Convection within a cylindrical cell containing a freezing fluid

The effects of convection upon freezing/melting processes within a cylindrical cell are studied numerically over a wide range of the Rayleigh number (Ra). Establishment of the steady state and the heat transfer across the cell are analyzed. A self-sustained oscillatory process characterized by the emergence and decay of vortices near the interface of the frozen and thawed zones is identified. At large Rayleigh numbers the solution is unstable.Tyumen'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 125–129, September–October, 1995.     

Freezing and thawing porous media: experimental study with a dielectric capacitive method

A capacitive sensor-based apparatus has been used to study the ice/water phase change in consolidated porous media subjected to freezing and thawing. This technique relies on the dielectric properties of water, ice, air, and the mineral substrate in the radio-frequency range. It gives directly the freezing and thawing temperature depressions and indirectly provides an estimation of pore size distribution through the Gibbs–Thomson relation. It also holds good promise for evaluating the amount of liquid water in frozen porous media by combining drying and freezing tests. To cite this article: T. Fen-Chong, A. Fabbri, C. R. Mecanique 333 (2005).     

Numerical simulation of coupled heat-fluid transport in freezing soils using finite volume method

A solution procedure using finite volume method has been established for the coupled heat-fluid transport model of freezing soils, and details about determination of the time step interval and discretization at special nodes have been introduced. Comparison between the simulation and the freezing experiments of silica flour and Zhangye loam has been conducted, and the calculated results are in general agreement with the experimental data. The research indicates that the moisture migration in the frozen zone is insignificant, and water mainly migrates from the frozen zone to the vicinity of the moving freezing front; the moving velocity of the freezing front has a great effect on the extent of moisture accumulation to the freezing front, and high extent of accumulation occurs when the freezing front advances slowly. Finally, an apparent heat capacity model has been suggested for the temperature calculation of the soil freezing process in low water content conditions; however, when the moisture migration is significant, water redistribution during the freezing process should be considered.     

Heat and mass transfer in unsaturated porous media with solid–liquid change

 A model on heat and mass transfer in unsaturated porous media with solid/liquid phase change was developed with extending the three-variable model previously proposed. The movement of air phase and its effect on the motion of water is considered. The model has been checked with comparison of the experimental results of the temperature distribution for two dimensional freezing process. The evolution of air pressure, water and ice saturation were predicted by solving the governing equations. The ice segregation and moisture movement toward the front of freezing were numerically simulated. Received on 8 December 1999     

Self-similar solution of the thawing soil problem

A mathematical model of phase transitions in frozen soils containing unfrozen water is proposed. It is shown that phase transitions in frozen soils always occupy an extended zone. The problem of the interaction of frozen rock with a salt solution is solved on the assumption that the interface between the solution and the frozen rock is permeable both for the liquid and for the dissolved impurity. This problem arises, for example, in drilling wells in frozen ground, when the circulating drilling solution is an aqueous salt solution [7]. A series of natural processes is based on the interaction between groundwaters having different, possibly negative, temperatures and different degrees of mineralization and the surrounding frozen rock [8] and on the thawing of the frozen bed of northern seas in contact with saline seawater [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 136–142, November–December, 1988.     

冻土力学的研究进展与思考

从冻结土的宏观力学性质,正冻土中的水、热迁移理论,正 冻土的水热力耦合模型四个方面分析综述了国内外冻土力学的发展 历史、研究现状与我国冻土力学研究中存在的问题,指出：（1）当 前冻土力学的研究内容应该从对冻结土的宏观强度与变形性质向更 切合实际工程需要的正冻土、正融土微、细观热、力学耦合性质方 面深化;（2）冻土力学的研究思路应该从对土样纯力学量的试验研 究向土样组构、级配、含水量、饱和度等土性指标在不同负温下对 土样颗粒排列与胶结特性的强度、变形影响机理方面转移;（3）冻 土力学的研究对象也应该从室内冻结试验的研究向具有各种不同水 热交换边界条件与水热迁移内在规律的冻土体发展。     

