Propagation of disturbances in supersonic vibrationally nonequilibrium gas flows

The propagation of finite disturbances in nonequilibrium supersonic gas flows is investigated, and the effect of entropy and acoustic disturbances on the inversion characteristics of the medium is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 128–134, March–April, 1990.     

Calculation of nonequilibrium flows in nozzles

This paper studies in the one-dimensional formulation the flow of a reacting gas with account for the nonequilibrium behavior of the chemical reactions; the pressure distribution along the stream filament is given. Viscosity, heat conduction, diffusion, and ionization are not taken into account. It is assumed that there is equilibrium excitation of the translational, rotational, and vibrational degrees of freedom.Several studies have already been made of nonequilibrium flows in nozzles [1–5]. It is known that in the calculation of nonequilibrium flows considerable difficulty arises in selecting the integration step in those regions where the flow is nearly equilibrium. It is found that with the use for numerical integration of the explicit difference schemes of the type of the Euler, Runge-Kutta, etc., methods the integration step for carrying out a stable calculation must be so small that the calculation becomes practically impossible. The present study proposes a method for calculating nonequilibrium flows using a single implicit difference scheme to calculate with a high degree of accuracy and a quite large step (exceeding the step in the explicit schemes by several orders) both those flow regions which are close to equilibrium and those regions where the flow deviates markedly from equilibrium. A program was compiled using this method for the M-20 electronic digital computer which permitted calculating in the one-dimensional approximation flows in nozzles with account for the nonequilibrium behavior of the chemical reactions for mixtures containing H, O, C, and N atoms.Some qualitative peculiarities of the nonequilibrium flows are demonstrated using as an example nonequilibrium air discharge. A comparison is made with experimental and theoretical results of other authors.The authors wish to thank L. F. Kuz'mina for her assistance in carrying out the present study.     

Local viscous,chemically nonequilibrium flows

A study is made of a chemically nonequilibrium flow in local regions near cold walls. It is found that in this case the chemically reactions can take place only on a catalytic surface, and the gas can be regarded as a binary mixture of atoms and molecules. As an example, a study is made of the aerodynamic heating of a small step on the surface of a plate in the case when the flow past the plate is described in the first approximation when the Reynolds number tends to infinity by the Navier-Stokes equations for an incompressible gas. It is found that the presence of the step increases the drag of this section of the body, for a noncatalytic surface leads to an additional heating of it, and for a catalytic surface weakens its catalytic activity and, therefore, reduces the heating of the step.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 137–144, May–June, 1984.I thank V. N. Gusev for helpful discussion of the results of this paper.     

Steady shock wave reflections in thermochemical nonequilibrium flows

The shock wave reflection phenomena in hypersonic steady air flows, including thermochemical nonequilibrium effects, are investigated. The main objectives are to study the influence of these effects on the two shock wave reflections (regular and Mach reflections), on the Mach stem height and on the hysteresis behavior. The air computations are performed using a multi-block MUSCL-TVD finite-volume scheme. The computational results with and without thermochemical effects in the air mixture flow at an upstream Mach number equal to 7 are compared. The comparison reveals a strong dependence of the transition angles, of the height and location of the Mach stem on the physical modeling of the gas flow. Received 17 February 2000 / Accepted 30 August 2000     

Thermal slip boundary conditions in vibrational nonequilibrium flows

This paper deals with new thermal jump boundary conditions at the wall in polyatomic gas flows. The calculations and results especially concern vibrational nonequilibrium conditions when the dissociation effects may be neglected. First the usual conditions are briefly described. Then the boundary conditions proposed in the paper are justified on the basis of previous experimental results and by developing direct heat flux calculations at the wall. Analytical expressions and numerical values of the various fluxes are presented.     

Investigation of nonequilibrium two-phase flows in axisymmetric laval nozzles

The singularities of two-phase flows in Laval nozzles were investigated within the framework of the model of a two-fluid continuous medium [1, 2] mainly in a quasi-one-dimensional approximation ([3] and the bibliography therein). Two-dimensional computations of such flows were performed only recently by using the method of buildup [4–7]. However, systematic computations to clarify the influence of the second phase on such fundamental nozzle characteristics as the magnitude of the specific impulse, its losses, and discharge coefficient were performed only in the quasi-one-dimensional approximation [8, 9] and only for the supersonic parts of the nozzle in the two-dimensional approximation under the assumption of uniform flow in the throat [10, 3]. Such an investigation is performed in this paper in the two-dimensional case for the nozzle as a whole, including the sub-, trans-, and supersonic flow domains, and a comparative analysis is given of the magnitudes of the loss of a unit pulse obtained in the quasi-one-dimensional approximation [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 86–91, November–December, 1977.     

On the geometry of nonequilibrium magneto gasdynamic flows

After formulation of the various dynamical and kinematical relations connecting the flow quantities with the geometrical parameters of the stream line trajectories, the expressions for the tangent, principal normal and binormal vectors and the curvature and torsion of the stream line have been obtained in-terms of the velocity components, the pressure, the density, the magnetic field and the relaxation variable. This is followed by expressing the equations governing the flow in the intrinsic forms. It has been shown that the non-equilibrium character of the gas decreases the total pressure gradient along the streamlines, but the total pressure remains constant along the binormals and if the stream lines are straight lines, the trajectories of the principal normals lie on the surface of the constant total pressure. Further, the expressions for vorticity components in terms of curvature of the stream line and the velocity gradients along the stream line and their principal normals and binormals have been obtained. Finally, a class of circular helical flows have been discussed.     

