Academic literature on the topic 'Diffusion-Inertia Model'

Bubble formation and dissolution have a wide range of industrial applications, from the production of beverages to foam manufacturing processes. The rate at which the bubble expands or contracts has a significant effect on these processes. In the current work, the hydrodynamics of an isolated bubble expanding due to mass transfer in a pool of supersaturated gas–liquid solution is investigated. The complete scalar transportation equation (advection–diffusion) is solved numerically. It is observed that the present model accurately predicted bubble growth when compared with existing approximated models and experiments. The effect of gas–liquid solution parameters such as inertia, viscosity, surface tension, diffusion coefficient, system pressure, and solubility of the gas has been investigated. It is found that the surface tension and inertia have a very minimal effect during the bubble expansion. However, it is observed that the viscosity, system pressure, diffusion, and solubility have a considerable effect on bubble growth.

This report reviews the feasibility of two-dimensional hydrodynamic models in bulk SiC and ZnO semiconductor materials. Although the single-gas hydrodynamic model is superior to the drift-diffusion or energy balance model, it is desirable to direct the efforts of future research in the direction of multi-valley hydrodynamic models. The hydrodynamic model is able to describe inertia effects which play an increasing role in different fields of micro and optoelectronics where simplified charge transport models like the drift-diffusion model and the energy balance model are no longer applicable. Results of extensive numerical simulations are shown for SiC and ZnO materials, which are in fair agreement with other theoretical or experimental methods.

Summary Loadings acting on a wellbore are more realistically regarded as dynamic rather than static, and the wellbore response under dynamic loading can be different from that under static loading. Under dynamic loading, the inertia term should be considered and the changing rate of loading could induce a change in the mechanical properties of the wellbore, which might compromise wellbore stability and integrity. In this paper, a fully coupled poroelastodynamic model is proposed to study wellbore behavior. This model not only considers fully coupled deformation/diffusion effects, but also includes both solid and fluid inertia terms. The implicit finite-difference method was applied to solve the governing equations, which allows this model to handle all kinds of dynamic loading conditions. After modifying the existing code only slightly, our numerical solution can neglect inertia terms. The numerical results were validated by comparing them to the analytical solution with a simulated sinusoidal boundary condition. To understand this model better, a sensitivity analysis was performed, and the influence of inertia terms was investigated. After that, the model was applied to analyze wellbore stability under tripping operations. The results show that the inertial effect is insignificant for tripping and a fully coupled, quasistatic model is recommended for wellbore stability under tripping operations. The fully coupled poroelastodynamic model should be used for rapid dynamic loading conditions, such as earthquakes and perforations.

Consider the gravity-driven flow of a thin liquid film down a vertical fibre. A model of two coupled evolution equations for the local film thickness h and the local flow rate q is formulated within the framework of the long-wave and boundary-layer approximations. The model accounts for inertia and streamwise viscous diffusion. Evolution equations obtained by previous authors are recovered in the appropriate limit. Comparisons to experimental results show good agreement in both linear and nonlinear regimes. Viscous diffusion effects are found to have a stabilizing dispersive effect on the linear waves. Time-dependent computations of the spatial evolution of the film reveal a strong influence of streamwise viscous diffusion on the dynamics of the flow and the wave selection process.

The paper describes a theory of particle deposition based formally on the conservation equations of particle mass and momentum. These equations are formulated in an Eulerian coordinate system and are then Reynolds averaged, a procedure which generates a number of turbulence correlations, two of which are of prime importance. One represents ‘turbulent diffusion’ and the other ‘turbophoresis’, a convective drift of particles down gradients of mean-square fluctuating velocity. Turbophoresis is not a small correction; it dominates the particle dynamic behaviour in the diffusion-impaction and inertia-moderated regimes.Adopting a simple model for the turbophoretic force, the theory is used to calculate deposition from fully developed turbulent pipe flow. Agreement with experimental measurements is good. It is found that the Saffman lift force plays an important role in the inertia-moderated regime but that the effect of gravity on deposition from vertical flows is negligible. The model also predicts an increase in particle concentration close to the wall in the diffusion-impaction regime, a result which is partially corroborated by an independent ‘direct numerical simulation’ study.The new deposition theory represents a considerable advance in physical understanding over previous free-flight theories. It also offers many avenues for future development, particularly in the simultaneous calculation of laminar (pure inertial) and turbulent particle transport in more complex two- and three-dimensional geometries.