Elastic behavior of saturated porous materials under undrained freezing

The elastic behavior of saturated porous materi- als under undrained freezing is investigated by using a poro- mechanical approach. Thermodynamic equilibria are used to describe the crystallization process of the partially frozen solution in bulk state and confined state in pores. By phase transition at freezing, fusion energy, thermal contraction of solid, solution and ice crystals, volume changes of crystallization build up remarkable pore pressure that induces expansion or shrinkage of solid matrix. Owing to the lower chemical potential when pore water mixes with salts, fewer ice forms in pores. Penetration of ice into the porous materials increases the capillary pressure, but limits effect on the pore liquid pressure and the strain of solid matrix. On the contrary, the pore pressure induced by solution density rises as salt concentration increases and causes significant shrinkage of solid matrix.     

Energy-separating properties of two-phase flow

A new, substantially nondissipative process of energy separation in two-phase flows has been investigated. Mixtures of air with water, kerosene, and an aqueous solution of diethylene glycol were studied at initial pressures of 3–20 bar. It was found that ice was formed in an air-water mixture issuing from a supersonic nozzle, and for a mixture of air with a nonfreezing diethylene-glycol solution the liquid obtained after nonequilibrium separation had a negative temperature. The possibility of effective freezing out of moisture on an uncooled solid surface exposed to a current of moist air from a supersonic nozzle was demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–55, November–December, 1976.     

Mathematical model of the dissociation of gas hydrates coexisting with ice in natural reservoirs

The dissociation of gas hydrate coexisting with ice in a low-temperature natural reservoir is investigated. A mathematical model of the process consisting of a generalization of the Stefan problem and containing two unknown moving phase transition boundaries — the hydrate dissociation and ice melting fronts — is constructed. It is shown that in high-permeability reservoirs the velocity of the dissociation surface is higher than that of the ice melting surface. As the permeability decreases, the fronts change places. The problem is solved in the self-similar approximation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 84–92, March–April, 1993.     

One-dimensional problems of frozen soil thawing due to solution seepage

One-dimensional problems of the thawing of a porous frozen soil by intensive injection of brine are considered. Assuming local thermodynamic equilibrium and negligible diffusion, these problems prove to be self-similar and allow for complete analytical study.Four soil thawing regimes can be distinguished depending on the ice melting behavior at the temperature and concentration fronts. Criteria for their occurrence are derived in terms of the temperature and concentration of the injected brine. Possible simplified formulations statements are also discussed.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 149–160, September–October, 1995.     

Effect of the percolation heat transfer component on the temperature field and thawing dynamics of soils

The effect of the convective heat transfer component on the temperature field and thawing front dynamics of soils is investigated for high fluid percolation velocities in the thawed zone. The steady state interchange and approximate self-similarity methods are used to obtain upper and lower bounds of the solution of the Stefan problem with a convective heat transfer component in a porous medium. From the results of the calculations conclusions are drawn concerning the accuracy and limits of applicability of the solutions obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–171, March–April, 1987.     

Rime- and glaze-ice accretion due to freezing rain falling vertically on a horizontal thermally insulated overhead line conductor

A theory of atmospheric icing due to freezing rain on an overhead line conductor (OHLC) is developed. The rain falls vertically on a horizontal OHLC that is thermally insulated. It is assumed that the collection efficiency of the accretion surface is unity and that this surface is in thermodynamic equilibrium with the environment.

For air temperature T_A 0°C and raindrop temperature T_D 0°C, the freezing rain accretes as rime ice, provided that the temperature of the ice surface T_l < 0°C. The evolution equation governing the mass transfer at the accretion surface is solved analytically, yielding the shape of the rime-ice surface. Equations governing the thermal state of the rime-ice deposit are also given. These determine the onset of wet growth or glaze accretion at the upper stagnation line during suitable environmental conditions.

