0
Research Papers: Techniques and Procedures

Relationship between accuracy and number of velocity particles of the finite-difference lattice Boltzmann method in velocity slip simulations

[+] Author and Article Information
Minoru Watari

 LBM Fluid Dynamics Laboratory, 3-2-1 Mitahora-higashi, Gifu 502-0003, Japanwatari-minoru@kvd.biglobe.ne.jp

J. Fluids Eng 132(10), 101401 (Oct 06, 2010) (11 pages) doi:10.1115/1.4002359 History: Received February 27, 2010; Revised August 10, 2010; Published October 06, 2010; Online October 06, 2010

Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier–Stokes equations in the N-S flow area, (b) conservation of momentum flow Pxy in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model’s angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable.

Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Typical velocity slip profile

Grahic Jump Location
Figure 2

Normalized Knudsen profile Y0

Grahic Jump Location
Figure 3

Unit vectors of moving particles of the octagon family: from left to right, octagon, double octagon, and triple octagon models

Grahic Jump Location
Figure 4

Average particle speed of the octagon family and the theoretical value

Grahic Jump Location
Figure 5

D2Q9 model particles

Grahic Jump Location
Figure 6

A flow between parallel plates

Grahic Jump Location
Figure 7

Nodes for the velocity slip simulation

Grahic Jump Location
Figure 8

Grid dependence study: rms error for the octagon model

Grahic Jump Location
Figure 9

Octagon family: velocity profile for three models with τ=0.05

Grahic Jump Location
Figure 10

Octagon family: velocity slip divided by the velocity gradient uy.slip/(duy/dx) versus Knudsen number

Grahic Jump Location
Figure 11

Octagon family: Knudsen profile for three models with τ=0.05

Grahic Jump Location
Figure 12

Relative angular situation between the model and the wall

Grahic Jump Location
Figure 13

Octagon family: Effect of angle to the wall for three models with τ=0.05

Grahic Jump Location
Figure 14

D2Q9 model: Knudsen profile by simulations for various τ

Grahic Jump Location
Figure 15

D2Q9 model: Velocity slip divided by the velocity gradient uy.slip/(duy/dx) versus the relaxation time constant τ

Grahic Jump Location
Figure 16

D2Q9 model: effect of the angle θ on the velocity slip for τ=0.05

Grahic Jump Location
Figure 17

Steady Knudsen solutions for the octagon model

Grahic Jump Location
Figure 18

Knudsen profile comparison between the simulation in Sec. 5 and the Knudsen simulation for the octagon model

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In