Viscous Heat-conducting Gas Research Articles

Principles of Unsteady High-Speed Flow Control Using a Time-Limited Thermally Stratified Energy Source

This study focused on the development of the unsteady impact of a thermally stratified energy source on a supersonic flow around an aerodynamic (AD) body in a viscous heat-conducting gas (air). Research was based on the Navier-Stokes equations. The freestream Mach number was 2. A new multi-vortex mechanism of the impact of a time-limited stratified energy source on the aerodynamic characteristics of a body was described. Almost complete destruction of the bow shock wave in the density field, due to the multiple generation of Richtmyer-Meshkov instabilities in the region of a stratified energy source, was obtained. The dependences of the dynamics of frontal drag and lift forces of a streamlined body on temperature in the source layers were studied. It was determined that, by changing the temperature in the layers of a stratified energy source, it was possible to obtain more intense vortices accompanying the Richtmyer-Meshkov instabilities, causing a temporary decrease in the drag force of an AD body and ensuring the emergence and unsteady change in the magnitude of the lift (pitch) forces. The main principles of unsteady flow control using a stratified energy source were established.

On the Global Solvability of a Boundary Value Problem for the Equations of a Viscous Heat-Conducting Gas under the Radiative Transfer Conditions

On the Global Solvability of a Boundary Value Problem for the Equations of a Viscous Heat-Conducting Gas under the Radiative Transfer Conditions

Local Solvability of the Flow Problem for the Equations of Motion of Two Interpene Crating Fluids

The paper is dedicated to the one-dimensional problem of the nonisothermal flow of a two-phase mixture of viscous incompressible fluids with inhomogeneous boundary conditions. The mathematical model describing the two viscous fluids mixture flow is based on the equations of mass conservation, momentum conservation for each phase, and on the energy conservation equation, in the large. Local in time solvability of the initial boundary value problem in S.L.Sobolev and Helder spaces is proved. Section 1 sets the problem set up and provides the short literature review on the topic close papers and the main result formulation. Section 2 explains the transformation of the original system of equations. Sections 3, 4 prove the existence of the strong and classic solutions on a small time interval with constant true density using the Bubnov-Galerkin method. Notionally, the proof of the theorem is based on the similar result proof for viscous heatconducting gas (Antonsev S.N., Kazhihov A.V., Monahov V.N. Boundary value problems of heterogeneous fluid mechanic). The particularity of the considered problem is the presence of inhomogeneous boundary conditions.

Influence of the boundary effect, viscosity factor and heat conductivity mechanism on the shock front evolution

In this paper a new economical discrete-analytical approach is applied to the problem penetrating of a shock wave in the shear layer of a viscous heat-conducting gas at high Reynolds numbers.

On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with degenerate heat conductivity

We consider the one dimensional compressible Navier-Stokes system with constant viscosity and the nonlinear heat conductivity being proportional to a positive power of the temperature which may be degenerate. This problem is imposed on the stress-free boundary condition, which reveals the motion of a viscous heat-conducting perfect polytropic gas with adiabatic ends putting into a vacuum. We prove that the solution of one dimensional compressible Navier-Stokes system with the stress-free boundary condition shares the same large-time behavior as the case of constant heat conductivity.

Numerical investigation of flows with condensation in micronozzles

The paper considers the numerical simulation of the flow of argon with account for the condensation process in the micronozzle and behind it. To describe phase transitions, the initial mathematical model of viscous heat-conducting gas flow is supplemented with the equation of formation and growth of condensation nuclei in the flow. The developed mathematical model allows for simulating the process of gas condensation at low pressures and temperatures. It is shown that the condensate mass fraction in the flow is not less than 1% at the pressure and temperature of 5 bar and 200 K, respectively, when argon flows out of a micronozzle to the environment with the pressure of 0.01 Pa. At the nozzle exit, the size of condensed particles reaches 80 angstroms. The obtained results confirm the necessity to take into account the condensation phenomenon in micronozzle flows of inert gases.

ON THE TURBULENCE IN A VISCOUS HEAT-CONDUCTING GAS

The problem of the emergence of turbulence is one of the unsolved problems of physics and technology of the 20th century. It is noted that in order to understand the emergence of turbulence in a viscous heat-conducting gas, it is necessary to take into account the compressibility of the medium. A definition of turbulence in a viscous heat-conducting gas is given, which is a cyclically repeating process of the emergence and decay of coherent vortex structures described by a vector wave equation. The decay of vortex structures is accompanied by an explosive, asymptotic increase in pressure pulsations, which triggers a new cycle of turbulence generation. The emergence and decay of coherent vortex structures in the boundary layer on a plate and in a round jet is considered.

Heat flux in supersonic flow past ballistic model at various angles of attack and wall temperatures

Supersonic flow of viscous heat-conducting gas around the ballistic model HB-2 and the resulting heat flux for M=3, angles of attack α=0°,8°,16°and various model surface temperatures were numerically studied using the compact version of the hyperbolic system of quasi-gasdynamic equations (CHQGD).Three-dimensional features of the flow structure and heat flux's dependence on the angle of attack and wall temperature were investigated. Longitudinal vortices on the model's leeward side near the symmetry plane were observed for α=16°. These flow separation regions significantly affect heat flux distribution on the model's leeward surface.

