The flow of a nonequilibrium ionized radiating gas around a body with consideration of temperature difference between electrons and ions

The flow around a blunt body at hypersonic speed by a current of nonequilibrium ionized monatomic nonviscous radiating gas is studied, with consideration of temperature difference between the electron gas and the ion-atom gas. Atomic excitation due to collisions with electrons and subsequent ionization, as well as photoionization, are taken into consideration. Since the value of the shock wave separation is small in comparison with the characteristic dimension of the body, the radiation transfer equation is written in the local onedimensional planar layer approximation. The influence of incident flow parameters upon the flow field across the shock wave and the distribution of radiation thermal flux are studied.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 9–14, January-February, 1972.     

Radiative relaxation kinetics of shock-heated xenon

The kinetics of the ionization and radiation processes taking place in xenon heated in strong shock waves (Mach numbers on the interval 10–20) are numerically investigated. A fairly complete model of the medium and the processes is used. The influence of the radiation efficiency is taken into account on the assumption that the radiation layer is homogeneous and isotropic at every instant of time. The calculated distribution of plasma brightness temperature along the luminous layer is compared with that measured in shock-tube experiments. The experimental data are satisfactorily described by the modeling.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 157–163, November–December, 1992.     

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.     

The ionization-rate constant at high temperatures high electron concentrations

The electron distribution function and the rate constant for ionization of atoms by electron impacts have been calculated as they apply to the conditions that are characteristic of a shock wave — namely, the energy distribution of the electrons and the ionization-rate constants are determined as functions of the temperature of the heavy particles. The energy dependence of the effective cross section for the excitation of an atom by electron impact is assumed to be linear. Equations of the Fokker-Planck type are used in the solution of the problem, and the range of temperatures and concentrations in which the deviation of the distribution from Maxwellian leads to a substantial change of the ionization-rate constant is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tecknicheskoi Fiziki, No. 2, pp. 32–40, March–April, 1971.     

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.     

Laser heating of its erosional low-temperature plasma in the process of gasdynamic motion

A study is made of the gasdynamical and optical properties of erosional laser plasma jets in the presence and absence of laser radiation. It is shown that in processes of plasma formation during the action of laser radiation of moderate intensity (q 10⁷ W/cm²) on absorbing materials, the heating of the disintegration products by the attacking laser radiation plays an important role. The temperature distribution is obtained along the plasma jet which forms during the laser attack counter to its propagation in a quartz tube confining the dispersion. The temperature maximum is found at the exit from the tube, is caused by the heating of the erosional laser plasma by the incident laser radiation in the process of its one-dimensional gasdynamical motion, and indicates the screening of the surface from the laser radiation. It is established that the screening is affected by the gasdynamical structure of the plasma jet and by the spacing of the plasma clusters corresponding to the regular pulses of laser radiation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 13–18, January–February, 1974.The authors are grateful to M. A. El'yashevich for his interest in the work.     

Vibrational relaxation of diatomic molecules in a non-Boltzmann thermostat

The action of resonance IR laser radiation on a molecular gas leads, at high-power absorption intensity, to a breakdown in the equilibrium (Boltzmann) energy distribution in the internal degrees of freedom [1]. Under realistic conditions, molecular gases usually are (due to small amounts of impurities or isotopic components) multicomponent systems. In this case resonance IR laser radiation (or other methods of selective action), disturbing the distribution function of the primary gas, does not interact directly with impurities. The problem thus arises of determining the distribution function of the impurity gas interacting with the nonequilibrium (non-Boltzmann) thermostat. The present paper, devoted to the solution of this problem, treats the distribution function of harmonic oscillators A, consisting of a small amount of impurities in a system of harmonic oscillators B with given nonequilibrium distribution functions of vibrational energy. The behavior of a system in a nonequilibrium thermostat was first considered in [2, 3] where, as well as in [4, 5], it was shown that in a non-Maxwellian thermostat with a small amount of harmonic oscillator impurities, a Boltzmann distribution in harmonic oscillator vibrational energies is established under stationary conditions, with a temperature differing from the gas-kinetic temperature of the thermostat, defined in terms of the mean-square velocity. The behavior of a small amount of impurities (heavy monoatomic particles and harmonic oscillators) in a non-Maxwellian thermostat of a light gas was further investigated in [6–8]. Unlike the papers mentioned, the present one considers the behavior of a small amount of harmonic oscillator impurities in a thermostat with a Maxwellian velocity distribution and with a nonequilibrium (non-Boltzmann) distribution in vibrational energies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1978.     

