Heat and mass transfer analogy for condensation of humid air in a vertical channel

This study examines energy transport associated with liquid film condensation in natural convection flows driven by differences in density due to temperature and concentration gradients. The condensation problem is based on the thin-film assumptions. The most common compositional gradient, which is encountered in humid air at ambient temperature is considered. A steady laminar Boussinesq flow of an ideal gas–vapor mixture is studied for the case of a vertical parallel plate channel. New correlations for the latent and sensible Nusselt numbers are established, and the heat and mass transfer analogy between the sensible Nusselt number and Sherwood number is demonstrated. Received on 15 November 1999     

Numerical investigation of transient heat and mass transfer in a parallel-flow liquid-desiccant absorber

Liquid desiccant systems have received significant attention as a way to reduce latent loads. Tests of liquid desiccant systems in humid climates have shown significant reductions in energy consumption. As moisture in the air is absorbed at the dehumidifier, the temperature of the liquid desiccant increases due to the addition of heat from the enthalpy of condensation of the water vapor. Thus, the coupled effects of heat and mass transfer are relevant for these applications. A two-dimensional mathematical model of the transient heat and mass transfer for an absorber where a thin film of liquid desiccant flows down its walls and dehumidifies the air in parallel-flow configuration is developed and the dynamics of the modeled system are analyzed.     

The optimum shape for converting rectangular fins when condensation occurs

There may be condensation on the fin surfaces of the air conditioning systems due to the temperature of the fin surfaces being below the dew point temperature of the water vapor in the surrounding air. Heat and mass transfer occur from the saturated air layer to the liquid water film and the latent heat of condensation is transferred to the fin. This study presents a quasilinearization solution for vertical rectangular fins when condensation occurs, assuming that the average convective heat and mass transfer coefficients are constant along the height of the fin. Rectangular fins with and without condensation on the surface have been compared and optimum fin dimensions have been given. The optimum fin length, the fin effectiveness and the average fin temperature in the case of condensation were found to be smaller than in the case of no condensation.     

Evaluation of Model Concepts to Describe Water Transport in Shallow Subsurface Soil and Across the Soil–Air Interface

Soil water evaporation plays a critical role in mass and energy exchanges across the land–atmosphere interface. Although much is known about this process, there is no agreement on the best modeling approaches to determine soil water evaporation due to the complexity of the numerical modeling scenarios and lack of experimental data available to validate such models. Existing studies show numerical and experimental discrepancies in the evaporation behavior and soil water distribution in soils at various scales, driving us to revisit the key process representation in subsurface soil. Therefore, the goal of this work is to test different mathematical formulations used to estimate evaporation from bare soils to critically evaluate the model formulations, assumptions and surface boundary conditions. This comparison required the development of three numerical models at the REV scale that vary in their complexity in characterizing water flow and evaporation, using the same modeling platform. The performance of the models was evaluated by comparing with experimental data generated from a soil tank/boundary layer wind tunnel experimental apparatus equipped with a sensor network to continuously monitor water–temperature–humidity variables. A series of experiments were performed in which the soil tank was packed with different soil types. Results demonstrate that the approaches vary in their ability to capture different stages of evaporation and no one approach can be deemed most appropriate for every scenario. When a proper top boundary condition and space discretization are defined, the Richards equation-based models (Richards model and Richards vapor model) can generally capture the evaporation behaviors across the entire range of soil saturations, comparing well with the experimental data. The simulation results of the non-equilibrium two-component two-phase model which considers vapor transport as an independent process generally agree well with the observations in terms of evaporation behavior and soil water dynamics. Certain differences in simulation results can be observed between equilibrium and non-equilibrium approaches. Comparisons of the models and the boundary layer formulations highlight the need to revisit key assumptions that influence evaporation behavior, highlighting the need to further understand water and vapor transport processes in soil to improve model accuracy.

