Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Condensation heat transfer in a rotating horizontal cylinder with a scraper

A dryer used in the drying process of paper production is usually a rotating horizontal cylinder in which steam condenses. This study concerns some experiments and analyses of condensate flow and heat transfer in a dryer with a scraper.

A laminar film model and a solid film model are introduced for the theoretical analyses. In the former the condensate flow is assumed to be laminar. In the latter the condensate film is assumed to adhere to the cylinder wall. In the analysis with the laminar film model, the film thickness diverges at relatively slow rotations. A criterion for the critical condition at which the divergence commences is proposed. From the solid film model, analytical expressions can be derived for the film thickness and the heat transmission coefficient through the condensate film and the cylinder wall.

The experiments are conducted with an acrylic resin cylinder and a stainless steel cylinder. The experimental result on heat transmission agrees with the analytical result for the solid film model if a condensate film about 25 μm thick remains in spite of scraping.     

Development of a PLIC-VOF method for the dynamic simulation of entry region flow in a laminar falling film

The present work describes a numerical procedure to simulate the development of hydrodynamic entry region in a gravity-driven laminar liquid film flow over an inclined plane. It provides a better insight into the physics of developing film in entry region. A novel numerical approach is proposed which has the potential to provide solutions for the complex physics of liquid film spreading on solid walls. The method employs an incompressible flow algorithm to solve the governing equations, a PLIC-VOF method to capture the free surface evolution and a continuum surface force (CSF) model to include the effect of surface tension. To account for the moving contact line on the solid substrate, a precursor film model based wall treatment is implemented. Liquid film flow has been simulated for the Reynolds number range of 5 ≤ Re ≤ 37.5, and the predicted results are found to agree well with the available analytical and experimental data.     

Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.     

Asymptotic model of slow three-dimensional liquid film flow in a space drop catcher

Slow steady-state film flows formed on the inner surface of a drop catcher funnel due to inertial deposition of drops of a dispersed working matter in the spacecraft cooling system are considered. A limiting asymptotic model of slow three-dimensional coolant film flow is constructed assuming that the deposited drops transfer all their mass, momentum, and energy to the film described by the equations of creeping viscous fluid flow in a thin layer of a priori unknown thickness. A first-order quasi-linear partial differential equation for the film thickness is derived. The shape of the film surface is investigated numerically as a function of parameters using the method of characteristics. The range of optimum parameters ensuring the steady-state film flow is found. The limits of existence of the solutions corresponding to the limiting model proposed are investigated.     

波纹竖板层流降膜蒸发传热的分析

对高粘度液体在等温正弦形波纹壁面上的自由降落与蒸发建立了摄动分析模型。得到了流动的分析解和蒸发传热的数值解。考察了壁面波纹的波幅和波数、液膜表面张力及贝克利数对流动与传热的影响,结果表明,加大波纹的波幅、适当选择波数、减小贝克利数可增强传热,而表面张力对蒸发传热的影响较小。     

A film flow model for analysing gravity-driven,thin wavy fluid films

To analyse the physics underlying gravity-driven runoff of thin wavy films, a film flow model is developed, and is solved with computational fluid dynamics. This model is based on the lubrication theory, and takes into account the gravitational, wall shear and surface tension forces. A key characteristic of the model is that it assumes only one computational cell over the film height, which enables studying film flow on larger computational domains. A main aim of this study is to perform a detailed validation of the numerical model. The film flow model is validated against several experiments of gravity-driven, thin fluid films on smooth surfaces. The time-averaged film thickness and the fluid speed profiles predicted by the model show very good agreement with experimental results. Similarly, the film flow model is able to predict the wave speeds with sufficient accuracy. The energy spectra of the waves, where higher frequency waves are present in film flows at higher Reynolds numbers, show an exponentially decaying trend at these high frequencies. The model performs better than the Nusselt equation for film flows, which under-predicts the time-averaged film thickness and over-predicts the time-averaged fluid speeds, even for flows at low Reynolds numbers. The film flow model is compared qualitatively for fingering behaviour. This model also allows to investigate film flows on large surfaces, which can be rough, curved and of complex geometrical shape.     

