Multiphase CFD Applied to Steam Condensation Phenomena in the Pressure Suppression Pool Marco Pellegrini - IAE Colin Josey, Emilio Baglietto - MIT N U P E C STAR Japanese Conference Yokohama, Japan – June 2 nd , 2015
BACKGROUND 2 DW Pressure RCIC system earthquake Time after scram [hour] -3 0 3 7 10 13 16 19 22 25 28 31 0.5 0.4 DW Pressure (MPa[abs]) UNIT 3 0.3 0.2 UNIT 2 0.1 0.0 3/11 3/11 3/12 3/12 3/12 3/12 3/13 12:00 18:00 0:00 6:00 12:00 18:00 0:00 Time [date] 6/9/2015 STAR Japanese Conference, Yokohama, Japan
RCIC MAIN DIFFERENCES 3 UNIT 2 UNIT 3 VERTICAL JET HORIZONTAL JETS steam flow steam flow 0.680 1.275 m m 0.033 2.577 m 0.283 m m Sparger detail Bottom closed • 1F3 RCIC worked at the same time • 1F2 RCIC suspected to have worked with cycling SRVs in two-phase flow • 1F2 torus suspected to have been flooded by the tsunami 6/9/2015 STAR Japanese Conference, Yokohama, Japan
EXPERIMENTAL ACTIVITIES AND COLLABORATIONS 4 TITech Facility SIET Facility G. Gregu, M. Takahashi scrubber pool 3 m 0.5 m 6/9/2015 STAR Japanese Conference, Yokohama, Japan
SPARGER STRATEGY 5 Vent pipe - RCIC 1F2 RCIC 1F3 T-quencher D 0.2 m D 0.1 m Subcooling [K] D 0.02 m Petrovich, Int, J. Heat and Mass Tr, 2007 Diameter [m] Steam mass flux [kg/m 2 -s] 6/9/2015 STAR Japanese Conference, Yokohama, Japan
CONDENSATION REGIME MAP 6 CHUGGING BUBBLING JETTING Subcooling [K] Experiment at SIET labs, Italy Visualization by Prof. L. Araneo, POLIMI Petrovich, Int, J. Heat and Mass Tr, 2007. Diameter [m] Steam mass flux [kg/m 2 -s] 6/9/2015 STAR Japanese Conference, Yokohama, Japan
TITech EXPERIMENT: CHUGGING PHENOMENOLOGY 7 1000 fps pressure signal – G. Gregu, POLIMI/TITech Mass flow rate: 3.9 g/s 100 pressure [kPa] T pool : 23.7 °C 0 -60 • 65ms: bubble formation at outlet • 170ms: bubble collapse • 258ms: condensation inside the pipe • 599ms: condensation inside the pipe • 997ms: condensation inside the pipe pressure [kPa] 100 • 1550ms: bubble formation at outlet • 1679ms: bubble collapse 0 -60 0.8 0 0.2 0.4 0.6 1 1.2 1.4 1.6 time [ms] 6/9/2015 STAR Japanese Conference, Yokohama, Japan
UNIT 3 RCIC SPARGER 8 Steam flow Steam flow T pool = 30 °C Visualization by L. Araneo, POLIMI 6/9/2015 STAR Japanese Conference, Yokohama, Japan
TWO-FLUID MODEL: MOMENTUM EQUATION 9 Two-fluid model approach Phase momentum equation � �� � � � � � � � � ∙ � � � � � � � � � � �� � �� � � � � � � � � ∙ � � � � � � � � � � � � ��� � � � � �� � � � � � �� � � � � drag force �� Interphase momentum transfer �� virtual mass force � � � � �� � � � � � �� �� � � � � � � � �� �� �� �� lift force �� ��� �� � turbulent dispersion force �� Standard Drag � �� � 1 � � � Schiller-Naumann � � ��� � � 2 � � � � �� �� 4 � Tomiyama � ��� � � ��, �� Bozzano-Dente correction factor 6/9/2015 STAR Japanese Conference, Yokohama, Japan
TWO FLUID MODEL: ENERGY EQUATION 10 Phase energy equation � �� � � � � � � � � ∙ � � � � � � � � � � � � � ∙ � � � � � � ���� � � � � � � � ∙ � � � � � � � ∙ � � � ���,� �� � � � ∙ � � ∙ � � � � � � �� � � � �� � � �� �� � Source term in the energy equation � ���� � � � � ∆� � �� � ��� �� ���� � � � � ∆�∆� ��� General bubble � � surface interaction length scale area density l t � � � �� Differently from two-fluid for boiling applications, the interaction length scale is generally differently defined from the area density in condensation applications. 6/9/2015 STAR Japanese Conference, Yokohama, Japan
TWO FLUID MODEL: ENERGY EQUATION 11 �� ���� � �� � ��� � � ∆�∆� ��� � � Main historical heat transfer models Formulation ��� �/� Model Reference ��/� � � ��� � Large eddy Fortesque and Pearson (1967) ��/� � � ��� � Small eddy Banerjee et al. (1968) � � �� �/� �� �/� Surface divergence Banerjee (1990) �/� � � � �0.3 �2.83�� � SD no shear Banerjee (1990) �/� �� �� � ��/� � 2.14�� � Surface renewal period Gas flow � � � � � � � l t v t ⁄ ⁄ � � � ⁄ � � � � � � � ⁄ � � � � � � � � � � T � 6/9/2015 STAR Japanese Conference, Yokohama, Japan