     

Phase Transitions in Flow through a Heat-Conducting Porous Skeleton

The features of one-dimensional seepage flows of a medium in the form of a liquid, vapor, or liquid-vapor mixture are considered. It is assumed that the temperatures of the medium and the porous skeleton through which it flows are determined both by the heat-conduction processes in the skeleton and the medium and by the phase transitions of the medium (evaporation or condensation). The phase transition fronts and their structure are investigated for a pure medium, i.e., a liquid or vapor but not a mixture, no at least one side of the front. Moreover, the possible existence of a form of flow, not considered earlier, in which in a certain region of space the thermodynamic state of the particles belongs to the phase transition interface between the pure state and the mixture. The flows are considered in general form without specifying the properties of the medium.     

跨音速湿空气非平衡凝结流动的数值研究

跨音速流动条件下湿空气中的水蒸气由于快速膨胀而发生非平衡凝结,凝结潜热对跨音速气流进行加热,会显著改变气流的流动特性。通过对商用计算流体动力学软件FLUENT进行二次开发,建立了湿空气非平衡凝结流动的数值求解方法。该方法可用于二维或三维、粘性或无粘、内流或外流的求解中。采用该方法分剐对缩放喷管、透平叶栅以及绕CA-0.1圆弧翼型的湿空气非平衡凝结流动进行了数值分析。计算结果表明：湿空气凝结手l起缩放喷管中的凝结激波、导致叶橱流动中总压降低;对于翼型周围的流动,在相对湿度分别为50％、57．1％、64.1％时,依次计算得到了单激波、五激波、双激波。     

An analysis of incipient frost formation

An analytical and experimental study of frost growth on a cooled plate being exposed to forced convective humid air stream was carried out. Attention is mainly focused on the incipient phenomena of the frost formation including the growth of supercooled water droplets which are based on condensation of water vapor leaving the air. Two kinds of the plates having different contact angles to water droplet (110 deg and 43 deg) are used as the testing ones. The effects of the velocity, humidity, and temperature of the air stream, the contact angle to water droplet, and the temperature of the cooled plate on the frost formation are extensively determined. An analytical model which is based on the experimental observations is found to closely predict the general trends in the growths of the supercooled water droplets and the porous frost layer.     

Rayleigh-Taylor instability of an interface in a nonwettable porous medium

The diffusion of vapor through the roof of an underground structure located beneath an aquifer is considered. In the process of evaporation, an interface between the upper water-saturated layer and the lower layer containing an air-vapor mixture is formed. A mathematical model of the evaporation process is proposed and a solution of the steady-state problem is found. It is shown that in the presence of capillary forces in the case of a nonwettable medium the solution is not unique. Using the normal mode method, it is shown that Rayleigh-Taylor instability of the interface can develop in the nonwettable porous medium. It is found that there are two scenarios of loss of stability corresponding to the occurrence of the most unstable wavenumber at zero and at infinity, respectively. It is shown that for zero wavenumber the stability limit is reached at the same time as the solution of the steady-state problem disappears.     

Effect of Interphase Heat Transfer on the Stability of a Turbulent Multicomponent Flow in a Vortex

The parameters of an axisymmetric turbulent two-phase swirling flow of a viscous heat-conducting gas containing a liquid dispersed phase in the presence of water vapor condensation on the particles are calculated. For the dispersed phase, a model taking into account the variation of the vapor concentration and the particle size due to condensation or evaporation is proposed. The distributions of the parameters of the basic unperturbed flow obtained numerically are used in the numerical solution of the linear problem of hydrodynamic stability within the time-dependent formulation. The parameters of small-amplitude harmonic perturbations propagating along the vortex axis are investigated in the linear formulation. A significant effect of heat release in the gas due to water vapor condensation on the parameters of the neutral perturbations and the neutral-stability curves is detected.     

A CFD model of frost formation based on dynamic meshes technique via secondary development of ANSYS fluent

