Use of Concentrated Solar Power Technology for a High Temperature Processes: Case Study of Uzbekistan

Abstract

The paper examines the state and prospects for the development of renewable energy use in Uzbekistan, presents the specific features and conditions of concentrated solar power (CSP) technology, analyzes the technological capabilities of high-temperature solar furnaces as one of the promising areas of CSP technology, and notes specific scientific directions in this area. A comparative analysis of the technical and optical-energy characteristics of high-temperature solar furnaces of well-known research centers and their application in solving of actual scientific and technical problems is carried out. The main parameters and energy characteristics of the Uzbek 1000 kWt solar furnace in Parkent (BSF) in comparison with the similar French (Odeillo) furnace are given. Special equipment and stands installed in the focal zone of the furnace for melting, synthesis, heat treatment and complex testing of various technical products in high-temperature conditions are presented. By the example of the analysis of the process of quenching high-temperature materials, some features of high-temperature processes are shown.

1. Introduction

1.1 Renewable energy sources in Uzbekistan

Currently, the use of renewable energy sources (RES) is a priority in most countries of the world, including Uzbekistan. Such a global situation is caused by many well-known objective factors, the main of which are: depletion of non-renewable energy resources of the Earth, colossal emission of carbon dioxide into the atmosphere, uneven distribution of fossil energy resources and different natural, geographical and climatic conditions of the countries of the world (the number of sunny days, the presence of rivers, etc.), political and economic conjuncture and others. Therefore, the intensive transition to the use of renewable energy sources is an important stage in the development of global energy [1, 2, 3, 4, 5].

In Uzbekistan, despite the high potential of, for example, solar energy, major projects on the use of alternative energy sources have not been implemented until recently. In 2020, the total installed capacity of renewable energy plants was 2 gigawatts and almost 100% of this capacity was accounted for by hydroelectric power plants [6]. In recent years, the situation has changed and now Uzbekistan pays special attention to the use of renewable energy [4, 7, 8]. A number of important laws on renewable energy have been adopted, an attractive investment climate has been formed, etc. In 2021, a photovoltaic power plant with a capacity of 100 MW was commissioned in Navoi region and in 2022 a similar station in the Samarkand region. This year, investment agreements were signed between the Ministry of Investments of Uzbekistan and ACWA Power, which provides for the commissioning of two solar photovoltaic plants with a total capacity of 1400 MW in the Tashkent and Samarkand regions and three energy storage systems with a total capacity of 1200 MW. It should be noted that by 2030 it is planned to produce 35% of electricity from renewable energy sources. To do this, 15,000 MW of capacity will be put into operation – 10,000 MW of solar power plants and 5000 MW of wind power plants [9].

At the same time, it should be noted that the introduction of small-scale developments (in power from several hundred watts to several hundred kilowatts) for renewable energy, mainly for photovoltaic installations and thermal collectors, in various organizations, in the agro-industrial sector, in social facilities, in individual and rural farms and etc. is developing at an accelerated step [10].

1.2 Concentrated solar power technology

One of the promising areas of renewable energy use is the technology of concentrated solar power (CSP). This category mainly includes solar point-focus concentrators (Dish), solar linear-focus concentrators (PTC, Fresnel) and tower-type solar stations. It should be noted that these installations, in addition to wide practical applications, in most cases are also unique scientific tools for conducting research in the field of high-temperature processes. The disadvantages of such systems include the high complexity of their installation and the high cost compared to photovoltaic systems. In addition, concentrating installations operate from direct solar radiation and therefore it is almost mandatory to have a tracking system for the Sun and therefore regions with a predominance of direct solar radiation are preferable for such tasks.

Despite these disadvantages of CSP technologies, due to the possibility of this technology to achieve high temperatures, up to 3000 degrees, CSP technologies have found wide applications in the world. For example, as noted in [11], CSP is a highly competitive technology for generating electricity, research in the field of solar materials science is known and relevant, in particular the successes of scientists from France and Uzbekistan [12, 13, 14, 15, 16, 17, 18, 19, 20]. The paper [20] provides a brief overview of the dynamics of the development of solar energy concentration technologies in the world in the period from 2010 to 2021 and assesses the possibility of using these technologies in Uzbekistan. It should be noted that the climatic conditions of Uzbekistan correspond to such and other necessary criteria [21, 22].

