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.     

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.     

Frost formation on a vertical plate in simultaneously developing flow

It is well recognized that frost formation on heat exchanger surfaces seriously affects the performance of a refrigeration system. Consequently, defrosting is essential, yet it is only effective when both analytical tools and comprehensive experimental data on frost formation are available. In air conditioning units, frost formation most commonly takes place in the entrance region of the heat exchanger. Therefore, in this study, an experimental investigation was undertaken to characterize the effect of environmental conditions on the frost growth occurring on a vertical plate in the hydrodynamically and thermally developing region. Several experiments were performed while four environmental parameters, inlet air temperature, inlet air humidity, air velocity and cooling surface temperature, were varied. The thickness, mass, and density of the frost layer were determined from the measured data and empirical correlations were reduced from dimensionless parameters.     

An analytical study of frost nucleation and growth during the crystal growth period

An analytical study was made to clarify the fundamental nature of the early stage of crystal growth period of frost formation phenomena. A suitable model was developed by using the principles of crystallization and nucleation theory. The effect of four dominant parameters of frost formation; plate temperature, air temperature, air humidity ratio and Reynolds number, was studied. Ice crystal density variation with temperature reported by cloud physicists is used in the model to predict the density variation of frost during the crystal growth period. The temperature variation in the frost layer is formulated and vapor diffusion through the frost layer is taken in the consideration.     

Frost formation mechanism analysis and frost growth prediction on ground aircraft

Frost predictions are needed to help the deicing operation decide. The mechanism of frost formation on aircraft surface under icing conditions has been analyzed. A simple theoretical frost growth prediction model by heat and mass transfer analysis has been presented. It produces a method to forecast the frost growth tendency. An experimental system for atmospheric frost reproduction is also presented. Effects of aircraft surface temperatures, air temperature on the frost growth is evaluated by this model.     

Mesoscale investigation of frost formation on a cold surface

Frost formation on a horizontal flat copper surface was experimentally investigated using microscopic observations. The experiments were carried out on −20 to 0 °C copper surfaces with 22 °C air and 15–85% relative humidities. The experiments showed that the frost formation on a cold surface generally begins with the formation and growth of condensate droplets, freezing of the super-cooled condensate droplets, formation and growth of initial frost crystals on the frozen droplets, growth of frost crystals accompanied by the collapse of some of the crystals, and finally frost layer growth. The freezing onset time and diameter of the super-cooled condensate droplets were characterized. The initial frost crystals can be classified into four groups according to their appearance and shape, with the variations of the frost crystal shape as a function of the cold surface temperature and air humidity.     

A rigorous analysis of simultaneous heat and mass transfer in the pasta drying process

This study presents a two dimensional analysis of coupled heat and mass transfer during the process of pasta drying. Velocity and temperature distributions of air flowing around the pasta are predicted in steady state condition. Using these profiles and the similarity between heat and mass boundary layers, local convective heat and mass transfer coefficients were determined on different points of pasta surface. By employing these values, the solution of coupled heat and mass transfer equations within the pasta object in unsteady state condition was obtained. Furthermore the effects of operating conditions such as velocity, temperature and relative humidity of air flow on drying rate of pasta were studied. Sensitivity analysis results show that the effects of air temperature and relative humidity on the rate of drying are more important than the effect of air velocity. Finally, the results obtained from this analysis were compared with the experimental data reported in the literatures and a good agreement was observed while, no adjustable parameter is used in the presented model.     

A new model for predicting performance of fin-and-tube heat exchanger under frost condition

Accurate prediction of frost characteristics has crucial influence on designing effective heat exchangers. In this paper, a new CFD (Computational Fluid Dynamics) model has been proposed to predict the frost behaviour. The initial period of frost formation can be predicted and the influence of surface structure can be considered. The numerical simulations have been carried out to investigate the performance of fin-and-tube heat exchanger under frost condition. The results have been validated by comparison of simulations with the data computed by empirical formulas. The transient local frost formation has been obtained. The average frost thickness, heat exchanger coefficient and pressure drop on air side has been analysed as well. In addition, the influence factors have also been discussed, such as fin pitch, relative humidity, air flow rate and evaporating temperature of refrigerant.     

