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Two-phase Flow (two-phase + flow)
Kinds of Two-phase Flow Selected AbstractsNumerical Simulation of the Hydrodynamics of Gas/Solid Two-Phase Flow in a Circulating Fluidized Bed with Different Inlet ConfigurationsCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 6 2009Y. Li Abstract The gas/solid flow characteristics in a circulating fluidized bed with two different inlet configurations were investigated by numerical simulation based on an Eulerian approach. In order to describe the interaction between the gas phase and the solid phase and the influence of the solid phase on the gas turbulence, a source term formulation with a more reasonable physical meaning was introduced. The simulation results were validated by the experimental data; then, the model was employed to examine the effect of the inlet configuration on the gas and solid feeding. The simulation results showed that, using the side feeding system, the distributions of solid flow and concentration were highly variable both over the column cross-section and along the column height. However, such variations can be improved by using the elbow inlet system where the gas and solid are fed from the bottom. [source] Direct Numerical Simulation of Dense Gas-Solid Two-Phase FlowsASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2000Y. Zhulin Based on Newton's law and the classical physical laws, Eulerian and Lagrangian methods are respectively used to deal with gas-field and discrete particles. The three-dimensional viscid air-field and three-dimensional discrete particle field are solved in each time step ,t. Collision and friction between individual particles are taken into account when establishing the mathematical models, including individual particle diameter, density, stiffness and friction coefficient. Particles mixing in ball mills, particles dropping from hoppers, and particles fluidizing in fluidized beds are used as examples of the simulations. Selected simulated results are compared to experimental results. [source] Two-phase flow in structured packings: Modeling and calculation on a macroscopic scaleAICHE JOURNAL, Issue 3 2008B. Mahr Abstract A model is presented that allows calculating the macroscopic flow field of counter-current two-phase flow in strongly anisotropic porous structures. It is applied to corrugated structured packings. All flow field variables and packing properties are averaged over the volume of an elementary cell. The anisotropic gas flow resistance is derived from measurements and from separate CFD calculations on 3D-X-ray CT scans. The liquid's flow resistance is calculated using an analytical model of liquid film flow on an inclined plate. Liquid flow along both preferential flow directions is represented by two separate phases, in order to consider horizontal forces despite their symmetry. Gas-liquid momentum transfer above the loading point is included. The macroscopic flow field is calculated for a 288 mm I.D. column containing four packing elements. Liquid spreading from a point source, for uniform irrigation, increased hold-up at the packing elements' joints and pressure drop are tested against experimental results. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Simulation of two-phase flow with sub-scale droplet and bubble effectsCOMPUTER GRAPHICS FORUM, Issue 2 2009Viorel Mihalef Abstract We present a new Eulerian-Lagrangian method for physics-based simulation of fluid flow, which includes automatic generation of sub-scale spray and bubbles. The Marker Level Set method is used to provide a simple geometric criterion for free marker generation. A filtering method, inspired from Weber number thresholding, further controls the free marker generation (in a physics-based manner). Two separate models are used, one for sub-scale droplets, the other for sub-scale bubbles. Droplets are evolved in a Newtonian manner, using a density-extension drag force field, while bubbles are evolved using a model based on Stokes' Law. We show that our model for sub-scale droplet and bubble dynamics is simple to couple with a full (macro-scale) Navier-Stokes two-phase flow model and is quite powerful in its applications. Our animations include coarse grained multiphase features interacting with fine scale multiphase features. [source] The Effect of the Anode Loading and Method of MEA Fabrication on DMFC PerformanceFUEL CELLS, Issue 3 2007T. V. Reshetenko Abstract The influence of the Pt-Ru anode loading and MEA preparation techniques on direct methanol fuel cell (DMFC) performance is studied. Two different anode catalyst layer preparation techniques are employed. One is the direct coating of anode catalyst ink on a membrane to form a catalyst coated membrane, CCManode, and the other is the coating of the ink on the diffusion layers, which generates a catalyst coated substrate, CCSanode. The power density of a combined CCManode/CCScathode MEA is higher than for a CCSanode/CCScathode MEA. The main difference in the performance is observed in the high current density region, where two-phase flow is present and mass transfer processes govern the performance. The CCManode and CCSanode have different macroscopic structures, while showing the same microscopic morphology. Based on their morphological