Energy Accommodation Coefficient Research Articles

Molecular-Dynamics-Derived Gas–Surface Models for Use in Direct-Simulation Monte Carlo

In the present work, molecular dynamics is used to study molecular nitrogen impinging on multilayered graphene and fused-quartz surfaces at different incidence speeds and angles to obtain energy accommodation coefficients for use in direct-simulation Monte Carlo. The trajectory molecular dynamics simulations were performed on these two surfaces to study the difference between atomistically smooth and rough cases. Based on the postcollision behavior of the nitrogen molecule, the molecular dynamics trajectories were classified into three categories, namely, single, and multiple with and without escape. The collision statistics for the three categories were found to depend on the incidence angle and the speed, and a strong correlation among incidence speed, angle, and surface topology in the probability distribution of the energy accommodation coefficients was observed. A direct-velocity-sampling gas–surface interaction model was implemented in direct-simulation Monte Carlo, which was found to predict flow and surface properties comparable to the Maxwell gas–surface interaction model when the molecular dynamics data used for velocity sampling were obtained from a rough (diffuse) surface.

The role of thermal energy accommodation and atomic recombination probabilities in low pressure oxygen plasmas

Surface interaction probabilities are critical parameters that determine the behaviour of low pressure plasmas and so are crucial input parameters for plasma simulations that play a key role in determining their accuracy. However, these parameters are difficult to estimate without in situ measurements. In this work, the role of two prominent surface interaction probabilities, the atomic oxygen recombination coefficient γO and the thermal energy accommodation coefficient αE in determining the plasma properties of low pressure inductively coupled oxygen plasmas are investigated using two-dimensional fluid-kinetic simulations. These plasmas are the type used for semiconductor processing. It was found that αE plays a crucial role in determining the neutral gas temperature and neutral gas density. Through this dependency, the value of αE also determines a range of other plasma properties such as the atomic oxygen density, the plasma potential, the electron temperature, and ion bombardment energy and neutral-to-ion flux ratio at the wafer holder. The main role of γO is in determining the atomic oxygen density and flux to the wafer holder along with the neutral-to-ion flux ratio. It was found that the plasma properties are most sensitive to each coefficient when the value of the coefficient is small causing the losses of atomic oxygen and thermal energy to be surface interaction limited rather than transport limited.

Energy accommodation coefficient extracted from acoustic resonator experiments.

We review values of the temperature jump coefficient ζT determined from measurements of the acoustic resonance frequencies facoust of helium-filled and argon-filled, spherical cavities near ambient temperature. We combine these values of ζT with literature data for tangential momentum accommodation coefficient (TMAC) and the Cercignani-Lampis model of the gas-surface interaction to obtain measurement-derived values of the normal energy accommodation coefficient (NEAC). We found that NEAC ranges from 0 to 0.1 for helium and from 0.61 to 0.85 for argon at ambient temperature for several different surfaces. We suggest that measurements of facoust of gas-filled, cylindrical cavities and of the non-radial modes of quasi-spherical cavities might separately determine TMAC and NEAC. Alternatively, TMAC and NEAC could be determined by measuring the heat transfer and momentum transfer between parallel rotating discs at low pressure.

Simulation of diatomic gas-wall interaction and accommodation coefficients for negative ion sources and accelerators.

Particle-wall interactions determine in different ways the operating conditions of plasma sources, ion accelerators, and beams operating in vacuum. For instance, a contribution to gas heating is given by ion neutralization at walls; beam losses and stray particle production-detrimental for high current negative ion systems such as beam sources for fusion-are caused by collisional processes with residual gas, with the gas density profile that is determined by the scattering of neutral particles at the walls. This paper shows that Molecular Dynamics (MD) studies at the nano-scale can provide accommodation parameters for gas-wall interactions, such as the momentum accommodation coefficient and energy accommodation coefficient: in non-isothermal flows (such as the neutral gas in the accelerator, coming from the plasma source), these affect the gas density gradients and influence efficiency and losses in particular of negative ion accelerators. For ideal surfaces, the computation also provides the angular distribution of scattered particles. Classical MD method has been applied to the case of diatomic hydrogen molecules. Single collision events, against a frozen wall or a fully thermal lattice, have been simulated by using probe molecules. Different modelling approximations are compared.