To simulate the non-uniform frost growth in flow direction for humid air flowing through a freezing channel, a 2D numerical frosting model based on dynamic meshes technique is developed in the current work via the secondary development of commercial ANSYS Fluent. The computation domain consists of both frost layer and humid air regions, and the local heat and vapor fluxes at the surface of frost layer are determined by numerical temperature and vapor fraction fields in the humid air region rather than by empirical correlations. The frost layer is treated as a growing packed bed with heat and mass transfer dominated by molecular diffusion, where local absorption coefficient of vapor desublimation and local vapor fraction are both determined by solving the pseudo steady vapor diffusion equation with a source term theoretically. The interface of frost layer and humid air regions is treated as two walls for the iteration of its temperature, of which the humid air side is specified with the temperature equal to the frost-side counterpart and the frost side takes the heat flux including the extra latent heat caused by vapor deposit. User-defined functions are compiled to implement the above treatments to ANSYS Fluent. Frosting experiments in the literature are simulated with the current model for validation. How the profile of frost layer evolves with time in the frosting process is explored. The contours and profiles of velocity, temperature and vapor fraction are presented to discuss the effects of heat and mass transfer on frost formation. Numerical results demonstrate that the proposed CFD model can predict the frost growth and densification with a relative deviation less than 5% compared with experiments. Besides, the computation load of current model is small due to no solution of complex multiphase flow. In addition, dynamic meshes help current model to capture the interface of frost layer and humid air regions accurately.     

Heat transfer and evaporation/condensation problems based on the linearized Boltzmann equation

A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve four basic problems, all based on the linearized Boltzmann equation for rigid-sphere interactions, that describe heat transfer and/or evaporation–condensation between two parallel surfaces or for the case of a semi-infinite half space. Relevant to the case of two surfaces, the basic problem of heat transfer driven by a temperature difference at two confining walls described by a general Maxwell gas–surface interaction law (a mixture of specular and diffuse reflection) is solved for the case where different accommodation coefficients can be used for each of the two bounding surfaces. In addition, the classical problem of “reverse temperature gradient” in the theory of evaporation and condensation is also solved for the case of two parallel liquid–vapor interfaces kept at different temperatures. In regard to half-space applications, an evaporation/condensation problem based on a presumed known interface condition and a heat-conduction problem (with no net flow) driven by energy flow from a bounding surface with know properties are each solved with what is considered a high degree of accuracy.     

Internal flow numerical simulation of a cross‐flow fan in refrigerant operating condition using user‐defined functions

In the paper, a cross‐flow fan in refrigerant operating condition is systematically simulated using user‐defined functions. Three‐dimensional simulations are acquired with Navier–Stokes equations coupled with k–ε turbulence model, and internal flow characteristics of an indoor split‐type air conditioner are obtained, which is mainly composed of cross‐flow fan and heat exchanger. It has systematically been simulated in the isothermal flow condition that the performance of cross‐flow fan may be reduced easily with dry or humid air, and in the refrigerant operating condition in which user‐defined functions are applied to the humid air, considered as a mixture of dry air and vapor. A density‐modulated function is adopted to deal with the condensation of the vapor at the heat‐transfer region approximately. The results show flow mechanism of the two gas‐phase flow, including phase‐vary process. The distribution of the parameters is not uniform at the inlet of the machine, the intensity and position of pressure and velocity vary along the axial direction of the fan, the distribution of vapor volume fraction and turbulent intensity in heat‐transfer region is obtained, and the external characteristic data of the indoor machine are obtained and analyzed. Compared with the experimental data, the calculated characteristic curves and designed parameters are on target. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.     

Migration of salts in the unsaturated zone caused by heating

Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating.Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil.Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts.A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed.The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.     

Some nonlinear problems of groundwater flow through a porous medium

Self-similar solutions of the equation of groundwater gravity flow through a porous medium are given. The water flows from a basin into an underground permeable reservoir bounded from below by an impervious bed. A periodic problem of flow through a porous medium in which the water level in the basin periodically oscillates is considered. It is shown that in this case the water table elevation effect, i.e., water pumping into the aquifer, develops at a sufficient distance from the littoral zone. The invariant-group solutions of the problem of flow through a porous medium are investigated with allowance for evaporation from the groundwater surface.     

Boiling in Porous Media: Model and Simulations

We present a modelization of the heat and mass transfers within a porous medium, which takes into account phase transitions. Classical equations are derived for the mass conservation equation, whereas the equation of energy relies on an entropy balance adapted to the case of a rigid porous medium. The approximation of the solution is obtained using a finite volume scheme coupled with the management of phase transitions. This model is shown to apply in the case of an experiment of heat generation in a porous medium. The vapor phase appearance is well reproduced by the simulations, and the size of the two-phase region is correctly predicted. A result of this study is the evidence of the discrepancy between the air – water capillary and relative permeability curves and water – water vapor ones.     

