Formation of gas flows with account for the effects of heat conduction,viscosity, diffusion,and chemical reactions

In this paper we examine the formation of one-dimensional-nonsteady gas flows with account for the influence of thermal conduction, viscosity, diffusion, and chemical reactions. An analogous problem but without account for the effect of diffusion and chemical reactions was examined in [1].It is shown that the effect of chemical reactions is not significant for short times-the gas behaves as an incompressible fluid. The results obtained may be used to calculate gas flows with discontinuous initial conditions with subsequent numerical integration of the Navier-Stokes equations.As examples we consider the flows of binary gas mixtures which arise upon application of thermal flux to the flat end of a moving piston (1) and during the decay of an arbitrary discontinuity (2).It is assumed that the internal degrees of freedom of the gas molecules are in equilibrium with the translational degrees of freedom.The author wishes to thank Yu. A. Dem'yanov for his guidance in this study.     

Three-dimensional chemically nonequilibrium viscous shock layer on a catalytic surface with allowance for associated heat transfer

A three-dimensional flow of dissociating air past blunt bodies is investigated in the framework of the thin viscous shock layer theory. Multicomponent diffusion and homogeneous chemical reactions, including dissociation, recombination, and exchange reactions, are taken into account. The generalized Rankine-Kugoniot conditions are specified on the shock wave and the conditions which take into account the heterogeneous catalytic reactions, on the surface of the body. The viscous shock layer equations are solved together with the heat equations inside the coating, which is carbon with a deposited thin film of SiO₂, or quartz. The case of a thermally insulated surface is also considered. The problem for the case of the motion of a body along the re-entry trajectory into Earth's atmosphere is investigated numerically. The temperature of the surface and the heat flux toward it are given as a dependence on the height (tine) of the flight for different cases of the specification of the catalytic reactions. It is shown that the difference between the heat fluxes towards the thermally insulated surface and the fluxes toward the heat-conducting surface in the neighborhood of the stagnation point is of the order of 6–12% for all the cases considered. This makes it possible to decouple the solution of the problem of heat conduction in the body.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–146, November–December, 1985.deceased     

Conjugated heat and mass transfer between a reactive solid and a gas in the presence of nonequilibrium chemical reactions

An investigation of a multicomponent boundary layer taking account of nonequilibrium chemical reactions has been made in a number of publications [1–3]; here, the temperature of the solid was assumed to be known or was determined from the condition of the conservation of energy at the interface between the gas and the solid, taking account of the solution of the equation of thermal conductivity in the solid phase. At the same time, heating of the material of a coating is an unavoidable step in any mechanism of thermokinetic decomposition and, in view of this, it is necessary to take account of the lag of the heat-transfer process inside the solid. Therefore, it is necessary to solve the equation of the energy balance in the solid phase simultaneously with the system of the equations of the boundary layer, i.e., the conjugate problem. The present article discusses the problem of flow around a solid in the vicinity of a frontal critical point, taking account of the dependence of the processes taking place in the solid body on the time, in the presence of two heterogeneous and one homogeneous reactions. The distributions of the velocity, the temperature, and the concentrations in the boundary layer are obtained, as well as the mass rate of entrainment of the material at different moments of time. The time of the change between kinetic and diffusion conditions of the course of the heterogeneous chemical reactions (the ignition time) is determined. It is established that, in the presence of a homogeneous chemical reaction, the mass rate of entrainment is less than with a frozen flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–128, March–April, 1974.     

Diffusion and adsorption of a radioactive gas in a porous medium

The results of solving the one-dimensional problem of the motion of a pulse of radioactive gas, carried through a porous medium by a stream of inert carrier with constant velocity, are generalized by the case of taking diffusion processes into account. For a delta-shaped input pulse, the solution is obtained of a system of equations which describes the migration of the pulse, taking diffusion washout and nonequilibrium adsorption into account. It is shown that in the case of equilibrium adsorption the time of appearance of the concentration maximum at the adsorber outlet depends on the decay constant and the coefficient of diffusion. Approximate solutions for strong- and weak-nonequilibrium adsorption and in the case of weak diffusion are considered. An estimate is carried out of the maximum magnitude of the diffusion coefficient, when its effect can be neglected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 85–90, September–October, 1976.The authors thank A. N. Gudkova for discussing the work.     