An inverse geometry problem in estimating frost growth on an evaporating tube

 When humid air comes into contact with a surface whose temperature is below the dew point of water vapor in air and also below the freezing point, frost deposition takes place over the surface. The phenomena of the frost growth are very complicated and therefore it is very difficult to model mathematically the behavior of frost growth and predict it. In the present study a transient inverse geometry heat conduction problem (shape identification problem) is solved using the conjugate gradient method (CGM) and boundary element method (BEM)-based inverse algorithm to estimate the unknown irregular frost thickness and shape. Results obtained by using the CGM to estimate the frost growth are justified based on the numerical experiments. It is concluded that the accurate frost shape can be estimated by the CGM except for the initial and final time. The reason and improvement of this singularity are addressed. Finally the effects of reducing the number of sensors and increasing the measurement errors on the inverse solutions are discussed. Received on 25 September 2000 / Published online: 29 November 2001     

Frost formation in vertical channels under natural convection

Processes involving heat transfer from a humid air stream to a cold plate, with simultaneous deposition of frost, are of great importance in a variety of refrigeration equipment. In this paper, frost growth on a cold, vertical plate in free convection has been experimentally investigated. The cold plate (0.095 m high, 0.282 m wide) was placed in vertical channels open at the top and bottom in order to permit the natural circulation of ambient air. The channels, rectangular in shape, were 2.395 m high and 0.36 m wide, with the depth set equal either to 20 mm, or 10 mm, or 6 mm in order to infer the influence of channel flow area on the natural convection and frost formation. The cold plate temperature and the air relative humidity were varied in the −40 to −4 °C and 31–85% range, respectively, with the air temperature held fixed at 27 °C (±1 °C). Several quantities (thickness, temperature and mass of frost, heat flux at the cold plate), were measured during the time-evolution of the process (7.5 h from the frost growth inception), and are presented as functions of the input parameters (relative humidity and cold plate temperature); in particular, the role exerted by the plate confinement on the frost growth is discussed. Data are recast in order to identify compact parameters able to correlate frost mass, thickness and density data.     

Rate of evaporation from the free surface of a heated liquid

A method and an experimental setup are developed for determining the intensity of evaporation from the free surface of water. During the measurement, the ambient air velocity and the water temperature can be varied. The mass and temperature of water, as well as the temperature, pressure, and humidity of the ambient air are measured as functions of time. The evaporation rates are calculated from the measured and recorded data in the cases of natural and forced convection.     

Heat and mass transfer characteristics of air bubbles and hot water by direct contact

 This paper has dealt with direct contact heat and mass transfer characteristics of air bubbles in a hot water layer. The experiments were carried out by bubbling air in the hot water layer under some experimental conditions of air flow rate, inlet air temperature and humidity as a dispersion fluid, and hot water temperature and hot water layer depth as a continuous fluid. Heat transfer and evaporation of water vapor from hot water to air bubbles occurred during air bubbles ascending into the hot water. Air bubble flow patterns were classified into three regions of independent air bubble flow, transition and air bubble combination growth. Non-dimensional correlation equations of direct contact heat and mass transfer between air bubbles and hot water were derived by some non- dimensional parameters for three regions of bubble flow pattern. Received on 14 July 2000 / Published online: 29 November 2001     

Effects of humidity and temperature on subcritical crack growth in sandstone

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. The influences of the surrounding environmental conditions and rock fabric on subcritical crack growth in sedimentary rocks in air are yet to be clarified, while the nature of subcritical crack growth in igneous rocks has been studied well. In this study, the influences of temperature and relative humidity on subcritical crack growth in Berea sandstone, Shirahama sandstone and Kushiro sandstone were investigated in air. The load relaxation method of Double Torsion (DT) testing method was used to measure both crack velocity and stress intensity factor under a controlled temperature and relative humidity.Results show that the change of the crack velocity at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. On the other hand, we show that the crack velocity increased by several orders of magnitude when the relative humidity increased threefold or fourfold under a constant temperature at a given stress intensity factor. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. It is therefore necessary to consider the additional mechanisms for subcritical crack growth in sandstone. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in sandstone in air is affected remarkably by the relative humidity and the amount of clays in rock.     

Theoretical study of the effect of liquid desiccant mass flow rate on the performance of a cross flow parallel-plate liquid desiccant-air dehumidifier

A computer simulation using MATLAB is investigated to predict the distribution of air stream parameters (humidity ratio and temperature) as well as desiccant parameters (temperature and concentration) inside the parallel plate absorber. The present absorber consists of fourteen parallel plates with a surface area per unit volume ratio of 80 m²/m³. Calcium chloride as a liquid desiccant flows through the top of the plates to the bottom while the air flows through the gap between the plates making it a cross flow configuration. The model results show the effect of desiccant mass flow rate on the performance of the dehumidifier (moisture removal and dehumidifier effectiveness). Performance comparisons between present cross-flow dehumidifier and another experimental cross-flow dehumidifier in the literature are carried out. The simulation is expected to help in optimizing of a cross flow dehumidifier.     

