Cercignani Lampis Research Articles

Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani–Lampis boundary condition

A polynomial expansion procedure and an analytical discrete-ordinates method are used to evaluate the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient as defined by a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary condition.

Application of the Cercignani–Lampis scattering kernel to calculations of rarefied gas flows. II. Slip and jump coefficients

The Cercignani–Lampis scattering kernel of the gas–surface interaction is applied to numerical calculations of the viscous slip coefficient, the thermal slip coefficient and the temperature jump coefficient. The S model of the Boltzmann equation is numerically solved by the discrete velocity method. The calculations have been carried out in the wide ranges of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data on the viscous slip coefficient the values of the accommodation coefficients are calculated for some gases and glass surface.

Application of the Cercignani–Lampis scattering kernel to calculations of rarefied gas flows. III. Poiseuille flow and thermal creep through a long tube

The Cercignani–Lampis scattering kernel of the gas–surface interaction is applied to numerical calculations of the Poiseuille flow and thermal creep through a long tube. The S model of the Boltzmann equation was numerically solved by the discrete velocity method. The calculations have been carried out in the wide ranges of the rarefaction parameter and of the accommodation coefficients. Comparing the present results with experimental data the values of the accommodation coefficients have been calculated.

Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients

Various model equations are used to define the viscous-slip and the thermal-slip coefficients in rarefied gas dynamics. More specifically, the BGK model, the S model, the variable collision model and the CES model are used to establish the slip coefficients basic to Kramers’ problem and the half-space problem of thermal creep. While the most general results are developed from use of the Maxwell boundary condition, results for the BGK model and the S model as defined by the Cercignani–Lampis boundary condition are also reported. An analytical discrete-ordinates method is used to establish the reported numerical results, and when available results from a numerical solution of the linearized Boltzmann equation are used as reference values. In addition to the numerical work based on model equations, the important issue of how to define meaningful ways (appropriate mean-free paths) to compare the results for the various models is discussed.

Application of the Cercignani–Lampis scattering kernel to calculations of rarefied gas flows. I. Plane flow between two parallel plates

The Cercignani–Lampis scattering kernel of the gas-surface interaction was applied to numerical calculations of the plane Poiseuille flow, thermal creep, mechanocaloric flux and heat flux. The S model of the Boltzmann equation was numerically solved by the discrete velocity method. The calculations have been carried out in wide ranges of the rarefaction parameter and of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data the value of the accommodation coefficients can be calculated.

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.

Some further extensions of the Cercignani–Lampis gas–surface interaction model

A recent paper has described extensions of the Cercignani–Lampis scattering kernel to cover (i) diffuse scattering with partial accommodation of translational kinetic energy and (ii) accommodation of vibrational energy of a diatomic molecule modelled as a rigid rotor/harmonic oscillator. The models are here further extended to cover the cases of partially diffuse scattering and of the anharmonic oscillator model of molecular vibration. The new models, like the old, satisfy detailed balance or reciprocity, thereby ensuring the preservation of an equilibrium distribution, and can be conveniently implemented in direct simulation Monte Carlo calculations. The results of some calculations are presented.

Direct simulation Monte Carlo calculations of rarefied flows with incomplete surface accommodation

Effects of incomplete surface accommodation in rarefied gas flows have been studied using the direct simulation Monte Carlo (DSMC) method in conjunction with the Cercignani–Lampis gas–surface interaction model. Two different flows have been studied, both of which have previously been simulated in DSMC calculations for the case of complete surface accommodation. These are (a) the flow over a sharp, slender circular cone at Mach 5.1 and (b) the flow over a flat-faced circular cylinder at Mach 25. In each case, the gas simulated was nitrogen. It was found that in case (a) the accommodation coefficient of the kinetic energy due to the tangential component of velocity has the greatest influence, whereas in case (b) that of the normal component is also important, having a drastic effect on the rarefied flow field.

Some extensions to the Cercignani–Lampis gas–surface scattering kernel

The Cercignani–Lampis gas–surface scattering kernel is extended to include two important cases not covered by the basic model. These are (a) diffuse scattering with partial energy accommodation, and (b) accommodation of vibrational energy of a diatomic molecule with equally spaced energy levels. Both extensions are easily implemented in direct simulation Monte Carlo (DSMC) calculations. The results of some test calculations are presented.