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.     

Different modes of heating when high-power radiation fluxes interact with a material

The gas-dynamic and thermal processes which occur when a high-power flux of laser radiation interacts with a material are investigated. Fluxes for which the sublimation energy can be neglected compared with the thermal and kinetic energy of the vapors formed are considered. The electron thermal conductivity is considered as well as the hydrodynamic dispersion. The properties of different modes of propagation of temperature waves in a moving medium are studied. The case of an infinitely large absorption coefficient is given particular attention.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 41–48, September–October, 1972.The authors thank A. A. Samarskii for useful discussions.     

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.     

Vaporization of matter through interaction with intense energy fluxes

Surface and volume mechanisms for the evaporation of matter through interaction with intense radiation fluxes are discussed. Calculations are performed which assume the existence of both fluctuation and steady-state bubbles in a material and which include superheating of the material ahead of the inward-travelling vaporization wave. The dependence of the incident energy flux density on the average thickness of the energy deposition zone for which the transition from surface to volume vaporization occurs is obtained for aluminum, copper, and lead.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnichekoi Fiziki, No. 5, pp. 49–57, September–October, 1972.The author thanks I. V. Nemchinov for suggesting the topic and for valuable discussions.     

Analytic investigation of friction and heat transfer in the neighborhood of a three-dimensional stagnation point at low and moderate Reynolds numbers

A study is made of hypersonic three-dimensional flow of a viscous gas past blunt bodies at low and moderate Reynolds numbers with allowance for the effects of slip and a jump of the temperature across the surface. The equations of the three-dimensional viscous shock layer are solved by an integral method of successive approximation and a finite-difference method in the neighborhood of the stagnation point. In the first approximation of the method an analytic solution to the problem is found. Analysis of the obtained solution leads to the proposal of a simple formula by means of which the calculation of the heat flux to a three-dimensional stagnation point is reduced to the calculation of the heat flux to an axisymmetric stagnation point. A formula for the relative heat flux obtained by generalizing Cheng's well-known formula [1] is given. The accuracy and range of applicability of the obtained expressions are estimated by comparing the analytic and numerical solutions. Three-dimensional problems of the theory of a supersonic viscous shock layer at small Reynolds numbers were considered earlier in [2–5] in a similar formulation but without allowance for the effects of slip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–150, March–April, 1988.     

Nonreacting chemical transport in two-phase reservoirs — Factoring diffusive and wave properties

The vertical transport of mass, energy andn unreacting chemical species in a two-phase reservoir is analysed when capillarity can be ignored. This results in a singular system of equations, comprising mixed parabolic and hyperbolic equations. We derive a natural factorisation of these equations into diffusive and wave equations. If diffusive or conductive effects are important for onlyN–1 of the chemical species, then there areN parabolic equations, andn+2–N wave equations. Each wave equation allows for the corresponding variable to be discontinous, or equivalently, for shock propagation to occur. Steady flows were shown to allow for more than two (vapour and liquid dominated) saturations for a given mass, energy and chemical flux, but when thermal conduction and chemical diffusion are unimportant, only the vapour and liquid dominated cases appear likely to occur. For infinitesimal shocks there is a continuous flux vector for each diffusive variable. The existence of these continuous flux vectors results in significant simplifications of the corresponding wave equations. It remains an open question if continuous flux vectors exist for finite shocks. General expressions are obtained for the diffusion and wave matrices, which require no knowledge of continuous flux vectors.     

Parameters of a stationary radially symmetrical jet of vapors heated by laser radiation

The solution [1] of the problem of the stationary radially symmetrical movement of vapors heated by monochromatic radiation is generalized for the case of an arbitrary (tabular) dependence of the coefficient of absorption and the adiabatic index on the temperature and density. The calculations of thermodynamical and optical properties of vapors of a number of elements carried out in a wide range of densities and temperatures and the solution referred to made it possible to determine the parameters of a stationary jet of vapors in a wide range of radiation flux densities and characteristic dimension. Some results of the calculations for carbon and aluminum are presented. It turns out that a characteristic property of the distribution pattern of parameters in a jet of vapors is the presence on the surface of a zone of cold vapors and a zone of their heating — the heating wave front. However, for large radiation flux densities the extent of the zone of cold vapors is not large. A rough estimate of the intensity of reradiation of the heated vapors is derived. It is shown that for characteristic dimensions of the vapor layer on the order of 0.3–1 cm the intensity of reradiation can be high enough that the pattern of movement found without considering reradiation can change somewhat. It is shown that the solution examined can be generalized also to the case where the transfer of energy by radiation of the continuous spectrum is taken into account.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 58–75, September–October, 1972.The authors are grateful to V. V. Novikova for great assistance in conducting the calculations for the stationary state problem and analyzing their results and to L. P. Markelova and V. A. Onishchuk for help in conducting the calculations of the thermodynamic and optical properties of the vapors.     

