Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-21T16:44:21.392Z Has data issue: false hasContentIssue false
  • English
  • Français

On condensation-induced waves

Published online by Cambridge University Press:  24 March 2010

WAN CHENG ,
XISHENG LUO  and
M. E. H. van DONGEN
WAN CHENG
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
XISHENG LUO*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
M. E. H. van DONGEN
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Complex wave patterns caused by unsteady heat release due to cloud formation in confined compressible flows are discussed. Two detailed numerical studies of condensation-induced waves are carried out. First, the response of a flow of nitrogen in a slender Laval nozzle to a sudden addition of water vapour at the nozzle entrance is considered. Condensation occurs just downstream of the nozzle throat, which initially leads to upstream- and downstream-moving shocks and an expansion fan downstream of the condensation front. Then, the flow becomes oscillatory and the expansion fan disappears, while upstream and much weaker downstream shocks are repeatedly generated. For a lower initial humidity, only a downstream starting shock is formed and a steady flow is established. Second, homogeneous condensation in an unsteady expansion fan in humid nitrogen is considered. In the initial phase, two condensation-induced shocks are found, moving upstream and downstream. The upstream-moving shock changes the shape of the expansion fan and has a strong influence on the condensation process itself. It is even quenching the nucleation process locally, which leads to a renewed condensation process more downstream. This process is repeated with asymptotically decreasing strength. The repeated interaction of the condensation-induced shocks with the main expansion wave leads to a distortion of the expansion wave towards its shape that can be expected on the basis of phase equilibrium, i.e. a self-similar wave structure consisting of dry part, a plateau of constant state and a wet part. The strengths of the condensation-induced waves, as well for the Laval nozzle flow as for the expansion fan, appear to be in qualitative agreement with the results from the analytical Rayleigh–Bartlmä model.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 651 , 25 May 2010 , pp. 145 - 164
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Adam, S. & Schnerr, G. H. 1997 Instabilities and bifurcation of nonequilibrium two-phase flows. J. Fluid Mech. 348, 1–28.CrossRefGoogle Scholar
Barschdorff, D. & Filippov, G. A. 1970 Analysis of special conditions of the work of Laval nozzles with local heat supply. Heat Trans. Sov. Res. 2, 76–87.Google Scholar
Bartlmä, F. 1963 Instationäre Strömungsvorgänge bei Uberschreiten der kritischen Wärmezufuhr. Z. Flugwiss 11, 160–168.Google Scholar
Bartlmä, F. 1975 Gasdynamik der Verbrennung. Springer.CrossRefGoogle Scholar
Chang, S. C. 1995 The method of space–time conservation element and solution element: a new approach for solving the Navier–Stokes and Euler equations. J. Comput. Phys. 119, 295–324.CrossRefGoogle Scholar
Cheng, W., Luo, X., Yang, J. & Wang, G. 2010 Numerical analysis of homogeneous condensation in rarefaction wave in a shock tube by the space–time CESE method. Comput. Fluids 39, 294–300.CrossRefGoogle Scholar
Chirikhin, A. V. 2007 Specific gasdynamical features of spontaneous condensation in an unsteady rarefaction wave. Fluid Dyn. 42 (1), 144–149.Google Scholar
Courant, R. & Friedrichs, K. O. 1985 Supersonic Flow and Shock Waves, 2nd edn.Springer.Google Scholar
Delale, C. F., Schnerr, G. H. & van Dongen, M. E. H. 2007 Condensation discontinuities and condensation induced shock waves. In Shock Wave Science and Technology Reference Library, Vol. 1., Multiphase Flows, pp. 187–230. Springer.CrossRefGoogle Scholar
van Dongen, M. E. H. 2001 Wave propagation in multi-phase media. In Handbook of Shock Waves, pp. 741–781. Academic Press.Google Scholar
van Dongen, M. E. H., Luo, X., Lamanna, G. & van Kaathoven, D. J. 2002 On condensation induced shock waves. In Proceedings of the 10th Chin. Symp. Shock Waves, pp. 1–11. Chinese Academy of Science.Google Scholar
Gyarmathy, G. 1982 The spherical droplet in gaseous carrier streams: review and synthesis. In Multiphase Science and Technology, vol. 1, pp. 99–279. Springer.Google Scholar
Hill, P. G. 1966 Condensation of water vapour during supersonic expansion in nozzles. J. Fluid Mech. 25, 593–620.Google Scholar
Holten, V., Labetski, D. G. & van Dongen, M. E. H. 2005 Homogeneous nucleation of water between 200 and 240 K: new wave tube data and estimation of the Tolman length. J. Chem. Phys. 123, 104505.CrossRefGoogle ScholarPubMed