La pollution de l'air, en particulier celle due aux particules fines et ultrafines, a des effets délétères considérables sur la santé humaine. Plusieurs études ont établi un lien direct entre l'exposition à la pollution particulaire et diverses maladies respiratoires et cardiovasculaires. À l'intérieur des véhicules, la menace est d'autant plus préoccupante en raison de concentrations importantes de polluants particulaires recensées. Par conséquent, l'amélioration de la qualité de l'air dans l'habitacle des véhicules est désormais une priorité majeure pour les constructeurs automobiles. Dans ce contexte, cette thèse vise à comprendre l'environnement intérieur des véhicules en caractérisant la distribution spatiale des polluants, en particulier des particules fines et ultrafines, en fonction de leur taille ainsi que de paramètres tels que la topologie de l'écoulement et le niveau de turbulence. Ces connaissances permettront notamment de cibler des solutions localisées de purification de l'air, d'optimiser l'emplacement des micro-capteurs qui équiperont de plus en plus les futurs véhicules, et de proposer des solutions pour une gestion efficace des systèmes de filtration en fonction de la répartition de ces particules et de leurs concentrations dans l'habitacle. Tout d'abord, une attention particulière a été accordée à la modélisation de l'écoulement monophasique. Deux approches de modélisation numérique ont été adoptées : l'approche RANS (Reynolds Averaged Navier-Stokes), basée sur la résolution des champs moyens des équations de Navier-Stokes, et l'approche de simulation à grande échelle LES (Large Eddy Simulation), qui consiste à résoudre les grandes structures contenant la majeure partie de l'énergie cinétique et à modéliser la contribution des plus petites échelles. Dans le cas de l'approche RANS, divers modèles de fermeture du premier et du second ordre ont été testés et comparés. En outre, une analyse de la structure de turbulence de l'écoulement dans l'habitacle a été réalisée à l'aide de la méthode du diagramme d'anisotropie de Lumely (Anisotropy Invariant Mapping). Enfin, pour valider les résultats des modèles numériques, une campagne de mesures du champ de vitesse, basée sur la technique de l'anémométrie à fil chaud, a été menée dans l'habitacle d'une voiture de type SUV. Ensuite, la dynamique des polluants particulaires dans l'habitacle de la voiture a été étudiée à l'aide du modèle DIM (Diffusion-Inertia Model). Ce modèle eulérien de diffusion inertielle des particules permet de prendre en compte différents mécanismes de transport, notamment le transport par le champ moyen, l'effet des forces volumiques (i.e. la gravité), la déviation des particules par rapport aux lignes de courant du fluide (effets centrifuges), la diffusion brownienne et turbulente, et la turbophorèse ou le transport par les gradients d'énergie cinétique turbulente. Le modèle a d'abord été validé sur des configurations standard telles que la dispersion dans des enceintes ventilées de petite échelle, le dépôt dans des coudes circulaires à 90°, ainsi que dans le cas du transport de particules dans un jet rond. Le modèle a ensuite été appliqué à la simulation du transport de particules à l'intérieur d'un véhicule à grande échelle. L'influence de la taille des particules sur les champs de concentration internes a d'abord été analysée. Ensuite, l'influence de la présence de passagers a été étudiée. Enfin, une campagne de mesures de la concentration de particules dans l'habitacle a été réalisée afin d'évaluer la pertinence du modèle diphasique. Cette étude a permis le développement d'un modèle complet de simulation de la dispersion des polluants particulaires dans un habitacle en fonction de conditions de ventilation et de caractéristiques des particules
Air pollution, especially that caused by fine and ultrafine particles, has significant deleterious effects on human health. Several studies have established a direct link between exposure to particulate pollution and various respiratory and cardiovascular diseases. Within vehicles, the threat is even more concerning due to the significant concentrations of particulate pollutants recorded. Therefore, improving air quality inside vehicle cabins is now a major priority for automotive manufacturers. In this context, this study aims to understand the interior environment of vehicles by characterizing the spatial distribution of pollutants, particularly fine and ultrafine particles, as a function of their size and parameters such as flow topology and turbulence level. This knowledge will be crucial for targeting localized air purification solutions, optimizing the placement of the micro-sensors that will equip future vehicles, and providing solutions for the more effective management of filtration systems as a function of the distribution and concentrations of these particles in the car cabin. First, special attention was devoted to modeling the single-phase flow. Two numerical modeling approaches have been adopted: the RANS (Reynolds Averaged Navier-Stokes) approach, based on solving the mean flow fields of the Navier-Stokes equations, and the LES (Large Eddy Simulation) approach, which involves solving the large structures containing the major part of the kinetic energy and modeling the contributions of the smaller scales. In the case of the RANS approach, various closure models, of first- and second-order, have been tested and compared. Furthermore, the turbulence structure of the flow inside the car cabin has been analyzed using Lumley's Anisotropy Invariant Mapping method (AIM). Finally, to validate the results of the numerical models, a velocity field measurement campaign, based on hot-wire anemometry technique, was conducted inside the cabin of an SUV-type car. Next, the dynamics of particulate pollutants in the car cabin was studied using the Diffusion-Inertia Model (DIM). This Eulerian model of inertial particle diffusion takes into account various transport mechanisms, including transport by the mean field, the effect of volume forces (i.e., gravity), particle deviation from fluid streamline (centrifugal effects), Brownian and turbulent diffusion, and turbophoresis or transport by turbulent kinetic energy gradients. The model was first validated on standard configurations such as dispersion in small-scale ventilated enclosures, deposition in 90° circular bends, and particle transport in a round jet flow. The model was then applied to simulate particle transport inside a large-scale vehicle. The influence of particle size on internal concentration fields was first analyzed. Then, the influence of passenger presence was studied. Finally, a particle concentration measurement campaign was conducted in the cabin to assess the relevance of the two-phase model. This study has led to the development of a complete model for simulating the dispersion of particulate pollutants inside a car cabin based on ventilation conditions and particle characteristics