It should be noted that the global generating potential of CSP is estimated at about a billion terawatt-hours (TWh) per year, which is tens of thousands of times higher than global electricity consumption [23]. It is predicted that by 2050, 12 and 25% of the total and electric energy consumed by mankind, respectively, will be generated using CSE technology [24]. Currently, linear-focus concentrators, which generate up to 80% of the energy generated using CSE technology, have found the greatest use among CSP-based installations [25].

In recent years, fundamental and scientific and technical research, as well as applied developments using CSP technology, have been actively carried out. Currently, there are several tens of thousands of solar installations for various purposes and capacities based on CSP technology in the world. There are about 100 large stations based on CSP technology in the world, and about the same number of such stations are planned to be built. The undisputed leaders in the use of CSP, especially for large projects, are Spain and the USA. In Australia, in the countries of North Africa, in Chile, Algeria, Morocco, Egypt, CSP technologies are also widely used. Recently, China, France, Germany, India, Israel, Italy and South Korea have been increasingly working in this direction. By the end of 2019, the shares of installed capacities of stations based on CSE by countries of the world were: Spain (37%), USA (28%), China (10), Morocco (8), South Africa (8), Israel (6) and the rest of the countries 3% [26].

1.3 Reasoning of the research directions

An analysis of the trends in the development of alternative energy sources shows that many countries are already paying special attention to these energy sources. The reasons for this, as already noted, are obvious - the lack of energy due to the growth of its consumption, the depletion of fossil energy sources, and serious global environmental problems. The way out of this situation is the uses of energy-saving and environmentally friendly energy production technologies, that is, Renewable Energy Sources (RES).

Here the most important thing is a reasonable understanding of this energy transition in each country and the importance of this step, the country’s contribution to solving global energy problems in preventing global climate change on our planet.

It should be noted that alternative energy sources are widely classified according to the types of their origin - solar energy, wind energy, geothermal energy, hydropower, ocean energy, bioenergy and others. At the same time, if we consider, for example, the total generation of electricity in the world, the share of RES is 27.3% (end of 2019, [4]). And here, 15.9% hydro, 5.9% wind, 2.8% solar panels, 2.2 biofuels and the rest 0.4% are geothermal, CSP and ocean energy.

This paper discusses the use of concentrated solar energy in the study of some high-temperature processes in the context of the use and presentation of solar technologies.

The main purpose of this work is to present the technological capabilities of the BSF in Parkent in the study of the above problems, as well as a description of the accompanying series of technological equipment. Before directly presenting the main material, we briefly presented the state and prospects of the uses of renewable energy sources in Uzbekistan and a brief overview of the technology of concentrated solar power (CSP). It would seem that the questions are far from the main topic.

However, if you look closely, these areas are interconnected, these materials complement each other, allow a more comprehensive understanding of the specific task under consideration and see its perspective. It should be noted that during the construction of the BSF (80s), the state and prospects of CSP technologies were analyzed and also, of course, local solar energy resources were studied, etc.

The reason for the analysis is the efficiency of the BSF, that is the results of high-temperature studies, along with other achievements, ultimately depend on the level of direct solar radiation, its daily and annual duration, and so on. For this reason, a modern meteorological station was built at the BSF location.

Thus, the studies presented in this paper make it possible to get acquainted with the unique technological capabilities of the BSF, the materials provide information on some well-known high-temperature solar furnaces, promote the development of research in the field of high-temperature processes and the development of cooperation with Uzbek scientists.

2. High temperature solar furnaces

As you know, to get 1 MWh of energy, you need to burn 250 kilograms of coal at a consumption of 0.67 tons of oxygen, with the formation of 0.9 tons of carbon dioxide, polluting the environment. The constant increase in energy consumption, depletion of fossil fuel reserves and environmental problems arising from its combustion pose the task of the energy economy of the Republic of Uzbekistan to search and develop new non-traditional energy sources, for example, renewable and environmentally friendly solar energy. There are 260 sunny days a year in Uzbekistan and the pace of development of solar technologies can become a determining factor in the development of savings.

High temperatures can be obtained, in particular, in solar high-temperature installations - solar concentrators. At the same time, the most suitable solar installations are point-focus concentrators.

