Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T07:07:14.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Transient motion of a confined rarefied gas due to wall heating or cooling

Published online by Cambridge University Press:  26 April 2006

Dean C. Wadsworth ,
Daniel A. Erwin  and
E. Phillip Muntz
Dean C. Wadsworth
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
Daniel A. Erwin
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
E. Phillip Muntz
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The transient motion that arises in a confined rarefied gas as a container wall is rapidly heated or cooled is simulated numerically. The Knudsen number based on nominal gas density and characteristic container dimension is varied from near-continuum to highly rarefied conditions. Solutions are generated with the direct simulation Monte Carlo method. Comparisons are made with finite-difference solutions of the Navier–Stokes equations, the limiting free-molecular values, and (continuum) results based on a small perturbation analysis. The wall heating and cooling scenarios considered induce relatively large acoustic disturbances in the gas, with characteristic flow speeds on the order of 20% of the local sound speed. Steady-state conditions are reached after on the order of 5 to 10 acoustic time units, here based on the initial speed of sound in the gas and the container dimension. As rarefaction increases, the initial gas response time is decreased. For the case of a rapid increase in wall temperature, transient rarefaction effects near the wall greatly alter gas response compared to the continuum predictions, even at relatively small nominal Knudsen number. For wall cooling, the continuum solution agrees well with direct simulation at that same Knudsen number. A local Knudsen number, based on the mean free path and the scale length of the temperature gradient, is found to be a more suitable indicator of transient rarefaction effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 219 - 235
Copyright
© 1993 Cambridge University Press

