Energy Accommodation Coefficient Research Articles

Influence of Gas-Surface and Gas-Gas interactions on the energy accommodation coefficient in non-equilibrium hypersonic gas flows

Accurate accommodation coefficients are crucial in predicting aerodynamic force and heating in hypersonic rarefied flows. This study employs molecular dynamics simulations to investigate the characteristics of non-equilibrium hypersonic flow and its impact on the energy accommodation coefficient (EAC). Our findings reveal that the non-equilibrium gas flow in the gas-surface interaction region comprises an equilibrium subsonic flow, an incident hypersonic flow, and its reflected counterpart. Gas-surface and gas–gas interactions occur simultaneously as gas atoms incident toward the solid surface, with the latter enhancing the EAC by altering the ratios of collision types. Overall, an increase in the ratios of trapping-desorption and permanent-adsorption collisions enhances the EAC at the interface. Results indicate that the number density of the subsonic flow determines the transition from immediate-reflection collisions to trapping-desorption collisions, while the ratio between the potential well depth and the internal energy of the subsonic flow determines the occurrence of permanent-adsorption collisions. These findings disclose the influence of the gas-surface and gas–gas interactions on the atomic collision types and EAC in a hypersonic flying interface, providing valuable insights for predicting the aerodynamic heating in rarefied gas flow.

Nanothermometry in rarefied gas using optically levitated nanodiamonds.

Heat transfer in gases in the continuum regime follows Fourier's law and is well understood. However, it has been long understood that in the subcontinuum, rarefied gas regime Fourier's law is no longer valid and various models have been proposed to describe heat transfer in these systems. These models have very limited experimental exploration for spherical geometries due to the difficulties involved. Optically levitated nanoparticles are presented as the ideal experimental system to study heat transfer in rarefied gases due to their isolation from their environment. Nanodiamonds with nitrogen-vacancy centers are used to measure temperature. As the pressure decreases so does the heat transfer to the rarefied gas and the nanodiamond temperature increases by over 200 K. These experiments demonstrate the utility of optically levitated nanoparticles to study heat transfer in any gas across a wide range of pressures. In the future, these measurements can be combined with models to empirically determine the energy accommodation coefficient of any gas.

Impact of surface physisorption on gas scattering dynamics

Engineering flow systems operating under low pressures and/or at the micro/nano scale generally include a physically adsorbed gas layer next to the surface. In this paper, we develop a scattering kernel that accounts for the effect of adsorption, arising from van der Waals interactions, on the dynamics of molecules impinging on solid smooth surfaces. In the limit of low bulk density, surface adsorption becomes negligible and the scattering kernel recovers consistently the Cercignani–Lampis model, which best describes molecular collisions with a clean, smooth surface. In the limit of high bulk density, a dense adsorbed molecular layer forms next to the surface and its presence is picked up by the Maxwell model with complete diffuse reflection, which better captures the multiple collisions suffered by molecules. A weight coefficient based on the Langmuir adsorption isotherm is incorporated into the modelling to handle the transition between these two limiting conditions of low and high densities. The proposed model is validated against high-fidelity molecular dynamics simulations that are performed for a variety of gas–surface combinations and adsorbed molecular layers with different densities. It is shown that the proposed model very well captures the scattering patterns of beams of gas molecules at different velocities impinging on surfaces, as well as momentum and energy accommodation coefficients in the entire range of explored conditions.

Comprehending Metal Particle Combustion: a Path Forward

AbstractThe paper discusses the physics required for accurate modeling of metal particle combustion and includes aspects previously neglected. Specifically, three physical phenomena are emphasized: 1) internal boiling on the condensed oxide‐metal interface; 2) condense‐luminescent loss during nano‐oxide formation; and, 3) suppressed heat transfer on the metal particle surface due to a low energy accommodation coefficient (EAC) are essential. The last two phenomena were explored in previous work. Internal particle interface boiling detailed in the current work enables the semi‐heterogeneous combustion of Al particles, an important process needing attention for accurate modeling. The interface boiling mechanism allowing for the semi‐heterogeneous combustion explains a number of experimental puzzles related to metal particle combustion. In particular, the semi‐heterogeneous combustion justifies the coexistence of two burning regimes of Al particles (slow and fast) recently observed. Based on reported findings, revising current numerical models for metal particle combustion to include these three physical phenomena is necessary. Implications toward enhancement of energetic performance for metal‐containing formulations are also discussed.

