Volume 19, Issue 7 (July 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://mme.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:   (3347 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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Article Type: Original Research | Subject: Gas Dynamics
Received: 2018/03/31 | Accepted: 2019/01/8 | Published: 2019/07/1

1. Chambre PA, Schaaf SA. Flow of rarefied gases. Princeton: Princeton University Press; 2017. [Link]
2. Bird GA. Approach to translational equilibrium in a rigid sphere gas. The Physics of Fluids. 1963;6(10):1518. [Link] [DOI:10.1063/1.1710976]
3. Kirkwood JG. The statistical mechanical theory of transport processes I. general theory. The Journal of Chemical Physics. 1946;14(3):180. [Link] [DOI:10.1063/1.1724117]
4. Cercignani C. The Boltzmann equation. In: Cercignani C. The Boltzmann equation and its applications, applied mathematical sciences. 67th Volume. New York: Springer; 1988. pp. 40-103. [Link] [DOI:10.1007/978-1-4612-1039-9_2]
5. Jenny P, Torrilhon M, Heinz S. A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion. Journal of Computational Physics. 2010;229(4):1077-1098. [Link] [DOI:10.1016/j.jcp.2009.10.008]
6. Gorji MH, Torrilhon M, Jenny P. Fokker-Planck model for computational studies of monatomic rarefied gas flows. Journal of Fluid Mechanics. 2011;680:574-601. [Link] [DOI:10.1017/jfm.2011.188]
7. Pawula RF. Approximation of the linear Boltzmann equation by the Fokker-Planck equation. Physical Review. 1967;162(1):186. [Link] [DOI:10.1103/PhysRev.162.186]
8. Bogomolov SV. On Fokker-Planck model for the Boltzmann collision integral at the moderate Knudsen numbers. Mathematical Models and Computer Simulations. 2009;1:739. [Link] [DOI:10.1134/S2070048209060088]
9. Risken H. The Fokker-Planck equation: Methods of solution and applications. Berlin: Springer-Verlag; 1989. [Link] [DOI:10.1007/978-3-642-61544-3]
10. Gorji MH, Jenny P. A Fokker-Planck based kinetic model for diatomic rarefied gas flows. Physics of Fluids. 2013;25(6):062002. [Link] [DOI:10.1063/1.4811399]
11. Truesdell C, Muncaster R. Fundamentals of Maxwell's kinetic theory of a simple monatomic gas. New York: Academic Press; 1980. [Link]
12. Rezapour Jaghargh V, Mahdavi AM, Roohi E. A thorough evaluation of the Fokker-Planck kinetic model in the couette flow. 17th Conference on Fluid Dynamics, Shahrood University of Technology. Shahrood: Physics Society of Iran; 2017. [Link]
13. Rezapour V, Mahdavi AM, Roohi E. Investigation of rarefied gas flow in micro/nano cavity by Fokker Planck approach. 26th Annual Conference of Mechanical Engineering. Semnan: Semnan University; 2018. [Link]
14. Mohammadzadeh AR, Roohi E, Niazmand H, Stefanov S, Myong RS. Thermal and second-law analysis of a micro- or nanocavity using direct-simulation Monte Carlo. Physical Review E; 2012;85:056305. [Link] [DOI:10.1103/PhysRevE.85.056310]

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