Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film

Theoretical and numerical investigations of the heat transfer and hydrodynamics in a liquid film flowing along an inclined substrate under the action of gravity with a local heat source have been performed. A two-dimensional model, based on the thin layer approximation, has been developed describing deformations of the film interface. Equation of a non-isothermal thin-film flow with linear dependence of viscosity and surface tension on temperature is derived. A generalized analytical formula for the film thickness as a function of liquid flow-rate is obtained. Marangoni flow, due to local temperature changes, opposes the gravitationally driven film flow and forms a horizontal bump near the upper edge of the heater. Attention is paid to the viscosity effect on the shape of the bump and the film thinning on the local heaters. A second order deformation of the free surface before the bump up to flow may exist. The criterion for the appearance of this deformation is found analytically.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

A study on flow and heat transfer characteristics for saturated falling-film evaporation of liquid oxygen in a vertical channel

In this study, a mathematical model for the laminar falling film is presented in order to simulate the evaporation heat transfer characteristics in falling liquid oxygen films. The model takes into account the effect of the interfacial shear. The values of the film thickness, the heat transfer coefficient as well as the interfacial shear are obtained under given conditions by solving the model with an iteration method. The influences of the inlet Reynolds number, channel length and the interfacial shear on the flow and heat transfer characteristics of the falling film evaporation are analyzed in detail. Effects of key factors on the circulation ratio of the inlet fluid mass flow rate to the generated vapor mass flow rate, an important design parameter for reboilers/condensers, are particularly analyzed. In addition, the variations of the average vapor velocity and interfacial film velocity are also discussed. The analysis results could provide theoretical guidance for the simulation and design of downflow reboilers/condensers applied in air separation units.     

On the dynamics and heat transfer of bubble train in micro-channel flow boiling

The dynamics and heat transfer characteristics of flow boiling bubble train moving in a micro channel is studied numerically. The coupled level set and volume of fluid (CLSVOF) is utilized to track interface and a non-equilibrium phase change model is applied to calculate the interface temperature as well as heat flux jump. The working fluid is R134a and the wall material is aluminum. The fluid enters the channel with a constant mass flux (335 kg/m² 1 s), and the boundary wall is heated with constant heat flux (14 kW/m²). The growth of bubbles and the transition of flow regime are compared to an experimental visualization. Moreover, the bubble evaporation rate and wall heat transfer coefficient have been examined, respectively. Local heat transfer is significantly enhanced by evaporation occurring vicinity of interface of the bubbles. The local wall temperature is found to be dependent on the thickness of the liquid film between the bubble train and the wall.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

A new generalised model for liquid film cooling in rocket combustion chambers

A one dimensional analytical model of liquid film cooling in rocket combustion chambers operating at subcritical conditions is developed. The approach followed involves the selection of a control volume for mass and energy balance. The coolant evaporation rate per area is obtained from this energy balance. The present model incorporates mass transfer via entrainment by adapting suitable correlations from literature pertaining to annular flow conditions. The model predicted favourably with the experimental data available in open literature and produced superior results compared to all existing models. Results are presented for a mixed gas–water system under different conditions. Results indicate that convection dominates the heat transfer at the gas–liquid interface. Effects of gas Reynolds number, coolant inlet temperature, combustion chamber pressure, mass flow ratio of the liquid coolant to the free stream and the free stream turbulence on the liquid film length are presented in detail.     

