The possibilities of organizing a repetitively pulsed process with given frequency characteristics in a cavity of constant volume with an external energy supply to the working gas mixture are considered. Modelling of gas-dynamic and thermal processes is carried out using the numerical solution of the conjugate heat transfer problem. The gas medium is described on the basis of a viscous compressible gas model. To find the temperature field in the walls of the structure, the equation of non-stationary heat conduction is solved. The conjugation of temperature fields in a gas and a solid is carried out using an iterative procedure. In the calculations, the geometrical parameters of the cavity, the density of the energy supply, the initial pressure, and the composition of the working mixture are varied. The results of calculations obtained in the framework of the one-dimensional and two-dimensional formulation of the problem under the action of both a single pulse and a series of pulses are compared. The results obtained demonstrate the possibility of implementing the required frequency characteristics of the process for given geometric and energy parameters. Keywords: pulse-periodical energy process, gas laser, coupled heat transfer, numerical simulation, energy supply, pulse.

Heating of oil and oil products is widely used to reduce energy loss during transportation. An approach is being developed to determine the effective length of the heat exchanger and the temperature of the cold heat carrier at its outlet in the case of a strong dependence of oil viscosity on temperature. The oil of the Uzen field (Kazakhstan) is considered as a heated heat carrier, and water is considered as a heating component. The method of the average-logarithmic temperature difference, modified for the case of variable viscosity, and methods of computational fluid dynamics are used for calculations. The results of numerical calculations are compared with the data obtained on the basis of a theoretical approach at constant viscosity. When using a theoretical approach with constant or variable viscosity, the heat transfer coefficients to cold and hot heat carriers are found using criterion dependencies. In the case of variable oil viscosity, the transition of the laminar flow regime to the turbulent one is manifested, which has a significant effect on the effective length of the heat exchanger. To solve this problem comprehensively, a mathematical model of hydrodynamics and heat transfer of heat carriers has been developed and multiparametric numerical calculations have been performed using the "Ansys Fluent" software package.

The possibilities of organizing a repetitively pulsed process with given frequency characteristics in a cavity of constant volume with an external energy supply to the working gas mixture are considered. Modelling of gas-dynamic and thermal processes is carried out using the numerical solution of the conjugate heat transfer problem. The gas medium is described on the basis of a viscous compressible gas model. To find the temperature field in the walls of the structure, the equation of non-stationary heat conduction is solved. The conjugation of temperature fields in a gas and a solid is carried out using an iterative procedure. In the calculations, the geometrical parameters of the cavity, the density of the energy supply, the initial pressure, and the composition of the working mixture are varied. The results of calculations obtained in the framework of the one-dimensional and two-dimensional formulation of the problem under the action of both a single pulse and a series of pulses are compared. The results obtained demonstrate the possibility of implementing the required frequency characteristics of the process for given geometric and energy parameters.

A simulation of the vibroacoustic processes proceeding in a long pipe with an obstacle in the form of a circular cylinder, in which a fluidflows, has been performed with regard for the action of the vortices formed downstream of the cylinder on the dynamics of the system. On the basis of the computational procedure developed, the vibroacoustic characteristics of the system have been determined. The distributions of the gasdynamic parameters of the fluid flow in the pipe and the vibroacoustic behavior of the system are discussed.

Высокотемпературные эффекты оказывают существенное влияние на характеристики летательных аппаратов, движущихся с гиперзвуковой скоростью. В связи со сложностью постановки физического эксперимента, методы математического моделирования играют важную роль для нахождения характеристик гиперзвуковых летательных аппаратов. Обсуждается построение и реализация математической модели, предназначенной для численного моделирования гиперзвукового обтекания тела с учетом неравновесных физико-химических процессов в высокотемпературном воздухе. Математическая модель включает в себя уравнения газовой динамики, уравнения модели турбулентности и уравнения химической кинетики. Проводится численное моделирование сверх- и гиперзвукового обтекания полусферы потоком воздуха с учетом высокотемпературных эффектов. Приводится критический обзор различных моделей, которые применяются для нахождения расстояния от фронта ударной волны до поверхности сферы. Результаты расчетов, полученные с использованием разработанного численного метода, сравниваются с данными физического эксперимента и расчетными данными, имеющимися в литературе, в широком диапазоне чисел Маха набегающего потока. Разработанная модель и результаты расчетов имеют значение для моделирования обтекания тел сложной конфигурации и проектирования высокоскоростных летательных аппаратов. High-temperature effects have a significant impact on the characteristics of aircraft moving at hypersonic speed. Due to the complexity of setting up a physical experiment, mathematical modelling plays an important role in finding the characteristics of hypersonic aircraft. The construction and implementation of a mathematical model for the numerical simulation of a hypersonic flow around a semi-sphere is discussed, taking into account non-equilibrium physical and chemical processes in high-temperature air. The mathematical model includes the equations of gas dynamics, the equations of the turbulence model and the equations of chemical kinetics. Numerical simulation of supersonic and hypersonic air flow around a hemi-sphere is carried out, taking into account high-temperature effects. A critical review of various models that are used to find the shock stand-off is given. The results of calculations obtained using the developed numerical method are compared with the data of a physical experiment and the computational data available in the literature in a wide range of Mach numbers. The developed model and computational results are important for simulation of flows around bodies of complex configuration and designing high-speed aircraft.

