Radiating hydrogen flow in axisymmetric nozzles

A considerable number of studies published in recent years have been devoted to the study of gas in channels and pipes. In view of the complexity of the question and the lack of analytic techniques, individual aspects of the problem are generally considered. The determination of the radiant field characteristics in regions of simple geometric form filled with a stationary radiating-absorbing medium has been carried out in several studies. The articles [1–3] are devoted to the calculation of the radiant field and the temperature field for a given flow of a perfect inviscid nonheat-conducting radiating gas with constant absorption coefficient. The flow is assumed to be irrotational [1, 2] or nearly potential [3]. The authors investigated the accuracy of the solution obtained with the aid of various approximate methods and found that the diffusion approximation yields a small error in calculating the radiation density field and the values of the radiant thermal fluxes for a quite broad class of wall reflecting properties. We may note also [4, 5], in which a calculation is made of one-dimensional steady flow of a viscous heat-conducting radiating perfect gas with constant transport coefficients.In [1–5] the absorption coefficient is considered constant. This assumption simplifies the solution process considerably, since as the independent variables we can take the corresponding optical thicknesses. The study [3] contains a remark that the calculation method proposed there may be used with a variable absorption coefficient. However, this possibility was not used in the calculations presented.For a constant absorption coefficient these studies yield a rather complete analysis of the methods for solving two-dimensional problems in geometrically simple regions in the absence of mechanical motion and one-dimensional problems with motion. They contain results obtained for the exact integral or integrodlfferential equations and present an analysis of the approximate methods. The study [3] considers broader possibilities of solving two-dimensional problems (using the Monte-Carlo method), but the flow is assumed known ahead of time.In the following we present a method for calculating the two-dimensional equilibrium flow of an inviscid non-heat-conducting radiating gas with variable absorption coefficient. As an example, we consider the flow of radiating-absorbing hydrogen in axisymmetric nozzles. It is assumed that the radiation is gray and is in local thermodynamic equilibrium. The transport equation is considered in the diffusion approximation. The nozzles examined have a semi-infinite cylindrical inlet section. The initial gas flow in the cylindrical section is supersonic. In the solution process we determine the radiation density field and all the flow parameters within the nozzle.The author wishes to thank Yu. D. Shmyglevskii for his continued interest in this study.     

One class of self-similar flows of a radiating gas

This article discusses self-similar statements of the problem of the motion of a completely radiating and absorbing gas. The field of radiation is assumed to be quasi-steady-state, and the contribution of the radiation to the internal energy, as well as the pressure and the viscosity of the medium, are not taken into account. The presence of local thermodynamic equilibrium is assumed. The absorption coefficient is approximated by a power function of the pressure and the density. Scattering of the radiation is not taken into account. Under these assumptions, there exist self-similar statements of the problem for one-dimensional unsteady-state flows (a strong detonation, the problem of plug-flow, motion under the effect of a radiation source, and others) and two-dimensional steady-state flows (flow in a diffuser, supersonic flow around a wedge or a cone). It is shown that there exists a non steady-state spherically symmetrical flow depending on four parameters; this flow is adiabatic in spite of the presence of radiation. This article is made up of seven sections. It is shown in the first section that the presence of radiation leads to the appearance of new dimensional constants, entering into the equations of the problem. The second section is devoted to self-similar nonsteady-state one-dimensional flows. The third section contains a detailed study of one class of such flows. In a partial case, adiabatic flows of a radiating gas are obtained. In the fourth and fifth sections, a detailed analysis is made of the initial and boundary conditions from the point of view of dimensionality. The sixth section describes self-similar two-dimensional steady-state flows of a radiating-absorbing gas. The seventh section consists of remarks with respect to approximations of the transfer equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 8–22, July–August, 1970.     

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.     

