Maxwell boundary condition and velocity dependent accommodation coefficient

2013 ◽  
Vol 25 (11) ◽  
pp. 112001 ◽  
Author(s):  
Henning Struchtrup
Keyword(s):  
Boundary Condition ◽  
Accommodation Coefficient ◽  
Maxwell Boundary Condition

Lattice Boltzmann Computations of Micro Channel and Micro Orifice Flows

2008 ◽  
Author(s):  
Taiho Yeom ◽  
Ignacio Zea Caloca ◽  
F. W. Chambers
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Navier Stokes ◽  
Reflection Factor ◽  
Micro Channel ◽  
Knudsen Numbers ◽  
Micro Flows ◽  
Bounce Back

Filtration in gas micro flows is an important problem complicated by possible slip flow for the filter media and the particles. Slip complicates Navier-Stokes solutions for the flow field. The direct simulation Monte Carlo method and its derivatives can be applied, but they are very complex. The Lattice Boltzmann Method (LBM) appears to offer some advantages for these slip and transitional flows. To evaluate the method, it was used to compute micro channel and micro orifice flows for a range of Knudsen numbers (Kn). The micro orifice simulates an array of micro filter fibers. The Lattice Bhatnagar-Gross-Krook (LBGK) single relaxation time approximation was used with the relaxation parameter accounting for density variations. The effects of different techniques for satisfying slip and no-slip boundary conditions were investigated. Both no-slip bounce-back and slip bounce-back boundary conditions were used. For the slip bounce-back boundary condition, the reflection factor and the accommodation coefficient were applied to improve accuracy. The micro channel computations were performed for conditions matching well-documented compressible slip-flow Navier-Stokes results in the literature. The channel had a length to height ratio of 100 and an inlet to outlet pressure ratio of 2.15. Knudsen numbers of 0.00194, 0.0194, and 0.194 were examined. The bounce-back boundary condition was applied at the top and bottom walls. A reflection factor of 0.85 provided the best agreement with the results in the literature for a Kn = 0.0194. The computed velocity profiles and the nonlinear streamwise pressure profile display excellent agreement with the Navier-Stokes results in the literature at this Knudsen number. At Kn = 0.00194, pure bounce back and bounce back with reflection factor both yield very good results. At Kn = 0.194, the bounce back with reflection factor results exhibit significant deviations from the literature. The accommodation coefficient scheme does not show good results for these micro flows. The reflection factor boundary condition also was applied for the micro orifice flows. The two-dimensional orifice computations were conducted with a 0.6 ratio of the open orifice area to the total area to match results in the literature. The micro orifice LBM results are in good agreement with the literature for Reynolds numbers between 4.8 and 12.5. In summary, the Lattice Boltzmann Method appears promising for micro filter computations, but improvements are needed for larger Knudsen numbers and more sophisticated relaxation time models may be needed for increased compressibility effects at higher Reynolds numbers.

Relationship between Maxwell Boundary Condition and Two Kinds of Stochastic Thermal Wall

2008 ◽  
Vol 77 (12) ◽  
pp. 124004 ◽  
Author(s):  
Shigeru Taniguchi ◽  
Asami Iwasaki ◽  
Masaru Sugiyama
Keyword(s):  
Boundary Condition ◽  
Maxwell Boundary Condition

Experimental Study on Measurement of Tangential Momentum Accommodation Coefficient in Microtube

2010 ◽  
Author(s):  
Hiroki Yamaguchi ◽  
Tsuneo Hanawa ◽  
Oto Yamamoto ◽  
Yu Matsuda ◽  
Yasuhiro Egami ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Knudsen Number ◽  
Mass Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Accommodation Coefficient ◽  
Surface Interaction ◽  
Slip Boundary ◽  
Tangential Momentum Accommodation Coefficient ◽  
Tangential Momentum

Along with the progress in micro- and nano-technologies, such as Micro Electro Mechanical Systems (MEMS) and μ-TAS (Micro-Total Analysis Systems), the Knudsen number, which is a non dimensional parameter for rarefaction, of the flow around and inside the systems becomes large. In such high Knudsen number flows, gas-surface interaction has become important for flow field analyses. To illustrate overall gas-surface interaction without any detailed processes, an accommodation coefficient, α, is the most widely used as an empirical parameter for a practical purpose. One of accommodation coefficients, the tangential momentum accommodation coefficient (TMAC) αt, is in closely related to the loss of the pressure through a micro channel. Therefore, TMAC is an important coefficient for flow inside micro/nano fluidic devices. To obtain TMAC from experiments, the mass flow rate measurements in a microtube were carried out using the constant volume method. The results obtained from the experiments were analyzed in frame of the Navier-Stokes equation associated with the second order velocity slip boundary condition. The mean Knudsen number was less than 0.3, where the velocity slip boundary condition is applicable. From the mass flow rates, the slip coefficient of the boundary condition was obtained, and then, TMAC was determined. The experimental apparatus showed very low leakage rate, and TMAC was determined with a high degree of accuracy. The TMACs of the same surface material with different dimensional parameters were compared for validation of the system.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document