Numerical and Experimental Study of Large Steam-Air Bubbles Injected in a Water Pool

Abstract In certain passive, future boiling water reactor concepts, during emergency cooling conditions, mixtures of steam and nitrogen are blown into a pool of water via a downward-facing open pipe; at its end, large gas bubbles form, break up, and rise in the water. We have developed a computer simulation program for the hydrodynamics of the process using an isothermal piecewise linear interface construction-volume of fluid method and carried out an experiment with flow rates up to 50 l/s into a tank of 1 m3 volume. Bubble frequencies and volumes can be predicted fairly well for the case of air injection. The experiments show that most of the condensation takes place before the bubble detaches from the pipe exit. The phenomena depend mainly on the volumetric flow rate of the gas and on a parameter measuring the shrinkage due to condensation. The rates of condensation were estimated to be very high.

[1]  Vijay K. Dhir,et al.  Numerical Simulation of Saturated Film Boiling on a Horizontal Surface , 1997 .

[2]  J. Sethian TRACKING INTERFACES WITH LEVEL SETS , 1997 .

[3]  J. J. Boulton-Stone A comparison of boundary integral methods for studying the motion of a two-dimensional bubble in an infinite fluid , 1993 .

[4]  Kunio Kuwahara,et al.  Direct numerical simulation of three‐dimensional open‐channel flow with zero‐shear gas–liquid interface , 1993 .

[5]  Tadashi Sakaguchi,et al.  Numerical Analysis of a Single Bubble by VOF Method. , 1993 .

[6]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[7]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[8]  Gretar Tryggvason,et al.  Head-on collision of drops—A numerical investigation , 1993 .

[9]  G. Yadigaroglu,et al.  Passive Advanced Light Water Reactor designs and the ALPHA program at the Paul Scherrer Institute , 1998 .

[10]  Thomas S. Lundgren,et al.  Oscillations of drops in zero gravity with weak viscous effects , 1988, Journal of Fluid Mechanics.

[11]  S. B. Chin,et al.  Stability of a numerical algorithm for gas bubble modelling , 1994 .

[12]  Jerzy M. Floryan,et al.  Numerical Methods for Viscous Flows With Moving Boundaries , 1989 .

[13]  J. Sethian Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[14]  Brahm D. Prasher Gas absorption into a turbulent liquid , 1973 .

[15]  C. Chan,et al.  A regime map for direct contact condensation , 1982 .

[16]  D. Juric,et al.  Computations of Boiling Flows , 1998 .

[17]  Yoichiro Matsumoto,et al.  Influence of Internal Phenomena on Gas Bubble Motion (Effects of Thermal Diffusion, Phase Change on the Gas-Liquid Interface and Mass Diffusion between Vapor and Noncondensable Gas in the Collapsing Phase) , 1994 .

[18]  J. Block Condensation-driven fluid motions , 1980 .

[19]  Koulis Pericleous,et al.  FREE SURFACE FLOW AND HEAT TRANSFER IN CAVITIES: THE SEA ALGORITHM , 1995 .

[20]  P. Bradshaw,et al.  Turbulence Models and Their Application in Hydraulics. By W. RODI. International Association for Hydraulic Research, Delft, 1980. Paperback US $15. , 1983, Journal of Fluid Mechanics.

[21]  John A. Trapp,et al.  A numerical technique for low-speed homogeneous two-phase flow with sharp interfaces , 1976 .

[22]  D. Hsieh Some Analytical Aspects of Bubble Dynamics , 1965 .

[23]  Yutaka Kukita,et al.  The vent-to-vent desynchronization effects on LOCA steam condensation loads in BWR pressure suppression pool , 1985 .

[24]  B. Smith A general numerical procedure for the treatment of moving interfaces in implicit continuous Eulerian (ICE) hydrodynamics , 1988 .

[25]  S. G. Bankoff,et al.  Some condensation studies pertinent to LWR safety , 1980 .

[26]  D. B. Kothe,et al.  RIPPLE: A NEW MODEL FOR INCOMPRESSIBLE FLOWS WITH FREE SURFACES , 1991 .

[27]  W. Nachbar,et al.  The conservation equations for independent coexistent continua and for multicomponent reacting gas mixtures , 1959 .

[28]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[29]  J. M. Delhaye,et al.  Jump conditions and entropy sources in two-phase systems , 1974 .

[30]  S. Hirschberg,et al.  Surface current and recirculating cells generated by bubble curtains and jets , 1991, Journal of Fluid Mechanics.

[31]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[32]  R. Viskanta Heat transfer to impinging isothermal gas and flame jets , 1993 .

