Academic literature on the topic 'Liquid film flow over complex surface'

Experimental results on hydrodynamics of cryogenic liquid film flow over the surface of the single elements of the structured packing are presented. Based on the comparison of experimental data, the effect of microtexture and perforation on the zones of liquid film spreading over a corrugated surface is shown for different values of the film Reynolds number. The results of experiments on dependence of a relative portion of liquid held in a single irrigated channel of the corrugated plates with different thicknesses on irrigation degree are presented. It is shown that microtexture, its direction relative to the gravity has a significant effect on redistribution of the local flow rate of liquid flowing over the surface with complex geometry

Results of experimental studies on hydrodynamics of the film flow of liquid nitrogen over the surface of the single elements of structured packing are presented. The effect of inclination angle of the large ribs and perforation on the zones of liquid film spreading over the corrugated surface with microtexture at different Reynolds numbers of the film is shown based on a comparison of experimental data. It is shown that the angle of large rib inclination has a significant influence on redistribution of the local flow rate of liquid flowing on the surface with complex geometry. Analysis of results of the high-speed video revealed that in a vicinity of the vertical lateral edges of corrugated plates, the intense rivulet flows are formed, including those with separation from the film flow surface. This negative factor can lead to significant liquid accumulation and flow near the vertical edges of the structured packing and on the inner wall of the heat exchanging apparatuses and, finally, to a significant increase in the degree of maldistribution of local liquid flow rate over the crosssection, for instance, of the distillation columns.

AbstractMicrotextured surfaces are commonly used to study complex hydrodynamic phenomena such as spreading and splashing of liquid droplets. However, although surface topography is known to modify near-surface flow, there is no theory able to quantitatively predict the dramatic changes in dynamics of liquid spreading and splashing. Here, we investigate experimentally water bells formed on micropatterned surfaces in order to characterize the hydrodynamics of inertia-dominated flows through regular porous layers. Water bells are self-suspended catenary-shaped liquid films created when a jet impinges on a horizontal disc called an impactor. We show that the presence of micrometre-sized posts regularly arranged on the impactor results in a decrease of the water bell radius and the loss of axisymmetry as open water bells adopt polygonal shapes. We introduce a simple model that captures the main features of the inertia-dominated flow and reveals the role of the hydrodynamic interactions between neighbouring posts. In addition to their applications for tunable jet atomization, these polygonal sheets provide a paradigmatic system for understanding inertia-dominated flow in porous media.

The breakdown of the liquid film at the wall in annular gas-liquid flow may lead to the formation of a stable dry patch. For the case of heat transfer surfaces this causes a hot spot. Dry patch stability depends on a balance of body and surface forces. In the present study the film is driven by the interfacial shear force and the gravity force is negligible. Hartley and Murgatroyd proposed a model for dry patches of shear driven films based on a balance of surface tension and inertia but the film contact angle had to be adjusted to an unrealistic value to fit the model to experimental data. Murgatroyd later proposed an additional force because the wall and the interfacial shear stresses on the film are unbalanced near the dry patch. The magnitude of the net shear force on the film is determined by a characteristic length, λ, over which this imbalance occurs. However, Murgatroyd did not validate the model with a mathematical solution for the distribution of the shear stresses but determined λ empirically to fit the experimental data. A new computational fluid dynamics (CFD) solution of the flow field in the film around the dry patch has been obtained. The CFD results confirm Murgatroyd’s hypothesis, although the details are more complex. In addition new experimental data for adiabatic upward annular air-water and air-ethylene glycol flows provide further validation for Murgatroyd’s model.

We present a computational study of free surface flows with rheologically complex interfaces in the film formation region of a slot coater. The equations of motion for incompressible Newtonian liquids in the bulk flow are coupled with the Boussinesq–Scriven constitutive equation for viscous interfaces in the dynamic boundary condition at the liquid-air free surface and solved with a mixed finite element method. We show that the interfacial viscosity plays a major role in the flow dynamics and operating limits of slot coating. We find that the interfacial viscosity makes viscous interfaces generally stiffer than their simple counterparts, affecting both the normal and the tangential stress jumps across the free surface. As a result, the interfacial viscosity counteracts the meniscus retraction and slows down the film flow, increasing the development length over the substrate and changing the topology of the recirculation region in the coating bead. Remarkably, we also find that the interfacial viscosity can substantially broaden the operating boundaries of the coating window associated with the low-flow limit, suggesting that surface-active components can be suitably designed to allow for the stable production of thinner films at higher speeds by tuning interfacial material properties in slot coating applications.

