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.     

Simulation of oxygen atom adsorption on an Al<Subscript>2</Subscript>O<Subscript>3</Subscript> surface by the density functional method

Several cluster models of oxygen atom adsorption on an Al₂O₃ surface are constructed on the basis of the density functional method. The performed quantum mechanical computations allow one to reveal a number of important features of the potential energy surface to describe the heterogeneous catalytic processes with the use of molecular dynamics methods. The heterogeneous recombination of oxygen atoms is simulated according to the Eley-Rideal mechanism. It is shown that the potential energy surface should be used with consideration of the internal relaxation of surface monolayers to correctly describe the process under study.     

Modeling of catalytic activity of an Al2O3 surface on the basis of the first principles

The adsorption, desorption, impact, and associative heterogeneous recombination rate coefficients are determined for atomic oxygen in the temperature range between 500 and 2000 K on the basis of quantum chemical data on the energy of interaction of atomic and molecular oxygen with the clusters that model an α-Al₂0₃ surface. These coefficients are used to calculate the heterogeneous recombination probabilities and the heat fluxes to the surface under the conditions similar to those of the MESOX facility.     

Catalytic properties of a copper transducer for determining flow parameters in a high-frequency induction plasmatron

The rate coefficients of the elementary stages of the complete system of heterogeneous catalytic recombination of dissociated oxygen on a copper oxide surface are determined on the basis of quantum-mechanics calculations within the framework of cluster models. The coefficients are used to calculate the dependence of the effective coefficient of heterogeneous catalytic recombination of oxygen atoms on the temperature and the partial pressure on a wide range of surface conditions. It is established that it can considerably vary depending on these conditions.     

Increased heat transfer to a titanium surface with oxygen injection into the nonequilibrium boundary layer

The results of an experimental and numerical investigation of the heat transfer between a subsonic jet of dissociated nitrogen and a titanium surface, through which molecular oxygen is blown into the jet, are presented. It is established that in the nonequilibrium boundary layer regime the dependence of the heat flux on the injected oxygen flow rate is nonmonotonic. At a certain flow rate the heat transfer to the titanium surface reaches a maximum that considerably exceeds (by 20%) the heat transfer to an impermeable wall. The observed increase in heat transfer in the presence of injection is attributed to the interaction of the gas-phase exchange reactions and the recombination of atoms on the titanium surface, which has sharply different catalytic properties with respect to the recombination of nitrogen and oxygen atoms.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–155, July–August, 1991.     

Analysis of catalytic properties of siliconized heat-shielding coatings

The catalytic properties of heat-shielding coatings (β-cristobalite and SiC) used on space vehicles are analyzed on the basis of the microscopic approach with consideration of the molecular structure of the near-surface layer. The heterogeneous recombination coefficient of oxygen atoms and the recombination energy accommodation coefficient are determined. The energy distribution by internal degrees of freedom is calculated. In particular, it is found that, when the energy of collision of atoms with the surface is small, the oxygen atom heterogeneous recombination is more efficient for SiC coatings, whereas this recombination is more efficient in the case of β-cristobalite if the collision energy is large. Nevertheless, the heat-transfer coefficient is greater for SiC coatings in the studied range of collision energy variations, since the recombination energy accommodation is larger.     

Ablation of Teflon in a stream of dissociated air

A numerical solution to the coupled problem of heat and mass transfer on an ablating Teflon surface is used to analyze the influence of nonequilibrium physicochemical processes in the boundary layer on ablation. The results of the numerical calculations are compared with the experimental data in the literature on the ablation of Teflon subject to high heat fluxes and with data on measurements of the concentrations of the components in a boundary layer containing Teflon ablation products. It is shown that an important factor that must be taken into account in interpreting experimental data, particularly at low pressures and high stagnation enthalpies, is the influence of the catalytic properties of the surface on the heat transfer. An approximate expression is derived for calculating the ablation rate; it is valid in the range of free-stream velocities 3 km/sec < V < 8 km/sec.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 103–109, May–June, 1984.     

Effect of a dispersed component on the nature of heat exchange during flow of a heterogeneous-jet around a barrier

Flow in a turbulent nonisothermal heterogeneous jet is characterized by considerable velocity [1, 2] and temperature disequilibrium [3] (u_s u and T_s T, where u_s, T_s and u, T are velocity and temperature of dispersed and gas components). As was shown in [4], an impurity is not passive, and it leads to suppression of jet turbulence (a result of interphase exchange by pulse and heat). Nonetheless, during reaction of a heterogeneous jet with a barrier orientated along the normal to the running flow, a significant increase is observed in heat emission characteristics in the vicinity of the point of deceleration [5] (for a single-phase jet an increase in heat exchange is typical with an increase in the intensity of turbulence [6]). The intensity of the change in heat emission in this case is a result of velocity and temperature disequilibrium for flow in jets, and it depends on a number of factors (temperature, concentration, phase condition of the dispersed impurity, etc.) and on the nature of the reaction of the dispersed component with the barrier surface [7]. There are numerous experimental data devoted to this. Apart from work in [5, 7], attention is drawn to [8] where an increase is also noted in the heat flow (by a factor of 1.4) at the deceleration point for a plane cylindrical end and a hemisphere. The aim of the present work is a study of the effect of a dispersed component on heat exchange with jet flow around a barrier.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 63–68, November–December, 1986.     