Aerothermodynamics of a sphere in a monatomic gas based onab initiointeratomic potentials over a wide range of gas rarefaction: transonic, supersonic and hypersonic flows

Aerothermodynamic characteristics of a sphere such as drag and energy transfer coefficients are calculated for Mach numbers varying from 1 to 10 over a wide range of the gas rarefaction degree spanning the free molecular, transitional and near hydrodynamic flow regimes. The effects of major factors determining the gas flow are studied using the direct simulation Monte Carlo method. To reveal the effect of gas species, the simulations are performed based onab initiointeratomic potentials for helium, neon, argon and krypton, as well as based on the hard sphere model. The impact of the accommodation coefficients is evaluated by applying the Cercignani–Lampis model of gas–surface interaction. The calculations are carried out for several values of the free stream and sphere temperatures. It is found that the effects of gas species on the drag and energy transfer coefficients are approximately 3 % and 6 %, respectively. The accommodation coefficients in the Cercignani–Lampis model strongly affect all aerothermodynamic characteristics. The drag and energy transfer coefficients calculated for different accommodation coefficients vary within 30 % and 200 %, respectively. It is found that the variation of the tangential momentum and normal energy accommodation coefficients can induce an increase of the drag coefficient compared to the case of diffuse gas–surface interaction. In hypersonic flows, the drag coefficient varies within 30 % when the sphere temperature varies from the free stream temperature to the stagnation temperature. The drag and energy transfer coefficients are found to be non-monotonic functions of the free stream temperature.

Investigation of energy accommodation coefficient at gas-solid interface of a hypersonic flying vehicle

An effective thermal protection system is crucial for hypersonic flying vehicles performing multiple cycles of flight under high aerodynamic heating loads. Accurate calculation of heat transfer between a flying vehicle and its front shock waves is not possible due to complex gas-solid interactions. In this study, it was observed that the energy accommodation coefficient (EAC) at the interface between the shock wave formed by monoatomic gas and the flying vehicle exhibited a decrease-increase trend, which is attributed to that the averaged lasting time for each gas atom interacting with the solid decreases exponentially while the interacting depth increases logarithmically with the increase of the flight velocity. A one-dimensional collision model disclosed that the minimum EACs at different spring-mass systems occurred at the same Deborah number, indicating that the incident velocity of gas atoms corresponding to the minimum EAC is proportional to the natural frequency of the spring-mass system. Our research results suggest that the EAC strongly depends on the vehicle flying velocity and provide a rule for the optimal design of an efficient thermal protection system.

Thermophoretic force on a sphere of arbitrary thermal conductivity in a rarefied gas

The thermophoretic force on a sphere with arbitrary thermal conductivity immersed in a rarefied gas subject to a uniform temperature gradient is calculated in the framework of kinetic theory of gases in a range of the Knudsen number which covers the free molecular, transition and continuum regimes of the gas flow around the sphere. The condition of continuity of the radial heat flux at the gas–solid interface is used to calculate the thermophoretic force as a superposition of the thermophoretic force on a sphere with an uniform temperature and the radiometric force on a sphere due to its thermal polarization. Both solutions were previously obtained from the Shakhov model to the linearized Boltzmann equation and the Cercignani–Lampis model of gas–surface interaction. To analyze the influence of the gas and particle thermal conductivities on the thermophoretic force, spheres of PolyStyrene Latex (PSL), glass and nickel in helium and argon gases are considered. The force is calculated for several values of tangential momentum accommodation coefficient and normal energy accommodation coefficient as introduced in the Cercignani–Lampis scattering kernel. A comparison with experimental data available in the literature allowed to extract the values of the accommodation coefficients for helium interaction with the particle surface.