Calculation of the kinetics of propagation of a powerful light beam in a transparent dielectric with impurities

A large number of studies have been dedicated to the interaction of powerful optical radiation with transparent dielectrics in the prebreakdown or breakdown regimes. However, the mechanism by which the material is destroyed has not been determined decisively, as indicated by the constant flow of new publications on this theme. Attempts to obtain destruction as the result of electron avalanche [1] give threshold power values orders of magnitude greater than experiment [2]. In connection with this, in recent years the accent has been to deal with the concept of microimpurities of foreign particles or inhomogeneities within the medium having dimensions so small that their presence and concentration is difficult to monitor. As it absorbs optical radiation, the microimpurity (inhomogeneity) is heated and warms the areas of the medium adjacent to itself, which areas then commence to absorb light with significantly more intensity than they did in the initial state [3]. As a result, increase in absorption within the medium commences, terminating in breakdown or destruction of the material around the inhomogeneity. In [4, 5] it was noted that an important role may be played in such a destruction mechanism by thermoelastic stresses in the medium, which factor was not considered in [3]. In [4, 5] it was proposed that the basic effect of thermoelastic stresses reduces to development of microfissures in the medium. However, thermoelastic stresses can lead to yet another effect — narrowing of the forbidden zone of the medium and increase (together with the analogous action of temperature growth) in the coefficient of absorption of the medium. In the present study, the kinetics of interaction of optical radiation with a dielectric medium containing spherical metal particles as an impurity will be calculated, and it will be shown that thermoelastic stresses produce a significant contribution to the increase in light absorption by the medium around a particle.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 60–66, September–October, 1978.     

Radiation parameters of an air flow heated in an electrodeless high-frequency plasma generator

The experimental results of measurements of the radiation parameters of a high-temperature air flow are discussed. The temperature, electron density, and absorption coefficient are measured by spectral methods. The presence of local thermodynamic equilibrium in the plasma is demonstrated. The measured spectral absorption coefficient of the plasma for T = 8500 °K in the wavelength range 0.26–0.9 is compared to the calculated values.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 44–50, November–December, 1977.The authors thank Yu. K. Rulev fox his help in performing the experiments.     

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.     

Measurement of amplification coefficients

This study will perform an analysis of errors occurring in the measurement of the coefficient of amplification of the optical medium of a laser by the method of irradiation with monochromatic laser radiation. These errors are related to lack of correspondence in parameters of the probe laser and the laser to be measured.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 3–12, May–June, 1974.     

Water vapor cooling when radiation of wavelength λ=2.8 μm is absorbed

Investigations of the processes arising under the influence of electromagnetic radiation on resonantly absorbing gaseous media have now been widely developed. Particular interest is shown in the penetration of a pulse of laser radiation through the atmosphere. The main component absorbing the radiation of both CO₂ and HF lasers (wavelengths, respectively, 10.6 and 2.8 m) in the earth's atmosphere is water vapor [1]. Numerous experimental investigations show that the integrated coefficient of laser radiation absorption by water vapor is fairly large [1–3], while at the same time the energy absorption leads to the heating of the medium in a channel around the beam and, as a consequence, to its defocusing. However, all these investigations were carried out with continuous sources of laser radiation or with pulses of fairly great duration. It will be shown below that gas cooling in the channel around the beam is possible when a pulse of radiation with wavelength 2.8 m whose duration is less than the vibrational-translational (V-T) relaxation time of the energy absorbed by the H₂O molecules passes through a stationary medium containing water vapor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 141–151, May–June, 1986.     

A method of calculating the radiation flux and its divergence in regions with stepped temperature and chemical composition distribution

An approximate method is proposed which makes it possible to compute the radiation flux and its divergence when the absorption cross section depends in a complex manner on the wavelength. Radiation scattering is ignored. The method is described for the case when the region occupied by the radiating and absorbing gas can be divided into finite number of subregions in which the temperature and the chemical composition are constant. Examples are given of the numerical calculations of the radiation flux.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 54–62, March–April, 1971.The author wishes to express his gratitude to É. Filippova for help in the computations.     

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.     