differences, it is expected that the combination of the CCManode and carbon paper provides the more homogeneous removal of CO2 at high currents. The authors suggest that the application of the CCManode with an optimal anode loading improves anode mass transfer, reduces methanol crossover, and enhances the electrochemical reactions. [source] The heat transfer heterogeneities of bends in flow boiling of hairpin tubesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 8 2009Meng Meng Abstract A series of visual experiments were conducted for liquid, vapor two-phase flow in hairpin tubes, and it was observed that most of the nucleation sites were located at the outer tube wall of the bend. From the simulation, it was concluded that the uneven velocity distribution in the bend induced the heat transfer heterogeneity. Furthermore, the nucleation of both the inner and outer tube wall of the bend and the wall temperature distribution were discussed to understand the physical phenomena. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20269 [source] Prediction method of critical power by film flow rate measurement and subchannel analysisHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2005Miyuki Akiba Abstract This paper presents a method that can estimate the critical power of boiling water reactors, BWRs, with regard to spacer geometry. The current experimental method for estimating the critical power for BWR design requires many trained experts and expensive facilities to conduct the experiments. In the present method, the liquid film flow rate of adiabatic gas-liquid two-phase flow and a subchannel analysis of the actual BWR flow condition are measured experimentally and analyzed. In the experiment, deposition enhancement coefficients of three spacer geometries,a ferrule, an egg-crate, and a ferrule spacer with twisted tape (CYCLONE spacer),were estimated by measuring the liquid film flow rate of air-water two-phase flow flowing up in a vertical square (4 × 4) rod bundle that simulated the rod bundle of a BWR. Using these coefficients, the critical powers for bundles using each type of spacer geometry were calculated in the subchannel analysis. This method was validated using previous critical power data in the actual BWR flow condition. The critical powers predicted by this method agreed well with those of the experimental data. The result confirmed the effectiveness of this experiment-simulation combined method, as well as the advantage over current experimental methods in terms of human and facility costs. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(5): 309,323, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20069 [source] A simplified model of gas,liquid two-phase flow pattern transitionHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 7 2004Koji Ito Abstract An experiment of upward gas,liquid two-phase flow was conducted in an air,water isothermal system under atmospheric pressure. The differential pressure was measured at the fully developed section by using a variable reluctance type transducer to classify the flow patterns and their transitions. The flow behavior was observed with a high-speed video camera. The probability density function (PDF) of the differential pressure signal was employed to identify the flow pattern. A simplified one-dimensional flow model was proposed to clarify dominant factors affecting the formation and transitions of flow patterns. The model dealt with the gas-component advection based on the spatiotemporal void fraction behaviors by considering the gas compressibility, the wake, and the liquid phase redistribution mechanism. The simulation results of the model indicated four kinds of the void wave patterns (ripple-like, rectangular, distorted rectangular, and uniform wave patterns) depending on gas and liquid volumetric fluxes. These void wave patterns corresponded well to the experimentally observed flow patterns. The transitions among void wave patterns agree well with the Mishima,Ishii flow pattern map. The friction loss estimated by the present model coincides fairly well with Chisholm's empirical formula. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 445,461, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20029 [source] Accelerating iterative solution methods using reduced-order models as solution predictorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006R. Markovinovi Abstract We propose the use of reduced-order models to accelerate the solution of systems of equations using iterative solvers in time stepping schemes for large-scale numerical simulation. The acceleration is achieved by determining an improved initial guess for the iterative process based on information in the solution vectors from previous time steps. The algorithm basically consists of two projection steps: (1) projecting the governing equations onto a subspace spanned by a low number of global empirical basis functions extracted from previous time step solutions, and (2) solving the governing equations in this reduced space and projecting the solution back on the original, high dimensional one. We applied the algorithm to numerical models for simulation of two-phase flow through heterogeneous porous media. In particular we considered implicit-pressure explicit-saturation (IMPES) schemes and investigated the scope to accelerate the iterative solution of the pressure equation, which is by far the most time-consuming part of any IMPES scheme. We achieved a substantial reduction in the number of iterations and an associated acceleration of the solution. Our largest test problem involved 93 500 variables, in which case we obtained a maximum reduction in computing time of 67%. The method is particularly attractive for problems with time-varying parameters or source terms. Copyright © 2006 John Wiley & Sons, Ltd. [source] Some results on the accuracy of an edge-based finite volume formulation for the solution of elliptic problems in non-homogeneous and non-isotropic mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009Darlan Karlo Elisiário de Carvalho Abstract The numerical simulation of elliptic type problems in strongly heterogeneous and anisotropic media represents a great challenge from mathematical and numerical point of views. The simulation of flows in non-homogeneous and non-isotropic porous media with full tensor diffusion coefficients, which is a common situation associated with the miscible displacement of contaminants in aquifers and the immiscible and incompressible two-phase flow of oil and water in petroleum reservoirs, involves the numerical solution of an elliptic type equation in which the diffusion coefficient can be discontinuous, varying orders of magnitude within short distances. In the present work, we present a vertex-centered edge-based finite volume method (EBFV) with median dual control volumes built over a primal mesh. This formulation is capable of handling the heterogeneous and anisotropic media using structured or unstructured, triangular or quadrilateral meshes. In the EBFV method, the discretization of the diffusion term is performed using a node-centered discretization implemented in two loops over the edges of the primary mesh. This formulation guarantees local conservation for problems with discontinuous coefficients, keeping second-order accuracy for smooth solutions on general triangular and orthogonal quadrilateral meshes. In order to show the convergence behavior of the proposed EBFV procedure, we solve three benchmark problems including full tensor, material heterogeneity and distributed source terms. For these three examples, numerical results compare favorably with others found in literature. A fourth problem, with highly non-smooth solution, has been included showing that the EBFV needs further improvement to formally guarantee monotonic solutions in such cases. Copyright © 2008 John Wiley & Sons, Ltd. [source] Geometrical interpretation of the multi-point flux approximation L-methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2009Yufei Cao Abstract In this paper, we first investigate the influence of different Dirichlet boundary discretizations on the convergence rate of the multi-point flux approximation (MPFA) L-method by the numerical comparisons between the MPFA O- and L-method, and show how important it is for this new method to handle Dirichlet boundary conditions in a suitable way. A new Dirichlet boundary strategy is proposed, which in some sense can well recover the superconvergence rate of the normal velocity. In the second part of the work, the MPFA L-method with homogeneous media is studied. A systematic concept and geometrical interpretations of the L-method are given and illustrated, which yield more insight into the L-method. Finally, we apply the MPFA L-method for two-phase flow in porous media on different quadrilateral grids and compare its numerical results for the pressure and saturation with the results of the two-point flux approximation method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Use of slopelimiter techniques in traditional numerical methods for multi-phase flow in pipelines and wellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2005R. J. Lorentzen Abstract The aim of this paper is to show how simple and traditional methods for simulating multi-phase flow can be improved by introducing higher order accuracy. Numerical diffusion is reduced to a minimum by using slopelimiter techniques, and better predictions of flow rates and pressure are obtained. Slopelimiter techniques, originally developed to achieve higher order of accuracy in Godunov's method, is applied to a method following a finite element approach and a predictor,corrector shooting technique. These methods are tested and compared to a Godunov-type scheme recently developed for multi-phase flow. Implementation of Godunov-type schemes for multi-phase flow tends to be a complicated and challenging task. Introducing the slopelimiter techniques in the finite element approach and the predictor,corrector shooting technique is however simple, and provides an overall reduction of the numerical diffusion. The focus is on using these techniques to improve the mass transport description, since this is the main concern in the applications needed. The presented schemes represent different semi-implicit approaches for simulating multi-phase flow. An evaluation of higher order extensions, as well as a comparison by itself, is of large interest. We present a model for two-phase flow in pipelines and wells, and an outline of the numerical methods and