Les instruments politiques sur les émissions de véhicules passagers visent à réduire les externalités négatives sur l'environnement causées par l'usage des véhicules. Des réglementations sur les émissions de CO2 ont été mises en place en Europe, aux États-Unis, en Chine et ailleurs. La cible réglementaire basée sur la moyenne des émissions des véhicules vendus par un constructeur devient plus contraignante au fil du temps. Cette thèse analyse comment les constructeurs automobiles anticipent et préparent leurs futurs portefeuilles de technologies afin de respecter les futurs objectifs politiques. Pour conduire cette analyse, cette thèse développe un modèle d'optimisation des choix technologiques sous la contrainte de diffusion technologique.Avec ce cadre de modélisation basé sur la limitation de la vitesse à laquelle une technologie peut se diffuser dans un marché, cette thèse étudie trois questions politiques. Dans un premier temps, nous analysons comment le type d'anticipation du futur peut modifier les choix technologiques faits à court et à long termes. Nous montrons qu'une anticipation du futur focalisée sur les objectifs de court terme peut empêcher l'atteinte de la cible à long terme. Respecter la cible à court terme n'est une condition ni nécessaire ni suffisante pour permettre le niveau d'émissions requis par la cible à long terme. De plus si l'anticipation du futur n'est pas parfaite, les choix technologiques vont être verrouillés dans des technologies à faible potentiel d'abattement créant ainsi une dépendance au sentier qui limite l'abattement potentiel à long terme.Dans un deuxième temps, nous nous intéressons à évaluer quantitativement comment l'indexation sur la masse des véhicules de la réglementation CO2 change les critères optimaux de choix. Nous montrons qu'il n'existe pas de différence significative dans le coût social de la mobilité entre les deux mécanismes de réglementation CO2 avec et sans indexation sur la masse pour une même cible d'émissions. Cependant les choix technologiques entre ces mécanismes sont différents, la réglementation CO2 indexée à la masse ne développe en aucun cas les technologies d'allègement.Dans un troisième temps, nous étudions comment les choix technologiques changent quand des politiques à objectifs multiples se superposent. Nous centrons notre analyse sur deux externalités associées à la mobilité: les émissions CO2 et la pollution de l'air locale. Nous montrons trois types d'impacts de la superposition de politiques. Premièrement, une politique technologiquement spécifique tel que le Mandat de Véhicule à Zéro Émission en combinaison avec la réglementation CO2 provoque le développement de technologies vertes coûteuses et empêche les technologies sales et peu coûteuses de disparaître. Dans le cas de l'application de la réglementation CO2 seule nous n'observons pas ce comportement. Deuxièmement, la superposition de politiques peut mener à un coût élevé quand les technologies adaptées à chacune des politiques sont très différentes. Troisièmement, nous trouvons un effet ambigu de la superposition de politiques relative à l'application d'une politique seule sur la performance environnementale
Policy instruments on passenger vehicle emissions aim at reducing negative environmental externalities from vehicles use. To regulate CO2 emissions, fuel economy standards have been put in place in Europe and in the US, among others. These standards are made more stringent over time. This thesis analyzes how automotive firms anticipate and prepare their future technology portfolio to comply with expected future standards. To do so, we develop a model of optimal technology choice that captures technology diffusion constraints.With this framework, this thesis investigates three policy questions. First, we ask how the form of anticipation can affect near- and long-term technology choices. We find that focusing solely on near-term objectives can lead to failure to comply with a long-term target. In fact, meeting the near-term target is not a necessary nor a sufficient condition to satisfy long-term compliance. Moreover, when there is partial anticipation, as in a myopic view of the future, technology choices will be stuck with low abatement technologies creating a path dependency that limits long-term abatement potential.Second, we ask how much indexing fuel economy standard to mass (as in Europe or China) changes the optimal technology. We show that, for the same emission target, there is no significant difference in the social cost of mobility for an average vehicle with and without mass index. Thus a heavier vehicle fleet has the same cost than a lighter one. However, the technology choices are different, and mass indexed fuel economy standards lead to sidestepping lightweight technologies despite being cost effective from a CO2 emissions abatement point of view.Third, we ask how technology choices change when policies with multiple objectives overlap. We focus on two externalities associated with mobility: CO2 emissions and local air pollution. We show three type of effects of overlapping policies. First, a technology specific policy such as the Zero Emission Vehicle Mandate in combination with a fuel economy standard induces carmakers to develop more expensive green technologies and prevents cheap, dirty technologies from disappearing compared to the case of a fuel economy standard alone. Second, the combination of policies can lead to very high costs when technologies adapted to each policy are very different. Third, we find an ambiguous effect of overlapping policies relative to single-objective policy in terms of emissions performance

