Qualitative analysis of the Navier-Stokes equations for evaporation-condensation problems

Physics of Fluids

Volumn 8, Issue 7, 1996, Pages 1764-1773

  Bobylev, A V ^a   Ostmo S ^b   Ytrehus, T ^b  

^a KELDYSH INSTITUTE OF APPLIED MATHEMATICS   (Russian Federation)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSATION; EVAPORATION; NAVIER-STOKES EQUATIONS;

EID: 0029673610     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.868959     Document Type: Article

References (28)

1. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994).
2. M. Morduchow and P.A. Libby, "On a complete solution of the one-dimensional flow equations of a viscous heat-conducting. compressible gas," J. Aero. Sci. 16, 674 (1949).
3. R. von Mises, "On the thickness of a steady shock wave," J. Aero. Sci. 17, 551 (1950).
4. G.S.S. Ludford, "The classification of one-dimensional flows and the general shock problem of a compressible, viscouss, heat-conducting fluid," J. Aero. Sci. 18, 830 (1951).
5. R. von Mises, Mathematical Theory of Compressible Fluid Flow (Academic. New York, 1958).
6. T. H. Moulden, Fundamentals of Transonic Flow (Wiley, New York, 1984).
7. H.M. Mott-Smith, "The solution of the Boltzmann equation for a shock wave," Phys. Rev. 82, 885 (1951).
8. Y. Onishi and Y. Sone, "Kinetic theory of slightly strong evaporation and condensation - Hydrodynamic equation and slip boundary condition for finite Reynolds number," J. Phys. Soc. Jpn. 47, 1676 (1979).
9. Y. Sone, K. Aoki, and I. Yamashita, "A study of unsteady strong condensation on a plane condensed phase with special interest in formation of steady profile," in Rarefied Gas Dynamics, edited by V. Boffi and C. Cercignani (Teubner, Stuttgart, 1986), p. 323.
10. K. Aoki and N. Masukawa, "Gas flows caused by evaporation and condensation on two parallel condensed phases and the negative temperature gradient: Numerical analysis by using a nonlinear kinetic equation," Phys. Fluids A 6, 1379 (1994).
11. T. Ytrehus, "Moment solutions in the kinetic theory of strong evaporation and condensation: Application in cometary dusty-gas dynamics," in Progress in Astronautics and Aeronautics, edited by B.D. Shizgal and D.P. Weaver (AIAA, Washington, D.C., 1994), Vol. 159, p. 503.
12. M. N. Kogan, "Kinetic theory in aerothermodynamics," Prog. Aerospace Sci. 29, 271 (1992).
13. Y.P. Pao, "Application of kinetic theory to the problem of evaporation and condensation," Phys. Fluids 14, 306, 1340 (1971).
14. Y. Sone and Y. Onishi, "Kinetic theory of evaporation and condensation - Hydrodynamic equation and slip boundary condition," J. Phys. Soc. Jpn. 44, 1981 (1978).
15. K. Aoki and C. Cercignani, "Evaporation and condensation on two parallel plates at finite Reynolds numbers," Phys. Fluids 26, 1163 (1983).
16. C. Cercignani, W. Fiszdon, and A. Frezzotti, "The paradox of the inverted temperature profiles between an evaporating and a condensing surface," Phys. Fluids A 28, 3237 (1985).
17. C. Cercignani, "Inverted temperature grdient in a vapor," in Progress in Astronautics and Aeronautics, edited by B.D. Shizgal and D.P. Weaver (AIAA, Washington, D.C., 1994). Vol. 159, p. 515.
18. M.S. Plesset, "Note on the flow of vapor between liquid surfaces," J. Chem. Phys. 20, 790 (1952).
19. F.E. Marble, "Some effects of phase exchange processes in the fluid dynamics of two phase media," International Symposium on Fluid Dynamics of Heterogeneous and Multiphase Media (Institute of Aerodynamics, Naples, Italy, 1996).
20. D.A. Labuntsov and A.P. Kryukov, "Analytsis of intensive evaporation and condensation," Int. J. Heat Mass Transfer 22, 989 (1979).
21. M. Lachowicz and T. Ytrehus, "Solution of the Navier-Stokes equations in the case of evaporation," Bull. Polish Acad. Sci., Technical Sciences 37, 453 (1989).
22. P.N. Shankar and M.D. Deshpande, "The gas dynamics of massive evaporation and condensation, "Philos. Trans. R. Soc. London A 335, 487 (1991).
23. C. Cercignani, "A nonlinear criticality problem in the kinetic theory of gases," in Mathematical Problems in the Kinetic Theory of Gases, edited by D. C. Pack and H. Neunzert (Peter Lang, Oberwolfach, 1980). p. 129.
24. S. Chapman and T.G. Cowling, The mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1990).
25. V.I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd ed. (Springer, New York, 1988).
26. K. Aoki and Y. Sone, "Gas flows around the condensed phase with strong evaporation and condensation - Fluid dynamic equation and its boundary condition on the interface and their application," in Advances in Kinetic Theory and Continuum Mechanics, edited by R. Gatignol and Soubbaramayer (Springer-Verlag, Berlin, 1991), p. 43.
27. K. Aoki, K. Nishino. Y. Sone, and H. Sugimoto, "Numerical analysis of steady flows of a gas condensing on or evaporation from its plane condensed phase on the basis of kinetic theory: Effect of gas motion along the condensed phase," Phys. Fluids A 3, 2260 (1991).
28. A.V. Bobylev, A. Pelczewski, and J. Schneider, "On approximation of the Boltzmann equation by discrete velocity models," C. R. Acad. Sci. Paris Ser. 1 320, 639 (1995).