Rubric: "2.5.12. Aerodynamics and heat transfer processes of aircraft (technical sciences)"
Timofeev V. N. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2021-4-80102
In the aspect of improving the methodology of mathematical modeling of subsonic detachable flow around elongated bodies with partial implementation of the concept of viscosity-inviolable interaction, the issues of organizing the iterative process of constructing the surface of an equivalent body are considered. A flow diagram with a semi-infinite equivalent surface was used. Numerical modeling was carried out according to the algorithms of the technique using the method of discrete vortices. For greater versatility, when constructing a calculated grid on the surface of an equivalent body, approximation with smoothing cubic splines was used. Data on the influence of the shape of the tail section of the equivalent surface on the distribution of speed and pressure during axisymmetric flow around bodies with a bottom section are presented.
Тимофеев В.Н. Методика организации итерационного процесса при моделировании дозвукового отрывного обтекания удлиненных тел с применением эквивалентной поверхности и кубических сплайнов. Математическое моделирование и численные методы, 2021, № 4, с. 80–102.
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.
Khayitkulov B. K. (National University of Uzbekistan)
doi: 10.18698/2309-3684-2024-1-5566
This work is devoted to the numerical solution of the non-stationary problem of optimal placement of heat sources of minimum power. The statement of the problem requires the simultaneous fulfillment of two conditions. The first condition is to ensure that the temperature is within the limits of minimum and maximum temperatures due to the optimal placement of heat sources with a minimum power in the rectangle. The second condition is that the total power of the heat sources used for heating is minimal. This problem was studied under stationary conditions in the works of other scientists. However, the problem was not considered in the non-stationary case. Since it is difficult to find a continuous solution to the boundary value problem, we are looking for a numerical solution to the problem. It is difficult to find an integral operator with a continuous kernel (Green's function). We find the numerical value of the Green's function in the form of a matrix. A new algorithm for the numerical solution of a non-stationary optimal control problem for the placement of heat sources with a minimum power in processes described by parabolic partial differential equations is proposed. A new technique for numerical solution is proposed. A mathematical and numerical model of the processes described by the heat conduction equation with constant coefficients given for the first boundary value problem is constructed. The boundary value problem is studied for the two-dimensional case. An implicit finite difference scheme was used to solve the problem numerically. According to this scheme, a system of difference equations was created. The formed system of difference equations is reduced to a linear programming problem. The problem of linear programming is solved using the M-method. For each time value, a linear programming problem is solved. A new approach to the numerical solution of problems is proposed. A general block diagram of the algorithm for solving the non-stationary problem of optimal control of the placement of heat sources with a minimum power is given. An algorithm and software for the numerical solution of the problem have been developed. A brief description of the software is given. On specific examples, it is shown that the numerical solution of the boundary value problem is within the specified limits, the sum of optimally placed heat sources with a minimum power gives a minimum to the functional. The results of the computational experiment are visualized.
Хайиткулов Б. Х. Численное моделирование нестационарной задачи оптимального размещения источников тепла минимальной мощности в однородной среде. Математическое моделирование и численные методы, 2024, № 1, с. 55–66.
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.
Mozzhorina T. Y. (Bauman Moscow State Technical University), Zakurazhnaya A. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-8599
In this paper, optimization of the control of the flight of a small spacecraft (spacecraft) on ion engines to the orbit of Venus is considered, taking into account the attraction of the Earth and the time of departure from the geostationary orbit. When solving the problem, the following assumptions were made: the orbits of the planets are circular, lying in the same plane. A detailed consideration of the influence of Venus when approaching the orbit of the planet was not considered. The problem is solved using the Pontryagin maximum principle by numerical targeting method. The spacecraft motion simulation was divided into 3 stages: acceleration of the spacecraft to a speed that allows overcoming the Earth's attraction with the help of short-term operation of the jet engine, optimization of control near the Earth at a distance of the spacecraft to the Earth of no more than 950 000 km and for the main interorbital flight between planets. The algorithm for solving the problem is implemented in the C++ programming language. Optimal control of the angle of action of the thrust vector is obtained. The analysis of the obtained results showed that, while minimizing the time to reach the orbit of Venus, in addition to significantly influencing the efficiency criterion of the longest interorbital section of the flight, the moment of the start (departure from Earth orbit) is fundamentally important.
Мозжорина Т.Ю., Закуражная А.А. Моделирование влияния времени схода с орбиты Земли на оптимальное управление перелетом малоразмерного КА на Венеру. Математическое моделирование и численные методы, 2024, № 2, с. 88–99.
Kreerenko S. S. (PJSC Beriev Aircraft Company), Kreerenko O. D. (PJSC Beriev Aircraft Company)
doi: 10.18698/2309-3684-2024-3-8199
The problem of modeling the longitudinal motion of a transport category aircraft and the parametric identification of the aerodynamic characteristics of the longitudinal motion: the components of the dimensionless coefficients of aerodynamic lift and pitching moment are considered. The problem is solved in a class of modular semiempirical dynamic models created by combining theoretical and neural network modeling. The performance and practical significance of the models is confirmed by the results of computational experiments. The development of a neural network model of the longitudinal movement of an aircraft was carried out in Python using the Tensorflow open software library for machine learning and the high-level Keras API as part of Tensorflow.
Крееренко С.С., Крееренко О.Д. Моделирование и параметрическая идентификация аэродинамических характеристик самолета транспортной категории с использованием нейросетей в среде Тensorflow. Математическое моделирование и численные методы, 2024, № 3, с. 81–99.