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

Abstract

We present simulation results of flows in the finite Knudsen range, which is in the slip and transition flow regime. Our implementations are based on the Lattice Boltzmann method and are accomplished within the Peano framework. We validate our code by solving two-and three-dimensional channel flow problems and compare our results with respective experiments from other research groups. We further apply our Lattice Boltzmann solver to the geometrical setup of a microreactor consisting of differently sized channels and a reactor chamber. Here, we apply static adaptive grids to further reduce computational costs. We further investigate the influence of using a simple BGK collision kernel in coarse grid regions which are further away from the slip boundaries. Our results are in good agreement with theory and non-adaptive simulations, demonstrating the validity and the capabilities of our adaptive simulation software for flow problems at finite Knudsen numbers.

An Integrated Method for Upscaling Pore-Network Characterization and Permeability Estimation: Example from the Mississippian Barnett Shale

“…The Avizo XLab Hydro solver has been validated by comparing it to theoretical models and standard glass bead-packing models (Zhang et al 2011). It is worthwhile to note that such validation does not consider the nanopore flow dynamics such as slip boundary and Knudsen diffusion (e.g., Verhaeghe et al 2009;Neumann and Rohrmann 2012). However, most of the pores in the FIB/SEM image reconstruction range from >20 nm to hundreds of nanometers.…”

Dimensional and Structural Control of Silica Aerogel Membranes for Miniaturized Motionless Gas Pumps

“…18 Aerogel materials can be made of silica, 19−24 carbon, 25−28 organic derived compounds 29−31 or other mineral type oxides. 32,33 From this list, silica-based aerogels show a unique combination of features such as high temperature resistance, 34 simple fabrication processes already scaled to industrial volumes 35,36 as well as straightforward functionalization (i.e., through nanodoping, addition of IR opacifiers, or catalytically active species).…”

An Innovative Technique for Estimation of Permeability of Shale Gas Reservoirs

“…Early efforts were mainly made on capturing slippage effect in the slip flow regime and the problem is well solved by application of various boundary conditions, such as bounce-back (Nie et al 2002), specular reflection (Lim et al 2002), diffusive reflection (Niu et al 2004) and combined forms of these boundary conditions (Tang et al 2004, Succi 2002. Recent efforts have been made to model the increased rarefaction effect of the transition flow (Shen et al 2004, Li et al 2011, Neumann and Rohrmann 2012, Kalarakis et al 2012) and associated Knudsen layer effect (Szalmás 2007, Guo and Zheng 2008, Dongari et al 2011, Tang et al 2008, Zhang et al 2006. One common approach to tackle this difficulty is the application of high-order Lattice Boltzmann (LB) models with increased number of discrete velocities; it is, however, found to fail to guarantee the improved accuracy for rarified flow (Kim et al 2008).…”

“…This effective viscosity was adopted by other researchers (Li et al 2011, Neumann and Rohrmann 2012, Kalarakis et al 2012 to extend the application of LBM to the transition flow and significant improvement was reached when matching the simulation results from LBM to those from DSMC in the transition flow regime. This Bosanquet-type effective viscosity, however, was actually previously proposed by Beskok and Karniadakis (1999) when investigating the rarefied gas flow and developing a physical-based model for the entire Kn flow regimes.…”