The inuence of non-equilibrium kinetic processes on macroscopic parameters in air flows is a challenging and an important problem. Particularly, simulation of flows with high-temperature effects is important near the surface of spacecraft or meteorites when they enter the Earth’s atmosphere. Non-equilibrium flows of a reacting five-component air mixture consisting of N2, O2, NO, N, O behind a shock wave at different altitudes in the Earth’s atmosphere and different speeds of the inlet flow are investigated. The lengths of the relaxation zones are considered to evaluate the applicability of one-temperature thermodynamics model for calculating the macroscopic fluid quantities behind the shock wave. The results of the flow simulation are obtained with in-house code developed for super-and hypersonic applications. The results from the code are compared with the results of numerical calculations computed with the equilibrium thermodynamics model

The development of a supersonic gas flow over a wedge in the process of interaction of a plane shock wave with the wedge was mathematically simulated on the basis of solution of the Euler equations for the nonstationary flow of a compressible inviscid gas in a two-dimensional space with regard for the high-temperature effects of ionization and dissociation of the gas arising in the gas flow due to the balanced chemical reactions proceeding in it. The results of solution of the problem on the supersonic gas flow over a wedge within the framework of the perfect-gas and real-gas models were compared. The influence of the high-temperature effects in this flow on its characteristics and the angle of inclination of a shock wave in it to the wedge was investigated.

The generation of noise by the flow of a compressible viscous gas over a circular cylinder as a result of the formation of vortices in it and the separation of them from the surface of the cylinder was considered. The sound field of this flow was calculated using the method of simulation of large vortices, and its acoustic characteristics were determined using the method of acoustic analogy based on the solution of the Ffowcs Williams–Hawkings equation. On the basis of the direct numerical simulation data on the indicated flow, its regimes at diff erent Reynolds numbers were investigated. The results of calculation of the acoustic characteristics of this flow within the framework of the two- and three-dimensional approaches to the solution of the Ffowcs Williams–Hawkings equation were compared. A good agreement has been obtained between the calculated gasdynamic and acoustic characteristics of a gas flow over a circular cylinder and the corresponding experimental and calculation data available in the literature.

The article is devoted to the study of the hydrodynamics of heat carriers in heat exchangers. Giventhe widespread use of this device, increasing its thermal and hydraulic characteristics has become so important for theirdesigners. In the work, the calculation of non-stationary flows of liquids through the heat exchanger tubes is carried out.Water ("hot" coolant) and oil ("cold" coolant) are used as heat carriers, between which heat exchange occurs through thesolid surface of the pipeline, which is the boundary between the heat carriers. When calculating the movement of oil, thefact was taken into account that the dynamic viscosity depends very much on temperature and, depending on temperature,the Reynolds numbers also change. And, as a consequence, when flowing through a sufficiently thin channel, the flow regimechanges, namely, the transition from the laminar flow regime to the turbulent one is manifested, while this effect is notobserved with the analytical calculation method for constant viscosity. The Reynolds-averaged Navier-Stokes equations,closed using the turbulence model, were used for numerical modeling of fluid dynamics of heat carriers. Verification of theheat exchanger calculations was carried out in the software package "Ansys Fluent".

Possibilities for using general-purpose graphics processing units to simulate compressible gas flows are discussed. Consideration is given to different schemes of computation of flows through the faces of the flow control volume and to the features of their implementation on graphics processing units. A solution of a number of model problems of gas dynamics on graphics processing units is presented and consideration is given to approaches to optimization of the program code connected with the use of different types of memory. A comparison is made between the rates of counting on a graphics processing unit and a central processor using grids having different resolution capabilities and various difference schemes of computation of flows.

Проводится численное моделирование обтекания гиперзвукового летательного аппарата с использованием модели высокотемпературного воздуха и гибридной архитектуры на основе высокопроизводительных графических процессорных устройств. Расчеты проводятся на основе уравнений Эйлера, для дискретизации которых применяется метод конечных объемов на неструктурированных сетках. Приводятся результаты исследования эффективности расчета гиперзвуковых течений газа на графических процессорах. Обсуждается время счета, достигнутое при использовании моделей совершенного и реального газа. Numerical simulation of the flow around a hypersonic aircraft is carried out using a high-temperature air model and a hybrid architecture based on high-performance graphics processing units. The calculations are performed with the Euler equations discretized by the finite volume method on unstructured meshes. The scalability of the developed implementations of the model is studied and the results of the study of the efficiency of calculating hypersonic gas flows on graphics processors are analyzed. The computational time spent with the perfect and real gas models is discussed.

The atmospheric composition behind a normal shock ahead of a hypersonic vehicle differs from the atmosphere ahead of the shock. Various models of air equilibrium composition are compared, analysis of areas of these models applicability is performed. Numerical simulations of flow in a channel with a step are performed using models of perfect gas and high-temperature air. The results computed with both models are compared.

