Modeling Corium Jet Breakup in Water Pool and Application to Ex-Vessel Fuel-Coolant Interaction Analysis

Transcription

1 Modeling Corium Jet Breakup in Water Pool and Application to Ex-Vessel Fuel-Coolant Interaction Analysis Kwang-Hyun Bang and Hyoung-Tak Kim Korea Maritime and Ocean University 1/41

2 Contents Introduction: FCI Melt Jet Breakup Model Jet Breakup Experiment (non-boiling) Jet Breakup Model TRACER-II Code Validation Calculations Reactor Calculations Effect of Pool Depth (Free-fall distance) Conclusions 2/41

3 Fuel-Coolant Interactions 196s : FBR Core Disruptive Accident, thermodynamic model 197s : LWR in WASH-14, -mode containment failure, triggering study of single drops, sodium-melt, simulant melts, explosion propagation models 198s : Explosion energetics, large-scale tests (FITS etc.), model development (mixing limit, codes, numerical method), SERG-1 (1985) 199s : Prototypic corium tests (FARO, KROTOS), ALWR features, code validation, SERG-2 (1995) 2s : OECD SERENA Ph. I & II (Codes, TROI, KROTOS) FCI: yet one of the unresolved issues of severe accident phenomena while molten corium and water be brought in proximity for degraded core coolability. 3/41

4 Multi-Physics Nature of FCI High temperature melt mixture of reactor core materials (~m) Jet breakup and drop formation Droplet breakup (~mm) Fine fragmentation(~1 m) Multiphase flow map (fluid & particles) Interfacial momentum transfer Interfacial heat transfer Shock wave propagation Solidification of melt drops TROI (KAERI) 4/41

5 Jet Breakup Experiment Real speed REC 4 fps REP 3 fps 5/41

6 Experimental Apparatus T melt Parameter Woods metal 72 o C 9383 kg/m 3 Cp 168 J/kgK 2.2x1-5 /K k 18.8 W/mK 2x1-7 m 2 /s ~1. N/m Corium Woods metal Density ratio Fr We /41

7 High-Speed Video 7/41

8 Debris Analysis Good Repeatability V et =5.5 m/s Test 1 Test 2 Test 3 Weight % Sieve Size [mm] 8/41

9 Overview of Jet Breakup Models Empirical et breakup length + local parameters JASMINE MC3D IKEMIX Rayleigh-Taylor instability: TEXAS (leading drop) Kelvin-Helmholtz instability: most of codes gd V D L l d.5 1, o o bar p o g g o o i f T T V c N V D L 2/ gd V D L l d 9/41

10 Kelvin-Helmholtz Instability Kelvin-Helmholtz Instability in melt-vapor film-liquid system (Epstein & Fauske, 1985) ] [ ) tanh( ) ( ] [ ] tanh [ k ikv n ikv n k ikv n k ikv n k k ikv n ikv n l l l g g g g l l l g g ) )( 3( ) ( 2 2, l l l l D o V V k g g g D V V k ) 3( ) ( 2 2, Thin Vapor Film Thick Vapor Film nt ikx ~ e mm D 2 ~. mm D 28 ~ 1/41

11 Kelvin-Helmholtz Instability Numerical solutions of KHI full dispersion equation Effect of Vapor Film Thickness Fastest Growing Wave Number 25 2 : k D =.5 mm = 1.8 mm = 2. mm = 3. mm V l -V =5 m/s V g -V =5 m/s V g -V =1 m/s V g -V =2 m/s n, s k D 1 3 V g -V =3 m/s k, m Vapor Film Thickness, mm 11/41

12 Kelvin-Helmholtz Instability Correlation construction of numerical solutions for use in an FCI code n n max max, k k D 1 n 1 k n max, max, o 5V V g ( n ) 1.5 D, D, ) 2 25Vg V ( kd, kd,, o h fg 1 3g x ( q" g( ) g l g rad q" l ) 1 3 max, 2 n max /n max,oo k D /k D,oo Data Fit Vapor Film Thickness, mm Data Fit Vapor Film Thickness, mm 12/41

13 Comparison to Debris Data If thin vapor film case (non-boiling, no steam) k d D, o D drop 2 2 l ( Vl V ) 3( )( ) 2 k D D / 2 l KHI d ~.2 mm Debris d ~ 2 mm (Middle of sieve interval) If entrained air? l Weight % 6 Exp. (V =5.5 m/s) 5 KHI prediction Debris Size, mm 13/41

14 Air Entrainment in Plunging Jet Active mechanism for gas transport and mixing in chemical processing devices Bell-shaped gas entrainment Air-layer thickness on et surface? controlled by amplitude of wavy et surface in air 14/41