An investigation of a model of the flow pattern transition mechanism in relation to the identification of annular flow of R134a in a vertical tube using various void fraction models and flow regime maps

In the present study, new experimental data are presented for literature on the prediction of film thickness and identification of flow regime during the co-current downward condensation in a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm. R134a and water are used as working fluids in the tube side and annular side of a double tube heat exchanger, respectively. Condensation experiments are done at mass fluxes of 300 and 515 kg m^?2 s^?1. The condensing temperatures are between 40 and 50 °C; heat fluxes are between 12.65 and 66.61 kW m^?2. The average experimental heat transfer coefficient of the refrigerant HFC-134a is calculated by applying an energy balance based on the energy transferred from the test section. A mathematical model by Barnea et al. based on the momentum balance of liquid and vapor phases is used to determine the condensation film thickness of R134a. The comparative film thickness values are determined indirectly using relevant measured data together with various void fraction models and correlations reported in the open literature. The effects of heat flux, mass flux, and condensation temperature on the film thickness and condensation heat transfer coefficient are also discussed for the laminar and turbulent flow conditions. There is a good agreement between the film thickness results obtained from the theoretical model and those obtained from six of 35 void fraction models in the high mass flux region of R134a. In spite of their different valid conditions, six well-known flow regime maps from the literature are found to be predictive for the annular flow conditions in the test tube in spite of their different operating conditions.     

A new solution for the rotation-driven spreading of a thin fluid film

Lie groups are used to solve the equation governing the flow of a thin liquid film subject to centrifugal spreading and viscous resistance. A new implicit solution is found. It is shown how this relates to the previous known solutions for the spreading of an initially flat film, the steady state and a separable solution. New permissible forms for the film evolution are also studied, including solutions exhibiting finite time blow-up. Near the contact line, where the film height tends to zero, an approximate explicit solution is obtained which may be used to describe a film with any size contact angle.     

Two-phase flow over a surface with the formation of a liquid film by particle deposition

A consistent asymptotic theory of wall flow with film formation is constructed with reference to subsonic two-phase flow over a blunt body. The external flow problem and the film equations are solved simultaneously. This formulation of the problem supplements the investigation carried out in [4] in which particles deposited on the surface were assumed to disappear from the flow. It is shown that depending on the values of the governing parameters the flow in the film should be described either by the boundary layer equations or by the equations of creeping flow in a layer of unknown thickness. At the outer edge of the film the mass, momentum and energy fluxes found from the numerical solution of the flow problem are given. The case of isothermal film flow on the front of a sphere is investigated. The thickness of the film and the friction and heat transfer coefficients near the axis of symmetry are found for nonisothermal flows. The conditions under which the presence of a film significantly reduces the heat flow to the wall are determined. A similar formulation of the problem (but with another type of mass, momentum and energy sources at the outer edge) is encountered in problems of film condensation on a cold surface [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 85–92, July–August, 1989.     

Simulation and measurement of 3D shear-driven thin liquid film flow in a duct

Three-dimensional flow behavior of thin liquid film that is shear-driven by turbulent air flow in a duct is measured and simulated. Its film thickness and width are reported as a function of air velocity, liquid flow rate, surface tension coefficient, and wall contact angle. The numerical component of this study is aimed at exploring and assessing the suitability of utilizing the FLUENT-CFD code and its existing components, i.e. Volume of Fluid model (VOF) along with selected turbulence model, for simulating the behavior of 3D shear-driven liquid film flow, through a comparison with measured results. The thickness and width of the shear-driven liquid film are measured using an interferometric technique that makes use of the phase shift between the reflections of incident light from the top and bottom surfaces of the thin liquid film. Such measurements are quite challenging due to the dynamic interfacial instabilities that develop in this flow. The results reveal that higher air flow velocity decreases the liquid film thickness but increases its width, while higher liquid flow rate increases both its thickness and width. Simulated results provide good estimates of the measured values, and reveal the need for considering a dynamic rather than a static wall contact angle in the model for improving the comparison with measured values.     

