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Wave splitting in a fluid of large heat capacity

Published online by Cambridge University Press:  21 April 2006

Philip A. Thompson ,
Humberto Craves ,
G. E. A. Meier ,
Yoon-Gon Kim  and
H.-D. Speckmann
Philip A. Thompson
Affiliation:
Rensselaer Polytechnic Institute, Troy, NY 12180–3590, USA
Humberto Craves
Affiliation:
Max-Planck-Institut für Strömungsforschung, D3400 Göttingen, Federal Republic of Germany
G. E. A. Meier
Affiliation:
Max-Planck-Institut für Strömungsforschung, D3400 Göttingen, Federal Republic of Germany
Yoon-Gon Kim
Affiliation:
Rensselaer Polytechnic Institute, Troy, NY 12180–3590, USA
H.-D. Speckmann
Affiliation:
Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt (DFVLR), D3400 Göttingen, Federal Republic of Germany
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Abstract

The splitting of a single pressure discontinuity into a propagating two-wave system is studied for the case of saturated-liquid expansion (liquid-evaporation wave splitting) and vapour compression (vapour-condensation wave splitting). Experimental results from the Max-Planck-Institut für Strömungsforschung and from Rensselaer Polytechnic Institute show that splitting occurs in test fluids of large molar heat capacity, such as iso-octane (Cv0/R ≈ 37). Each of the two forms of splitting results in a single-phase forerunner wave carrying a pressure discontinuity followed by a phase-change wave, also with a pressure discontinuity. The thermodynamic state between the forerunner wave and the phase-change wave is metastable (supersaturated liquid or vapour). The waves are quantitatively described by systems of adiabats, e.g. shock adiabats. It appears that nucleation processes are predominantly homogeneous.

In vapour-compression shock-wave splitting, a combined wave (liquefaction shock) splits into discrete forerunner and condensation waves at a triple point, the intersection of a liquefaction shockfront, forerunner shock and condensation discontinuity: such a point occurs just at critical supersaturation (i.e. the Wilson-line state), where condensation is spontaneous and immediate. For shock waves that produce a metastable state of subcritical supersaturation, condensation is delayed, that is, the condensation discontinuity propagates more slowly; for a split-shock system, the condensation discontinuity propagates subsonically. The pressure amplitude of a real split-shock system is much larger than that predicted by an equilibrium model.

In liquid-evaporation wave splitting, the forerunner wave is an acoustic expansion wave and the second wave an evaporation wave with a propagation velocity approximately determined by the Chapman-Jouguet condition for deflagration. Such evaporation wavefronts are increasingly distinct as the temperature approaches the critical-point value. The evaporation rates across the wavefront are comparable to those found in vapour explosions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 385 - 414
Copyright
© 1987 Cambridge University Press

