Gas-surface Interaction Research Articles

A conservative discrete ordinate method for solving semiclassical Boltzmann-BGK equation with Maxwell type wall boundary condition

A robust and efficient numerical method in phase space combining the conservative discrete ordinate method and high order spatial discretization is proposed for the semiclassical Boltzmann equation with Bhatnagar–Gross–Krook (BGK) relaxation time approximation. A general Maxwell type partially diffuse and partially specular reflection solid wall boundary condition for modeling the gas–surface interactions for semiclassical rarefied gas flows is devised. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to evolve the solution in physical space and time. The conservation property of the BGK collision integral is ensured to be fulfilled at the discrete quadrature level approximation. Both specular and diffuse reflection boundary conditions are implemented. Extensive computations of one- and two-dimensional semiclassical rarefied gas dynamical flows covering wide range of flow regimes for three statistics are presented to illustrate the method and boundary conditions treatment. The effect of accommodation coefficient on the rarefied flow field is also examined.

Microstructure and gas-surface interaction studies of a low-density carbon-bonded carbon fiber composite in atmospheric entry plasmas

Carbon-bonded carbon fiber (CBCF) composites are a cost-effective solution for the production of low-density carbon-phenolic Thermal Protection Systems (TPS). This new TPS for spacecraft requires new experimental data for model development and validation. Ablation experiments of a CBCF composite were carried out in an inductively-coupled plasma generator to assess the performance in high-enthalpy flows. Surface temperatures up to 2900K led to strong surface ablation and test samples of hemispherical shape responded with constant surface temperatures and recession rates. Cylindrical samples experienced a continuous surface temperature increase. Emission spectra of the cyano radical CN were indicative of a 4–5mm reactive boundary layer. Deviation from thermal equilibrium was found by comparison to simulated spectra. Micrographs revealed an oxidation zone in the order of 0.2mm at the surface, suggesting a gas phase diffusion controlled ablation regime. Strong corrosion of the fibers in nitrogen plasma is attributed to wall nitridation.

J0540106 マイクロ流路を通過する水分子の質量流量の計測

Along with the development of micro- and nano-technologies, gas-surface interaction becomes important due to large surface area-to-volume ratio in micro-scale gas flows. In such flows, the Knudsen number (Kn) is often employed as a parameter of rarefaction of flows. When 0.01<Kn≦0.1, a flow is classified as the slip flow with a finite velocity slip at boundary. In this regime, the mass flow rate increases from the rate in the continuum regime because of the velocity slip. The mass flow rate depends on the combination of molecule and surface. In this study, we measured the mass flow rate of water molecules to investigate the characteristics on gas properties. The constant-volume technique was employed for measuring the mass flow rate through a micro channel. The obtained results suggested that the adsorption of water molecules on the measurement system influenced the accurate measurement of the mass flow rate.

Molecular free paths in nanoscale gas flows

Average distance traveled by gas molecules between intermolecular collisions, known as the mean free path (MFP), is a key parameter for characterizing gas flows in the entire Knudsen regime. Recent literature presents variations in MFP as a function of the surface confinement, which is in disagreement with the kinetic theory and leads to wrong physical interpretations of nanoscale gas flows. This controversy occurs due to erroneous definition and calculation practices, such as consideration of gas wall collisions, using local bins smaller than a MFP, and utilizing time frames shorter than a mean collision time in the MFP calculations. This study reports proper molecular MFP calculations in nanoscale confinements by using realistic molecular surfaces. We utilize molecular dynamics (MD) simulations to calculate gas MFP in three-dimensional periodic systems of various sizes and for force-driven gas flows confined in nano-channels. Studies performed in the transition flow regime in various size nano-channels and under a range of gas–surface interaction strengths have shown isotropic mean travelled distance and MFP values in agreement with the kinetic theory regardless of the surface forces and surface adsorption effects. Comparison of the velocity profiles obtained in MD simulations with the linearized Boltzmann solutions at predicted Knudsen values shows good agreement in the bulk of the channels, while deviations in the near wall region due to the influence of surface forces are reported.