Численное исследование нестационарного течения газа в камере сгорания прямоточного воздушно-реактивного двигателя с учетом процесса теплообмена

Проведено численное исследование нестационарного турбулентного сверхзвукового течения в камере сгорания прямоточного воздушно-реактивного двигателя. Описана методика экспериментального измерения температуры на стенке осесимметричного канала в камере сгорания двигателя. Математическое моделирование обтекания исследуемой модели двигателя проводилось для скоростей набегающего потока M = 5 ... 7. Начальные и граничные условия задачи соответствовали реальному аэродинамическому эксперименту. Проанализированы результаты численного расчета. Рассмотрено изменение распределения температуры вдоль стенки канала с течением времени. Проведена оценка согласованности полученных экспериментальных данных с результатами математического моделирования. Purpose. The aim of this study is a numerical simulation of unsteady supersonic gas flow in a working path of ramjet engine under conditions identical to aerodynamic tests. Free stream velocity corresponding to Mach numbers M=5 ... 7 are considered. Methodology. Presented study addresses the methods of physical and numerical simulation. The probing device for thermometric that allows to recording the temperature values along the wall of internal duct was proposed. To describe the motion of a viscous heat-conducting gas the unsteady Reynolds averaged Navier - Stokes equations are considered. The flow turbulence is accounted by the modified SST model. The problem was solved in ANSYS Fluent using finite-volume method. The initial and boundary conditions for unsteady calculation are set according to conditions of real aerodynamic tests. The coupled heat transfer for supersonic flow and elements of ramjet engine model are realized by setting of thermophysical properties of materials. The reliability testing of numerical simulation has been made to compare the results of calculations and the data of thermometric experimental tests. Findings. Numerical simulation of aerodynamic tests for ramjet engine was carried out. The agreement between the results of numerical calculations and experimental measurements for the velocity in the channel under consideration was obtained; the error was shown to be 2%. The temperature values were obtained in the area of contact of the supersonic flow with the surface of the measuring device for the external incident flow velocities for Mach numbers M = 5 ... 7. The process of heating the material in the channel that simulated the section of the engine combustion chamber was analyzed. The temperature distribution was studied depending on the position of the material layer under consideration relative to the contact zone with the flow. Value. In the course of the work, the fields of flow around the model of a ramjet engine were obtained, including the region of supersonic flow in the inner part of axisymmetric channel. The analysis of the temperature fields showed that to improve the quality of the results, it is necessary to take into account the depth of the calorimetric sensor. The obtained results will be used to estimate the time of interaction of the supersonic flow with the fuel surface required to reach the combustion temperature.

Acoustic radiation by a Hill vortex in viscous heat-conducting gas

Acoustic radiation by a Hill vortex has been studied on the basis of the Navier – Stokes equations. We used the expansion of unknown functions into power series of the initial vorticity which was assumed to be small. The Navier-Stokes equations were reduced to a parabolic system with constant coefficients for higher derivatives. The problem is set in such a manner. The vorticity is defined inside a sphere at t = 0. The initial density and the temperature are assumed to be constant throughout the whole space. The solution is represented as a power series whose coefficients are multiple integrals. They have been calculated with the aid of Korobov grids. The density oscillations have been investigated. The frequency spectra were studied at various distances from the vortex. The results may be useful for modelling decaying grid turbulence.

Studying the efficiency of cooling and resistance of ribbed tubular elements

The cooling of compressed medium when passing through the set of ribbed tubular elements is numerically investigated. Numerical experiments are carried out with the model of viscous heat conductive turbulent compressed gas by the control volume method with application of different numerical schemes and algorithms. The process of convective heat exchange between the cold ribbed surface and the hot gas flow is studied as well as the heat conductance processes in tubular elements. After processing the obtained results recommendations are given on the arrangement of the set of ribbed tubular elements to provide the assigned temperature characteristics of the cooling system; and the engineering technique of evaluating the thermohydraulic parameters of the cooling system is developed.

Hypersonic Flow past Sharp Plate and Double Wedge with an Electromagnetic Actuator

The two-dimensional problem of hypersonic flow past a sharp plate and a double wedge on whose surfaces there are electrodes meant for generation of d.c. glow discharge that has a thermal and force influence upon compressed gas flow near the surface is considered. The problem is solved in the self-consistent formulation in which the gas discharge parameters are determined by the gas flow and boundary layer conditions and the flow field structure depends on the local force and thermal impacts generated by the discharge. Therefore, the system of the Navier–Stokes equations and the energy conservation equation for viscous heat-conducting gas is integrated together with the system of equations of the diffusive-drift model for description of the electrodynamic glow discharge structure in gas flow. The influence of the external magnetic field with the vector of magnetic induction perpendicular to the vector of gas flow velocity is taken into account. The effect of the glow discharge parameters on the structure of shock-wave interaction on the sharp plate and the double wedge is investigated.