Experimental results on the parameters of the film flow of cryogenic liquid over the surface of single elements of the structured packing consisting of two corrugated plates are presented. The effect of microtexture and its direction relative to the direction of gravity on liquid distribution along the packing at different irrigation degrees is shown based on the comparison with experimental data. Experimental results on the degree of liquid flowing through the contact points in the packing with plates are presented relative to the irrigation degree. It is shown that microtexture and its direction have a significant influence on redistribution of the local liquid flow, flowing on the structured surface of complex geometry, along the packing.

The occurrence of thermocapillary convection in a Hele-Shaw cell in the presence of the surfactant film on the free surface is experimentally investigated. It is shown that at certain values of the control parameter two different zones are formed on the surface – the zone free from impurities and the stagnant zone. In the first zone, the onset and development of an intense Marangoni convection is observed, while in the stagnant zone the velocity of the motion on the surface is lower by about two orders of magnitude. This study clearly demonstrates that the analysis of the temperature profile provides sufficient information about both the distribution of tangential stresses over the surface and the degree of compression of the surfactant film. In addition, due to a simple linear law of temperature variation on the surface of the stagnant zone, the distribution of the surfactant molecules over the surface can be predicted based on the known equation of state for the film of the examined surfactant. Thus, the application of a set of simple experimental techniques to the examined model problem allowed us to obtain complete information on the state of a complex system consisting of a liquid layer and a surface film of the surfactant, the structure of the volumetric flow, the velocity of the liquid at the surface, the distribution of shear stresses and surfactant molecules over the surface.

AbstractFull numerical simulations of the Navier–Stokes equations for four cases of vertically falling liquid films with three-dimensional surface waves have been performed. Flow conditions are based on several previous experimental studies where the streamwise and spanwise wavelengths were imposed, which we exploit by simulating periodic wave segments. The considered flows are laminar but approach conditions at which intermittent wave-induced turbulence has been observed elsewhere. Working liquids range from water to silicone oil and cover a large interval of the Kapitza number ($\textit {Ka}=18\mbox{--}3923$), which relates capillary to viscous forces. Simulations were performed on a supercomputer, using a finite-volume code and the volume of fluid and continuum surface force methods to account for the multiphase nature of the flow. Our results show that surface waves, consisting of large horseshoe-shaped wave humps concentrating most of the liquid and preceded by capillary ripples on a thin residual film, segregate the flow field into two regions: an inertia-dominated one in the large humps, where the local Reynolds number is up to five times larger than its mean value, and a visco-capillary region, where capillary and/or viscous forces dominate. In the inertial region, an intricate structure of different-scale vortices arises, which is more complicated than film thickness variations there suggest. Conversely, the flow in the visco-capillary region of large-$\textit {Ka} $ fluids is entirely governed by the local free-surface curvature through the action of capillary forces, which impose the pressure distribution in the liquid film. This results in flow separation zones underneath the capillary troughs and a spanwise cellular flow pattern in the region of capillary wave interference. In some cases, capillary waves bridge the large horseshoe humps in the spanwise direction, coupling the two aforementioned regions and leading the flow to oscillate between three- and two-dimensional wave patterns. This persists over long times, as we show by simulations with the low-dimensional model of Scheid et al. (J. Fluid Mech., vol. 562, 2006, pp. 183–222) after satisfactory comparison with our direct simulations at short times. The governing mechanism is connected to the bridging capillary waves, which drain liquid from the horseshoe humps, decreasing their amplitude and wave speed and causing them to retract in the streamwise direction. Overall, it is observed that spanwise flow structures (not accounted for in two-dimensional investigations) are particularly complex due to the absence of gravity in this direction.

Hydrogels consist of a cross-linked polymer matrix imbibed with a solvent such as water at volume fractions that can exceed 90%. They are important in many scientific and engineering applications due to their tunable physiochemical properties, biocompatibility, and ultralow friction. Their multiphase structure leads to a complex interfacial rheology, yet a detailed, microscopic understanding of hydrogel friction is still emerging. Using a custom-built tribometer, here we identify three distinct regimes of frictional behavior for polyacrylic acid (PAA), polyacrylamide (PAAm), and agarose hydrogel spheres on smooth surfaces. We find that at low velocities, friction is controlled by hydrodynamic flow through the porous hydrogel network and is inversely proportional to the characteristic pore size. At high velocities, a mesoscopic, lubricating liquid film forms between the gel and surface that obeys elastohydrodynamic theory. Between these regimes, the frictional force decreases by an order of magnitude and displays slow relaxation over several minutes. Our results can be interpreted as an interfacial shear thinning of the polymers with an increasing relaxation time due to the confinement of entanglements. This transition can be tuned by varying the solvent salt concentration, solvent viscosity, and sliding geometry at the interface.

