Aleksandr Fyodorovich Galkin

The purpose of this work is to determine the degree of change in the thermophysical characteristics of the snow cover during compaction. A new indicator, the snow cover compaction coefficient, is introduced. The dependences of the change in the main characteristics of the snow cover on the compaction coefficient have been obtained. The change in the following characteristics has been considered: thermal conductivity, thermal diffusivity, thermal resistance, thermal inertia, thermal stability, and the Fourier and Stefan criteria. A summary table has been constructed, which makes it possible to determine the form of relationship between the above main characteristics and the compaction factor. It has been established that the form of functional relationship between the thermal conductivity coefficient and the snow density plays a crucial role in the quantitative relationship between the characteristics and the compaction factor. For example, if we assume a linear relationship between the thermal conductivity coefficient and the density, the degree of reduction in thermal resistance during snow reclamation is proportional to the square of the compaction factor, while if we assume a parabolic relationship between the thermal conductivity coefficient and the density, the degree of reduction in thermal resistance is proportional to the third power of the compaction factor. The values of the considered thermophysical parameters are obtained from the compaction factor for the case of the dependence of thermal conductivity coefficient λ on the snow density ρ in the form of a truncated polynomial of an arbitrary degree n. Graphical dependencies of individual indicators on the form of initial functional relationships of the initial values obtained theoretically and from experimental studies and field observations are presented. It is also shown that the percentage discrepancy in the calculation results caused by the choice of exponential function of the thermal conductivity coefficient on density increases for almost all of the thermal properties with an increase in the value of the compaction coefficient and considerably exceeds the value allowed in engineering calculations. For example, the discrepancy of thermal resistance of snow cover when the compaction coefficient is 2.0 is 50%, and with compaction coefficient equal to 4.0 it is 75%. The main quantitative relationships of change in thermal conductivity coefficients of snow and thermal resistance of snow cover depending on the compaction degree have been formulated.

The subject of the study were man-made rock heaps in the cryolithozone. In particular, the methodology for calculating the thermal conductivity coefficient of the rock heaps during the summer and winter periods was of interest, taking into account the possible partial filling of the heap space with water or ice. The convective component of heat exchange (which is decisive in the winter period) was not considered in this work. Only the basic value of the thermal conductivity coefficient of the heaps was investigated, which was presented as a two- and three-phase heterogeneous system. Since the stability of rock heaps largely depends on the thermal regime of the base, which, in turn, is determined by thermal resistance, that is, the thermal conductivity coefficient and the height of the heap layer, such research is relevant. This is related to the active development of mineral deposits by open-pit mining in the cryolithozone. The research method included a comparative assessment of three popular formulas for determining the thermal conductivity coefficient of heterogeneous systems. Classical formulas by Lichtenecker, Bruggeman, and Maxwell were studied. Both complete and simplified versions of the formulas were considered. As a result of the studies, it was found that all formulas yield similar results, and the discrepancy does not exceed the values acceptable in engineering practice. Therefore, any of them can be used for forecasting the thermal regime of dry heaps. Using Lichtenecker's formula for a three-phase system, the degree of change in the thermal conductivity coefficient of man-made heap during the summer and winter periods was investigated. A dimensionless criterion for the change in the thermal conductivity coefficient of the rock mass upon wetting was obtained. It was established for the first time that the increase in the thermal conductivity coefficient of the rock heap upon wetting is equal to the ratio of the thermal conductivity coefficients of water (ice) to air raised to the power equal to the volumetric moisture content (ice content) of the rock heap's voids. This pattern defines the scientific novelty of the research. In addition, an expression was obtained to determine the limiting humidity value of man-made heaps, at which the thermal conductivity coefficient changes within the accuracy of engineering forecasting during the summer and winter periods. This result confirms the practical value of the work performed.