АНАЛИЗ ФОРМИРОВАНИЯ ТЕЧЕНИЙ ВЯЗКОГО ТЕПЛОПРОВОДНОГО ГАЗА ПРИ МАЛЫХ ВОЗМУЩЕНИЯХ ПАРАМЕТРОВ

Formation of one-dimensional flows arising as a result of interaction of a viscous heat-conducting gas and a heat-conducting wall in the process of reflection of a normally incident weak shock wave is considered. Formation of the flow field with small perturbations of parameters is studied on the basis of the Navier -Stokes equations linearized around the values of the parameters in the initial state, and the wall temperature distribution is modeled by linear heat equation. Analytical solutions of the linearized system of equations are obtained that allow one to analyze the influence of viscosity, thermal conductivity, and other factors on the formation of a continuous flow field structure with the formation of dissipative and ideal inviscid and non-heat-conducting zones.

Non-degenerate stationary solution for outflow problem on the 1-D viscous heat-conducting gas with radiation

Non-degenerate stationary solution for outflow problem on the 1-D viscous heat-conducting gas with radiation

Global existence and uniqueness of solutions to the initial boundary value problem of 3D Navier–Stokes equations with Cattaneo law

In this paper, we prove the global existence and uniqueness of solutions to the initial boundary value problem of 3D Navier–Stokes equations with Cattaneo law for viscous heat-conductive gas. We know that the change in the heat conduction law affects the energy equation directly, so the key is to prove the existence of the solution of the linear energy equation. To prove the key point, we make great use of the idea about positive definite matrix by the properties and related theorem of parabolic linear equations.

Asymptotic Estimate of Stability of a Supersonic Boundary Layer in a Vibrationally Excited Gas on a Plate

An asymptotic theory of the neutral stability curve of a supersonic boundary layer in a vibrationally excited molecular gas on a flat plate is constructed. The equations of the two-temperature viscous heat-conducting gas dynamics are considered as the initial mathematical model of the flow. On the basis of their linearization about the self-similar boundary layer solution for a perfect gas, a spectral problem is derived for the eighth-order system of linear ordinary differential equations. An algebraic secular equation with a typical decoupling into inviscid and viscous parts is derived from the linear combination of the boundary values of its solutions decreasing outside the boundary layer which solved numerically. It is shown that the neutral stability curves calculated in this way confirm the effect of increasing flow stability against the background of the relaxation process and within 12–15% agree with the previously obtained results of the direct numerical solution of the full spectral problem. The solution of the simplified system of equations for calculating the critical Reynolds number gives a similar result.

Calculation of gas flow rates in concentrated fire vortices

The article presents the results of numerical simulation of the generation of free fire vortices in the laboratory without the use of special twisting devices. A. Yu. Varaksin, the corresponding member of the Russian Academy of Sciences, in his experimental studies has described the principal possibility of physical modeling of the occurrence of concentrated fire vortices. In the model of a compressible continuous medium for the complete system of Navier — Stokes equations, an initial-boundary value problem has been proposed that describes complex three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling heat flows. We has constructed approximate solutions of the complete Navier — Stokes system of equations and has determined velocity characteristics of threedimensional unsteady gas flows initiated by local heating of the underlying surface by nineteen heat sources, using explicit difference schemes and the proposed initial-boundary conditions.

Linear stability of a supersonic boundary layer on a plate under conditions of vibrational excitation and of viscous stratification

An asymptotic theory of the neutral stability curve for a supersonic boundary layer of a vibrationally excited molecular gas on a plate is developed. The initial mathematical model of flow consists of equations of two-temperature viscous heat-conducting gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the inviscid and viscous parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In this case, the critical Reynolds number increases with excitation enhancement of the internal degrees of freedom of molecules, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number.

Propagation of a Shock Wave through a Viscous Heat-Conducting Gas in a Long Microchannel

The problem of unsteady gas flow in a channel between parallel plates initiated by the initial discontinuity of the pressure and density (Riemann problem) in the channel cross-section at the high pressure drops and moderately low Knudsen numbers is solved numerically on the basis of the full system of Navier—Stokes equations. The finite-difference scheme of the second order with respect to the spatial variables and time is used. The effect of the gas viscosity and thermal conductivity on the velocity of the shock wave and the nature of flow behind it is studied under the conditions of long channel and low gas density in the low-pressure section. The numerical solution obtained is compared with the available experimental and computational data.

Simulation of a Spatial Flow in an Axisymmetric Nozzle with Nonsymmetrical Critical and Exit Sections

Using a conservative numerical method, a flow of viscous heat-conducting gas in the diffusor part of a spatial axisymmetric nozzle with a slanting exit section and partially overlapped critical section is simulated. The computations are carried out in a wide variation range of the parameters affecting the behavior and structure of the flow. The effect of the critical section’s area and pressure in the confusor part on the flow parameters in the diffusor part of the nozzle, position of flow separation points, and longitudinal and cross-sectional forces acting on the internal part of the nozzle is investigated. The distributions of the flow parameters in the nozzle are reported. The computations are carried out using parallel algorithms implemented on a computer system with a cluster architecture.