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Instabilities of Compressible Flows with Internal Heat Addition

  • G. H. Schnerr
Part of the International Centre for Mechanical Sciences book series (CISM, volume 369)

Abstract

Flows of heterogeneous media and multiphase flows such as mixtures of pure vapors, vapor/carrier gas mixtures, gas flows with solid particles and droplets prevail in many engineering problems in fluid mechanics and industry. Phase transition of rapidly expanding vapor or vapor/carrier gas mixtures is usually not observed at thermodynamic equilibrium. Because heat is added to the flow by condensation of a component of the fluid itself, flow and heat addition cannot be separated. Moreover, when dealing with water vapor, flow and condensation process are coupled in the most sensitive transonic flow regime. Due to the kinetics of nucleation and droplet growth the heat addition starts near Mach number one at maximum mass flux density where any small disturbance leads to global changes of the flow pattern. Internal heat addition after nonequilibrium phase transition immediately causes thermal choking (Delale, Schnerr and Zierep [1]) with steady or unsteady moving shock waves and instabilities like high frequency pressure oscillations. Self-excitation develops because of the instantaneous interaction of the shock with the phase transition process. Control and handling of these steady and unsteady two-phase flows require a well founded understanding of gasdynamics, of nonequilibrium condensation kinetics and their interaction in the most sensitive transonic flow regime.

Therefore, the lectures start with an elementary introduction in gasdynamics of compressible flows with given internal heat addition which allows discussion and explanation of important phenomena. Decoupling of heat addition and flow simplifies the problems essentially and illustrates the different dynamics of aperiodic and self-excited instabilities.