15 Air Entrainment in Plunging Jet Jet surface instability due to relative velocity Rayleigh solution For free-fall of 1.5 m, t 2h / g ~ 1 For o o.55s ~ 1 m, ~.1mm Air thickness of.1 mm, d drop ~ 1.64 mm k n t max max.7 R o.34 R 1 max ln o 3 o 1/ 2 15/41

16 Comparison of Predictions 6 5 Exp. (V =5.5 m/s) Model prediction 4 Weight % Melt-Water Melt-Air-Water Melt-Air Debris Size, mm 16/41

17 Comparison to FCI Experiments Mixing tests: FARO L28 (Ispra), TROI TS-VISU (KAERI) TRACER-II code calculations Ar gas supply for aerosol removal Pyrometer-1 Furnace Vessel ID Elevation (mm) 481 FVSP1 FVT 43 Cold Crucible R.F. Generator 15 kw PVSP4 PVT4 PVDP4 GAS PVSP5 PVT5 PVDP5 GAS5 ` ` Pyrometer-2 Nozzle, 175 Intermediate melt catcher and release valve assembly Catcher, PVT1 PVDP1 IVDP13 IVT23 IVDP12 57 IVT12 IVT22 IVT21 VFDP 13 VFDP 12 VFDP 11 IVDP11 IVT11 IVT29 3 t IVDP14 IVT24 2 IVT25 IVT13 2 IVT26 IVT IVT27 2 Test Section IVT PVT2 PVDP2 Water, , nozzle 6 PVT3 PVDP3 T.S., Pressure Vessel ID 2, -46 IVDL11 ET; Explosive (PETN 1g) (Unit : mm) 17/41

18 FARO L28 Mass-Average Drop Size Cover Gas Pressure TRACER-II FARO L28 Debris: 2~4 mm 46% Cover Gas Pressure, MPa Mass-Averaged Drop Size, cm.7 FARO L28 Data TRACER-II Addtional heat transfer or et breakup upon impact on pool surface /41

19 TROI TS-VISU Mass-Average Drop Size Mass-Averaged Drop Size, cm 2. TRACER-II TROI TS-VISU Debris >.4 cm 39%.2~.4 cm 33% d=.66 cm /41

20 TRACER-II Code Transient, 2-D, 4-field model, Eulerian Jet, Drops, Liquid(+debris), Vapor(+NCG) Mass, momentum, energy equations. Melt et & droplets breakup model Melt diameter transport equation Inter-phase exchange models Fine fragmentation model Equation of state (allow meta-stable states) 2/41

21 TRACER-II Modeling Limitations Uniform mesh size, 2-D (x-y or r-z) Jet enters only at boundaries Melt solidification when Tm < Tsolidus Debris : instantly quenched in coolant, d=.1 mm No chemical reaction model (for, e.g., Zr oxidation) Recommended: mesh size > et diameter (global multiphase modeling of et breakup and heat transfer) 21/41

22 TROI TS-4 Analysis Melt 8:2 UO2/ZrO2 Melt mass 14.3 kg Melt Temp. 311 K Melt velocity 2.46 m/s* Pressure 2.31 bar Water temp. 333 K Jet diameter 5 cm Free fall in gas.6 m Water depth 1. m Pool diameter.6 m * At H=1.6 m det=5 cm 1.6 m Inect starts at t=.325 s of TROI time Steam 4 K (sat) 1. m Δr=5 cm Δz=1 cm Water 333 K Trigger at t=.715 (TS: t=1.4) P=14 MPa.3 m 22/41

23 TROI TS-4 Analysis (cont.) Jet Front Location & Triggering Time 16 Mass-Averaged Drop Size, cm Elevation, cm 2. TRACER-II Camera Thermocouples TG2 Mass-Average Drop Size.8 TRACER-II TG1 (TROI) /41

24 TROI TS-4 Analysis (cont.) 4 TG1 (.715 s) z=.2 m z=.4 m z=.6 m z=.8 m Center Pressure, MPa z=.2 m z=.4 m z=.6 m z=.8 m 15 Pressure, MPa.8 2 Wall /41

25 TROI TS-4 Analysis (cont.) Pressure(MPa) TG1 (.715 s) PIVDP14(MPa) (.8 m) PIVDP13(MPa) (.6 m) PIVDP12(MPa) (.4 m) PIVDP11(MPa) (.2 m) Time(s) 25/41