The mechanics of a free surface viscous liquid curtain flowing steadily between two vertical guide wires under the influence of gravity is investigated. The Navier-Stokes equation is integrated over the film thickness and an integro-differential equation is derived for the average film velocity. An approximate nonlinear differential equation, attributed to G. I. Taylor, is obtained by neglecting the higher order terms. An analytical solution is obtained for a similar equation which neglects the surface tension effects and the results are compared with the experimental measurements of Brown (1961).

Le défi de construire un solveur pour la simulation du refroidissement à l'huile dans les extrémités des bobinages des moteurs électriques est l'objet de cette étude. Le premier segment se concentre sur les phénomènes de transfert thermique du flux de film liquide sur une surface complexe pré-mouillée. L'objectif est de comprendre les mécanismes d'interaction entre le liquide et la surface complexe. Une analyse détaillée des résultats de la simulation est réalisée, en tenant compte des effets de paramètres variables tels que le nombre de Reynolds et le nombre de Prandtl. Suite à cela, un solveur précis VOF à deux phases couplé avec un modèle d'angle de contact dynamique est mis en œuvre pour tenir compte de ce type de géométrie des bobinages où le film liquide s'écoule par-dessus. Tout d'abord, l'algorithme PISO équilibré est développé, améliorant le calcul des gradients dans l'équation de la quantité de mouvement, et modifiant l'algorithme de Rhie et Chow. Cette méthode révisée assure que la force de tension superficielle et les gradients de pression sont discrétisés de manière identique au même emplacement. De plus, l'algorithme de Rhie et Chow est modifié en intégrant la force de tension superficielle, pour équilibrer les forces de pression. La méthode de la fonction de hauteur est intégrée au code CONVERGE CFD, remplaçant la fraction de vide lisse (SVF) pour une estimation de la courbure. Par la suite, l'angle dérivé du modèle d'angle de contact dynamique est utilisé pour modifier la courbure des cellules d'interface murale. Une explication approfondie de l'algorithme est fournie, ainsi que les cas de test de simulation et leur corrélation avec les données expérimentales. S'appuyant sur les travaux précédents, un ensemble de simulations est mené pour étudier les phénomènes de mouillage de l'écoulement liquide sur une surface complexe plate. En cette occasion, la surface est sèche, et le phénomène de mouillage est étudié. Cette partie présente la méthodologie de simulation numérique utilisée pour modéliser ces phénomènes, en plus des résultats de la simulation. Une analyse détaillée de ces résultats est présentée, notamment les effets de la méthode de calcul de la courbure, la variation de l'angle de contact d'équilibre et du nombre de Reynolds
The challenge of constructing a solver for the simulation of oil cooling in electric motor end-windings is the focus of this study. The initial segment concentrates on heat transfer phenomena of liquid film flow over a pre-wetted, complex surface. The goal is to understand the interaction mechanisms between the liquid and the intricate surface. A detailed analysis of the simulation results, taking into account the effects of varying parameters like Reynold number and Prandtl number. Following this, an accurate VOF two-phase flow solver coupling with a dynamic contact angle model is implemented to take into account this kind of geometry of windings where the liquid film flows over. Firstly, the Well-balanced PISO algorithm is developed, improving the calculation of gradients in the momentum equation, and modifying the Rhie and Chow algorithm. This revised method ensures that the surface tension force and pressure gradients are discretized identically at the same location. Additionally, the Rhie and Chow algorithm is modified by incorporating the surface tension force, to equilibrate the pressure forces. The Height Function method is integrated into the CONVERGE CFD code, replacing Smooth Void Fraction (SVF) for a curvature estimate. Subsequently, the angle derived from the dynamic contact angle model is utilized to modify the curvature of the interface wall cells. A thorough explanation of the algorithm is provided, along with the simulation test cases and their correlation with experimental data. Building upon previous work, a set of simulations are conducted to study the wetting phenomena of liquid flow over a flat complex surface. On this occasion, the surface is dry, and the wetting phenomena is studied. This part introduces the numerical simulation methodology used to model these phenomena, in addition to the simulation results. Detailed analysis of these results is presented, including the effects of curvature calculation method, varying the equilibrium contact angle and Reynolds number