Keywords

Mach Number Compressible Flow Heat Addition Subsonic Flow Laval Nozzle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Delale, C.F., Schnerr, G.H. and Zierep, J.: The mathematical theory of thermal choking in nozzle flows, Z. Angew. Math. Phys., 44 (1993), 943 - 976.CrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    Wegener, P.P and Mack, L.M.: Condensation in Supersonic and Hypersonic Wind Tunnels, in: Advances in Appl. Mechanics, Vol. 5 (Eds. H.L. Dryden, Th. von Kârmân ), 1958, 307 - 447.Google Scholar
  3. [3]
    Zierep, J.: Strömungen mit Energiezufuhr, 2nd edn., G. Braun Verlag, Karlsruhe, Germany 1990.Google Scholar
  4. [4]
    Bartlmä, F.: Berechnung des Strömungsvorganges bei Überschreiten der kritischen Wärmezufuhr, DVL Bericht No. 168 1961.Google Scholar
  5. [5]
    Bartlmä, F.: Gasdynamik der Verbrennung, Springer Verlag, Wien New York 1975.CrossRefGoogle Scholar
  6. [6]
    Möhring, W.: On flows with heat addition in Laval nozzles, in: Recent Developments in Theoretical and Experimental Fluid Mechanics (Eds. U. Müller, K.G. Roesner, B. Schmidt ), Springer Verlag, Berlin, Heidelberg, New York, 1979, 179 - 185.CrossRefGoogle Scholar
  7. [7]
    Younis, S.: Stationäre Strömung durch Lavaldüsen mit Wärmezufuhr, Diplomarbeit, Universität Karlsruhe (TH ) 1987.Google Scholar
  8. [8]
    Gibbs, J.W.: The collected works of J. Willard Gibbs, Vol. 1, Longmans, Green and Co., New York 1928.Google Scholar
  9. [9]
    Einstein, A.: Ann. Physik, 33 (1910), 1275.Google Scholar
  10. [10]
    Volmer, M.: Kinetik der Phasenbildung, Steinkopff—Verlag, Leipzig 1939.Google Scholar
  11. [11]
    Becker, R. and Döring, W. Kinetische Behandlung der Keimbildung in übersättigten Dämpfen, Ann. Physik, 24 (1935).Google Scholar
  12. [12]
    Farkas, L.: Keimbildungsgeschwindigkeit in übersättigten Dämpfen, Z. Phys. Chem., 125 (1927), 236.Google Scholar
  13. [13]
    Wegener, P.P.: Nonequilibrium flows, Vol. 1, Marcel Dekker, New York, London 1969.Google Scholar
  14. [14]
    Schnerr, G.H. and Dohrmann, U.: Transonic flow around airfoils with relaxation and energy supply by homogeneous condensation, AIAA Journal, 28 (1990), 1187 - 1193.CrossRefGoogle Scholar
  15. [15]
    Pal, P. and Hoare, M.R.: Thermodynamic properties and homogeneous nucleation of molecular clusters of nitrogen, J. Chem. Phys., 91 (1987), 2474 - 2497.CrossRefGoogle Scholar
  16. [16]
    Pal, P.: The harmonic (11M) and quasi–anharmonic (QAH) treatments in the evaluation of the thermodynamic properties of Lennard–Jones clusters at the onset of homogeneous nucleation, in: Flows with phase transition — EUROMECH Colloquium 331, Book of Abstracts (Eds.: G.E.A. Meier, G.H. Schnerr, J. Zierep), DLR Mitteilungen No. 94-11, Göttingen 1995.Google Scholar
  17. [17]
    Gyarmathy, G.: The spherical droplet in gaseous carrier streams: review and synthesis, in: Handbook of Chemistry and Physics, 62nd edition, 1981-82, Multiphase Science and Technology, Vol. 1, McGraw–Hill, New York 1982, 99 - 279.Google Scholar
  18. [18]
    Young, J.B.: The condensation and evaporation of liquid droplets at arbitrary Knudsen number in the presence of an inert gas, Int. J. Heat Mass Transfer, 36 (1993), 2941 - 2956.CrossRefMATHGoogle Scholar
  19. [19]
    Sone, Y. and Onishi, Y.: Kinetic theory of evaporation and condensation — hydrodynamic equation and slip boundary condition, J. Phys. Soc. Japan, 44 (1987) 1981 - 1994.CrossRefGoogle Scholar
  20. [20]
    Dillmann, A. aiid Meier, G.E.A.: A refined droplet approach to the problem of homogeneous nucleation from i,he vapor phase, J. Chem. Phys., 94 (1991), 3872 - 3884.CrossRefGoogle Scholar
  21. [21]
    Fisher, M.E.: Rept. Progr. Phys., 30 (1967), 615.CrossRefGoogle Scholar
  22. [22]
    Delale, C.F.: A comparison of nucleation theories in transonic nozzle flows with homogeneous condensation, DLR Mitteilungen No. 94-37, Göttingen 1994.Google Scholar
  23. [23]
    Dohrmann, U.: Ein numerisches Verfahren zur Berechnung stationärer transsonischer Strömungen mit Energiezufuhr durch homogene Kondensation, Dissertation, Fakultät für Maschinenbau, Universität Karlsruhe (TH ) 1989.Google Scholar
  24. [24]
    Mundinger, G.: Numerische Simulation instationärer Lavaldüsenströmungen mit Energiezufuhr durch homogene Kondensation, Dissertation, Fakultät für Maschinenbau, Universität Karlsruhe (TH ) 1994.Google Scholar
  25. [25]
    Delale, C.F., Schnerr, G.H. and Zierep, J.: Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows, Phys. Fluids A, 5 (1993) 2969 - 2981.CrossRefMATHGoogle Scholar
  26. [26]
    Delale, C.F., Schnerr, G.H. and Zierep, J.: Asymptotic solution of transonic nozzle flows with homogeneous condensation. II. Supercritical flows, Phys. Fluids A, 5 (1993), 2982-2995.Google Scholar
  27. [27]
    Schnerr, G.H.: 2–D transonic flow with energy supply by homgeneous condensation: Onset condition and 2–D structure of steady Laval nozzle flow, Exp. Fluids, 7 (1989), 145 - 156.CrossRefGoogle Scholar
  28. [28]
    Bartlmä, F.: Ebene Überschallströmung mit Relaxation, in: Applied Mechanics, Proceedings of the IUTAM Symp. München, Germany 1964 (Ed.: H. Görtler ), Springer–Verlag, 1966, 1056 - 1060Google Scholar
  29. [29]
    Meier, G.E.A., Schnerr, G.H. and Zierep, J.: Flows with phase transition — EUROMECH Colloquium 331, Book of Abstracts (Eds.: G.E.A. Meier, G.H. Schnerr, J. Zierep), DLR Mitteilungen No. 94-11, Göttingen 1995.Google Scholar
  30. [30]
    Schmidt, B.: Beobachtungen über das Verhalten der durch Wasserdampfkondensation ausgelösten Störungen in einer Überschall-Windkanaldiise, Dissertation, Fakultät für Maschinenbau, Universität Karlsruhe (TH ) 1962.Google Scholar
  31. [31]
    Barschdorff, D.: Kurzzeitfeuchtemessung und ihre Anwendung bei Kondensationserscheinungen in Lavaldüsen, Strömungsmechanik und Strömungsmaschinen, Vol. 6 (1967), 1839.Google Scholar
  32. [32]
    Saltanov, G.A. and Tkalenko, R.A.: Investigation of transonic unsteady-state flow in the presence of phase transformations, Zh. Prikl. Mek. i Tek. Fiz. (UdSSR), 6 (1975), 42 - 48.Google Scholar
  33. [33]
    White, A.J. and Young, J.B.: A time-marching method for the prediction of two-dimensional, unsteady flows of condensing steam, J. of Propulsion and Power, 9 (1993), 579 - 587.CrossRefGoogle Scholar
  34. [34]
    Schnerr, G.H., Adam, S., Lanzenberger, K. and Schulz, R.: Multiphase flows: Condensation and cavitation problems, in: Computational Fluid Dynamics REVIEW, Vol. 1 (Eds.: M. Hafez, K. Oshima ), John Wiley and Sons, New York, London 1995.Google Scholar
  35. [35]
    Collignan, B.: Contribution à Etude de la Condensation Instationnaire en Ecoulement Transsonique, Ph.D. Thesis, Université Pierre and Marie Curie, Paris, France (1994).Google Scholar
  36. [36] Schnerr, G.H., Adam, S. and Mundinger G.: Shocks in high speed two-phase flow, in Proc.: German Japanese Symposium on Multi-Phase Flow, Kernforschungszentrum Karlsruhe (KFK)
    Eds. U. Müller, T. Saito, K. Rust), KFK report 5389, 1994, 271 - 283.Google Scholar
  37. [37]
    Schnerr, G.H. and Adam, S.: New instabilities of homogeneously condensing flows, in: Flows with phase transition — EUROMECH Colloquium 331, Book of Abstracts (Eds.: G.E.A. Meier, G.H. Schnerr, J. Zierep), DLR Mitteilungen No. 94-11, Göttingen 1995.Google Scholar

Copyright information

© Springer-Verlag Wien 1996

Authors and Affiliations

  • G. H. Schnerr
    • 1
  1. 1.University of Karlsruhe (TH)KarlsruheGermany

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