Radiative and convective heat transfer during blowing into a compressed hypersonic layer of two-phase products from the ablation of a covering

The study examines the screening of the radiative heat flux in conditions of hypersonic flow around blunt bodies with ablated carbon-based coverings. In contrast to the studies already known [1–3], allowance is made for the presence of condensed microscopic particles in the products of ablation. In [4] the problem of radiative transfer is considered in a layer of two-phase ablation products with parametrically prescribed dimensions, particle temperature, and layer thickness. The present study uses a closed system of equations which describes the processes of heat and mass transfer. This gives rise to considerable differences in the numerical results, according to the degree of screening.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 161–166, November–December 1985.deceased     

Heat exchange between a selectively emitting liquid and a laminar gas flow in the presence of an external source of radiation

An investigation is conducted in the solution of a number of practical problems of the radiative and combined heat exchange in nonuniform systems having widely different physical properties. The processes of thermal interaction between the ocean and the atmosphere have been treated in the paper [1], the effect of thermal radiation on the melting and solidification of semitransparent crystals has been investigated in [2], the flow of a selectively emitting gas around the lateral surface of an object evaporating under the action of radiative heating has been discussed in [3], and heat transfer from a jet to the molten mass of glass in a glassmaking furnace tank has been investigated in [4]. The radiative and combined heat exchange between a selectively emitting liquid and a transparent heat-conducting laminar gas flow in the case of a specified external thermal radiation field is discussed in this paper. The energy conservation equations are set up taking into account the heat transfer by radiation, convection, and molecular thermal conduction. A differential approximation is used in calculating the values of the radiation fluxes. A system of fundamental computational equations is solved by the method of finite differences and iterations and by the Runge-Kutta method. The results of the calculations are presented in the form of graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 116–122, May–June, 1976.     

Determination of the body shape for minimum radiative heating along a flight trajectory

Space vehicles are subject to intense aerodynamic heating in planetary entry. According to estimates in [1], the heat shield mass for entry of a probe into the atmospheres of the outer planets can make up 20–50% of its total mass; here the radiative component predominates in the aerodynamic heating. It is therefore interesting to investigate methods of reducing the heat flux to the nose region of a vehicle. Analysis shows [2–6] that, for a given atmospheric composition, the heat-shield weight is determined by the trajectory, the body shape, the heat-protection method, and the chemical composition and the thermophysical and optical properties of the heat shield material. In such a general statement of the problem, optimization of the heat-shield mass depends on many parameters, and has not been solved hitherto. A number of papers have examined simpler problems, associated with reducing spacevehicle heating: optimization of the trajectory from the condition that the total heat flux to the body stagnation point should be a minimum for given probe parameters [2, 3], optimization of the characteristic probe size for a given trajectory [2–4], and optimization of the probe shape in a class of conical bodies at a given trajectory point [3, 5, 6J. In [7] a variational problem was formulated to determine the shape of an axisymmetric body from the condition that the radiative heat flux to the body at a given trajectory point should be a minimum for the entire surface, and an analytical solution was found for this in limiting cases. The present paper investigates a more general variational problem: determination of the shape of an axisymmetric body from the condition that the total radiative influx of heat to the body along its atmospheric trajectory should be a minimum. A solution has been obtained for a class of slender bodies for different isoperimetric conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–100, March–April, 1978.     

Investigation of supersonic radiative flow past bodies at low altitudes

The radiative heat transfer problem for bodies traveling through the earth's atmosphere, as formulated in [1, 3], is considered in the case of low altitudes, i.e., for high gas densities and optical thicknesses in the shock layer. These factors require the use of improved methods of calculation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 182–184, May–June, 1991.     