Effects of inlet conditions on film evaporation along an inclined plate

The evaporation of falling water liquid film in air flow is used in different solar energy applications as drying, distillation and desalination, and desiccant systems. The good understanding of the hydrodynamics and heat exchange in falling liquid film and gas flow, with interfacial heat and mass transfer, can be applied in improving solar systems performance. The solar system performance is dependent on the operating conditions, system conception and related to several physical parameters, where the effects of some of these parameters are not completely clarified. In the present numerical study, we examine the effects of inlet conditions on the evaporation processes along the gas–liquid interface. The liquid film streams over an inclined plate subjected to different thermal conditions. Liquid and gas flows are approached by two coupled laminar boundary-layers. The numerical solution is obtained by utilizing an implicit finite-difference box method. In this analysis an air–water system is considered and the coupled effects of inclination, inlet liquid mass flow rate and gas velocity are examined. The results show that, for imposed heat flux or uniform wall temperature, the effect of inclination is highly dependent on the liquid mass flow rate and gas velocity. An increase in the liquid mass flow rate causes an enhancement of the effect of inclination on the heat and mass transfer. The inclination affects the heat and mass transfer, especially at lower gas velocities. In the range of inclination angles of 0–10°, an increase in the inclination improves the evaporation by increasing the vapor mass flow rate. The maximum effect of inclination is nearly achieved at an inclination angle of 10°.     

Flow and heat transfer characteristics of the evaporating extended meniscus in a micro-capillary channel

A mathematical model is developed to predict the transport phenomena during evaporation in the extended meniscus region of a micro-capillary channel. In this model, the vapor pressure variation and the disjoining pressure effect are included and the friction force at the liquid-vapor interface is considered as well. The results show that the local heat transfer coefficient has an extremely large value in the thin film region. The heat transfer rate, however, is larger for the meniscus than for the thin film region. The maximum liquid velocity appears at approximately 40% of the extended meniscus region and the variation of the heat flux has a negligible effect on the maximum liquid velocity. It is also found that the length of the extended meniscus region is affected by the heat flux, the channel height and the dispersion constant.     

Slip and micro flow characteristics near a wall of evaporating thin films in a micro channel

The microscopic liquid flow and heat transfer characteristics near the solid–liquid interface in the evaporating thin film region of a mini channel were investigated based on the augmented Young–Laplace equation and kinetic theory. A physical model using the boundary layer approximation and a constant slip length was developed to obtain the solid–liquid interfacial thermal resistances and interfacial temperatures. The results show that the ordered micro layer and micro flow near the wall reduce the effective liquid superheat and the liquid pressure difference mainly due to the reduced capillary pressure gradient. The solid–liquid interfacial thermal resistances and U‐shaped temperature drops tend to reduce the thin film spreading and heat transfer. The effects of the solid–liquid interfacial thermal resistances on the thin film evaporation outweigh the effects of the thermal conductivity enhancement due to the liquid ordering. The concepts of the micro flow and ordered adsorbed flowing micro layer are clarified to express the Kapitza resistance analytically in terms of the slip length and micro layer thickness. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 460–474, 2010; Published online 3 June 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20310     

Two-phase flow of refrigerants during evaporation under constant heat flux in a horizontal tube

This paper presents the results of simulations using a two-phase separated flow model to study the heat transfer and flow characteristics of refrigerants during evaporation in a horizontal tube. A one-dimensional annular flow model of the evaporation of refrigerants under constant heat flux is developed. The basic physical equations governing flow are established from the conservation of mass, energy and momentum. The model is validated by comparing it with the experimental data reported in literature. The present model can be used to predict the variation of the temperature, heat transfer coefficient and pressure drop of various pure refrigerants flowing along a horizontal tube. It is found that the refrigerant temperature decreases along the tube corresponding to the decreasing of its saturation pressure. The liquid heat transfer coefficient increases with the axial length due to the reducing thickness of the liquid film. The evaporation rate of liquid refrigerant tends to decrease with increasing axial length, due to the decreasing latent heat transfer through the liquid–vapor interface. The developed model can be considered as an effective tool for evaporator design and can be used to choose appropriate refrigerants under designed conditions.     