Method of computing the chemically nonequilibrium gas flow in a heated tube in almost equilibrium or frozen states

The solution of equations describing turbulent isobaric flow of a chemically reacting gas in a heated tube is investigated analytically. Solutions of the ordinary nonlinear differential equations are obtained for almost frozen flow by the perturbation method, and for almost equilibrium flow by an asymptotic method taking account of the zero and first approximations, Linear differential equations in variations are written down to find the subsequent approximations.Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 8–14, July–August, 1973.     

Shock slip-relations for thermal and chemical nonequilibrium flows

This paper appears to be the first where the multi-temperature shock slip-relations for the thermal and chemical nonequilibrium flows are derived. The derivation is based on analysis of the influences of thermal nonequilibrium and viscous effects on the mass, momentum and emergy flux balance relations at the shock wave. When the relaxation times for all internal energy modes tend to zero, the multi-tmperature shock slip-relations are converted into single-temperature ones for thermal equilibrium flows. The present results can be applied to flow over vehicles of different geometries with or without angles of attack. In addition, the present single-temperature shock slip-relations are compared with those in the literature, and some defects and limitations in the latter are clarified. The project supported by the National Natural Science Foundation of China and the National Defence Science and Industry Commission of China.     

Feasibility study of whole-field pressure measurements in gas flows: molecular tagging manometry

Outlined in this paper are the theoretical foundation, implementation framework and experimental demonstration of a new diagnostic technique for non-intrusive, whole-field measurement of pressure within gasses. The new technique, which is referred to as molecular tagging manometry (MTM), relies on oxygen quenching of phosphorescence emission from photo-excited tracers in oxygen-containing gases. As the pressure increases, the density of oxygen becomes larger, leading to a shorter emission lifetime: a working principle that is similar to pressure sensitive paint but applied within the body of the flow rather than on the wall. Using an experimental apparatus that is built around a pressure vessel, the viability of MTM is demonstrated for the first time using acetone as a tracer. Furthermore, the experimentally recorded response is compared to theoretical predictions, and the sensitivity of MTM’s response to the uncertainty of various parameters is analyzed.     

Wave interaction in a nonequilibrium gas flow

By employing the method of multiple time scales, we derive here the transport equations for the primary amplitudes of resonantly interacting high-frequency waves propagating into a non-equilibrium gas flow. Evolutionary behavior of non-resonant wave modes culminating into shocks or no shocks, together with their asymptotic decay behavior, is studied. Effects of non-linearity, which are noticeable over times of order O(ε^-1), are examined, and the model evolution equations for resonantly interacting multi-wave modes are derived.     

Transport phenomena in a nonequilibrium dissociating gas

A disturbance of a quasiequilibrium distribution due either to a relaxation process or hydrodynamic perturbations can significantly influence the rate of the relaxation process in a gas. The expression for this rate then contains additional terms proportional to the spatial derivatives of the hydrodynamic variables [1–2]. According to the estimates of [2], the effect is clearly manifested in a nonequilibrium dissociating gas. The present authors have estimated [3] some of the additional terms in the initial stage of dissociation in a pure diatomic gas. In the present paper, expressions are obtained for the coefficients of the additional terms of the hydrodynamic equations in a dissociating diatomic gas for all dissociation laws. Estimates made for the example of oxygen show that the contribution of the additional terms to the hydrodynamic equations is comparable with the contribution of the ordinary Navier-Stokes terms.     

Solution of variational problems of gasdynamics of supersonic nonequilibrium flows

The problem of the optimization of the supersonic portion of a nozzle for gas flow in the case of certain nonequilibrium processes was solved in [1, 2]. The authors examined the flow scheme in which the closing Mach line of the first family arrives at the initial rarefaction wave fan. At the same time, in [3] in the solution of the analogous problem for the case of gas flow with foreign particles it was shown that it is advisable to consider also a different scheme, in which the closing characteristic arrives at the axis of symmetry outside the initial rarefaction wave fan. In the following we present results of a study of such a scheme for gas flow with nonequilibrium processes taking place. The necessary conditions which define the optimum contour are obtained and, in particular, the conditions which define the coordinate x and the magnitude of the angle at the corner points.     

Derivation of a linear theory for nonequilibrium and equilibrium flows

Conventional linear theory of nonequilibrium and equilibrium gas flows yields correct results only for very small deviations of the stream parameters from the unperturbed values. Moreover, if in linearization we take the coordinates in planar flow as independent variables, then the flow past concave and convex corners is described in exactly the same fashion. In this case the characteristic emanating from the corner is (depending on the type of corner) a compression or rarefaction shock. In the case of a break in the wall of an axisymmetric channel the shock intensity approaches infinity with approach to the centerline, which indicates a deficiency of this type of linear theory. In the following we use a modification which eliminates the deficiencies noted above. This involves conversion to new independent and dependent variables such that the coefficients of the exact equations being linearized become weakly varying functions of the unknown parameters, the linearized boundary conditions coincide with the exact conditions at all or part of the boundaries, and the rarefaction shocks become rarefaction wave bundles of finite width. The last condition is achieved as a result of the fact that, in accordance with the Lighthill method of deformable coordinates [1], we take as one of the independent variables a quantity which maintains a constant value on each characteristic of the bundle of characteristics emanating from the break point [for equilibrium flows the semicharacteristic (or characteristic) independent variables were used in deriving the linear theory, for example, in [2–4]]. The study was based on the example of two-dimensional stationary nonequilibrium flow of an inviscid and nonheatconducting gas. In this case we find that boththelinear equations at a finite distance from the walls and the boundary conditions for determining the potential and nonequilibrium parameters outside the rarefaction wave bundles coincide with the equations and the conditions of conventional linear theory [5], while the relations associating the values of the parameters on the closing characteristics of each bundle (outside the bundles the same value of the characteristic variable corresponds to these characteristics) at some distance from the axis or from some reflecting surface are identical to the conditions on the rarefaction shocks. This fact makes it possible to use several results of conventional linear theory.