Surface Slip Effect on Thermal Environment of Hypersonic Non-Equilibrium Flows

Boundary slip effect caused by low gas density has an important influence on the thermal environment of the vehicles. Numerical studies on the boundary slip effect and accommodation for moment and energy have been carried out in this paper. The simulations considering slip boundary and surface catalysis are validated with Arc-jet test data. Mechanism and rules of impact on surface heat flux by different boundary slip level (Knudsen number from 0.0028 to 0.05) has been investigated in typical hypersonic flow conditions. The results show that mechanisms of boundary slip effect on mass diffusion heat flux and convective heat flux are different; slip boundary diminishes the convective heat, whereas enhances the mass diffusion heat flux. Smaller moment and energy accommodation coefficient is equivalent to more rarefaction. As Knudsen number goes up, the influences of accommodation on heatflux are enhanced, it mainly affects the convective heat flux.

Influence of gas–surface interaction on gaseous transmission probability through conical and spherical ducts

Gas flows through ducts are used in the metrology of vacuum in order to develop a continuous flow standard. Usually, the diffuse scattering is assumed for those particles which undergo collisions with the duct surface. However, many experiments pointed out a significant deviation from the diffuse scattering especially for light gases like helium. As a consequence, the conductance calculated on the basis of the diffuse scattering can be different from the real one leading to an additional uncertainty which is usually neglected. In the present work, the conductance of conical and spherical ducts applying the Cercignani–Lampis model of the gas–surface interaction is calculated. It is shown that in contrast to previous works, the energy accommodation can significantly affect isothermal gas flows. Moreover, a decrease of the accommodation coefficients not always leads to an increase of the transmission probability, but in some situations a smaller energy accommodation coefficient corresponds to a smaller conductance.

Accommodative dependence of thermophoresis in gases in the Knudsen regime

The role of accommodation coefficients of energy, as well as tangential and normal momenta, in the phenomenon of thermophoresis of a spherical aerosol particle in the free molecule (Knudsen) regime is studied. The feature of this work is that it does not involve any assumptions about the distribution function of gas molecules reflected from the molecule’s surface. The accommodation coefficients are introduced in equations directly via momentum and energy flows. Expressions for the thermophoresis force and velocity, as well as for the thermal polarization of a particle (difference of temperatures in the direction of the incoming gas flow) have been obtained. It is shown that, in the Knudsen regime, the thermophoresis force and velocity depend only on the accommodation coefficients of momentum and do not depend on the accommodation coefficient of energy. The magnitude of thermal polarization, on the contrary, is directly proportional to the accommodation coefficient of energy and does not depend on the accommodation coefficients of momentum.

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.

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.

Energy Accommodation between Noble Gases and Carbon Nanotubes

Molecular dynamics simulations are used to predict the energy accommodation coefficients (EACs) between the noble gases He, Ne, and Ar and the outside of single-walled carbon nanotubes (CNTs) with diameters between 0.41 and 6.10 nm at a temperature of 300 K. The EAC increases monotonically with CNT diameter and approaches the value predicted for graphene. The EAC also increases monotonically with gas atom mass. The CNT EAC data collapse to a linear trend when they are normalized by the graphene EAC and plotted versus the depth of their potential energy well on the CNT normalized by that for graphene. The EACs are used to estimate that the thermal boundary conductance between noble gases and graphene will be of order 0.1 MW/m2·K at a gas pressure of 1 atm, corresponding to a gas Kapitza length of order 100 nm.

A Molecular Dynamics Study of Energy and Momentum Accommodation Coefficients in the Transitional Knudsen Numbers

The principal aim of this work is to study the thermophysical aspects of gas interaction on the walls of nano-channels using a three dimensional Molecular Dynamics (MD) model. The complete physics of gas-surface interaction in micro/nano channels in the non continuum regime is yet to be understood. The important parameters that are relevant to such interactions include energy and momentum accommodation coefficients. The study reported in this paper aims at implementing a relatively simple methodology for calculating different accommodation coefficients. Energy accommodation coefficient (EAC) and normal momentum accommodation coefficient (NMAC) are the main focus of the study. The accommodation coefficients for the different equilibrium states are calculated. Instead of tracking individual collision, a collection of collisions are considered for the calculations. The EAC and NMAC reported here are found to be influenced by gas-wall temperature difference and Knudsen number in the transition regime.