The subject of the research was the snow cover, which largely determines the formation of the temperature regime of the active layer and the layer of annual heat turnover in the cryolithozone. In particular, the process of thermal interaction between the atmosphere and permafrost soil in the presence of snow cover was investigated. The relevance of the research is justified by the problem of forecasting and reconstructing the impact of climate change on the temperature regime of the cryolithozone, as well as the search for and development of new methods and means of snow amelioration of soils. The aim of the research was to determine the effect of changing the thermal resistance of the snow cover during winter amelioration on the surface temperature of the soil. The main task of the research was to establish a functional dependence of the change in the surface temperature of the frozen soil base under different thermal resistances of the snow cover. Special attention was given to studying the change in surface temperature of the soil during winter amelioration through the compaction of the snow cover. To achieve the goal, elements of natural scale theory were used, through which the main simplices (parametric criteria) for determining the functional dependence between the dimensionless surface temperature of the soil and the snow cover compaction coefficient during winter amelioration were obtained. The scientific novelty of the research results lies in the fact that for the first time an analytical dependence has been obtained that allows for a rapid assessment of the change in the surface temperature of the soil when compacting the snow cover during the winter amelioration period. The obtained dependence in the form of dimensionless parametric criteria allows for the evaluation of the effectiveness of snow amelioration in different climatic zones. Additionally, it is possible to choose the necessary degree of compaction of the snow cover to achieve a specified surface temperature of the soil base within a given cooling (frost) period of the soil base of engineering structures. This has not only theoretical but also practical significance, for example, in creating artificial frozen blocks in the foundations of rock ovals when extracting mineral deposits using open-pit methods in areas of viscous and island permafrost.

The subject of the research was the snow cover, which largely determines the formation of the thermal regime of the active layer and the layer of annual heat turnover in the cryolithozone. In particular, the process of changing the thermal conductivity coefficient of snow depending on density, as a comprehensive indicator, was considered. The research is relevant for the problem of predicting and reconstructing the influence of climate change on the thermal regime of the cryolithozone, as well as the search for and development of new methods and means of snow melioration of soils. The aim of the research was to obtain formulas for determining the thermal conductivity simplex of snow based on traditional functional dependencies obtained by well-known researchers (Abels, Brecht, Schwander, Schwerdtfeger, Yen) and to compare the level of discrepancies in the results of calculating the thermal conductivity simplexes according to various formulas. The author paid great attention to comparing different simplexes for five types of snow: new, granular, rime, firn, and bubble ice. To achieve the goal, elements of the theory of natural scales were used, through which the main simplices (parametric criteria) for determining the thermal conductivity coefficients of snow were obtained. The scientific novelty of the work lies in obtaining computational dependencies for the thermal conductivity simplices as a function of the density simplex across the entire possible range of variation of snow types: new, granular, rime, firn, and bubble ice. As a result of a comprehensive analysis, a comparison of the consistency of calculations according to various simplices was conducted, compared with a reference simplex, for which the parametric criterion of Abels was adopted. It was found that the values of individual simplices for different types of snow sometimes differ significantly. Moreover, for denser types of snow, this difference is less noticeable and usually falls within the accepted confidence interval. An assessment of the consistency of various simplices with each other and with the reference simplex, taken as the Abels simplex, was made. It was shown that there is also a regularity for the paired comparison of simplices: the degree of disagreement between different simplices depends on the type of snow, and with the increase in the density simplex (firn, bubble ice), it decreases and falls within the accepted confidence interval.

The purpose of the work was to evaluate the thermal (energy) and economic efficiency of using thermal insulation paints as a substitute for traditional thermal insulation materials. A comparison of the paint parameters declared by the manufacturers (thermal conductivity coefficient) with the maximum possible parameters (from the standpoint of the theory of thermal conductivity) makes it possible to give an objective assessment of the scope and energy efficiency of using heat-protective paints in the construction industry and the energy sector. The data of theoretical calculations of the thermal conductivity coefficient of paints using the Schwerdtfeiger formula are presented, which are in good agreement with experimental data obtained by other authors. It is shown that the coefficient of thermal conductivity of paints has a minus of the second order and is not lower than the coefficient of thermal conductivity of traditional thermal insulation materials. The thermophysical parameters of thermal insulation paints claimed by manufacturers do not correspond to reality and, in principle, cannot provide effective thermal protection of engineering structures. To assess energy efficiency, two main characteristics of thermal protection from the compared materials were calculated; the degree of increase in thermal resistance and the degree of decrease in heat flow of the insulated object. It is shown that it is not possible to achieve the required degree of thermal protection of objects using the proposed paints. The economic assessment of the effectiveness of using thermal insulation paints both separately and in combination with traditional thermal insulation has shown their complete lack of competitiveness. To achieve the same thermal effect when using “thermal insulation paints” one needs to spend, on average, 100 times more just on materials. With the combined use of “thermal insulation paints” together with traditional thermal insulation materials (in particular, mineral wool), the cost of achieving an equal thermal effect increases, on average, by a factor of 6, with an increase in thermal resistance of only 1.04 times. The general conclusion is that thermal insulation paints cannot be used for thermal protection of objects and energy saving in the form advertised by manufacturers.