Advances in medical technology have altered the need for certain types of surgery to be performed in traditional inpatient hospital settings. Less invasive surgical procedures allow a growing number of medical treatments to take place on an outpatient basis. Hospitals face growing competition from ambulatory surgery centers (ASCs). The competitive threats posed by ASCs are important, given that inpatient surgery has been the cornerstone of hospital services for over a century. Additional research is needed to understand how surgical volume shifts between and within acute care general hospitals (ACGHs) and ASCs. This study investigates how medical technology within the hospital industry is changing medical services delivery. The main purposes of this study are to (1) test Clayton M. Christensen’s theory of disruptive innovation in health care, and (2) examine the effects of disruptive innovation on appendectomy, cholecystectomy, and bariatric surgery (ACBS) utilization. Disruptive innovation theory contends that advanced technology combined with innovative business models—located outside of traditional product markets or delivery systems—will produce simplified, quality products and services at lower costs with broader accessibility. Consequently, new markets will emerge, and conventional industry leaders will experience a loss of market share to “non-traditional” new entrants into the marketplace. The underlying assumption of this work is that ASCs (innovative business models) have adopted laparoscopy (innovative technology) and their unification has initiated disruptive innovation within the hospital industry. The disruptive effects have spawned shifts in surgical volumes from open to laparoscopic procedures, from inpatient to ambulatory settings, and from hospitals to ASCs. The research hypothesizes that: (1) there will be larger increases in the percentage of laparoscopic ACBS performed than open ACBS procedures; (2) ambulatory ACBS will experience larger percent increases than inpatient ACBS procedures; and (3) ASCs will experience larger percent increases than ACGHs. The study tracks the utilization of open, laparoscopic, inpatient and ambulatory ACBS. The research questions that guide the inquiry are: 1. How has ACBS utilization changed over this time? 2. Do ACGHs and ASCs differ in the utilization of ACBS? 3. How do states differ in the utilization of ACBS? 4. Do study findings support disruptive innovation theory in the hospital industry? The quantitative study employs a panel design using hospital discharge data from 2004 and 2009. The unit of analysis is the facility. The sampling frame is comprised of ACGHs and ASCs in Florida and Wisconsin. The study employs exploratory and confirmatory data analysis. This work finds that disruptive innovation theory is an effective model for assessing the hospital industry. The model provides a useful framework for analyzing the interplay between ACGHs and ASCs. While study findings did not support the stated hypotheses, the impact of government interventions into the competitive marketplace supports the claims of disruptive innovation theory. Regulations that intervened in the hospital industry facilitated interactions between ASCs and ACGHs, reducing the number of ASCs performing ACBS and altering the trajectory of ACBS volume by shifting surgeries from ASCs to ACGHs.