The geometric shape of the reflecting surface of such concentrators is usually formed by the rotation of conic sections - spheres, parabolas and hyperbolas. Examples of such concentrators are: spherical concentrator, paraboloid concentrator (Dish system), parabolic trough concentrator (PTC), hyperboloid concentrator (Cassegrain optical system) and others. At the same time, when designing such installations, in order to facilitate the technological processes of forming reflective surfaces of installations, various simplified technical solutions are used. An example of such approaches is the concentrators with facets, the use of Fresnel reflectors, the use of approximately close to ideal geometric shapes, and others. As shown in [27], paraboloid concentrators have the highest concentrating capacity.

In the aspect of the use of solar radiation, the most technologically effective is its concentration on the surface by means of mirror concentrating systems (MCS). To date, there are many MCS of various sizes and the level of concentration of solar radiation. Among high-temperature solar furnaces, first of all, it is necessary to note the unique large poly-heliostat solar furnaces with a capacity of 1000 kW (Figure 1) in Parkent (Uzbekistan, 1987) and in Odeillo (France, 1971) [28, 29]. It has become generally accepted that the abbreviation BSF - Big Solar Furnace is used to identify these furnaces. The diameters of the concentrators of these furnaces are 54 m with a focal length of 18 m. The density distribution of concentrated solar energy in the focal zone of these furnaces has the form of a Gaussian distribution with a diameter of almost 1 m and a concentration of about 10,000 times. In these furnaces, in the best condition of their optical elements, a temperature of about 3000 degrees is reached. The maximum energy density reaches up to 750 Wt/cm², the spot diameter is about 1 m. Such densities of the concentrated solar radiation flux make it possible to implement high-temperature physico-chemical processes leading to the synthesis of new materials with a special microstructure, the production of hydrogen by thermochemical method, the generation of electrical and thermal energy, laser radiation and etc. In addition, it should be noted that the high accuracy of the optical elements of the BSF allows it to be used as a multifunctional ground-based Cherenkov telescope for recording Cherenkov flashes from broad atmospheric showers of cosmic rays with an energy of ${\mathrm{E}}_0={10}^{13}-{10}^{15}\mathrm{eV}$.

Figure 1.

General view of BSF in Parkent and Odeillo.

Thus, it can be stated that BSF, in addition to being an environmentally friendly melting furnace, is also a unique research tool for conducting high-temperature studies and has a number of important significant advantages compared to other high-temperature solar furnaces, and they are as follows:

1. High furnace capacity, ≈ up to 1 MW.

2. High levels of the coefficient of concentration of solar radiation, 4500÷10,000.

3. Large size of the focal spot of the furnace, ≈ 80÷100 cm.

4. The presence of 62 heliostats, which allows manipulating the focal distribution of energy.

5. The presence of automatic control system of heliostats (ACS), which allows you to flexibly control the movements of heliostats.

6. Simulation of 62 narrow-aperture concentrators.

7. The ability to control the concentrated solar energy flux in technological processes.

8. The ability to measure and control the optical-energy characteristics of the furnace, etc.

The Institute of Materials Science has developed and created various small solar furnaces (SSF) with an average capacity of 1500 Wt and a couple of them have been exported to Egypt (Tabbin Institute of Metallurgy, TIMS, Cairo) and India (International Powder Metallurgy Center, ARCI, Hyderabad). The exported furnaces are identical to each other and have a thermal power of 1500 watts. The installation consists of a single flat heliostat with size of 2.8 × 2.8 m, a single paraboloid concentrator with a diameter of 2 m, a solar sensor and auxiliary measuring instruments and the necessary equipment for its operation. The heliostat of the installation has an automated system for tracking of the Sun. These furnaces are shown in the Figure 2.

Figure 2.

Installed solar furnaces in Egypt and the Republic of India.

