Radiation of a shock layer during hypersonic flow of air about a spherical segment

The problem on the flow of radiating air about a spherical segment is solved. A comparison of results obtained with investigations of the flow of a radiating gas about a sphere and the flow of gas about a spherical segment, with radiation left out of account, is made. The influence of radiation in the neighborhood of the rim of the segment on the flow in the shock layer is considered, and it is shown that it does not exert a significant influence on the fields of the gas-dynamical parameters because the latter are determined by processes occurring near the axis of symmetry, due to the phenomenon of radiation freezing.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 101–106, January–February, 1972.     

Gas-dynamic processes in a strongly radiation-heated layer of gas which accelerates a barrier

Numerical methods involving two variables have been used to study gasdynamic processes in a gas layer next to a barrier. A flow of gas arises because of absorption by the gas of intense radiation. It is shown that cumulative effects can occur leading to the establishment of a quasisteady flow and heating regime if the radiation is applied for a prolonged period.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 131–137, November–December, 1982.     

Calculation of the boundary layer of a transparent gas on a radiating surface

Heat transfer in the laminar boundary layer of a transparent gas flowing aroud a plane radiating surface is studied. Radiative heat-transfer processes in gases may be divided into two main groups. The first involves heat transfer in absorbing and radiating media. In this case, the effect of radiation lies in the introduction of new terms into the energy equation, representing internal heat sources and sinks. The second group embraces heat-transfer processes in a transparent gas when the effect of radiation on convection expresses itself solely by way of the boundary conditions. Here we study a case of practical importance belonging to the second group: heat transfer in the laminary boundary layer of a transparent gas flowing around a flat plate with the thermal flux q_w specified on its surface.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–110, January–February, 1972.     

Investigation of an Electromagnetic Pulse Generated by a System on a Standard Spacecraft

Results on generation of an electromagnetic pulse on a spacecraft under the action of X-ray and gamma radiation are described. The computational technology used is based on a hierarchical system of mathematical models constructed on a system of the Maxwell-Vlasov equations and spacecraft models that rather accurately describe all physical processes typical of origination of secondary electromagnetic fields and the object geometry. It is shown that polarization components of the electric field, which are directed normal to irradiated surfaces, depend weakly on geometric factors and are mainly determined by the photon radiation flux density. Formation of the magnetic field is determined by the dynamics of variation of the first derivative of the dipole moment of the electron layer formed owing to emission of particles under the action of ionization radiation and depends on the object shape, characteristic size of the irradiated surface, and spacecraft attitude.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 3–13, September–October, 2005.     

Motion of a gas shock layer with a free boundary under nonadiabatic conditions

This paper is a study of the effect of heat input (removal) on the characteristics of a shock layer produced by a gas at high supersonic velocity encountering a mobile boundary, which for generality is assumed to be free. We will use the Chernyi method, which was employed previously to solve the problem of a shock layer in an adiabatic flow [1, 2]. The results obtained can be useful for analysis of the effect of radiation (absorption) and processes involving the relaxation of internal degrees of freedom of molecules, condensation, chemical reactions, etc., whose effect on the gasdynamics of the flow in a shock layer may be similar to heat input or removal [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 152–154, May–June, 1976.The author thanks A. K. Rebrov for discussion of the results.     

Hypersonic flow past a wing at large angles of attack with detached shock wave

The thin shock layer method [1–3] has been used to solve the problem of hypersonic flow past the windward surface of a delta wing at large angles of attack, when the shock wave is detached from the leading edge (but attached to the apex of the wing) and the velocity of the gas in the shock layer is of the same order as the speed of sound. A classification of the regimes of flow past a delta wing at large angles of attack has been made. A general solution has been obtained for the problem of three-dimensional hypersonic flow past the wing allowing for nonequilibrium physicochemical processes of thermal radiation of the gas at high temperatures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 149–157, May–June, 1985.     

