Relaxation Gas Dynamics Research Articles

Invariant solutions of one‐dimensional equations of two‐temperature relaxation gas dynamics

The group analysis method is applied to the plane one‐dimensional equations of two‐temperature gas dynamics. The complete classification of the equations with respect to admitted Lie group is studied. All invariant solutions are analyzed and their comparisons with the known invariant solutions of the ideal gas dynamics system are presented.

Systematization of relaxation gas dynamics equations. A review

The phenomenological theory of relaxation gas dynamics equations is outlined for laminar flows of multicomponent reacting gases in an approximation analogous to the Navier-Stokes approximation. A system of general equations of relaxation gas dynamics including the level kinetics equations for all excited internal degrees of freedom is formulated on the basis of notions of continuum mechanics. A procedure of going over to particular cases characterized by certain relations between the relaxation times is described and examples of the corresponding closed systems of gas dynamics equations including systems containing the balance equations of the level or mode approximations for the vibrational energy levels of molecules of a gas mixture are given. A method of constructing a database of the models of the rate constants of physicochemical processes as coefficients in the source terms of the balance equations is considered.

Analysis and computation of non-equilibrium two-phase flows

Non-equilibrium fluid mechanics and thermodynamics of two-phase vapour-droplet and gas-particle flow are considered. Formation of the droplets as well as their subsequent interaction with the vapour are discussed. A new theory of nucleation in steam turbines is developed that reproduces many aspects of measured droplet size spectra which cannot be explained by any available steady-flow theories. (Steam turbines are responsible for 80% of global electricity production and the presence of moisture significantly reduces turbine efficiency costing 50 million pounds per annum in UK alone.) Fluid dynamic interactions discussed include flow instabilities induced by condensation, condensation wave theory, relaxation gas dynamics for vapour-droplet flow, thermal choking due to non-equilibrium condensation, the structure of shock waves and their development through unsteady processes, and jump conditions and the interpretation of total pressure in two-phase flows.

Generalised scaling of an electrogasdynamic CO combustion-product laser

A method is proposed for generalised scaling of a CO laser with a high-frequency discharge in a supersonic stream of combustion products. This laser can operate efficiently without an electron gun and without continuous formation of large amounts of the CO mixture. A theoretical analysis, based on simultaneous solution of a system of equations describing the kinetics of relaxation proceses and gas dynamics, does not yield the explicit parametric dependences of the main parameters of a CO laser. However, acceptable assumptions can be made and these allow the use of general similarity laws for the scaling of a cw electric-discharge CO laser with a high-velocity stream of a mixture of CO and monatomic gases. The results of such scaling can be generalised to a CO mixture, produced by the combustion of a chemical fuel, by calculations of the energy balance of electrons in a discharge that takes place in combustion products. After the determination of the fraction of the electric-field energy acquired by the vibrational levels of the CO molecules, the main parameters of an electrogasdynamic CO combustion-product laser can be calculated with the aid of similarity laws derived for cw CO lasers with electric-discharge excitation of a high-velocity stream of a mixture of CO and monatomic gases.

Shock-wave stratification in inhomogeneous media

The analysis of phenomena associated with shock-wave propagation in inhomogeneous media is needed for the solution of a large number of problems of explosion physics, relaxation gasdynamics of supersonic flows, and astrophysics. A number of theoretical and experimental papers (1-7) are devoted to different aspects of shock interaction with gases in which signif- icant temperature and density gradients exist. Curving of the shock front and attenuation of its intensity in a heated layer above a plate surface were observed in (i, 2). The re- sults of experiments (i) were compared with a computation based on a one-dimensional model of the decay of a discontinuity, developed for the average parameters of the heated layer. The possibility is indicated of shock front blurring if the velocity of its propagation in the unperturbed domain is less than the speed of sound within the thermal inhomogeneity. Features of shock propagation in mixtures of unmixed or partially mixed gases with dif- ferent thermophysical properties were studied in (3, 4, 6, 7). The good agreement between flow patterns under normal shock incidence on the boundary of preliminarily unmixed gases obtained by using two-dimensional computations and the results of experiments is shown in (7). Reports have recently appeared about the anomalous phenomena during shock propagation in substantially inhomogeneous and nonequilibrium media (gas glow discharge plasmm (8-ii), or the plasma being formed because of optical or microwave-breakdown in air (12-14)). A considerable increase in the shock velocity, its damping, the formation of a jet, and deforma- tion and dissipation of the wave front have b~en noticed. The correct theoretical treatment of the roles of the thermal, relaxation, and gasdynamic effects in these cases requires a detailed examination of the substantially inhomogeneous and nonstationary flow pattern. By using two-dimensional computations shock propagation (with Mach number M) is inves- tigated in a plane channel in this paper, which contains a domain of temperature stratifica- tion of the gas (Fig. I, I and II). The problem is characterized by the geometric dimen- sions: h is the hot gas domain with temperature T 2 > Ti, where T i is the cold gas tempera- ture (Fig. i, I), and H is the channel transverse dimension. The pressure ahead of the wave is constant and equal to Pi. The gas is characterized by a constant ratio between the speci- fic heats 7. The wave is propagated along the coordinate X and at time t = 0 the wave front coincides with the axis OY. Computations were performed in Euler coordinates according to the Maccormac monotonized scheme (15).