A gas-surface interaction kernel for diatomic rarefied gas flows based on the Cercignani-Lampis-Lord model

This work presents a kinetic wall boundary model for diatomic gas molecules. The model is derived by generalizing the Cercignani-Lampis-Lord gas-surface interaction kernel in order to account for the gas internal degrees of freedom. Here, opposed to the extensions by Lord [“Some extensions to the Cercignani-Lampis gas-surface scattering kernel,” Phys. Fluids 3, 706–710 (1991)], energy exchange between different molecular modes is honored and thus, different physical phenomena arising from inelastic gas–surface collisions can be described. For practical implementations of the model, a Monte–Carlo algorithm was devised, which significantly reduces the computational cost associated with sampling. Comparisons of model predictions with experimental and molecular dynamics data exhibit good agreement. Moreover, simulation studies are performed to demonstrate how energy transfers between different modes due to wall collisions can be exploited for gas separation.

Numerical investigation of the effect of boundary conditions for a highly rarefied gas flow using the GPU accelerated Boltzmann solver

The effect of the gas–surface interaction model on the rarefied gas flow between parallel plates is investigated on the basis of the Boltzmann kinetic equation. The Cercignani–Lampis model for diffuse scattering with incomplete energy accommodation is provided as the boundary condition on plates. The numerical analysis of the heat transfer problem between parallel plates with uniform and sinusoidal temperature distributions is carried out. The computational algorithm is adapted for solving the Boltzmann equation onto Graphics Processing Units (GPUs). The speedup of the GPU-accelerated computation is up to 50 times as compared to the CPU one. It was found that a non-uniform temperature distribution on plates induced a steady flow. In addition, the flow field strongly depends on the value of accommodation coefficients imposed in the Cercignani–Lampis model and this effect is more visible for high Knudsen numbers. Presented results are in good agreement with open literature ones obtained by means of the direct simulation Monte Carlo method.

Single-crystal adsorption calorimetry on well-defined surfaces: from single crystals to supported nanoparticles.

Single-crystal adsorption calorimetry (SCAC) measures the energetics of gas-surface interactions in a direct way and can be applied to a broad range of well-defined model surfaces. In this Personal Account we review some of the recent advances in understanding the interaction of gaseous molecules with single-crystal surfaces and well-defined supported metallic nanoparticles by this powerful technique. SCAC was applied on single-crystal surfaces to determine formation enthalpies of adsorbed molecular fragments typically formed during heterogeneously catalyzed reactions involving hydrocarbons. On supported metal nanoparticles, the binding energies of gaseous species were determined by SCAC as a function of the particle size. The reported data provide valuable information for ongoing research in many fields of heterogeneous catalysis and materials science. In addition, direct calorimetric measurements serve as benchmarks for the improvement of computational approaches to understanding surface chemistry.

Thermodynamics and Kinetics of SiC CVD Epitaxy

One of the challenges in modeling epitaxial growth is to establish a connection between the experimental conditions and microstructure and epitaxial quality of the films. At the core of this problem is the need to have accurate models of the heterogeneous chemistry during epitaxy that can bridge reactor scale with atomic scale simulations and take into account the impact of film microstructure. In this work we focus on the heterogeneous chemistry models for SiC epitaxy by CVD. First, we carry out a sensitivity analysis of existing models in the literature, and we identify their limitations as well as the main reaction pathways that can be found at different experimental conditions. We then cast these models in the context of the step-flow growth. This allow us to rationalize the expected dependence of the different sticking probability values on the miscut angle and, more generally, on the surface terrace to step site ratio. Finally we show how these models can be used to bridge reactor-scale and atomistic simulations by providing sticking probabilities that depend on the surface morphology and the atomistic details of gas-surface interaction.

직접모사법을 이용한 지구 저궤도 파라볼릭 안테나 탑재 위성의 항력 예측

저궤도에서 운용되는 위성은 대기 저항에 의한 연료소모가 크며, 연료소모는 임무수명 및 발사무게에 영향을 미치게 되어 위성 형상에 따른 항력의 예측이 중요하다. 본 논문에서는 직접모사법을 이용하여 파라볼릭 안테나를 탑재한 저궤도 위성의 임무고도의 변화와 받음각에 따른 항력 및 항력 계수의 변화를 살펴보았다. 저궤도의 희박 기체의 거동을 모사하는 직접모사법의 적용성을 검증하기 위해 스타샤인(Starshine) 위성의 비행데이터를 이용하여 고도, 대기와 표면의 상호작용에 따른 항력 계수를 비교하였다. 결론적으로 계산결과로부터 저궤도 위성의 정밀한 궤도수명 계산에 적합한 항력 계수를 도출하였다. Consumption of the fuel on the satellite operating in low earth orbit, is increased due to the air resistance and the amount of increase makes the satellite lifetime decrease or the satellite mass risen. Therefore the prediction of drag force of the satellite is important. In the paper, drag force and drag coefficient analysis of the parabolic antenna satellite in low earth orbit using direct simulation monte carlo method (DSMC) is conducted according to the mission altitude and angle of attack. To verify the DSMC simulated rarefied air movement, Starshine satellite drag coefficient according to the altitude and gas-surface interaction are compared with the flight data. Finally, from the analysis results, it leads to appropriate satellite drag coefficient for orbit lifetime calculation.