В рамках статистического подхода, основанного на кинетическом уравнении для функции плотности вероятности распределения скорости и температуры частиц, построена континуальная модель, описывающая псевдотурбулентные течения дисперсной фазы. Введение функции плотности вероятности позволяет получить статистическое описание ансамбля частиц вместо динамического описания отдельных частиц на основе уравнений движения и теплопереноса типа Ланжевена. На основе уравнений для первых и вторых моментов дисперсной фазы проводится численное моделирование нестационарного течения газовзвеси, возникающего при взаимодействии ударной волны с облаком частиц. Основные уравнения имеют гиперболический тип, записываются в консервативной форме и решаются с использованием численного метода типа Годунова повышенного порядка точности. Обсуждается влияние двумерных эффектов на формирование ударно-волновой структуры течения и пространственно-временн´ые зависимости концентрации частиц и других параметров потока. A statistical approach based on the kinetic equation for the probability density function of the distribution of particle velocity and temperature is used to develop a continuum model describing pseudoturbulent flows of the dispersed phase. The introduction of the probability density function allows one to obtain a statistical description of an ensemble of particles instead of a dynamic description of individual particles based on Langevin equations of motion and heat transfer. The equations for the first and second moments of the dispersed phase are derived and the numerical simulation of the unsteady gas–particle flow arising due to the interaction of a shock wave with a cloud of particles is performed. The governing equations are of the hyperbolic type and are written in a conservative form. They are solved by a Godunov numerical method of high order of accuracy. Two-dimensional effects on the formation of the shock-wave structure of the gasparticle flow and distributions of particle concentration and other flow quantities in time and space are discussed.

На основе модели взаимопроникающих континуумов проводится численное моделирование нестационарного течения газовзвеси, возникающего при взаимодействии ударной волны со слоем инертных частиц. Каждая фаза описывается набором уравнений, выражающих законы сохранения массы, импульса и энергии. Межфазное взаимодействие учитывается при помощи источниковых членов в уравнениях изменения количества движения и энергии. Основные уравнения для газовой и дисперсной фаз имеют гиперболический тип, допускают запись в консервативной форме и решаются с использованием численного метода типа Годунова повышенного порядка точности. Для дискретизации уравнений по времени применяется метод Рунге-Кутты 3-го порядка. Построенная модель позволяет рассчитывать широкий спектр режимов течения газовзвеси, возникающих при изменении объемной концентрации дисперсной фазы. Обсуждаются вопросы, связанные с замыканием математической модели, а также детали реализации численной модели. Приводятся ударно-волновая структура течения и пространственно-временные зависимости концентрации частиц и других параметров потока. A numerical simulation of the unsteady gas-particle flow arising from the shock-wave interaction with a layer of inert particles is performed based on a continuum model. Each phase is described by a set of equations describing the conservation laws of mass, momentum and energy. The interphase interaction is taken into account using source terms in the momentum and energy equations. The governing equations for the gas and dispersed phases are of a hyperbolic type, they can be written in a conservative form and can be solved with a Godunov-type numerical method. A third order Runge-Kutta method is used to discretize the governing equations in time. The proposed model allows one to calculate a wide range of gas-particle flow regimes occurring when the volume concentration of the dispersed phase varies. The closure of the mathematical model and some details of numerical model implementation are discussed. The shock-wave flow structure as well as the space-time dependencies of particle concentration and other flow parameters are presented.

The formation dynamics of the parameters of a microwave discharge in air localized at electric field maxima created by a specially developed focusing system is investigated using numerical simulations within an extended hydrodynamic model. All main parameters of the microwave discharge plasma are determined. The results on neutral gas heating demonstrate good agreement with the earlier experimental results.

The use of general purpose graphics processors for the numerical solution of problems in dynamics of viscous incompressible fluid is discussed. Specific features of the parallel implementation of the splitting scheme (projection method) are considered. The system of difference equations produced by the discretization of Poisson's equations for pressure is solved using the multigrid method. Anumber of benchmark problems are solved on graphics processors, and approaches to the optimization of program code by using different memory types are discussed. The speedup of computations on graphics processors is compared with the computations on the central processor using grids with different resolution and different decompositions of the initial data into blocks.

When gas flows at a high speed in a channel with a variable cross sectional area and high-intensity energy supply, it experiences complicated physical and chemical processes producing high-temperature gas effects. High-temperature gas effects are a key issue related to design and optimization of nozzles of plasmatron of alternating current. The finite volume method is applied to solve unsteady compressible Euler equations with high-temperature gas effects. Solutions of some benchmark test cases are reported, and comparison between computational results of chemically equilibrium and perfect air flowfields is performed. The results of numerical simulation of one-dimensional and two-dimensional under- and over-expanded nozzle flows with a moving region of energy supply are presented. Output nozzle parameters are calculated as functions of a number and time of burning of plasmatron arcs. The results obtained show a qualitative pattern of gas dynamics and thermal processes in the nozzle with unsteady energy supply demonstrating the displacement of the nozzle shock wave towards the nozzle outlet in the over-expanded nozzle flow in comparison to perfect gas flow.