Physical and mathematical modeling of a supersonic flow around a cylinder with a porous insert

Results of numerical and experimental modeling of a supersonic flow (M_∞ = 4.85) around a model of a streamwise-aligned cylinder with a cellular-porous insert permeable for the gas on the frontal face of the cylinder are described. Experimental data on the influence of the pore structure and the length of the porous cylindrical insert on the model drag, pressure on the frontal face of the cylinder, and flow pattern are obtained. Numerical modeling includes solving Favre-averaged Navier-Stokes equations, which describe the motion of a viscous compressible heat-conducting gas. The system is supplemented with a source term taking into account the drag of the porous body within the framework of the continuum model of filtration. Data on pressure and velocity fields inside the porous body are obtained in calculations, and the shape of an effective pointed body whose drag is equal to the drag of the model considered is determined. The calculated results are compared with the measured data and schlieren visualization of the flow field.     

Unsteady-state flow of a gas in a channel,resulting from the motion of a piston,with magnetohydrodynamic offtake of energy and luminescence of the gas

The present paper discusses the one-dimensional unsteady-state flow of a gas resulting from the motion of a piston in the presence of weak perturbing factors, with which the investigation of the perturbed (with respect to the usual self-similar conditions) motion reduces to the solution of ordinary differential equations, is indicated. The distributions of the parameters of the gas between the piston and the shock wave are found. The conditions under which there is acceleration or slowing down of the shock front are clarified. As an example, this paper considers the unsteady-state motion of a conducting gas in a channel with solid electrodes under conditions where electrical energy is generated, and the flow of a gas taking radiation into account, under the assumption of optical transparency of the medium. The theory developed is used to solve the problem of the motion of a thin wedge with a high supersonic velocity in an external axial magnetic field, taking account of the luminescence of the layer of heated gas between the wedge and the shock wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 17–25, September–October, 1970.     

Motion of a piston in a cylindrical tunnel with allowance for the additional mass of the gas

We propose to derive relations for the motion of a piston, taking into account the variation of its mass due to the additional mass of the gas entrained by the motion of the piston. We show that the gas entrained by the piston has an appreciable effect on the acceleration of the piston and the acceleration length, with the piston attaining a velocity close to the limiting value.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–169, September–October, 1971.     

Effect of Interphase Heat Transfer on the Stability of a Turbulent Multicomponent Flow in a Vortex

The parameters of an axisymmetric turbulent two-phase swirling flow of a viscous heat-conducting gas containing a liquid dispersed phase in the presence of water vapor condensation on the particles are calculated. For the dispersed phase, a model taking into account the variation of the vapor concentration and the particle size due to condensation or evaporation is proposed. The distributions of the parameters of the basic unperturbed flow obtained numerically are used in the numerical solution of the linear problem of hydrodynamic stability within the time-dependent formulation. The parameters of small-amplitude harmonic perturbations propagating along the vortex axis are investigated in the linear formulation. A significant effect of heat release in the gas due to water vapor condensation on the parameters of the neutral perturbations and the neutral-stability curves is detected.     

Self-similar problems of convective diffusion in the presence of heterogeneous chemical reactions with allowance for thermal diffusion effects

A number of studies have been made of the problem of the effect of a temperature gradient on mass transfer in a forced viscous fluid flow. The question of allowing for thermal diffusion effects has been examined in connection with flow around bodies [1–4], duct flow [5], and jet flows [6,7]. Recently, in addition to the problem of thermal diffusion separation, the attention of investigators has been claimed by the problem of taking into account the effect of thermal diffusion on mass transfer in a convective flow in the presence of chemical reactions on the flow surfaces [4].     

Adiabatic heating (cooling) of a supercritical fluid with variation in its physical properties

The piston effect (adiabatic heating or cooling) is investigated numerically for a fluid with parameters in the neighborhood of the thermodynamic critical point. The fluid represents a plane layer on one of whose boundaries a jump in temperature takes place. The temperature of the medium is higher than the critical temperature and the mean density is equal to the critical density. The mathematical model includes the Navier–Stokes and energy equations for a heat-conducting compressible gas and the Van der Waals equation of state. The characteristics of the linear piston effect (properties of fluid are almost invariable) are compared the analytic data. The features of the nonlinear piston effect accompanied by significant variation in the physical properties of the medium are investigated.     