Extraction of Tangential Momentum and Normal Energy Accommodation Coefficients by Comparing Variational Solutions of the Boltzmann Equation with Experiments on Thermal Creep Gas Flow in Microchannels

In the present paper, we provide an analytical expression for the first- and second-order thermal slip coefficients, σ1,T and σ2,T, by means of a variational technique that applies to the integrodifferential form of the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules. The Cercignani-Lampis scattering kernel of the gas-surface interaction has been considered in order to take into account the influence of the accommodation coefficients (αt, αn) on the slip parameters. Comparing our theoretical results with recent experimental data on the mass flow rate and the slip coefficient for five noble gases (helium, neon, argon, krypton, and xenon), we found out that there is a continuous set of values for the pair (αt, αn) which leads to the same thermal slip parameters. To uniquely determine the accommodation coefficients, we took into account a further series of measurements carried out with the same experimental apparatus, where the thermal molecular pressure exponent γ has been also evaluated. Therefore, the new method proposed in the present work for extracting the accommodation coefficients relies on two steps. First of all, since γ mainly depends on αt, we fix the tangential momentum accommodation coefficient in such a way as to obtain a fair agreement between theoretical and experimental results. Then, among the multiple pairs of variational solutions for (αt, αn), giving the same thermal slip coefficients (chosen to closely approximate the measurements), we select the unique pair with the previously determined value of αt. The analysis carried out in the present work confirms that both accommodation coefficients increase by increasing the molecular weight of the considered gases, as already highlighted in the literature.

On heavy particle-wall interaction in axisymmetric plasma discharges

The effects of heavy particle-wall interaction on a cylindrical plasma source discharge are investigated, through hybrid particle-in-cell/fluid simulations. The bulk plasma is considered quasineutral with isothermal electrons, and with no secondary electron emission from the walls. The neutral gas wall reflection model is shown to play a major role in determining the conditions for a self-sustained and stationary plasma discharge. A hysteresis cycle on the injection mass flow rate is found when neutrals deviate from a purely diffuse reflection at the walls, with the mass utilization efficiency changing up to 20% between purely specular and diffuse scenarios. However, as the ratio of ionization mean free path to macroscopic length is decreased, the neutral-wall reflection model becomes irrelevant. Finally, even small deviations from unity of the ion energy accommodation coefficient at the walls are seen to have a major impact on both the ion and neutral distribution functions, and ultimately the mass utilization efficiency. This behavior stresses out the importance of a precise experimental determination of this parameter for accurate simulations.

Modeling rarefied gas-solid surface interactions for Couette flow with different wall temperatures using an unsupervised machine learning technique.

In rarefied gas flows, discontinuity phenomena such as velocity slip and temperature jump commonly appear in the gas layer adjacent to a solid boundary. Due to the physical complexity of the interactions at the gas-solid interface, particularly in the case of systems with local nonequilibrium state, boundary models with limited number of parameters cannot completely describe the reflection of gas molecules at the boundary. In this work, the Gaussian mixture (GM) model, which is an unsupervised machine learning technique, is employed to construct a statistical gas-solid surface scattering model based on the collisional data obtained from molecular dynamics (MD) simulations. The GM model is applied to study Couette flow for different inert gases (Ar and He) confined between two parallel infinite gold walls at different temperatures. A direct comparison between the results obtained from the GM model and the Cercignani-Lampis-Lord (CLL) scattering kernel against the MD collisional data in terms of the distribution of the predicted postcollisional velocities, and accommodation coefficients has shown that the results from the GM model are an excellent match with the MD results outperforming the CLL scattering kernel. As an example, for He gas, while the predicted energy accommodation coefficient by the CLL model is more than two times higher than the MD predictions, the value computed by the GM model is in excellent agreement with the MD results. This superior performance of the GM model confirms its high potential to derive a generalized boundary condition in systems encountered with highly nonequilibrium and complex gas flow conditions.

Radiometric force on a sphere in a rarefied gas based on the Cercignani–Lampis model of gas–surface interaction

The radiometric force on a sphere due to its thermal polarization in a rarefied gas flow being in equilibrium is investigated on the basis of a kinetic model to the linearized Boltzmann equation. The scattering kernel proposed by Cercignani and Lampis to model the gas–surface interaction using two accommodation coefficients, namely, the tangential momentum accommodation coefficient and the normal energy accommodation coefficient, is employed as the boundary condition. The radiometric force on the sphere, as well as the flow field of the gas around it, is calculated in a wide range of the gas rarefaction, defined as the ratio of the sphere radius to an equivalent free path of gaseous particles, covering the free molecular, transition, and continuum regimes. The discrete velocity method is employed to solve the kinetic equation numerically. The calculations are carried out for values of accommodation coefficients considering most situations encountered in practice. To confirm the reliability of the calculations, the reciprocity relation between the cross phenomena is verified numerically within a numerical error of 0.1%. The temperature drop between two diametrically opposite points of the spherical surface in the direction of the gas flow stream, which characterizes the thermal polarization effect, is compared to experimental data for a spherical particle of Pyrex glass immersed in helium and argon gases.