Influence of nonequilibrium radiation on rarefied gas flow around blunt bodies

The hypersonic nonequilibrium rarefied gas flow is investigated in the neighborhood of the stagnation streamline ahead of a blunt body by taking into account nonequilibrium radiation due to electron excitation for air and carbon dioxide. The analysis is on the basis of a numerical solution of the Navier—Stokes equations simplified under the assumption of local self-similarity of the flow with the Shockwave structure taken into account. It is shown that at low densities, when the shock wave and shock layer thicknesses are of the same order of magnitudes, the two-layer Cheng model becomes inapplicable in the presence of radiation. In this case, the governing process is diffusion of the electronically excited molecules from the shock layer into the forward part of the shock front. The mechanism of the formation of a second luminous plateau on the diagram of the nonequilibrium radiation intensity density is discussed. The combined influence of the limit in collisions and the diffusion transport processes on the intensity of molecular band radiation is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 81–87, November–December, 1974.The author is grateful to V. V. Lunev for discussion and remarks during performance of the research.     

Investigation of flow past blunt bodies with allowance for radiation by the large-particle method

Much recent work has been done on developing methods of solving gas-dynamic problems in which radiation plays a part (see, for example, [1–7]). This is because the temperature in the shock layer associated with flight in the atmosphere at hypersonic velocities can reach values exceeding 10⁴ °K. In such a case, heat transfer by radiation can make an important contribution to the total heat transfer. With increasing flight velocities, the importance of radiation in heat transfer increases and then becomes predominant. In the present paper, the large-particle method as developed by Belotserkovskii and Davydov [8] is developed to calculate flows with radiation around blunt bodies, including the case when there is distributed blowing from the surface of the bodies into the shock layer, which simulates ablation of a heat-shielding covering under the influence of strong heating by radiation. The results are given of systematic calculations of flow past blunt bodies of various shapes by a stream of radiating air, and the results are compared with the data of other methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1982.     

Unsteady thermocapillary convection in a nonuniformly heated fluid layer

In many technological processes, thin extended layers of nonuniformly heated fluid are used [1–3]. If they are sufficiently thin, thermocapillary forces have a decisive influence on the occurrence and development of motion of the fluid [4–6]. Investigation of convective motion in such a layer is of great interest for estimating the intensity of heat and mass transfer in technological processes. This paper is a study of unsteady thermocapillary motion in a layer of viscous incompressible fluid with free surface in which a thermal inhomogeneity is created at the initial time. Approximate expressions are obtained for the fields of the velocity, temperature, and pressure in the fluid, and also for the shape of the free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1991.     

Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

Nonlinear Disturbances and Weak Discontinuities in a Supersonic Boundary Layer

The processes of wave disturbance propagation in a supersonic boundary layer with self-induced pressure [1–4] are analyzed. The application of a new mathematical apparatus, namely, the theory of characteristics for systems of differential equations with operator coefficients [5–8], makes it possible to obtain generalized characteristics of the discrete and continuous spectra of the governing system of equations. It is shown that the discontinuities in the derivatives of the solution of the boundary layer equations are concentrated on the generalized characteristics. It is established that in the process of flow evolution the amplitude of the weak discontinuity in the derivatives may increase without bound, which indicates the possibility of breaking of nonlinear waves traveling in the boundary layer.     

Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

Structure of the heating layer ahead of the front of a strong intensely emitting shock wave

The problem of the structure and brightness of strong shock waves arises in the investigation of such phenomena as the motion of large meteoroids in the atmosphere, optical and electrical discharges, the development of strong explosions, and other similar processes and in the creation of powerful radiation sources based on them. This problem also has a general physics interest. As the propagation velocity of a strong shock wave increases the gas temperature behind its front and the role of emission grow. Part of the radiation emitted by the gas heated and compressed in a shock wave is absorbed ahead of the front, forming the so-called heating layer. The quasisteady structure of a strong intensely emitting shock wave was studied in [1, 2]. In this case a diffusional approximation and the assumption of a gray gas were used to describe the radiation transfer. They introduced the concept of a wave of critical amplitude, when the maximum temperature T_- in the heating layer reaches the temperature T_a determined on the basis of the conservation laws, i.e., from the usual shock adiabat; it is shown that behind a compression shock moving through an already heated gas there is a temperature peak in which the maximum temperature T₊ exceeds T_a. The problem of the quasisteady structure of an emitting shock wave in air of normal density was solved numerically in [3]. The angular distribution of the radiation was approximately taken into account — it was assigned by a simple cosinusoidal law. The spectral effects were taken into account in a multigroup approximation. They introduced 38 spectral intervals, which is insufficient to describe a radiation spectrum with allowance for the numerous lines and absorption bands.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1978.     