Heat transfer effects in nano-aluminum combustion at high temperatures

Recent measurements of nano-aluminum combustion in which burning time and peak particle temperature are measured simultaneously have suggested that heat transfer models currently used for burning nanoparticles may significantly overestimate heat losses during combustion. By applying conventional non-continuum heat transfer correlations to burning nano-aluminum particles, the observed peak temperatures, which greatly exceed the ambient temperature, should only be observable if the burning time were very short, of the order of 1μs, whereas the observed burning time is two orders of magnitude larger. These observations can be reconciled if the energy accommodation coefficient for these conditions is of the order of 0.005, which is the value suggested by Altman, instead of approximately unity, which is the common assumption. Experimental data obtained in the heterogeneous shock tube under a wide array of conditions are compared with basic heat transfer models, and the agreement of both peak temperature values and emission intensity traces for low energy accommodation coefficients supports the hypothesis of Altman and co-workers.

Performance evaluation of Maxwell and Cercignani-Lampis gas-wall interaction models in the modeling of thermally driven rarefied gas transport

A systematic study on the performance of two empirical gas-wall interaction models, the Maxwell model and the Cercignani-Lampis (CL) model, in the entire Knudsen range is conducted. The models are evaluated by examining the accuracy of key macroscopic quantities such as temperature, density, and pressure, in three benchmark thermal problems, namely the Fourier thermal problem, the Knudsen force problem, and the thermal transpiration problem. The reference solutions are obtained from a validated hybrid DSMC-MD algorithm developed in-house. It has been found that while both models predict temperature and density reasonably well in the Fourier thermal problem, the pressure profile obtained from Maxwell model exhibits a trend that opposes that from the reference solution. As a consequence, the Maxwell model is unable to predict the orientation change of the Knudsen force acting on a cold cylinder embedded in a hot cylindrical enclosure at a certain Knudsen number. In the simulation of the thermal transpiration coefficient, although all three models overestimate the coefficient, the coefficient obtained from CL model is the closest to the reference solution. The Maxwell model performs the worst. The cause of the overestimated coefficient is investigated and its link to the overly constrained correlation between the tangential momentum accommodation coefficient and the tangential energy accommodation coefficient inherent in the models is pointed out. Directions for further improvement of models are suggested.

Gas–Surface Energy Exchange in Collisions of Helium Atoms with Aligned Single-Walled Carbon Nanotube Arrays

Since gas flows in micro/nano devices are dominated by the interaction of gas molecules and solid surfaces, surface modification technique is one of the critical issues for optimizing the thermal performance of these devices. In this paper, we demonstrate the successful application of vertically aligned single-walled carbon nanotubes (VA-SWNTs) as surface modification material to enhance the energy accommodation of gas molecules on surfaces. The scattering of gas molecules on quartz surfaces covered with VA-SWNTs is investigated by the molecular beam technique. The energy accommodation coefficients of helium, which tend to be small even for rough surfaces because of the large mass mismatch between helium and surface atoms, are close to unity on the modified surfaces. The measurement with the free-standing films further reveals that the high accommodation is attributed to the unique morphology of the films with high porosity, which allows gas molecules to penetrate into the films and realizes a large numbe...

Semi-Empirical Satellite Accommodation Model for Spherical and Randomly Tumbling Objects

Orbits of launch-vehicle upper stages and spheres were observed by U.S. Air Force Space Command, and the resulting observations were converted by the Space Analysis Office to fitted ballistic coefficients by comparing the observed orbit with an orbit predicted by an atmospheric-drag model. The ballistic coefficients contain signals that result from atmospheric variability not captured by the model as well as signals that correspond to changes in the satellite-drag coefficient. For objects in highly elliptical orbits with perigee altitudes below 200 km a 50% change in ballistic coefficient can be observed. This drastic change is associated with both changes in the energy accommodation coefficient driven by atomic-oxygen adsorption and entry into a transition flow region where a diffuse shock forms ahead of the satellite near perigee. Furthermore, the observed ballistic coefficients for objects in near-circular orbits ( speeds) do not match those of objects in highly eccentric orbits ( speeds near perigee). This difference is attributed to a decrease in adsorption efficiency postulated by previous researchers that is formalized in this work into a semi-empirical model. The model parameters suggest that the average binding energy of atomic oxygen on satellite surfaces is about 5.7 eV.