A brief review of research on variation of thermal resistance of snow cover and formulas to determine the thermal conductivity coefficient of snow are presented. This article aims to establish the regularities of variation in thermal resistance of snow when compressive melioration is applied to the snow cover. A criterion consisting of ratio of initial thermal resistance to the thermal resistance after compression is introduced. Two practically relevant cases, a full and partial compression, whereby the snow density after compression is a constant and a variable respectively, are considered. It is demonstrated that the area where it can be assumed that the snow density after compression is a constant has a low confidence interval and in practical applications it needs to be accounted for that the snow cover is not fully compressed under load. The calculation results are presented in a generalized dimensionless form that includes an indicator of arbitrary exponent in an approximated formula to determine the thermal conductivity coefficient from snow density. It has been established that the type of functional dependence of thermal conductivity coefficient on snow density has a significant influence on the calculation results of the thermal resistance of snow cover. The boundary values of snow compression coefficient within the permissible error level (10 %) were found. For example, for a linear dependence of the thermal conductivity coefficient on density the permissible compression coefficient is no higher than 1.25. For a quadratic dependence, it is 1.11. The results of variant calculations are presented as 2D and 3D charts, which allow quickly assessing the assumptions and conclusions.

The aim of this study was to establish criteria for the economic feasibility of using new thermal insulation materials in place of traditionally used materials for the thermal protection of engineering structures. Two scenarios were considered: the complete replacement of one material with another and the combined use of traditional and new thermal insulation materials. The criterion used was the ratio of the cost of materials required to achieve the standard thermal resistance of the entire insulation system. New indicators describing the relationship between the economic and thermophysical properties of materials were developed, particularly relating the specific cost of thermal insulation materials (cost per unit volume) to their thermal conductivity coefficient. To generalize the analysis, novel indicators were introduced: price simplex, thermal simplex, and thermal resistance simplex.We concluded, from an economic perspective, the use of new materials instead of traditional ones is justified if the ratio of the costs of the new and traditional materials does not exceed the reciprocal of the ratio of their thermal conductivity coefficients—that is, if the price simplex is lower than the reciprocal of the thermal simplex. Specific examples demonstrate the application of this methodology in evaluating the feasibility of using thin-film thermal insulation materials instead of mineral wool to achieve equivalent thermal protection. The analysis shows that, at current prices, thin-film materials are tens of times more expensive than traditional mineral wool insulation, even when accounting for a significant reduction in mineral wool’s thermal resistance due to moisture during operation. The results of these calculations clearly illustrate the newly established relationship between the economic and thermophysical characteristics of thermal insulation materials.

The subject of the study is a snow cover consisting of an arbitrary number of layers of varying thickness and different snow densities. The thermal resistance of such a cover has been investigated. One of the key parameters in the study of the interaction of various engineering structures with snow is the thermal resistance of the snow cover. The aim of the work was to assess the accuracy of calculating the thermal resistance of a layered snow cover when averaging the snow density with depth. Two approaches to determining the thermal resistance of the snow cover have been considered: as a layered structure and as an equivalent homogeneous structure with a constant average density calculated as a weighted average. Classical formulas for determining the thermal conductivity coefficient based on the density of the snow cover—namely, the formulas by G.P. Abels and N.I. Osokin—were used for calculations of thermal resistance. A comparison of two calculation methods for computing the thermal resistance of the snow cover was carried out: as the sum of the thermal resistances of the layers and as a single-layer structure with weighted average density. The analysis of numerical and graphical data allowed for the following main conclusions. With a nonlinear relationship between the thermal conductivity coefficient and the snow density, the error increases with the increase in the compaction coefficient of one of the layers. For example, when the density of a layer doubles, the relative calculation error ranges from 20% to 30.0% and depends on the ratio of the thicknesses of the individual layers. It was established that when the compaction of one layer is less than 1.6 times, the use of the concept of "average snow cover density" in thermal calculations for determining the thermal resistance of the snow cover is quite acceptable. In this case, the error will not exceed the allowable value in engineering practice. With increased compaction, it is necessary to calculate the total thermal resistance of the snow cover as the sum of the thermal resistances of individual layers, as is customary in building thermal physics for determining the thermal resistance of enclosing structures. Further research should focus on determining the accuracy of thermal resistance calculations as the snow density depends on the layer thickness, as well as accounting for the influence of snow structure with constant density on the thermal conductivity coefficient. It is also of interest to compare these theoretical calculations with existing data from field observations.

