Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T20:56:01.490Z Has data issue: false hasContentIssue false

Numerical Simulation of Rarefied Gas Flows with Specified Heat Flux Boundary Conditions

Published online by Cambridge University Press:  03 June 2015

Jianping Meng
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, United Kingdom
Yonghao Zhang*
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical & Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, United Kingdom
Jason M. Reese
Affiliation:
School of Engineering, University of Edinburgh, Edinburgh EH9 3JL, United Kingdom
*
*Corresponding author. Email addresses: [email protected] (J. P. Meng), [email protected] (Y. H. Zhang), [email protected] (J. M. Reese)
Get access

Abstract

We investigate unidirectional rarefied flows confined between two infinite parallel plates with specified heat flux boundary conditions. Both Couette and force-driven Poiseuille flows are considered. The flow behaviors are analyzed numerically by solving the Shakhov model of the Boltzmann equation. We find that a zero-heat-flux wall can significantly influence the flow behavior, including the velocity slip and temperature jump at the wall, especially for high-speed flows. The predicted bimodal-like temperature profile for force-driven flows cannot even be qualitatively captured by the Navier-Stokes-Fourier equations.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ivanov, M. S. and Gimelshein, S. F.. Computational hypersonic rarefied flows. Annu. Rev. Fluid Mech., 30(1) (1998), 469505.Google Scholar
[2]Ho, C. M. and Tai, Y. C.. Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu. Rev. Fluid Mech., 30(1) (1998), 579612.Google Scholar
[3]Bird, G. A.. Monte Carlo simulation of gas flows. Annu. Rev. Fluid Mech., 10(1) (1978), 1131.CrossRefGoogle Scholar
[4]Yen, S. M.. Numerical solution of the nonlinear Boltzmann equation for nonequilibrium gas flow problems. Annu. Rev. Fluid Mech., 16(1) (1984), 6797.Google Scholar
[5]Radtke, G. A., Hadjiconstantinou, N. G., and Wagner, W.. Low-noise Monte Carlo simulation of the variable hard sphere gas. Phys. Fluids, 23(3) (2011), 030606.Google Scholar
[6]Struchtrup, H.. Derivation of 13 moment equations for rarefied gas flow to second order accuracy for arbitrary interaction potentials. Multiscale Model. Simul., 3(1) (2005), 221243.Google Scholar
[7]Gu, X. J. and Emerson, D. R.. A high-order moment approach for capturing non-equilibrium phenomena in the transition regime. J. Fluid Mech., 636(-1) (2009), 177216.Google Scholar
[8]Meng, J. P., Zhang, Y. H., Hadjiconstantinou, N. G., Radtke, G. A., and Shan, X. W.. Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows. J. Fluid Mech., 718 (2013), 347370.Google Scholar
[9]Akhlaghi, H., Roohi, E. and Stefanov, S., A new iterative wall heat flux specifying technique in DSMC for heating/cooling simulations of MEMS/NEMS, Int. J. Therm. Sci., 59 (2012), 111125.Google Scholar
[10]Wang, Q. W., Zhao, C. L., Zheng, M. and N. Wu, Y. E., Numerical investigation of rarefied diatomic gas flow and heat transfer in microchannel using dsmc with heat flux specified boundary conditiond part I: Numerical method and validation, Numerical Heat Transfer Part B, 53 (2008), 160173.Google Scholar
[11]Klinc, T. and Kušer, I.Slip coefficients for general gas-surface interaction, Phys. Fluids, 15 (1972), 10181022Google Scholar
[12]Alexeenko, A. A., Levin, D. A., Gimelshein, S. F., Collins, R. J. and Markelov, G. N.. Numerical simulation of high-temperature Gas flows in a millimeter-Scale thruster, J. Therm. Heat Trans., 16 (2002), 1016.Google Scholar
[13]Markelov, G. N., Kudryavtsev, A. N. and Ivanov, M. S., Rarefaction effects on separation of hypersonic laminar flows, AIP Conference Proceedings, 585 (2001), 707.Google Scholar
[14]Markelov, G. N. and Ivanov, M. S., Numerical study of 2D/3D micronozzle flows, AIP Conference Proceedings, 585 (2001), 539.CrossRefGoogle Scholar
[15]Sengil, N. and Edis, F. O.. Implementation of parallel DSMC method to adiabatic piston problem. In Parallel Computational Fluid Dynamics 2007, volume 67 of Lecture Notes in Computational Science and Engineering, pages 7582. Springer Berlin Heidelberg, 2009.Google Scholar
[16]Mohammadzadeh, A., Roohi, E., Niazmand, H., and Stefanov, S.. Dsmc solution for the adi-abatic and isothermal micro/nano lid-driven cavity. In Proceedings of the 3rd GASMEMS Workshop - Bertinoro, 2011.Google Scholar
[17]Kumar, R., Titov, E., and Levin, D.. Comparison of statistical BGK and DSMC methods with theoretical solutions for two classicalfluid flow problems. In Fluid Dynamics and Co-located Conferences, American Institute of Aeronautics and Astronautics, 2009.Google Scholar
[18]Burt, J. M. and Boyd, I. D.. Evaluation of a particle method for the ellipsoidal statistical Bhatnagar-Gross-Krook equation. In 44th AIAA Aerospace Sciences Meeting and Exhibit, 2006.Google Scholar
[19]Shakhov, E. M.. Generalization of the Krook kinetic relaxation equation. Fluid Dyn., 3(5) (1968), 9596.Google Scholar
[20]Shakhov, E. M.. Approximate kinetic equations in rarefied gas theory. Fluid Dyn, 3(1) (1968), 112115.Google Scholar
[21]Platkowski, T. and Illner, R.. Discrete velocity models of the Boltzmann equation: A survey on the mathematical aspects of the theory. SIAM Review, 30(2) (1988), 213255.Google Scholar
[22]Sone, Y., Kinetic theory and fluid Dynamics, BIRKHÄUSER 2002.Google Scholar
[23]Aoki, K., Takata, S., and Nakanishi, T.. Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force. Phys. Rev. E, 65 (2002), 026315.CrossRefGoogle ScholarPubMed
[24]Meng, J. P., Wu, L., Reese, J. M., and Zhang, Y. H.. Assessment of the ellipsoidal–statistical Bhatnagar–Gross–Krook model for force-driven Poiseuille flows. J. Comput. Phys., 251(0)(2013), 383395.Google Scholar