Desorption Kinetics of O and CO from Graphitic Carbon Surfaces

The desorption of O/CO from graphitic carbon surfaces is investigated using a one-dimensional model describing the adsorbate interactions with the surface phonon bath. The kinetics of desorption are described through the solution of a master equation for the time-dependent population of the adsorbate in an oscillator state, which is modified through thermal fluctuations at the surface. The interaction of the adsorbate with the surface phonons is explicitly captured by using the computed phonon density Of states (PDOS) of the surface. The coupling of the adsorbate with the phonon bath results in the transition of the adsorbate up and down a vibrational ladder. The adsorbate-surface interaction is represented in the model using a Morse potential, which allows for the desorption process to be directly modeled as a transition from bound to free (continuum) state. The PDOS is a property of the material and the lattice; and is highly sensitive to the presence of defects. The effect of etch pits along with random surface defects on the PDOS is considered in the present work. The presence of defects causes a redshift and broadening of the PDOS, which in turn changes the phonon frequency modes available for adsorbate coupling at the surface. Using the realistic PDOS distributions, the phonon-induced desorption (PID) model was used to compute the transition and desorption rates for both pristine and defective systems. Mathissens rule is used to compute the phonon relaxation time for pristine and defective systems based on the phonon scattering times for each of the different scattering processes. First, the desorption rates of the pristine system is fitted against the experimental values to obtain the Morse potential parameters for each of the observed adatoms. These Morse potential parameters are used along with the defective PDOS and phonon relaxation time to compute the desorption rates for the defective system. The defective system rates (both transition and desorption) were consistently lower in comparison with the pristine system. The difference between the transition rates is more significant at lower initial states due to higher energy spacing between the levels. In the case of the desorption rates, the difference between the defective and pristine system is more significant at higher temperatures. The desorption rates for each of the system shows an order of magnitude decrease with the strongly bound systems exhibiting the greatest reduction in the desorption rates

Consistent treatment of transport properties of weakly-ionized gas mixtures in DSMC

The direct simulation Monte Carlo (DSMC) is a probabilistic, particle-based computational technique, that is widely used for solving rarefied and highly non-equilibrium flows. The transport properties in DSMC are obtained as a result of the transport of mass, momentum and energy during binary collision processes between the simulated particles. The details of the collision processes, and therefore, the transport properties are dictated by the collision cross-section models employed in DSMC. In the DSMC method, phenomenological models are used for describing the collisional interaction of the simulated particles in the gas. Accurate modeling of transport properties is absolutely critical in any computational solver for obtaining physically realistic solutions of the flow field. In this work, a systematic approach for calibrating the DSMC collision model parameters to achieve consistency in the transport processes is presented. The DSMC collision cross-section model parameters are calibrated for high temperature conditions by matching the collision integrals from DSMC against physically accurate collision integrals that are currently employed in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and Data Parallel Line Relaxation (DPLR) high temperature CFD solvers. The DSMC parameter values are computed for the widely used Variable Hard Sphere (VHS) and Variable Soft Sphere (VSS) models using both the collision-averaged and collision-specific pairing approaches. An analysis on the applicability of the pairing approaches revealed that, each specific collision process needs to be treated independently (i.e., collision-specific pairing approach) in order to obtain physically accurate collision integrals and transport properties. In addition, the validity of the VHS and the VSS model to adequately capture the various phenomena occurring during the different types of collisional interactions in a weakly-ionized gas mixture is examined. Use of the VSS model, that could account for the anisotropic scattering of the collision process, was found to be necessary to achieve consistency in transport processes of ionized gases. The agreement of the VSS transport properties as determined by the ab initio based collision integral fits was found to be within 6% in the entire temperature range, regardless of the composition of the mixture. The recommended model parameter values can readily be applied to any gas mixture involving binary collisional interactions between the chemical species presented, for the specified temperature range. This general procedure is used for calibrating the collision model parameters for the interactions in some important gas systems and an extensive set of calibrated collision model parameters are presented. The recommended best-fit parameter values are provided for neutral gas mixtures over a temperature range of 1000-5000 K, and for ionized gas systems over a temperature range of 1000-20,000 K. Finally, the effect of the calibrated parameters are studied by comparing the flow field solutions computed using the calibrated parameters and Bird’s values for a neutral and ionized air mixture. Comparison of stagnation line heat flux values show significant differences (up to 40%) in the calibrated collision-specific VSS parameters with respect to Bird’s collision-averaged VHS model values