[33]  Stanley K. Widener Analytical Simulation of Boiling Water Reactor Pressure Suppression Pool Swell , 1986 .

[34]  C.K.B. Lee Turbulent heat transfer on the surface of a steam-chugging bubble , 1983 .

[35]  Víctor Manuel García Mollá,et al.  Use of high accuracy schemes to handle free surfaces in computing unsteady two-phase flows , 1998 .

[36]  W. Rider,et al.  Stretching and tearing interface tracking methods , 1995 .

[37]  Wei Shyy,et al.  Computational Fluid Dynamics with Moving Boundaries , 1995 .

[38]  Mujid S. Kazimi,et al.  Theoretical modeling of forced convection condensation of steam in a vertical tube in the presence of a noncondensable gas , 1994 .

[39]  Harold R. Jacobs Direct-Contact Condensation , 1988 .

[40]  Brian L. Smith,et al.  A novel technique for including surface tension in PLIC-VOF methods , 2002 .

[41]  G. D. Raithby,et al.  Transient deformation and evaporation of droplets at intermediate Reynolds numbers , 1994 .

[42]  C. W. Hirt,et al.  SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries , 1980 .

[43]  M. Rudman INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 24, 671–691 (1997) VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS , 2022 .

[44]  J. Bugg,et al.  Modelling the initial motion of large cylindrical and spherical bubbles , 1991 .

[45]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[46]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[47]  W. Rodi,et al.  Experiments on vertical plane buoyant jets in shallow water , 1986, Journal of Fluid Mechanics.

[48]  Alexandre J. Chorin,et al.  Curvature and solidification , 1985 .

[49]  H. Nariai,et al.  Boundaries between regimes of pressure oscillation induced by steam condensation in pressure suppression containment , 1987 .

[50]  J. C. Martin An experimental study of the collapse of liquid column on a rigid horizontal plane , 1952 .

[51]  Yasuhiro Murakami,et al.  Turbulence structure and mass transfer across a sheared air–water interface in wind-driven turbulence , 1993, Journal of Fluid Mechanics.

[52]  Robert I. Nigmatulin,et al.  Dynamics, heat and mass transfer of vapour-gas bubbles in a liquid , 1981 .

[53]  Kuo-Shing Liang,et al.  Experimental and analytical study of direct contact condensation of steam in water , 1994 .

[54]  H. D. Baehr,et al.  Thermodynamik : eine Einführung in die Grundlagen und ihre technischen Anwendungen , 1973 .

[55]  Per F. Peterson,et al.  Diffusion Layer Theory for Turbulent Vapor Condensation With Noncondensable Gases , 1993 .

[56]  Yongxue Wang,et al.  COMPUTATION OF WAVE BREAKING ON SLOPING BEACH BY VOF METHOD , 1993 .

[57]  Bram van Leer,et al.  Upwind-difference methods for aerodynamic problems governed by the Euler equations , 1985 .

[58]  Nasser Ashgriz,et al.  FLAIR: fluz line-segment model for advection and interface reconstruction , 1991 .

[59]  Ross Taylor,et al.  Multicomponent mass transfer , 1993 .

[60]  Nasser Ashgriz,et al.  A computational method for determining curvatures , 1989 .

[61]  Y. Tsay Effects of binary mixture condensation on turbulent mixed convection heat and mass transfer in a vertical channel , 1996 .

[62]  E. D. Hughes,et al.  Direct contact condensation and momentum transfer in turbulent separated flows , 1991 .

[63]  J. F. Davidson,et al.  The initial motion of a gas bubble formed in an inviscid liquid Part 1. The two-dimensional bubble , 1962, Journal of Fluid Mechanics.

[64]  Donald S. Scott,et al.  An eddy cell model of mass transfer into the surface of a turbulent liquid , 1970 .

[65]  T. Yabe,et al.  Simulation technique for dynamic evaporation processes , 1995 .

[66]  J. Milgram Mean flow in round bubble plumes , 1983, Journal of Fluid Mechanics.

[67]  J. Bugg An Investigation of large bubble dynamics , 1991 .

[68]  Farzad Mashayek,et al.  A hybrid finite‐element–volume‐of‐fluid method for simulating free surface flows and interfaces , 1995 .

[69]  Peter E. Raad,et al.  Velocity Boundary Conditions for the Simulation of Free Surface Fluid Flow , 1995 .

[70]  D. Contractor,et al.  Valve Closure: Method for Controlling Transients , 1994 .

[71]  Direct Numerical Simulation of Turbulence Structure at a Wavy-Sheared Air-water Interface , 1995 .