Method of effective sections to take account of selectivity of radiation and absorption in a hot gas

A method, economical in computing time, for solving radiation transfer problems by using the integrated characteristics of the absorption spectrum, the effective sections, is elucidated. The shock layer ahead of a body around which a hypersonic gas flows is analyzed in the presence of intensive mass delivery from the surface. The machine time in the computational examples is shortened 120-fold as compared with an exact computation, and the error in calculating the radiation fluxes does not exceed 15–25%.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi FizikL, No. 5, pp. 76–83, September–October, 1972.The author is grateful to G. A. Tirskii for supervising the research and to É. S. Filippov for aid in carrying out the computations.     

Supersonic transverse rarefied gas flow past a strip

The supersonic flow of a monatomic gas consisting of hard spherical particles past a flat strip normal to the flow is investigated using the direct simulation Monte-Carlo (DSMC) method. The calculations are performed over the Knudsen and Mach number ranges 0.015–5 and 1.8–15, respectively. The structure of the compressed layer and the aerodynamic characteristics are systematically studied for the Mach number 5 and various Knudsen numbers. The dependences of the compressed-layer thickness in molecular free paths are found. The nonequilibrium processes in the neighborhood of the strip are described on the basis of the data on the temperature anisotropy with respect to three coordinates.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 159–167. Original Russian Text Copyright © 2005 by Maltsev and Rebrov.     

Relaxation of a liquid layer under the action of capillary forces

The theory of creeping motion is used to study the relaxation of an infinite viscous fluid layer (membrane) of nonuniform thickness. The propagation of boundary perturbations in a semi-infinite layer under the action of surface-tension forces is also considered. The layer has at least one common boundary with a gas. It is found that relaxation processes of an infinite layer or the propagation of boundary perturbations inside a bounded layer are non-monotonic, and that wave-like surface perturbations always arise. Relaxation times are determined. Maximum distances are found over which separate regions of the layer can affect each other.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 73–77, January–February, 1970.The author wishes to thank V. G. Levich for discussions.     

Influence of the macrotransport processes in gases on the change in the hydrodynamic parameters in the presence of a resonance radiation pulse

The effect of a resonance radiation pulse on the gas parameters is investigated. It is assumed that the pulse duration is large enough for the diffusion and heat conduction to be taken into account. It is shown that the diffusion and heat conduction may be significantly influenced by the processes of excitation of the internal degrees of freedom of the molecules.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 120–128, July–August, 1992.     

Nonmonotonic dependence of the convective heat flux on the rate of blowing of opaque admixtures into a radiating H-He shock layer

The results are given of calculations of radiative and convective heat transfer in a radiating H-He shock layer in the neighborhood of the stagnation point of a blunt body when graphite ablation products are blown from the surface. It is found that under the conditions in the shock layer characteristic for motion of the body in the atmosphere of Jupiter [3] the dependence of the convective flux on the blowing rate is essentially nonmonotonic. The maximal value is comparable with the radiative flux to the surface under these conditions. It is shown that a decisive part in the mechanism which increases the convective flux is played by the presence near the surface of particles which effectively absorb radiative energy in the spectral regions in which an appreciable radiation flux reaches the boundary layer; the difference between the transport properties of the blown and the oncoming gases is also important.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 106–113, May–June, 1981.     

Radiative and convective heat transfer in hypersonic flow around a blunt body

The heat transfer in the vicinity of the critical point is investigated for hypersonic air flow around a blunt body. The gas-dynamical conservation equations are solved simultaneously with the radiative transport equation in integral form. Allowance is made for the viscosity, heat conduction, and the actual radiation parameters of air, including spectral line emission. Profiles are obtained for the thermodynamic variables along the critical line. The dependence of the radiative and convective components of the aerodynamic heating on the velocity and pressure ahead of the shock front as well as the radius of curvature of the blunt nose section is discussed. Approximate relations having the form of similarity laws are derived for the heat fluxes in the vicinity of the critical point. The limits of applicability of the thermodynamic equilibrium approximation in the shock-compressed layer are discussed. The influence of absorption of radiation from the compressed layer by the cold freestream on the aerodynamic heating is considered. Attention is given in this case to the dependence of the spectral absorption coefficient for the cold air on the intensity of the radiation incident upon it.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–123, September–October, 1972.