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

The Porous Microstructure Analysis (PuMA) software is a suite of tools for the analysis of porous materials and generation of material microstructures. From microstructural data, often obtained through X-ray microtomography, PuMA can determine a number of effective material properties and perform material response simulations. Version 2.2 includes capabilities for computing volume fractions, porosity, specific surface area, effective thermal and electrical conductivities, and continuum and rarefied diffusive tortuosity. PuMA can also simulate competitive diffusion/reaction processes at the micro-scale, such as surface oxidation. In this poster, recent advancements to the PuMA software are detailed, including the full refactoring of PuMA into v3.0, a new module to compute heat conduction in anisotropic materials, a particle method for simulating molecular beam experiments, a new finite-volume Laplace solver, complex fibrous material generation, woven material generation, and a coupling of PuMA with the DAKOTA software for advanced statistics

Development of physical models for the mesoscopic simulation of gas-surface interactions

This work is focused on the development of physically consistent models for the mesoscopic and macroscopic simulation of gas-surface interactions relevant for hypersonics and high-temperature aerothermodynamic applications. Both nonreactive and reactive interactions are considered with a special focus on desorption. The aim of the work is to employ microscopic information in the form of detailed experiments, numerical simulations, and fundamental theories, as a basis to construct general, accurate and physically realistic models for the interaction of oxygen: atomic (reactive) and molecular (non-reactive) with carbon surfaces: flat (vitreous) and complex porous microstructure (FiberForm®) at high temperatures ranging from 500 K to 2000 K. These models may be employed directly in conventional computational fluid dynamics (CFD), kinetic simulation, and material response tools for the study of non-equilibrium gas-surface interactions. A detailed finite-rate surface chemistry model for the interaction of oxygen with vitreous carbon (VC) surface is developed from molecular beam experimental data using direct simulation Monte Carlo (DSMC). First, a generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the DSMC solver. The various mechanisms include adsorption, desorption, Eley-Rideal (ER), and several types of Langmuir-Hinshelwood (LH) mechanisms. 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). 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. This framework is used to numerically simulate the hyperthermal pulsed beam surface scattering experiments. Next, a general methodology for constructing finite rate surface chemistry models using time-of flight (TOF) and angular distribution data obtained from pulsed hyperthermal beam experiments is presented. A detailed study is performed to analyze the TOF distributions corresponding to the various reaction mechanisms at diverse conditions using the DSMC surface chemistry framework. This information is used to identify and isolate the products formed through different reaction mechanisms from the molecular beam experimental data of oxygen on vitreous carbon. A general methodology to derive the reaction rate constants which takes into account the pulsed nature of the beam is described and used to derive the rates within the vitreous carbon oxidation model. The constructed finite rate surface chemistry model provides excellent agreement with the experimental TOF and angular distribution as well as the total product fluxes. As a next step, the derived vitreous carbon oxidation model is extended to FiberForm®, which is used as a precursor of NASA’s TPS material Phenolic Impregnated Carbon Ablator (PICA). The purpose of this study is to investigate the reactive interaction of fibrous carbon with atomic oxygen in a complex microstructure, which is the primary source of carbon removal at lower temperatures. The detailed microstructure of FiberForm® obtained from X-ray micro-tomography is used in the porous microstructure analysis (PuMA) simulations to capture the complexity of the porous and fibrous characteristic of FiberForm®. Comparison between the experimental and PuMA time-of-flight (TOF) distributions are presented for both the reactive interaction of the oxygen beam and the nonreactive interaction of the argon beam. It was also found that a significantly higher amount of CO (up to 30% of the total product flux) is generated when the beam interacted with FiberForm®, when compared with vitreous carbon. This is postulated to be primarily a result of multiple collisions of oxygen with the fibers, resulting in an higher effective rate of CO production. Multiple collisions are also found to thermalize the O atoms, in addition to the adsorption/desorption process. The effect of microstructure is concluded to be crucial in determining the final composition and energy distributions of the products. Thus, an effective model for the oxygen interaction with FiberForm®, fully accounting for the detailed microstructure, for use in Computational Fluid Dynamics (CFD) and