Different Implementations of Diffuse Reflection with Incomplete Accommodation for Drag Coefficient Modeling

Diffuse reflection with incomplete accommodation is the favored gas–surface interaction model for calculating the drag coefficient of satellites in low Earth orbit, where drag is the largest source of uncertainty in the orbital trajectory of satellites. Closed-form solutions have incorporated the variation of the energy accommodation coefficient through equating the total energy of the incident and reflected flows; however, this leads to an incorrect reflected velocity distribution for incomplete accommodation. The problem is highlighted by investigating the velocity distribution functions for a gas reflected from a flat plate at zero accommodation. A physically accurate implementation for diffuse reflection with incomplete accommodation based on the Cercignani–Lampis–Lord gas–surface interaction model is compared with the closed-form solutions that equate the incident and reflected energy of the flow. The Cercignani–Lampis–Lord gas–surface interaction model shows the conservation of energy on a molecule-by-molecule basis for zero accommodation, as expected, whereas the closed-form method only conserves energy on average. The macroscopic effect of the different velocity distributions manifests in differences of in the drag coefficient of a flat plate, sphere, and the GRACE satellite at zero accommodation and differences larger than 1% for energy accommodation coefficients less than 0.90.

Gas-surface interactions using accommodation coefficients for a dilute and a dense gas in a micro- or nanochannel: heat flux predictions using combined molecular dynamics and Monte Carlo techniques.

The influence of gas-surface interactions of a dilute gas confined between two parallel walls on the heat flux predictions is investigated using a combined Monte Carlo (MC) and molecular dynamics (MD) approach. The accommodation coefficients are computed from the temperature of incident and reflected molecules in molecular dynamics and used as effective coefficients in Maxwell-like boundary conditions in Monte Carlo simulations. Hydrophobic and hydrophilic wall interactions are studied, and the effect of the gas-surface interaction potential on the heat flux and other characteristic parameters like density and temperature is shown. The heat flux dependence on the accommodation coefficient is shown for different fluid-wall mass ratios. We find that the accommodation coefficient is increasing considerably when the mass ratio is decreased. An effective map of the heat flux depending on the accommodation coefficient is given and we show that MC heat flux predictions using Maxwell boundary conditions based on the accommodation coefficient give good results when compared to pure molecular dynamics heat predictions. The accommodation coefficients computed for a dilute gas for different gas-wall interaction parameters and mass ratios are transferred to compute the heat flux predictions for a dense gas. Comparison of the heat fluxes derived using explicit MD, MC with Maxwell-like boundary conditions based on the accommodation coefficients, and pure Maxwell boundary conditions are discussed. A map of the heat flux dependence on the accommodation coefficients for a dense gas, and the effective accommodation coefficients for different gas-wall interactions are given. In the end, this approach is applied to study the gas-surface interactions of argon and xenon molecules on a platinum surface. The derived accommodation coefficients are compared with values of experimental results.

Implicit Coupling Approach for Simulation of Charring Carbon Ablators

This study demonstrates that coupling of a material thermal response code and a flow solver with nonequilibrium gas–surface interaction for simulation of charring carbon ablators can be performed using an implicit approach. The material thermal response code used in this study is the three-dimensional version of fully implicit ablation and thermal response program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting Navier–Stokes equations using data-parallel line relaxation method. Coupling between the material response and flow codes is performed by solving the surface mass balance in the flow solver and the surface energy balance in the material response code. Thus, the material surface recession is predicted in the flow code, and the surface temperature and pyrolysis gas injection rate are computed in the material response code. It is demonstrated that the time-lagged explicit approach is sufficient for simulations at low surface heating conditions, in which the surface ablation rate is not a strong function of the surface temperature. At elevated surface heating conditions, the implicit approach has to be taken because the carbon ablation rate becomes a stiff function of the surface temperature, and thus the explicit approach appears to be inappropriate, resulting in severe numerical oscillations of predicted surface temperature. Implicit coupling for simulation of arc-jet models is performed, and the predictions are compared with measured data. Implicit coupling for trajectory-based simulation of Stardust forebody heat shield is also conducted. The predicted stagnation point total recession is compared with that predicted using the chemical equilibrium surface assumption.

