate. Pool boiling experiments with dilute metallic colloids have been conducted to investigate several parameters impacting the system. The experimental data available in the literature is obtained by flow experiments, which do not help in correlating boiling mechanism with the deposition amount or structure. With the help of experimental evidences and analysis, previously proposed hypothesis for particle transport to the contact line due to hydrophobicity has been challenged. The experimental observations suggest that deposition occurs around the bubble surface contact line and extends underneath area of the bubble microlayer as well. During the evaporation the concentration gradient of a non-volatile species is created, which induces osmotic pressure. The osmotic pressure developed inside the microlayer draws more particles inside the microlayer region or towards contact line. The colloidal escape time is slower than the evaporation time, which leads to the aggregation of particles in the evaporating micro-layer. These aggregated particles deposit onto or are removed from the heating surface, depending upon their total interaction potential. Interaction potential has been computed with the help of surface charge and van der Waals potential for the materials in aqueous solutions. Based upon the interaction-force boundary layer thickness, which is governed by debye radius (or ionic concentration and pH), a simplified quantitative model for the attachment kinetics is proposed. This attachment kinetics model gives reasonable results in predicting attachment rate against data reported by previous researchers. The attachment kinetics study has been done for different pH levels and particle sizes for hematite particles. Quantification of colloidal transport under boiling scenarios is done with the help of overall average evaporation rates because generally waiting times for bubbles at the same position is much larger than growth times. In other words, from a larger measurable scale perspective, frequency of bubbles dictates the rate of collection of particles rather than evaporation rate during micro-layer evaporation of one bubble. The combination of attachment kinetics and colloidal transport kinetics has been used to make a consolidated model for prediction of the amount of deposition and is validated with the help of high fidelity experimental data. In an attempt to understand and explain boiling characteristics, high speed visualization of bubble dynamics from a single artificial large cavity and multiple naturally occurring cavities is conducted. A bubble growth and departure dynamics model is developed for artificial active sites and is validated with the experimental data. The variation of bubble departure diameter with wall temperature is analyzed with experimental results and shows coherence with earlier studies. However, deposit traces after boiling experiments show that bubble contact diameter is essential to predict bubble departure dynamics, which has been ignored previously by various researchers. The relationship between porosity of colloid deposits and bubbles under the influence of Jakob number, sub-cooling and particle size has been developed. This also can be further utilized in variational wettability of the surface. Designing porous surfaces can having vast range of applications varying from high wettability, such as high critical heat flux boilers, to low wettability, such as efficient condensers.

Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice

We present a theoretical study of the recently observed dynamical regimes of paramagnetic colloidal particles externally driven above a regular lattice of magnetic bubbles [P. Tierno, T. H. Johansen, and T. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007)]. An external precessing magnetic field alters the potential generated by the surface of the film in such a way to either drive the particle circularly around one bubble, ballistically through the array, or in triangular orbits on the interstitial regions between the bubbles. In the ballistic regime, we observe different trajectories performed by the particles phase locked with the external driving. Superdiffusive motion, which was experimentally found bridging the localized and delocalized dynamics, emerge only by introducing a certain degree of randomness into the bubbles size distribution.