The subject of the research is the functional relationship between the thermal conductivity coefficient of snow and its density in a layered structure of the snow cover with various types of snow. The purpose of the research: to determine the range of possible averaging of the thermal conductivity values of a two-layer snow cover, including granular snow and hoarfrost. To achieve this goal, a comparative assessment of the accuracy of formulas for determining the thermal conductivity coefficient of granular snow and hoarfrost was made, which, at the same density, differ in thermal physical characteristics due to varying structures. Well-known linear formulas by Pavlov, Sulakvelidze, and Chernov for hoarfrost and granular snow were used for comparison. The influence of temperature on snow properties was not considered. The two-layer snow cover was regarded as a medium with arbitrarily varying layers in height, the thermal conductivity of each of which is defined by different formulas. To obtain the average thermal conductivity coefficient, the concept of a weighted average parameter was used. In this case, it is the sum of the products of the thermal conductivity coefficient of each layer by its thickness, divided by the thickness of the entire snow cover. The overall formula includes an arbitrary ratio of the layers in the snow cover. As a result of the analysis of variant calculations, the following patterns emerging from the averaging of the thermal conductivity coefficient of the two-layer snow cover were established. When ignoring the presence of layers in the snow cover and calculating its thermal conductivity only according to the formula characteristic of granular snow, the maximum absolute error (depending on the ratio of layer thicknesses) does not exceed 50%. When calculating using the formula characteristic of hoarfrost, the maximum absolute error is approximately twice as large and amounts to almost 100%. The scientific novelty of the research lies in establishing a general quantitative pattern of change in the error of calculating the thermal conductivity coefficient of layered snow cover when using formulas derived for granular snow or only according to formulas characteristic of hoarfrost. The results of variant calculations of the errors that arise when not accounting for the layered structure of the snow cover and when considering layering using the weighted average thermal conductivity coefficient are presented in the form of 2D and 3D graphs, allowing for a visual confirmation of the validity of the conducted research and the conclusions drawn.

The subject of this research is automobile roads in permafrost zones, which are subject to the negative effects of cryogenesis. The focus of the study is on thermal insulation coatings based on mixtures of insulating and heat-accumulating construction materials. The work aimed to determine the area of economic efficiency of using mixtures of construction thermal insulation materials in road pavement structures for the cryolithozone. One possible option for reducing the construction costs of roads in the cryolithozone is the use of thermal insulation layers in road pavements made from thermal protection mixtures, which consist of a heat-accumulating binder (such as sand or gravel) and a heat-insulating filler (expanded clay, azurite, polystyrene granules, or glass debris). The influence of the thermal-physical characteristics of the binder and filler on the economic viability of using thermal insulation mixtures in road pavements has been investigated. To facilitate the analysis, two new dimensionless simplexes have been introduced. The thermal-physical simplex characterizes the ratio of the thermal conductivity coefficients of the filler and binder. The economic simplex characterizes the ratio of the cost per unit volume of the filler to the cost per unit volume of the binder. A target function has been constructed, allowing for the calculation of the conditions under which the ratio of the cost of filler to the cost of binder makes the use of material mixtures (compared to a homogeneous equivalent layer of binder with respect to thermal resistance) economically efficient. Basic quantitative patterns have been obtained, characterizing the relationship between the concentration of the filler and the dimensionless simplexes: thermal-physical and economic. A dependency has been derived for determining the limiting value of the dimensionless cost simplex, enabling the identification of the boundary of economic efficiency when using thermal insulation mixtures with varied thermal and physical properties. It has been shown that thermal insulation material mixtures can be recommended as an economically efficient alternative to homogeneous construction materials when designing road pavements. A 3D graph has been constructed to quickly assess the conditions under which the specific cost simplex value makes it advisable to apply a particular thermal insulation binary mixture in road pavements.