Investigation of a model of the Soyuz spacecraft washed by the control jets of the Apollo spacecraft

During mission design for the joint flight of the Soyuz and Apollo spacecraft in the ÉPAS program, a preliminary analysis was made of the thermal and force interactions of the motor jets of the Apollo control system on the Soyuz spacecraft. It was shown that the flow over the service, command, and docking modules of Apollo formed shock waves which intersected the communication antennas, the solar cells, and other structural elements of Soyuz during the docking. The flight program provided for possible simultaneous operation of four motors of the control system. In that case the jets interact, forming a complex three-dimensional flow. In the regions where shock waves interact with the Soyuz structural elements, the local convective heat fluxes, which are significant in magnitude, increase, since the temperatures and pressures in the Apollo engine combustion chambers are 3000 °K and 7·10⁵ Pa, respectively. The need for reliable operation of all devices of Soyuz located in the jet interaction zone required experimental investigations to be performed to determine the heat flux to the structure and the surface pressures on the spacecraft, with particular attention being paid to modeling of the phenomena. It should be noted that the results of analogous investigations carried out earlier by the USA with reference to the manned lunar flight program could not be used because of the difference of the Soyuz geometry and the newly developed docking module in the ÉPAS mission from the Apollo lunar module geometry.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–133, May–June, 1977.     

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.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Subsonic Radiation Gas Dynamics in a Laser Plasma Generator Channel

The radiation gasdynamic processes in the channel of an air laser plasma generator operating at atmospheric pressure are analyzed. In the multigroup approximation a numerical radiation gasdynamic model is formulated on the basis of the equations of motion of a viscous heat-conducting gas and the selective thermal radiation transport equation. Laminar and turbulent subsonic generator operation regimes are considered.For the purpose of approximately describing the turbulent gas and plasma mixing the Navier-Stokes equations averaged after Reynolds and the k-ε turbulence model are used. The problem is solved in the time-dependent two-dimensional axisymmetric formulation.Strong radiation-gasdynamic interaction regimes are investigated. In these regimes the energy losses due to radiation from the high-temperature region of the laser plasma and the absorption of its thermal self-radiation by the surrounding plasma and gas layers (radiation reabsorption) appreciably affect the gasdynamic flow structure. Two methods of integrating the selective thermal radiation transport equation in the generator channel are discussed. In one of these the thermal radiation transport is calculated inside the heated volume and in the other the radiation heat fluxes are calculated on the surfaces bounding the volume. The results of calculating the spectral and integral radiation heat fluxes on the inner surface of the generator are given.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 126–143.Original Russian Text Copyright © 2005 by Surzhikov.     

Thermal effect of a freely expanding gas jet on a flat plate

An experimental investigation was made into the thermal effect of a single gas jet on a plate at Mach numbers of the nozzles in the range 2–6.1, specific heat ratio = 1.4, total pressure difference up to 6·10⁷, gas temperature 450–520 °K in the forechamber, and pressure in the forechamber (10–20)· 10⁵ Pa. The proposed dimensionless numbers made it possible to obtain generalized dependences of the distribution of the heat flux to the plate on the conditions of the problem. A method of approximate calculation of the heat fluxes is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 119–126, July–August, 1981.     

Nonisothermal rarefied gas flow through a narrow slit

The nonisothermal flow of gas through a narrow slit under the influence of small pressure and temperature differences is investigated. The flow field and the mass and heat fluxes are found. It is shown that the heat transfer between the gas and the diaphragm, caused by the pressure difference, leads to a thermal polarization effect. The Onsager reciprocity relation is checked.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 171–175, July–August, 1990.     

Investigation of heat flux at the forward critical point of bodies placed in a high-temperature subsonic stream

We present the results of measurements of the total heat flux at the forward critical point of axially symmetric models placed in a high-temperature subsonic stream of air and nitrogen in an apparatus which uses a high-frequency inductive discharge [1] to heat the gas. The heat fluxes were measured for cylindrical models whose forward part had one of three possible shapes: a hemisphere, a hemisphere with a blunt nose, or a flat circular end-face. A water-cooled calorimeter sensor was set up at the forward critical point of the model; the calorimeter sensor was made of different materials, so that it was possible to estimate the radiant and convective components of the total heat flux and determine the effect of the sensor material on the heat flux measured. The convective component of the heat flux was compared to a calculated value obtained by Fay and Riddell's formula. The heat-flux values found for two shapes of models were used in determining the effective radius of streamline flow for a model with a plane end-face.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 133–141, September–October, 1973.The authors are grateful to N. I. Nesterov for his help with the work.     