Ces travaux de thèse s'incrivent dans le cadre du traitement de gaz acides et captage CO2 dans les colonnes à garnissages structurés. Les gaz à traiter réagissent avec un liquide s'écoulant à contre-courant sur des plaques métalliques dont la compléxité géométrique permet d'accroître l'aire d'échange, et donc l'efficacité du procédé. Dans un contexte de modélisation multi-échelles des contacteurs à garnissages structurés, les écoulements gaz-liquide à la plus petite échelle géométrique des plaques de garnissages (de l'ordre de l'épaisseur du film liquide) sont étudiés, pour améliorer la compréhension et la modélisation des écoulements diphasiques et phénomènes de mouillage dans les garnissages. L'objectif final est de développer une méthodologie CFD pour reproduire des écoulements diphasiques 3D sur des géométries complexes telles que les plaques de garnissages. Pour ce faire, il est nécessaire de progresser en méthodes numériques et de proposer des méthodes expérimentales pour observer des écoulements de film liquide sur des géométries complexes. Ces travaux comprennent une partie numérique et une partie expérimentale. Un écoulement sur une plaque de garnissage structuré peut présenter des zones sèches, et donc des lignes de contact (dynamiques), ce qui présente un défi en simulation numérique à cause des différentes échelles de l'écoulement. La méthodologie employée ici en simulation numérique consiste à résoudre l'écoulement jusqu'à une échelle intermédiaire en modélisant les effets des plus petites échelles. Le code de calcul Two-Phase Level-Set a été utilisé et modifié dans ce but. Différentes méthodes level-set ont d'abord été testées de manière à identifier une méthode satisfaisante quant à la réduction des erreurs de conservation de masse, un problème rencontré en level-set. Il est ici montré que certaines combinaisons de schémas de discrétisation spatiale et temporelle permettent de réduire considérablement ces erreurs de conservation de masse. Après avoir réalisé de nombreux tests de validation, une nouvelle méthode numérique est proposée pour simuler les grandes échelles d'écoulements diphasiques 3D avec ligne de contact dynamique en level-set, dans des conditions réalistes. La méthode est ici validée pour des écoulements axisymétriques de gouttes simulés en 3D, en régime visqueux et en régime inertiel, et pour des écoulements de gouttes sur plan incliné. Les résultats sont en très bon accord avec d'autres travaux numériques et expérimentaux. Afin de faciliter l'utilisation de cette méthodologie pour des applications industrielles, un modèle sous-maille similaire a été implémenté dans un code VOF commercial; les résultats sont aussi en très bon accord avec d'autres travaux. En plus de ces développements numériques, une campagne expérimentale est mise en oeuvre pour observer des écoulements de film liquide sur une plaque de garnissage structuré. Les méthodes expérimentales employées sont d'abord testées et validées pour des écoulements de film plat ou ondulé sur plan incliné, et ensuite utilisées pour observer des écoulements de film sur des plaques de garnissage. L'épaisseur de film liquide est mesurée aux creux et aux crêtes des picots des plaques de garnissages, pour différents débits, par imagerie confocale chromatique. Des lois de puissance de l'épaisseur de film en fonction du Reynolds sont proposées; celles-ci sont très différentes suivant la position des relevés de mesure, aux creux ou aux crêtes des picots. La vitesse à l'interface de l'écoulement gaz-liquide est aussi mesurée, par PIV et PTV, en utilisant des particules hydrophobes. Les résultats montrent que le liquide a tendance à dévier du creux des canaux (corrugations), et la norme de la vitesse semblent présenter des extremums correspondant aux creux et crêtes des picots. [...]
The work described in this thesis is motivated by the use of structured packing columns in acid gas treatment and post-combustion CO2 capture. In a counter-current mode, flue gases react with the liquid that flows down over metal sheets, the geometrical complexity of which allows increasing the specific interfacial area, and thereby the overall efficiency of the process. In the context of multiscale modeling of structured-packing contacting devices, the focus in this work is on the gas-liquid flows at the smallest geometrical scale of packing sheets, of the order of the liquid film thickness, aiming to improve understanding and modeling of two-phase flows and wetting phenomena in structured packings. The ultimate objective is to build up a CFD methodology to reproduce 3D two-phase flows over complex surfaces such as structured packing sheets. For this purpose, progress is necessary both in pertinent computational methods and in the adaptation of experimental methods for observing liquid film flows over complex surfaces. This thesis therefore consists of computational and experimental parts. Flows over structured packing sheets may exhibit dry zones, and hence (moving) contact lines, the numerical simulation of which presents a computational challenge due to the disparity in length scales involved. Here, the methodology for large-scale numerical simulations of flows with moving contact lines consists in resolving the flow down to an intermediate scale and modeling effects of smaller ones. The parallelized freeware Two-Phase Level-Set has been extended for this purpose. First though, because some level-set methods have been reproached to yield mass conservation issues, an assessment is made of the mass conservation properties of a range of level-set methods. It is demonstrated that the combined use of some spatial and temporal discretization schemes allows to drastically reduce mass conservation errors in level-set methods. Having thus implemented a level-set method with satisfactory performance at such tests (and others), a novel numerical method is proposed to perform 3D large-scale simulations of flows with moving contact lines in level-set, under realistic conditions. Validation tests of axisymmetric droplet spreading in a viscous, and in an inertial regime, simulated in 3D, and sliding drops are shown to be in excellent agreement with prior experimental and numerical work. The results show that complex contact-line dynamics observed in prior experimental studies on sliding droplets can be simulated using the present large-scale methodology. To facilitate dissemination of this work in industrial applications, a similar subgrid model has been implemented in a commercial volume-of-fluid code; results of validation tests are shown to be in excellent agreement with other work. These computational developments are accompanied by an experimental campaign to observe liquid film flows over structured packing sheets. All experimental methods used herein are tested and validated for flat and wavy films down an inclined plane before being used for observing liquid film flows over packing sheets. The film thickness is measured at local troughs and crests of small-scale corrugations of the structured packing sheet, for different flow rates, by Chromatic Confocal Imaging. Power laws of the Reynolds number for the mean liquid film thickness are suggested, with significant differences for measurements at crests compared to that at troughs. Interface velocity measurements are also performed by PIV and PTV using hydrophobic particles. Results reveal that the liquid tends to deviate from troughs of large-scale corrugations, and seems to exhibit local extrema of the velocity magnitude corresponding to troughs and crests of small-scale corrugations. [...]