Molecular dynamics simulations on scattering of single Ar, N2, and CO2 molecules on realistic surfaces

The understanding of rarefied gas flows is of great interest since microelectromechanical systems are becoming ever smaller and intensification of all gas-related tasks in process engineering takes place on the microscale. With increasing rarefaction the influence of gas-surface interactions on momentum and energy transport becomes more significant producing rarefaction effects, such as wall slip. These gas-surface interactions are commonly described by means of accommodation coefficients that are input parameters for scattering kernels in rarefied gas flow simulations. In this context the tangential momentum accommodation coefficient (TMAC) is the most important input parameter since it allows to define the boundary conditions.In this work we present an approach in molecular dynamics simulations to determine the TMAC of a three-dimensional system on the basis of a few thousand single gas-surface collisions using a comparatively small super cell instead of relying on a large(r) system with a specific flow geometry which is the typical approach in literature. We demonstrate that TMAC results obtained by this method are in good agreement with results in relevant literature. The advantage of this method is the small number of atoms in the cell reducing the computational effort. Thus, the approach allows to analyze the interactions of realistic gas molecules (Ar, N2, and CO2) with realistic surfaces (Pt-, Si-, and hydroxylated Si-surfaces). This includes gas molecules with rotational degrees of freedom as well as surfaces with moving surface groups, whereby partial charges of the different atoms are taken into account. Furthermore, the presented approach allows for systematic investigation of each influencing parameter, such as temperature, electrostatic interactions, moving surface atoms, and interactions with chemical surface groups. Additionally, this approach is used to analyze the dependencies of angular scattering distributions on temperature and the incident angle of the impinging molecule.

Velocity distribution and velocity correlation of mixture of gases in a nanochannel

Molecular dynamics study of non-reacting and disparate mass binary gas mixture is conducted. To investigate the gas–surface interaction properties of the gas mixture, in non-continuum regime, the rarefied gas confined in a nanochannel is considered. While keeping the bulk number density a constant, the interaction properties of gas mixtures at different molar concentration of individual components are determined. The study discusses the calculation of accommodation coefficients and prediction of the reflected gas distribution using accommodation coefficients. The Maxwell-type model that use calculated values of accommodation coefficients accurately predicts the reflected tangential and normal distributions. The model is validated for different wall-fluid conditions. The velocity correlation of individual gases demonstrates that the individual components of gas mixture are accommodated in different proportion. The result from the study will be beneficial in the analysis and development of potential applications involving the flow of gas mixture in a nanochannel.

Computation of Hypersonic Flows Using the Direct Simulation Monte Carlo Method

The direct simulation Monte Carlo method has evolved over 50 years into a powerful numerical technique for the computation of complex, nonequilibrium gas flows. In this context, “nonequilibrium” means that the velocity distribution function is not in an equilibrium form due to a low number of intermolecular collisions within a fluid element. In hypersonic flow, nonequilibrium conditions occur at high altitude and in regions of flowfields with small length scales. In this paper, the theoretical basis of the direct simulation Monte Carlo technique is discussed. In addition, the methods used in direct simulation Monte Carlo are described for simulation of high-temperature, real gas effects and gas–surface interactions. Several examples of the application of direct simulation Monte Carlo to flows around blunt hypersonic vehicles are presented to illustrate current capabilities. Areas are highlighted where further research on the direct simulation Monte Carlo technique is required.

Comparing Physical Drag Coefficients Computed Using Different Gas–Surface Interaction Models

Drag coefficient is a major source of uncertainty in calculating the aerodynamic forces on satellites in low Earth orbit. Closed-form solutions are available for simple geometries under the assumption of free molecular flow; however, most satellites have complex geometries, and a more sophisticated method of calculating the drag coefficient is needed. This work builds toward modeling physical drag coefficients using the direct simulation Monte Carlo method capable of accurately modeling flow shadowing and concave geometries. The direct simulation three-dimensional visual program and the direct simulation Monte Carlo analysis code are used to compare the effects of two separate gas–surface interaction models: diffuse reflection with incomplete accommodation and quasi-specular Cercignani–Lampis–Lord models. Results show that the two gas–surface interaction models compare well at altitudes below during solar maximum conditions and below during solar minimum conditions. The difference in drag coefficient of a sphere at calculated using the two gas–surface interaction models is during solar maximum and increases to during solar minimum. The difference in drag coefficient of the GRACE satellite computed using the two gas–surface interaction models at differs by during solar minimum conditions and by during solar maximum conditions.