Exact solution for heat transport of Newtonian fluid with quadratic order thermal slip in a porous medium

In this communication, an analytical solution for the thermal transfer of Newtonian fluid flow with quadratic order thermal and velocity slips is presented for the first time. The flow of a Newtonian fluid over a stretching sheet which is embedded in a porous medium is considered. Karniadakis and Beskok’s quadratic order slip boundary conditions are taking into account. A closed form of analytical solution of momentum equation is used to derive the analytical solution of heat transfer equation in terms of confluent hyper-geometric function with quadratic order thermal slip boundary condition. Accuracy of present results is assured with the numerical solution obtained by Iterative Power Series method with shooting technique. The impacts of porous medium parameter, tangential momentum accommodation coefficient, energy accommodation coefficient on velocity and temperature profiles, skin friction coefficient and reduced Nusselt number are discussed. The Nusselt number increases with the higher estimations of tangential momentum and energy accommodation coefficients.

Gas-surface interaction effects on rarefied gas flows around microbeams induced by temperature fields

Without any initial pressure gradient, gas flows can be induced by temperature gradient and exert Knudsen (thermal) force on immersed structures. In order to investigate the influence of surface accommodation coefficients on rarefied gas flows around a cold-hot arm pair, the direct simulation Monte Carlo (DSMC) method is applied in combination with the Cercignani-Lampis-Lord (CLL) gas-surface interaction model. The research results highlight the sensitivity of flow fields, thermal fields, pressure and Knudsen force to the variations of normal energy accommodation coefficient (NEAC), and tangential momentum accommodation coefficient (TMAC). In particular, Knudsen force is a nonlinear function of NEAC and TMAC respectively. With the accommodation coefficients decreasing, the slope of the curve (absolute value) increases. Furthermore, Knudsen force has a decreasing-increasing (in the opposite direction) trend with the decrease of NEAC. In contrast, Knudsen force keeps increasing with the decrease of TMAC. For example, Knudsen force increases approximately by 1.98, 2.37, and 8.37 times with pressures of 155 Pa, 387 Pa, and 966 Pa respectively when TMAC decreases from 1.0 to 0.1.

Gas-surface interactions modelling influence on satellite aerodynamics and thermosphere mass density

The satellite acceleration data from the CHAMP, GRACE, GOCE, and Swarm missions provide detailed information on the thermosphere density over the last two decades. Recent work on reducing errors in modelling the spacecraft geometry has greatly reduced scale differences between the thermosphere data sets from these missions. However, residual inconsistencies between the data sets and between data and models are still present. To a large extent, these differences originate in the modelling of the gas-surface interactions (GSI), which is part of the satellite aerodynamic modelling used in the acceleration to density data processing. Physics-based GSI models require in-situ atmospheric composition and temperature data that are not measured by any of the above-mentioned satellites and, as a consequence, rely on thermosphere models for these inputs. To reduce the dependence on existing thermosphere models, we choose a GSI model with a constant energy accommodation coefficient per mission, which we optimize exploiting particular attitude manoeuvres and wind analyses to increase the self-consistency of the multi-mission thermosphere mass density data sets. We compare our results with those based on variable energy accommodation obtained by different studies and semi-empirical models to show the principal differences. The presented comparisons provide novel opportunity to quantify the discrepancies between current GSI models. Among the presented data, density variations with variable accommodation are within ±10%, and peaks can reach up to 15% at the poles. The largest differences occur during low solar activity periods. In addition, we utilize a series of attitude manoeuvres performed in May 2014 by the Swarm A and C satellites, which are flying in close proximity, to evaluate the residual inconsistency of the density observations as a function of the energy accommodation coefficient. Our analysis demonstrates that an energy accommodation coefficient of 0.85 maximizes the consistency of the Swarm density observations during the attitude manoeuvres. Using such coefficient, for Swarm A and Swarm C, the new density would be lower in magnitude with a 4–5% difference. In recent studies, similar energy accommodation coefficients were retrieved for the CHAMP and GOCE missions by investigating thermospheric winds. These new values for the energy accommodation coefficient provide a higher consistency among different missions and models. A comparison of neutral densities between current thermosphere models and observations indicates that semi-empirical models such as NRLMSISE-00 and DTM-2013 significantly overestimate the density, and that an overall higher consistency between the observations from the different missions can be achieved with the presented assumptions. The new densities from this work provide consistencies of 4.13% and 3.65% between the minimum and maximum mean ratios among the selected missions with NRLMSISE-00 and DTM-2013, respectively. A comparison with the WACCM-X general circulation model is also performed. Similar to the other models, WACCM-X seems to provide higher estimates of mass density especially under high and moderate solar activities. This work has the objective to guide density data users over the multiple data sets and highlight the remaining uncertainties associated with different GSI models.