Combined radiative and convective heat transfer in a three-dimensional rectangular channel at different wall temperatures

 This paper deals with a numerical study of combined convective and radiative heat transfer in a three-dimensional rectangular duct with hydrodynamically and thermally developing laminar flow. The gas is assumed to be an incompressible, absorbing, emitting, isotropically scattering, gray medium. Isothermal, gray, diffuse boundary walls at different temperatures are assumed. The finite-volume method (FVM) is adopted to describe both convective and radiative heat transfer. The coupled continuity and momentum equations are solved by means of SIMPLER algorithm. Numerical results for the radiative flux show very good agreement with the available data. The effects of aspect ratio, optical thickness, scattering albedo and wall emissivity on the mean bulk temperature are also investigated. By splitting the heat flux into convective and radiative contributions, the relative importance of these components is assessed for a typical range of values of the parameters. Received on 9 February 1999     

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.     

System of equations for describing dynamical problems associated with the mechanics of lung parenchyma

In [1], which is an expanded version of the paper [2], the equations of conservation of mass and momentum are shown to be valid for dynamical problems of lung parenchyma. This system of equations is now closed by means of the heat flux equation. As in [1, 2], the heat flux equation is obtained on the basis of the methods of the mechanics of heterogeneous media [3] and anatomical data on the structure of lung parenchyma.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 21–29, May–June, 1988.     

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.     

A nonequilibrium viscous shock-wave layer in the vicinity of the critical point with the associated heat exchange taken into account

Results are presented in this article of numerical calculations of a viscous shock layer with the associated heat exchange in the vicinity of the critical point of a spherical blunt body taken into account in the presence of nonequilibrium chemical processes in the shock layer and on the surface of the body about which the flow takes place. A number of papers [1–4], in which specification of the surface temperature of the obstacle was utilized, have been devoted to the numerical investigation of a nonequilibrium viscous shock layer. At the same time the surface temperature of a body varies in actual flight due to heating, and together with this there is catalytic activity of the material, which appreciably complicates the problem and necessitates the simultaneous treatment of the course of processes in the gaseous and solid phases. The use of a separate formulation is difficult in this case, since the formulas for the thermal flux from the gaseous phase are of an estimative nature [5] when a volume nonequilibrium chemical reaction is present for a surface having an arbitrary catalytic activity. Taking account of the associated heat exchange has been done before for a number of problems of boundary-layer theory [6, 7], and in this case it has permitted determining the characteristics which are most important from the practical standpoint under conditions of flight along a specified trajectory, as well as under specified time-independent conditions of flight at altitudes at which the approximation of a viscous shock layer is valid. The effect of catalytic activity is discussed for a number of surface materials, and it is shown that the use of the formulas of boundary layer theory can appreciably distort the behavior of the surface temperature as a function of time for a certain altitude range.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 108–114, May–June, 1979.     

Strong mass injection at the surface of a blunt body in a supersonic flow

The case of supersonic flow over a blunt body when another gas is injected through the surface of the body in accordance with a given law is theoretically investigated. If molecular transport processes are neglected, the flow between the shock wave and the surface of the body should be regarded as two-layer, that is, as consisting of the flow in the shock layer between the shock wave and the contact surface and the flow in the layer of injected gas. A numerical solution of the problem is obtained near the front of the body and its accuracy is estimated. Approximate analytic solutions are obtained in the injected-gas layer: a constant-density solution and a solution of the boundary-layer type in the local similarity approximation. Near the flow axis the numerical and analytic solutions are fairly close, but at a distance from the axis the assumptions made reduce the accuracy of the approximate solutions. The flow in question can serve as a gas-dynamic model of a series of problems describing the radiant heating of blunt bodies in a hypersonic flow. In the presence of intense radiative heat transfer, vaporization is so great that the thickness of the vapor layer is comparable with the thickness of the shock layer. Moreover, the thermal shielding of various kinds of obstacles in channels through which a radiating plasma flows can be organized by means of the forced injection of a strong absorber. The formulation of a similar problem was reported in [1], but the results of the solution were not given. A two-layer model of the flow of an ideal gas over a blunt body was used in [2, 3] for the analysis of radiative heat transfer. In [2] the neighborhood of the stagnation point is considered. In [3] preliminary results relating to two-layer flow over blunt cones are presented. The solution is obtained by Maslen's approximate method.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 89–97, March–April, 1972.     

