Estudo fenomenológico e numérico do escoamento estratificado óleo-água ondulado e com mistura na interface

Escoamentos bifásicos estão presentes em diversos processos naturais e industriais, como na indústria de petróleo. Podem apresentar-se em diferentes configurações topológicas, ou, padrões de escoamento, entre eles o escoamento estratificado ondulado e o estratificado com mistura na interface. Os escoamentos bifásicos estratificados óleo-água têm sido utilizados como uma forma conveniente de evitar a formação de emulsões de água em óleo em oleodutos e possuem uma ocorrência comum em poços de petróleo direcionais. Quando a onda interfacial ultrapassa determinado limite geométrico e cinemático, surge o fenômeno do entranhamento de gotas, representado por misturas entre as fases junto à interface que promovem um aumento na queda de pressão. Modelos têm sido apresentados pela literatura na tentativa de descrever o fenômeno do entranhamento de gotas. Neste trabalho é apresentada uma nova proposta de modelagem matemática unidimensional para o entranhamento de gotas com o objetivo de melhorar a previsão dos parâmetros envolvidos, em especial, da fração volumétrica de óleo e da queda de pressão bifásica. Também foi utilizada simulação numérica computacional, CFD (Computational Fluid Dynamics), com o uso de software comercial para obtenção dos valores dos parâmetros do escoamento estratificado ondulado óleo-água (fração volumétrica de óleo, queda de pressão, amplitude e comprimento da onda interfacial). Os resultados da modelagem fenomenológica para entranhamento e os de CFD foram comparados com bancos de dados experimentais. Os resultados em CFD mostram concordância com os resultados experimentais, tanto na análise qualitativa das propriedades geométricas das ondas interfaciais, quanto na comparação direta com os dados para fração volumétrica e queda de pressão. Os resultados numéricos da modelagem fenomenológica para fatores de entranhamento apresentam boa concordância com dados da literatura.

Phase diagram of a polydisperse soft-spheres model for liquids and colloids

The phase diagram of soft spheres with size dispersion is studied by means of an optimized Monte Carlo algorithm which allows us to equilibrate below the kinetic glass transition for all size distributions. The system ubiquitously undergoes a first-order freezing transition. While for a small size dispersion the frozen phase has a crystalline structure, large density inhomogeneities appear in the highly disperse systems. Studying the interplay between the equilibrium phase diagram and the kinetic glass transition, we argue that the experimentally found terminal polydispersity of colloids is a purely kinetic phenomenon.

Fate and Transport of Naproxen in a Sandy Aquifer Material: Saturated Column Studies and Model Evaluation

Naproxen-C14H14O3 is a nonsteroidal anti-inflammatory drug which has been found at detectable concentrations in wastewater, surface water, and groundwater. Naproxen is relatively hydrophilic and is in anionic form at pH between 6 and 8. In this study, column experiments were performed using an unconsolidated aquifer material from an area near Barcelona (Spain) to assess transport and reaction mechanisms of Naproxen in the aquifer matrix under different pore water fluxes. Results were evaluated using HYDRUS-1D, which was used to estimate transport parameters. Batch sorption isotherms for Naproxen conformed with the linear model with a sorption coefficient of 0.42 (cm3 g−1), suggesting a low sorption affinity. Naproxen breakthrough curves (BTCs) measured in soil columns under steady-state, saturated water flow conditions displayed similar behavior, with no apparent hysteresis in sorption or dependence of retardation (R, 3.85-4.24) on pore water velocities. Soil sorption did not show any significant decrease for increasing flow rates, as observed from Naproxen recovery in the effluent. Sorption parameters estimated by the model suggest that Naproxen has a low sorption affinity to aquifer matrix. Most sorption of Naproxen occurred on the instantaneous sorption sites, with the kinetic sorption sites representing only about 10 to 40% of total sorption.

Thermal Runaway in Tubular Reactor Systems with n-th Order Kinetics

This paper addresses the problem of predicting the critical parameters that characterize thermal runaway in a tubular reactor with wall cooling, introducing a new view of the n-th order kinetics reactions. The paper describes the trajectories of the system in the temperature-(concentration)n plane, and deduces the conditions for the thermal risk.

A new continuum model for traffic flow /

"Final report under contract DOT-RD-82018."