Average absorption coefficient for optically thin media

Modifications are considered of the mean Planck absorption coefficient for a section of an absorbing medium adjacent to a source section, taking into account temperature inequalities of blackbody radiation and the absorption cross section of the medium, as well as the effect of the length of the section, which is small. Equations are presented for an analogous coefficient determining self-absorption of radiation by the gas.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 12–15, January–February, 1970.     

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.     

Gelation of a radiation crosslinked model polyethylene

A radiation crosslinked model linear low-density polyethylene (LLDPE) exhibits power-law relaxation,G(t) =St ^–n at its gel point (GP). The relaxation exponent has a value of about 0.46. The relaxation behavior is dominated by power laws, not only directly at GP, but in a very broad vicinity of GP and in a frequency window, which narrows with distance from the gel point. The power law exponent decreases with increasing radiation dose (increasing extent of crosslinking). Independent measurements of the gel fraction and the molecular-weight distribution of the radiated samples' soluble fraction support the rheological observations.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Thermal structure of convective vortex lattices

The thermal structure of the convective motions of a rotating plane layer of fluid is experimentally investigated in the regular vortex structure regime. It is found that in such a system the intense vortex motion leads to a temperature distribution such that the mean fluid temperature falls linearly from the bottom of the layer to the surface, the temperature gradient being determined by the rate of rotation and depth of the fluid. By dimensional analysis it is shown that this gradient corresponds to heat transfer in which the Nusselt number isolines are parallel to the convection curve. The horizontal structure of the temperature field is investigated; it corresponds to motion in which the fluid descends within a narrow vortex-sink and rises along the edges of a cylinder which determines the characteristic dimension of the structure in rotating fluid convection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–166, November–December, 1987.The author wishes to thank G. S. Golitsyn for his constant interest in the work.     

Asymptotic analysis of stationary distribution of the front of a two-stage consecutive exothermic reaction in a condensed medium

An approximate theory of the stationary distribution of the plane front of a two-stage exothermic consecutive chemical reaction in a condensed medium is developed in the article. The method of joined asymptotic expansions is used in constructing the solutions. The ratio of the sum of the activation energies of the reactions to the final adiabatic combustion temperature is a parameter of the expansion. The characteristic limiting states of the stationary distribution of the wave corresponding to different values of the parameters figuring in the problem are shown. Approximate analytical expressions for the wave velocity and distribution of concentrations are obtained for each of the states.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 75–87, January–February, 1973.     

Radiational properties of the decomposition products of a model around which flows a subsonic high-temperature plasma stream

Models made of an asbestos plastic were tested in a subsonic jet of air heated to T = 8500 °K with p = 1 atm. The multicomponent thermal boundary layer arising at the decomposing surface of the model has a complex structure. At the surface of the model, in the critical region of the boundary layer, there is a sublayer with an extension of 1.5-2 mm where the temperature of the gas is constant and its composition is unchanged to a great degree and is mainly determined by the decomposition products of the asbestos plastic. In this region the spectral distribution of the intensity of the radiation of the vapors of the asbestos plastic was obtained in a range of 0.3-0.9, which makes it possible to calculate the spectral coefficients of absorption for a temperature of 3500 °K. The radiating power of the vapors is compared with the radiation of an air plasma of the oncoming flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 76– 80, November–December 1978.The authors are indebted to Yu. K. Rulev for his aid in carrying out the experiment.     

