Lattice Boltzmann approach for the simulation of rarefied gas flow in the slip flow regime

2013 ◽  
Vol 27 (6) ◽  
pp. 1753-1761 ◽  
Author(s):  
Namgyun Jeong
Keyword(s):  
Flow Regime ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Rarefied Gas Flow ◽  
Slip Flow Regime

Behaviour of rarefied gas flow near the junction of a suddenly expanding tube

2013 ◽  
Vol 739 ◽  
pp. 363-391 ◽  
Author(s):  
Vijay Varade ◽  
Amit Agrawal ◽  
A. M. Pradeep
Keyword(s):  
Flow Regime ◽  
Mass Flow ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Sudden Expansion ◽  
Momentum Balance ◽  
Straight Tube ◽  
Rarefied Gas Flow ◽  
Slip Flow Regime

AbstractThis paper presents an experimental study of isothermal rarefied gas flow through a tube with sudden expansion in the slip flow regime. The measurements reported here are for nitrogen flowing at low pressures in conventional tubes with sudden expansion area ratios of 1.48, 3.74, 12.43 and 64. The flow is dynamically similar to gas flow in a microchannel as the Knudsen number $(0. 0001\lt \mathit{Kn}\lt 0. 075)$ falls in the slip flow regime; the Reynolds number in the smaller section (${\mathit{Re}}_{s} $) ranges between 0.2 and 837. The static pressure along the wall is measured for different mass flow rates controlled by a mass flow controller and analysed to understand the flow behaviour. The velocity profiles are obtained through a momentum balance and using the pressure measurements. A discontinuity in the slope of pressure at the sudden expansion junction is noted and given special attention. The absence of flow separation is another key feature observed from the measurements. The streamlines are found to be concave near the junction. It is demonstrated that the flow ‘senses’ the oncoming sudden expansion junction and starts adjusting itself much before reaching the junction; this interesting behaviour is attributed to an increased axial momentum diffusion and wall slip. The additional acceleration of the central core of the gas flow causes an increase in the wall shear stress and a larger pressure drop as compared with a straight tube. These results are not previously available and should help in improving understanding of gaseous slip flows.

Lattice Boltzmann Simulation of Rarefied Gas Flow Along Moving Rigid Objects in Micro-Cavities

2015 ◽  
Author(s):  
Weilin Yang ◽  
Hongxia Li ◽  
TieJun Zhang ◽  
Ibrahim M. Elfadel
Keyword(s):  
Free Path ◽  
Lattice Boltzmann ◽  
Path Length ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Free Path Length ◽  
Mean Free Path ◽  
Fluid Simulation ◽  
Transition Flow ◽  
Rarefied Gas Flow

Rarefied gas flow plays an important role in the design and performance analysis of micro-electro-mechanical systems (MEMS) under high-vacuum conditions. The rarefaction can be evaluated by the Knudsen number (Kn), which is the ratio of the molecular mean free path length and the characteristic length. In micro systems, the rarefied gas flow usually stays in the slip- and transition-flow regions (10−3 < Kn < 10), and may even go into the free molecular flow region (Kn > 10). As a result, conventional design tools based on continuum Navier-Stokes equation solvers are not applicable to analyzing rarefaction phenomena in MEMS under vacuum conditions. In this paper, we investigate the rarefied gas flow by using the lattice Boltzmann method (LBM), which is suitable for mesoscopic fluid simulation. The gas pressure determines the mean free path length and Kn, which further influences the relaxation time in the collision procedure of LBM. Here, we focus on the problem of squeezed film damping caused by an oscillating rigid object in a cavity. We propose an improved LBM with an immersed boundary approach, where an adjustable force term is used to quantify the interaction between the moving object and adjacent fluid, and further determines the slip velocity. With the proposed approach, the rarefied gas flow in MEMS with squeezed film damping is characterized. Different factors that affect the damping coefficient, such as pressure of gas and frequency of oscillation, are investigated in our simulation studies.