Numerical investigation of heat and mass transfer from an evaporating meniscus in a heated open groove

The process of evaporation from a meniscus into air is more complicated than in enclosed chambers filled with pure vapor. The vapor pressure at the liquid–gas interface depends on both of the evaporation and the vapor transport in the gas environment. Heat and mass transport from an evaporating meniscus in an open heated V-groove is numerically investigated and the results are compared to experiments. The evaporation is coupled to the vapor transport in the gas domain. Conjugate heat transfer is considered in the solid walls, and the liquid and gas domains. The flow induced in the liquid due to Marangoni effects, as well as natural convection in the gas due to thermal expansivity and vapor concentration gradients are simulated. The calculated evaporation rates are found to agree reasonably well with experimentally measured values. The convection in the gas domain has a significant influence on the overall heat transfer and the wall temperature distribution. The evaporation rate near the contact lines on either end of the meniscus is high. Heat transfer through the thin liquid film near the heated wall is found to be very efficient. A small temperature valley is obtained at the contact line which is consistent with the experimental observation.     

Heat and mass transfer from a supercritical lox spray

The injection, evaporation and diffusion of liquid oxygen in a high pressure airstream in a parallel wall mixing channel is analyzed and computationally solved. The droplet evaporation in the supercritical environment is treated by a non-isothermal droplet heat transfer model which accounts for the finite thermal conductivity of oxygen droplets and the gas film. The non-ideal gas effects in the gas phase are modeled by the Redlich-Kwong equation of state. The mixture density and enthalpy are determined by applying the ideal-solution limit which is shown to be valid for the prevailing conditions. The coupled dynamics of droplet and gas phases is calculated by solving numerically the Navier-Stokes equations in two dimensions. The turbulence effects are modeled by a two equation (k-ε) model. The results show that the non-ideal gas behavior prevails over a large portion of the mixing channel. Furthermore, the injected liquid oxygen droplets achieve critical temperature very quickly, and as a result they evaporate in the vicinity of the injection point. The effects of injection angle on oxygen mixing characteristics is also investigated.     

剪切层流蒸发液膜的传热特性

为克服理论分析中气液界面对流换热难以计算的问题,基于气相传热模型,建立了在同向或反向切应力作用下层流饱和蒸发液膜的传热模型,推导出无量纲液膜厚度和壁面对流换热系数与流动长度、界面切应力和初始雷诺数间的理论关系式.研究表明,受液膜蒸发的影响,液膜厚度沿流动长度不断减小,换热传热系数不断增加;同向切应力具有减薄液膜厚度和增大传热系数的作用;反向切应力则具有相反的作用,其影响更为明显.这一理论模型可以反映层流饱和蒸发液膜的传热特性.     

A Numerical Study of the Thermal Entrance Effect in Miniature Thermal Conductivity Detectors

The microchannel flow in miniature TCDs (thermal conductivity detectors) is investigated numerically. Solutions based on the boundary-layer approximation are not very accurate near the channel inlet for low Reynolds numbers. As a result the full Navier-Stokes equations were solved to analyze the gas flow in a miniature TCD. The effects of channel size and inlet and boundary conditions on the heat transfer rate were examined. When the gas stream is not preheated, the distance for a miniature TCD to reach the conduction-dominant region is approximately two to three times the thermal entry length of a constant property pipe flow subject to a uniform thermal boundary condition. If the gas inlet temperature is in the vicinity of the mean gas temperature in the conduction-dominant region, the entrance length is much shorter and very close to that of a constant property pipe flow with uniform surface temperature or heat flux.     

The effect of heated wall thickness and materials on nucleate boiling at high heat flux

The present work is to numerically investigate the effect of heater side factors on the nucleate boiling at high heat flux, which is characterized by the existence of macrolayer. Two-region equations are proposed to study both thermo-capillary driven flow in the liquid layer and heat conduction in the solid wall. The numerical results indicate that the thermo-capillary driven flow in the macrolayer and evaporation at the vapor-liquid interface constitute a very efficient heat transfer mechanism to explain the high heat transfer coefficient of nucleate boiling heat transfer near CHF. For a very thin wall and/or wall with a poor thermal conductivity (heat side factors) are found to have significant effect on flow pattern in the liquid layer and the temperature distribution in the heated wall.     