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

Alofs, D. J., Flagan, R. C. & Springer, G. S. 1971 Density distribution measurements in rarefied gases contained between parallel plates at high temperature differences. Phys. Fluids 14, 529– 533.Google Scholar
Aoki, L., Sone, Y., Nishino, K. & Sugimoto, H. 1991 Numerical analysis of unsteady motion of a rarefied gas caused by sudden changes of wall temperature with special interest in the propagation of a discontinuity in the velocity distribution function. In Rarefied Gas Dynamics, Proc. 17th Intl Symp. on Rarefied Gas Dynamics, Aachen 1990 (ed. A. E. Beylich), pp. 222– 231. VCH.
Bird, G. A. 1976 Molecular Gas Dynamics. Oxford University Press.
Bird, G. A. 1983 Definition of mean free path for real gases. Phys. Fluids 26, 3222– 3223.Google Scholar
Bird, G. A. 1987 Direct simulation of high-vorticity gas flows. Phys. Fluids 30, 364– 366.Google Scholar
Bird, G. A. 1991 A contemporary implementation of the direct simulation Monte Carlo method. In Microscopic Simulations of Complex Hydrodynamic Phenomena. NATO ASI, Alghero, Sardinia.
Clarke, J. F., Kassoy, D. R. & Riley, N. 1984a Shocks generated in a confined gas due to rapid heat addition at the boundary. I. weak shock waves. Proc. R. Soc. Lond. A 393, 309– 329.Google Scholar
Clarke, J. F., Kassoy, D. R. & Riley, N. 1984b Shocks generated in a confined gas due to rapid heat addition at the boundary. II. strong shock waves. Proc. R. Soc. Lond. A 393, 331– 351.Google Scholar
Eckert, E. R. G. & Carlson, W. O. 1961 Natural convection in an air layer enclosed between two vertical plates with different temperatures. Intl. J. Heat Mass Transfer 2, 106– 120.Google Scholar
Fiscko, K. A. & Chapman, D. R. 1988 Comparison of Burnett, super-Burnett and Monte Carlo solutions for hypersonic shock structure. In Rarefied Gas Dynamics: Theoretical and Computational Techniques (Progress in Astronautics and Aeronautics, vol. 118) (ed. E. P. Muntz, D. P. Weaver & D. H. Campbell), pp. 374– 395. AIAA.
Gupta, R. N., Scott, C. D. & Moss, J. N. 1985 Slip boundary equations for multi-component nonequilibrium airflow. NASA TP 2452.
Huang, A. B. 1967 A general discrete ordinate method for the dynamics of rarefied gases. Rarefied Gasdynamic and Plasma Lab. Rep. 4. School of Aerospace Engineering, Georgia Institute of Technology.
Huang, A. B. & Hwang, P. F. 1973 Test of statistical models for gases with and without internal energy states. Phys. Fluids 16, 466– 475.Google Scholar
Kassoy, D. R. 1979 The response of a confined gas to a thermal disturbance. I: Slow transients. SIAM J. Appl. Maths 36, 624– 634.Google Scholar
Koura, K. 1990 Direct simulation of vortex shedding in dilute gas flows past an inclined flat plate. Phys. Fluids A 2, 209– 213.Google Scholar
Koura, K. 1991 Direct simulation of vortex shedding in dilute gas flows past bluff bodies. In Rarefied Gas Dynamics, Proc. 17th Intl Symp. on Rarefied Gas Dynamics, Aachen 1990 (ed. A. E. Beylich), pp. 695– 702. VCH.
Koura, K. & Kondo, J. 1969 Solutions of unsteady nonlinear molecular flow problems by the Monte Carlo method. In Rarefied Gas Dynamics – Sixth Symp. (ed. L. Trilling & H. Y. Wachman), vol. I, pp. 181– 184. Academic.
Larkin, B. K. 1967 Heat flow to a confined fluid in zero gravity. In Thermophysics of Spacecraft and Planetary Bodies (ed. G. B. Heller). Progress in Astronautics and Aeronautics, vol. 20, pp. 819– 832. AIAA.
Liepmann, H. W. & Roshko, A. 1957 Elements of Gas Dynamics. John Wiley.
Liu, C.-Y. & Lees, L. 1961 Kinetic theory description of plane compressible Couette flow. In Rarefied Gas Dynamics, Second Intl Symp. (ed. L. Talbot). Academic.
MacCormack, R. W. & Baldwin, B. S. 1975 A numerical method for solving the Navier–Stokes equations with application to shock-boundary layer interaction. AIAA Paper 75-1.
Moody, F. J. 1990 Introduction to Unsteady Thermofluid Mechanics. John Wiley.
Muntz, E. P., Shifflet, G., Erwin, D. A. & Kunc, J. A. 1992 Transient pressure driven microdevices. In Micromechanical Systems (ed. D. Cho, J. P. Peterson, A. P. Pisano & C. Friedrich). ASME DSC, vol. 40.
Patterson, G. N. 1971 Introduction to the Kinetic Theory of Gas Flows. University of Toronto Press.
Perlmutter, M. 1967 Analysis of transient heat transfer through a collisionless gas enclosed between parallel plates. ASME Paper 67-HT-53.
Pham-Van-Diep, G. C., Erwin, D. A. & Muntz, E. P. 1991 Testing continuum descriptions of low-Mach-number shock structures. J. Fluid Mech. 232, 403– 413.Google Scholar
Present, R. D. 1958 Kinetic Theory of Gases. McGraw-Hill.
Radhwan, A. M. & Kassoy, D. R. 1984 The response of a confined gas to a thermal disturbance: Rapid boundary heating. J. Engng Maths 18, 133– 156.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory, 4th edn. McGraw-Hill.
Wadsworth, D. C. 1992 Slip effects in a confined rarefied gas, I: Temperature slip. Phys. Fluids (submitted).Google Scholar
Wetzel, W. & Oertel, H. 1987 Gas-kinetical simulation of vortex flows. Acta Mechanica 70, 127– 143.Google Scholar
Willis, D. R. 1962 Heat transfer in a rarefied gas between parallel plates at large temperature ratios. Rep. 615. Princeton University James Forrestal Research Center, Gas Dynamics Laboratory.
Yoshizawa, Y. A. 1969 Monte Carlo calculation of unsteady rarefied gas flow between parallel plates. In Rarefied Gas Dynamics – Sixth Symp. (ed. L. Trilling & H. Y. Wachman), vol. I, pp. 177– 180. Academic.
Zhong, X., MacCormack, R. W. & Chapman, D. R. 1991 Evaluation of slip boundary conditions for the Burnett equations with application to hypersonic leading edge flow. In Fourth Intl Symp. on Computational Fluid Dynamics, vol. II. University of California, Davis.