Description of flows of multicom ponent ionized mixtures in chemical equilibrium within the limits of the navier-stokes and prandtl equations

By eliminating the electrical field originating because of separation of the charged components, the Navier-Stokes equations for partially ionized multicomponent reacting gas mixtures without external electromagnetic fields are reduced to equations analogous to the equations for a chemically reacting mixture of neutral gases. Formulations of problems about flows in chemical equilibrium taking account of ionization, thermo- and barodiffusion reactions for arbitrary mixtures with different diffusion properties of the components are examined within the scope of the complete Navier-Stokes equations and the Prandtl equations of an asymptotically thin boundary layer around both impermeable and thermochemically destructible walls.     

Numerical modeling of detonation combustion of hydrogen-air mixtures in a convergent-divergent nozzle

The flow of igniting hydrogen-air mixtures entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered. A possibility of stabilizing detonation combustion is numerically investigated at different freestream Mach numbers with account for nonuniform distribution of hydrogen concentration at the nozzle entry. The investigation is performed on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. A detailed model of chemical reactions is used. The calculated thrust is compared with the drag of a conical housing containing the supersonic nozzle considered.     

Quasi-Hydrodynamic Model of Multiphase Fluid Flows Taking into Account Phase Interaction

A quasi-hydrodynamic system of equations describing flows of a heat-conducting viscous compressible multiphase multicomponent fluid is constructed taking into account surface effects. The system was obtained by generalizing the methods of obtaining a single-phase quasi-hydrodynamic system and a multicomponent flow model with surface effects based on the concept of microforces and microstresses. The equations are derived using the Coleman–Noll procedure. The results of the simulations show that the constructed model is applicable for modeling multiphase multicomponent flows with allowance for surface effects on the interfaces.     

Separation in a centrifuge-model

Summary The gas centrifuges which were used for isotope separation ^1,2) have cylindrical rotors. In consequence of the equality of the relaxation times for diffusion and gas motion, and taking into account the pressure-dependence of the diffusion constant, the time-dependent equation for a cylindrical centrifuge is rather complicated ³). Therefore a simple centrifuge-model where gas motion does not need to be considered is of interest. Though the theoretical maximum peripheral velocity for this model is up to 2-times higher than for a cylindrical rotor ¹), this interest is only mathematical.     

Chemical relaxation in a viscous shock

We consider the flow of a nonequilibrium dissociating diatomic gas in a normal compression shock with account for viscosity and heat conductivity. The distribution of gas parameters in the flow is found by numerically solving the Navier-Stokes and chemical kinetics equations. The greatest difficulty in numerical integration comes from the singular points of this system at which the initial conditions are given. These points lead to instability of the numerical results when the problem is solved by standard numerical methods. An integration method is proposed that yields stable numerical results-continuous profiles of the distribution of the basic gas parameters in the shock are obtained.We consider steady one-dimensional flow in which the gas passes from equilibrium state 1 to another equilibrium state 2, which has higher values for temperature, density, and pressure. Such a flow is termed a normal compression shock.The parameter distribution in normal shock for nonequilibrium chemical processes has usually been calculated [1–3] without account for the transport phenomena (viscosity, heat conduction, and diffusion). The presence of an infinitely thin shock front perpendicular to the flow velocity direction was postulated. It was assumed that the flow is undisturbed ahead of the shock front. The gas parameters (velocity, density, and temperature) change discontinuously across the shock front, but the gas composition does not change. The composition change due to reactions takes place behind the shock front. The gas parameter distribution behind the front was calculated by solving the system of gasdynamic and chemical kinetics equations using the initial values determined from the Hugoniot conditions at the front to state 2 far downstream.Several studies (for example, [4, 5]) do account for transport phenomena in calculating parameter distribution in a compression shock, but not for nonequilibrium chemical reactions. These problems are solved by integrating the Navier-Stokes equations continuously from state 1 in the oncoming flow to state 2 downstream.We present a solution to the problem of normal compression shock in nonequilibrium dissociating oxygen with account for viscosity and heat conduction using the Navier-Stokes equations.     