Effect of Moisture Movement on Tested Thermal Conductivity of Moist Aerated Autoclaved Concrete

The purpose of this work was to study both theoretically and experimentally the process of moisture redistribution and heat transfer due to phase changes during the tests of thermal conductivity in aerated autoclaved concrete (AAC) moist specimens. The different moisture contents of the test samples were obtained in climatic chamber at equilibrium conditions reached with constant air temperature and variable relative humidity. The moist specimens were sealed inside highly impermeable polyethylene bag, as required by UNI 10051, and placed in a heat flow meter apparatus. During the experimental thermal conductivity measurements, the temperature and heat flow rate were measured under transient and steady state conditions. A theoretical analysis of the heat and mass transfer process was performed and then a suitable numerical model was used to predict the moisture redistribution and heat transfer due to the phase changes. The theoretical model has been compared against the experimental data. Substantial agreement between numerical results and experimental data was found. Then several numerical simulations have been performed to study the influence of the errors due to phase changes and non-uniform moisture distribution during the test of thermal conductivity of moist AAC specimens.     

Study on heat transfer performance of spray cooling: model and analysis

In consideration of droplet–film impaction, film formation, film motion, bubble boiling (both wall nucleation bubbles and secondary nucleation bubbles), droplet–bubble interaction, bulk air convection and radiation, a model to predict the heat and mass transfer in spray cooling was presented in this paper. The droplet–film impaction was modeled based on an empirical correlation related with droplet Weber number. The film formation, film motion, bubble growth, and bubble motion were modeled based on dynamics fundamentals. The model was validated by the experimental results provided in this paper, and a favorable comparison was demonstrated with a deviation below 10%. The film thickness, film velocity, and non-uniform surface temperature distribution were obtained numerically, and then analyzed. A parameters sensitivity analysis was made to obtain the influence of spray angle, surface heat flux density, and spray flow rate on the surface temperature distribution, respectively. It can be concluded that the heat transfer induced by droplet–film impaction and film-surface convection is dominant in spray cooling under conditions that the heated surface is not superheated. However, the effect of boiling bubbles increases rapidly while the heated surface becomes superheated.     

Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

Combustion of a Powder Layer of Methane Hydrate: The Influence of Layer Height and Air Velocity Above the Layer

The paper studies the dissociation and combustion of a layer of methane hydrate powder at a forced air flow over the upper surface of the layer (the air velocity is directed parallel to the upper surface of the layer). The influence of the layer thickness and air velocity on the combustion of gas hydrate is investigated. The calculated curves for the effect of the heat transfer coefficient, external convection and vapor concentration on the combustion temperature are obtained. The layer thickness and the air velocity significantly affect the dissociation rate of methane hydrate.

     

Nonlinear waves in a liquid film on a near-horizontal surface

Nonlinear waves in a liquid film on a slightly inclined rigid plane are studied. A mathematical model is reduced to a system of two evolutionary equations for the layer thickness and the local fluid mass flow. In addition to viscous forces, gravity, and surface tension, the pressure difference over the layer thickness, induced by the gravity force projection on the normal to the underlying surface, is also taken into account. Spatially periodic solutions developing with time from small initial disturbances into regular nonlinear waves are considered. A spectral representation of the solution, the Galerkin method with respect to the uniform coordinate, and subsequent numerical calculation of the corresponding dynamic system on large time intervals are employed. Different variants in the space of the three governing parameters are calculated and some basic mechanisms of nonlinear dynamics of the two-dimensional waves are detected. The calculation results are compared with the existing experimental data. It is shown that the theoretical conclusions can be used to interpret and predict experiments.     

A numerical investigation of droplet impact on a heated wall in the film boiling regime

In this research, a novel approach is proposed to simulate the impingement of a water droplet on a superheated wall by solving conservation equations of mass, momentum and energy. Due to high temperature of the surface, a vapor layer is formed between droplet and surface. The vapor layer is captured using a very fine mesh near the surface. The level set method is applied for interface tracking and appropriate jump conditions are imposed at the interface by the ghost fluid method. The proposed algorithm is validated by comparing numerical results to the available experimental and analytical solutions. The effect of impact velocity, surfactant and polymer additives on the heat removal is studied. Simulations show that an increase in impact velocity enhances the heat removal. On the other hand, polymer additive has no significant effect while surfactant enhances dissipated heat by increasing the contact time or even by sticking the droplet on the surface.