Abstract The effect of particle inertia on small particles diffusing in a turbulent wall bounded flow is calculated. The equation for a single particle is simplified assuming the particle response time is small compared to the time scale associated with turbulent fluctuations. Continuum equations are obtained from the single particle equation by consideration of mass and momentum conservation in a control volume by the use of volume averaging. Turbulent averaging is then carried out and the resulting correlations are modelled using results borrowed from second moment turbulence clo sure theory. Simplified forms are obtained for the constant stress region in a wall boundary layer, where the effect of inertia is found to enhance the particle flux. Finally, a numerical calculation of flow structure and the suspended sediment concentration over rippled bed under surface wave motion, using second moment turbulence closure model, is performed in order to simulate the characteristic phenomenon such as the vortex for mation and vortex lift-off over a sand rippled bed. A good agreement is obtained between the calculated values and experimental data.

The paper is aimed at the application of a model for simulating the dispersed turbulent flows. The model presented proceeds from a kinetic equation for the probability density function of the particle velocity distribution in turbulent flow. This approach is called the diffusion-inertia model (DIM). Applications of the model to droplet and bubble flows are presented. In the case of vaporized liquid, the interphase heat and mass transfer is introduced by adding the corresponding governing equations. This extended version of the DIM was applied to simulating the boiling water flow in a heated pipe.

Abstract Fluid flow in unconventional porous media is extremely complex due to the many physical processes and forces that governs fluid flow, such as diffusion, inertia, viscous flow, and sorption. Furthermore, modeling fluid flow in poor porous media often disregards the mentioned forces, assuming viscous transport is the predominant controller. This work introduces a new comprehensive flow model suitable for tight unconventional reservoirs, including viscous, inertia, diffusion, and sorption forces, to account for fluid transport in the three scales. The new model addresses 1-D linear flow in tight unconventional reservoirs and has been mathematically derived and numerically solved using MATLAB software and tested against a synthetic case study. The new models have been numerically solved and analyzed using synthetic data with previously published models that cater to the same phenomena and analyzed. In addition to studying the flow regimes effecting gas flow in porous media. It has been observed that the diffusion system becomes more prominent in regulating flow velocity with low permeability of the formation rock and low viscosity of the flowing fluid. Additionally, as a result, the sorption mechanism contribution to the flow increases with low permeability of the medium and low viscosity of the flowing fluid as it affects the concentration of gas, leading to release gas from being trapped in pores and rock surfaces.

