RT - Journal Article T1 - Evaluation of Rarefied Shear Flow in Micro/Nano Geometries Using Fokker-Planck Technique JF - mdrsjrns YR - 2019 JO - mdrsjrns VO - 19 IS - 7 UR - http://mme.modares.ac.ir/article-15-18308-en.html SP - 1721 EP - 1732 K1 - Knudsen Number K1 - Shear-driven flow K1 - Micro/Nano Flow K1 - Fokker Planck Approach AB - In this article, rarefied gas flow was investigated and analyzed by the Fokker-Planck approach in different Knudsen numbers and Mach numbers at subsonic and supersonic regimes. The presented Fokker-Planck approach is used to solve the rarefied gas flows in different shear-driven micro/nano geometries like one-dimensional Couette flow and the two-dimensional cavity problem. Boltzmann's equation, and especially statistical technique of the Direct Simulation Monte Carlo (DSMC), are precise tools for simulating non-equilibrium flows. However, as the Knudsen number becomes small, the computational costs of the DSMC are greatly increased. In order to cope with this challenge, the Fokker-Planck approximation of the Boltzmann equation is considered in this article. The developed code replaces the molecular collisions in DSMC with a set of continuous stochastic differential equations. In this study, the Fokker-Planck method was evaluated in the Couette flow in the subsonic Mach number of 0.16 (wall velocity was 50 m/s) and in the supersonic Mach number of 3.1 (wall velocity was 1000 m/s), where Knudsen numbers range from 0.005-0.3. Also, the cavity flow with a wall Mach number of 0.93 (wall velocity was 300 m/s) in Knudsen numbers ranging from 0.05-20 was investigated. The results show that by increasing speed and Knudsen numbers, the accuracy of Fokker-Planck increases. In addition, despite using larger number of simulator particles, the rapid convergence and lower computational costs relative to other methods are the features of this method. LA eng UL http://mme.modares.ac.ir/article-15-18308-en.html M3 ER -