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The Galilean invariant thermodynamically compatible conservation laws that admit a class of generalized solutions is analyzed. The main feature of the generalized solutions considered in this paper is that they describe smooth solutions with the kinetic energy and total pressure loss, which accompany the dynamic process of heat supply. The principal properties of the generalized solutions analyzed in Godunov’s works are the Galilean invariance and thermodynamic compatibilty of the original conservation laws under the closed mathematical formulation of the thermal gas-dynamic process.

Thermodynamic compatibility of the mass, momentum, and energy conservation laws that describe the motion of heat conducting gas in the presence of radiation heat exchange is considered. The study is based on the one-velocity two-component mathematical model of continuous compressible medium with the gas and radiation components. The work uses experimental data for radiation and other experimental data of modern physics.

The process of generating turbulence in edge wakes has been simulated and the results of the simulation are presented. The proposed mathematical model follows from a special procedure, which aims to average the flow parameters on scales comparable with the free path of molecules. The examined mechanism of generating turbulence is described by an expended set of Euler and Navier-Stokes nonstationary equations, with additional dispersive summands of the third order, which are obtained, if one uses the averaging procedure. The basic hydrodynamic equations are integrated by means of the well-known Godunov procedure of the second order. The calculated averaged performances of the turbulent flows agree with the experimental data.

Information model of plasmochemical processes for synthesis of nano-and ultradispersed oxide materials was developed on the basis of the CALS concept (Continuous Acquisition and Life cycle Support) for the example of ultrapure tin oxides.

A numerical method for solving the problem of three-dimensional viscous cascade flow is developed and its accuracy is estimated.

The results are presented on a numerical study of the propagation of strongly underexpanded jets of an ideal gas in a flooded space with Mach numbers at the nozzle cut slightly exceeding unity. In this case the angle of turn of the stream in the vicinity of the rim of the conical nozzle can exceed 90‡ and the boundary of the jet turns back beyond the cross section of the nozzle cut. It is shown that the square root of the expansion ratio of the discharge is a self-similarity parameter for the geometrical dimensions of the calculated jets. The dependence of the longitudinal dimensions of such jets on the Mach number at the nozzle cut is close to linear. The effect of the adiabatic index on the shape of the jet boundary and the suspended compression shock is illustrated. The integration of the steady system of gasdynamic equations describing the two-dimensional supersonic flow of a nonviscous and thermally nonconducting gas, performed by a monotonie finite-difference system of through calculation of the first order of accuracy, was proposed in [1, 2] and generalized to the case of arbitrary orientation of the velocity vector in the plane of flow in [3].

The results are presented of the numerical investigation of the interaction of a supersonic axisymmetrical jet of a nonviscous and nonthermally conductive gas, flowing from a conical nozzle into a space with reduced pressure, with a plane obstacle. The presence of a triple point of intersection of the shock wave issuing from the obstacle with the trailing and reflected oblique compression shock is characteristic for the conditions considered in the paper. The solution of the problem is obtained by numerical integration of the gasdynamic equations by means of monotonic difference schemes of a straight-through calculation with first-order accuracy. The interaction of supersonic gas jets with surfaces is a vast problem and is one of the trends being developed intensively in the theory of jet streams. Of the whole multiplicity of problems of practical interest, the two-dimensional case of the “normal” collision between a supersonic axisymmetrical jet and a plane obstacle has been studied in most detail. As a result of the investigations carried out, many characteristic mechanisms of these flows have been revealed. Together with the numerous experimental papers, several reports have been published (for example, [1–4]) in which various numerical methods are employed to solve this problem. In addition to the method of integral relations used in [1], an implicit difference scheme [2] and explicit schemes of straight-through calculation [3, 4] have been used to calculate the subsonic zone of increased pressure in front of the obstacle. However, an extensive investigation of the special features of the action of a supersonic underexpanded jet on a plane obstacle, at a very small distance from the nozzle exit, still has not been carried out up to the present. In this paper, a solution of this problem is undertaken by the numerical method described in [4] using difference schemes [5, 8].

The use of the time-establishment process in solving problems relating to the steady flow of an ideal (nonviscous and heat-insulating) gas around a cascade of profiles is considered. Chief attention is paid to the role of the Chaplygin-Zhukovskii condition, which is needed [1, 2] when solving these as steady-state problems. Results obtained during the time-establishment process with and without the application of the condition in question are presented. In both cases certain time-independent distributions of the parameters satisfying the equations and conditions of the steady-state problem (or more precisely their finite-difference analog) are produced during the establishment process. Comparison of the resultant distributions shows that the difference between the two cases lies within the limits of computing error, the results of the calculations agreeing quite well with experimental data.

An explicit divergence difference scheme of third order of approximation with respect to the spatial variables is used to calculate two-dimensional steady flows of an inviscid gas that does not conduct heat in contracting-expanding nozzles in the presence of nonequilibrium physicochemical processes. The flow structure is demonstrated for a three-component vibrationally nonequilibrium gas mixture in planar Laval nozzles with different radii of curvature of the nozzle profile in the neighborhood of the critical section.

Wave fronts are well known to be the regions of space where the properties of motion vary sharply in a certain direction. This means that one of the components of the gradients of density, velocity, stress, etc., at the wave fronts exceeds essentially not only other components but also corresponding gradients outside the fronts. The large gradients require that the analysis of motion within the fronts (the front structure) be based on equations more detailed than those sufficient in the surroundings. Meanwhile these more detailed equations admit simplification of the boundary-layer type because the fronts are necessarily slender in one direction. In the “external” approximation the fronts are represented by discontinuity surfaces (Figure 1, a).

A large part of the known results of Laval nozzle theory relates to the inverse problem, in which the velocity distribution on some line (usually the axis of symmetry) is given rather than the nozzle contour. Many important properties of transonic flows have been disclosed as a result of numerous studies, whose basic results were presented together with an extensive bibliography in Ryzhov's monograph [1]. The solution of the inverse problem has recently been used not only to analyze the qualitative characteristics but also to construct nozzles with rather marked variation of the slope of the generator, which are of practical interest. In this connection we note the work of Pirumov [2] and also the studies of Hopkins and Hill [3, 4]. The latter authors, in addition to the classical Laval nozzle, studied several nozzle schemes with a centerbody. Pirumov used a specially developed numerical method for the solution of the inverse problem (we note that in the subsonic part of the nozzle the corresponding Cauchy problem is incorrect), while Hopkins and Hill used a series expansion which was preceded by a change of variables.

A large number of studies have been published which define bodies of minimal drag and nozzles of maximal thrust. A study has been made of the region of existence of the various solutions in planar flow, and it has been shown that the optimal profile in the presence of a length limitation may have a blunt end, which is a segment of a boundary extremum. The results of these studies and also the required bibiliography are contained in [1–3].