碩士
國立成功大學
航空太空工程學系碩博士班
94
Abstract Subject：Applying MEMS Thermal Film Sensors Array and Liquid-crystal Flow Visualization Technique on Investigating Flow Reattachment over a Surface-mounted Rectangular Block Student：Jung-Chun Tsao Advisor：J. J. Miau The purpose of this paper is to investigate the three-dimensional, unsteady behaviors of flow reattachment over a surface-mounted rectangular block, whose ratio of width versus height of the block is equal to 4. The cholesterol- type liquid-crystal mixed with toluene and oligomer (one kind of polymer) has been used as a non-intrusive means of flow visualization. The temperature range of the liquid-crystal is between 43℃and 60℃, and the uncertainty can be less than 0.9%. As found from the liquid-crystal flow visualization, the reattachment length is around 3.15H, for the Reynolds numbers at 3.17×104, 4.22×104, and 5.12×104, respectively. The finger-type structures inferring the three- dimensional vortices stretched in the reattachment region on the top of the model have been found in the visualization. There are approximately four finger-type structures located near the trailing edge of the model, and all of its spanwise length scales are around 1H. The intensity of the finger-type structures are varying with time, but almost fixed spatially. Also, the three-dimensional unsteady behavior of the flow reattachment over the surface-mounted rectangular block can be comfirmed by the digital image (hue level) analysis of the visualization. In order to verify the result of the visualization, the self-made MEMS thermal film sensors and the X-type hot-wire were further employed. The DC amplifier circuit was in corporated with the thermal tuft. The cross-correlation analysis of the thermal film signals and hot-wire signals were made to gain better understandings on flow reattachment and finger-type structures. It has been found that the reattachment length is between 3.2H and 3.5H, and the dimensions of each finger-type structures are between 0.99H to 1.1H. The results obtained are consistent with those obtained by the liquid-crystal visualization.

Geometrically complex, high aspect ratio microstructures have been successfully formed in Bulk Metallic Glass (BMG) via superplastic forming against silicon dies [1–3]. Although nanoscale features have been created in a similar fashion, there exists a demand to develop these metallic nanofeatures into high aspect ratio nanostructures with controlled geometries. In past research a process model was created to predict the achievable nanoscale feature sizes and aspect ratios through a flow model [4]. The flow model assumes force equilibrium with a viscous term to account for the required force to produce flow and a capillary pressure term required to overcome surface effects which are significant at the nanoscale. In this paper, a thin film model to predict the pressure distribution across the BMG during the forming process when it is in the supercooled liquid state is presented. Silicon molds with various nanofeatures were produced using Deep Reactive Ion Etching to achieve high aspect ratio dies over a relatively large area in order to validate these models.