Use of computational fluid dynamics in the design of bubble column reactors

Investigations into the modelling techniques that depict the transport of discrete phases (gas bubbles or solid particles) and model biochemical reactions in a bubble column reactor are discussed here. The mixture model was used to calculate gas-liquid, solid-liquid and gasliquid-solid interactions. Multiphase flow is a difficult phenomenon to capture, particularly in bubble columns where the major driving force is caused by the injection of gas bubbles. The gas bubbles cause a large density difference to occur that results in transient multi-dimensional fluid motion. Standard design procedures do not account for the transient motion, due to the simplifying assumptions of steady plug flow. Computational fluid dynamics (CFD) can assist in expanding the understanding of complex flows in bubble columns by characterising the flow phenomena for many geometrical configurations. Therefore, CFD has a role in the education of chemical and biochemical engineers, providing the examples of flow phenomena that many engineers may not experience, even through experimentation. The performance of the mixture model was investigated for three domains (plane, rectangular and cylindrical) and three flow models (laminar, k-e turbulence and the Reynolds stresses). mThis investigation raised many questions about how gas-liquid interactions are captured numerically. To answer some of these questions the analogy between thermal convection in a cavity and gas-liquid flow in bubble columns was invoked. This involved modelling the buoyant motion of air in a narrow cavity for a number of turbulence schemes. The difference in density was caused by a temperature gradient that acted across the width of the cavity. Multiple vortices were obtained when the Reynolds stresses were utilised with the addition of a basic flow profile after each time step. To implement the three-phase models an alternative mixture model was developed and compared against a commercially available mixture model for three turbulence schemes. The scheme where just the Reynolds stresses model was employed, predicted the transient motion of the fluids quite well for both mixture models. Solid-liquid and then alternative formulations of gas-liquid-solid model were compared against one another. The alternative form of the mixture model was found to perform particularly well for both gas and solid phase transport when calculating two and three-phase flow. The improvement in the solutions obtained was a result of the inclusion of the Reynolds stresses model and differences in the mixture models employed. The differences between the alternative mixture models were found in the volume fraction equation (flux and deviatoric stress tensor terms) and the viscosity formulation for the mixture phase.

Heterogeneous mass transfer in fluidized beds by computational fluid dynamics

The main objective of this research is to estimate and characterize heterogeneous mass transfer coefficients in bench- and pilot-scale fluidized bed processes by the means of computational fluid dynamics (CFD). A further objective is to benchmark the heterogeneous mass transfer coefficients predicted by fine-grid Eulerian CFD simulations against empirical data presented in the scientific literature. First, a fine-grid two-dimensional Eulerian CFD model with a solid and gas phase has been designed. The model is applied for transient two-dimensional simulations of char combustion in small-scale bubbling and turbulent fluidized beds. The same approach is used to simulate a novel fluidized bed energy conversion process developed for the carbon capture, chemical looping combustion operated with a gaseous fuel. In order to analyze the results of the CFD simulations, two one-dimensional fluidized bed models have been formulated. The single-phase and bubble-emulsion models were applied to derive the average gas-bed and interphase mass transfer coefficients, respectively. In the analysis, the effects of various fluidized bed operation parameters, such as fluidization, velocity, particle and bubble diameter, reactor size, and chemical kinetics, on the heterogeneous mass transfer coefficients in the lower fluidized bed are evaluated extensively. The analysis shows that the fine-grid Eulerian CFD model can predict the heterogeneous mass transfer coefficients quantitatively with acceptable accuracy. Qualitatively, the CFD-based research of fluidized bed process revealed several new scientific results, such as parametrical relationships. The huge variance of seven orders of magnitude within the bed Sherwood numbers presented in the literature could be explained by the change of controlling mechanisms in the overall heterogeneous mass transfer process with the varied process conditions. The research opens new process-specific insights into the reactive fluidized bed processes, such as a strong mass transfer control over heterogeneous reaction rate, a dominance of interphase mass transfer in the fine-particle fluidized beds and a strong chemical kinetic dependence of the average gas-bed mass transfer. The obtained mass transfer coefficients can be applied in fluidized bed models used for various engineering design, reactor scale-up and process research tasks, and they consequently provide an enhanced prediction accuracy of the performance of fluidized bed processes.

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

Are mortgage lenders guilty of the housing bubble? A UK perspective

Existing theoretical models of house prices and credit rely on continuous rationality of consumers, an assumption that has been frequently questioned in recent years. Meanwhile, empirical investigations of the relationship between prices and credit are often based on national-level data, which is then tested for structural breaks and asymmetric responses, usually with subsamples. Earlier author argues that local markets are structurally different from one another and so the coefficients of any estimated housing market model should vary from region to region. We investigate differences in the price–credit relationship for 12 regions of the UK. Markov-switching is introduced to capture asymmetric market behaviours and turning points. Results show that credit abundance had a large impact on house prices in Greater London and nearby regions alongside a strong positive feedback effect from past house price movements. This impact is even larger in Greater London and the South East of England when house prices are falling, which are the only instances where the credit effect is more prominent than the positive feedback effect. A strong positive feedback effect from past lending activity is also present in the loan dynamics. Furthermore, bubble probabilities extracted using a discrete Kalman filter neatly capture market turning points.

