# Volume 24 № 3 2022

**1. Sergey S. Makarov, Mikhail Yu. Alies**

**
Mathematical Model and Numerical Simulation of Conjugate Heat Transfer During Cooling of a High-Temperature Metal Body by a Gas-Liquid Medium Flow. **P. 287-295. Download

A mathematical model of conjugate heat transfer in a heterogeneous system "solid body - gas-liquid medium" is proposed, taking into account the description of vaporization in a liquid flow. The results of the numerical modeling of the heat transfer during cooling a metal cylinder by a gas-liquid medium flow in a vertical annular channel are presented. The results are obtained on the basis of the mathematical model of the conjugate heat transfer of the gas-liquid-medium flow and the metal cylinder in a two-dimensional nonstationary formulation taking into account the axisymmetry of the cooling medium flow relative to the longitudinal axis of the cylinder. To solve the system of differential equations the control volume approach is used. The flow field parameters are calculated by the SIMPLE algorithm. For the iterative solution of the systems of linear algebraic equations the Gauss-Seidel method with under-relaxation is used. The results of the numerical simulation are verified by comparing the results of the numerical simulation with the results of the field experiment. The calculation results for the heat exchange parameters at cooling the high-temperature metal cylinder by the gas-liquid flow are obtained taking into account evaporation. The values of the rate of cooling the cylinder by the laminar flow of the cooling medium are determined. New results of cylinder temperature variations depending on the proportion of air in the gas-liquid medium flow and the cooling rate field of the cylinder over time are obtained.

* Keywords*: mathematical model, numerical simulation, conjugate heat transfer, cooling, high-temperature body, gas-liquid medium, parametric analysis.

**DOI:**https://doi.org/10.15350/17270529.2022.3.23

**2. Dmitry S. Dudin, Ilya E. Keller**

** ****Review of Approaches to Formulating Coupled Equations of Interdiffusion in Viscoelastic Media.** P. 296-311. Download

The coupled systems of equilibrium and diffusion equations for viscoelastic media are analyzed in various reference frames that are used for studying processes in metal substitution alloys with the vacancy mechanism of diffusion. The reference frames are

classified into three groups according to the restrictions imposed on fluxes. The absence of the total diffusion flux describes the first group of the reference systems, which leads to the connection of the diffusion coefficients for the components. The second group is characterized by the sum of the spatial fluxes equal to zero. The second group is used for modeling diffusion processes without mechanical processes. In the last system there are no restrictions applied to the fluxes and the diffusion coefficients are independent. To formulate the models, the theory of mixtures is taken within the framework of the classical linear thermodynamics of irreversible processes and phenomenological description. The diffusion and mechanical process coupling is provided by the constitutive relations satisfying the thermodynamic inequality. The features of receiving the final local form of the thermodynamic inequality are considered when the Maxwell and Kelvin-Voigt viscoelastic models define a deformation behavior. Approaches are discussed for describing the separation of atomic processes into diffusion and deformation parts in the nonequilibrium vacancy flow when the material undergoes diffusion and mechanical deformations. Hypotheses allowing the identification of the diffusivities in a coupled equation system are considered depending on the method of motion separation. The relation between diffusion coefficients is determined that allows writing the balance equations in different reference frames. The reference frames are used for the experimental identification of the diffusion coefficients, construction of rheological relations or simplification of the equations. The formulations within the framework of the molecular incompressibility hypothesis are considered separately. It is shown that the Kelvin-Voigt model is inapplicable and the viscous rheological element in the Maxwell model is completely determined by the diffusion process in this case.