Numerical Modeling of Interior Ballistics Processes in Light Gas Guns

An improved procedure for modeling the operation of a light-gas gun is proposed. The motion of working bodies in both the firing chamber and the light-gas chamber is studied within the framework of the mechanics of heterogeneous media. The problem of barrel heating taking into account its melting and removal of thermal ablation products into the medium inside the bore is solved in a coupled formulation. Heat and mass transfer and friction on the barrel surface are calculated using empirical dependences. The deformable piston is considered compressible and elastoviscoplastic. Allowance is made for the presence of a clearance between the lateral surface of the piston and the barrel bore walls and the associated gas flow between the firing and the light-gas chamber. Calculation results are given.     

A modified model for isothermal homogeneous and heterogeneous reactions in the boundary-layer flow of a nanofluid

The homogeneous and heterogeneous reactions in the boundary-layer of a flat surface are considered. The autocatalysts are assumed to be of regular sizes, while the solution is a dilute nanofluid. The heat release due to the chemical reactions is taken into account. The Buongiorno's model is used to describe the behaviors of this reaction system. This configuration makes the current model be different from all previous publications. Multiple solutions are given numerically to the rescaled nonlinear system, whose stability is verified. The results show that the strength coefficients of the homogeneous and heterogeneous reactions are key factors to cause the appearance of the multiple solutions in the distribution of the chemical reactions. Nanofluids enhance the diffusion of heat and help maintain the stability of chemical reactions.     

Nonequilibrium dissociation of diatomic molecules in flows with convective and diffusive particle transport

The nonequilibrium effects in the kinetics of the thermal dissociation which occurs in a streaming gas of diatomic molecules are investigated. Expressions are obtained for the macroscopic reaction rate and the vibrational energy distribution of the molecules, taking into account the influence of the gas motion. Cases of flows with convective and diffusive particle transport are considered. The dissociating molecules are simulated by cutoff harmonic oscillators. The vibrational kinetics is described in the framework of the so-called diffusion approximation.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1985.     

Relaxation of anharmonic molecules

The inclusion of anharmonic effects is important in vibrational population inversions in CO-lasers [1, 2], in relaxation processes in jets [3], in thermal dissociation [1], in the kinetics of chemical reactions with high thresholds [4], etc. Usually these effects are studied by including anharmonic corrections to the kinetic constants in the discrete model of single-quantum transitions or in the diffusion approximation [1, 2]. In [5] a method was given of solving the relaxation equations fro arbitrary forms of the rate constants and the spectrum of the molecule. The method is valid when the ratio of the population densities of neighboring levels varies smoothly with quantum number. It was shown in [5] that this approximation can be used to construct analytical solutions for a wide class of problems. In the present paper the method of [5] is extended to the case of equations with variable coefficients. The properties of the solutions for VT-relaxation of anharmonic molecules are analyzed, and the inclusion of sources is considered. A simple method of taking into account multiple-quantum transitions is given, as well as an extension of the method to an arbitrary mixture of gases. The population densities are calculated and the possibility of using our solutions in relaxation gas dynamics is discussed.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 3, pp. 22–31, May–June, 1986.     

Analytical investigation of steady convection of a near-critical Van der Waals gas in a porous thin annular cylinder embedded in a heat-conducting medium

Natural convection of a near-critical Van der Waals gas in a horizontal porous thin annular cylinder embedded in a heat-conducting space with a temperature gradient given at infinity is considered. The two-dimensional problem in a plane orthogonal to the cylinder axis is investigated using analytical methods, accurate to quantities of the order of the annulus thickness. A criterion of the onset of an annulus-section-average flow is obtained. The critical Rayleigh-Darcy number is determined for the general case in which the physical properties of the gas can considerably vary throughout the medium. Several limiting cases are considered and the ranges of their applicability are discussed. It is shown that, as the thermodynamic critical point is approached, the asymptotics of the critical Rayleigh-Darcy number depend on the relation between non-Boussinesq parameters, such as hydrostatic compressibility criteria, the temperature difference, and the nearness to the critical point. In the case of steady convection, an analytical solution is also derived in the case in which the above-mentioned stability threshold is exceeded and the physical properties of the gas vary throughout space only slightly. A comparison with the case of a perfect gas is made.