the extensions to second order spatial accuracy. Several examples motivated by applications in underbalanced drilling are presented, and the advantages of using higher order schemes are illustrated. Copyright © 2005 John Wiley & Sons, Ltd. [source] Transport mechanisms and performance simulation of a PEM fuel cellINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 6 2008Geng-Po Ren Abstract A three-dimensional, gas,liquid two-phase flow and transport model has been developed and utilized to simulate the multi-dimensional, multi-phase flow and transport phenomena in both the anode and cathode sides in a proton exchange membrane (PEM) fuel cell and the cell performance with different influencing operational and geometric parameters. The simulations are presented with an emphasis on the physical insight and fundamental understanding afforded by the detailed distributions of velocity vector, oxygen concentration, water vapor concentration, liquid water concentration, water content in the PEM, net water flux per proton flux, local current density, and overpotential. Cell performances with different influencing factors are also presented and discussed. The comparison of the model prediction and experimental data shows a good agreement. Copyright © 2007 John Wiley & Sons, Ltd. [source] An assessment of friction factor and viscosity correlations for model prediction of refrigerant flow in capillary tubesINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 3 2005Zhang Yufeng Abstract In this paper, a homogeneous model including the metastable liquid and metastable two-phase region is presented to assess the effects of various friction factor equations and two-phase viscosity correlations on simulating the behaviour of capillary tubes. Both straight and coiled capillary tubes are considered and R-22 is used for comparison. The predicted pressure distribution, tube lengths or mass flow rates are compared with experimental data reported in literature. It is confirmed that the predicting accuracy with homogeneous model can be improved by employing the suitable correlations of friction factor and two-phase viscosity. For straight capillaries, the Churchill and Colebrook friction factor correlations give almost the same simulating results. However, the numerical results show that the optimum combination of correlations of friction factor and two-phase viscosity may be different when compared with different experimental data. For coiled capillaries, the Mori and Nakayama friction factor correlation agrees well with Ito's formula for single liquid-phase flow. Together with Giri's friction factor equation for two-phase flow, Cicchitti viscosity model best predicts the measured mass flow rate with an average error of 4.88%. Copyright © 2004 John Wiley & Sons, Ltd. [source] Modelling of the fluid dynamic processes in a high-recirculation airlift reactorINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 6 2001David A. Sanders Abstract This paper describes the creation of two models of the steady-state fluid dynamic processes occurring in a high-recirculation airlift reactor. The new models were created to provide information to assist in the design of a reactor, in particular considering the selection of parameters to adjust in order to achieve a steady state solution. The modelling of two-phase flow of air and water in small-scale airlift bioreactors is considered. This modelling was applied to the high-recirculation airlift reactor process. New computer simulations were created and tests performed to evaluate the new models. The results of this evaluation are presented. The evaluation showed that variation of the superficial gas velocity or the simultaneous variation of the downcomer and riser diameters could be used to produce a steady-state design solution. Copyright © 2001 John Wiley & Sons, Ltd. [source] Liquid,liquid two-phase flow in pore array microstructured devices for scaling-up of nanoparticle preparationAICHE JOURNAL, Issue 12 2009Shaowei Li Abstract Nanoparticles have been produced by a T-junction microchannel device in our previous work (Li et al., Langmuir. 2008;24:4194-4199). As a scaling-up strategy, pore array microstructured devices were designed to prepare nanoparticles in this article. H2SO4 and BaCl2, respectively, in two phases to form BaSO4 nanoparticles was used as a test system. The characteristics of a well controlled liquid,liquid two-phase flow in the pore array microstructured devices were presented. Nanoparticles with small size and good dispersibility were produced through drop or disk flows in the microstructured devices. The influence of mass transfer and chemical reaction on interfacial tension and flow patterns was discussed based on the experiments. Meanwhile, the effect of the two phase flow patterns on the nanoparticle size was discussed. It was found that the increase of the amount of mass transfer and chemical reaction could change the flow patterns from disk flow to drop flow. The droplet diameter could be changed in a wide range. Flow patterns could be distinguished based on the measured interfacial tension in different concentrations. The prepared nanoparticles were ranged from 10 nm to 30 nm. Apparently the particle size was decreased with the increase of the droplet size in both the drop flow region and the disk flow region whereas it had a reverse trend in the transition region. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Snap-off of a liquid drop immersed in another liquid flowing through a constricted capillaryAICHE JOURNAL, Issue 8 2009T. J. Peña Abstract Emulsions are encountered at different stages of oil production processes, often impacting many aspects of oilfield operations. Emulsions may form as oil and water come in contact inside the reservoir rock, valves, pumps, and other equipments. Snap-off is a possible mechanism to explain emulsion formation in two-phase flow in porous media. Quartz capillary tubes with a constriction (pore neck) served to analyze snap-off of long ("infinite") oil droplets as a function of capillary number and oil-water viscosity ratio. The flow of large oil drops through the constriction and the drop break-up process were visualized using an optical microscope. Snap-off occurrence was mapped as a function of flow parameters. High oil viscosity suppresses the breakup process, whereas snap-up was always observed at low dispersed-phase viscosity. At moderate viscosity oil/water ratio, snap-off was observed only at low capillary number. Mechanistic explanations based on competing forces in the liquid phases were proposed. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Two-phase flow in structured packings: Modeling and calculation on a macroscopic scaleAICHE JOURNAL, Issue 3 2008B. Mahr Abstract A model is presented that allows calculating the macroscopic flow field of counter-current two-phase flow in strongly anisotropic porous structures. It is applied to corrugated structured packings. All flow field variables and packing properties are averaged over the volume of an elementary cell. The anisotropic gas flow resistance is derived from measurements and from separate CFD calculations on 3D-X-ray CT scans. The liquid's flow resistance is calculated using an analytical model of liquid film flow on an inclined plate. Liquid flow along both preferential flow directions is represented by two separate phases, in order to consider horizontal forces despite their symmetry. Gas-liquid momentum transfer above the loading point is included. The macroscopic flow field is calculated for a 288 mm I.D. column containing four packing elements. Liquid spreading from a point source, for uniform irrigation, increased hold-up at the packing elements' joints and pressure drop are tested against experimental results. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] Phase separation of liquid-liquid two-phase flow at a T-junctionAICHE JOURNAL, Issue 1 2006L. Yang Abstract The phase separation of liquid-liquid two-phase flow at a T-junction has been studied using kerosene and deionized water as working fluids and a T-junction with a horizontal main pipe and a vertically upward side arm. Separation data are evaluated by a new criterion: separation efficiency. The results show that the T-junction is highly efficient at separating two immiscible liquids when the flows approaching the T-junction are stratified and when the fractional mass take offs close to the inlet kerosene mass fraction. A new model has been proposed for the phase separation. Comparison between the model and the experimental data shows that the data is well represented by the model. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] Stretching operational life of trickle-bed filters by liquid-induced pulse flowAICHE JOURNAL, Issue 7 2005Ion Iliuta Abstract When dilute liquid suspensions contaminated with fine solids are treated in catalytic trickle-bed reactors, bed plugging develops and increases the resistance to two-phase flow until ultimate unit shutdown for bed substitution with pristine catalyst. The release of deposited fines, or the inhibition of fines deposition over some regions of the collector, is expected to alleviate the plugging if liquid flow shock or periodic operation policies are implemented. Current physical models linking gas,liquid phase flow to space,time evolution of fines deposition and release are unable to depict this new type of filtration in trickle beds. This work attempts to fill in this gap by developing a dynamic multiphase flow deep-bed filtration model. The model incorporates the physical effects of porosity and effective specific surface area changes as a result of fines deposition/release, gas and suspension inertial effects, and coupling effects between the filtration parameters and the interfacial momentum exchange force terms. The release of the fine particles from the collector surface was assumed to be induced by the colloidal forces in the case of Brownian particles or by the hydrodynamic forces in the case of non-Brownian particles. An important finding of the work was that for noncolloidal fines both induced pulsing and liquid flow shock operations conferred substantial improvements (measured in terms of reduction in specific deposit and pressure drop) in the mitigation of plugging in trickle-bed reactors. However, because of the highest critical shear stress for fines in the colloidal range, induced pulsing did not substantiate any practically useful effect. © 2005 American Institute of Chemical Engineers AIChE J, 2005 [source] Biomass accumulation and clogging