Film thickness measurements in liquid–liquid slug flow regimes

At present there is significant interest in the development of small scale medical diagnostic equipment. These devices offer faster processing times and require smaller sample volumes than equivalent macro scale systems. Although significant attention has been focused upon their outputs, little attention has been devoted to the detailed fluid mechanics that govern the flow mechanisms within these devices. Conventionally, the samples in these small scale devices are segmented into distinct discrete droplets or slugs which are suspended in an organic carrier phase. Separating these slugs from the channel wall is a very thin film of the organic carrier phase.The magnitude of this film is the focus of the present study and the effects of sample slug length and carrier phase fluidic properties on the film are examined over a range of Capillary numbers. A non-intrusive optical technique was used to capture images of the flow from which the magnitude of the film was determined.The experimental results show that the film is not constant along the length of the slug; however above a threshold value for slug length, a region of constant film thickness exists. When compared with existing correlations in the literature, the experimental data showed reasonable agreement with the Bretherton model when the Capillary number was calculated based on the mean two phase flow velocity. However, significant differences were observed when the Capillary number was redefined to account for the mean velocity at the liquid interface, i.e., the mean slug velocity.Analysis of the experimental data revealed that it fell into two distinct flow regimes; a visco-capillary regime and a visco-inertial regime. A modified Taylor expression is presented to estimate the magnitude of the film for flows in the visco-capillary regime while a new model is put forward, based on Capillary and Weber numbers, for flows in the visco-inertial regime. Overall, this study provides some novel insights into parameters, such as aqueous slug length and carrier phase fluidic properties, that affect the thickness of the film in liquid–liquid slug flow regimes.     

Mass transfer with gas desorption from the surface of a liquid film in the presence of a cocurrent flow

Results of a thcoretical and experimental study of dynamics and mass transfer during desorption of a gas from a liquid film in the presence of a cocurrent air flow are presented. The calculation model is based on solving integral momentum and diffusion relations for the gaseous and liquid phascs. Both laminar and turbulent regimes of the film flow are analyzed. The experimental study of mass transfer was conducted for carbon dioxide desorption from a water film. Criterial relations for mass transfer in the gaseous and liquid phases are obtained. The experiments showed that the heat-transfer coefficients for the case under study are one order of magnitude grcater than those for the flow of a smooth film. Possible mechanisms of such an appreciable intensification of the liquid-film mass transfer in a cocurrent gas flow are discussed. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 131–138, July–August, 2000.     

Flow regime transition criteria for two-phase flow in a vertical annulus

In this work, a new flow regime transition model is proposed for two-phase flows in a vertical annulus. Following previous works, the flow regimes considered are bubbly (B), slug (S) or cap-slug (CS), churn (C) and annular (A). The B to CS transition is modeled using the maximum bubble package criteria of small bubbles. The S to C transition takes place for small annulus perimeter flow channels and it is assumed to occur when the mean void fraction over the entire region exceeds that over the slug–bubble section. If the annulus perimeter is larger that the distorted bubble limit the cap-slug flow regime will be considered since in these conditions it is not possible to distinguish between cap and partial-slug bubbles. The CS to C transition is modeled using the maximum bubble package criteria. However, this transition considers the coalescence of cap and spherical bubbles in order to take into account the flow channel geometry. Finally, the C to A transition is modeled assuming two different mechanisms, (a) flow reversal in the liquid film section along large bubbles; (b) destruction on liquid slugs or large waves by entrainment or deformation. In the S to C and C to A flow regime transitions the annulus flow channel is considered as a rectangular flow channel with no side walls. In all the modeled transitions the drift-flux model is used to obtain the final correlations. The final equations for every flow regime transition are easy to be implemented in computational codes and not experimental input is needed. The prediction accuracy of the newly developed model has been checked against air–water as well as boiling flow regime maps. In all the cases, the new developed model shows better predicting capabilities than the existing correlations most used in literature.     

An updated three-zone heat transfer model for slug flow boiling in microchannels

This work proposes a novel physics-based model for the fluid mechanics and heat transfer associated with slug flow boiling in horizontal circular microchannels to update the widely used three-zone model of Thome et al. (2004). The heat transfer model has a convective boiling nature and predicts the time-dependent variation of the local heat transfer coefficient during the cyclic passage of a liquid slug, an evaporating elongated bubble and a vapor plug. The capillary flow theory, extended to incorporate evaporation effects, is applied to estimate the bubble velocity along the channel. A liquid film thickness prediction method also considering bubble proximity effects, which may limit the radial extension of the film, is included. The minimum liquid film thickness at dryout is set to the channel wall roughness. Theoretical heat transfer models accounting for the thermal inertia of the liquid film and for the recirculating flow within the liquid slug are utilized. The heat transfer model is compared to experimental data taken from three independent studies. The 833 slug flow boiling data points cover the fluids R134a, R245fa and R236fa, and channel diameters below 1 mm. The proposed evaporation model predicts more than 80% of the database to within ±30%. It demonstrates a stronger contribution to heat transfer by the liquid slugs and correspondingly less by the thin film evaporation process compared to the original three-zone model. This model represents a new step towards a complete physics-based modelling of the bubble dynamics and heat transfer within microchannels under evaporating flow conditions.     

