Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2021 number 3

Solutions of one-dimensional equations of gas dynamics and the equations describing the behavior of a nonlinear elastic material are reduced to solving a system of homogeneous differential equations written in Riemann invariants. It is shown that the solution of the Cauchy problem for such a system allowing for a differential constraint is reduced to solving a system of ordinary differential equations. Examples of solutions for certain initial data are given.

Complete group analysis of the system of one-dimensional unsteady equations of the dynamics of a vibrationally excited gas is performed in the case of cylindrical and spherical symmetry. It is shown that the admitted Lie algebra does not contain the scaling generator of independent variables that defines the well-known self-similar solutions of strong shock wave problems for the similar system of the gas dynamics equations of an ideal gas. A modification of the characteristic relaxation time is proposed, which makes it possible to extend the admitted Lie algebra of the system by the generator of simultaneous scaling of independent variables and introduce a class of self-similar solutions. Using the problem of a strong linear explosion as an example, it is shown that the solution of the modified system of equations is physically consistent and fairly accurately describes the well-known effect of the divergence of static and vibrational temperatures behind the wave front.

A review of results obtained in recent years by the authors in studying the stability of flows with separation of the laminar boundary layer under the condition of flow modulation in space and time is presented. These results provide an idea about the influence of periodic inhomogeneities of the separation region on the development of its hydrodynamic disturbances and the transition to the turbulent state near the body surface in a low-velocity air flow.

It is revealed that the local equilibrium approximation (algebraic parametrization of triple correlations of turbulent fluctuations of a vertical velocity component) in the problem of a plane momentumless turbulent wake is a differential constraint for a third-order closure model. The results of numerical experiments that confirm the feasibility of the used known algebraic parametrization of this third-order correlation moment are presented.

Implicit finite-volume predictor-corrector algorithms based on the splitting method are proposed for the numerical solution of the Navier-Stokes equations written in integral form for a compressible gas, and the properties of these algorithms are investigated. An economical algorithm for splitting equations into physical processes and spatial variables is considered. Numerical solutions of two-dimensional and spatial fluid dynamics problems are determined and compared with the known computational results. It can be concluded on the basis of the estimates obtained and calculations performed that the proposed algorithms are effective.

Mathematical methods are developed to describe helium sorption by microspheres with a certain dispersion distribution. An analytical solution of the problem is derived and applied to expand the experimental dependences of the degree of helium absorption by microspheres on time into harmonics. As a result, the time characteristics of the sorption process can be analyzed.

Results of numerical simulations of fracture of nanocrystals of the TiAl3 intermetallic compound by the molecular dynamics method are reported. The TiAl3 nanocrystals are subjected to uniaxial tension in a wide range of temperatures (300-1200 K). It is demonstrated that tension of nanocrystals of the TiAl3 intermetallic compound heated approximately up to 1000 K first leads to a phase transition from the crystalline to liquid state, followed by their fracture. Fracture of a heated TiAl3 nanowire is preceded by deformation in the superplasticity regime.

The influence of a quenching air jet on physical and chemical properties and morphology of titanium dioxide, silicon dioxide, and TiO2-SiO2 composite particles synthesized by the single-stage chloride method in a flow-type plasma-chemical reactor is studied. The results of the simulations and analysis of the specimens show that the physical and chemical properties of the powder and the morphology of its particles can be controlled. It is demonstrated that the results of mathematical simulations of the synthesis of TiO2 and SiO2 particles agree well with the experimental data obtained in the study.

The linear and nonlinear stability of two-layer Poiseuille flow in a horizontal channel is considered, and the stability of this flow is compared with the stability of the same flow in a vertical channel. In the first step, the Navier-Stokes equations in both phases are linearized, and the dynamics of periodic perturbations is determined by solving the spectral problem in a wide range of the Reynolds number of the liquid and the gas velocity. The neutral and fastest growing perturbations of the unstable mode are calculated. In the second step, nonlinear wave modes of Poiseuille flow in the horizontal channel are calculated using the full Navier-Stokes equations for both fluids.

The dynamics of death of cardiac muscle cells during the acute phase of myocardial infarction has been studied numerically. The problem is considered in the local and spatially distributed formulations. The adequacy of the mathematical model is confirmed by the quantitatively agreement between the results of numerical solution of the problem and experimental data. The adopted models were used to investigate the trigger mechanism of transition from a favorable scenario for the development of an acute myocardial infarction to a scenario characterized by a rapid increase in the level of myocardial damage on the third - fifth day of myocardial infarction. For these scenarios of the development of a myocardial infarction, the process of demarcation inflammation has been investigated. It has been shown that the results of studies, including evaluations of the effectiveness of cytokine anti-inflammatory therapeutic strategies are consistent with available data of laboratory studies.