in trickle-bed bioreactorsAICHE JOURNAL, Issue 10 2004Ion Iliuta Abstract Excessive biomass formation in two-phase flow trickle-bed bioreactors induces clogging and leads to the progressive obstruction of the bed that is accompanied with a buildup in pressure drop and flow channeling. Currently, physical models linking the two-phase flow to the space-time evolution of biological clogging are virtually nonexistent. An attempt has been made with this contribution to fill in this gap by developing a unidirectional dynamic multiphase flow model based on the volume-average mass, momentum, and species balance equations. Phenol biodegradation by Pseudomonas putida as the predominant species immobilized on activated carbon was chosen as a case study to illustrate the consequences of formation of excessive amounts of biomass. Furthermore, in developing the transient model, the following basic processes were assumed to occur and have been accounted for in the mathematical model: oxygen transport from gas into liquid bulks, phenol, and oxygen transport from the liquid phase to the biofilm surface, simultaneous diffusion and reaction of phenol and oxygen within biofilm, as well as their simultaneous diffusion and adsorption within the porous supporting particles. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2541,2551, 2004 [source] CFD modeling of flow patterns and hydraulics of commercial-scale sieve traysAICHE JOURNAL, Issue 4 2003Getye Gesit A computational fluid dynamics (CFD) model was used to predict the flow patterns and hydraulics of a commercial-scale sieve tray. The model considers the 3-D two-phase flow of gas and liquid in which each phase is treated as an interpenetrating continuum having separate transport equations. Interaction between the two phases occurs via an interphase momentum transfer. For the CFD analysis, the commercial packages CFX5.4 and CFX4.4 of AEA Technology were employed. Velocity distributions, clear liquid height, froth height, and liquid holdup fraction in froth were predicted for various combinations of gas and liquid flow rates. Tray geometry and operating conditions were based on the experimental work that Solari and Bell carried out in a 1.22-m diameter air,water simulator in 1986 at Fractionation Research Inc. Predicted results were found to be in good agreement with the experimental data of these authors. The objective of the work was studying the extent to which CFD can be used as a prediction and design tool for industrial trays. The simulation results are such that CFD can be used as an invaluable tool in tray design and analysis. [source] Non-homogeneous Navier,Stokes systems with order-parameter-dependent stressesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2010Helmut Abels Abstract We consider the Navier,Stokes system with variable density and variable viscosity coupled to a transport equation for an order-parameter c. Moreover, an extra stress depending on c and ,c, which describes surface tension like effects, is included in the Navier,Stokes system. Such a system arises, e.g. for certain models of granular flows and as a diffuse interface model for a two-phase flow of viscous incompressible fluids. The so-called density-dependent Navier,Stokes system is also a special case of our system. We prove short-time existence of strong solution in Lq -Sobolev spaces with q>d. We consider the case of a bounded domain and an asymptotically flat layer with a combination of a Dirichlet boundary condition and a free surface boundary condition. The result is based on a maximal regularity result for the linearized system. Copyright © 2010 John Wiley & Sons, Ltd. [source] Sizing of throttling device for gas/liquid two-phase flow part 1: Safety valvesPROCESS SAFETY PROGRESS, Issue 4 2004Ralf Diener The calculation of the mass flow rate through throttling devices is difficult when handling two-phase flow, especially when boiling liquids flow into these fittings. Safety valves are typically oversized by a significant extent, if sizing methods like the ,-method (originally developed by J. Leung), are used in case of low-quality inlet flow. Within this method the boiling delay of the liquid and the influence of the boiling delay on the mass flow rate are not considered. In this paper the HNE-DS model is proposed, where the compressibility coefficient , is extended by adding a boiling delay coefficient. It includes the degree of thermodynamic nonequilibrium at the start of the nucleation of small mass fractions of vapor upstream of the fitting. In Part 1 the sizing of safety valves is described. Additionally, the derivation of the HNE-DS method is given in detail. Part 2 considers the mass flow rate through short nozzles, orifices, and control valves. The HNE-DS model can be used for all those fittings. A comparison with experimental results on safety valves with steam/water and air/water flow has emphasized the excellent accuracy of the new model. © 2004 American Institute of Chemical Engineers Process Saf Prog, 2004 [source] Fire exposure of liquid-filled vesselsPROCESS SAFETY PROGRESS, Issue 1 2003Larry L. Simpson Pressure vessels in the chemical industry generally have top-mounted pressure relief valves (PRVs) sized to handle fire exposure and other possible scenarios. Designers usually