Estimating abundance and spatial distribution patterns of the bubble crab Dotilla fenestrata (Crustacea : Brachyura)

The bubble crab Dotilla fenestrata forms very dense populations on the sand flats of the eastern coast of Inhaca Island, Mozambique, making it an interesting biological model to examine spatial distribution patterns and test the relative efficiency of common sampling methods. Due to its apparent ecological importance within the sandy intertidal community, understanding the factors ruling the dynamics of Dotilla populations is also a key issue. In this study, different techniques of estimating crab density are described, and the trends of spatial distribution of the different population categories are shown. The studied populations are arranged in discrete patches located at the well-drained crests of nearly parallel mega sand ripples. For a given sample size, there was an obvious gain in precision by using a stratified random sampling technique, considering discrete patches as strata, compared to the simple random design. Density average and variance differed considerably among patches since juveniles and ovigerous females were found clumped, with higher densities at the lower and upper shore levels, respectively. Burrow counting was found to be an adequate method for large-scale sampling, although consistently underestimating actual crab density by nearly half. Regression analyses suggested that crabs smaller than 2.9 mm carapace width tend to be undetected in visual burrow counts. A visual survey of sampling plots over several patches of a large Dotilla population showed that crab density varied in an interesting oscillating pattern, apparently following the topography of the sand flat. Patches extending to the lower shore contained higher densities than those mostly covering the higher shore. Within-patch density variability also pointed to the same trend, but the density increment towards the lowest shore level varied greatly among the patches compared.

Dynamics of gas bubbles encapsulated by a viscoelastic fluid shell under acoustic fields

The dynamics of a gas-filled microbubble encapsulated by a viscoelastic fluid shell immersed in a Newtonian liquid and subject to an external pressure field is theoretically studied. The problem is formulated by considering a nonlinear Oldroyd type constitutive equation to model the rheological behavior of the fluid shell. Heat and mass transfer across the surface bubble have been neglected but radiation losses due to the compressibility of the surrounding liquid have been taken into account. Bubble collapse under sudden increase of the external pressure as well as nonlinear radial oscillations under ultrasound fields are investigated. The numerical results obtained show that the elasticity of the fluid coating intensifies oscillatory collapse and produces a strong increase of the amplitudes of radial oscillations which may become chaotic even for moderate driving pressure amplitudes. The role played by the elongational viscosity has also been analyzed and its influence on both, bubble collapse and radial oscillations, has been recognized. According to the theoretical predictions provided in the present work, a microbubble coated by a viscoelastic fluid shell is an oscillating system that, under acoustic driving, may experience volume oscillations of large amplitude, being, however, more stable than a free bubble. Thus, it could be expected that such a system may have a suitable behavior as an echogenic agent.

Farm-level Capital: Capital positions, structures, the dynamics of farm-level investments, capital accumulation and leverage positions. Factor Markets Working Paper No. 7, October 2011

This Factor Markets Working Paper describes and highlights the key issues of farm capital structures, the dynamics of investments and accumulation of farm capital, and the financial leverage and borrowing rates on farms in selected European countries. Data collected from the Farm Account Data Network (FADN) suggest that the European farming sector uses quite different farm business strategies, capabilities to generate capital revenues, and segmented agricultural loan market regimes. Such diverse business strategies have substantial, and perhaps more substantial than expected, implications for the financial leverage and performance of farms. Different countries adopt different approaches to evaluating agricultural assets, or the agricultural asset markets simply differ substantially depending on the country in question. This has implications for most of the financial indicators. In those countries that have seen rapidly increasing asset prices at the margin, which were revised accordingly in the accounting systems for the whole stock of assets, firm values increased significantly, even though the firms had been disinvesting. If there is an asset price bubble and it bursts, there may be serious knock-on effects for some countries.