material response codes, is presented. In order to construct the effective surface chemistry model for FiberForm®, the VC model was applied to the detailed microstructure of FiberForm® to obtain the product fluxes at various porosities. At higher porosities, higher mole fractions of CO and lower amounts of O (up to 10% of the total product flux) were observed. This is due to the greater penetration of the incoming beam atoms into the microstructure leading to more collisions with the surface, resulting in the higher mole fraction of CO. This effect is more pronounced at higher temperatures when the probability of CO formation during a single collision is smaller. The effective model reaction mechanisms are assumed to be the same as that of the VC model, as well as the desorption rate constant values. Simulations performed using the constructed effective rates with a flat plate provided excellent agreement with the experimental TOF and angular distributions, and with the analyzed experimental fluxes. This effective model also provides excellent agreement with the PuMA data for the entire porosity range of interest. In order to study the non-reactive (inelastic) scattering process, Molecular dynamics /Quasi-classical trajectory (MD-QCT) simulations and molecule-surface scattering (MSS) theory are used. The system of interest in this work is the gas-surface interactions of O2 molecules striking a carbon surface. MD-QCT technique uses quasi-classical methods to represent the internal energies of the systems within MD and thus can be used to model accurate post-reaction and post-collision molecular internal energy distributions. The MSS theory employs a theoretical framework which accounts for several mechanisms of energy transfer between the substrate and gas particles including multi-phonon excitations, and translational, rotational and vibrational energy transfer. This framework is quasi-classical and employs classical treatment of translational and rotational modes while the vibrational mode is considered quantum-mechanically. A range of initial translational energies of the molecule and the surface temperature is considered to elucidate the dependence of the scattered molecule properties on these parameters. The quantities of interest in this work are the final energy (translational, rotational and vibrational) and polar angular distributions. The values of the fitted MSS model parameters are presented along with their variation with the initial molecule translational energy and the surface temperature, along with the physical significance of their variation. Finally, the desorption of O/CO from graphitic carbon surfaces is investigated using a one-dimensional model describing the adsorbate interactions with the surface phonon bath. The kinetics of desorption are described through the solution of a master equation for the time-dependent population of the adsorbate in an oscillator state, which is modified through thermal fluctuations at the surface. The interaction of the adsorbate with the surface phonons is explicitly captured by using the computed phonon density of states (PDOS) of the surface. The coupling of the adsorbate with the phonon bath results in the transition of the adsorbate up and down a vibrational ladder. The adsorbate-surface interaction is represented in the model using a Morse potential, which allows for the desorption process to be directly modeled as a transition from bound to free (continuum) state. The PDOS is an important input within the phonon-induced desorption (PID) model, which is a property of the material and the lattice and is highly sensitive to the presence of defects. The effect of random surface defects, etch pits, and adsorbates on the PDOS is considered in the present work. The presence of defects causes a redshift and broadening of the PDOS, which in turn changes the phonon frequency modes available for adsorbate coupling at the surface. This PDOS including defects is used within the PID model to predict the desorption rate constant. Using the realistic PDOS distributions, the PID model was used to compute the transition and desorption rates for both pristine and defective systems. Mathissen’s rule is used to compute the phonon relaxation time for pristine and defective systems based on the phonon scattering times for each of the different scattering processes. First, the desorption rates of the pristine system is fitted against the experimental values to obtain the Morse potential parameters for each of the observed adatoms. These Morse potential parameters are used along with the defective PDOS and phonon relaxation time to compute the desorption rates for the defective system. The defective system rates (both transition and desorption) were consistently lower in comparison with the pristine system. The difference between the transition rates is more significant at lower initial states due to higher energy spacing between the levels. In the case of the desorption rates, the difference between the defective and pristine system is more significant at higher temperatures. The desorption rates for each of the system shows an order of magnitude decrease with the strongly bound systems exhibiting the greatest reduction in the desorption rates