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References

Abbott, M. M. 1973 Cubic equations of state. AIChE. J. 19, 596–601.Google Scholar
Bethe, H. A. 1942 The theory of shock waves for an arbitrary equation of state. Rep. 545, p. 57. Office of Scientific Research and Development, Washington.
Chaves, H. 1980 Verdampfungswellen in retrograden Flüssigkeiten. Diplomarbeit, Georg-August-Universität. Göttingen.
Chaves, H. 1984 Phasenübergänge und Wellen bei der Entspannung von Fluiden hoher spezifischer Wäerme. Dissertation, Georg-August-Universität. Göttingen.
Chaves, H., Lang, H., Meier, G. E. A. & Speckmann, H.-D. 1985 Adiabatic phase transitions and wavesplitting in fluids of high specific heat. In Flow of Real Fluids (ed. G. E. A. Meier & F. Obermeier). Lecture Notes in Physics, vol. 235, pp. 115–124. Springer.
Dettleff, G., Meier, G. E. A., Speckmann, H.-D., Thompson, P. A. & Yoon, C. 1982 Experiments in shock liquefaction. In Proc. 13th Intl Symp. on Shock Tubes and Waves (ed. C. E. Trainor & J. G. Hall), pp. 616–623. State University of New York Press, Albany.
Dettleff, G., Thompson, P. A., Meier, G. E. A. & Speckmann, H.-D. 1979 An experimental study of liquefaction shock waves. J. Fluid Mech. 95, 279–304.Google Scholar
Dobbins, R. A. 1983 A theory of the Wilson line for steam at low pressures. Trans. ASME I: J. Fluids Engng 105, 414–422.Google Scholar
Ermakov, G. V. & Skripov, V. P. 1968 Experimental determination of the specific volumes of a superheated liquid. High Temperature 6, 86–92.Google Scholar
Gust, W. H. & Young, D. A. 1979 High Pressure Science and Technology (ed. K. D. Timmerhaus & M. S. Barber), vol. I, pp. 944–952. Plenum.
Hayes, W. D. 1958 The basic theory of gasdynamic discontinuities. In Fundamentals of Gasdynamics (ed. H. W. Emmons), pp. 416–481. Princeton University Press.
Hobbs, D. E. 1983 A virial equation of state utilizing the principle of corresponding states. Dissertation, Rensselaer Polytechnic Institute.
Liepmann, H. W. & Laguna, G. A. 1984 Nonlinear interactions in the fluid mechanics of helium II. Ann. Rev. Fluid Mech. 16, 139–178.Google Scholar
Lighthill, M. J. 1956 Viscosity effects in sound waves of finite amplitude. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davis), pp. 250–351. Cambridge University Press.
Mcqueen, R. G. & Marsh, S. P. 1968 Hugoniots of graphites of various initial densities and the equation of state of carbon. In Behavior of Dense Media under High Dynamic Pressures, pp. 207–216. Gordon and Breach.
Meier, G. E. A. & Thompson, P. A. 1985 Real gas dynamics of fluids with high specific heat. In Flow of Real Fluids (ed. G. E. A. Meier & F. Obermeier). Lecture Notes in Physics, vol. 235, pp. 103–114. Springer.
Mihalas, D. & Mihalas, B. W. 1984 Foundations of Radiation Hydrodynamics, pp. 611–649. Oxford University Press.
Puttendörfer, E. 1982 Schallnahe Strömung eines retrograden Fluides. Diplomarbeit, Georg-August-Universität, Göttingen.
Shepherd, J. E. & Sturtevant, B. 1982 Rapid evaporation at the superheat limit. J. Fluid Mech. 121, 379–402.Google Scholar
Smith, J. A. 1968 Experimentally determined of the shock reflection process in ionizing xenon. Phys. Fluids 11, 2150–2161.Google Scholar
Speckmann, H.-D. 1984 Aufspaltung von Kondensationsstosswellen in Fluiden höher spezifischer Wärme. Dissertation, Georg-August-Universität, Göttingen.
Thompson, P. A. 1972 Compressible-Fluid Dynamics, pp. 315–326. McGraw-Hill.
Thompson, P. A. 1983 Shock-wave series for real fluids. Phys. Fluids 26, 3471–3474.Google Scholar
Thompson, P. A., Carofano, G. C. & Kim, Y.-G. 1986 Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube. J. Fluid Mech. 166, 57–92.Google Scholar
Thompson, P. A. & Kim, Y.-G. 1983 Direct observation of shock splitting in a vapor-liquid system. Phys. Fluids 26, 3211–3215.Google Scholar
Thompson, P. A., Kim, Y.-G. & Meier, G. E. A. 1984 Shock tube studies with incident liquefaction shocks. In Proc. 14th Intl Symp. on Shock Tubes and Waves (ed. R. D. Archer & B. E. Milton), pp. 413–420. New South Wales University Press, Sydney.
Wegener, P. P. & Wu, B. J. C. 1977 Gasdynamics and homogeneous nucleation. Adv. Colloid Interface Sci. 7, 325–417.Google Scholar
Wong, H. & Bershader, D. 1966 Thermal equilibration behind an ionizing shock. J. Fluid Mech. 26, 459–479.Google Scholar
Yamada, T. 1973 An improved generalizated equation of state. AIChE. J. 19, 286–291.Google Scholar
Yoon, C. 1985 Incident-shock liquefaction experiments with retrograde substances. Dissertation, Rensselaer Polytechnic Institute.
Zel'Dovich, Ya. B. & Raizer, Yu. P. 1967 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, vol. 2 (ed. W. D. Hayes & R. F. Probstein), pp. 750–756. Academic.