Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-27T17:14:08.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of homogeneous condensation in compressible flows: Ludwieg-tube experiments and simulations

Published online by Cambridge University Press:  23 January 2007

XISHENG LUO ,
GRAZIA LAMANNA ,
A. P. C. HOLTEN  and
M. E. H. VAN DONGEN
XISHENG LUO
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
GRAZIA LAMANNA
Affiliation:
Institute of Aerospace Thermodynamics, Universität Stuttgart, Stuttgart, Germany
A. P. C. HOLTEN
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
M. E. H. VAN DONGEN
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

Effects of homogeneous nucleation and subsequent droplet growth in compressible flows in humid nitrogen are investigated numerically and experimentally. A Ludwieg tube is employed to produce expansion flows. Corresponding to different configurations, three types of experiment are carried out in such a tube. First, the phase transition in a strong unsteady expansion wave is investigated to demonstrate the mutual interaction between the unsteady flow and the condensation process and also the formation of condensation-induced shock waves. The role of condensation-induced shocks in the gradual transition from a frozen initial structure to an equilibrium structure is explained. Second, the condensing flow in a slender supersonic nozzle G2 is considered. Particular attention is given to condensation-induced oscillations and to the transition from symmetrical mode-1 oscillations to asymmetrical mode-2 oscillations in a starting nozzle flow, as first observed by Adam & Schnerr. The transition is also found numerically, but the amplitude, frequency and transition time are not yet well predicted. Third, a sharp-edged obstacle is placed in the tube to generate a starting vortex. Condensation in the vortex is found. Owing to the release of latent heat of condensation, an increase in the pressure and temperature in the vortex core is observed. Condensation-induced shock waves are found, for a sufficiently high initial saturation ratio, which interact with the starting vortex, resulting in a very complex flow. As time proceeds, a subsonic or transonic free jet is formed downstream of the sharp-edged obstacle, which becomes oscillatory for a relatively high main-flow velocity and for a sufficiently high humidity.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 339 - 366
Copyright
Copyright © Cambridge University Press 2007