Comparisons are made between the Advection-Diffusion Equation (ADE) approach for particle transport and the two fluid model approach based on the PDF method. In principal the ADE approach offers a simpler way of calculating the inertial deposition of particles in a turbulent boundary layer than that based on the PDF approach. However the ADE equations that have recently been used are only strictly valid for a simple Gaussian process when particle inertia is small. Using a prescribed but in general non-Gaussian random particle velocity field, it is shown that the net particle mass flux contains an extra drift term to that from the mean velocity of the particle velocity field, associated with the compressibility of the velocity field. Furthermore the diffusive flux in general depends not only upon the gradient of the mean concentration (true only for a Gaussian random flow field) but also upon higher order derivatives whose relative contribution depends on diffusion coefficients Dijk... etc. These coefficients depend upon the statistical moments associated with random displacements and compressibility of the particle flow field along particle trajectories which in turn depend upon particle inertia. In contrast the PDF approach offers the advantage of using a simple gradient (Gaussian) approximation in particle phase space which can lead to a non-Gaussian spatial dispersion process when particle inertia is important. Conditions based on the particle mean free path are derived for which a simple ADE is appropriate. Some of the features of particle transport in an inhomogeneous turbulent flow are illustrated by examining particle dispersion in a random flow field composed of pairs of counter rotating vortices which has an rms velocity which increase linearly from a stagnation point.

A continuous random walk (CRW) turbulent diffusion model was developed for Lagrangian particles within flow fields simulated by hybrid RANS/LES methodologies. For RANS flow-fields, the conventional time-scale and length-scale constants were determined by the turbulence intensity and dissipation values computed by the single-phase solver with a k-ω (Menter SST) model and subsequent comparison with turbulent particle diffusion experimental results of Snyder & Lumley (1971). This allowed validation against data for four particle types ranging from hollow glass to copper shot in grid-generated turbulence. The stochastic diffusion model was then extended to utilize the Nichols-Nelson k-ω hybrid RANS-LES turbulence model in a more complex turbulent flow resulting from the unsteady, three dimensional wake of a cylinder at Mach number of 0.1 and Reynolds number (ReD) of 800. The gas flow was computed with a 5th-order upwind-biased scheme. Throughout the wake, the sub-grid random walk model yielded good predictions of particle diffusion as compared with DNS. Also, these results indicate that crossing trajectory effects and inertia-based drift corrections are critical to handling a variety of particle Stokes numbers as well as regions of non-homogeneous turbulence, even when most of the kinetic energy is captured with the resolved-scales of an LES approach.

Although many years have past from the pioneer work of Lord Rayleigh [1] on bubble growth in the inertia controlled regime and later from Scriven [2], Plesset and Zwick [3] for the diffusion controlled regime, we are still missing mathematical model able to predict accurately both situations. Advances in computational power open the possibility of exploring up-close the transport phenomena in the vicinity of the liquid-vapor interface at an unprecedented resolution. Nonetheless, a high numerical resolution is not enough to fully solve the general problem of bubble growth. New models based on a sharp-interface interpretation of the liquid-vapor interface, have proven to provide accurate results in the diffusion controlled regime, however, these models must assume the interface temperature at the saturation value, restricting their application to physical situations where the evaporation rate satisfies the Stefan condition and bubbles are big enough as to neglect the curvature effects in the interface temperature. In an attempt to provide a more general framework to study bubble growth, a new phase-field model has recently been derived, where no assumption is made on the interface temperature. In this new model, the evaporation rate depends on the local interface temperature and not directly on the heat balance at the liquid-vapor interface. In principle, this particular feature of the model should allow us to simulate both, the inertia and diffusion controlled regimes, but the model has only been validated for the latter. The next step in the validation process is the simulation of bubble growth under convective conditions. Experiments of single bubbles growing and rising up under normal gravity conditions have shown that the growth exponent is about 0.8, in contrast to the value of 1.0 for the inertial controlled regime and 0.5 for the diffusion controlled regime. In this work, fully three dimensional phase-field simulations of bubble growth under convective conditions are presented, where the predicted bubble size and growth exponent compare very well to experimental observations.