Planar gas flows with weak energy supply

Perfect gas flows in an unlimited space, which occur during rectilinear motion of a system of distributed heat sources, are investigated. The next modes in order of growth of the number M are examined: the heat conductive, convective, subsonic, transonic, supersonic, hypersonic. Examples of computations are presented. Flows with distributed heat sources attract ever-increasing attention. Such flows are important, e.g., in the problem of radiation propagation [1–5], in the analysis of a gasdynamic laser resonator and the optical characteristics of a ray [6]. Changes in the density because of absorption of the ray energy, which can result in an essential redistribution of the radiation intensity, are of great interest in these problems. Theoretical investigations of a general nature with distributed heat supply [7–10] are also important for the development of further applications. Gas flows for a given distribution of relatively weak heat sources switched on at a certain time are examined in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–102, September–October, 1978.     

Experimental investigation of the heat exchange in separation zones ahead of cylindrical obstacles

Results of an experimental investigation of the heat exchange in turbulent boundary layer separation zones ahead of cylindrical obstacles at a subsonic air stream velocity are elucidated. The investigation was conducted for changes in the ratio between the obstacle diameter and altitude between 0.25 and 4, between the boundary layer thickness at the separation point and the obstacle altitude between 0.09 and 0.7, between the Reynolds number computed by means of the free stream parameters and the obstacle height between 10⁴ and 4·10⁵. The Mach number reached 0.85. The temperature factor was 0.7. It is shown that the distribution of the heat transfer coefficients in the separation zone depends on the Reynolds and Euler numbers, the ratio between the boundary layer displacement thickness and the diameter (or altitude) of the obstacle, and the ratio between the diameter and the altitude. Criterial dependences are obtained which extend the heat-exchange results at characteristic points of the separation zones, as are also dimensionless distributions of the heat transfer coefficients to determine the heat fluxes on a plate in the plane of symmetry of the separation zone ahead of obstacles.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 6, pp. 83–89, November–December, 1972.The authors are grateful to V. S. Avduevskii for discussing the research results.     

A method for calculating the two-dimensional temperature field of a reservoir with thermal injection

In [1–3] and other studies devoted to the determination of the temperature field of an oil reservoir when injecting into it a fluid with a temperature different from that of the initial reservoir temperature, the one-dimensional fluid flow (linear or radial) was considered in the case of an injection gallery or a single injection well in the reservoir. The problem was formulated in [4] with an arbitrary distribution of wells, but the solution was obtained only for the integral thermal-loss characteristic. To evaluate the coverage of the reservoir by the thermal effect, we must know the temperature distribution in the multi-well reservoir system at any instant of time. In this paper we propose a method for calculating the reservoir temperature field in the case of two-dimensional fluid flow using the simplifying assumptions which were used earlier by Lauwerier [1] and other authors to describe the thermal phenomena in a reservoir.     

Effect of external radiation on the distortion of a vitreous body in a flow of gas

The semitransparency of a material, which determines the penetration of external radiation into the inside layers, affects significantly the temperature profile in the body [1, 2]. Since the viscosity of a melt of viscous materials depends strongly on the temperature, deformation of the temperature profile close to the surface leads to considerable change of the rate of spread of the liquid film, which has a significant effect on the rate of distortion of the body. In the present paper, the problem of distortion is formulated taking into account the transfer of radiation inside the body. The dependence of the distortion parameters and the degree of blackness of the body on the fraction of radiation in the external thermal flux and the mean free path of the radiation inside the material is determined. A sufficient condition is also obtained for the presence of a temperature maximum inside the body in a more general case than in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–134, July–August, 1976.The author thanks G. A. Tirskii for a discussion of the posing of the problem.     

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.     

Measurement of the cyanogen concentration profile in a thermal boundary layer on models being destroyed by a heat flux

The distribution of the concentration of the CN radical across the boundary layer was obtained in experiments on metals made of high-temperature materials which were placed in an air stream heated to 8500K. The concentration was calculated on the basis of the measured absolute intensity of radiation of the rotational lines of CN with consideration of the temperature profile obtained in [1], A high-frequency electrodeless discharge was used for heating the air.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 139–141, May–June, 1976.