** Keywords**: interdiffusion, reference systems, viscoelasticity, coupled equations, Kirkendall effect.

**DOI: **https://doi.org/10.15350/17270529.2022.3.24

**3. Pavel V. Gulyaev, Andrey A. Shushkov**

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Technology for Creating Reference Marks on the Surface of Pyrolytic Graphite. **P. 312-318. Download

This paper considers the use of nanomarking for the probe positioning in scanning probe microscopy. A feature of the presented studies is that they are performed on a substrate of highly oriented pyrolytic graphite, which is widely used as a substrate for nanostructures. For marking, a Berkovich nanoindenter and a nanohardness tester Nanotest-600 were used. Preliminary studies have shown that when marking, some imprints may have reduced geometric dimensions. It is shown that local zones of increased and decreased hardness, comparable to the size of imprints, can be present on the surface of pyrographite. The detailed images of imprints obtained in different areas of the substrate are presented. It has been established that the appearance of prints with significant swelling of the material is possible. The loading-unloading characteristics in the zone with unstable imprints are constructed. The effect of swelling and delamination of the material on the loading-unloading characteristics and the depth of the imprint is described. It is shown that several loading-unloading cycles can improve the clarity of the imprint. Comparative studies of marking obtained by single and multiple indentation at each point were carried out. The profilometry of the indentations, performed on a scanning probe microscope, showed a large area and depth of the indentations obtained by multiple indentations.

** Keywords**: reference labels, scanning probe microscope, SPM imaging, nanoobjects, nanomarking, nanoindentation, NanoTest 600.

**DOI:**https://doi.org/10.15350/17270529.2022.3.25

**4. Artem A. Shaklein, Stanislav A. Trubachev, Gabriela Morar, Nikita A. Balobanov, Ekaterina A. Mitrukova**

**
Numerical Simulation of Solid Fuel Combustion. A review.** P. 319-331. Download

The combustion of solid fuel is presented in various fields and mainly aimed at the controlled transformation of the of chemical-bond energy into heat. Most of energy consumed by the world is generated by the burning of fossil fuels and almost 30 percent account for solid fuel. General mechanisms of the solid fuel combustion have already been revealed and described. However, in combustion theory there are still unresolved issues; e.g., there are no detailed kinetic mechanisms for the combustion of many combustible products of the thermal degradation of solid combustible materials. In addition, the detailed resolution of combustion chemistry still requires excessive computational resources to solve a stiff system of ordinary differential equations, which govern time-dependent conversion of all considered species. In practice, such drawbacks limit the possibility of effective solutions for the energy conversion to heat, reduction of pollutant formation and environmental pollution with exhaust gases. Progress in computational power and software design makes it possible to solve conservation equations for gas and solid state presented in two- and three-dimensional formulations. Such models allow to numerically predict detailed parameters of a combustion system: local (heat fluxes, flame temperature, gas flow velocity) and macroscopic (fuel-mass loss rate, amount of pollutants formed) data. The specific features of the up-to-date level of mathematical models employed to numerically predict solid fuel burning behavior are described in the present paper. The paper provides a review of studies carried out in the recent decade. The subject of the research is the coverage of numerous fields such as incineration of solid waste, burning of fossil fuels, solid propellant rocket engine, forest fire, flame spread over solid fuel, etc. The gas-phase combustion is shown to be resolved mainly by one-step reaction or several reactions. Yet, employing a detailed chemical mechanism provides adequate local heat release (reactions have different heat effect) and allows to consider elementary reactions and evaluate the concentrations of many species including pollutants. Thus, efforts should be addressed to the development of methods to reduce time cost for performing the calculations of equations of chemical kinetics such as the flamelet approach to numerical modeling of solid fuel combustion.