TWO FLUID MODEL: INTERFACIAL AREA DENSITY 12 Example of volume EULERIAN-EULERIAN TWO-FLUID APPROACH fraction Sauter mean diameter � � L More proper in case of boiling applications volume fraction Magnitude of Volume 3L 1.00 Fraction Gradient 0.75 0.50 � � 0.25 0.00 6/9/2015 STAR Japanese Conference, Yokohama, Japan
COMPRESSIBILITY EFFECT 13 Constant or temperature WATER dependent density Pressure limit ρ � � � STEAM �� P incompressible compressible volume fraction 1.00 0.75 0.50 0.25 0.00 6/9/2015 STAR Japanese Conference, Yokohama, Japan
TITech EXPERIMENT: MESH SENSITIVITY 14 TEST CONDITIONS Pipe diameter = 2.7 cm 0.5 m Mass flow rate = 5.58 g/s Mass flux = 9.75 kg/m 2 -s Pool bulk T = 19 ºC 0.5 m Steam T = 100 ºC (saturated) COARSE FINE 200,000 cells 800,000 cells 6/9/2015 STAR Japanese Conference, Yokohama, Japan
CHUGGING AT LARGE SUBCOOLING AND MASS FLUX 15 volume fraction volume fraction 1.00 COARSE FINE 1.00 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00 T pool = 19 ºC T pool = 19 ºC 30 Condensation mass transfer [g/s] fine mesh 25 20 15 Inlet mass flow rate 10 5.58 g/s 5 coarse mesh 0 0 5 10 15 Time [ms] 6/9/2015 STAR Japanese Conference, Yokohama, Japan
NON ENCAPSULATING BUBBLE 16 6.0 ms 6.8 ms 6.9 ms 7.0 ms 7.2 ms 30 40 35 25 Mass transfer [g/s] Total area [cm 2 ] 30 20 25 15 20 15 10 10 5 5 0 0 0 2.5 5 7.5 10 12.5 Time [ms] 6/9/2015 STAR Japanese Conference, Yokohama, Japan
CHUGGING: LOW SUBCOOLING AND MASS FLUX 17 SIET facility Pipe diameter = 0.2 m Mass flow rate = 0.1 kg/s Mass flux = 3.18 kg/m 2 -s Pool bulk T = 65 ºC Steam T = 100 ºC (saturated) implosion • Pressure starts decreasing 4 below zero due to condensation interface within the pipe Pressure [kPa] 2 greater than inlet mass flow rate of steam • An implosion time is reached at 0 the minimum pressure value • Afterwards the interface flows in -2 the pipe and the steams gets Marks and Andeed, 1979 compressed 0 100 200 300 400 6/9/2015 STAR Japanese Conference, Yokohama, Japan
CHUGGING: PHENOMENA INTERPRETATION 18 INTERFACE LOW PRESSURE IMPLOSION MOVING UPWARD 20 ms 40 ms implosion • Pressure starts decreasing 4 below zero due to condensation interface within the pipe Pressure [kPa] 2 greater than inlet mass flow rate of steam • An implosion time is reached at 0 the minimum pressure value • Afterwards the interface flows in -2 the pipe and the steams Marks and Andeed, 1979 compressed 0 100 200 300 400 6/9/2015 STAR Japanese Conference, Yokohama, Japan
RAYLEIGH-TAYLOR INSTABILITY 19 Gravitation field Accelerating flow field HEAVY FLUID LIGHT FLUID g A separator LIGHT FLUID HEAVY FLUID 6/9/2015 STAR Japanese Conference, Yokohama, Japan
RAYLEIGH-TAYLOR INSTABILITY 20 Gravitation field Accelerating flow field steam HEAVY FLUID g P steam LIGHT FLUID A water P water 6/9/2015 STAR Japanese Conference, Yokohama, Japan
APPROACH FOR RTI IMPLEMENTATION 21 Amplitude growth description viscosity C. Josey, E. d f g k A n Baglietto, 2013 n ( , , , , ) surface dt tension acceleration Atwood number wave Classic instability theory number n Agk Classical theory Duff et al. Physics of Fluid , 1962 Duff 2 4 2 n Agk k k Livescu, Physics of Fluid , 2004 Livescu 2 k n Ag k w s wave number 6/9/2015 STAR Japanese Conference, Yokohama, Japan
IMPLEMENTATION OF THE RTI IN STAR-CCM+ 22 Duff and Livescu combined model for RTI �� � � � ν � � � � ν� � � � �� � � � � � � Acceleration term Wave number term Ag w P w s k max 3 w g Final terms for area growth 2 k n t t e a 1 t t i s 6/9/2015 STAR Japanese Conference, Yokohama, Japan
POOLEX: LOW SUBCOOLING AND MASS FLUX 23 POOLEX facility detail Experiment conditions at steam inlet the POOLEX Pipe diameter = 0.2 m T pool = 62 ° C Steam Mass Flux = 8 kg/m 2 s Domain Discretization velocity inlet pressure outlet adiabatic walls Mesh elements: 405,067 6/9/2015 STAR Japanese Conference, Yokohama, Japan
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