Numerical investigation of the coupled interaction between an unsteady aerodynamic flow field and a water film coating on a circular cylinder

Rain–wind induced vibration is an aeroelastic phenomenon that occurs on the inclined cables of cable-stayed bridges and arises due to the interaction between the unsteady wind loading and the formation of water rivulets on the cable surface. A new numerical method has been developed at the University of Strathclyde to simulate the influence of the external flow field on the rivulet dynamics and vice versa. The approach is to couple a Discrete Vortex Method solver to determine the external flow field and unsteady aerodynamic loading, and a pseudo-spectral solver based on lubrication theory to model the evolution and growth of the water rivulets on the cable surface under external loading. Results of this coupled model are presented, to provide detailed information on the development of water rivulets and their interaction with the aerodynamic field. In particular, the effect of the initial water film thickness and the angle of attack in plane on the resulting rivulets are investigated. The results are consistent with previous full scale and experimental observations with rivulets forming on the upper surface of the cable only in configurations where rain–wind induced vibration has been observed. Additionally, the thickness of the lower rivulet is found to be self-limiting in all configurations. The results demonstrate that the model can be used to enhance the understanding of the underlying physical mechanisms of rain–wind-induced vibration.     

A numerical experiment on the interaction between a film and a turbulent jet

This work is focused on the study of the impingement of a turbulent plane jet on a moving film. A computational fluid dynamics code has been used to simulate the interaction between the turbulent plane jet and the moving film. Since the problem of coupling between turbulence and free surface flow is poorly understood and experiments in this problem are difficult to carry out, this new numerical tool has been designed to give insight into global and local parameters of the free surface flow. To cite this article: D. Lacanette et al., C. R. Mecanique 333 (2005).     

Fundamentals of a liquid (soap) film tunnel

 The continuously running liquid film tunnel (LFT) is a novel device suitable for the study of two-dimensional flows. In this innovation, the films start from a reservoir, run over a horizontal or non-horizontal wire frame and get pulled/washed by a water sheet or by gravity of liquid film. How-ever, despite the simple design and widespread application of LFT, its working mechanisms are not well understood. In the present work, an experimental effort for explaining these mechanisms is reported. The results show that both film velocities and film flow rates increase with water sheet velocity up to a saturation level. This behavior is described via a force balance between the shear force produced by the water sheet and the opposing pulling force of reservoir and boundary layer frictions. The results also show that the average film thickness depends on the surfactant concentration. This is as predicted by a model based on Langmuir’s adsorption theory, in which the liquid film contains two external monolayers of surfactant and a slab of surfactant solution in between. When a film is drawn from the reservoir to the water sheet, the surfactant molecules start migrating from the former to the latter. To restore the thermodynamic equilibrium, the dragged film pulls more surfactant due to Marangoni elasticity, and thus a flow is established. The film flow soon reaches an equilibrium rate as required by the force balance mentioned above. Received: 15 August 1996/Accepted: 12 November 1996     

The role of external influences in the formation of waves on the surface of a flowing-down film of a viscous fluid

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave regimes of the film freely flowing down a vertical surface. The first case describes a ferromagnetic fluid film affected by the magnetic field, and the second case touches upon a dielectric fluid film affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces have a great impact on the flow.     

Stability of a vertical liquid film with consideration of the marangoni effect and heat exchange with the environment

The stability of a free vertical liquid film under the combined action of gravity and thermocapillary forces has been studied. An exact solution of the Navier-Stokes and thermal conductivity equations is obtained for the case of plane steady flow with constant film thickness. It is shown that if the free surfaces of the film are perfectly heat insulated, the liquid flow rate through the cross section of the layer is zero. It is found that to close the model with consideration of the heat exchange with the environment, it is necessary to specify the liquid flow rate and the derivative of the temperature with respect to the longitudinal coordinate or the flow rate and the film thickness. The stability of the solution with constant film thickness at small wave numbers is studied. A solution of the spectral problem for perturbations in the form of damped oscillations is obtained.