** Keywords**: combustion, chemical mechanism, solid fuel, numerical simulation.

**DOI: **https://doi.org/10.15350/17270529.2022.3.26

**5. Mikhail A. Korepanov, Rudolf R. Sharifullin**** **

**Simulation of Processes in a Diesel Heater with Indirect Heating. **P. 332-343. Download

The results of the mathematical modeling of the processes occurring in an indirect diesel heater are presented. The aim of the study was to develop technical solutions for optimizing and improving thermogasdynamic and thermal processes in the heater. It is proposed to make the flow sections of the three passes of the heat exchanger different in area, because when moving through the heat exchanger, the combustion products cool down; this leads to the increase of their density. In addition, the flow volume decreases and as a result, with equal flow sections, the flow rate of the combustion products decreases, and in the exit zone of their chamber, on the contrary, it becomes very large. The total angles of passage sections of the passages were selected equal to 160, 112 and 88 degrees. Such distribution of the flow sections of the gas ducts makes it possible to reduce the hydraulic resistance of the heat exchanger by 20 % by maintaining an approximately constant flow rate of the combustion products compared with a heat exchanger with equal flow sections of the gas ducts. The comparison of the results of the numerical simulation with the full-scale experiment shows good qualitative and quantitative agreement between the values of the controlled quantities such as velocity and temperature of gas flows.

** Keywords**: diesel heater, thermogasdynamics, combustion, temperature field, velocity field.

**DOI: **https://doi.org/10.15350/17270529.2022.3.27

**6. Artemii N. Beltiukov, Andrey I. Chukavin**

**Formation of Nanostructured Gold Coatings on Porous Alumina with Plasmon Response in the Visible Spectral Region.** P. 344-355. Dowload

In the present paper, the features of the formation of gold nanoparticles during vacuum thermal deposition on the surface of an anodic alumina membrane are studied depending on the parameters of its porous structure, the amount of deposited material, and annealing. The influence of the morphology of the obtained samples on their optical properties is discussed. Regularities have been established for the formation of gold nanoparticles during vacuum thermal deposition of gold films 10, 15 and 20 nm thick on the surface of an AOA membrane with the distances of 60 and 100 nm between the pore centers and pore diameters from 20 to 50 nm. Regardless of the diameter of pores and distance between them, the gold films have a fine-grained structure and one wide minimum in the transmission spectra. As a result of annealing at 400 °C, gold nanoparticles are formed, passing through the stages of film rupture into filamentous worm-shaped structures. Annealing can be stopped at one of the stages which may lead to the appearance of additional plasmon peaks in the spectra depending on the morphology of the gold structures . The frequency of the plasmon response in the visible and near infrared spectral regions can be controlled by selecting the appropriate thicknesses of gold coatings and thermal annealing conditions. Thus, the joint analysis of the results of scanning electron microscopy and VID-NIR spectroscopy showed that, depending on the morphology, the gold nanostructures demonstrate both one and two resonant peaks in the optical transmission spectra associated with the excitation of plasmons. The latter are of particular interest, since they can be used in two-mode surface plasmon resonance sensors with increased sensitivity and selectivity.

** Keywords**: gold nanoparticles, anodic alumina, plasmon resonance, scanning electron microscopy, absorption spectrophotometry.

**DOI: **https://doi.org/10.15350/17270529.2022.3.28

**7. Vladimir G. Lebedev, Sergey A. Korobeynikov, Mikhail G. Vasin, Vladimir I. Ladyanov **** **

**
Dynamics of the Linear Compounds Formation: Phase-Field Approach.** P. 356-369. Download

A phase-field model of the dissolution and growth of a phase of constant composition in contact with a phase of variable composition in a binary solution is proposed. Due to the lack of thermodynamically justified determination of the chemical potential for phases of constant composition (stoichiometry, or compounds), it is proposed to use the slope tangent of the straight line that connects the Gibbs energy values of the phase of variable composition and the stoichiometric phase as the chemical potential of stoichiometry, when the said phases are in contact , inside the diffuse boundary. The equations of the phase field obtained as a result of this choice describe qualitatively satisfactorily the processes of dissolution and growth of both compounds and phases of variable composition. The numerical simulation of an isothermal one-dimensional problem of directional solidification was used to verify the model. The simulation results show that in a certain range of initial impurity concentrations in the liquid, stoichiometry can grow at a constant rate. In this case, due to the one-dimensionality of the considered problem an additional bend appears in the phase field function. At the remaining values of the impurity concentration in the liquid, the boundary between the phases rapidly comes to phase equilibrium. With small driving forces in the system, there is the competition between diffusion and kinetic (front motion) processes. Its presence is manifested in long relaxation times during the transition to a stationary mode.

