This paper addresses the problem of modeling the catalytic recombination of oxygen on silicon dioxide, the principal material making up the Space Shuttle thermal protection tiles. A new mechanism involving the surface oxygen of the silicon-dioxide matrix itself is proposed. The detailed rate equations describing the proposed mechanism are written and solved at steady state. The predicted rates are shown to match catalytic data specifically collected for the silicon-dioxide/oxygen system.

Model for oxygen recombination on silicon-dioxide surfaces

An analytic model to describe the heterogeneous recombination of a single atomic species on silicalike surfaces is developed. The theoretical investigation herein presented provides ready-to-use expressions for the surface atomic recombination probability γ obtained as a function of surface characteristics such as the densities of adsorption sites and the activation energies for the different elementary surface processes. The model takes into account physisorption, chemisorption, thermal desorption, surface diffusion, and both Eley-Rideal (E-R) and Langmuir-Hinshelwood (L-H) recombination mechanisms. The results are applied to the cases of nitrogen and oxygen recombination on silica and to oxygen recombination on Pyrex. However, since the derivation is kept in a very general form, it allows the exploration of several distinct limit cases and provides a deeper understanding of the underlaying surface kinetics. The dependence of the recombination probability with the wall temperature and with the gas pressure is studied in detail. It is found that γ can have a complex nonmonotonic behavior with the wall temperature, as a result of the competition between E-R and L-H recombination processes. The transition from first- to second-order recombinations (and vice-versa) with pressure is studied and debated.

Analytical Model of Heterogeneous Atomic Recombination on Silicalike Surfaces

This article briefly reviews the model for recombination of oxygen on a silicon-dioxide surface presented in detail in a previous paper. Data for oxygen recombination on reaction-cure d glass (RCG), a silicon-dioxid ebased material, is presented and compared with the Si-O2 recombination model. The model is modified slightly to better represent the oxygen-RCG system, but the essential feature of the model, the participation of the oxygen of the surface matrix itself, remains unchanged. The ramifications of the model toward the production of excited molecular oxygen is examined as it may pertain to surface heating during a re-entry. Data indicating that the predicted production of singlet-delta oxygen, and no higher-electronic-state oxygen is given in support of the model.

Model for Oxygen Recombination on Reaction-Cured Glass

A self-consistent model for bulk and surface kinetic processes in low-pressure flowing discharges in N 2 -O 2 mixtures is presented. The model has a small number of input parameters and includes a large number of physical-chemical reactions that enable one to determine the concentrations of the different neutral (including NO and NO 2 ) and ionic species, as well as the populations of excited N 2 , O 2 , N, and O electronic states and N 2 vibrational levels, the density N e of free electrons, their average kinetic energy and transport properties, the electric field, the average (across the tube) gas temperature, and the wall temperature. The kinetic model for surface processes, which is coupled to that for the bulk plasma, takes into account the processes of physical and chemical adsorption and desorption of N and O atoms, surface diffusion of these atoms, and surface chemical reactions leading to the formation of gas-phase N 2 , O 2 , NO, and NO 2 molecules. The probabilities for surface losses of N, O, and NO and the rates for surface production of gas-phase NO and NO 2 molecules have been obtained as a function of the surface temperature and the fluxes of gas-phase N and O atoms and NO molecules to the surface

Self-Consistent Modeling of Volume and Surface Processes in Air Plasma

Temperature-dependent catalytic recombination coefficients are used to calculate the heat flux to the Space Shuttle Orbiter. With variable entropy boundary-layer edge properties obtained from a reacting inviscid flow-field calculation, the reacting boundary-layer equations are solved along the forward 50 percent of the windward centerline using the boundary-layer integral matrix procedure. The results are compared with fully catalytic and noncatalytic reacting solutions, with equilibrium solutions, and with the Orbiter-design heating rates. The fully catalytic heat fluxes are about equal to the equilibrium predictions; whereas, the finite catalytic results are about 12 to 27 percent lower than the fully catalytic results (approaching the noncatalytic results downstream) and as much as 30 to 50 percent lower than design predictions away from the nose area.

Space Shuttle laminar heating with finite-rate catalytic recombination

A simple method of predicting aerodynamic heating and corresponding radiation equilibrium surface temperature-time histories for critical locations on space shuttle orbiter-type vehicles is presented. The method is based on a generalization of correlation equations developed earlier by Rosner for predicting the energy transfer and radiation equilibrium temperatures of surfaces with arbitrary catalytic activity and total hemispheric emittance. Recently obtained experimental data for O and N atom recombination probabilities on candidate material surfaces above 1000 K are used to assess nonequilibrium effects for a range of nose radii and a specific space shuttle re-entry trajectory. It is concluded that low catalytic activity will be especially important in locations of large effective nose radii by both increasing oxidation-resistant coating lifetime and reducing energy transfer into the vehicle.

Daniel E. Rosner

Papers

Non-equilibrium stagnation region aerodynamic heating of hypersonic glide vehicles