For environmental conditions producing an ice surface at temperature T_l = 0°gC, the freezing accretes as glaze. Equations governing the heat and mass transfer at the surface determine the shape of the glaze surface and the downward viscous motion of the unfrozen water. For T_D < 0°C, glaze evolution equations are developed for T_A 0°C and T_A 0°C. Analytical solutions of these equations are obtained. In particular, when T_D < −T_A < 0°C, the evolution equation predicts a novel limiting growth that is triangular in shape. Further study of the mass and heat transfer conditions, in the neighborhood of this final stage of glaze accretion, shows that it is maintained in thermodynamic equilibrium with its warm air environment.     

Multizone combustion of condensed systems

In the general case the combustion of condensed systems is of a stage-wise character and the combustion front is multizone [1, 2]. Following the investigation of two-zone models [3–5] it became clear that, during multizone combustion, one of the zones of heat evolution is the controlling zone. The velocity of the front is equal to the velocity of the controlling zone; however, with a change in the parameters of the system, there is the possibility of a transition of the controlling role from one zone to another, as well as of the coalescence and splitting of zones. This paper discusses a generalization of the two-zone problem which makes it possible to go over to the analysis of a complex, multizone front and shows that, for a front with two reactions (in the condensed phase and in the gas) and with dispersion, there are in all three possible arrangements of the zones of heat evolution (two three-zone variants and one two-zone variant). All possible types of dependence of the combustion rate on the depth of the dispersion are found.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 99–105, November–December, 1972.     

Wall jumps in temperature,partial pressures and populations of multicomponent mixtures of nonequilibrium polyatomic gases

The Maxwell-Loyalka method is used to derive formulas for the jumps in the macroparameters of a multicomponent nonequilibrium gas mixture. It is assumed that within the kinetic (Knudsen) wall layer one group of internal states of the molecules is close to equilibrium at the translational temperature, while another group and homogeneous chemical reactions are excited fairly slowly, so that they may be considered to be frozen and the corresponding inelastic collision integrals in the kinetic equations can be neglected. However, at the wall different groups of internal states of the molecules may be excited and chemical reactions may take place. The final calculation formulas are obtained under a series of simplifying assumptions in accordance with the recommendations made in [1, 2].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 133–141, March–April, 1993.The author is grateful to N. K. Makashev for important comments.     

Analytical study on the freezing and thawing processes of biological skin with finite thickness

 The moving heat source model and the Green's function method were applied to solve for the phase change problems involved in the freezing and thawing processes of biological skins with finite thickness. The transient temperature distributions, the cooling and warming rates, etc. inside the skin subject to two typical boundary conditions (the convective or plate cooling) often encountered in skin cryo-preservation are analytically predicted. And the heat transfer performances of these two freezing (or thawing) approaches are comparatively discussed. Implications of the present closed form analytical solution to the other biological phase change problems such as the skin cryosurgery or rewarming by microwave were also suggested. Received on 4 May 2000 / Published online: 29 November 2001     

An icing physics study by using lifetime-based molecular tagging thermometry technique

An experimental investigation was conducted to quantify the unsteady heat transfer and phase changing process within small icing water droplets in order to elucidate underlying physics to improve our understanding of the important micro-physical process of icing phenomena. A novel, lifetime-based molecular tagging thermometry (MTT) technique was developed and implemented to achieve temporally-and-spatially resolved temperature distribution measurements to reveal the time evolution of the unsteady heat transfer and dynamic phase changing process within micro-sized water droplets in the course of icing process. It was found that, after a water droplet impinged onto a frozen cold surface, the liquid water at the bottom of the droplet would be frozen and turned to solid ice rapidly, while the upper portion of the droplet was still in liquid state. As the time goes by, the interface between the liquid phase water and solid phase ice was found to move upward continuously with more and more liquid water within the droplet turned to solid ice. Interestingly, the averaged temperature of the remaining liquid water within the small icing droplet was found to increase, rather than decrease, continuously in the course of icing process. The temperature increase of the remaining liquid water is believed to be due to the heat release of the latent heat during solidification process. The volume expansion of the water droplet during the icing process was found to be mainly upward to cause droplet height growth rather than radial to enlarge the contact area of the droplet on the test plate. As a result, the spherical-cap-shaped water droplet was found to turn to a prolate-spheroid-shaped ice crystal with cusp-like top at the end of the icing process. The required freezing time for the water droplets to turn to ice crystals completely was found to depend on the surface temperature of the test plate strongly, which would decrease exponentially as the surface temperature of the frozen cold test plate decreases.     