The mathematical simulation of various condensation regimes in turbulent isobaric jets

Mathematical models are considered and calculations made for flows in turbulent isobaric steam—air jets in the presence of condensation of the water vapor they contain. The models consist of gasdynamic equations for a turbulent jet, equations for a differential two-parameter model of turbulence, thermodynamic relations, and kinetic equations. A study is made of steam—air jets in a regime of condensation in equilibrium, when the flow region is broken down into zones of frozen flow and flow in equilibrium, described by the equations for a turbulent jet with the use of the traditional thermodynamic relations and of the thermodynamic relations for condensation in equilibrium. An analysis is made of the influence of pulsating motion on the kinetic parameters: rate of nucleation, the critical size of the nuclei, and rate of growth of the drops. It is shown that the rate of nucleation, determined from a quasilaminar averaging model, is several orders of magnitude less than the mean value obtained by averaging using the density distribution of the passive admixture concentration probability. A numerical study is made of the heterogeneous condensation in turbulent jets on extraneous particles entering from the nozzle. Kinetic equations are written down for the case when the rate of growth of the drops does not depend on their radius. A study is made of the dynamics of the transition of heterogeneous condensation from disequilibrium to equilibriumTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–67, January–February, 1985.     

Vapor flows with evaporation and condensation in the continuum limit: effect of a trace of noncondensable gas

Steady flows of a vapor with evaporation and condensation on the boundary consisting of the condensed phase of the vapor are considered in the following situation: (i) the boundary is of arbitrary smooth shape; (ii) the Knudsen number Kn, the ratio of the typical mean free path of the vapor molecules to the characteristic length of the system, is small; (iii) a small amount of a noncondensable gas is contained in the system; more specifically, the amount is such that the average concentration of the noncondensable gas is of the order of Kn in the case of a closed domain (the case of an infinite domain is also discussed). The steady behavior of the vapor and the noncondensable gas, in particular, that in the continuum limit where Kn vanishes, is investigated by means of a systematic asymptotic analysis based on kinetic theory. In this situation, the average concentration of the noncondensable gas becomes infinitely small in the continuum limit in the case of a closed domain. However, it is shown that the noncondensable gas accumulates in the infinitely thin Knudsen layer on the boundary where condensation is taking place and has a significant effect on the global vapor flow in the continuum limit. An example demonstrating such an effect is also given.     

非饱和正冻土的三场耦合理论框架

在``饱和正冻土的理论构架'的基础上,假定了冻土体内的空气的流动是一 种Darcy流,进一步考虑了非饱和土中气相的影响,提议了一种综合考虑两种极端 情况：(1) 气体与外界完全相通. (2) 气体与外界完全不相通的相关水、热、力相 耦合的多孔多相介质理论构架------半连通、半封闭非饱和正冻土理论构架. 重点讨论了较简单的气体半连通半封闭的非饱和孔隙冻土体的三场耦合模型. 为 检验三场耦合分析模型及所开发的针对冻土工程三场耦合模型的软件系统3G2001 的合理性与正确性, 与214国道花石峡 试验路基实测的地温变化和路基路面变形 进行了对比验证, 对比结果显示: 路基中分析所得的温度场与实测值变化规律一 致, 量化相差大都在10\%$\sim$20\%以内; 分析所得耦合变形随时间的变化也与 实测值完全一致, 路中的分析变形与实测相差也在10%-20%以内     

Kinetic theory analysis of explosive boiling of a liquid droplet

The process of rapid phase transition from highly superheated liquid to vapor is frequently so fast and violent that it is called explosive boiling. The paper uses the kinetic theory of evaporation to study growth of an internal vapor bubble produced by homogeneous nucleation within a highly superheated liquid droplet boiling explosively in a hot medium. Evaporation/condensation coefficient is estimated by comparing the predictions of the theory with available experimental data. We show that the value of the evaporation coefficient can be very low for high reduced temperatures (0.06 for butane at 378 K), in agreement with recent molecular dynamic simulations.