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.     

Initiation of Combustion in a Supersonic Hydrogen-Air Mixture Flow by CO<Subscript>2</Subscript>-Laser Radiation

Features of the ignition kinetics of an H₂/air mixture in the supersonic flow behind an inclined shock front are analyzed when asymmetric vibrations of a small amount (<1%) of O₃ molecules specially introduced into the initial mixture are excited by 9.7 μm wavelength radiation. It is shown that this radiation leads to intensification of the chain reactions and makes it possible to organize combustion at small distances from the front (of the order of 1 m) of even relatively weak shocks at small values of the laser radiation energies absorbed by the gas. This method of initiating combustion in a supersonic flow is 10–100 times more efficient than the thermal method.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 157–167.Original Russian Text Copyright © 2005 by Lukhovitskii, Starik, and Titova.     

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.     

Distribution of radiant thermal flux over the surface of a sphere for hypersonic flow of a nonviscous radiating gas past the sphere

In the present study using the Newtonian approximation [1] we obtain an analytical solution to the problem of flow of a steady, uniform, hypersonic, nonviscous, radiating gas past a sphere. The three-dimensional radiative-loss approximation is used. A distribution is found for the gasdynamic parameters in the shock layer, the withdrawal of the shock wave and the radiant thermal flux to the surface of the sphere. The Newtonian approximation was used earlier in [2, 3] to analyze a gas flow with radiation near the critical line. In [2] the radiation field was considered in the differential approximation, with the optical absorption coefficient being assumed constant. In [3] the integrodifferential energy equation with account of radiation was solved numerically for a gray gas. In [4–7] the problem of the flow of a nonviscous, nonheat-conducting gas behind a shock wave with account of radiation was solved numerically. To calculate the radiation field in [4, 7] the three-dimensional radiative-loss approximation was used; in [5, 6] the self-absorption of the gas was taken into account. A comparison of the equations obtained in the present study for radiant flow from radiating air to a sphere with the numerical calculations [4–7] shows them to have satisfactory accuracy.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 44–49, November–December, 1972.In conclusion the author thanks G. A. Tirskii and É. A. Gershbein for discussion and valuable remarks.     

Role of bubble boiling in the interaction of intense radiation with matter

The model of stable evaporation [1–4] is widely used to study the interaction of intense radiation with matter. In this model the radiation flux normally incident on a planar surface of the body is constant in magnitude, which also guarantees stationarity of parameter distributions in a coordinate system related to the surface. An assumption of the model is that evaporation occurs at the surface only. As noted in [1, 2], however, in establishing metal evaporation the surface is found to be in a liquid overheated state. Consequently, the evaporation mechanism can be complicated by bubble boiling. This process is usually neglected due to the fact that the surface tension coefficient of metals is large (if the temperature is not too close to the critical temperature), and, consequently, the probability of bubble formation is low [2]. Quantitative estimates are needed to justify this statement. Such estimates were carried out in [5, 6], where it has been shown that there exists a certain intensity flux q_*, above which surface evaporation is modified by bulk boiling. A number of inaccuracies, however, were admitted in [5, 6], which, as shown below, strongly distort the boundaries of the evaporation mechanisms in several cases. The purpose of the present study is to remove these inaccuracies and calculate the quantity q_* more correctly.Translated from Zhumal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 35–44, May–June, 1979.The author is grateful to M. N. Kogan and N. K. Makashev for useful discussions.     

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.     

Numerical calculation of the problem of cooling of a spherical volume of nonequilibrium-ionized radiating helium

The method is described and the results are presented for numerical calculations of a system of equations of nonsteady gasdynamics, radiation transfer in the continuous spectrum, and the kinetics of collisional ionization and ionization by radiation, which describe the dispersion and cooling of a spherical volume of He. A comparison is made with calculations performed on the assumption of thermodynamic equilibrium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 36–41, March–April, 1976.     