The present study is motivated by interest in understanding of physical mechanisms that govern the effect of material and micro-structural characteristics of heat surface on boiling heat transfer and burnout at high heat fluxes. The effect was reported and investigated experimentally and analytically over several past decades. Only recently, with the advent of nanotechnology including microscale manufacturing, it becomes possible to perform high heat-flux boiling experiments with control of surface conditions. Of particular importance for practice is the potential for significant enhancement of boiling heat transfer (BHT) and critical heat flux (CHF) in pool and flow boiling on heaters with specially manufactured and controlled micro-structured surfaces. This enhancement is very important to a very wide range of engineering applications, like heat exchanger and cooling system, where maximum flux is needed. Currently, there are many controlled experiments that investigate such effect and they lend themselves a subject for detailed computational analysis. The focus of this study is micro-hydrodynamics of the evaporating thin liquid film at the receding triple contact line, corresponding to formation of dry spot in the footprint of a growing bubble. Parametric investigations are performed to assess the hypotheses that micro-structured surfaces enhance resilience to burnout due to residual liquid in the dry patch after contact line receding. Towards the study objective, a particle-based (mesh-less) method of computational fluid dynamics called Smoothed Particle Hydrodynamics (SPH) is adopted. The SPH method is selected for its capability to handle fluid dynamics in complex geometries and free surface problems without mass loss (characteristic of alternative interface capturing schemes used in mesh-based methods). Both surface tension and surface adhesion (hydrophilicity) are implemented and tested. The solid (heater) surface and manufactured micro-structures are represented by solid-type particles. Heat transfer, phase change (evaporation) and vapor dynamics are not included in the present simulation. The bouncing drop case measures the contact time of water droplet with solid surface. This case is used for “mesh” sensitivity (particle size) study and calibration of boundary conditions and surface tension coefficient. Subsequently, case studies are formulated and performed for contact line dynamics on heater surfaces with the fabricated Micro Pillar Arrays surfaces (MPA) and smooth surface. Variable characteristics include surface tension and pillar density on structured surface (modified by changing distance between pillars). First of all, residual fluid are found in all simulations with structured surface, while fluid are drained for smooth cases. For structured surface, it’s found that after the contact line recedes, fluid with higher surface tension resides in the dry patch more than fluid with lower coefficient, and the relation tends to be non-linear. While for smooth surface, all fluid will be drained after certain time and the relations are non-monotonic; it’s also found that the amount of residual fluid increase as the distance between pillars decreases until a limit. The fluid then starts to decrease with pillars being set further apart. The increase starts from 30 μm and the limit is around 10 μm.

Bulk Metallic Glass (BMG) has been molded against silicon dies to fabricate both microstructures and nanostructures. At the microscale, geometrically complex, high aspect ratio microfeatures have been developed into controlled geometries [1–4]. A demand exists to control the nanofeatures in a similar manner. In past research, a thin film model was presented to predict the pressure distribution across the BMG during the molding process when it is in the supercooled liquid state [5]. In this paper, a flow model is presented to predict the achievable nanoscale feature sizes and aspect ratios. This model contains a viscous term to account for the required force to produce flow, and a capillary pressure term to account for the required energy to overcome surface effects. Silicon molds are being produced with various trench sizes over a relatively large area in order to validate these models.

В статье приводятся уравнения распределения скорости по поверхности сетчатого элемента, при стекании жидкости в ламинарном режиме. Преобразование формул происходит на основе принятых допущений. Произведён анализ полученных уравнений и даны рекомендации к дальнейшему использованию. The article presents the equations of the velocity distribution over the surface of the mesh element, when the liquid flows in the laminar mode. The transformation of formulas takes place on the basis of accepted assumptions. The obtained equations are analyzed and recommendations for further use are given.

Abstract The performance of a falling-film heat exchanger is strongly linked to the surface characteristics and the heat transfer processes that take place over the tubes. The primary aim of this numerical study is to characterize the influence of surface wettability of tubes on the falling film flow mode and its associated surface heat transfer. Surface wettability is generally characterized by the contact angle and, in this study, the wettability characteristics ranged from superhydrophilic to a superhydrophobic tube surface. The dynamic motion of the triple contact line connecting the solid, liquid and gas phases over the tube surface is replicated with the help of the Kistler’s dynamic contact angle model. The volume of Fluid (VOF) simulations was carried out for the flow and heat transfer of liquid flow over horizontal tubes with different surface wettabilities. The mass flow rate is such that the flow is in the jet mode where the liquid flows in the form of jets in between the horizontal tubes. This corresponds to a liquid mass flow rate per unit tube length of 0.06 and 0.18 Kg/m-s, under which the inline and staggered jets modes of flow are observed. Under the two flow rates and different surface wettabilities, the liquid flow hydrodynamics over the tube surfaces was explored in terms of the liquid film thickness, the contact areas (solid-liquid and liquid-air) between the different phases, and the heat transfer coefficient. The axial resistance imposed by the increasing contact angle tends to inhibit the extent of the liquid spreading over the tube surface and this, in turn, influences the liquid film thickness and the wetted area of the tube surface. A significant decrement in the heat transfer rate from the tube surfaces was observed as the equilibrium contact angle ranged from 2° to 175°. Heat transfer characteristics were quantified over a wide range of contact angles for the two mass flow rates. Fluid recirculations were observed in the liquid bulk which had a major impact on the heat transfer distribution over the tube surface.