** Keywords**: phase field, microstructure, stoichiometry, nonequilibrium thermodynamics, fast solidification processes.

**DOI: **https://doi.org/10.15350/17270529.2022.3.29

**8. Elena B. Dolgusheva**

**
Temperature Dependence of Lattice Thermal Conductivity of Metastable Phases of FCC-Ti and -Zr.** P. 370-376. Download

The metastable phases of a material have other, possibly, anomalous properties compared to its stable structural state. The structural, elastic, and dynamic properties of metastable phases with a face-centered cubic lattice of transition metals titanium and zirconium with highly anharmonic interatomic interaction calculated earlier by the method of molecular dynamics with multiparticle potentials constructed in the embedded atom model, are in good agreement with previous theoretical calculations. It is shown that it is possible to use the method of nonequilibrium molecular dynamics to calculate the lattice thermal conductivity of metastable phases of transition metals. To calculate the thermal conductivity, the eHEX algorithm based on the method of nonequilibrium molecular dynamics, built into the LAMMPS package is used. Earlier the test calculations of the lattice thermal conductivity for the aluminum crystallites with a cross section of 5×5 nm and lengths of 20 and 40 nm have shown that this approach gives the values of the lattice thermal conductivity coefficient consistent with the results of the first-principles calculations obtained by the density-functional theory, taking into account only the phonon-phonon interaction. With a decrease in the size of the basic crystallite, the thermal conductivity coefficient decreases; this is due to the depletion of the low-frequency region of the phonon spectrum the contribution of which to thermal conductivity becomes insignificant with an increase in temperature. At high temperatures, the thermal conductivity coefficient does not depend on the size of the crystallites and coincides with the coefficient obtained by the first-principles calculations. Applying the same approach, and taking into account only the linear region of the temperature distribution along the direction of heat flow propagation, the curves of the temperature dependence of the lattice thermal conductivity coefficients of the metastable cubic face-centered structural phases of titanium and zirconium are obtained for the crystallites with cross section of 12×12, and lengths of 48 and 96 unit cells. Knowledge of the temperature behavior of the phonon thermal conductivity of these important structural metals can be useful when creating devices whit a metal/metal or metal/semiconductor interface.

* Keywords*: non-equilibrium molecular dynamics method, lattice thermal conductivity, metastable phases.

**DOI: **https://doi.org/10.15350/17270529.2022.3.30

**9. Svetlana G. Menshikova **** **

**
Viscosity and Solidification of the Al**_{100-}_{х}**Cu**_{х}** (х=5, 10, 17, 25 at.%) Melts.** P. 377-387. Download

The method of damped torsional vibrations was used to study the temperature dependences of the viscosity of melts of the Al-Cu binary system containing 5, 10 (hypoeutectic); 17 (eutectic) and 25 (hypereutectic) at.% of copper. For all compositions near a temperature of 800 °C, a deviation of the viscosity polytherms from the Arrhenius dependence was found, which was associated with the features of the structural state of the melts. The samples were obtained by melt spinning; the comparative study of the samples was performed using X-ray diffraction analysis and electron microscopy taking into account the quenching temperature (750 and 1200 °C) and alloy composition. In a hypoeutectic alloy with a higher copper content, regardless of the melt quenching temperature, a more supersaturated Al(Cu) solid solution is formed. The temperature treatment of the melts before quenching affects the structure and mechanical characteristics of the solid samples formed during spinning. All samples are crystalline and represented by α-Al and Al_{2}Cu phases. The effect of the melt heat treatment on the morphology, size and lattice periods of the structural constituents of the alloys of all compositions is shown. The selected heat-treatment modes are reflected in the average value of the microhardness of the alloys. The hypoeutectic alloys with a higher copper content have higher microhardness values due to a more dispersed structure, a larger volume fraction of finely dispersed eutectics, and a more supersaturated Al(Cu) solid solution. In the hypoeutectic alloys, higher microhardness values are in the alloys with a higher concentration due to a larger amount of the hard component - Al_{2}Cu aluminides.

