Rubric: "1.1.9. Mechanics of liquid, gas and plasma (technical sciences)"
Aksenov A. G. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2023-4-314
A countercurrent vortex of a gas centrifuge is simulated. The mathematical model of the motion of a viscous heat-conducting gas includes an equation for density, velocities and specific energy in cylindrical geometry. After the introduction of the grid, the partial derivatives over the space are replaced by finite differences, and the problem is reduced to a system of ordinary differential equations (ODES). This technique is called the Lines Method. Since the flow is supersonic, and the design area includes thin boundary layers, the ODE system is stiff due to the presence of different-time scales and a decay. In the language of mathematics, this means a significant difference between the eigenvalues of the Jacobi matrix and the negative real parts. Therefore, to solve the problem, it is useful to use the implicit Geer method for the ODE system without splitting the problem into physical processes and directions. An effective method for solving the Jacobin matrix inversion is the use of the cyclic reduction method in the matrix variant. As an example, the countercurrent flow arising due to the temperature gradient is demonstrated.
Аксенов А.Г. Двумерная модель и метод расчета противотока во вращающемся вязком теплопроводном газе. Математическое моделирование и численные методы, 2023, № 4, с. 3–14.
Lopato A. I. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2023-4-1526
The work is devoted to numerical studies of detonation initiation in a gas mixture in a rectangular channel with a profiled end. Detonation is initiated as a result of the interaction of shock waves which are formed as a result of the reflection of an incident shock wave of relatively low intensity from the end of the channel. The mathematical model includes the system of gas dynamics equations supplemented by Arrhenius kinetics for a model hydrogen-oxygen mixture with tabular kinetic parameters corresponding to the operating range of pressures and temperatures of the mixture. Numerical calculations are carried out using the finite volume method. The construction of computational grids consisting of triangular cells is carried out using the free software SALOME. The numerical algorithm is parallelized by the computational domain decomposition method using the METIS library. The exchange of grid functions between computational cores is carried out using the functions of the MPI library. The problem of acceleration of the parallel algorithm realized in the code is considered in comparison with the case of the linear dependence of the number of computational cores. A number of calculations were carried out using a different number of triangular cells and a comparison of patterns of detonation initiation was carried out. The performed calculations show that the detonation initiation time is approximately the same in all computations. The main difference in detonation patterns is associated with gas flow and Physical and chemical reactions in the mixture.
Лопато А.И. Математическое моделирование инициирования детонации в канале с профилированным торцом с использованием параллельных вычислений. Математическое моделирование и численные методы, 2023, № 4, с. 15–26
533.6.011.5:533.6.011.72:519.6 Numerical simulation of hysteresis around a flat nozzle
Maksimov F. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2023-4-2746
The results of numerical simulation of two-dimensional plane laminar flows near two inclined plates forming a constricting nozzle along the velocity vector of an incoming supersonic perfect gas flow are presented. A multi-block computational technology is applied with the use of local curvilinear grids adapted to the surface of bodies, which have finite areas of overlap with a global rectangular grid for the entire computational domain. Viscous boundary layers are resolved on local grids using the Navier-Stokes equations, and the effects of aerodynamic interference of accompanying shock-wave structures are described in terms of the Euler equations. In areas of grid overlap, function interpolation is applied up to the boundaries of the transition from one grid to another. With a successive increase or decrease in the Mach number of the oncoming supersonic flow, a qualitative rearrangement of the flow structure near the nozzle is detected - either a detached shock wave and a subsonic flow zone in front of the nozzle, or oblique shocks near inclined plates are formed. A hysteresis is revealed, which is expressed in the fact that in a certain range of Mach numbers, the flow structure and the aerodynamic load on the nozzle depend not only on the value, but also on the prehistory of the change in the Mach number. The possibility of changing the flow structure by introducing a density inhomogeneity into the oncoming flow is shown.
Максимов Ф.А. Численное моделирование гистерезиса при обтекании плоского сопла. Математическое моделирование и численные методы, 2023, № 4,с. 27–46.
550.388.2 Mathematical modeling of the impact of radio waves on the lower ionosphere
Stupitskij E. L. (Institute for Computer Aided Design of the Russian Academy of Sciences), Moiseeva D. S. (Institute for Computer Aided Design of the Russian Academy of Sciences), Motorin A. A. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2024-1-6792
The paper presents numerical studies of the parameters of the lower ionosphere when heated by high-frequency radio waves of various frequencies and powers. The main attention is paid to the interrelation between the energy and kinetic parameters of the disturbed D-region of the ionosphere in the processes that determine the absorption and transformation of the radio beam energy flux in space and time. The possibility of a significant difference in the behavior of the parameters of the disturbed region in the daytime and at nighttime, both in magnitude and in space-time distribution, is shown. In the absence of sufficiently reliable values of the rate constants for a number of important kinetic processes, numerical studies were carried out in stages with the gradual addition of individual processes and kinetic blocks corresponding at the same time to a certain physical content. It is shown that the energy thresholds for inelastic collisions of electrons with air molecules are the main ones. This approach made it possible to detect the effect of the emergence of a self-oscillating mode of changing parameters if the main channel for energy losses in inelastic processes is the most energy-intensive process – ionization. This effect may play a role in plasma studies using high-frequency inductive and capacitive discharges. The results of calculations of the ionization and optical parameters of the disturbed D-region for daytime conditions are presented. The electron temperature, density, emission coefficients in the visible and infrared ranges of the spectrum are obtained for various values of the power of the radio beam and its frequency in the lower ionosphere. The influence on the electron temperature and on the general behavior of the parameters of energy losses by electrons on the excitation of vibrational and metastable states of molecules has been studied in detail. It is shown that under nighttime conditions, when the electron concentration begins at altitudes of about 80 km, and the concentration of heavy particles decreases by two orders of magnitude compared to the average D-region, large-scale gas-dynamic motion can develop with sufficient radio emission power The algorithm was developed based on the McCormack method and two-dimensional gas-dynamic calculations of the behavior of the parameters of the perturbed region were performed with some simplifications of the kinetics.
Ступицкий Е.Л., Моисеева Д.С., Моторин А.А. Математическое моделирование воздействия радиоизлучения на нижнюю ионосферу. Математическое моделирование и численные методы, 2024, № 1, с. 67–92.
Lopato A. I. (Institute for Computer Aided Design of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2024-3-6580
The work is dedicated to the numerical study of pulsating gaseous detonation wave propagation. The mathematical model is based on the Euler equations written for the multicomponent gas and supplemented by the detailed chemical reactions model of Petersen and Hanson. to describe the combustion of the hydrogen–air mixture. This kinetics model is effective and efficient in describing processes in hydrogen-air and hydrogen-oxygen mixtures. The numerical algorithm is based on the finite volume approach, essentially non-oscillatory scheme, AUSM numerical flux and the Runge–Kutta method for time integration. Direct initiation of detonation at the closed end of a channel filled with a stoichiometric hydrogen-air mixture is considered. Mathematical modeling of the propagation of a pulsating detonation wave was carried out. The peculiarities of high-frequency and high-amplitude pulsations modes are discussed.
Лопато А.И. Математическое моделирование распространения пульсирующей волны газовой детонации в водородно-воздушной смеси с использованием детальной кинетики химических реакций. Математическое моделирование и численные методы, 2024, № 3, с. 65–80.