Body shape with minimum total radiant energy flux toward its surface

During a space vehicle's entry into a planet's atmosphere at hypersonic speed one of the important problems is the aerodynamical surface heating due to convective and radiant heat fluxes from the gas after passing through a strong shock wave. Due to the high destructive action of this heating, an important problem is the selection of the aerodynamic shape allowing the minimum heat influx to its surface. The problem of determining the shapes of an axisymmetric body from the condition of minimum total convective heat flux along the lateral face of the body was considered under various assumptions in [1–7]. There are a number of entry conditions (for example, into the earth's atmosphere with a speed of 11 km/ sec at an altitude of about 60 km [12]) during which the radiative component becomes dominant in the total heat flux toward the body. A numerical solution of the problem of hypersonic flow of a nonviscous, non-heat-conducting radiating gas around a body is obtained at this time only for a limited class of bodies and primarily for certain entry conditions (for example, [8–12]). On the basis of these calculations it is impossible to make general conclusions concerning arbitrary body shapes. Therefore, approximate methods were proposed which permit the distribution of radiant heat flux to be obtained for an arbitrary axisymmetric body in a wide range of flight conditions [13–15]. In the present work an expression is derived for the total radiant heat flux over the entire body surface and similarity criteria are found. A variational problem is formulated to determine the shape of an axisymmetric body from the condition of minimum total radiant-heat flux over the entire body surface. It is solved analytically for the class of thin bodies and in the case of a strongly radiating gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 84–89, July–August, 1976.     

Transient radiative-conductive heat transfer in a flat layer of a selectively absorbing and radiating medium

Results of a numerical solution of the unsteady boundary-value problem of radiative-conductive heat transfer in a flat layer of a selective nonscattering medium with semitransparent mirrorreflecting boundaries are presented. This problem reduces to a nonlinear integral equation in the unknown temperature with the use of a Green function. The optical properties of the walls are shown to have a strong effect on the formation of a temperature field in the layer. The intensity of heating of the layer depends on the radiative fluxes to a greater extent than on the conductive fluxes. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 105–109. January–February, 1998.     

Magnetohydrodynamic flow past a plate by the presence of radiation

An analysis of the unsteady magnetohydrodynamic flow of a viscous and electrically conducting fluid past to a plate by the presence of radiation is considered. The fluid is a gray, absorbing-emitting but nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Analytical solutions for the mean temperature, velocity and the magnetic field have been derived and the effect of the radiation on the temperature is discussed. Received on 20 November 1997     

Radiative and convective heat transfer in a plane layer of absorbent curtain

An examination is made of the thermal state of a plane layer of gray gas injected into a turbulent stream of high temperature gas flowing over a permeable flat plate.Similarity-type formulations of problems are encountered both in examination of flow near a stagnation point, and also in analysis of the lifting of the boundary layer by intense injection through a porous plate [1]. The examination described relates to the following idealized formulation of the problem (Fig. la).In a plane layer of gray absorbing medium, formed by plane-parallel diffusely radiating surfaces (1-porous plate; 2-boundary of high temperature turbulent gas stream), heat transfer is accomplished by radiation and convection of the layer normal to the surfaces and by molecular heat conduction. All the physical and optical properties of the medium and of the boundary surfaces are assumed to be constant, independent of temperature.The temperature of the wetted surface of the specimen and also that of the fictitious surface determining the upper bound of the lift-off region, are given.Also assumed given is the velocity of the injected medium, which is constant throughout the entire lift-off layer. This idealization appreciably facilitates our examination without in principle changing its features.A very simplified examination of this problem was given in [2]. The special case of a medium with low optical thickness was examined in [3,4].The problem was examined in [5] under the assumption that molecular heat conduction in the medium is negligibly small.In the formulation considered the generalized energy equation has the form     

Efficiency of a radiative-evaporative aircraft thermal protection system

The coupled boundary-value problem of nonstationary heat and mass transfer within the outer thermal insulation layer and the vapor outlet channel of a combined radiative-evaporative thermal protection system is formulated. The overall dimensional and weight characteristics of the system are calculated for a set of its parameters and two specified modes of the external heat flux and pressure variation, schematically modeling hypersonic aircraft flights 30 min and 60 min long with a maximum heat flux of 10⁵ W/m². Combined and passive radiative thermal protection systems are compared under the above-mentioned external conditions. It is shown that both the thickness of the outer thermal insulation layer and the total weight of the combined thermal protection system may be considerably less than the passive equivalents.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 24–36, January–February, 1995.     

