Summary
The flow of a condensing gas is treated as a two-phase-flow, in which the size of the condensate-droplets may vary due to transfer of mass, momentum, and heat; the formation of new droplets is disregarded. An ordinary differential equation for the temporal variation of the amplitude of a one-dimensional acceleration wave is deduced, which holds along the path of the wave. Especially, if the wave propagates into a mixture at rest with spatial variation of the volume fraction of the droplets, the variation of the amplitude is given by the sum of three terms, one of which is quadratic in the amplitude and the others are linear. The quadratic term is solely determined by nonlinear effects in the pure gas and leads to a growth. The first linear term is given by the dissipative effect of the velocity relaxation; this term is the same as for the flow of a mixture of a gas and small solid particles. The second linear term is determined by the combined dissipative effects of the temperature relaxation and the mass transfer; both linear terms lead to a decay. Further, conditions are discussed, on which shock waves are formed.
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References
Thomas, T. Y.: The growth and decay of sonic discontinuities in ideal gases. J. Math. Mech.6, 455–469 (1957).
Varley, E., Cumberbatch, E.: Non-linear theory of wave-front propagation. J. Inst. Maths. Applics.1, 101–112 (1965).
Varley, E., Dunwoody, J.: The effect of non-linearity at an acceleration wave. J. Mech. Phys. Solids13, 17–28 (1965).
Becker, E., Schmitt, H.: Die Entstehung von ebenen, zylinder- und kugelsymmetrischen Verdichtungsstößen in relaxierenden Gasen. Ing.-Arch.36, 335–347 (1968).
Becker, E.: Die Entstehung von Verdichtungsstößen in kompressiblen Medien. Ing.-Arch.39, 302–316 (1970).
Bürger, W.: Relaxation effects on acceleration waves. Fluid Dyn. Trans.6, II, 77–86 (1972).
Coleman, B. D., Gurtin, M. E.: Growth and decay of discontinuities in fluids with internal state variables. Phys. Fluids10, 1454–1458 (1967).
Schmitt, H.: Entstehung von Verdichtungsstößen in strahlenden Gasen. ZAMM52, 529–534 (1972).
Schmitt, H.: Entstehung von Verdichtungsstößen in realen Gasen. Darmstadt: D. Thesis 1971.
Singh, R. S., Sharma, V. D.: Amplification of finite-amplitude waves in a radiating gas. AIAA-J.19, 252–254 (1981).
Srinivasan, S., Ram, R.: Propagation of sonic waves in radiating gases. ZAMM57, 191–193 (1977).
Schmitt, H.: Fortpflanzung schwacher Unstetigkeiten bei nichtlinearen Wellen-ausbreitungsvorgängen. ZAMM48, T241-T244 (1968).
Teipel, I.: Über die Fortpflanzung von schwachen Stoßwellen in der Magnetogasdynamik. ZAMM46, T221-T223 (1966).
Singh, R. S., Sharma, V. D.: Propagation of discontinuities along bi-characteristics in magnetohydrodynamics. Phys. Fluids23, 648–649 (1980).
Schmitt, H.: Comments on “Propagation of discontinuities along bi-characteristics in magnetohydrodynamics”. Phys. Fluids25, 214 (1982).
Schmitt-v. Schubert, B.: Strömungen von Gasen mit festen Teilchen. Darmstadt: D. Thesis 1968.
Pai, S. I., Sharma, V. D., Menon, S.: Time evolution of discontinuities at the wave head in a non-equilibrium two-phase flow of a mixture of a gas and dusty particles. Acta Mech.46, 1–13 (1983).
Bürger, W.: Schwache Unstetigkeiten in der modernen Kontinuumsmechanik. In: Methoden und Verfahren der mathematischen Physik, Band II (Martensen, E., Brosowski, B., eds.). Mannheim: Bibliogr. Inst. 1969.
Thomas, T. Y.: Extended compatibility conditions for study of surfaces of discontinuity in continuum mechanics. J. Math. Mech.6, 311–322 (1957).
Jeffrey, A.: The development of jump discontinuities in non-linear hyperbolic systems of equations in two independent variables. Arch. Rat. Mech. Anal.14, 27–37 (1963).
Yamamoto, Y., Kobayashi, S., Takano, A.: Analysis on the propagation of finite amplitude disturbances in gas-particle mixtures. Trans. Japan Soc. Aero. Space Sci.22, 229–240 (1980).
Schmitt-v. Schubert, B.: Änderung der Größe von Stickstofftröpfchen in einer Strömung von gasförmigem Stickstoff. DFVLR-FB 83-12 (1983).
Millikan, R. A.: The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces. Phys. Rev.22, 1–23 (1923).
Vincenti, W. G., Kruger, C. H.: Introduction to physical gas dynamics, p. 414. New York-London: John Wiley 1965.
Lang, H.: Heat and mass exchange of a droplet in a polyatomic gas. Phys. Fluids26, 2109–2114 (1983).
Truesdell, C., Toupin, R. A.: The classical field theories, p. 504. In: Encyclopedia of physics, Vol. III/1 (Flügge, S., ed.). Berlin-Heidelberg: Springer 1960.
Marconi, F., Rudman, S., Calia, V.: Numerical study of one-dimensional unsteady particle-laden flows with shocks. AIAA-J.19, 1294–1301 (1981).
Schmitt, H.: Einfluß von Kondensationsvorgängen auf die Entstehung von Verdichtungsstößen ZAMM65, T236-T237 (1985).
Bürger, W.: Zur Entstehung von Verdichtungsstößen beim “Kolbenversuch” in Gasen mit thermodynamischer Relaxation. ZAMM46, 149–151 (1966).
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Schmitt, H. Acceleration waves in condensing gases. Acta Mechanica 78, 109–128 (1989). https://doi.org/10.1007/BF01174004
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DOI: https://doi.org/10.1007/BF01174004