Stretching Fields and Flow Mixing Enhancement of Rarified Gases in Micro-Grooved Channels by the Lattice-Boltzmann Method

The Eulerian and Lagrangian characteristics of a rarified gas flow have been investigated and related to flow mixing enhancement in micro grooved channels. The governing Boltzmann Transport Equation (BTE) is solved by the Lattice-Boltzmann method (LBM) for the Knudsen number range of 0.01−0.1. First, the Eulerian flow characteristics are determined by performing numerical simulations for different Knudsen numbers, pressure ratio and accommodation coefficients with the objective of obtaining reliable velocity characteristics and flow patterns, and determining the transition characteristics from the macro to microscale. The numerical predictions are compared to existing analytical and numerical results. Then, the Lagrangian characteristics are obtained by integrating the Eulerian velocity field by a 4t order Runge-Kutta scheme. Ten thousands (10,000) pairs of fluid particles are used to determine fluid particle Lagrangian trajectories, future stretching fields, and Lagrangian Lyapunov exponents, which are used for determining the grooved channel regions with high and low flow mixing enhancement. Our results demonstrate that rarified gas flows develop a future stretching field leading to the existence of Lagrangian chaos and flow mixing enhancement for very low, stable and time independent Reynolds number flow regime. This flow behavior departure from the well accepted concept that Lagrangian chaos and flow mixing enhancement need a time dependent 2D flow.