The Temperature Field Evolution and Water Migration Law of Coal under Low-Temperature Freezing Conditions

This study examines the evolution law of the coal temperature field under low-temperature freezing conditions. The temperature inside coal samples with different water contents was measured in real-time at several measurement points in different locations inside the sample under the condition of low-temperature medium (liquid nitrogen) freezing. The temperature change curve was then used to analyse the laws of temperature propagation and the movement of the freezing front of the coal, which revealed the mechanism of internal water migration in the coal under low-temperature freezing conditions. The results indicate that the greater the water content of the coal sample, the greater the temperature propagation rate. The reasons for this are the phase change of ice and water inside the coal during the freezing process; the increase in the contact area of the ice and coal matrix caused by the volume expansion; and the joint action of the two. The process of the movement of the freezing front is due to the greater adsorption force of the ice lens than that of the coal matrix. Thus, the water molecules adsorbed in the unfrozen area of the coal matrix migrate towards the freezing front and form a new ice lens. Considering the temperature gradient and water content of the coal samples, Darcy’s permeation equation and water migration equation for the inside of the coal under freezing conditions were derived, and the segregation potential and matrix potential were analysed. The obtained theoretical and experimental results were found to be consistent. The higher the water content of the coal samples, the smaller the matrix potential for the hindrance of water migration. Furthermore, the larger the temperature gradient, the larger the segregation potential, and the faster the water migration rate.

MODEL OF DECOMPRESSION MELTING MECHANISM IN CONVECTIVE-UNSTABLE THERMAL LITHOSPHERE (FIRST APPROXIMATION)

We propose a model of decompression melting, separation, migration and freezing of the melt in the upper mantle during the convective instability process. The model takes into account differences between phase diagrams of the melt and the matrix and the resultant features of the melt’s behavior, without calculating reaction rates in a multicomponent medium. It is constructed under an explicit concept of the local thermodynamic equilibrium of the existing phases. Therefore, we further develop the first approximation of the descriptions of convection in the upper mantle and the formation of large epicontinental sedimentary basins, which have been presented in earlier publications. Our computational experiments show that primary melting of the upper mantle’s fertile material occurs intensively in a narrow frontal part of the ascending hot material flow. Then, the depleted and partially melted material rises farther upward from the front of primary melting. Melting of the depleted material continues at lower pressures in a rather wide range of depths (120–77 km). Further, the migrating melt is supplied by two sources, i.e. a deep-seated one, wherein the fertile material melts, and the medium-depth one, wherein melting of the depleted material takes place. Once the temperature and pressure rates of the melt reach the values corresponding to those of its solidus, a narrow freezing front is formed. Its width is almost similar to the primary melting front. As the ascending convective flow develops, the freezing front shifts upward. As a result, a quite thick (around 40–50 km) basalt-saturated layer occurs above the freezing front. An important observation in our modeling experiments is that, despite a considerably large total volume of the melted material, a one-time melt content in the mantle does not exceed tenths of one percent, when we consider averaging to volumes with a linear size of about 1.0 km. The basalt melt extraction depletes iron in the mantle and significantly reduces the mantle density. Considering the calculated basalt-depletion values for the matrix at 0.1–0.2, the density deficit doubles in comparison to the thermal expansion of the material. Logically, both the Rayleigh number and the intensity of convection also double (and this is confirmed by the calculations), which means that convection is enhanced after the melting start.Testing of the model shows that it gives a reasonable picture that is consistent with the available geological and geophysical data on the structure of the lithosphere underneath the currently developing epicontinental sedimentary basins. Furthermore, within the limits of its detail, this model is consistent with the results of modeling experiments focused on melting and melting dynamics, which are based on calculations of reactions between components of the mantle material.

Physical statement of the problem for a numerical model of soil freezing and heaving taking into account heat and mass transfer

Существуют два основных подхода решения задачи тепломассопереноса при численном моделировании промерзания грунтов: 1) решение методом конечных разностей с учетом граничных условий (границей, например, является фронт промерзания); 2) решение методом конечных элементов без учета границ модели. Оба подхода имеют существенные недостатки, что оставляет проблему решения задачи для численной модели промерзания грунтов острой и актуальной. В данной работе представлена физическая постановка промерзания, которая позволяет создать численную модель, базирующуюся на решении методом конечных элементов, но при этом отражающую ход фронта промерзания - то есть модель, в которой объединены оба подхода к решению задачи промерзания грунтов. Для подтверждения корректности модели был проделан ряд экспериментов по физическому моделированию промерзания модельного грунта и выполнен сравнительный анализ полученных экспериментальных данных и результатов расчетов на базе представленной численной модели с такими же граничными условиями, как в экспериментах. There are two basic approaches to solving the problem of heat and mass transfer in the numerical modeling of soil freezing: 1) using the finite difference method taking into account boundary conditions (the boundary, for example, is the freezing front); 2) using the finite element method without consideration of model boundaries. Both approaches have significant drawbacks, which leaves the issue of solving the problem for the numerical model of soil freezing acute and up-to-date. This article provides the physical setting of freezing that allows us to create a numerical model based on the solution by the finite element method, but at the same time reflecting the route of the freezing front, i.e. the model that combines both approaches to solving the problem of soil freezing. In order to confirm the correctness of the model, a number of experiments on physical modeling of model soil freezing have been performed, and a comparative analysis of the experimental data obtained and the calculation results based on the provided numerical model with the same boundary conditions as in the experiments was performed.