Relaxation processes in multiatomic gases. II

The kinetic equation for an optically inactive component of a mixture of gases is solved in the dissipative approximation. The transport coefficients, the relaxation pressure, and the sources in the equations of the kinetics and relaxation gas dynamics are determined. A diatomic gas with weak excitation of the vibrational states of the molecules is considered, and the relaxation pressure and the relaxation times are determined in the two-moment approximation. The kinetic equations and the equation of radiative transfer are determined in the nondissipative approximation for vibrational-rotational relaxation.

Relaxation processes in multiatomic gases. I

The kinetic equation for an optically inactive component of a mixture of gases is solved in the dissipative approximation. The transport coefficients, the relaxation pressure, and the sources in the equations of the kinetics and relaxation gas dynamics are determined. A diatomic gas with weak excitation of the vibrational states of the molecules is considered, and the relaxation pressure and the relaxation times are determined in the two-moment approximation. The kinetic equations and the equation of radiative transfer are determined in the nondissipative approximation for vibrational-rotational relaxation.

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.

Nonequilibrium gas-surface-solid in problems of relaxation gasdynamics

The study of nonequilibrium flows is one of the main problems of physical gasdynamics. As shown by experiment [I-3], most of them can be solved by the theory of multiple temperature equilibrium, when the investigated gas mixture is fully determined by a comparatively small number of macroparameters. The justification of the corresponding models of relaxation hydrodynamics by the apparatus of the kinetic theory of gases was given in [4-5], while the boundary conditions to these models in the whole range of variation of accomodation coefficients were obtained in [6]. In recent years, with developing studies on effects of catalytic properties of surfaces on thermal flows, the improvement of radio-wave propagation through plasma for~lations, obtaining flows in strongly nonequilibrium populations of quantum levels, the use of multiphase flows for isotope separation, etc. it became necessary to study relaxation effects not only in the gas, but also on the boundary with the surface, as well as inside the solid phase, such as, for example, in aerosol particles. The kinetic theory for this class of problems has not yet been developed, even within the multiple temperature approximation. In the present work this problem has been solved phenomenologically, constructing a hydrodynamic model with the use of balance conditions of energy flows within and on the boundary of interacting phases. We consider specifically the set ofprocesses occurring in a multiple-phase multiple-temperature flow, in which solid particles are found, formed of molecular crystals. At the initial moment of time t = 0 the translational--rotational and vibrational temperatures T G and TiG of the gas equal the particle temperature TL (TG = TiG = TL), inside which the intramolecular vibrational degrees of freedom are excited, TiL ~TL. This can be done by constructing a source, for ezample, by an electron beam [7]. For t > 0 the gas excitation starts by heterogeneous mechanisms of energy exchange on the particle surfaces. The energies of vibrational quanta in the gas and of particles are assumed to be near these quantities, for example, in a flow containing the gas and aerosol particles of nitrogen. The latter, thus, emerge in the role of energy carriers [8, 9]. By the estimates obtained in [8], the system with an energy carrier being a complex of a large number of molecules in the solid state can possess a high specific energy capacity ~]03 J/g. Therefore, the dynamic problem on the redistribution of intramo!ecular vibrational energy in the ga~-surface--solid system is of much interest. The solution of this problem is the main goal of the present paper. It must be kept in mind that accomodation coefficients of various energy shapes appear in the system of equations describing the relaxation processes. To obtain the structural shape of these coefficients it is necessary to solve the quantummechanical problem of interaction of molecules with the surface, particularly the problem of the resonance exchange probability of vibrational energies. Of principal value is obtaining estimates of characteristic time scales of redistribution of intramolecular vibrational energy inside particles of various sizes. The solution of these problems is also included in this work.

Relaxation Effects in Gas Dynamics

Classical gas dynamics is by definition the dynamics of gases that are in local thermodynamic equilibrium everywhere in the flow field so that their thermodynamic behaviour is completely specified by two independent variables of state, for example by pressurepand densityp. The fundamental assumption of local thermodynamic equilibrium is not valid in many flow situations of practical importance, and this fact has given rise to a revision and generalisation of classical gas dynamics. This generalisation is usually called “relaxation gas dynamics”. Ten years ago J. Ackeret mentioned this subject briefly at the end of the Daniel and Florence Guggenheim Memorial Lecture onThe Role of Entropy in the Aerospace Sciences.He gave that lecture at the 2nd International Congress of the Aeronautical Sciences in Zürich (12th September 1960) and he said on that occcasion: “Non-equilibrium states are of growing importance, for strictly speaking, exact (thermodynamic) equilibrium occurs only relatively seldom in gas dynamics. However, a rational theory of nonequilibrium states must necessarily be extremely complicated….