A finite difference solution for freezing brine on cold substrates of spongy ice

The process of rapid freezing of a thin layer of brine, suddenly in contact with a cold substrate of brine-spongy ice, is investigated. The mechanism of intermittent ice accretion on cold substrates, which occurs in a short period of time, is different from the slow freezing of salt water and must be evaluated using a differential analysis. Investigation of rapid freezing fills a gap of knowledge related to intermittent icing of superstructures, which has usually been studied using control volume methods. The equation of transient heat conduction through brine-spongy ice is developed. Rapid freezing causes complete solute trapping, which makes the salinity constant and stable at the phase interface. A finite difference method, using uniformly-spaced fixed-grid mesh, is employed as a numerical scheme for calculating the rate of ice accretion. A method is presented for discretization at nodes close to the phase interface for preventing the instability of numerical solutions when the phase interface passes the adjacent nodes. The discretization is based on the Method of Lines (MOL) which is a numerical-iterative method of solution. Numerical results show that higher salinities and lower initial temperatures of brine-spongy substrates have the potential to create a thicker layer of new ice. Experimental studies show that the model and numerical solutions accurately predict the rapid freezing of brine on a cold substrate of brine-spongy ice.     

Distribution of the degree of vapor dryness in thermal action on oil seams

Injection of water vapor is an effective method of thermal action on oil-bearing seams in order to intensify the oil output and increase its yield [1]. In determining the technological characteristics of this process, it is necessary to know the dimensions of the vapor and hot liquid zones created in the seam, and also the distribution in the seam of the degree of vapor dryness. There are already well-known studies of the determination of vapor and hot liquid zones [2, 3], but the distribution of the degree of vapor dryness has not been considered. In the present study a method similar to the known method of successive interchange of steady states [4] is used in order to obtain an equation for the calculation of the distribution of the degree of vapor dryness when the vapor is injected with unchanged flow rate into a homogeneous seam. As a consequence, equations have also been obtained for the calculation of the vapor and hot liquid zones.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–176, January–February, 1986.     

Coupled problems of heat and mass transfer in a viscous fluid when a phase transition occurs

The investigation of heat and mass transfer processes involves, as a rule, solution of coupled problems of mathematical physics in which the coupling is realized through contiguous boundaries. In some cases, when the conditions at the contiguous boundaries can be specified in the form of simple correlation connections the overall problem can be analyzed by means of successive approximation by separate parametric solution of each problem separately; this is the case, for example, for the problem of a boundary layer on a wall that is not thermally insulated. When the correlation connections are complicated or the successive approximations do not converge (cases near equilibrium) or the contiguous boundaries themselves cannot be determined in advance, the problems do not separate and it is necessary to solve them simultaneously. Of this type is the considered problem of the flow and heat transfer of a fluid when a phase transition occurs. Problems of this kind arise in particular in the case of internal cooling of a shell by the heats of phase transitions of energy-bearing substances. In the present paper, analytic solutions are obtained for problems of the flow and heat transfer of a liquid (or gas) formed as a result of the phase transition of a solid when strongly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 46–50, March–April, 1984.     

Numerical investigation and self-similar solutions of the glacier-ocean interaction problem

The mathematical modeling of the heat and mass transfer processes in glaciers is an effective means of investigating and predicting their development. A full explanation of the problem of constructing appropriate mathematical models is given in [1–5]. By analyzing the equations involved [3, 6] it is possible to establish the principal factors and dimensionless numbers determining glacier dynamics and provide justification for neglecting the secondary terms. In particular, a simplified closed system of differential equations for the detailed calculation of all the hydrodynamic characteristics of the glacier can be obtained for K_hj « 1 up to O(K _h ² ), where K_h is the ratio of the vertical and horizontal scales of the ice mass investigated (K_h 10^–4–10^–6). In this case many of the qualitative characteristics of glacier dynamics are preserved even in one-dimensional models within the subisothermal approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1986.