Thermal regelation of single particles and particle clusters in ice

We investigated kinetics of thermal regelation of single particles and particle clusters in a temperature gradient using experiments and mathematical models. We find that clusters migrate at a constant rate, while single particles accelerate towards the freezing front.

Experimental Study on Moisture Migration of Unsaturated Loess during the Freezing Process

To reveal the water-heat transfer mechanism of unsaturated loess, the effects of soil dry density (1.30 g/cm3, 1.50 g/cm3, and 1.65 g/cm3), moisture content (13.3%, 16.2%, and 19.4%), cold end temperature (−7°C, −10°C, and −13°C), and freezing mode on moisture migration in unsaturated loess in this paper are studied through indoor tests of moisture migration under the freezing action of large-size unsaturated loess. The results show that the temperature change in soil samples in the freezing process can be divided into three stages: rapid cooling stage, slow cooling stage, and stable stage. The higher the dry density, the closer the freezing front is to the cold end, with the initial moisture content having little effect on the freezing front, while the temperature at the cold end has a significant effect on the location of the freezing front. The total amount of moisture migration decreases with the increase of dry density, increases with the increase of moisture content, and increases with the decrease of cold end temperature. The freezing mode directly affects the distribution of moisture content and total amount of moisture migration in the frozen area.

Application of the Segregation Potential Model to Freezing Soil in a Closed System

Previous studies have shown that an accurate prediction of frost heaves largely depends on the pore water pressure and hydraulic conductivity of frozen fringes, which are difficult to determine. The segregation potential model can avoid this problem; however, the conventional segregation potential is considered to be approximately unchanged at a steady state and only valid in an open system without dehydration in the unfrozen zone. Based on Darcy’s law and the conventional segregation potential, the segregation potential was expressed as a function of the pore water pressure at the base of the ice lens, the pore water pressure at the freezing front, the freezing temperature, the segregation freezing temperature and the hydraulic conductivity of the frozen fringe. This expression indicates that the segregation potential under quasi-steady-state conditions is not a constant in a closed system, since the pore water pressure at the freezing front varies with the freezing time owing to the dehydration of the unfrozen zone, and that when the pore water pressure at the freezing front is equal to that at the base of the ice lens, the water migration and frost heave will be terminated. To analyze the possibility of applying the segregation potential model in a closed system, a series of one-sided frost heave tests under external pressure in a closed system were carried out in a laboratory, and the existing frost heaving test data from the literature were also analyzed. The results indicate that the calculated frost heave was close to the tested data, which shows the applicability of the model in a closed system. In addition, the results show the rationality of calculating the segregation potential from the frost heaving test by comparing the potential with that calculated from the numerical simulation results. This study attempted to extend the segregation potential model to freezing soil in a closed system and is significant to the study of frost heaves.

Ice Formation due to Condensation of Moist Air on Commercial Wicks

Heat pipes are valuable heat transfer devices that can be used in space; however, when exposed to the extremely low temperature of space, the working fluid can freeze. Currently, there are different methods to help mitigate freezing effects, including non-condensable gas-charged heat pipes and understanding ice formation on surfaces (e.g., typically surfaces with hydrophobic coatings). However, there is limited research about ice formation on wicks. Different wicking structures may delay freezing or mitigate freezing effects. This paper will investigate ice formation on two surfaces — commercial sintered and grooved wicks. An indoor environmental chamber was used to control ambient air temperature (i.e., 22°C) and relative humidity (i.e., 60% RH) and a Peltier cooler was used to control the surface temperature (i.e., −5°C). The resulting condensation of water onto the surface and then freezing was recorded for an hour and analyzed for the time freezing began on the surface (i.e., ice is initially visible) and the time freezing was complete on the surface. Initial results indicate that the sintered wick begins to freeze first (on average at 10.73 minutes versus 13.66 for the grooved wick) and the freezing front propagates faster (taking on average 10.83 minutes versus 12.44 minutes for the grooved wick). From the analysis, it is seen that the wicking surface structure influences the initial freezing time and the rate the freezing front propagates across the surface. These differences and the causes are investigated in this paper. These differences can, in the future, be exploited to design an optimal freeze-tolerant heat pipe and heat pipe freezing models.

Development of Superhydrophobic Coatings for Metal Surfaces

Provides information about the results of the evaluation of anti-icing properties of coatings. It is shown, that the hysteresis of wetting of the superhydrophobic surface based on the developed composition is 3,7 degrees. The critical angle of rolling of a drop of water from an inclined surface is determined. The results of the evaluation of the kinetics of freezing of a water droplet on a superhydrophobic surface are given. It is shown, that in the initial period there is a transfer of heat from the surface to a drop of water. Then there is a movement of the freezing front from the substrate upwards.

The issue of switching between non-freezing and freezing in soils

<p>The freezing process in soils is important in many natural systems and, consequently, it is of great interest to model it accurately. <br>The freezing of water in soil is coupled to the heat equation as freezing releases latent heat and temperature is an important variable that determines whether water is in solid or liquid state. In soils, water can remain liquid under sub-zero temperatures (freezing-point depression). This effect is often modeled with the Clapeyron equation. With the Clapeyron equation, a temperature dependent pressure head definition for the total water content (liquid + frozen water) and the liquid water can be derived. When the temperature of the soil system falls below the freezing point, the system switches between the pressure head definitions. However, this switch can cause a discontinuity at the freezing front leading to numerical issues and unrealistic results.</p><p>To compensate for the discontinuity, we discuss the use of regularisation of the switching term on, both, synthetic and experimental data of case studies of freezing column experiments. </p>