Cercignani Lampis Model Research Articles

Radiometric forces exerted on a perforated membrane

The radiometric force exerted on a thin perforated membrane and the heat flux from the membrane to a surrounding gas are calculated by the direct simulation Monte Carlo method over wide ranges of the gas rarefaction and membrane porosity. Ab initio potentials are used to model the intermolecular collisions. We find that perforations increase the force several times in the viscous regime of flow but decrease the force in the free-molecular and transitional regimes. The influence of the accommodation coefficients is studied by applying the Cercignani–Lampis model. The effects of gas species, degree of non-equilibrium, and environment temperature are found to have relatively small effects on dimensionless quantities such that the reported results can be applied to wide ranges of these factors and, hence, to numerous practical situations such as the levitation of centimeter-scale membranes at upper atmospheric altitudes.

Impact of random nanoscale roughness on gas-scattering dynamics.

The impact of nanoscale wall roughness on rarefied gas transport is widely acknowledged, yet the associated scattering dynamics largely remain elusive. In this paper, we develop a scattering kernel for surfaces having nanoscale roughness that distinctly characterizes the two major types of interactions between gas molecules and rough surfaces. Namely these are (a) the weak perturbations arising from the thermal motion of wall atoms, essentially gas-phonon collisions, which are captured by the well-established Cercignani-Lampis model, and (b) the hard collisions owing to the irregularities of the rough, static potential energy surface, which are generally described by the fully diffuse model. Drawing an analogy between wave-surface and gas-surface scattering, a pseudo Debye-Waller factor is incorporated into the modeling as a weighting coefficient to allow the transition between smooth and rough surface conditions. The proposed scattering kernel is validated through high-fidelity molecular dynamics simulations that are performed for systems with varying roughness, temperature, and gas-surface combinations. The results indicate that the model well captures the scattering dynamics of gas molecular beams impinging on surfaces at different velocities, specifically for the accommodation coefficients and reflection patterns. Additionally, in flow and heat transport cases, it accurately predicts macroscopic quantities such as velocity slip and temperature jumps across the range of tested conditions.

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.

A modified Cercignani–Lampis model with independent momentum and thermal accommodation coefficients for gas molecules scattering on surfaces

To accurately predict the aerodynamic forces and heating of hypersonic vehicles, an elaborate gas–surface interaction (GSI) model is essential to describe the rarefied gas effect at the interface. By far, the Cercignani–Lampis (CL) model is the most sophisticated GSI model, but it has not been systematically examined under hypersonic conditions where the gas flow possesses large velocity and temperature differences relative to the boundary surface. In this work, the accuracy of the CL model is first assessed by comparing with molecular dynamics simulation results under a variety of conditions of temperature and velocity differences, surface temperature, and surface roughness. It is found that the tangential scattering kernel of CL model is perfect only when the surface is smooth and the gas kinetic energy is close to the surface kinetic energy. To accurately capture the momentum and temperature of the reflected gas molecules, a modified CL model with independent momentum and thermal accommodation coefficients is developed. A hybrid diffusive and modified CL model is further proposed to account for the adsorption phenomenon. With these modifications, the new GSI model can accurately describe the scattering of gas molecules in a wider range of hypersonic rarefied gas flows.

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.

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.

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.

Drag and thermophoresis on a sphere in a rarefied gas based on the Cercignani–Lampis model of gas–surface interaction

Abstract

Prediction of thermal conductance and friction coefficients at a solid-gas interface from statistical learning of collisions

In this paper, we present the construction of statistical models of gas-wall collision based on data issued from molecular dynamics (MD) simulations and use them to predict the velocity slip and temperature jump coefficients at the gas-solid interface. The Gaussian mixture (GM) model, an unsupervised learning technique, is chosen for this purpose. The model shares some similarities with the well-known Cercignani-Lampis model in kinetic theory but it is more robust due to the unlimited number of Gaussian functions used and the ability to deal with correlated data of high dimensions. Applications to real gas-wall systems (argon-gold and helium-gold) confirm the good performance of the model. The trained GM model predicts physical and statistical properties including accommodation, friction, and thermal conductance coefficients in excellent agreement with the MD model.

A time-dependent method for the measurement of mass flow rate of gases in microchannels

