Accurate and efficient computation of the Boltzmann equation for Couette flow : influence of intermolecular potentials on Knudsen layer function and viscous slip coefficient

The Couette flow is one of the fundamental problems of rarefied gas dynamics, which has been investigated extensively based on the linearized Boltzmann equation (LBE) of hard-sphere molecules and simplified kinetic model equations. However, how the different intermolecular potentials affect the viscous slip coefficient and the structure of Knudsen layer remains unclear. Here, a novel synthetic iteration scheme (SIS) is developed for the LBE to find solutions of Couette flow accurately and efficiently: the velocity distribution function is first solved by the conventional iterative scheme, then it is modified such that in each iteration i) the flow velocity is guided by an ordinary differential equation that is asymptotic-preserving at the Navier–Stokes limit and ii) the shear stress is equal to the average shear stress. Based on the Bhatnagar–Gross–Krook model, the SIS is assessed to be efficient and accurate. Then we investigate the Knudsen layer function for gases interacting through the inverse power-law, shielded Coulomb, and Lennard-Jones potentials, subject to diffuse-specular and Cercignani–Lampis gas-surface boundary conditions. When the tangential momentum accommodation coefficient (TMAC) is not larger than one, the Knudsen layer function is strongly affected by the potential, where its value and width increase with the effective viscosity index of gas molecules. Moreover, the Knudsen layer function exhibits similarities among different values of TMAC when the intermolecular potential is fixed. For Cercignani–Lampis boundary condition with TMAC larger than one, both the viscous slip coefficient and Knudsen layer function are affected by the intermolecular potential, especially when the “backward” scattering limit is approached. With the asymptotic theory by Jiang and Luo (2016) [14] for the singular behavior of the velocity gradient in the vicinity of solid surfaces, we find that the whole Knudsen layer function can be well fitted by the power series ∑ n=0 2∑ m=0 2c n,mx n(xln⁡x) m, where x is the distance to the solid surface. Finally, the experimental data of the Knudsen layer profile are explained by the LBE solution with proper values of the viscosity index and TMAC

Modélisation des écoulements de gaz raréfiés au travers de filtres fibreux par la méthode de Boltzmann sur réseau

RÉSUMÉ: Les particules fines suspendues dans l’air (aussi nommées aérosols) sont nocives pour la santé humaine et pour l’environnement. La filtration des aérosols (ou la séparation de ces particules de l’air) est donc un procédé d’une importance cruciale. Les filtres fibreux sont généralement choisis pour leur haute performance et leur compacité. L’ajout de nanofibres (<1 μm) déposées sur une couche de microfibres ou mélangées à des microfibres a été proposé pour améliorer ces filtres. La théorie de la fibre unique est souvent utilisée pour prédire la performance des filtres à aérosols. Cependant, cette théorie prend pour acquis que les fibres d’un filtre sont toutes du même diamètre et ignore donc les impacts potentiels de la structure multicouche. La simulation numérique directe des écoulements gazeux au travers de milieux fibreux doit être utilisée pour tenir compte des interactions entre les fibres. Or, les effets de raréfaction qui apparaissent autour des nanofibres doivent être considérés pour prédire quantitativement la performance des milieux filtrants.----------ABSTRACT: Suspensions of fine particles (also called aerosols) are harmful to human health and the environment. The filtration of airborne particles (or the separation of these particles from the air) is therefore a process of crucial importance. Fibrous filters are generally chosen for their high performance and compactness. The addition of nanofibers (<1 μm) deposited on a layer of microfibers or mixed with microfibers has been proposed to improve these filters. The single fiber theory is often used to predict the performance of aerosol filters. However, this theory assumes that the fibers of a filter are all the same diameter and therefore ignores the potential impacts of the multilayer structure. Direct numerical simulation of gas flows through fibrous media must be used to account for the interactions between the fibers. However, the rarefaction effects that occur around nanofibers must be considered to quantitatively predict the performance of the filter media