Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Abstract

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electromechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.

Lattice Boltzmann Simulations in the Slip and Transition Flow Regime with the Peano Framework

“…Their results show excellent agreement in the slip flow regime, however, they point out deficiencies of the slip flow model for higher Knudsen numbers. A respective extension to the transition flow regime has been developed recently by Li et al [2]. Another approach to rarefied gas modeling using Lattice Boltzmann methods is reported in [22,23] where-based on the Hermite projection method-higher-order Lattice Boltzmann models are constructed and yield promising results for both slip and transition flow regime.…”

“…In the following, we shortly describe the models that our implementations are based on; see [2,6,26] for detailed discussions. We subsequently describe a simple bounce-back based extension for geometrical setups of branched duct structures; all our discussions apply analogously to two-and three-dimensional scenarios.…”

“…The model extensions described above have been validated in [2] and [6] for two-dimensional channel scenarios with planar boundaries. For detailed discussions on microscopic slip effects, see [12], as well as [13] for a review on slip models for gas microflows.…”

“…The BGK model induces numerical slip which-in contrast to the tuned MRT models-may yield unphysical results as discussed in [6]; a tuning of the BGK operator to remove these artifacts may not be possible. For a derivation of the tuned relaxation parameter sets for the MRT collision operator, see [2] and [6].…”

“…Different methods have been proposed over the last years to extend existing continuum approaches to the finite Knudsen regime, i.e. to the slip and transition flow regime [2][3][4][5][6][7][8]. In this context, the Lattice Boltzmann method (LBM) has attracted particular attention, due to its kinetic origin and implementational simplicity.…”