Accurate measurement methods are required in the analysis of thermodynamic non-equilibrium effects associated with rarefied gas flows. For example, for the specific case of accommodation coefficients measurements, the quantity of interest is often the mass flow rate along the channel. For this purpose, the following paper presents a new time-dependent version of the well-known constant volume method for the accurate measurement of mass flow rates of gases in microchannels. The technique proposed here is an improvement in respect to the classic technique since it can be used for transient experiments. Moreover, it can be applied to configurations with arbitrary upstream and downstream reservoirs dimensions. Particularly, the proposed method relies on the assumption that the flow conductance varies linearly during the experiments and thus the pressure variations in the reservoirs can be fitted by a well-defined exponential function. Then, the instantaneous mass flow rate through the channel can be determined directly from the pressure fitting coefficients. A great advantage of the time-dependent constant volume method is that the measurements can be obtained from a single experiment for a wide range of rarefaction conditions, since the mean pressure between the reservoirs is allowed to change with time. Moreover, this technique represents a convenient manner to provide raw data of pressure variation with time in the reservoirs and transient mass flow rate in the channel by simply providing the fitting coefficients of the theoretically derived functions. A clear geometric criterion is also presented to determine when such mass flow rate measurements can be considered as quasi-steady, corresponding closely to results obtained under steady conditions, when ideally the channel connects two infinite reservoirs at different pressures. Results for flows of nitrogen through a stainless steel microtube (L=92.22±0.01 mm and D=435.5±3.5 µm) were obtained from 118 independent experiments, provided in this work, using two different experimental setups and three different configurations of the system volumes. As expected, no deviation was observed between all experimental campaigns in terms of the reduced mass flow rate. In addition, all results indicate that nitrogen can be considered completely accommodated at the surface of the microtube used, with α=0.986±0.019 when the diffuse-specular gas-surface interaction model is adopted and αt=0.991±0.020 (αn=1) when the Cercignani-Lampis model is adopted.

A physical-based gas–surface interaction model for rarefied gas flow simulation

Empirical gas–surface interaction models, such as the Maxwell model and the Cercignani–Lampis model, are widely used as the boundary condition in rarefied gas flow simulations. The accuracy of these models in the prediction of macroscopic behavior of rarefied gas flows is less satisfactory in some cases especially the highly non-equilibrium ones. Molecular dynamics simulation can accurately resolve the gas–surface interaction process at atomic scale, and hence can predict accurate macroscopic behavior. They are however too computationally expensive to be applied in real problems. In this work, a statistical physical-based gas–surface interaction model, which complies with the basic relations of boundary condition, is developed based on the framework of the washboard model. In virtue of its physical basis, this new model is capable of capturing some important relations/trends for which the classic empirical models fail to model correctly. As such, the new model is much more accurate than the classic models, and in the meantime is more efficient than MD simulations. Therefore, it can serve as a more accurate and efficient boundary condition for rarefied gas flow simulations.

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.

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.

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.

Maxwell boundary condition and velocity dependent accommodation coefficient

A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.

The Effect of Boundary Conditions for Highly Rarefied Gas flow

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 adopted for solving the Boltzmann equation onto Graphics Processing Units (GPUs). The speedup of the GPU- accelerated computation is 50 times as compared to CPU one. It was found that nonuniform temperature distribution on the plates induced a steady flow. In addition, the flow field strongly depends on the value of the accommodation coefficients imposing in the Cercignani–Lampis model and this effect is more visible for high Knudsen number. Presented results are in agreement with ones obtained by means of the direct simulation Monte Carlo method in

Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations

For understanding the behavior of a gas close to a channel wall it is important to model the gas-wall interactions as detailed as possible. When using molecular dynamics simulations these interactions can be modeled explicitly, but the computations are time consuming. Replacing the explicit wall with a wall model reduces the computational time but the same characteristics should still remain. Elaborate wall models, such as the Maxwell-Yamamoto model or the Cercignani-Lampis model need a phenomenological parameter (the accommodation coefficient) for the description of the gas-wall interaction as an input. Therefore, computing these accommodation coefficients in a reliable way is very important. In this paper, two systems (platinum walls with either argon or xenon gas confined between them) are investigated and are used for comparison of the accommodation coefficients for the wall models and the explicit molecular dynamics simulations. Velocity correlations between incoming and outgoing particles colliding with the wall have been used to compare explicit simulations and wall models even further. Furthermore, based on these velocity correlations, a method to compute the accommodation coefficients is presented, and these newly computed accommodation coefficients are used to show improved correlation behavior for the wall models.

On computing the thermal-slip coefficient from Kramers’ problem

Classical techniques are used to derive a variant of an Onsager relation (used typically for Poiseuille flow and thermal-creep flow) that yields a convenient relationship between the heat flow of Kramers’ problem and the thermal-slip coefficient. The analysis is based on the linearized Boltzmann equation for rigid-sphere interactions, and wall interactions are described by a general law that includes, for example, the Maxwell model (a mixture of specular and diffuse reflection) and the Cercignani–Lampis model.

Generalized boundary conditions for the S-model kinetic equations basic to flow in a plane channel

An analytical version of the discrete-ordinates method is used to solve the classical problems of Poiseuille flow and thermal-creep flow in a plane channel. The kinetic theory for the rarefied-gas flow is based on the S model (a generalization of the BGK model), and in addition to the use of the diffuse–specular reflection model (based on a single accommodation coefficient) for describing particle scattering from the channel walls, the Cercignani–Lampis model defined in terms of normal and tangential accommodation coefficients is implemented. The established solution is tested numerically, and results for the velocity and heat-flow profiles, the particle-flow rate and the heat-flow rate thought to be correct to many significant figures are reported for various values of the channel width.