Development of physical models for the mesoscopic simulation of gas-surface interactions

This work is focused on the development of physically consistent models for the mesoscopic and macroscopic simulation of gas-surface interactions relevant for hypersonics and high-temperature aerothermodynamic applications. Both nonreactive and reactive interactions are considered with a special focus on desorption. The aim of the work is to employ microscopic information in the form of detailed experiments, numerical simulations, and fundamental theories, as a basis to construct general, accurate and physically realistic models for the interaction of oxygen: atomic (reactive) and molecular (non-reactive) with carbon surfaces: flat (vitreous) and complex porous microstructure (FiberForm®) at high temperatures ranging from 500 K to 2000 K. These models may be employed directly in conventional computational fluid dynamics (CFD), kinetic simulation, and material response tools for the study of non-equilibrium gas-surface interactions. A detailed finite-rate surface chemistry model for the interaction of oxygen with vitreous carbon (VC) surface is developed from molecular beam experimental data using direct simulation Monte Carlo (DSMC). First, a generalized finite-rate surface chemistry framework incorporating a comprehensive list of reaction mechanisms is developed and implemented into the DSMC solver. The various mechanisms include adsorption, desorption, Eley-Rideal (ER), and several types of Langmuir-Hinshelwood (LH) mechanisms. 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). 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. This framework is used to numerically simulate the hyperthermal pulsed beam surface scattering experiments. Next, a general methodology for constructing finite rate surface chemistry models using time-of flight (TOF) and angular distribution data obtained from pulsed hyperthermal beam experiments is presented. A detailed study is performed to analyze the TOF distributions corresponding to the various reaction mechanisms at diverse conditions using the DSMC surface chemistry framework. This information is used to identify and isolate the products formed through different reaction mechanisms from the molecular beam experimental data of oxygen on vitreous carbon. A general methodology to derive the reaction rate constants which takes into account the pulsed nature of the beam is described and used to derive the rates within the vitreous carbon oxidation model. The constructed finite rate surface chemistry model provides excellent agreement with the experimental TOF and angular distribution as well as the total product fluxes. As a next step, the derived vitreous carbon oxidation model is extended to FiberForm®, which is used as a precursor of NASA’s TPS material Phenolic Impregnated Carbon Ablator (PICA). The purpose of this study is to investigate the reactive interaction of fibrous carbon with atomic oxygen in a complex microstructure, which is the primary source of carbon removal at lower temperatures. The detailed microstructure of FiberForm® obtained from X-ray micro-tomography is used in the porous microstructure analysis (PuMA) simulations to capture the complexity of the porous and fibrous characteristic of FiberForm®. Comparison between the experimental and PuMA time-of-flight (TOF) distributions are presented for both the reactive interaction of the oxygen beam and the nonreactive interaction of the argon beam. It was also found that a significantly higher amount of CO (up to 30% of the total product flux) is generated when the beam interacted with FiberForm®, when compared with vitreous carbon. This is postulated to be primarily a result of multiple collisions of oxygen with the fibers, resulting in an higher effective rate of CO production. Multiple collisions are also found to thermalize the O atoms, in addition to the adsorption/desorption process. The effect of microstructure is concluded to be crucial in determining the final composition and energy distributions of the products. Thus, an effective model for the oxygen interaction with FiberForm®, fully accounting for the detailed microstructure, for use in Computational Fluid Dynamics (CFD) and material response codes, is presented. In order to construct the effective surface chemistry model for FiberForm®, the VC model was applied to the detailed microstructure of FiberForm® to obtain the product fluxes at various porosities. At higher porosities, higher mole fractions of CO and lower amounts of O (up to 10% of the total product flux) were observed. This is due to the greater penetration of the incoming beam atoms into the microstructure leading to more collisions with the surface, resulting