Simulation of heterogeneous atom recombination on spacecraft heat shield coatings using the methods of molecular dynamics

An efficient method of investigating the processes of interaction between gas mixtures and catalytic surfaces is developed within the framework of classical molecular dynamics. The recombination and chemical-energy accommodation coefficients on the catalytic surface can be determined with fewer computational resources than in the quantum-mechanical and semiclassical approaches. Oxygen atom recombination on a β-cristobalite surface of the type frequently used in spacecraft heat shield systems is investigated. The probability of atom recombination and the recombination energy accommodation coefficient obtained are in satisfactory agreement with the available experimental data and calculations made by means of the semiclassical method. The hypothesis that the probability of the Eley-Rideal reaction decreases and the probability of atom adsorption increases with increase in the atom collision energy is confirmed. It is attributable to the tendency of atoms to be trapped in the potential well and be desorbed in the atomic state when the surface collision energy is high instead of entering into a recombination reaction and then being desorbed in the molecular state.     

Three-Dimensional Problem of Radiative Gasdynamics of the Apollo-4 Command Module during Superorbital Atmospheric Entry

The three-dimensional problem of radiative gasdynamics of the superorbital entry of the Apollo-4 command module into the dense terrestrial atmosphere at an angle of attack of 25° is numerically solved. The flow conditions corresponding to the flight velocity V_∞ = 10.5 km/s at an altitude H = 67.3 km are considered in detail. The distributions of the densities of convective and radiative heat fluxes along the surface in a flow are obtained. The spectral composition of the thermal radiation attaining the surface is studied. The results of the calculations are successfully compared with the data of two-dimensional calculations.     

Determination of heat fluxes in the neighborhood of a double curvature stagnation point in a flow of dissociating gas of arbitrary chemical composition

Numerical solutions are obtained for the equations of a uniform compressible boundary layer with variable physical properties in the vicinity of a stagnation point with different principal curvatures in the presence of an injected gas with the same properties as the incident flow. The results of the numerical solutions are approximated for the heat flux in the form of a relation that depends on the variation of the product of viscosity and density across the boundary layer and on the ratio of the principal radii of curvature.Using the concepts of effective diffusion coefficients in a multicomponent boundary layer, previously introduced by the author in [1], and the generalized analogy between heat and mass transfer in the presence of injection, together with the numerical solutions obtained, it is always possible, even without additional solutions of the boundary-layer equations, to derive final formulas for the heat fluxes in a flow of dissociating gas of arbitrary chemical composition, provided that we make the fundamental assumption that all recombination reactions take place at the surface.By way of example, formulas are given for the heat transfer to the surface of a body from dissociating air, regarded as a five-component mixture of the gases O, N, NO, O₂, N₂, and from a dissociating mixture of carbon dioxide and molecular nitrogen of arbitrary composition, regarded as an eleven-component mixture of the gases O, N, C, NO, C₂, O₂, N₂, CO, CN, C₃, CO₂.In the process of obtaining and analyzing these solutions it was found that, in computing the heat flux, a multicomponent mixture can be replaced with an effective binary mixture with a single diffusion coefficient only when the former can be divided into two groups of components with different (but similar) diffusion properties. In this case the concentrations of one group at the surface must be zero, while the diffusion flows of the second group at the surface are expressible, using the laws of mass conservation of the chemical elements, in terms of the diffusion flows of the first. Then the single effective diffusion coefficient is the binary diffusion coefficient D(A,M), where A relates to one group of components and M to the other.In view of the small amount of NO(c(NO) < 0.05), the diffusion transport of energy in dissociated air maybe described with the aid of a single binary diffusion coefficient D(A, M)(A=O, N, M=O₂, N₂, NO). However even in the case of complete dissociation into O and C atoms at the outer edge of the boundary layer, the diffusion transport of energy in dissociated carbon dioxide can not be described accurately enough by means of a model of a binary mixture with a single diffusion coefficient, since the diffusion properties of the O and C atoms are distinctly different.     