Area rule for integral quantities

In hydrodynamics and aerodynamics there is an area rule for nearly axisymmetric bodies. It states that the drag [1–3], the coefficient of heat transfer and the ablation [4], and also the wake parameters [5] of a three-dimensional body are equal to the analogous quantities for an axisymmetric body which has the same distribution of the cross sectional area along the axis. In some cases, the area rule holds for bodies which depart strongly from axial symmetry [6]. It is shown in the present paper that equality also holds for other integral quantities and not only in hydrodynamic problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–159, July–August, 1981.We thank Yu. B. Lifshits for helpful comments.     

Solution of ablation equation with a low degree of asymmetry

The change of body shape (ablation) in a high-temperature gas stream has been the subject of numerous studies involving the consideration of two-dimensional and, to a lesser extent, three-dimensional problems (for a bibliography, see [11). In [1], the problem of three-dimensional ablation under the influence of convective or radiative heat transfer was posed in a simplified integrolocal form. In this paper, a semianalytic solution is proposed for similar, almost axisymmetric problems in the same formulation. By means of linearization (used only to substantiate the method, not in the computational algorithm), the general problem is reduced to a set of isolated two-dimensional problems for each harmonic of the Fourier series in the circumferential variable. Calculated examples indicate a perfectly finite region of applicability of the method with respect to the degree of asymmetry of the problem. The method can be used to provide an efficient means of calculating the complex problem of ablation and dynamics of a body moving in the atmosphere. For high-frequency oscillations, a simple solution of this (generally very awkward) problem is obtained within the framework of the corresponding asymptotic theories.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–137, January–February, 1988.     

Composite heat transfer in case of steady laminar flow of a gray fluid with large optical density past a horizontal plate embedded in a saturated porous medium

The present paper discusses the problem of composite heat transfer and viscous friction of a moving gray medium with large optical density. Expressions for temperature and velocity distributions and the ratio of the radiative component to convective component of heat flux are obtained. It is observed that for a given value ofB the ratio of radiative heat flux to convective heat flux is maximum at the edge of the boundary layer and tends to an asymptotic value as the boundary is reached. However, for a given value ofK δ, the ratio of heat fluxes increases with increase inB (the porous parameter). The results also show that as the wall temperature approaches the value of free stream temperature, the ratio of heat fluxes decreases.     

Heat transfer at and near the stagnation point in turbulent flow over bodies

Results are presented of experimental investigations of heat transfer in the neighborhood of the stagnation point in flow of a turbulent gas over bodies. It is assumed that the outer flow is capable of rendering the boundary layer turbulent over the whole body surface, i.e., the hypothesis is invoked that there is a turbulent stagnation point. Using the method of integral relations [1] and the flat plate heat-transfer law, transformed in such a way as to satisfy the heat-transfer conditions at the stagnation point, simple formulas have been obtained for calculating the heat flux.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 177–181, July–August, 1975.     

Interaction of mixed convection in two-sided lid driven differentially heated square enclosure with radiation in presence of participating medium

The current study addresses the mathematical modeling aspects of transport phenomena in steady, two-dimensional, laminar flow accompanied by heat transfer in a lid-driven differentially heated cavity in presence of radiatively absorbing, emitting and scattering gray medium. The walls of the enclosure are considered to be opaque, diffusive and gray. Mixed convection is the outcome of the interaction of forced convection induced by the moving vertical hot and cold wall with the natural convection induced due to the differentially heated enclosure. Two different orientations of the wall movement have been considered to simulate opposing and aiding mixed convection phenomenon and to study its interaction with radiation. Vorticity-stream function formulation of N–S equation has been employed. The discrete ordinate method has been used in modeling the radiative transport equation followed with finite volume method as discretisation technique. The effect of influencing parameters on fluid flow and heat transfer has been studied.