Nonequilibrium molecular dynamics study on energy accommodation coefficient on condensing liquid surface—Molecular boundary conditions for heat and mass transfer

Nonequilibrium molecular dynamics (NEMD) studies have been conducted to determine molecular boundary conditions at vapor–liquid interfaces for the kinetic theory of condensation and evaporation. In previous studies, a microscopic formulation of the condensation coefficient was defined as the condensation probability of vapor molecules based on equilibrium molecular dynamics simulations and transition state theory. The condensation coefficient was presented as a function of the translation energy of incoming molecules and surface temperature. Based on this, the velocity distributions of evaporating and reflecting molecules were theoretically expressed under equilibrium conditions. In a practical nonequilibrium situation, the energy transfer by the reflecting molecules is important along with the condensation/evaporation probability. However, it is unclear whether the results obtained under equilibrium conditions can be applied under nonequilibrium conditions. This study, therefore, defines the energy accommodation coefficient of reflecting molecules by comparing the energy transfer due to reflection with that under equilibrium conditions. NEMD simulations are conducted using two surfaces facing each other, an evaporating surface and a condensing surface, for argon molecules under different nonequilibrium conditions. The results show that the velocity distribution of reflecting molecules deviates from those under equilibrium conditions, and the energy accommodation coefficient decreases as nonequilibrium conditions increase. Additionally, an inverted temperature profile is observed. Reflecting molecules play an important role in the sensible heat transfer on the condensing surface, and they are not accommodated on the condensing surface. Thus, they raise the temperature in the vicinity of the condensing surface under nonequilibrium conditions.

Molecular dynamics simulations of energy accommodation between gases and polymers for ultra-low thermal conductivity insulation

Determining the energy accommodation between gases and solids is essential to developing porous thermal insulation materials with ultra-low effective thermal conductivity that reduce energy use, greenhouse gas emissions, and fossil fuel consumption. The energy accommodation coefficients of most gases, however, have been rarely studied, especially with respect to solids that have relatively high thermal resistivity, e.g., polymers. In this work, by using all-atom nonequilibrium molecular dynamics simulations, we reveal the accommodation coefficients of He, Ar, N2, and O2 with polymers, mainly polystyrene. We find that their values are around 0.51, 0.72, 0.79, and 0.90, respectively, suggesting a critical reexamination of the commonly used theoretical maximum value of 1. We have also conducted experiments and validated the value for air, which is about 0.81. Such a change in accommodation coefficients can lead to a reduction of about 70%, 50%, 35%, and 20% in the thermal conductivity of He, Ar, N2, and O2 gases in nano pores (below 100 nm) or at low pressures (below 1 millibar). With these new accommodation coefficients, we find that in a 10 nm pore with ambient pressure at 300 K, the gas thermal conductivity of He, Ar, N2, and O2 in porous polystyrene can be as low as 9.7 × 10−4, 3.4 × 10−4, 7.3 × 10−4, and 8.5 × 10−4 W·m−1·K−1, respectively, which are two to three orders of magnitude lower than their bulk values, promising higher thermal resistivity of insulation materials. This work reveals the fundamental energy exchange between gases and polymers, providing important guidance for designing high-performance thermal insulation materials for various applications.

Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani–Lampis boundary conditions: Comparison with experimental results

In the present paper, a variational method is applied to solve the Boltzmann equation based on the true linearized collision operator for hard-sphere molecules and the Cercignani–Lampis boundary conditions. This technique allows us to obtain an explicit relation between the first- and second-order thermal slip coefficients and the tangential momentum and normal energy accommodation coefficients, defined in the frame of the Cercignani–Lampis scattering kernel. Comparing the theoretical results with the experimental data from the work of Yamaguchi et al. [“Mass flow rate measurement of thermal creep flow from transitional to slip flow regime,” J. Fluid Mech. 795, 690 (2016)], a pair of accommodation coefficients has been extracted for each noble gas considered in the experiments. Then, these values have been used to compute, by means of our variational technique, the temperature-driven mass flow rates, and the outputs have been compared with the measurements for helium, neon, and argon. Good agreement has been obtained between the theoretical and the experimental data, within the range of validity of the proposed second-order slip model. For all the gases analyzed, the tangential accommodation coefficient is found to be much larger than the normal energy coefficient. The general trend, according to which, by increasing the molecular weight of the different gases, the values of both accommodation coefficients also increase, is confirmed in this study.

Drag reduction through shape optimisation for satellites in Very Low Earth Orbit

Operating satellites at altitudes in Very Low Earth Orbit (VLEO) has many advantages. However, due to the higher atmospheric density of this region, satellites encounter significantly higher atmospheric drag. Depending on the mission, this may require a propulsive system to maintain the orbit which costs both fuel mass and volume. It is therefore desirable to reduce the drag in order to either reduce these costs or to extend the operational life. In this paper a series of viable aeroshell profiles are identified for satellites operating in VLEO using a Radial Basis Function-based surrogate model with data generated using both Panel Methods and Discrete Simulation Monte Carlo simulations. It was demonstrated that a maximum drag reduction of between 21% and 35% was achievable for the profiles when optimising a bi-conic profile for minimum drag based on Discreet Simulation Monte Carlo simulations with an energy accommodation coefficient of 0.95. Accounting for the loss of internal volume and assuming the reduction in fuel mass results in an equally proportioned reduction in fuel system volume it was observed that only a 13% to 27% reduction was achieved.

Effect of Melting on Energy Accommodation Coefficients of Aluminum–Noble Gas Systems

Molecular dynamics simulations are conducted to investigate the effect of melting on energy accommodation coefficient (EAC) of Al-noble gas systems. The accommodation coefficients are computed for a gas temperature of 3000 K and slab temperatures in the range of 600-1500 K. Three different noble gases: helium, argon and xenon, are considered. Density functional theory (DFT) derived gas-metal interatomic potentials are used to obtain accurate predictions of accommodation coefficients. An abrupt jump in the accommodation coefficient upon melting is observed for argon and xenon, whereas the accommodation coefficient is negligibly affected for helium gas. The effects of gas-metal potential and gas atom mass are probed separately and it is found that the gas-metal potential has a negligible effect on the magnitude of EAC jumps. The gas atom mass, on the other hand, exerted a strong effect; heavier gases exhibited greater EAC jumps than lighter gases. The underlying physics is then unraveled by studying the effects of surface roughness and lattice dynamics on accommodation coefficient. Surface roughness increases the tangential EACs significantly for all gases, but the normal EACs are not as strongly amplified. Analysis of vibrational density of states of solid and liquid slabs suggests the activation of low frequency vibrational modes upon melting. This coupled with the roughening of surface upon melting results in an abrupt jump in the accommodation coefficient, especially for heavier gases.

On the possible coexistence of two different regimes of metal particle combustion

The coexistence of two regimes of aluminum (Al) particle combustion is discussed. A slower regime occurs at a low energy accommodation coefficient (EAC) and is usually observed in Al combustion experiments. A faster regime at high EAC is also possible. The combustion enhancement observed for pre-treated Al particles can be interpreted as a switch from the slower combustion regime to the faster regime. The value of EAC is controlled by the thermionic emission of electrons. A relationship between Al particle pre-treatment and the work function, which governs the thermionic emission, and, therefore, the EAC, is a subject of further studies.