Volume 19, Issue 7 (2019)                   Modares Mechanical Engineering 2019, 19(7): 1721-1732 | Back to browse issues page

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Rezapour Jaghargh V, Mahdavi A, Roohi E. Evaluation of Rarefied Shear Flow in Micro/Nano Geometries Using Fokker-Planck Technique. Modares Mechanical Engineering. 2019; 19 (7) :1721-1732
URL: http://journals.modares.ac.ir/article-15-18308-en.html
1- Mechanical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran
2- Mechanical Engineering Department, Engineering Faculty, Ferdowsi University of Mashhad, Mashhad, Iran , e.roohi@um.ac.ir
Abstract:   (219 Views)
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.
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Received: 2018/03/31 | Accepted: 2019/01/8 | Published: 2019/07/1

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