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

Abraham, F. F. 1974 Homogeneous Nucleation Theory. Academic.Google Scholar
Adam, S. & Schnerr, G. H. 1997 Instabilities and bifurcation of nonequilibrium two-phase flows. J. Fluid Mech. 348, 1–28.Google Scholar
Blythe, P. A. & Shih, C. J. 1976 Condensation shocks in nozzle flows. J. Fluid Mech. 76, 593–621.Google Scholar
Courant, R. & Friedrichs, K. O. 1985 Supersonic Flow and Shock Waves, 2nd edn. Springer.Google Scholar
Delale, C. F. & van Dongen, M. E. H. 1998 Thermal choking in two-dimensional expansion flows. Z. Angew. Math. Phys. 49, 515–537.CrossRefGoogle Scholar
Delale, C. F., Lamanna, G. & van Dongen, M. E. H. 2001 On stability of stationary shock waves in nozzle flows with homogeneous condensation. Phys. Fluids 13, 2706–2719.CrossRefGoogle Scholar
Delale, C. F., Schnerr, G. H. & Zierep, J. 1993a Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows. Phys. Fluids A 5, 2969–2981.Google Scholar
Delale, C. F., Schnerr, G. H. & Zierep, J. 1993b Asymptotic solution of transonic nozzle flows with homogeneous condensation. II. Supercritical flows. Phys. Fluids A 5, 2982–2995.CrossRefGoogle Scholar
Delale, C. F., Schnerr, G. H. & Zierep, J. 1993c The mathematical theory of thermal choking in nozzle flows. Z. Angew. Math. Phys. 44, 943–976.Google Scholar
van Dongen, M. E. H., Luo, X., Lamanna, G. & van Kaathoven, D. J. 2002 On condensation induced shock waves. In Proc. 10th Chinese Symp. an Shock Waves, pp. 1–11. Chinese Academy of Science, Yellow Mountain, China.Google Scholar
Frank, W. 1985 Condensation phenomena in supersonic nozzles. Acta Mechanica 54, 135–156.CrossRefGoogle Scholar
Gyarmathy, G. 1982 The spherical droplet in gaseous carrier streams: review and synthesis. In Multiphase Science and Technology, vol. 1. Springer.Google Scholar
Heath, C. H., Streletzky, K. A., Wyslouzil, B. E., Wölk, J. & Strey, R. 2003 Small angle neutron scattering from D 2O−H 2O nanodroplets and binary nucleation rates in a supersonic nozzle. J. Chem. Phys. 118, 5465–5473.Google Scholar
Hill, P. G. 1966 Condensation of water vapor 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 estamation of the tolman length. J. Chem. Phys. 123, 104505.CrossRefGoogle ScholarPubMed
Kashchiev, D. 2000 Nucleation: Basic Theory with Applications. Butterworth-Heineman.Google Scholar
Koop, T. 2004 Homogeneous ice nucleation in water and aqueous solutions. Z. Phys. Chem. 218, 1231–1258.Google Scholar
Kotake, S. & Glass, I. I. 1978 Survey of flows with nucleation and condensation. UTIAS Rev. 42. University of Toronto.Google Scholar
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. Exps. Fluids 32, 381–395.Google Scholar
Lee, J. C. & Rusak, Z. 2001a Parametric investigation of nonadiabatic flow around airfoils. Phys. Fluids 13, 315–323.CrossRefGoogle Scholar
Lee, J. C. & Rusak, Z. 2001b Transonic flow of moist air around a thin airfoil with equilibrium condensation. J. Aircraft 38, 693–720.Google Scholar
Looijmans, K. N. H. & van Dongen, M. E. H. 1997 A pulse-expansion wave tube for nucleation studies at high pressures. Exps. Fluids 23, 54–63.Google Scholar
Ludwieg, H. 1955 Der Rohrwindkanal. Z. Flugwiss 3 (7), 206–216.Google Scholar
Ludwieg, H. 1957 Agard report 143. Tech. Rep. NATO Headquarters, Scheveningen, Holland.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.Google Scholar
Luo, X. 2004 Unsteady flows with phase transition. PhD thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.Google 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. Fuild Mech. 548, 403–430.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
Oswatitsch, K. 1942 Kondensationserscheinungen in überschalldüsen. Z. Angew. Math. Mech. 22, 1–14.Google Scholar
Owczarek, J. A. 1964 Fundamentals of Gas Dynamics. International Co.Google Scholar
Peeters, P., Luijten, C. C. M. & van Dongen, M. E. H. 2001b Transitional droplet growth and diffusion coefficients. Intl J. heat Mass Transfer 44, 181–193.Google Scholar
Peeters, P., Pieterse, G. & van Dongen, M. E. H. 2004 Multi-component droplet growth. I. experiments with supersaturated n-nonane vapor and water vapor in methane. Phys. Fluids 16, 2567–2574.Google Scholar
Prandtl, 1936 Atti del Convegno Volta, 1st edn., vol. XIV. Roma: Reale Academia D'Italia.Google Scholar
Prast, B. 1997 Condensation in supersonic expansion flows: theory and numerical evaluation. SAI, Eindhoven University of Technology, Eindhoven.Google Scholar
Put, F. 2003 Numerical simulation of condensation in transonic flows. PhD thesis, University of Twente, Enschede, The Netherlands.Google Scholar
Put, F., Kelleners, P. H., Hagmeijer, R. & Hoeijmakers, H. W. M. 2001 Numerical simulation of condensing real gas flows. In Proc. CFD2001. Atlanta, Ge, USA: ASME PVP-VOL. 424-1.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.Google Scholar
Saltanov, G. A. & Tkalenko, R. A. 1975 Investigation of transonic unsteady state flow in the presence of phase transformations. Zh. Prikl. Mek. ITek. Fiz. (UdSSR) 6, 28–42.Google Scholar
Schnerr, G. H., Adam, S. & Mundinger, G. 1994 New modes of perodic shock formation in compressible two-phase flows. In IUTAM Symp. on Waves in Liquid/Gas and Liquid/Vapor Two-Phase Systems (ed. Morioka, S. & van Wijngaarden, L.), pp. 377–386. Kluwer.Google Scholar
Schnerr, G. H. & Dohrmann, U. 1990 Transonic flow around airfoils with relaxation and energy supply by homogeneous condensation. AIAA J. 28, 1187–1193.Google Scholar
Schnerr, G. H. & Dohrmann, U. 1994 Drag and lift in non-adiabatic transonic flow. AIAA J. 32, 101–107.Google Scholar
Sichel, M. 1981 Unsteady transonic nozzle flow with heat addition. AIAA J. 19, 165–177.Google Scholar
Smolders, H. J., Niessen, E. M. J. & van Dongen, M. E. H. 1992 The random choice method applied to non-linear wave propagation in gas-vapour-drolets mixtures. Computers Fluids 21 (1), 63–75.Google 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. Comp. Phys. 150, 143–180.CrossRefGoogle Scholar
Vargaftik, N. B. 1975 Tables on the thermophysical properties of liquids and gases, 2nd edn. Wiley.Google Scholar
Wegener, P. P. 1969 Gasdynamics of expansion flows with condensation and homogeneous nucleation of water vapor. In Nonequilibrium Flows, pp. 163–243. Marcel Dekker.Google Scholar
Wegener, P. P. 1975 Nonequilibrium flow with condensation. Acta Mechanica 21, 65–91.CrossRefGoogle Scholar
Wegener, P. P. & Cagliostro, D. J. 1973 Periodic nozzle flow with heat addition. Combust. Sci. Tech. 6, 269–277.Google Scholar
Wegener, P. P. & Mack, L. M. 1958 Condensation in supersonic and hypersonic wind tunnels. In Advances in Applied Mechanics, vol. 5, pp. 307–447. Academic.Google Scholar
Wegener, P. P. & Mirabel, P. 1987 Homogeneous nucleation in supersaturated vapors. Natur Wissenschaften 74, 111–119.Google Scholar
Wegener, P. P. & Wu, B. J. C. 1977 Gasdynamics and homogeneous nucleation. Adv. Colloid Interface Sci. 7, 326–417.Google Scholar
White, A. J. & Young, J. B. 1993 Time-marching method for prediciton of two-dimensional unsteady flows of condensing steam. J. Propulsion Power 9, 579–587.Google Scholar
Wölk, J. & Strey, R. 2001 Homogeneous nucleation of H 2O and D 2O in comparison: The isotope effect. J. Phys. Chem. B 105, 11683–11701.Google Scholar
Wölk, J., Strey, R., Heath, C. H. & Wyslouzil, B. E. 2002 Empirical function for homogeneous water nucleation rates. J. Chem. Phys. 117 (10), 4954–4960.Google Scholar
Zierep, J. 1990 Strömungen mit Energiezufuhr, 2nd edn. Karlsruhe: G. Braun.Google Scholar