Computational study of thermal dependence of accommodation coefficients in a nano-channel and the prediction of velocity profiles

A molecular dynamics (MD) study of the flow of rarefied gas in a nano-channel with infinite parallel wall is reported. Nano-channels are considered to be more appropriate option in the cooling of microelectronic devices in the near future. The momentum and the energy transfer between the gas and the surface is a significant parameter which account for many important properties. The study aims at the calculation of energy and momentum accommodation coefficients for different gas–wall temperature combinations, and also its dependence on Knudsen number and gas–wall temperature difference. The different gas–wall temperature combinations are achieved by controlling the wall temperature as well as the gas temperature. The incident and reflected velocity distributions are obtained and the reflected distributions in different directions are predicted using Maxwell-type boundary conditions. It is shown that the partial energy accommodation coefficients are sufficient to predict the velocity distribution in tangential and normal directions. The statistical deviation of the predicted distribution from the distributions obtained from MD simulation is found to be very low. The accommodation coefficients are found to vary linearly with the natural logarithm of gas–wall temperature difference. The tangential components of momentum showed a strong correlation with the incident speed of the particles.

Effect of nonuniform accommodation coefficient distribution on the couette flow

The Couette flow is considered for surfaces with nonuniformly distributed energy accommodation coefficients α. It is shown that at Knudsen numbers greater or of the order of unity heat fluxes and viscous stresses can be considerably optimized by varying the surface distribution of α at a fixed integral value. At the same time, for Kn ≪ 1 the flows with nonuniformly distributed α are similar with the flow with a constant accommodation coefficient equal to its mean value.

Molecular-dynamics study of Poiseuille flow in a nanochannel and calculation of energy and momentum accommodation coefficients

We report a molecular-dynamics study of flow of Lennard-Jones fluid through a nanochannel where size effects predominate. The momentum and energy accommodation coefficients, which determine the amount of slip and temperature jumps, are calculated for a three-dimensional Poiseuille flow through a nano-sized channel. Accommodation coefficients are calculated by considering a " gravity"- (acceleration field) driven Poiseuille flow between two infinite parallel walls that are maintained at a fixed temperature. The Knudsen number (Kn) dependency of the accommodation coefficients, slip length, and velocity profiles is investigated. The system is also studied by varying the strength of gravity. The accommodation coefficients are found to approach a limiting value with an increase in gravity and Kn. For low values of Kn (<0.15), the slip length obtained from the velocity profiles is found to match closely the results obtained from the linear slip model. Using the calculated values of accommodation coefficients, the first- and second-order slip models are validated in the early transition regime. The study demonstrates the applicability of the Navier-Stokes equation with the second-order slip model in the early transition regime.

Measuring Absolute Thermospheric Densities And Accommodation Coefficients Using Paddlewheel Satellites: Past Findings, Present Uses, And Future Mission Concepts

The first absolute measurement of thermospheric density was made by combining simultaneous observations of spin and semimajor axis decay of Explorer VI. Providing two independent measures of the interaction with the airstream enabled the determination of both air density and drag coefficient. Then by using a realistic model of the gas-surface interaction, the energy accommodation coefficient was determined. Only four such measurements were made prior to the time of writing. In this paper, we review the history of paddlewheel measurements and explain their importance to ongoing work in satellite drag. Next, a novel concept for paddlewheel satellites based on the CubeSat platform is discussed along with the relevant design parameters. A rudimentary error analysis for paddlewheel measurements evaluated the feasibility of these designs and it was found that the drag torques generated on a three-kilogram paddlewheel are within the measurement capabilities of today’s technologies. For certain types of paddlewheel configurations, the use of direct simulation methods is important for accurately analyzing the data. This is because a paddlewheel with the spin axis oriented in the orbit normal direction undergoes significant flow-shadowing and this is not easily represented by analytical methods. Increasing the availability of accommodation measurements via the paddlewheel method represents an improvement in the accuracy of Earth’s total density models as well as the understanding of gas-surface interactions in low Earth orbit. This is of profound importance in the prediction of satellite orbits as well as the understanding of atmospheric phenomena.

Tangential momentum and thermal accommodation coefficients for hydrogen molecules on graphite surface

The scattering of hydrogen molecules from graphite surface was studied through molecular dynamics simulation. The trajectories of the hydrogen molecules and surface atoms were calculated. The distributions of velocity and energy after reflection were obtained depending on direction and quantity of the initial velocity. The energy and tangential momentum accommodation coefficients were calculated for cases where incident velocity distribution can be approximated by Maxwellian function and mean velocity is negligible. Obtained coefficients are in satisfactory agreement with experimental data.