One of the challenges in the numerical simulation of a system of particles in a fluid flow is to balance the need for an accurate representation of the flow around individual particles with the feasibility of simulating the fully-coupled dynamics of large numbers of particles. Over the past few years, several techniques have been developed for the direct numerical simulation of dispersed two-phase flows. Examples include the ALE-FEM formulation described by Hu et al. [1] and the DLM method of Patankar et al. [2]. The former uses a finite element mesh that conforms to the shape and position of each particle and evolves dynamically as the particles move, while the latter employs a fixed mesh and constraints are imposed in the volume of fluid occupied by the particle to reproduce a corresponding rigid body motion. In both the aim is to fully resolve the flow dynamics for each particle and there is a corresponding demand for high resolution of the flow. A typical approach used for gas-solid flows has been the point-force method that combines a Lagrangian tracking of individual particles with an Eulerian formulation for force feedback on the fluid flow. The latter approach has worked well for very small particles in systems of negligible void fraction but significant mass loading. The resolution level is very low and often the particles are smaller than the spacing between grid points. Its success comes from the averaging effect of large numbers of small particles and the fact that the influence of an individual particle is weak. The approach though is inaccurate for liquid-solid or bubbly flows when the individual particles are of finite size and the void fractions may easily be larger than 1%. In tracking the individual particles an equation of motion is formulated that relates the particle acceleration to the fluid forces acting on the particle, and these forces such as drag and lift are parameterized in terms of the local fluid velocity, velocity gradients and history of the fluid motion. Once flow modification is included however, it is harder to specify the local flow. The parameterizations also become more complex as effects of finite Reynolds number or wall boundaries are included. As a numerical procedure, the force-coupling method (FCM) does not require the same level of resolution as the DLM or ALE-FEM schemes and avoids the limitations of the point-force method. It gives a self-consistent scheme for simulating the dynamics of a system of small particle using a fixed numerical mesh and resolves the flow except close to the surface of each particle. Distributed, finite force-multipoles are used to represent the particles, and FCM is able to predict quite well the motion of isolated particles in shear flows and the interaction between moving particles. The method also provides insights into how the two-phase flow may be described theoretically and modeled. The idea of the force-coupling method was first introduced by Maxey et al. [3]. The basic elements of the method are given by Maxey & Patel [4] and Lomholt & Maxey [5]. In the basic version of the method, fluid is assumed to fill the whole flow domain, including the volume occupied by the particles. The presence of each particle is represented by a finite force monopole that generates a body force distribution f(x,t) on the fluid, which transmits the resultant force of the particles on the flow to the fluid. The velocity field u(x,t) is incompressible and satisfies ∇·u=0(1)ρDuDt=−∇p+μ∇2u+f(x,t),(2) where μ is the fluid viscosity and p is the pressure. The body force due to the presence of NP bubbles is f(x,t)=∑n=1NpF(n)Δ(x−Y(n)(t)),(3)Y(n)(t) is the position of the nth spherical particle and F(n)(t) is the force this exerts on the fluid. The force monopole for each particle is determined by the function Δ(x), which is specified as a Gaussian envelope Δ(x)=(2πσ2)−3/2exp(−x2/2σ2)(4) and the length scale σ is set in terms of the particle radius a as a/σ = π. The velocity of each particle V(n)(t) is found by forming a local average of the fluid velocity over the region occupied by the particle as V(n)(t)=∫u(x,t)Δ(x−Y(n)(t))d3x.(5) If mP and mF denote the mass of a particle and the mass of displaced fluid, the force of the particle acting on the fluid is F(n)=(mP−mF)(g−dV(n)dt).(6) This force is the sum of the net external force due to buoyancy of the particle and the excess inertia of the particle over the corresponding volume of displaced fluid. In addition a short-range, conservative force barrier is imposed to represent collisions between particles and prevent overlap. A similar barrier force is imposed, normal to the wall, to represent collisions between a particle and a rigid wall. With this scheme the body forces induce a fluid motion equivalent to that of the particles. The dynamics of the particles and the fluid are considered as one system where fluid drag on the particles, added-mass effects and lift forces are internal to the system. The method does not resolve flow details near to the surface of a particle, and indeed the no-slip condition is not satisfied on surface. At distances of about half a particle radius from the surface the flow though is fairly well represented. While there is no explicit boundary condition on the particle surface, the condition (5) ensures that the bubble and the surrounding fluid move together. The method has been applied to a variety of flow problems. Lomholt et al. [6] compared experimental results for the buoyant rise of particles in a vertical channel filled with liquid with results from corresponding simulations with FCM. The particle Reynolds numbers were in the range of 0 to 5 and the results agreed well. The wake-capture and the drafting, kissing and tumbling of pairs of particles, or of a group of three particles were found to match. Comparisons have made too with full direct numerical simulations performed with a spectral element code [7]. Liu et al. [8] examined the motion of particles in a channel at both low and finite Reynolds numbers, up to Re = 10. There was in general good agreement between the FCM results and the DNS for the particle motion, and the flow details were consistent away from the particle surface. There has been extensive work in the past on the sedimentation of particles in a homogeneous suspension, mainly for conditions of Stokes flow. Climent & Maxey [9] have verified that the FCM scheme reproduces many of the standard features found for Stokes suspensions. The results for finite Reynolds numbers illustrate how the structure of the suspension changes as fluid inertia is introduced, in particular limiting the growth in velocity fluctuation levels with system size. Further work has been done by Dance [10] on sedimenting suspensions in bounded containers. Recently we have been studying the dynamics of drag reduction by injecting micro-bubbles into a turbulent channel flow. This has been proven through experiments over the past 30 years to be an effective means for drag reduction but the details of the mechanisms involved have not been determined. Numerical simulations by Xu et al. [11] have shown clear evidence of drag reduction for a range of bubble sizes. A key feature is the need to maintain a concentration of bubbles in the near-wall region. In the talk, the method will be described and example results given. Specific issues relevant to gas-solid flows will be discussed.