Determination of the Effective Probabilities of Catalytic Reactions on the Surfaces of Heat Shield Materials in Dissociated Carbon Dioxide Flows

The effect of heterogeneous catalysis on the heat transfer to cold and heated surfaces in subsonic dissociated carbon dioxide jet flows is studied experimentally, using a 100 kW inductive plasma generator, and simulated numerically. The effective probabilities of the heterogeneous reactions CO + O → CO₂ and O + O → O₂ on molybdenum (T_w=300 K) and quartz (T_w=470–620 K) surfaces, the Buran heat shield tile coating (T_w = 1470—1670 K), and two oxidation-resistant carbon-carbon coating materials (T_w=1420—1840 K) are determined by comparing the experimental and calculated data on the heat fluxes at the stagnation point of models at a pressure of 0.1 atm.     

Determination of heat transfer coefficients on the surfaces of plastic tubes

 The paper discusses the statistical steady heat and momentum transfer problem in the inlet section of the plastic tubes. The modified two equation k–ɛ turbulent model utilizing variability of turbulent Prandtl number, Pr_t, was used for the analysis. Considering the thermophysical anisotropy of the tube material, a balance of local temperatures and local heat fluxes on the boundary between the fluid and the tube wall was assumed (conjugate heat transfer problem). The thermal boundary condition on the external surface of the tube (temperature) measured in the experiment was taken into account. The boundary problem described was solved by the control volume method. The values of the parameters of Pr and Re obtained from the experiments were included in the numerical calculations. Based on the results obtained, profiles of mean fluid temperatures, local Nusselt numbers on the internal and external surface of the tube, and profiles of temperatures on the internal surface of the tube and inside of the tube wall were determined. The analysis shows that changes in Pr_tand turbulence intensity, Tu, influence the local values of Nusselt numbers, and it also shows that the results for the local Nusselt numbers inside the tube obtained from numerical calculations are of great accuracy in comparison with results published in the available literature. Received on 11 June 2001     

Diffusion separation of chemical elements on a catalytic surface

An asymptotic expansion of the solution, for large Schmidt numbers, of the system of equations of a chemically nonequilibrium multicomponent boundary layer on the catalytic surface of a blunt body [1] is used to obtain expressions for the diffusion fluxes of the reaction products and chemical elements and the heat flux as functions of the gradients of the reaction product concentrations, chemical element concentrations and enthalpy across the boundary layer. It is shown that when the body is exposed to a supersonic air flow, the diffusion separation of the chemical element oxygen depends importantly on the atom concentration at the outer edge of the boundary layer and the nature of the homogeneous and heterogeneous catalytic reactions. If the surface promotes the rapid recombination of oxygen atoms and is chemically neutral with respect to nitrogen atoms, then an excess of the chemical element oxygen is formed on the body. Otherwise we get an enhanced concentration of the element nitrogen. As distinct from the case of an ideally catalytic wall [2–4], on a surface possessing the property of catalytic selectivity the diffusion separation of chemical elements takes place even when only atoms are present at the outer edge of the boundary layer. On a chemically neutral surface diffusion separation may be caused by homogeneous recombination reactions between oxygen and nitrogen atoms if their rate constants are essentially different.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–121, July–August, 1988.     

Three-dimensional chemically nonequilibrium viscous shock layer on a catalytic surface with allowance for associated heat transfer

A three-dimensional flow of dissociating air past blunt bodies is investigated in the framework of the thin viscous shock layer theory. Multicomponent diffusion and homogeneous chemical reactions, including dissociation, recombination, and exchange reactions, are taken into account. The generalized Rankine-Kugoniot conditions are specified on the shock wave and the conditions which take into account the heterogeneous catalytic reactions, on the surface of the body. The viscous shock layer equations are solved together with the heat equations inside the coating, which is carbon with a deposited thin film of SiO₂, or quartz. The case of a thermally insulated surface is also considered. The problem for the case of the motion of a body along the re-entry trajectory into Earth's atmosphere is investigated numerically. The temperature of the surface and the heat flux toward it are given as a dependence on the height (tine) of the flight for different cases of the specification of the catalytic reactions. It is shown that the difference between the heat fluxes towards the thermally insulated surface and the fluxes toward the heat-conducting surface in the neighborhood of the stagnation point is of the order of 6–12% for all the cases considered. This makes it possible to decouple the solution of the problem of heat conduction in the body.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–146, November–December, 1985.deceased     

Effect of the incomplete accommodation of the heterogeneous recombination energy on heat fluxes to a quartz surface

Taking both the heterogeneous catalytic processes, including the surface formation of particles with excited internal degrees of freedom, and the processes of multicomponent diffusion and heat transfer in the MESOX apparatus fully into account makes it possible to obtain a recombination coefficient and an accommodation coefficient of the oxygen-atoms-on-quartz recombination energy which are in good agreement with the experimental data. The heterogeneous catalysis model constructed can be used effectively for predicting the heat fluxes to the surface of reentry vehicles on their entry into the Earth’s atmosphere.     