Interaction of a wave with an obstacle in a multicomponent two-phase medium

The author's model [1] of a multicomponent liquid medium with nonlinear limiting compression diagrams and constant coefficient of viscosity is improved by the introduction of a coefficient of viscosity that varies during the deformation. The new model is used to obtain a numerical solution to the problem of the propagation of a plane wave produced by a shock load and the interaction of the wave with a fixed obstacle. Such a problem was solved earlier [2] in the case of a viscous medium for linear diagrams of static and dynamic compression and constant coefficient of viscosity. It is shown that the nonlinearity of the diagram of static compression leads with increasing pressure first to an increase in the reflection coefficient and then to a decrease of it. If the load has a sufficient duration, the initial section of the obstacle is subject to a succession of several waves, the number of which increases with increasing duration and amplitude of the load. The calculation was made for glycerine with air bubbles. It is assumed that at pressures up to 400·10⁵ N/m² glycerine is a linearly elastic medium In this case, the dynamic compression diagram of the two-component glycerine—gas-bubble medium is linear.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 183–187, May–June, 1981.I thank Yu. A. Sozonenko for discussion and valuable comments.     

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.     

Modeling of Heat and Mass Transfer in Absorption in Two–Phase Binary Systems used in Heat Pumps

Results of modeling of heat– and mass–transfer processes proceeding simultaneously in vapor absorption on tube banks are described. Theoretical models of film absorption are presented. The calculation results are compared with experimental data on steam absorption by the lithium bromide solution on a vertical tube. In calculation of transfer processes in absorption on horizontal tubes, the possibility of using solutions for the initial thermal length and for the section with a linear temperature profile is substantiated. The calculations are illustrated by the example of a multipass absorber.     

Steady two-phase flow in a vertical tube subject to combined free and forced convection

Using the two-velocity, two-temperature model of a continuous medium, the viscousgravitational flow of a mixture of incompressible liquid and solid particles in a vertical round tube is considered. The free-convection equations are written down on the basis of the general equation of motion and the energy equation of a two-phase medium [1, 2]. Using a finite Hankel integral transformation, a solution is constructed for the case of a linear wall-temperature distribution along the tube. The results of some practical calculations of the velocity and temperature fields over the cross section of the tube are presented, together with the dimensionless heat-transfer coefficient expressed as a function of the Rayleigh number and phase concentration. Here it is assumed that the dynamic and thermal-interaction coefficients between the phases correspond to the Stokes mode of flow for each particle, as a result of which the velocity and thermal phase lag is very small [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 132–136, July–August, 1975.     

Some self-similar solutions of two-temperature hydrodynamic equations with allowance for nonlinear heat conduction and exothermic reactions

Processes occurring in plasma produced as a result of the interaction of powerful radiation fluxes with matter can be divided into three stages: absorption of radiation on the matter boundary, subsequent heating and compression of the central part of the target for the purpose of creating the conditions necessary for the initiation of an exothermic reaction and, finally, propagation of an exothermic reaction wave through the ambient matter. The present paper is devoted to an investigation of the last stage, a reaction wave igniting initially cold matter. The main method for the theoretical investigation of the processes described is a numerical solution of the equations of motion of a two-temperature gas with allowance for the physical processes occurring in a completely ionized medium: electron heat conduction, radiative losses, energy transfer between electrons and ions, and others. In view of the complicated nonlinear nature of the system of partial differential equations describing the process, searches for possible self-similar solutions are of interest. These solutions can be used as tests in calculating a complete system of equations; by means of them it is also possible to investigate asymptotic laws of exothermic reaction wave propagation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 145–151, March–April, 1986.     

Calculations for a cylindrical electric arc with allowance for energy transfer by radiation with the hydrogen at a pressure of 100 atm