Wall spray interactions play an important role in the combustion efficiency prediction of turbojet or ramjet. They generate complex physical phenomena such as rebound onto wall or rebound onto wetted surface, splashing, deposition, film formation, film streaming and film atomization. ONERA/DMAE has been working on these subjects for few years, and some wall-drop interaction models have been developed and integrated into CFD-industrial-codes. In order to improve this work, a basic experimental study has been performed to analyze wall liquid film inside a combustion chamber. This is a cold flow experiment, where a liquid film is flowing on a hot tilted plate put on the bottom wall of the tunnel. Ethanol enriched with fluoresceine is used as fuel. The liquid emerges from a pipe with a diameter of 1 mm. Afterwards the film flow is canalized in a groove. It is streaming on the hot plate which temperature should be fixed from 300 K to 700 K by an element heating controlled electronically. The film thickness is measured with a non-intrusive technique based on the laser trace displacement at the liquid film interface. Indeed, when the film thickness varies, the trace of the laser plan is moving. Thus, it is enough to know the optical magnification used and the angle of the CCD camera to obtain the film thickness. This technique gives only the thickness of the film, so its velocity has to be estimated using flow rate conservation. The goal of the present experiment is to create an experimental data-base on wall liquid film behavior in terms of thickness, velocity and surface instabilities evolution (with an FFT analysis) for numerical comparison.

This paper presents heat transfer coefficient and film cooling effectiveness measurements over a constant curvature concave surface. The coolant flow is ejected into the mainstream through a row of either simple holes or forward-expanded holes maintained at a streamwise injection angle (γ) of 35°. A transient liquid crystal thermography was employed to measure both the local heat transfer coefficient and film cooling effectiveness over the film-cooled concave test piece. With a pitch-to-diameter ratio (P/d) of 3, each forward-expanded injection hole has an expanded angle of 8° at the exit plane. In current study, the effect of blowing ratio (M) on film cooling performance was also investigated by varying the blowing ratio range from 0.5 to 1.5. Measurements were performed at mainstream Reynolds number (Red) of 2000 with turbulence intensity (Tu) of 2%, and coolant-to-mainstream density ratio (ρc/ρm) of 1.05. The curvature strength (2r/d) of test piece is 86.5. Comparisons were made with baseline cases of concave surface test piece with simple hole configuration done in prior studies. For forward-expanded hole configuration, measured results showed that both the laterally averaged heat transfer coefficient and film cooling effectiveness increase with increasing blowing ratio downstream of X/d = 10. A better film protection effect can be observed at M = 0.5 since coolant flows ejected at this blowing ratio might stay closer to the concave surface than other blowing ratios in present tested range for both hole configurations. As far as the hole shape is concerned, the forward-expanded hole injection provides better surface protection than the simple hole injection.

Heat transfer enhancement area attracts the close attention of the researchers and engineers worldwide for the last decades. The most popular techniques nowadays to enhance heat transfer from the surface is to extend it with the fins, studs, etc. or to profile it with the elements of artificial roughness, winglets, dimples, etc. Those types of surface enhancement allow improving the thermal efficiency of the heat transfer equipment with minimal design modification and without significant capital expenses. One of the interesting and promising techniques of the surface profiling is the formation on the surface the arrangement of spherical dimples, which generate intensive vortex structure near the surface, increase flow turbulence and, as a result, enhance heat and mass transfer between a profiled surface and a liquid (or gas) flowing over it [1–3]. In this connection, it is interesting to establish whether surface profiling will also enhance the heat transfer intensity between a liquid film on such a surface and ambient air. Unfortunately, authors were not able to find any publications on this subject in the open domain. At the same time, the investigation of this process could be of great interest for the engineering practice, in particular, for the cooling towers advancement. In the present work, the authors discuss some experimental results obtained for the different profile parameters and flow regimes.

Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.