Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime. II. Application to curved boundaries

Lattice Boltzmann modeling and simulation of velocity and concentration slip effects on the catalytic reaction rate of strongly nonequimolar reactions in microflows

A lattice Boltzmann (LB) interfacial gas-solid three-dimensional model is developed for isothermal multicomponent flows with strongly nonequimolar catalytic reactions, further accounting for the presence of velocity slips and concentration jumps. The model includes diffusion coefficients of all reactive species in the calculation of the catalytic reaction rates as well as an updated velocity at the reactive boundary node. Lattice Boltzmann simulations are performed in a catalytic channel-flow geometry under a wide range of Knudsen (Kn) and surface Damköhler (Da_{s}) numbers. Comparisons with simulations from a computational fluid dynamics (CFD) Navier-Stokes solver show good agreement in the continuum regime (Kn<0.01) in terms of flow velocity and reactive species distributions, while comparisons with direct simulation Monte Carlo results from the literature attest to the model's applicability in capturing the correct slip velocity at Kn as high as 0.1, even with a significantly reduced number of grid points (N=10) in the cross-flow direction. Theoretical and numerical results demonstrate that the term Da_{s}×Kn×A_{2} (where A_{2} is a function of the mass accommodation coefficient) determines the significance of the concentration jump on the catalytic reaction rate. The developed model is applicable for many catalytic microflow systems with complex geometries (such as reactors with porous networks) and large velocity/concentration slips (such as catalytic microthrusters for space applications).

Improved curved-boundary scheme for lattice Boltzmann simulation of microscale gas flow with second-order slip condition

An improved curved-boundary scheme with second-order velocity slip condition for multiple-relaxation-time-lattice Boltzmann (MRT-LB) simulation of microgas flow is proposed. The proposed interpolation bounce-back (IBB)-explicit counter-extrapolation (ECE) scheme adopts the IBB method to describe the curved boundary, while the ECE method is employed to predict the slip velocity on gas-solid interface. To incorporate the effect of second-order velocity slip term and the influence of boundary curvature, a slip velocity model is also derived, from which the gas slip velocity is captured by the ECE discretization method. The influence of fictitious slip velocity can be eliminated by adopting the present ECE method, and the influence of actual offset between the lattice node and the physical boundary can be well considered by the IBB method. The proposed IBB-ECE boundary scheme is then implemented with the MRT-LB model and tested by simulations of force-driven gas flow in horizontal (inclined) microchannel, gas flow around a micro-cylinder, and Couette flow between two micro-cylinders. Numerical results show that the proposed IBB-ECE scheme improves the computational accuracy of gas slip flow (0.001<Kn≤0.1) when compared with other boundary schemes reported in the literature, and provides a precise and easy implementing scheme for curved boundary with second-order slip condition.

Lattice Boltzmann method with moment-based boundary conditions for rarefied flow in the slip regime

A lattice Boltzmann method with moment-based boundary conditions is used to compute flow in the slip regime. Navier-Maxwell slip conditions and Burnett-order stress conditions that are consistent with the discrete velocity Boltzmann equation are imposed locally on stationary and moving boundaries. Micro-Couette and micro-lid-driven cavity flows are studied numerically at Knudsen and Mach numbers of the order O(10^{-1}). The Couette results for velocity and the deviatoric stress at second order in Knudsen number are in excellent agreement with analytical solutions, and the cavity results are in excellent agreement with existing data. The algorithm is shown to compute nonequilibrium effects in the pressure that are in very good agreement with DSMC simulations of the Boltzmann equation but not captured by the Navier-Stokes equations.

Enhanced single-node lattice Boltzmann boundary condition for fluid flows

We propose a procedure to implement Dirichlet velocity boundary conditions for complex shapes that use data from a single node only, in the context of the lattice Boltzmann method. Two ideas are at the base of this approach. The first is to generalize the geometrical description of boundary conditions combining bounce-back rule with interpolations. The second is to enhance them by limiting the interpolation extension to the proximity of the boundary. Despite its local nature, the resulting method exhibits second-order convergence for the velocity field and shows similar or better accuracy than the well-established Bouzidi's scheme for curved walls [M. Bouzidi, M. Firdaouss, and P. Lallemand, Phys. Fluids 13, 3452 (2001)]PHFLE61070-663110.1063/1.1399290. Among the infinite number of possibilities, we identify several meaningful variants of the method, discerned by their approximation of the second-order nonequilibrium terms and their interpolation coefficients. For each one, we provide two parametrized versions that produce viscosity independent accuracy at steady state. The method proves to be suitable to simulate moving rigid objects or surfaces moving following either the rigid body dynamics or a prescribed kinematic. Also, it applies uniformly and without modifications in the whole domain for any shape, including corners, narrow gaps, or any other singular geometry.

Permeability Estimation of Regular Porous Structures: A Benchmark for Comparison of Methods

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

Reviving the local second-order boundary approach within the two-relaxation-time lattice Boltzmann modelling

This work addresses the Dirichlet boundary condition for momentum in the lattice Boltzmann method (LBM), with focus on the steady-state Stokes flow modelling inside non-trivial shaped ducts. For this task, we revisit a local and highly accurate boundary scheme, called the local second-order boundary (LSOB) method. This work reformulates the LSOB within the two-relaxation-time (TRT) framework, which achieves a more standardized and easy to use algorithm due to the pivotal parametrization TRT properties. The LSOB explicitly reconstructs the unknown boundary populations in the form of a Chapman-Enskog expansion, where not only first- but also second-order momentum derivatives are locally extracted with the TRT symmetry argument, through a simple local linear algebra procedure, with no need to compute their non-local finite-difference approximations. Here, two LSOB strategies are considered to realize the wall boundary condition, the original one called Lwall and a novel one Lnode, which operate with the wall and node variables, roughly speaking. These two approaches are worked out for both plane and curved walls, including the corners. Their performance is assessed against well-established LBM boundary schemes such as the bounce-back, the local second-order accurate CLI scheme and two different parabolic multi-reflection (MR) schemes. They are all evaluated for 3D duct flows with rectangular, triangular, circular and annular cross-sections, mimicking the geometrical challenges of real porous structures. Numerical tests confirm that LSOB competes with the parabolic MR accuracy in this problem class, requiring only a single node to operate. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.