assume that the fire scenario causes liquid to boil and vapor to vent, regardless of the initial liquid level. Under some circumstances, however, a high liquid level, together with thermal expansion, can result in a vessel being full of liquid when the PRV opens. If so, the initial fluid discharged through the PRV would be a two-phase gas-liquid stream. This paper analyzes non-reactive phenomena occurring during the heat-up and venting process in non-agitated liquid-filled pressure vessels. A new criterion is developed to determine if the vapor-venting sizing assumption is justified. Results from several cases show that pressures in most liquid-filled vessels sized for vapor-only flow will be below the ASME Code-allowable values during fire exposure. Hence, the common industry practice of ignoring two-phase flow when sizing fire cases is usually justified. [source] Oil,water two-phase flow in microchannels: Flow patterns and pressure drop measurementsTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2008Abdelkader Salim Abstract This paper investigates oil,water two-phase flows in microchannels of 793 and 667 µm hydraulic diameters made of quartz and glass, respectively. By injecting one fluid at a constant flow rate and the second at variable flow rate, different flow patterns were identified and mapped and the corresponding two-phase pressure drops were measured. Measurements of the pressure drops were interpreted using the homogeneous and Lockhart,Martinelli models developed for two-phase flows in pipes. The results show similarity to both liquid,liquid flow in pipes and to gas,liquid flow in microchannels. We find a strong dependence of pressure drop on flow rates, microchannel material, and the first fluid injected into the microchannel. On étudie dans cet article les écoulements diphasiques huile-eau dans des micro-canaux de 793 µm et 667 µm de diamètre hydraulique faits de quartz et de verre, respectivement. En injectant un fluide à un débit constant et le second à un débit variable, différents schémas d'écoulements ont été observés et représentés en diagrammes, et les pertes de charge diphasiques correspondantes ont été mesurées. Les mesures de perte de charge ont été interprétées à l'aide du modèle homogène et du modèle de Lockhart,Martinelli mis au point pour les écoulements diphasiques dans les conduites. Les résultats montrent une similarité à la fois avec l'écoulement liquide-liquide et l'écoulement liquide de gaz dans des micro-canaux. On a trouvé une forte dépendance de la perte de charge aux débits, au matériau des micro-canaux et au premier fluide injecté dans le micro-canal. [source] Corrosion inhibition of carbon steel under two-phase flow (water-petroleum) simulated by turbulently agitated systemTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2008Qasim J. M. Slaiman Abstract The corrosion of carbon steel in single-phase (water with 0.1N NaCl) and two immiscible phases (kerosene-water) using turbulently agitated system was investigated. The experiments were carried out for Reynolds number (Re) range of 38 000 to 95 000 using circular disc turbine agitator at 40°C. In two-phase system, test runs were carried out in aqueous phase (water) concentrations of 1% vol, 5% vol, 8% vol, and 16.4% vol mixed with kerosene at various Re. The effect of Re, percent of dispersed phase, dispersed droplet diameter, and number of droplets per unit volume on the corrosion rate were investigated and discussed. Test runs were carried out using two types of inhibitors: sodium nitrite of concentrations 20, 40, and 60 ppm and sodium hexapolyphosphate of concentrations 485, 970, and 1940 ppm in a solution containing 8% vol aqueous phase (water) mixed with kerosene (continuous phase) at 40°C for the whole range of Re. It was found that increasing Re increased the corrosion rate and the presence of water enhanced the corrosion rate by increasing the solution electrical conductivity. For two-phase solution containing 8% vol and 16% vol of water, the corrosion rate was higher than single phase (100% vol water). The main parameters that play the major role in determining the corrosion rate in two phases were concentration of oxygen, solution electrical conductivity, and the interfacial area between the two phases (dispersed and continuous). Sodium nitrite and sodium hexapolyphosphate were found to be efficient inhibitors in two-phase solution for the investigated range of Re. On a étudié la corrosion de l'acier au carbone dans des conditions monophasiques (eau avec 0,1N de NaCl) et diphasiques immiscibles (kérosène-eau) à l'aide d'un système agité turbulent. Les expériences ont été menées pour une gamme de nombre de Reynolds (Re) de 38000 à 95000, avec un agitateur de type Rushton à 40°C. Des tests pour le système diphasique ont été effectuées dans des concentrations de phase aqueuse (eau) de 1%, 5%, 8% et 16,4% en volume, mélangée à du kérosène pour différentes valeurs de Re. L'effet du nombre de Reynolds (Re), le pourcentage de la phase dispersée, le diamètre des gouttelettes dispersées et le nombre de gouttelettes par unité de volume sur le taux de corrosion a été étudié et analysé. Les essais ont été réalisés avec deux types d'inhibiteurs: du nitrite de sodium à des concentrations de 20, 40 et 60 ppm et de l'hexapolyphosphate