Currently, fundamental and applied research in the field of solar materials science using high-temperature solar furnaces is carried out in many leading scientific centers of the world. They are, for example, NREL (USA), Sandia National Laboratory, USA, PROMES (France), Plataforma Solar de Almernia (PSA, Spain) ETH Zurich (Switzerland), Paul Scherrer Institute (Switzerland), DLR (Germany), The Weizmann Institute of Science (Israel), HRFSF (Mexico), Masdar Institute Solar Platform (Abu Dhabi, UAE), Institute of Materials Science (Uzbekistan) and many others. It should be noted that [30] presents a fairly detailed analysis of the characteristics of various solar furnaces used for the production of “green” hydrogen, in particular, the possibilities of the Parkent solar furnace are also noted there. In the well-known work [31], a number of important studies in the field of high-temperature processes performed using solar furnaces are presented in sufficient detail - solar surface hardening of steel, refinement of nanomaterials, solar synthesis of fullerenes and carbon nanotubes.

3. Measurement of highly concentrated solar flux

It should be noted that any complex technological installation without a system for monitoring and measuring the relevant parameters and its performance characteristics cannot be operated efficiently and reliably. In this regard, a Big Solar Furnace is equipped with modern devices for measuring the density of concentrated solar energy, the temperature of the materials under study and devices for monitoring the flow of high-temperature processes. These include a high-temperature pyrometer for remote measurement of the temperature of materials (IMPAC IGA 12, Tmax = 3500°C), a thermal imager (FLIR A655), various radiometers, photometers, digital thermometers, a vision system (developed by the Institute of Materials Science), etc.

Thus, one of the important problems in the operation of high-temperature solar installations is the measurement of the flux density in the focal zone of the concentrator. For this purpose, calorimetric, radiometric and photometric methods are widely used, as well as television measuring systems.

The most common method of measuring the energy flux density in the focal plane of the Mirror Concentrating System (MCS) is the calorimetric method, based on measuring the amount of heat transferred by the surface of the calorimeter to the coolant. The calorimetric method consists in measuring the amount of energy transferred from the MCS into the beam-receiving cavity at different diameters of the inlet holes (Figure 3).

Figure 3.

Design of the flow calorimeter. 1-thin-walled copper tubes; 2-sheet copper; 3-thermal insulation; 4-diaphragm; 5-inlet.

Special diaphragms are installed tightly to the inlet of the radiating cavity so that the center of the orifice of the diaphragms coincides with the center of the orifice of the radiating cavity. The main advantage of the calorimetric method is to obtain an absolute value of the energy distribution, as well as the ability to measure radiant fluxes in a wide range of energy densities up to 1000 Wt/cm², with a relative error of 10–15%.

The radiometric measurement method, like the calorimetric one, is based on the thermal effect of radiant energy, however, the flow density in this case is judged directly by measuring the thermo-EMF or thermal resistance of the receiving surface. Modern designs of radiometers with cooling of the measuring part make it possible to measure consistently high levels of flux density up to 1.5*10⁷ Wt/m². However, radiometers measure only relative values of the flux density.

One of the modern and informative methods of measuring the values of the flux density is the so-called system of technical view-STV. In this method, the irradiance is determined based on the image of the focal spot. The obtained relative values are then converted to absolute values using calibration coefficients. STV allows you to instantly get all the information about the focal spot. The obtained data is easily processed using graphic editors on personal computers.

Pyrometers operating on the basis of the laws of thermal radiation of heated bodies are widely used to measure high temperatures. It is known that the flow of radiant energy (Q) falling on the surface of the body is partially reflected (R), partially passes (D), and the rest is absorbed (A), and Q = R + D + A. The absorbed energy is converted into the energy of the thermal motion of the molecules. The material absorbing the rays heats up and emits radiant energy in the form of electromagnetic waves of various lengths, the intensity of which increases with increasing temperature.

To measure the flow density and temperature of materials, a FLIR thermal imager with sensitive microbolometers elements is used, which register the radiation of the melt at a wavelength of 8 microns. The functionality of the FLIR thermal imager allows you to study the processes of heating, melting of materials in the focal area of the BSF. Most likely, the processes of heating, melting of the material in the concentrated solar irradiation (CSI) flow are accompanied by the processes of radiation, convection, as well as losses due to thermal conductivity, depending on the phase state, the granularity of the material in the initial state. Such features should be taken into account when modeling the process of interaction of concentrated solar radiation with materials.