Investigation of heat transfer on models in subsonic jets of an induction plasmatron

The results are given of an investigation of the flow parameters in an induction plasmatron and of heat transfer on water-cooled models in subsonic jets of dissociated air in the range of pressures p = 5·10³–1.0·10⁵ N/m². The obtained experimental data confirm the well-known theoretical conclusion that the catalytic activity of the surface influences the heat fluxes at low pressures when the boundary layer flow is nonequilibrium. The problem of the flow of a subsonic jet of a viscous heat-conducting gas past a model of cylindrical shape with flat end has been solved numerically. The experimental and calculated data are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 6, pp. 129–135, November–December, 1983.We are very grateful to Yu, K. Rulev and V. M. Mysova for assistance in the experiment.     

Two-phase mass injection from the stagnation zone of a blunt body in a hypersonic flow

A mathematical model of the hypersonic steady gas flow over the stagnation zone of an axisymmetric blunt body with given two-phase injection from the surface is proposed. The two-continuum model of a dusty gas [3] is used for describing the flow in the region of the wall. The problem is solved in the boundary layer and thin viscous shock layer approximations. On the basis of the numerical calculations the distribution of the parameters of the carrier and dispersed phases near the axis of symmetry is obtained. The similarity parameters determining the convective heat transfer are found. The stagnation point heat fluxes with and without particles are compared. The range of parameters on which particles can significantly reduce the heat transfer is determined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 60–66, July–August, 1992.     

A spatial laminar boundary layer on a streamline in conical external flow of a uniform gas in the absence of sources and sinks

Theoretical study of a three-dimensional laminar boundary layer is a complex problem, but it can be substantially simplified in certain particular cases and even reduced to the solution of ordinary differential equations.One such particular case is the flow of a compressible gas on a streamline in conical external flow. The case is of considerable practical importance because the local heat fluxes may take extremal values on such lines.Such flow, except for the conical case, has been examined [1–4], and an approximate method has been given [1] on the basis of integral relationships and a special form for the approximating functions. A numerical solution has been given [2, 3] for such flow around an infinite cylinder. It was assumed in [1–3] that the Prandtl number and the specific heats were constant, and that the dynamic viscosity was proportional to temperature. Heat transfer has been examined [4] near a cylinder exposed to a flow of dissociated air.Here we give results from numerical solution of a system of ordinary differential equations for the flow of a compressible gas in a laminar boundary layer on streamlines in conical external flow, with or without influx or withdrawal of a homogeneous gas. It is assumed that the gas is perfect and that the dynamic viscosity has a power-law temperature dependence.     

Investigation of the Influence of Different Heterogeneous Recombination Mechanisms on the Heat Fluxes to a Catalytic Surface in Dissociated Carbon Dioxide

A kinetic model of heterogeneous recombination in dissociated carbon dioxide on high-temperature heat-shield coatings is developed; the model takes into account the nonequilibrium adsorption-desorption reactions of oxygen atoms and their recombination in the Eley-Rideal and Langmuir-Hinshelwood reactions. On the basis of a comparison of the calculated heat fluxes in dissociated carbon dioxide with those measured in the VGU-3 plasma generator of the Institute for Problems in Mechanics of the Russian Academy of Sciences (IPM RAS) and the available literature data, the parameters of the catalysis model are chosen for the glassy coating of the Buran orbiter tile heat shield based on the SiO₂–B₂O₃–SiB₄ system. The effects of heterogeneous recombination proceeding in accordance with the Langmuir-Hinshelwood mechanism, as well as the processes involving carbon atoms and those involving physically adsorbed oxygen atoms, on the heat fluxes to the glassy coating are analyzed on the surface temperature range from 300 to 2000 K.     

Nonstationary Gas Filtration Caused by an Intense Thermal Action on a Damp Porous Medium

A mathematical model and an algorithm are proposed for evaluating nonstationary heat and mass transfer in a porous medium that contains a mechanically absorbed liquid and a two–component gas (vapor—inert gas mixture). The case of an intense thermal action on a damp porous mixture caused by an external heat flux and convective heat transfer is considered. Typical flow regions and typical regions of the interaction between the phases are described.     