An approximate method is described for the consideration of energy transfer by radiation during the utilization of real properties of a gas (in particular, the frequency-dependent absorption coefficient under conditions of local thermal equilibrium). With increasing pressure, it becomes necessary to take self-absorption into account over almost the entire frequency spectrum.Calculations are carried out for a wall-stabilized cylindrical electric arc in hydrogen as an example for a pressure of 100 atm and channel radii of 0.3, 1, and 3 cm at values of current strength up to the order of 10 A. The strong effect of radiation on the current-voltage characteristic of the arc, the gas temperature, and the nature of its distribution over the arc radius is demonstrated.The process of energy transfer by radiation plays a significant and sometimes predominant role in the thermal balance of electric arcs with high current strengths [1–9]. Calculations have been performed for cylindrical arcs in atmospheres of argon and hydrogen [5, 7] with allowance for energy transfer by radiation and for atmospheric pressure in which case the gas is essentially transparent to radiation. Approximate estimates were obtained for the self-absorbed portion of the radiation.The role played by radiation increases with increasing current strength, arc radius, and pressure, while self-absorption in this process extends over an increasingly large region of the spectrum. Hence, calculations must be carried out for the arc if conditions are such that the gas in the arc does not transmit radiation.In [10–13], an approximate method was developed for taking into account energy transfer by radiation in the presence of intense selfabsorption as applied to heat transfer problems under conditions of local thermal equilibrium with allowance for the variation of the absorption coefficient as a function of the frequency. The conditions for local thermal equilibrium in an arc passing through an argon or hydrogen atmosphere are fulfilled for pressures greater than atmospheric pressure and for current strengths greater than 10 A [14–16], The results of [10–12] were used as the foundation for calculations based on an electric arc in argon at atmospheric pressure, under which conditions, self-absorption affects only the transitions to the ground state. The part played by radiation in the heat transfer process is smaller than the part played in the energy transfer by conduction. Calculations confirmed the results of [5, 7].The role of energy transfer by radiation in the energy balance of the arc increases with increasing pressure, while in turn, the role of the continuous spectrum increases for the radiation. The results of calculations performed for a wall-stabilized arc burning in an atmosphere of hydrogen at a pressure of 100 atm are given in the present paper. In this case, almost the entire energy supply is lost by radiation. The approximate method of accounting for energy transfer by radiation is demonstrated by an example.Notation and T gas density and temperature, respectively - u velocity - c_p heat capacity of the gas at constant pressure - coefficient of thermal conductivity - coefficient of electrical conductivity - x and r cylindrical coordinates - r₀ channel radius - I current strength - E electric field strength - u ° equilibrium value of radiation energy density - u value of radiation energy density - radiation frequency - divergence of energy flux density transported by radiation - k absorption coefficient - c speed of light - _i emissivity of the i-th region of the spectrum     

Radiation of waves by a sphere harmonically oscillating to-and-fro in a viscous medium

The theory of the radiation of sound by a sphere in an ideal medium is presented in detail in [1–3]. The emission of waves by a sphere oscillating to-and-fro in a viscous incompressible liquid is analyzed in [4, 5]. The present paper gives a precise solution to the problem of the radiation of sound by a sphere oscillating in a viscous medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1970.     

Boundary-layer development in the initial section of a tube with injection

Results are presented of a theoretical and experimental investigation of turbulent boundarylayer development in the initial section of a tube in the presence of injection. It is hence considered that there is no main flow. Formulas are derived to compute the friction coefficient and the dynamic characteristics of the flow in the hydrodynamic stabilization section for subsonic gas-motion velocities. The proposed method of computation is compared with the results of an experimental investigation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 56–59, July–August, 1970.     

Stress–Strain State of a Ferromagnetic with a Paraboloidal Inclusion in a Homogeneous Magnetic Field

The stress–strain state of an infinite elastic soft ferromagnetic medium with an elliptic paraboloidal inclusion is analyzed. The material of the inclusion is a soft ferromagnetic too. The medium is in a magnetic field directed along the minor axis of the elliptic section of the paraboloid by a plane perpendicular to its axis. The main characteristics of the stress–strain state and induced magnetic fields in the medium and inclusion are determined. The features of the stress distribution over the inclusion boundary are studied     

Transfer of energy from an evaporating drop in a vapor medium

The article considers the temperature distribution around an evaporating drop in a vapor medium. The transfer of energy is effected by molecular thermal conductivity, convection, and radiation. The mean length of the free flight path of the radiation considerably exceeds the characteristic distance at which the temperature changes. The times required for relaxation of the temperature to a steady-state value are determined, as well as the characteristic distances at which the temperature distribution changes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 74–78, January–February, 1972.The authors thank V. G. Levich for his evaluation of the results obtained.