Study on laminar film condensation of saturated steam on a vertical flat plate for consideration of various physical factors including variable thermophysical properties

The extended theory of the steady state laminar film condensation process of pure saturated vapour at atmospheric pressure on an isothermal vertical flat plate is established. Its equations provide a complete account of the physical process for consideration of various physical factors including variable thermophysical properties, except for surface tension at the liquid-vapour film interface. First, similarity considerations are proposed to transform the governing system of partial differential equations and its boundary conditions into the corresponding dimensionless system. Then, the dimensionless new system is computed numerically in two steps: First neglecting shear force at the interface, so that the initial values of the boundary conditionsW _{xl, s} andW _{yl, s} are obtained. Then, the calculations of a problem of the three-point boundary-value for coupling the equations of liquid film with those of vapour film are carried out. Furthermore, the correlations for heat transfer coefficient and mass flow rate are proposed by analysis of heat and mass transfer and it is found that the heat transfer coefficient is function of dimensionless temperature gradient $\dot L$ , and that the condensate mass flow rate is function of the mass flow rate parameter (η _lδ W _{xl, s} ? 4W _{yl, s} )of liquid. In addition, the corresponding heat and mass transfer correlations expressed by subcooled temperature Δt are developed. According to Nusselt's theory four different assumptions are set up for an investigation of the effects of the film condensation of saturated vapour, so that the validity of Nusselt's theory can be further clarified. Quantitative comparisons from the results of the heat transfer coefficient and mass flow rate of the condensate indicate that the effect of variable thermophysical properties on the heat and mass transfer is appreciable. The effect of thermal convection in the condensate film is obviously larger than those of shear force at liquid-vapour interface, and the effect of the inertia in the condensate film is very small. Finally, it is also shown that Nusselt's theory, in using Drew reference temperature, will decrease the heat transfer coefficient by at most 5.11%, and will increase the mass flow rate of the condensate by at most 2.45%, provided that the effect of the surface tension is not taken into account.     

Transformational-zone method of calculation of complex heat exchange during flow of optically active medium inside tube of diffuse grey surface

The paper presents analytical and experimental investigations of influence of radiative heat transfer on complex heat exchange during flow of optically active gas inside a pipe of diffusegrey properties. It was assumed that the pipe is heated from the outside by a constant heat flux and gas flowing inside is both absorbing and emitting and of small optical density. The influence of length and radiative properties of the pipe surface and of the gas temperature distribution on the wall and in the gas were analysed. The influence of radiative energy transfer on overall heat transfer coefficient was estimated. Mathematical model of radiative convective heat exchange in a system of one-dimensional temperature field, based on zone division method of Hottel and surface transformation, was verified numerically and experimentally. The results of numerical calculations were compared with experimental results obtained during carbone dioxide (CO₂) flow inside electrically heated ceramic tube. The set of nonlinear differential equations was solved by Runge-Kutta method with Hamming modification and with the use of separable-kernel method.     

Free convective heat transfer and criterion of onset of free convection in a horizontal melt layer of ice heated by upper rigid surface

An experimental and analytical investigation pertaining to the effect of density inversion of water on the free convective heat transfer and the onset of free convection in a horizontal melt layer of ice heated by upper rigid surface is carried out. Temperatures of the upper surface are varied from 1°C to 15°C, with Rayleigh number ranging from 2 × 10² to 1 × 10⁵. From the present study, it can be demonstrated both experimentally and analytically that the density inversion of water plays an influential role in such a melt layer and the onset of free convection and the free convective heat transfer are considerably affected by the temperature of upper rigid surface T₂, in the case of T₂ ≤ 8° C, unlike the results obtained for common fluids without density inversion.     

Component desorption effect on the material catalyticity in high-temperature multicomponent gases

The distinctive features of the formation of the catalyticity of materials with respect to atom recombination on the material surface are investigated for mixtures of different high-temperature gases under conditions of hypersonic atmospheric flight or bench setups. It is shown that in general the catalyticity constants (heterogenous recombination probabilities) of individual components determined experimentally in dissociated flows of “pure” gases are improperly used for calculating the heat fluxes to material surfaces in multicomponent gas flows, owing to differences in the occupation of the surface by atoms in pure gases and mixtures. This effect must be taken into account in interpreting the experimental data which so far have been the only source of information on material catalyticity in gas mixtures. Otherwise, the results of calculations of the heat transfer to hypersonic flight vehicles could turn out to be invalid. Examples of the possible effect of ignoring this factor on the calculated heat fluxes are presented.