in the higher mole fraction of CO. This effect is more pronounced at higher temperatures when the probability of CO formation during a single collision is smaller. The effective model reaction mechanisms are assumed to be the same as that of the VC model, as well as the desorption rate constant values. Simulations performed using the constructed effective rates with a flat plate provided excellent agreement with the experimental TOF and angular distributions, and with the analyzed experimental fluxes. This effective model also provides excellent agreement with the PuMA data for the entire porosity range of interest. In order to study the non-reactive (inelastic) scattering process, Molecular dynamics /Quasi-classical trajectory (MD-QCT) simulations and molecule-surface scattering (MSS) theory are used. The system of interest in this work is the gas-surface interactions of O2 molecules striking a carbon surface. MD-QCT technique uses quasi-classical methods to represent the internal energies of the systems within MD and thus can be used to model accurate post-reaction and post-collision molecular internal energy distributions. The MSS theory employs a theoretical framework which accounts for several mechanisms of energy transfer between the substrate and gas particles including multi-phonon excitations, and translational, rotational and vibrational energy transfer. This framework is quasi-classical and employs classical treatment of translational and rotational modes while the vibrational mode is considered quantum-mechanically. A range of initial translational energies of the molecule and the surface temperature is considered to elucidate the dependence of the scattered molecule properties on these parameters. The quantities of interest in this work are the final energy (translational, rotational and vibrational) and polar angular distributions. The values of the fitted MSS model parameters are presented along with their variation with the initial molecule translational energy and the surface temperature, along with the physical significance of their variation. Finally, the desorption of O/CO from graphitic carbon surfaces is investigated using a one-dimensional model describing the adsorbate interactions with the surface phonon bath. The kinetics of desorption are described through the solution of a master equation for the time-dependent population of the adsorbate in an oscillator state, which is modified through thermal fluctuations at the surface. The interaction of the adsorbate with the surface phonons is explicitly captured by using the computed phonon density of states (PDOS) of the surface. The coupling of the adsorbate with the phonon bath results in the transition of the adsorbate up and down a vibrational ladder. The adsorbate-surface interaction is represented in the model using a Morse potential, which allows for the desorption process to be directly modeled as a transition from bound to free (continuum) state. The PDOS is an important input within the phonon-induced desorption (PID) model, which is a property of the material and the lattice and is highly sensitive to the presence of defects. The effect of random surface defects, etch pits, and adsorbates on the PDOS is considered in the present work. The presence of defects causes a redshift and broadening of the PDOS, which in turn changes the phonon frequency modes available for adsorbate coupling at the surface. This PDOS including defects is used within the PID model to predict the desorption rate constant. Using the realistic PDOS distributions, the PID model was used to compute the transition and desorption rates for both pristine and defective systems. Mathissen’s rule is used to compute the phonon relaxation time for pristine and defective systems based on the phonon scattering times for each of the different scattering processes. First, the desorption rates of the pristine system is fitted against the experimental values to obtain the Morse potential parameters for each of the observed adatoms. These Morse potential parameters are used along with the defective PDOS and phonon relaxation time to compute the desorption rates for the defective system. The defective system rates (both transition and desorption) were consistently lower in comparison with the pristine system. The difference between the transition rates is more significant at lower initial states due to higher energy spacing between the levels. In the case of the desorption rates, the difference between the defective and pristine system is more significant at higher temperatures. The desorption rates for each of the system shows an order of magnitude decrease with the strongly bound systems exhibiting the greatest reduction in the desorption rates