Convection of a viscous incompressible gas in rectangular regions with inlet and outlet channels

A study is made of two-dimensional problems of thermal convection of a viscous incompressible gas in rectangular regions that have gas inlet and outlet channels in the presence of a temperature difference between the bottom and the top (the bottom is heated). In contrast to the well-studied case of natural convection, when no-slip conditions are specified on all boundaries of the region and motion in the region occurs only through the temperature difference [1–4], the heat transfer in the investigated flows is complicated by the additional influence of the forced convection of the gas due to the motion of gas through the inlet and outlet channels. Flows of such type simulate well the processes that take place in many heat transfer devices and in ventilated and air-conditioned industrial premises. Two formulations of the problem are considered. In the first, the gas flow through the inlet and outlet channels is assumed given, and the solution of the problem is determined by the dimensionless Prandtl, Grashof, and Reynolds numbers. In the second case, this flow rate is not given but determined during the solution of the problem. The motion in the region arises from the difference between the temperatures of the bottom and the top of the region, and the motion, in its turn, causes a flow of gas through the inlet and outlet channels. As in the case of natural convection, the solution of the problem in this case is determined by only two dimensionless numbers — the Grashof and Prandtl numbers. By numerical solution of the boundary-value problems for the equations of heat transfer a study is made of the influence of the characteristic dimensionless numbers on the hydrodynamic and temperature fields and the heat fluxes through the boundaries of the region. The solutions of the problems in the two formulations are compared for different positions of the outlet channels.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 126–131, September–October, 1979.We thank G. I. Petrov for discussing the results.     

Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow     

Problems of heat transfer and thermal protection of entry vehicles for an unmanned mission to mars

The problems of heat transfer and thermal protection for an orbitalMartian lander touching down on the planetary surface are investigated. A broad scenario of the mission is given and several possible aerodynamic shapes are considered. Several versions of the landing on the planetary surface are studied. The version with intermediate orbiting of an artificial Mars satellite using aerodynamic deceleration in the atmosphere is adopted as the main variant. The landing on the planetary surface is realized from satellite orbit. This landing pattern requires reusable thermal protection. The convective and radiative heat fluxes are calculated at characteristic points on the surface of a vehicle of the chosen shape. For this shape the necessary weight of thermal protective coating consisting of indestructible reusable TZMK material, used previously for shielding the Buran orbiter, is determined.     

Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number

The Couette flow of binary gaseous mixtures is studied on the basis of the McCormack model of the Boltzmann equation, which was solved numerically by the discrete velocity method. The calculations were carried out for three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. The stress tensor and bulk velocity of both species were calculated for several values of the gas rarefaction in the range from 0.01 to 40 for three values of the molar concentrations: 0.1,0.5 and 0.9. The numerical solution together with an analytical solution based on the slip boundary condition cover the whole range of the gas rarefaction. It was showed that the Couette flow is weakly affected by the intermolecular interaction law.     

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.     

Effect of inelastic collisions on the first-order slip coefficients for a diatomic gas with rotational degrees of freedom

When solving problems of inhomogeneous gas dynamics in the slip regime, it is necessary to know the boundary conditions for the velocity, temperature, heat fluxes, etc., that is, the boundary conditions for the gas macroparameters. In particular, such problems arise in developing the theory of thermophoresis of moderately large aerosol particles [1].The problem of monatomic and molecular (di- and polyatomic) gas slip along a boundary surface is considered in many publications (see, for example, [2–8]). The first-order effects include the isothermal and thermal gas slips characterized by the coefficients C_m and K_TS, respectively.In contrast to a monatomic gas, the molecules of diatomic and polyatomic gases have internal degrees of freedom, which considerably complicates the kinetic equation [9]. The lack of reliable models for the intermolecular interaction potential predetermines the need to construct model kinetic equations [10].In this study, for a diatomic gas whose molecules have rotational degrees of freedom, we propose a model kinetic equation obtained by developing the approach described in [6]. With the use of this model equation, the problem of diatomic gas slip along a plane surface is solved. As a result, for diatomic gases the coefficients C_m and K_TS, which depend on the thermophysical gas parameters and the intensity of inelastic collisions, are obtained.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 176–182. Original Russian Text Copyright © 2004 by Poddoskin.     

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.     

Jumps in the density and temperature of one of the components of a binary gas mixture over the plane surface of a liquid

We consider a problem concerning the vaporization (or condensation) of one of the components of a binary gas mixture situated over the plane surface of a liquid. The kinetic equation in the model form of [1] is used to describe the system. As is well known, this model agrees well with experiment and is simpler than the Boltzmann equation so far as mathematical relations are concerned. This model fails to describe a number of effects because it is assumed that the collision time of the particles is independent of their velocity. This relates primarily to the phenomenon of thermal diffusion of the gases. Thus the formulas given below are applicable to gas mixtures having a small thermal-diffusion coefficient. The model equation is solved by an approximate method developed in [2]. In [3] the temperature jump of a single-component gas at a solid wall is calculated by this method, and the method is also employed in [4] in the calculation of the slipping rate of a binary gas mixture in the field of a temperature gradient. In both cases the results agree with numerical calculations by other authors within an accuracy of 1.5%.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 142–148, September–October, 1973.