26 KROTOS KS-4 Analysis Melt 8:2 UO2/ZrO2 Melt mass 3.21 kg Melt Temp K Melt velocity 2.3 m/s Pressure 2.1 bar Water temp. 332 K Jet diameter 3 cm Free fall in gas.49 m Water depth m Pool diameter.2 m det=3. cm 1.6 m Pour time of 3.21 kg det=3. cm.27 s In KS-4 test,.75 s det=1.8 cm (et thinning?) Steam 4 K (sat) 1.1 m Δr=2 cm Δz=5 cm Water 332 K.1 m Trigger at t=.85 (KS4: t=1.4) P=15 MPa 26/41

27 KROTOS KS-4 Analysis (cont.) Jet Front Location & Triggering Time Mass-Averaged Drop Size, cm TRACER-II KS-4 data 14 Elevation, cm Mass-Average Drop Size TRACER-II d=.35 mm TG2.6 TG1 (KROTOS) 27/41

28 KROTOS KS-4 Analysis (cont.) 3 Pressure, MPa 25 K K1 K2 K3 K4 K5 K6 TG1 (1.4 s) K K1 K2 K3 K4 K5 K6 TG2 (.59 s) 25 Pressure, MPa /41

29 KROTOS KS-4 Analysis (cont.) Pour time of.75 s and det=1.8 cm 3.21 kg Jet Front Location & Triggering Time 16 Mass-Averaged Drop Size, cm Elevation, cm 2. TRACER-II KS-4 data Mass-Average Drop Size TRACER-II TG (.85 s) /41

30 KROTOS KS-4 Analysis (cont.) Pour time of.75 s and det=1.8 cm 3.21 kg 3 K K1 K2 K3 K4 K5 K6 Pressure, MPa Peak Pressure (MPa) PT KS-4 TRACER-II K K K K K K /41

31 Ex-Vessel FCI (PWR) Partially-flooded cavity A few meters deep of water and free-fall air space Mitigation of MCCI and longterm debris coolability Case of most FCI studies Deep-pool cavity Flooded above the bottom of reactor vessel In-vessel retention with external reactor vessel cooling (IVR-ERVC) 31/41

32 Reactor Calculations (PWR) Free fall No free fall 32/41

33 Partially-Flooded Cavity 7. Steam 4. Water D, axi-symmetric Top-side open (constant P=2 bars) Δr=3 cm, Δz=1 cm (8x7) V_et = 4.1 m/s D_et = 3 cm P = 2 bars Tcorium = 3228 K (3 K sup.) Twater = 343 K (5 K sub.) 33/41

34 Deep-Pool Cavity 7. Water D, axi-symmetric Top-side open (constant P=2 bars) Δr=3 cm, Δz=1 cm (8x7) V_et = 4.1 m/s D_et = 3 cm P = 2 bars Tcorium = 3228 K (3 K sup.) Twater = 343 K (5 K sub.) 34/41

35 Mixing: drop diameter 12 4 m deep 7 m deep 6 Melt Front Height, cm Average Melt Drop Diameter, cm m deep 7 m deep Melt Leading Edge Position 1. Melt Drop Diameter 35/41

36 Mixing: melt mass Total melt poured Total melt drop Liquid melt drop 2 Mass, kg Mass, kg 5 Total melt poured Total melt drop Liquid melt drop m deep m deep 36/41

37 Mixing: volume fractions 4 m deep 7 m deep 37/41

38 Explosion Pressure: 4 m deep 1 2 Pressure, MPa z=. m z=.5 m z=1.5 m z=2.5 m z=3.5 m 15 Pressure, MPa z=. m z=.5 m z=1.5 m z=2.5 m z=3.5 m Center.6 Wall 38/41

39 Explosion Pressure: 7 m deep 1 Z=. m Z=.5 m Z=2.5 m Z=4.5 m Z=6.5 m 2 1 z=. m z=.5 m z=2.5 m z=4.5 m z=6.5 m 8 Pressure, MPa Pressure, MPa Center.3 Wall 39/41

40 Impulse at Cavity Wall Impulse, kpa-s 5 Impulse, kpa-s 2 z=. m z=.5 m z=1.5 m z=2.5 m z=3.5 m z=. m z=.5 m z=2.5 m z=4.5 m z=6.5 m m deep m deep 4/41

41 Conclusions Jet breakup model has been improved by obtaining numerical solutions of K-H instability in et-vapor filmwater system. Analyses of FARO L28 and TROI VISU showed that the new et breakup model can predict melt drop size with reasonable accuracy. TRACER-II code showed reasonable predictions of TROI TS-4 and KROTOS KS-4 tests results. In partially-flooded PWR cavity, average drop size was 23 mm, peak pressure at wall was 13 MPa, max. impulse at wall was 5 kpa s. In deep-pool cavity, average drop size was 97 mm, peak pressure at wall was 6 MPa, max. impulse at wall was 15 kpa s, larger than partially-flooded due to higher constraint. 41/41