** Keywords**: melt viscosity, concentration, ultrafast quenching, solidification, microstructure, melt spinning.

**DOI: **https://doi.org/10.15350/17270529.2022.3.31

**10. Anastasia S. Tugbaeva, Alexander G. Itskov, Vladimir N. Milich, Vladimir A. Shirokov**

**
Distinguishing Underwater Objects Based on Periodogram Analysis of Reflected Sonar Signals. **P. 388-399. Download

In the present article a method is proposed for solving the actual scientific and applied problem related to the echolocation of underwater objects in order to detect, coordinate and recognize them. Hydroacoustic signals are the main tool used to study the underwater environment. Due to the phenomena of refraction, multipath and multipath effects, hydroacoustic signals reflected from underwater objects are subject to significant variability. Therefore, for using hydroacoustic echolocation signals to obtain information about underwater objects, it is essential to search for distinguishing features that are resistant to the above-listed factors of variability. It is proposed to use the methods of periodogram analysis for the analysis of reflected hydroacoustic signals. The use of algorithms based on the Fourier transform and the classical Buy-Ballo scheme are considered. These classical algorithms for searching for hidden periodicities are usually used in the analysis of time series and can also be effectively used to analyze reflected hydroacoustic signals. As acting signals, a sinusoidal signal with constant amplitude, a sinusoidal signal with amplitude varying according to the normal law, and a sinusoidal signal modulated by the Barker code were studied. The features of the analysis of reflected signals are discussed from the point of view of distinguishing features. It has been established that such features can be the characteristic of the periodograms obtained by the Fourier and Buy-Ballo algorithms. The studied set of distinguishing features includes the duration of the useful signal, and the minimum and maximum values of the signal amplitudes. The experimental study of three types of underwater objects carried out in the experimental basin of the Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences confirms that periodogram analysis for distinguishing underwater objects by reflected hydroacoustic signals is very promising. The features of creating a convenient interface for signal processing, extracting properties and distinguishing between test objects are also described.

** Keywords**: hydroacoustics, underwater objects, recognition, hydroacoustic signal, periodogram.

**DOI:**https://doi.org/10.15350/17270529.2022.3.32

**11. Nikolai M. Barbin, Marina A. Shumilova, Oleg Y. Goncharov**

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Thermodynamic Modeling of High-temperature Behavior of Sodium and Potassium Arsenites. **P. 400-407. Download

The widespread use of inorganic arsenic compounds in various branches of industry requires the study of their physicochemical properties, including thermal processes with their participation. During the calculations, the systems of sodium arsenite, potassium arsenite, sodium arsenite with the addition of sodium fluoride, and potassium arsenite with the addition of potassium fluoride were considered. The pyrolysis of arsenites upon heating to temperatures of 1900 K in an argon atmosphere was analyzed by thermodynamic modeling. It has been established that sodium and potassium arsenites, being stable compounds, undergo pyrolysis upon heating to 1900 K with the formation of a melt (solid solution). With increasing temperature, the composition of the melt is averaged over the anions AsO_{3}^{3-} and AsO_{4}^{3-} regardless of whether the arsenites or arsenates of alkali metals have been initially taken. In the pyrolysis of all the studied systems up to 1000-1500 K, the main component of the gas phase is As_{4}O_{6}. At higher temperatures, a set of compounds AsO, AsO_{2}, As_{4}O_{6}, Na, NaO (KO), Na_{2}O (K_{2}O), O, O_{2} is formed in the gas phase. When fluorides are added in all systems in the gas phase above 1000 K, NaF (KF) vapors are formed, which does not significantly affect the content of other components in the gas phase. The thermal stability of all the studied systems is characterized by similar values and decreases with increasing temperature. At temperatures above 1600 K, the stability of the K_{3}AsO_{3} system is higher than that of the other systems.

** Keywords**: sodium arsenites, potassium arsenites, sodium fluorides, potassium fluorides, thermodynamic modeling.

**DOI:**https://doi.org/10.15350/17270529.2022.3.33