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.     

Effects of the interaction between radiation and a disintegrating vitreous material

This article considers the disintegration of a vitreous semitransparent material at the critical point in a stream of radiating gas. A study is made of the effect on the rate of disintegration of the indeterminacy of the effect of interaction between the radiation and the gaseous disintegration products and of the spectral distribution of the density of the radiation flux of the gas with respect to the semitransparancy of the material. An analysis of the error of the gray approximation with calculation of the disintegration of materials with a semitransparency window is also given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 133–137, September–October, 1978.     

On radiative heat transfer in a plane layer of an absorbing medium

Recently there has arisen increased interest in the study of radiative heat transfer between geometrically simple systems, both as autonomous problems and as elements of more complex problems.Problems of this kind have been treated by many authors [1–111 who have considered gray, diffusely emitting and absorbing boundaries and gray nonscattering media. In most cases these investigations were restricted either to the derivation of approximate formulas for the net radiative flux, without an exact analysis of the temperature distribution in the layer [5–7], or to numerical computation [1–4], In the latter case, with the exception of [8], which contains a numerical analysis for the case of optical symmetry, no attempt was made to analyze the effect of the optical properties of the boundaries on the temperature field in the layer.These papers can be divided into two groups according to the method of analysis used. The first group includes papers based on the integral equations of radiative transfer, with the corresponding integral analytical methods [1, 2], Similar in nature are [3, 4] which use the slab method, applicable to electrical-analog computation, as well as a recent paper [8] based on probability methods.The second group of papers [5–7] is based on the so-called differential methods. Of particular interest is [7], which develops these methods to an advanced degree. In several papers the problem of radiative transfer is analyzed in conjunction with more complex problems (cf., e.g. [10, 11]).In the present work we shall attempt to carry out an approximate analytical study of problems connected with radiative heat transfer in a plane layer of an absorbing, emitting, nonscattering gray medium with temperature-independent optical properties. The layer is bounded by two parallel, diffusely emitting and diffusely reflecting, isothermal, gray planes.The paper presents the fundamental formulation of the problem, which consists in: (a) the determination of the net heat flux on the basis of given temperature distribution (direct formulation), and (b) the determination of the temperature distribution on the basis of given distribution of the net radiative heat source per unit volume and boundary temperatures (inverse formulation). The analysis is based on integral methods appropriate to the integral equations which represent the net total and hemispherical radiation flux densities [12].The author would like to thank S. S. Kutateladze for his interest in this work.     

Effect of rotational degrees of freedom of molecules on energy flux in attenuated gas

On the basis of model kinetic equations a solution is obtained by a numerical method for the flow of attenuated gas around a sphere. The effect of rotational degrees of freedom on the energy flux to the body is investigated. Values of the ratio between the energy flux Q and its free-molecular value Q* for monatomic and diatomic gases are compared; for the comparison, the dimensionless temperature of the body, the gas velocity at infinity, and the law of viscosity must be the same in the two cases. For sufficiently cold bodies (when the body temperature is below the equilibrium temperature for a diatomic gas) the difference between Q/Q* for monatomic and diatomic gases is insignificant. For a diatomic gas when the body temperature is close to equilibrium, the ratio Q/Q* is found to have a nonmonotonic dependence on the Knudsen force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 119–124, September–October, 1977.     

Interface crack with a contact zone in an isotropic bimaterial under thermomechanical loading

A plane problem for a thermally insulated interface crack with a contact zone in an isotropic bimaterial under tension–shear mechanical loading and a temperature flux is considered. The expressions for the stresses and the electrical flux as well as for the derivatives of the displacement and the temperature jumps at the material interfaces via sectionally holomorphic mechanical and thermal potential functions are given. After the solution of the thermal problem the inhomogeneous combined Dirichlet–Riemann boundary value problem is formulated and solved exactly. The stresses at the interface and the stress intensity factors at the singular points are presented in a clear analytical form. Special attention is devoted to the case of a small contact zone when the stress intensity factors can be presented in form similar to the associated presentation for an “open” crack model. A transcendental equation and an asymptotic analytic formula for the determination of the real contact zone length are derived. It is shown that for a certain bimaterial this length as well as the correspondent stress intensity factor are defined by a single parameter which depends on the normal-shear loading and the heat flux.     

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.