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A DSMC Surface Chemistry Model for Carbon-Based Ablators

A detailed molecular surface chemistry model for the DSMC (Direct Simulation Monte Carlo) method is proposed and implemented into the SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) DSMC solver. Molchanova et al. constructed a molecular model for surface recombination in DSMC that includes different surface processes (adsorption, desoprtion, Eley-Rideal and Langmuir-Hinshelwood). All surface processes can be divided into two groups: surface mechanisms, which involve only the particle adsorbed by the surface (desorption and Langmuir-Hinshelwood), and impact mechanisms, which also involve gas-phase particles (adsorption, Eley-Rideal). Using a similar approach, the 14-reaction kinetic model of oxygen-carbon interaction suggested by Zhlukhtov and Abe, as well as more recent models by Alba et al., Poovathinghal et al., and a new model developed in the scope of this work, are implemented in SPARTA. The computational results for the different oxidation models are compared with experimental results from Murray et al. (oxidation of a vitreous carbon surface due to a hyperthermal beam of O and O2), with a particular focus on fluxes, angular and Time-Of-Flight distributions of scattered particles.

oxidation↗

Development of a Detailed Surface Chemistry Framework in DSMC

Many of the current direct simulation Monte Carlo (DSMC) codes still employ only simple surface catalysis models. These include only basic mechanisms such as dissociation, recombination, and exchange reactions, without any provision for adsorption and finite rate kinetics. Incorporating finite rate chemistry at the surface is increasingly becoming a necessity for various applications such as high speed re-entry flows over thermal protection systems (TPS), micro-electro-mechanical systems (MEMS), surface catalysis, etc. In the recent years, relatively few works have examined finite-rate surface reaction modeling using the DSMC method.In this work, a generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the DSMC solver SPARTA. The various mechanisms include adsorption, desorption, Langmuir-Hinshelwood (LH), Eley-Rideal (ER), Collision Induced (CI), condensation, sublimation, etc. The approach is to stochastically model the various competing reactions occurring on a set of active sites. Both gas-surface (e.g., ER, CI) and pure-surface (e.g., LH, desorption) reaction mechanisms are incorporated. The reaction mechanisms could also be catalytic or surface altering based on the participation of the bulk-phase species (e.g., bulk carbon atoms). Marschall and MacLean developed a general formulation in which multiple phases and surface sites are used and we adopt a similar convention in the current work. Microscopic parameters of reaction probabilities (for gas-surface reactions) and frequencies (for pure-surface reactions) that are require for DSMC are computed from the surface properties and macroscopic parameters such as rate constants, sticking coefficients, etc. The energy and angular distributions of the products are decided based on the reaction type and input parameters. Thus, the user has the capability to model various surface reactions via user-specified reaction rate constants, surface properties and parameters.

Gas↗

Development of a Detailed Surface Chemistry Framework in DSMC

A generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the Direct Simulation Monte Carlo (DSMC) solver SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer). The various mechanisms include adsorption, desorption, Eley-Rideal (ER), and several types of Langmuir-Hinshelwood (LH) mechanisms. The approach is to stochastically model the various competing reactions occurring on a set of active sites. Both gas-surface (e.g., adsorption, ER) and pure-surface (e.g., desorption) reaction mechanisms are incorporated, and the framework also includes catalytic or surface altering mechanisms involving the participation of the bulk-phase species (e.g., bulk carbon atoms). Marschall and MacLean developed a general formulation in which multiple phases and surface sites are used and a similar convention is adopted in the current work. Expressions for the microscopic parameters of reaction probabilities (for gas-surface reactions) and frequencies (for pure-surface reactions) that are required for DSMC are derived from the surface properties and macroscopic parameters such as rate constants, sticking coefficients, etc. The energy and angular distributions of the products are specified according to the reaction type and input parameters. This framework also presents physically consistent procedures to accurately compute the reaction probabilities and frequencies in the case of multiple reactions. The result is a modeling tool with a wide variety of surface reactions characterized via user-specified reaction rate constants, surface properties and parameters.

Surface Chemistry↗

Implementation of active sites to capture pitting of oxidizing carbon materials in DSMC.