Lamanna, G. 2000 On nucleation and droplet growth in condensing nozzle flows. PhD thesis, Eindhoven University of Technology.Google Scholar
Lamanna, G., van Poppel, J. & van Dongen, M. E. H. 2002 Experimental determination of droplet size and density field in condensing flows. Exp. Fluids 32, 381–395.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamom.Google Scholar
Lee, J. C. & Rusak, Z. 2001 Parametric investigation of nonadiabatic flow around airfoils. Phys. Fluids 13, 315–323.CrossRefGoogle Scholar
Li, L., Sun, X., Feng, Z. & Li, G. 2005 Transonic flow of moist air around an NACA0012 airfoil with non-equilibrium condensation. Progr. Nat. Sci. 15 (9), 838–842.Google Scholar
Luijten, C. C. M. 1998 Nucleation and droplet growth at high pressure. PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.Google Scholar
Luijten, C. C. M., Peeters, P. & van Dongen, M. E. H. 1999 Nucleation at high pressure. II. Wave tube data and analysis. J. Chem. Phys. 111, 8535–8544.CrossRefGoogle Scholar
Luo, X. 2004 Unsteady flows with phase transition. PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.Google Scholar
Luo, X., Lamanna, G., Holten, A. P. C. & van Dongen, M. E. H. 2007 a Effects of homogeneous condensation in compressible flows: Ludwieg-tube experiments and simulations. J. Fluid Mech. 572, 339–366.CrossRefGoogle Scholar
Luo, X., Prast, B., van Dongen, M. E. H., Hoeijmakers, H. W. M. & Yang, J. 2006 On phase transition in compressible flows: modelling and validation. J. Fluid Mech. 548, 403–430.Google Scholar
Luo, X., Wang, M., Yang, J. & Wang, G. 2007 b The space–time CESE method applied to phase transition of water vapour in compressible flows. Comput. Fluids 36, 1247–1258.Google Scholar
Mundinger, G. 1994 Numerische Simulation Instationärer Lavaldüsenströmungen mit Energiezufuhr durch Homogene Kondensation. PhD thesis, Universität Karlsruhe, Germany.Google Scholar
Oran, E. S. & Boris, J. P. 1987 Numerical Simulation of Reactive Flow. Elsevier.Google Scholar
Peeters, P., Luijten, C. C. M. & van Dongen, M. E. H. 2001 Transitional droplet growth and diffusion coefficients. Intl J. Heat Mass Trans. 44, 181–193.CrossRefGoogle Scholar
Petr, V., Kolovratnik, M. & Hanzal, V. 2003 Instrumentation and tests on droplet nucleation in LP steam turbines. Power Plant Chem. 5, 389–395.Google Scholar
Prandtl 1936 Atti del Convegno Volta, 1st edn., vol. XIV. Reale Academia D'Italia.Google Scholar
Prast, B. 1997 Condensation in supersonic expansion flows: theory and numerical evaluation. Stan Ackermans Institute, Report I11, Eindhoven University of Technology, Eindhoven, The Netherlands.Google Scholar
Rusak, Z. & Lee, J. C. 2000 Transonic flow of moist air around a thin airfoil with nonequilibrium and homogeneous condensation. J. Fluid Mech. 403, 173–199.CrossRefGoogle Scholar
Schnerr, G. H. 2005 Unsteadiness in condensing flow: dynamics of internal flows with phase transition and application to turbomachinery. Proc. IMechE, Part C: J. Mech. Engng Sci. 219, 1369–1410.CrossRefGoogle Scholar
Sislian, J. P. & Glass, I. I. 1976 Condensation of water vapour in rarefaction waves: I. Homogeneous nucleation. AIAA J. 14 (12), 1731–1737.CrossRefGoogle Scholar
Smolders, H. J. & van Dongen, M. E. H. 1992 Shock wave structure in a mixture of gas, vapour and droplets. Shock Waves 2 (4), 255–267.CrossRefGoogle Scholar
Smolders, H. J., Niessen, E. M. J. & van Dongen, M. E. H. 1989 On the similarity character of an unsteady rarefaction wave in a gas–vapour mixture with condensation. In IUTAM Symposium Göttingen/Germany (ed. Meier, G. E. A. & Thompson, P. A.). Springer.Google Scholar
Smolders, H. J., Niessen, E. M. J. & van Dongen, M. E. H. 1992 The random choice method applied to nonlinear wave propagation in gas–vapour–droplets mixtures. Comput. Fluids 21 (1), 63–75.CrossRefGoogle Scholar
Sun, M. 1998 Numerical and experimental studies of shock wave interaction with bodies. PhD thesis, Tohoku University, Sendai, Japan.Google Scholar
Sun, M. & Takayama, K. 1999 Conservative smoothing on an adaptive quadrilateral grid. J. Comput. Phys. 150, 143–180.Google Scholar
Thompson, P. A. 1972 Compressible Fluid Dynamics. McGrow-Hill.CrossRefGoogle Scholar
Wegener, P. P. 1975 Nonequilibrium flow with condensation. Acta Mech. 21, 65–91.CrossRefGoogle Scholar
Wölk, J. & Strey, R. 2001 Homogeneous nucleation of H2O and D2O in comparison: the isotope effect. J. Phys. Chem. B 105, 11683–11701.CrossRefGoogle Scholar
Yu, S. T. J. & Chang, S. C. 1997 Treatments of stiff source terms in conservation laws by the method of space–time conservation element/solution element. AIAA Paper 1997-0435.CrossRefGoogle Scholar
Zierep, J. 1969 Schallnahe Strömungen mit Wärmezufuhr. Acta Mech. 8 (1–2), 126–132.CrossRefGoogle Scholar
Zierep, J. 1990 Strömungen mit Energiezufuhr, 2nd edn.G. Braun.Google Scholar