Skip to main content

New approaches to modeling rarefied gas flow in the slip and transition regime

  • Conference paper
  • First Online:
Parallel Computational Fluid Dynamics 2007

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 67))

  • 506 Accesses

Abstract

Rarefied gas dynamics, which has been explored for more than a century, studies device being considered. Traditionally, it has been used to study high-speed highaltitude flow applications, such as space re-entry vehicles, and flows under ultra-low pressure (vacuum) conditions, where ??has a large value. However, recent technological developments have enabled major advances in fabricating miniaturized devices such as micro-electro-mechanical systems (MEMS). Gas flow in micro-scale devices can suffer from rarefaction effects because the characteristic length of the device is so small that it is comparable to the mean free path of the gas, even under atmospheric conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Gad-el-hak, The Fluid Mechanics of Microdevices – The Freeman Scholar Lecture, Fluids Eng. 121:5–33. 1999.

    Article  Google Scholar 

  2. C. Cercignani, The Boltzmann Equation and Its Applications (Springer, New York, 1988).

    Book  MATH  Google Scholar 

  3. S. Champman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, 1970).

    Google Scholar 

  4. H. Grad, Asymptotic Theory of the Boltzmann Equation, Phys. Fluids 6:147–181, 1963.

    Article  MathSciNet  Google Scholar 

  5. A. V. bobylev, The Champman-Enskog and Grad Method for Solving the Boltzmann Equation, Sov. Phys.-Dokl. 27:29–31, 1982.

    Google Scholar 

  6. H. Grad, On the Kinetic Theory of Rarefied Gases, Commun. Pure Appl. Math. 2:331–407, 1949.

    Google Scholar 

  7. C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell’s Kinetic Theory of a Simple Monotomic Gas (Academic Press, New York, 1980).

    Google Scholar 

  8. S. Chen and G. D. Doolen, Lattice Boltzmann Method For Fluid Flows, Ann. Rev. Fluid Mech. 30:329–64, 1998.

    Article  MathSciNet  Google Scholar 

  9. X. Shan, X.-F. Yuan and H. Chen, Kinetic Theory Representation of Hydrodynamcis: A Way Beyond the Navier-Stokes Equation, J. Fluid Mech. 550:413–441, 2006.

    Article  MathSciNet  Google Scholar 

  10. G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Claredon Press, Oxford, 1994).

    Google Scholar 

  11. H. Struchtrup, Macroscopic Transport Equations for Rarefied Gas Flows (Springer-Verlag, Berlin-Heidelberg, 2005).

    MATH  Google Scholar 

  12. A. N. Gorban, I.V. Karlin and A. Y. Zinovyev,Constructive Methods of Invariant Manifolds for Kinetic Problems, Phys. Rep. 396:197–403, 2004.

    Article  MathSciNet  Google Scholar 

  13. I. V. Karlin, A. N. Gorban, G. Dukek and T. F. nonenmacher, Dynamic Correction to Moment Approximations, Phys. Rev. E. 57:1668–1672, 1998.

    Google Scholar 

  14. H. Struchtrup and M. Torrihon, Regularization of Grad’s 13 Moment Equations: Derivation and Linear Analysis, Phys. Fluids 15:2668–2680, 2003.

    Article  Google Scholar 

  15. M. Torrihon and H. Struchtrup, Regularized 13 Moment Equation: Shock Structure Calculations and Comparison to Burnett Models, J. Fluid Mech. 513: 171–198, 2004.

    Google Scholar 

  16. X. J. Gu and D. R. Emerson, A Computational Strategy for the Regularized 13 Moment Equations With Enhanced Wall-boundary Conditions. J. Comput. Phys. 225:263–283, 2007.

    Article  Google Scholar 

  17. J. C. Maxwell, On Stresses in Rarified Gases Arising From Inequalities of Temperature, Phil. Trans. Roy. Soc. Lond.) 170:231–256, 1879.

    Google Scholar 

  18. X. J. Gu and D. R. Emerson, How Far Can 13 Moments Go in Modelling Micro-Scale Gas Phenomena? Nanoscale and Microscale Thermophysical Eng. 11:85–97, 2007.

    Google Scholar 

  19. X. J. Gu and D. R. Emerson, A high-order moments approach for capturing nonequilibrium phenomena in the transition regime, in preparation, 2007.

    Google Scholar 

  20. E. F. Toro, 1999 Riemann Solvers and Numerical Methods for Fluids Dynamics: A Practical Introduction, 2nd ed., (Springer, Berlin, 1999).

    Google Scholar 

  21. J. H. Ferziger and M. Perić, Computational Methods for Fluid Dynamics, 2nd Ed, (Springer-Verlag, Berlin,-Heidelberg, 1999).

    MATH  Google Scholar 

  22. P. H. Gaskell and A. K. C. Lau, Curvature-compensated convective-transport – SMART, A new boundedness-preserving transport algorithm. Int. J. Numer. Meth. Fluids 8:617–641, 1988.

    MathSciNet  Google Scholar 

  23. M. A. Alves, P. J. Oliveria and F. T. Pinho, A convergent and universally bounded interpolation scheme for the treatment of advection. Int. J. Numer. Meth. Fluids 41:47–75, 2003.

    Article  Google Scholar 

  24. X. J. Gu and R. W. Barber and D. R. Emerson, Parallel Computational Fluid Dynamics – Advanced Numerical Methods, Software and Applications (B. Chetverushkin, A. Ecer, J. Periaux, N. Satofuka, P. Fox, Eds., Elsevier Science, pp.497–504, 2004).

    Google Scholar 

  25. S. V. Patankar, Numerical Heat Transfer and Fluid Flow. (McGraw-Hill, New York, 1980).

    Google Scholar 

  26. C. M. Rhie and W. L. Chow, Numerical study of turbulent flow past an airfoil with trailing edge separation, AIAA J., 21:1525–1532, 1983.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gu, X., Emerson, D. (2009). New approaches to modeling rarefied gas flow in the slip and transition regime. In: Parallel Computational Fluid Dynamics 2007. Lecture Notes in Computational Science and Engineering, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92744-0_4

Download citation

Publish with us

Policies and ethics