The effect of liquid film evaporation on flow boiling heat transfer in a micro tube

Flow boiling in micro channels is attracting large attention since it leads to large heat transfer area per unit volume. Generated vapor bubbles in micro channels are elongated due to the restriction of channel wall, and thus slug flow becomes one of the main flow regimes. In slug flow, sequential bubbles are confined by the liquid slugs, and thin liquid film is formed between tube wall and bubble. Liquid film evaporation is one of the main heat transfer mechanisms in micro channels and liquid film thickness is a very important parameter which determines heat transfer coefficient. In the present study, liquid film thickness is measured by laser focus displacement meter under flow boiling condition and compared with the correlation proposed for an adiabatic flow. The relationship between liquid film thickness and heat transfer coefficient is also investigated. Initial liquid film thickness under flow boiling condition can be predicted well by the correlation proposed under adiabatic condition. Under flow boiling condition, liquid film surface fluctuates due to high vapor velocity and shows periodic pattern against time. Frequency of periodic pattern increases with heat flux. At low quality, heat transfer coefficients calculated from measured liquid film thickness show good accordance with heat transfer coefficients obtained directly from wall temperature measurements.     

波纹管降膜蒸发器传热性能数值模拟

为了理解波纹管降膜蒸发过程中涉及的液膜传热过程,本文采用VOF法建立了二维气-液两相分层流动CFD模型,考虑了液相流量,传热温差,蒸发温度,液相粘度等参数对传热效果的影响,根据模拟结果给出了波纹管降膜蒸发器的流量可操作范围。模拟结果和实验数据比较吻合。     

Influence of dispersion forces on phase equilibria between thin liquid films and their vapour

Heat transfer and nucleation processes in nucleate boiling strongly depend on the phase equilibrium at the liquid-vapour interface. In a certain region between heated wall and a vapour bubble where a thin liquid film is adsorbed, phase equilibria are considerably influenced by dispersion forces acting on the liquid film. As shown in the paper in such systems the chemical potential, decisive for phase equilibria between liquid films and their vapour, contains an additional term for the action of dispersion forces, and differs from the chemical potential of dispersion-free systems, though their chemical potential is usually taken in the literature for systems with dispersion forces. With the aid of the chemical potential the Kelvin equations for the pressures at the liquid-vapour interface were derived. It turned out that the Gibbs assumption of a geometrical interface between extremely thin liquid films in equilibrium with its vapour does not hold. Instead, following the ideas of van der Waals junior, the small but finite transition interlayer between both phases had to be introduced.As numerical examples illustrate, the dispersion forces considerably influence the pressures at the liquid-vapour interface. In nucleate boiling processes the driving pressure difference for evaporation undergoes a maximum within a tiny area underneath vapour bubbles. As could be shown the maximum driving pressure difference between gas-side interface and gas-core is a considerable fraction of the vapour pressure itself and contributes significantly to the high heat fluxes in nucleate boiling.     

Effects of surface roughness of capillary wall on the profile of thin liquid film and evaporation heat transfer

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Numerical study of liquid film cooling in a rocket combustion chamber

A numerical study is reported to investigate the liquid film cooling in a rocket combustion chamber. Mass, momentum and heat transfer characteristics through the interface are considered in detail. A marching procedure is employed for solution of the respective governing equations for the liquid film and gas stream together. The standard turbulence k–ε model is used to simulate the turbulence gas flow and a modified van Driest model is adopted to simulate the turbulent liquid film flow. Radiation of gas stream is also considered and simulated with the flux model. Downstream of the liquid film the gaseous film cooling is numerically studied simultaneously. Results are presented for a mixed gases–water system under different condition. Various effects on the liquid film length are examined in detail. There is a good agreement between the numerical prediction and experimental result on the liquid film length.