4. Equipment and stands for melting, synthesis, heat treatment and complex testing of materials and various technical products

BSF is a complex optical-mechanical, electrical system and its successful operation requires appropriate instrumentation, instruments and specific equipment for high-temperature processes. These include, for example, meters -radiometers, calorimeters, digitization systems (system of technical view-STV), photometers, actinometers, computer interface systems, pyrometers, thermal sights etc., modern theodolites, levelers, narrow-aperture lasers, spotting tubes and others.

In the focal zone of the BSF various melting units are installed - furnaces of “bucket” and “rotary” types, for example. Figure 4 shows the scheme of a water - cooled furnace of the plate type – this is a typical scheme of melting furnaces.

Figure 4.

Water-cooled plate type furnace: (1) metal body, (2) material being smelted, (3) material feed, (4) melt zone, (5) melt stream, (6) water jet, (7) barrier, (8) cold water reservoir.

The ladle furnace is designed for experimental melting in small portions with constant stirring during the melting process in order to achieve homogeneity of the fused material. The furnace allows you to cook the charge, lighten the glass mass and then carry out a one-time production of the entire portion of the melt. The control of the furnace by means of swings makes it possible to mix the liquid phase during the melting process to achieve better clarification and homogenization. The highest melting performance is achieved when the zone with the maximum concentration of light energy is located on the vertical surface of the melted materials. Therefore, for high-performance melting, it is necessary that the irradiated surface of the material forms a right angle with the optical axis of the furnace. However, in the case of powder materials, this is not possible. Therefore, blocks of a certain size are pressed from powder material. A “rotary” type furnace is convenient for melting compressed blocks.

In a “rotary” type furnace (Figure 5), the charge is cooked on the surface and during the melting process, the glass mass is clarified in the hot zone of the focal area. Frit is obtained from clarified glass for further ceramic processing. The “rotary” type furnace is quite simple and convenient for operation, and is currently the main BSF equipment for melting high-temperature materials. The ladle furnace is designed for experimental melting in small portions with constant stirring during the melting process in order to achieve homogeneity of the fused material and to avoid delamination of the melting products.

Figure 5.

General view of rotary smelting furnace, located at focus of the BSF.

This type allows you to overheat the liquid state and unload the melted mass once. There is a swing system that allows you to form a continuous flow of melt and adjust its speed. The materials of the procedure are melted in a ladle furnace mounted on a coordinate trolley, which manifests itself in the degree of freedom (Figure 6).

Figure 6.

A melting furnace of the “bucket” type.

The upper inner part of the furnace is used as a reflector of energy coming from the lower part of the concentrator. Such a device provides additional heating to the molten material and is maintained in a horizontal position. When the material is pumped in the liquid phase, it moves from one part of the furnace to the opposite through the focal spot. The oven allows you to cook the charge, lighten the glass mass. The control of the furnace by means of swings makes it possible to move the liquid phase during the melting process and achieve better clarification and homogenization. Passing through the focal spot, the material is constantly heated and mixed, thus achieving homogeneity of the fused material. Passing through the focal spot, the material is constantly heated and mixed, thus achieving homogeneity of the fused material.

Along with the advantages of high purity and homogeneity, preservation of stoichiometry, implementation of highly gradient conditions, the possibility of overheating the melt in the air and its subsequent cooling in a controlled mode seems promising. Such conditions make it possible to stabilize new phases, vary the phase composition, morphology of the target material, and as a consequence, its properties.

When the surface of the melted material is inserted as much as possible perpendicular to the flow of concentrated solar radiation, a high melting performance is observed. Consequently, the surface of the material irradiated by the concentrator must have the shape of a vertical wall and form a right angle with the optical axis of the solar furnace. In practice, it is not always possible to obtain a vertical wall due to the powder state of the material. To obtain a vertical wall, the powdered material is pressed into plates. Such materials are easy to melt in water-cooled “rotary” type melting furnaces. To ensure these conditions, a water-cooled “rotary” type furnace has been created.

In a “rotary” type furnace, the charge is cooked on the surface and in the process of draining in the hot zone of the focal spot, the glass mass is clarified. Frit is obtained from clarified glass for further ceramic processing. The “rotary” type furnace is quite simple and convenient to operate, currently it is the main BSF equipment for melting high-temperature materials. When synthesizing glasses, special attention should be paid, firstly, to the degree of overheating of the melt, and secondly, to its cooling rate. It is advisable to use ultrafast quenching methods that allow increasing the melt cooling rate to 10⁴ degrees/s.