Is the Lattice Boltzmann Method Applicable to Rarefied Gas Flows? Comprehensive Evaluation of the Higher-Order Models

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Minoru Watari
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Higher Order ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Slip Flow Regime ◽  
Boltzmann Method ◽  
Higher Order Models

Lattice Boltzmann method (LBM) whose equilibrium distribution function contains higher-order terms is called higher-order LBM. It is expected that nonequilibrium physics beyond the Navier–Stokes can be accurately captured using the higher-order LBM. Relationship between the level of higher-order and the simulation accuracy of rarefied gas flows is studied. Theoretical basis for constructing higher-order LBM is presented. On this basis, specific higher-order models are constructed. To confirm that the models have been correctly constructed, verification simulations are performed focusing on the continuum regime: sound wave and supersonic flow in Laval nozzle. With applications to microelectromechanical systems (MEMS) in mind, low Mach number flows are studied. Shear flow and heat conduction between parallel walls in the slip flow regime are investigated to confirm the relaxation process in the Knudsen layer. Problems between concentric cylinders are investigated from the slip flow regime to the free molecule regime to confirm the effect of boundary curvature. The accuracy is discussed comparing the simulation results with pioneers' studies. Models of the fourth-order give sufficient accuracy even for highly rarefied gas flows. Increase of the particle directions is necessary as the Knudsen number increases.

scholarly journals A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media

2020 ◽  
Vol 135 (1) ◽  
pp. 219-242
Author(s):  
Francesc Pérez-Ràfols ◽  
Fredrik Forsberg ◽  
Gunnar Hellström ◽  
Andreas Almqvist
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Gas Flow ◽  
Present Model ◽  
Rarefied Gas ◽  
Slip Flow ◽  
Local Scale ◽  
Heterogeneous Porous Media ◽  
Scale Model ◽  
Rarefied Gas Flow

Abstract This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.

DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: Effect of Mach number and wall temperature

2020 ◽  
pp. 095441002095987
Author(s):  
Deepak Nabapure ◽  
Ram Chandra Murthy K
Keyword(s):  
Mach Number ◽  
Flow Regime ◽  
Surface Properties ◽  
Wall Temperature ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Transitional Flow ◽  
Flow Properties ◽  
Rarefied Gas Flow ◽  
Backward Facing Step

Rarefied gas flow over a backward-facing step (BFS) is often encountered in separating flows prevalent in aerodynamic flows, engine flows, condensers, space vehicles, heat transfer systems, and microflows. Direct Simulation Monte Carlo (DSMC) is a powerful tool to investigate such flows. The purpose of this research is to assess the impact of Mach number and wall temperature on the flow and surface properties in the transitional flow regime. The Mach numbers considered are 5, 10, 25, 30, and the ratio of the temperature of the wall to that of freestream considered are 1, 2, 4, 8. The Reynolds number for the cases studied is 8.6, 17.2, 43, and 51.7, respectively. Typically the flow properties near the wall are found to increase with both Mach number and wall temperature owing to compressibility and viscous dissipation effects. The variation in flow properties is more sensitive to Mach number than the wall temperature. The surface properties are found to decrease with Mach number and increase with wall temperature. Moreover, in the wake of the step, the vortex’s recirculation length is reasonably independent of both free stream Mach number and wall temperature, whereas it decreases with Knudsen number.

Friction Factor Correlations for Gas Flow in Slip Flow Regime

2007 ◽  
Vol 129 (10) ◽  
pp. 1268-1276 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Stephen E. Turner ◽  
Mohammad Faghri
Keyword(s):  
Friction Factor ◽  
Flow Regime ◽  
Gas Flow ◽  
Slip Flow ◽  
Channel Height ◽  
Inlet Temperature ◽  
Arbitrary Lagrangian Eulerian ◽  
Knudsen Numbers ◽  
Wide Range ◽  
Slip Flow Regime

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

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