Melting of a layer of ice with air bubbles exposed to an artificial thermal radiation source is studied by mathematical modeling within the framework of the one-phase Stefan problem. The radiative part of the problem of radiative-conductive heat transfer in the ice layer is solved numerically by a modified average flux method taking into account the volumetric absorption and scattering of radiation in the medium and the selectivity of the radiation. The anisotropic scattering of radiation by air bubbles is taken into account using a transport approximation. It is shown that the calculation results are in satisfactory agreement with experimental data.

Models of poroelasticity and discrete cracks serve as a basis for a numerical study of filtration in deformable fractured porous media. The influence of the stress-strain state of a medium on its filtration properties is considered. Oil displacement from fractured formations is investigated. It is shown that compressive stresses have a significant impact on the efficiency of oil displacement. Calculations are carried out for three versions of randomly developed systems of cracks with different degrees of coupling.

A computational and experimental analysis of the properties and fundamental features of a turbulent boundary layer on an elongated axisymmetric body of revolution under conditions of an incompressible flow around it at the Reynolds number Re_L = 4.33 x 10⁶ is carried out. It is shown that the experimental values of the local and integral parameters of the boundary layer on the body of revolution are in reasonable agreement with the results of a numerical calculation performed by solving the Reynolds-averaged Navier-Stokes equations using the low-Reynolds version of the k-w SST turbulence model. The data obtained indicate the need for careful contouring of the aft part of the body of revolution in order to minimize losses caused by the bottom drag of the aft end.

The propagation of a short compression pulse in heterogeneous targets containing ceramic inclusions of various sizes is studied numerically. The case of a heterogeneous material with inclusions of macroscopic size is considered. It is shown that during propagation in all targets, the initial shape of the shock pulse evolves to a shape corresponding to an elastic stress-strain state in which its amplitude and length do not depend on the distance traveled. It is found that for heterogeneous materials with large inclusions, the rate of decrease in pulse amplitude is greater than for heterogeneous materials with small inclusions.

Adaptation of a mathematical model of gas diffusion combustion for different flow rates of CO-H₂ and a constant coal flow rate is carried out. It is shown that the results of calculating the main characteristics of the flame are in satisfactory agreement with experimental data and can be used to determine the structure of pulverized coal-gas flow, gas composition, particle and gas temperature, carbon combustion efficiency, etc. The proposed model is suitable for analyzing the stability of coal-gas flame and the transient processes accompanying changes in the mode of supply of the fuel-oxidizer medium

This paper presents a study of the atomization and combustion of coal-water slurry fuel sprayed by a pneumatic nozzle based on the use of wall and cumulative jets and the Coanda effect. The droplet size distribution of coal-water fuel slurry at the nozzle outlet was measured by shadow photography. In the region of fuel ignition, the characteristic droplet size in the flow is 20 μm and the coal particle size is 100 μm. The results of experiments on an uncooled firing stand with an uncooled 5 MW furnace showed the possibility of efficient co-combustion of coal-water slurry fuel and pulverized coal using the developed burner.

A case of two-dimensional motion of thermal waters under the action of two wells comprising a spaced dipole is investigated on the basis of a reservoir model in the form of a heterogeneous structure consisting of disjoint continua, one of which is embedded into the other. Calculations are performed for specific physical parameters of the reservoir and active wells.

A method is proposed to improve the aerodynamic performance of small-sized flying vehicles. The method is based on fundamental gas-dynamic phenomena, such as local separation of the boundary layer accompanied by the formation of the so-called separation bubbles, separation of the turbulent boundary layer, and flow shedding from the leading edge of the airfoil, which alter the entire flow structure around the body. Publications where the relationship of these phenomena is established and those that describe a control method eliminating the adverse consequences of flow separation with the use of a wavy surface of the airfoil are reviewed. The method is simple in implementation and offers many prospects. The area of its applicability are determined, and criteria of optimizing the wavy surface of the airfoil for particular operation conditions are provided. Results of investigations are reported, which show that the use of a wavy surface of wings or blades of flying vehicles can improve their aerodynamic characteristics. Various structural elements of the boundary layer are noted, such as local separation bubbles or a general separation region, and criteria of their emergence are given, which assists in verification of numerical experiments.

The accuracy of numerical calculations of the dynamics of vortex filaments is estimated via the truncation method using the example of the motion of helical vortices. In the case of helical vortices with uniform vorticity distribution in Rankine core, there are two more analytical approaches to solving the problem. These approaches are used to determine the minimum admissible distance between vortex filaments or their elements to ensure the accuracy of calculations when using the truncation method. There is an established error that occurs in the calculations based on the truncation method in the case of convergence of the windings of a helical vortex.