A cold model study of raceway hysteresis

The effect of a gas flow field on the size of raceway has been studied experimentally using a two-dimensional (2-D) cold model. It is observed that as the blast velocity from the tuyere increases, raceway size increases, and when the blast velocity is decreased from its highest value, raceway size does not change much until the velocity reaches a critical velocity. Below the critical velocity, raceway size decreases with decreasing velocity but is always larger than that for the same velocity when the velocity increased. This phenomenon is called raceway hysteresis. Raceway hysteresis has been studied in the presence of different gas flow rates and different particle densities. Raceway hysteresis has been observed in all the experiments. The effect of liquid flow, with various superficial velocities, on raceway hysteresis has also been studied. A study of raceway size hysteresis shows that interparticle and particle-wall friction have a very large effect on raceway size. A hypothesis has been proposed to describe the hysteresis phenomenon in the packed beds. The relevance of hysteresis to blast furnace raceways has been discussed. Existing literature correlations for raceway size ignore the frictional effects. Therefore, their applicability to the ironmaking blast furnace is questionable.

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

Simulation of a complete reflected shock tunnel showing a vortex mechanism for flow contamination

Simulations of a complete reflected shock tunnel facility have been performed with the aim of providing a better understanding of the flow through these facilities. In particular, the analysis is focused on the premature contamination of the test flow with the driver gas. The axisymmetric simulations model the full geometry of the shock tunnel and incorporate an iris-based model of the primary diaphragm rupture mechanics, an ideal secondary diaphragm and account for turbulence in the shock tube boundary layer with the Baldwin-Lomax eddy viscosity model. Two operating conditions were examined: one resulting in an over-tailored mode of operation and the other resulting in approximately tailored operation. The accuracy of the simulations is assessed through comparison with experimental measurements of static pressure, pitot pressure and stagnation temperature. It is shown that the widely-accepted driver gas contamination mechanism in which driver gas 'jets' along the walls through action of the bifurcated foot of the reflected shock, does not directly transport the driver gas to the nozzle at these conditions. Instead, driver gas laden vortices are generated by the bifurcated reflected shock. These vortices prevent jetting of the driver gas along the walls and convect driver gas away from the shock tube wall and downstream into the nozzle. Additional vorticity generated by the interaction of the reflected shock and the contact surface enhances the process in the over-tailored case. However, the basic mechanism appears to operate in a similar way for both the over-tailored and the approximately tailored conditions.

Ocular blood flow measurements in healthy human myopic eyes

Background. To evaluate the haemodynamic features of young healthy myopes and emmetropes, in order to ascertain the perfusion profile of human myopia and its relationship with axial length prior to reaching a degenerative state. Methods The retrobulbar, microretinal and pulsatile ocular blood flow (POBF) of one eye of each of twenty-two high myopes (N=22, mean spherical equivalent (MSE) =-5.00D), low myopes (N=22, MSE-1.00 to-4.50D) and emmetropes (N=22, MSE±0.50D) was analyzed using color Doppler Imaging, Heidelberg retinal flowmetry and ocular blood flow analyser (OBF) respectively. Intraocular pressure, axial length (AL), systemic blood pressure, and body mass index were measured. Results. When compared to the emmetropes and low myopes, the AL was greater in high myopia (p<0.0001). High myopes showed higher central retinal artery resistance index (CRA RI) (p=0.004), higher peak systolic to end diastolic velocities ratio (CRA ratio) and lower end diastolic velocity (CRA EDv) compared to low myopes (p=0.014, p=0.037). Compared to emmetropes, high myopes showed lower OBFamplitude (OBFa) (p=0.016). The POBF correlated significantly with the systolic and diastolic blood velocities of the CRA (p=0.016, p=0.036). MSE and AL correlated negatively with OBFa (p=0.03, p=0.003), OBF volume (p=0.02, p<0.001), POBF (p=0.01, p<0.001) and positively with CRA RI (p=0.007, p=0.05). Conclusion. High myopes exhibited significantly reduced pulse amplitude and CRA blood velocity, the first of which may be due to an OBF measurement artefact or real decreased ocular blood flow pulsatility. Axial length and refractive error correlated moderately with the ocular pulse and with the resistance index of the CRA, which in turn correlated amongst themselves. It is hypothesized that the compromised pulsatile and CRA haemodynamics observed in young healthy myopes is an early feature of the decrease in ocular blood flow reported in pathological myopia. Such vascular features would increase the susceptibility for vascular and age-related eye diseases.

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.

Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

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.