[72]  L YoungsD,et al.  Time-dependent multi-material flow with large fluid distortion. , 1982 .

[73]  S. Osher,et al.  A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows , 1996 .

[74]  R. Meyder,et al.  The mechanism of violent condensation shocks , 1987 .

[75]  Y. Matsumoto,et al.  Influence of Internal Phenomena on Gas Bubble Motion : Effects of Transport Phenomena and Mist Formation inside Bubble in the Expanding Phase , 1994 .

[76]  J. Monaghan Simulating Free Surface Flows with SPH , 1994 .

[77]  G. F. Schultheiss,et al.  Simulation of small break LOCA effects on BWR-pressure suppression systems , 1987 .

[78]  H. P. Greenspan,et al.  Flow over a containment dyke , 1978, Journal of Fluid Mechanics.

[79]  P. V. Danckwerts Significance of Liquid-Film Coefficients in Gas Absorption , 1951 .

[80]  Peter Smereka,et al.  Axisymmetric free boundary problems , 1997, Journal of Fluid Mechanics.

[81]  Balasubramanya T. Nadiga,et al.  Investigations of a Two-Phase Fluid Model , 1995, comp-gas/9511003.

[82]  Franz Mayinger,et al.  Measurement of heat transfer at the phase interface of condensing bubbles , 1992 .

[83]  James M. Hyman,et al.  Numerical methods for tracking interfaces , 1984 .

[84]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[85]  Gretar Tryggvason,et al.  The rise of bubbles in a vertical shear flow , 1997 .

[86]  D. R. Taylor,et al.  An investigation of oscillating flow in tubes , 1984 .

[87]  M. Rudman A Volume-Tracking Method for Incompressible Multifluid Flows with Large Density Variations , 1998 .

[88]  Numerical solution of axisymmetric cavity flows using the boundary element method , 1993 .

[89]  M. Rashidi,et al.  Mechanisms of heat and mass transport at gas-liquid interfaces , 1991 .

[90]  Y. X. Wang,et al.  NUMERICAL SIMULATION OF BREAKING WAVES AGAINST VERTICAL WALL , 1992 .

[91]  Gerardo Trapaga,et al.  Mathematical modeling of the isothermal impingement of liquid droplets in spraying processes , 1991 .

[92]  J. Brock,et al.  Volume tracking of interfaces having surface tension in two and three dimensions , 1996 .

[93]  V. Dhir,et al.  Hydrodynamics of a bubble formed at vent pipe exit , 1982 .

[94]  J. M. Davidson,et al.  The initial motion of a gas bubble formed in an inviscid liquid , 1963, Journal of Fluid Mechanics.

[95]  Isao Kataoka,et al.  Local instant formulation of two-phase flow , 1986 .

[96]  L. Fan,et al.  The surface-renewal theory of interphase transport: a stochastic treatment , 1993 .

[97]  J. Bugg,et al.  Modelling large‐bubble formation at submerged orifices , 1993 .

[98]  W. Zielke Frequency dependent friction in transient pipe flow , 1968 .

[99]  R. Higbie,et al.  The Rate of Absorption of a Pure Gas into a Still Liquid during Short Periods of Exposure , 1935 .

[100]  C. L. Tien,et al.  Axisymmetric Interfacial Condensation Model , 1989 .

[101]  S. Garimella,et al.  Analysis of bubble rise using the VOF method. 2: Bubble interactions, wall effects and evaporation , 1996 .

[102]  G. Son,et al.  Numerical Simulation of Film Boiling Near Critical Pressures With a Level Set Method , 1998 .

[103]  Glenn R. Price,et al.  Evaluating the Effective Friction Factor and Overall Heat Transfer Coefficient During Unsteady Pipeline Operation , 1999 .

[104]  C. Peskin Numerical analysis of blood flow in the heart , 1977 .

[105]  Li,et al.  Two-dimensional Navier-Stokes simulation of deformation and breakup of liquid patches. , 1995, Physical review letters.

[106]  Roger H. Rangel,et al.  Numerical simulation of substrate impact and freezing of droplets in plasma spray processes , 1993 .

[107]  J. H. Harker,et al.  Fluid flow, heat transfer and mass transfer , 1996 .

[108]  I N Bronstein,et al.  Taschenbuch der Mathematik , 1966 .

[109]  H. C. Simpson Bubbles, drops and particles , 1980 .

[110]  W. Lee,et al.  Single-eddy model for random surface renewal , 1988 .

[111]  A. K. Trikha,et al.  An Efficient Method for Simulating Frequency-Dependent Friction in Transient Liquid Flow , 1975 .