In this work we demonstrate a newly developed capability to capture pitting of carbon fibers in DSMC simulations, specifically using the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code [1]. State-of-the-art reactive surface models in DSMC compute collision dependent carbon consumption rates (usually through desorption of CO) based on a set of surface reactions that has been derived from molecular beam experiments [2]. The reactivity on each carbon surface element is constant in those models, such that the carbon surface recedes uniformly as a result of ablation. However, it is well known that in reality the carbon surface has locally different reaction rates due to the presence of defects at the atomic scale [3]. These defective sites have a much higher reactivity than the average sites (2-3 orders of magnitude) and are first to react during ablation leading to its removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these ”active” sites (as shown in Fig. 1). In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. Recently a detailed surface chemistry framework was developed in SPARTA, capable of incorporating various reaction mechanisms such as adsorption, desorption, Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) mechanisms [4]. Within this framework, we have implemented the capability of a single surface having multiple site sets with different reactivities. Using this feature, we can simulate the presence of active sites on carbon surfaces, whose reactivity is much greater than an average site as a result of defects. We have implemented the active site fraction as a property of surface elements within SPARTA, which is directly proportional to the local reactivity of each surface element. By introducing an initial distribution of the active site fraction across the carbon surface, and propagating it in a manner that mimics the evolution of real reacting carbon surfaces, we are able to capture the formation and growth of etch pits as a result of surface consumption reactions such as oxidation.

DSMC↗

Implementation of Active Sites in DSMC to Capture Pitting of Oxidizing Carbon Materials

In this work we demonstrate a newly developed capability to capture pitting of carbon fibers in DSMC simulations, specifically using the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code. State-of-the-art reactive surface models in DSMC compute collision dependent carbon consumption rates (usually through desorption of CO) based on a set of surface reactions that has been derived from molecular beam experiments. The reactivity on each carbon surface element is constant in those models, such that the carbon surface recedes uniformly as a result of ablation. However, it is well known that in reality the carbon surface has locally different reaction rates due to the presence of defects at the atomic scale. These defective sites have a much higher reactivity than the average sites (2-3 orders of magnitude) and are first to react during ablation leading to its removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these ”active” sites. In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. Recently a detailed surface chemistry framework was developed in SPARTA, capable of incorporating various reaction mechanisms such as adsorption, desorption, Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) mechanisms. Within this framework, we have implemented the capability of a single surface having multiple site sets with different reactivities. Using this feature, we can simulate the presence of active sites on carbon surfaces, whose reactivity is much greater than an average site as a result of defects. We have implemented the active site fraction as a property of surface elements within SPARTA, which is directly proportional to the local reactivity of each surface element. By introducing an initial distribution of the active site fraction across the carbon surface, and propagating it in a manner that mimics the evolution of real reacting carbon surfaces, we are able to capture the formation and growth of etch pits as a result of surface consumption reactions such as oxidation.

DSMC↗

Simulation of etch pit formation through active sites in carbon fiber micro-structures

Erosion of carbon due to oxidation does not occur uniformly but through localized etch pit formation as a result of active surface sites. In this work we demonstrate a newly developed capability to capture pitting of carbon fiber microstructures such as FiberForm, which is commonly used as the base material for NASA’s spacecraft ablative thermal protection systems (TPS). The simulations are performed at the meso-scale in order to capture the pit formation and growth using direct simulation Monte Carlo (DSMC), specifically using the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code. Legacy and latest models both assume uniform reactivity of carbon surface sites with oxygen even at the meso-scale level. However, in reality the carbon surface has locally different reaction rates due to the presence of defects at the atomic scale. The defective nature of these sites enhances their reactivity with atmospheric gases compared to the non-defective sites (2-3 orders of magnitude) and are termed as “active sites”. Thus, these sites tend to be the first to react and eventually get removed through the formation of gasses such as CO, CO2, and CN. Their removal results in all the neighboring atoms becoming defective, thus leading to chain reaction of localized carbon removal and formation of etch pits. Capturing the formation of pits during the ablation simulation of carbon micro-structures is critical to predicting their structural failure. Recently a detailed surface chemistry framework was developed in SPARTA, capable of incorporating various reaction mechanisms such as adsorption, desorption, Eley-Rideal (ER) and Langmuir-Hinshelwood (LH) mechanisms. We have implemented the capability of a single surface having multiple site sets with different reactivities within this framework. We have used this feature to model the presence of active sites on carbon surfaces, whose reactivity is orders of magnitude higher than that of the passive sites due to the presence of defects. The active site fraction is a property of surface elements within SPARTA and is directly proportional to the local reactivity of each surface element. By introducing an initial distribution of the active site fraction across the carbon surface and propagating it in a manner that mimics the evolution of real reacting carbon surfaces, we can capture the formation and growth of etch pits as a result of surface consumption reactions such as oxidation.

DSMC↗