An Improved model of the finite difference lattice Boltzmann method which allows us to consider gas-liquid two component flows with a large density ratio like air-water flows was proposed. Simulations of the two component fluids which have a free interface and a large density ratio were demonstrated. The model which has compressibility of fluid and allows us to consider the pressure waves propagating in water like water hammers was presented. The basic idea is to decrease a density fluctuation by giving a large pressure gradient. The compressibility of liquid was controlled by choosing the bulk modulus. In order to simulate immiscible two fluids, the modulated diffusion scheme proposed by Latva-Kokko et al. was employed. The scheme is able to produce a smooth interface by allowing a certain amount of interface diffusion. The continuum surface force proposed by Brackbill et al. was employed as surface tension. A collapse of liquid column was calculated in order to confirm the relation between the inertia of liquid with a large density and the gravity, and the appropriate result was obtained.

A verification of the applicability of the discontinuous random walk (DWR) Lagrangian Particle Tracking (LPT) model to calculate deposition in annular two-phase flow has been conducted. The comparison of simulation results to experimental data of deposition of mono-sized droplets shows that the model follows the correct trend in inertia-moderated regime, but is un-reliable in diffusion-impaction deposition regime. The comparison to other experimental studies of annular flow of different density ratios between the two phases reveals that the density ratio is incorrectly incorporated into the model, since the experimental trend is reversed. It can be concluded that the applicability of DWR LPT model for deposition calculation in steam-water flow at BWR conditions cannot be validated by solely comparing the simulation results to air-water experimental data.

A base fluid (e.g., water, ethanol, oil) in which nano-sized (1–100 nm) particles of a different material are dispersed, is known as a nanofluid. Nanofluids are attractive because the presence of the nanoparticles enhances energy transport considerably. As a result, nanofluids have higher thermal conductivity and single-phase heat transfer coefficients than their base fluids. In particular, the heat transfer coefficient increases appear to go beyond the mere thermal-conductivity effect, and cannot be predicted by traditional pure-fluid correlations such as Dittus-Boelter’s. In the nanofluid literature this behavior is generally attributed to thermal dispersion and intensified turbulence, brought about by nanoparticle motion. To test the validity of this assumption, we have considered seven slip mechanisms that can produce a relative velocity between the nanoparticles and the base fluid. These are inertia, Brownian diffusion, thermophoresis, diffusiophoresis, Magnus effect, fluid drainage and gravity. We concluded that, of these seven, only Brownian diffusion and thermophoresis are important slip mechanisms in nanofluids. Based on this finding, we developed a two-component four-equation non-homogeneous equilibrium model for mass, momentum and heat transport in nanofluids. A non-dimensional analysis of the equations suggests that energy transfer by nanoparticle dispersion is negligible, and thus cannot explain the abnormal heat transfer coefficient increases. Furthermore, a comparison of the nanoparticle and turbulent eddy scales clearly indicates that the nanoparticles move homogeneously with the fluid in the presence of turbulent eddies, so an effect on turbulence intensity is also doubtful.

In direct numerical simulations (DNS) of multiphase flows it is frequently found that features much smaller than the “dominant” flow scales emerge. Those features consist of thin films, filaments, drops, and boundary layers, and usually surface tension is strong so the geometry is simple. Inertia effects are also small so the flow is simple and often there is a clear separation of scales between those features and the rest of the flow. Thus it is often possible to describe the evolution of this flow by analytical models. Here we discuss two examples of the use of analytical models to account for small-scale features in DNS of multiphase flows. For the flow in the film beneath a drop sliding down a sloping wall we capture the evolution of films that are too thin to be accurately resolved using a grid that is sufficient for the rest of the flow by a thin film model. The other example is the mass transfer from a gas bubbly rising in a liquid. Since diffusion of mass is much slower than the diffusion of momentum, the mass transfer boundary layer is very thin and can be captured by a simple boundary layer model.