Drag Coefficient Model Using the Cercignani–Lampis–Lord Gas–Surface Interaction Model

Drag coefficient calculations using the Cercignani–Lampis–Lord quasi-specular gas–surface interaction model have been used to derive modified closed-form solutions for several simple geometries. The key component of the modified closed-form solutions is a relation between the normal energy and normal momentum accommodation coefficients, which is valid within over the global parameter space. The modified closed-form solutions are made self-consistent by relating the effective energy accommodation to the partial pressure of atomic oxygen through a Langmuir isotherm. The modified closed-form solutions are compared to fitted drag coefficients and drag coefficients computed using two other gas–surface interaction models: diffuse reflection with incomplete accommodation and Maxwell’s model. Comparison during solar maximum conditions shows that both the diffuse reflection with incomplete accommodation and Cercignani–Lampis–Lord models agree with fitted drag coefficients within below altitude. Further comparison shows that solar minimum drag coefficients are up to higher than those at solar maximum based on global ionosphere–thermosphere model atmospheric properties. Drag coefficients computed with atmospheric properties from the Naval Research Laboratory mass spectrometer incoherent scatter extended model and the global ionosphere–thermosphere model agree within at solar maximum but disagree by up to at solar minimum.

Ordering and growth of rare gas films (Xe, Kr, Ar, and Ne) on the pseudo-ten-fold quasicrystalline approximant Al13Co4(100) surface

Adsorption of the rare gases Kr, Ar, and Ne on the complex alloy surface Al13Co4(100) was studied using grand canonical Monte Carlo (GCMC) computer simulations. This surface is an approximant to the ten-fold decagonal Al–Ni–Co quasicrystalline surface, on which rare gas adsorption was studied previously. Comparison of adsorption results on the periodic Al13Co4(100) surface with those of the quasiperiodic Al–Ni–Co surface indicates some similarities, such as layer-by-layer growth, and some dissimilarities, such as the formation of Archimedes tiling phases (Mikhael et al 2008 Nature 454 501, Shechtman et al 1984 Phys. Rev. Lett. 53 1951, Macia 2006 Rep. Prog. Phys. 69 397, Schmiedeberg et al 2010 Eur. Phys. J. E 32 25–34, Kromer et al 2012 Phys. Rev. Lett. 108 218301, Schmiedeberg and Stark 2008 Phys. Rev. Lett. 101 218302). The conditions under which Archimedes tiling phases (ATP) emerge on Al13Co4(100) are examined and their presence is related to the gas–gas and gas–surface interaction parameters.

Gas-surface interaction and boundary conditions for the Boltzmann equation

In this paper we revisit the derivation of boundaryconditions for the Boltzmann Equation. The interaction between thewall atoms and the gas molecules within a thin surface layer isdescribed by a kinetic equation introduced in [10] and usedin [1]. This equation includes a Vlasov term and a linearmolecule-phonon collision term and is coupled with the Boltzmannequation describing the evolution of the gas in the bulkflow. Boundary conditions are formally derived from this model byusing classical tools of kinetic theory such as scaling and systematicasymptotic expansion. In a first step this method is applied to thesimplified case of a flat wall. Then it is extented to walls withnanoscale roughness allowing to obtain more complex scatteringpatterns related to the morphology of the wall. It is proved that theobtained scattering kernels satisfy the classical imposed propertiesof non-negativeness, normalization and reciprocity introduced byCercignani [13].

Fast Surface Potential Response to Gas in Air at the Room Temperature

Abstract The surface potential response to a gas-surface interaction is proposed as the basis for the development of a new family of biocompatible chemical sensors. It is experimentally demonstrated that response to gas is fast at room temperatures in the multi-layer arrangement of the metal and metal oxide films with thickness less than 20 nm. For these structures, the tests prove that the response time is 10 to 60 seconds at 295 K. An unexpected memory of the chemical response can be obtained in the TiO 2-x based detectors with the special arrangement of the films.