The introduction of concentrated solar radiation from the concentrator to the target can also be varied with the help of special shutters and a screen made of metallic aluminum and cooled with water. In this case, it is possible to sequentially and/or simultaneously inject a concentrated stream onto the sample. Pyrometric measurements revealed that with gradual input of the flow, the heating rate was 1000 degrees/min, and with rapid input of the flow - 700÷ 1000 degrees/sec.

5. Features of high-temperature processes

In materials science there is a fundamental triad of obtaining materials with desired properties: “method of synthesis - morphology - properties”. It should be noted that materials with a favorable combination of different properties can easily be obtained by liquid state quenching. Materials obtained from the melt exhibit high values of mechanical and dielectric properties. Of course, such materials are widely used in various industries. As for melts, it should be noted that, unlike ordinary liquids, crystal-like groups, microcrystallites, are present in the structure of melts. The mutual arrangement of groups in the melt strongly affects the structure and properties of the resulting material. On the other hand, the quality of the melt is determined by the rate of heating of the substance to the melting temperature and above, as well as the rate of cooling of the melt.

The use of solar technologies makes it possible to increase the heating rate hundreds of times and obtain a structure from clusters of a certain composition, using the methods of fast (10³ degrees/s) and ultrafast (10⁴ degrees/c) tempering. Thus, the modeling of the processes of heating and cooling of materials in the flow of CSI is of both scientific and practical interest. Heating. The complete equation of the heating process will be written as

$$\frac{d{T}_s}{\mathit{dt}}=-\frac{\alpha }{\mathit{c\rho d}}\left(T_s-T_0\right)-\frac{\epsilon {\sigma }_0}{\mathit{c\rho d}}\left(T_s^4-T_0^4\right)+\frac{\left(1-R\right)}{\mathit{c\rho d}}E$$E1

where α is the proportionality coefficient, called the heat transfer coefficient, W/ (m² K); c is the specific heat capacity W/kgK; ρ is the density g/cm³; d is the layer thickness, m; T_s is the surface temperature of the body and T₀ is the ambient temperature, K; ε is the degree of blackness, σ₀ - Stefan-Boltzmann constant, E is the density of the flux of concentrated solar radiation in units (W/m²); R is the reflection coefficient of the heated material. The equation consists of three terms and the first term describes convective heat transfer, the second is related to heat losses due to thermal radiation, and the third is due to the absorption of solar radiation energy.

We can state that the process of heating a material in a field of concentrated solar radiation consists of three parts: heating a solid material to melting; the transition of a solid material into a liquid - melting, heating a liquid material. The boundary temperature values ​​can be determined from the equation:

$$\frac{d{T}_s}{\mathit{dt}}=0,\mathrm{at}{T}_s=T_m$$E2

Т_m is melting temperature.

The incoming heat Q is balanced with the melting heat Q_m, that is

$$Q-Q_m=Q-\mathit{\lambda m}=Q-\mathit{\text{λρSd}}=0$$E3

$$Q=\left[\left(1-R\right)E-\alpha \left(T_m-T_0\right)-\in {\sigma }_0\left(T_m^4-T_0^4\right)\right]S{t}_m$$E4

$$t_m=\frac{\mathit{\lambda \rho d}}{\left[\left(1-R\right)T_s-\alpha \left(T_m-T_0\right)-\beta \left(T_m^4-T_0^4\right)\right]}$$E5

where, λ is the specific heat of melting, J/kg; m is the mass of the material, kg; S is the surface area absorbing solar radiation, m2. The initial conditions for the studied materials (pyroxene rocks) were chosen as follows: c = 711 J/kgK, ρ = 3.2 g/cm³; α = 100 J/(m² K); d = 0.05 m; T0 = 320 K; E = 750 W/cm²; R = 0.15; Tm = 1660 K; λ = 4200 J/kg.

The calculation was carried out in the MATLAB program. Figure 7 shows the dependence of the temperature of a material sample on the time of exposure to a concentrated stream of solar radiation.

Figure 7.

The dependence of temperature on the time of exposure to a concentrated stream of solar radiation.