de sodium à des concentrations de 485, 970 et 1940 ppm dans une solution contenant 8% en volume de phase aqueuse (eau) mélangée à du kérosène (phase aqueuse) à 40°C pour la gamme complète de Re. On a trouvé que l'augmentation du Re augmentait le taux de corrosion et que la présence d'eau améliorait le taux de corrosion en augmentant la conductivité électrique des solutions. Pour la solution diphasique contenant 8% et 16% en volume d'eau, le taux de corrosion est plus grand qu'en monophasique (100% en volume d'eau). Les principaux paramètres qui jouent un rôle majeur dans la détermination du taux de corrosion dans la solution diphasique sont la concentration d'oxygène, la conductivité électrique de la solution et l'aire interfaciale entre les deux phases (dispersée et continue). On a trouvé que le nitrite de sodium et l'hexapolyphosphate étaient des inhibiteurs efficaces dans la solution diphasique pour la gamme de Re étudié. [source] Fluid flow in an impacting symmetrical tee junction II: two-phase air/water flowASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2009A. P. Doherty Abstract A universal flow regime map was presented for two-phase flow in a horizontal pipe. Data were given on two-phase gas/liquid flow in a symmetrical impacting tee junction. The flow regimes in the inlet arm of the tee were those expected for a straight pipe. This was not so for the outlet arm where, in most cases, flow regimes occurred earlier than expected. At low liquid outlet flows the stratified regime was reinforced into higher gas flows than expected. The liquid hold-up exhibited variations over the tee junction. The pressure drop in the inlet arm agreed with similar data for the straight pipe, but in the tee outlets was below that expected for the straight pipe. The tee junction pressure drop showed some parallels to the corresponding single-phase flow data but the le/d dimensionless values for the junction pressure drop showed a wide variation, in contrast to the single-phase junction data. A model was presented based on the Lockhard,Martinelli theory that enabled the tee pressure drop to be predicted. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Fluid flow in an impacting symmetrical tee junction III: three-phase air/water/oil flowASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2009A. P. Doherty Abstract Results are presented on three-phase air/oil/water horizontal flow in a 0.026 m i.d. symmetrical impacting tee junction. The flow regimes observed agreed with an existing three-phase flow map. The inversion from water-dominated (WD) to oil-dominated (OD) flow was at an oil-to-liquid volumetric ratio of fo = 0.285. The inversion was at a low fo value because of the relatively tranquil conditions studied. Retention of oil on the pipe wall at the air/water two-phase condition at fo = 0 resulted in a dramatic increase in the pressure drop above that expected for the two-phase flow. The pressure drop in the tee junction arms increased with liquid-flow rate. The actual tee junction pressure drop showed a similar pattern to that observed in the inlet arm. The pressure drop was relatively constant in the OD region but showed a dramatic increase in the WD and inversion regions at low fo values. Non-dimensionalising the junction pressure drop as le/d gave a similar pattern but the scatter of data increased. The tee pressure loss data were modelled using the Lockhart-Martinelli ,G parameter and gave similar but different correlations for the WD and OD regions. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Two-phase bifurcated dividing pipe flowASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 1 2009A. Murphy Abstract Data are reported on the pressure drop of co-current air,water two-phase flow through 0.0454 m i.d. bifurcations with included angles of 60°, 90°, 120° and 180°. The pressure changes on account of the angles at the junctions depended on the superficial phase velocities and the angle of bifurcation. For the 60° lowest angle of bifurcation the pressure drop was insensitive to flow rates if the superficial liquid velocity was in the lower range at and below 0.1 m s,1. For higher liquid flows the pressure loss increased dramatically, particularly in the annular-type regimes. When the angle at the junction was increased, negative values of pressure loss, i.e. an increase in pressure was recorded across the bifurcation in the gas velocity region under 10 m s,1 and liquid rates at and above 0.1 m s,1 in the slug and blow-through slug regimes. The effect coincided with liquid separation from the inner inlet pipe wall of the junction and its subsequent reformation on the downstream walls. A second less dramatic increase in junction pressure drop occurred at the lowest liquid flow rate of 0.05 m s,1 for the tee (180° bifurcation) that was due both to the smooth transition of liquid through the junction and the damping of surface waves in stratified-type flow. A flow regime map was presented for the tee junction. The inlet flow showed agreement with the map but the flow regimes found in the outlet arms of the junction tended to form earlier than expected being triggered by the pressure disturbances in the passage through the bifurcation. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] | |||||||||||||||||||