Wall Boundary Model Research Articles

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.

壁面での各種境界条件を考慮したMPSポリゴン壁境界モデルの改良

壁面での各種境界条件を考慮したMPSポリゴン壁境界モデルの改良

Wall boundary model for primitive chain network simulations

In condensed polymeric liquids confined in slit channels, the movement of chains is constrained by two factors: entanglement among the chains and the excluded volume between the chains and the wall. In this study, we propose a wall boundary (WB) model for the primitive chain network (PCN) model, which describes the dynamics of polymer chains in bulk based on coarse graining upon the characteristic molecular weight of the entanglement. The proposed WB model is based on the assumptions that (i) polymers are not stuck but simply reflected randomly by the wall, and (ii) subchains below the entanglement length scale behave like those in bulk even near the wall. Using the WB model, we simulate the dynamics of entangled polymer chains confined in slit channels. The results show that as the slit narrows, the chains are compressed in the direction normal to the wall, while they are expanded in the parallel direction. In addition, the relaxation time of the end-to-end vector increases, and the diffusivity of the center of mass decreases. The compression in the normal direction is a natural effect of confinement, while the expansion is introduced by a hooking process near the wall. The trends revealed that the relaxation time and diffusivity depend on the increase in friction due to an increased number of entanglements near the wall, which is also associated with the hooking process in the PCN model. These results are expected within the assumptions of the PCN model. Thus, the proposed WB model can successfully reproduce the effects of wall confinement on chains.

A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions

The challenge of modeling low-speed rarefied gas flow in the transition regime is well known. In this paper, we propose a numerical solution procedure for the regularized 13 moment equations within a finite-volume framework. The stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first-order approximation. To model confined flows, a complete set of wall boundary conditions for the 13 moment equations are derived based on the Maxwell wall-boundary model. This has been achieved by expanding the molecular distribution function to fourth-order accuracy in Hermite polynomials. Empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation Monte Carlo data. The numerical predictions obtained from the regularized 13 moment equations and the Navier–Stokes–Fourier equations are compared with data generated using the direct simulation Monte Carlo method for planar Couette flow. For a range of wall velocities and Knudsen numbers (0.012–1.0), the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation Monte Carlo data. The results also highlight limitations that are caused by the use of a first-order expansion of the third moment.

The effect of heavy ions on the formation and structure of cometary bow shocks

A hybrid simulation model is used to investigate the effects of heavy cometary ions on the formation and structure of a cometary bow shock. The calculations are carried out over various Mach numbers and heavy ion velocity distribution functions. The model is based on previous formulations for phenomena in the solar wind and at the earth's bow shock. The generation of the shock is described in terms of particles injected from one side of the simulation field and reflected from the other end of the field, i.e., a solid wall boundary model. This technique permits the steep buildup of the ion density near the cometary nucleus, followed by coupling of the incident and reflected ion streams to produce a shock. It is shown that at low Mach numbers (up to Mach 2) the shock is transitory and periodically formed by protons, then destroyed by heavy ions (O+). Slightly higher Mach numbers lead to a true stationary shock. An examination of coupling effects between the solar wind and the heavy ions at low Mach numbers by using the Rankine-Hugoniot relations reveals that the ions and the solar wind protons cannot be treated as a single fluid calculating the shock characteristics.