Figure 8 clearly demonstrates the process of heating the material and shows the non-monotonic nature of the temperature change over time in three sections. At the beginning, heating of the solid material is observed until it passes into the liquid state. The duration of the first section is 80 seconds and has a speed of 1385 deg./s.

Figure 8.

Melt cooling curves on a solar furnace by the “firecracker” method, with heat transfer coefficients a) 1-α = 500 J/(m² K), 2- α = 1000 J/(m² K). hk = 100mkm, v = 1 m/s. b) Heat transfer coefficient α = 10,000 J/(m² K), hk = 10mkm, v = 10 m/s.

It is known that as the temperature of the body rises, the rate of thermal motion and the amplitude of oscillations of its atoms should increase, which are forced to move away from each other over long distances, i.e. distant order disappears. And the destruction of the crystal lattice begins, i.e. the solid melts.

In the second section, melting is observed, which lasts about 100 seconds. At the end, an equilibrium state of the liquid is established. In the third section, the liquid material is heated. As can be seen from the curve, the maximum flux of incident solar radiation corresponds to heating saturation.

5.1 Cooling

It follows from the above that the cooling rate of the melt is the determining factor in the degree of amorphism of the quenched material. In turn, the cooling rate is determined by the conditions of heat transfer, the temperature of the melt, the material of the hardening system, etc.

There is such a value of the cooling rate Vc, which depends on the level of thermophysical parameters of the material and the nature of the interaction between particles and fluctuates over a wide range (from 10² deg./s for inorganic glasses and melts of certain metals to 10⁶–10⁸ deg./s for metals). High cooling rates are typical for small thicknesses of the cooled melt. In this work, the melts were cooled in three ways: - collapse of the melt according to the “hammer-anvil” principle between water-cooled rods (“clapperboard”), in which the melt is quenched at high speed; − pouring liquid drops into water; − cooling on the water-cooled surface of the substrate.

The amount of heat released through the surface of the body S per unit of time depends on the temperature difference between the surface of the body Ts and the environment T₀ (T_s > T₀):

$$\frac{\mathit{dQ}}{\mathit{dt}}=-\alpha \left(T_s-T_0\right)S$$E6

If we assume that the temperature distribution inside the droplet is uniform, as well as the heat input, we obtain

$$∆Q=\mathit{cm}∆T$$E7

Eq. (6) can be rewritten as:

$$\frac{d{T}_s}{\mathit{dt}}=-\frac{\mathrm{\alpha }}{\mathit{cm}}\left(T_s-T_0\right)S$$E8

where c and m are the specific heat and the mass of the droplet, respectively.

It should be noted that, as a result of melt compression, its contact surface changes with time; its shape changes from spherical to lamellar. This means that S in (8) is a function of time S = S(t).

Such a dependence can be revealed within the framework of the following boundary conditions. We assume that when compressed between two rods moving against each other with an average speed v, a spherical drop of volume V after time t gradually takes a disk-like shape (for example, due to the wetting effect) of radius R and height h, depending on time. So the volume V is preserved, and the height of the drop changes as h(t) = d-vt. This allows you to determine the area of ​​​​the end face of the disk S, as follows:

$$S\left(t\right)=\frac{\mathrm{V}}{h\left(t\right)}=\frac{V}{d-\mathit{vt}}$$E9

where d is the diameter of the ball.

Taking into account the fact that heat is transferred simultaneously from both ends of the disk, we can replace S with 2S, and from expressions (9) and (8) we can come to

$$\frac{d{T}_s}{\mathit{dt}}=\frac{\mathrm{\alpha }}{\mathit{cm}}\left(T_s-T_0\right)\frac{v}{d-\mathit{vt}}$$E10

To solve, we will need to find the following integral

$$I=\underset{0}{\overset{t}{\int }}\frac{\mathit{dt}}{d-\mathit{vt}}=-\frac{1}{v}ln\left(\frac{d-\mathit{vt}}{d}\right)$$E11

Thus, for the general solution of Eq. (10) we obtain

$$T_s=\left\{\begin{array}{l}{T}_0+\left(T_{s0}-T_0\right)e^{-\frac{2\mathit{\alpha V}}{\mathit{cmv}}ln\left(\frac{d}{d-\mathit{vt}}\right)}\mathrm{при}t\le t_0\\ T_0+\left(T_{s1}-T_0\right)e^{-\frac{2\mathit{\alpha Vt}}{\mathit{cm}{h}_k}}\mathrm{при}t>t_0\end{array}\right.$$E12

where

$$T_{s1}=T_0+\left(T_{s0}-T_0\right)e^{-\frac{2\mathit{\alpha V}}{\mathit{cmv}}ln\left(\frac{d}{h_k}\right)}$$E13

Where h_k is the final thickness of the disk and

$$t_0=\frac{d-h_k}{v}$$E14

The process of cooling by the “damper” method under the condition α = 500 J/(m2K) (curve 1), α = 1000 J/(m²K) (curve 2) has the character of a nonmonotonic decrease in time (Figure 8).

From Figure 9, it was revealed that when the melt is cooled by pouring it into water, the cooling rate is about 10³ K/s. While it follows from Figure 10 that the cooling of the melt on the surface of the water-cooled substrate proceeds at a rate of 20 K/s at d = 0.1, α = 1000 J/(m² K).

Figure 9.

The curve of melt cooling in a solar furnace by draining liquid droplets into water at α = 1000 W/(m² K).

Figure 10.

The cooling curve on the surface of a water-cooled furnace at d = 0.1, α = 1000 J/ (m² K).

The analysis of the curve in Figure 9 shows that the melt cooling rates in a solar furnace by draining liquid droplets into water are about 10³ K/s. Figure 10 shows the cooling curve of the material (melt) in a solar furnace by cooling on the surface of a water-cooled substrate at d = 0.1, α = 1000 J/(m² K). The analysis of the curve in Figure 11 shows that the melt cooling rate in a solar furnace by cooling on the surface of a water-cooled furnace is about 20 K/s. Thus, by choosing the melt cooling method, different cooling rates can be achieved: 10²; 10³ and 10⁴ K/s. For pyroxene melts at high cooling rates T > 10³ K/s, the condition of homogeneous nucleation and growth of crystalline grains is fulfilled. In this case, the grain size is determined by diffusion.

Figure 11.

Dependence of the particle size of the material on the quenching rate.

$$d\sim \mathit{\tau U}\sim C\left(\frac{∆T^3}{T_m^2}\right)exp\left(-\frac{E}{k{T}_{\mathit{cr}}}\right)$$E15

where τ is the average grain growth time corresponding to the crystallization time, s; U is the grain growth rate of microns/s; C is a value depending on the cooling rate, melting temperature and enthalpy, surface tension, specific volume of the solid phase and Debye frequency of microns; T_sg is the melt crystallization temperature, K; DT is the value supercooling (DT = T_m - T_cr), K; E is the effective activation energy of diffusion, eV.

Figure 11 shows the dependence of the grain size of the material on the quenching rate. It can be seen from Figure 11 that approximating this dependence to the maximum possible quenching rate makes it possible to determine the size of clusters in the liquid state of matter. To obtain a hardened material with nanosized particles, it is necessary to cool the melt at a rate above 10⁶ deg./s.

The processes of heating, melting and cooling of pyroxene rocks in a stream of concentrated high-density solar radiation are well described within the framework of a mathematical model, taking into account the initial conditions. The results of the calculations are in good agreement with the experimentally observed ones.

The strongest influence on the dispersion of the fused material is exerted by the rate of cooling of the melt, which can be carried out by three methods: arbitrarily on the surface of a water-cooled substrate; pouring into water (hardening); anvil - by the collapse of the melt with copper rods (superhardening). Thus, to obtain a fused material with nanosized particles, it is necessary to superharden the melt at a rate above 106 deg./s.

Thus, during the synthesis of materials under the influence of concentrated solar radiation, the melt can be overheated and cooled at different rates, which makes it possible to change and fix the states of a certain phase composition and microstructure, thereby regulating the properties of the resulting material.

Thus, the processes of heating, melting and cooling of materials (pyroxene rocks) on a large solar furnace were simulated.

The proposed mathematical model, taking into account real conditions, quite well describes the processes of heating, melting and cooling of pyroxene rocks in a stream of concentrated solar radiation. It turned out that the dispersion of the obtained material depends on the rate of cooling of the melt, which is set by the method of its implementation. For example, a nanomaterial can be obtained by cooling the melt at a rate above 10⁶ deg./s.