1. 1 Multiphase Flow Phenomena in SGTR: Importance Ranking and Scaling Nam Dinh Division of Nuclear Power Safety Royal Institute of Technology (KTH) Stockholm, Sweden

2. 2 Outline  Multiphase Flow Phenomena in SGTR Context - Revisited  Pressure Shock Wave  Concluding Remarks  Sloshing  Steam Explosion  Transportability of Steam Bubbles to the Reactor Core

3. 3 SGTR EFIT 15..25 MPa, 350..500 o C LFR 2000 MWth 0.3 MPa, 500..600 o C

4. 4 Economy Risk Eliminate the intermediate HLM loop Risk of SGTR R = P(o)*C(?) Measures to reduce P of SGTR (materials, quality, operation, maitenance) Measures to reduce C of SGTR (design, control systems, EOP) SGTR Safety: Risk-Oriented Approach What are Consequences? Systematic Approach?

5. 5 SGTR-Induced Threats  Rupture-induced pressure shock wave  Steam Generation-Induced Sloshing  Steam Explosion  Steam Transport to the Reactor Core  Dynamic Loadings and Impact on Reactor Equipment  Causing Secondary Failures  Transport of Steam to the Core and Core Voiding  Reactivity Insertion with Potential for Power Excursion

6. 6 System Behavior – Primary Side The first stage is related to the rupture moment, and associated with dynamic interactions between the discharged jet flow and molten lead. The threat posed by this stage is the formation and propagation a pressure wave. The second stage is related to the formation and expansion of the mixing zone that leads to lead displacement and pool sloshing, with potential for mechanical damages. The third stage is initiated by a trigger that causes the pre-mixture to enter a CCI regime and lead to an energetic steam explosion. The fourth stage is transport of the multiphase mixture toward the reactor core, causing core voiding with potential reactivity consequences. Receiving Side

7. 7 Today Messages  Prediction of core voiding is subject to multiphase flow patterns dynamics governed by bubble length scale (steam dispersal & coalescence)  Initial-phase data exist but more are needed  New experiments in relevant flow regimes. Scaling.  Safety-by-design: Limiting design/operation conditions need to be established  High-fidelity 3D CFD simulation of (lead, water, vapor) system  Analytical experiments for constitutive relations  Integral experiments for validation  The mechanical effect of dynamic and energetic threats are expected to be insignificant  Careful treatment of the driving side (secondary loop)

8. 8 Water 14 MPa 335 o C  14 mm Liquid Lead (Pb) Gas Space 0.1MPa, Void fraction: 10% --85% Normal Operation Steam Generator Tube Rupture

9. 9 Water 14 MPa 335 o C Rupture site  10…50 mm Accident Initiation: Tube Rupture

10. 10 Water 14 MPa 335 o C Accident Situation: Water-Lead Interactions High Pressure Discharge of Water/Steam into Lead (HLM) Depressurization Waves Accurate Simulation of the Secondary-Side Dynamics is Important

11. 11 Multi-fluid Mixing (Lead, Water, Steam) Dynamic and Energetic Interactions (Steam Explosion) Formation of a Bubbly Mixture Forces that Facilitate the Mixture’s Transport Fine Bubbly Mixture Transport of Voided Coolant to the Reactor Core SGTR Multiphase Flow Phenomenology Again, … Bubble and Droplet Sizes (Length Scales) are Key

12. 12 Secondary Side is the Driving Force The SGTR interactions are limited by the dynamics of the secondary (supply) side. Failure location: probability? System approach  self-limiting threat! 1 2 3 EFIT – AnsaldoNucleare

13. 13 Primary Side – Pressure Wave Two-phase flashing and expansion similar to Boiling Liquid Expanding Vapor Explosion (BLEVE) due to a vessel burst. Characteristic length and time scales are: L* = (M R a T a /P a ) 1/3, t* = L*/U*, where the velocity scale is defined as U* = {2E/M} 1/2 and the energy that drives the expansion is determined as E = M  h 0a = M (h 0 – h a ); with h 0 and h a being the initial (pre-BLEVE) mixture (liquid) enthalpy and mixture enthalpy after flash evaporation (at ambient condition), respectively.

14. 14 Primary Side – Pressure Wave The ambient mixture enthalpy is h a related to the saturation enthalpies of liquid and vapor as h a = x v h v,a + (1- x v )h l,a, where x v is the mass fraction of vapor after flash evaporation of a superheated liquid. x v can be determined from the isentropic expansion as x v = (s l,0 – s l,a )/(s v,0 – s l,a ), M -- the mass of instantaneous exposure can be estimated from the volume formed by the breach area (A) and pipe diameter (D), thus fairly small volume (10 -5 –10 -6 m 3 ).

15. 15 Primary Side – Pressure Wave The pressure wave magnitude can be predicted and shown to be negligible (say 0.1P a ) for structures in a distance equal to a so-called energy-based radius r* determined as r* = (E/P a ) 1/3. The value  h 0a in a SGTR event can be found in a typical range up to few (two-three) hundreds kJ/kg. Consequently, r* is predicted to be in a fairly narrow range of 5-10 cm. Even with a mass of order of liter (10 -3 m 3 ) suddenly exposed to low pressure expansion, we would have r* ~ 0.5 m, and the same conclusion about negligible loading on structures applies. Thus, the first stage poses no significant threat to structures.

16. 16 Key Data  Beznosov et al (2005) “a steam–water mixture, and 100– 350°C, 1–25 MPa steam were bubbled through 0.6–2 mm in diameter openings (tube 14x2 mm), under a layer of lead ranging in thickness from 100 to 3000 mm, at temperatures 350–600°C” Water injection (at 30 MPa, 335 o C) into lead at 0.8 MPa liquid water No explosion reported. Limited expansion. Large fraction of liquid water upon discharge means limited (immediate) expansion, followed by gradual evaporation in film boiling mode

17. 17 As a reference case, we can assume that no mixing occurs, so the two- phase mixture ejected from the secondary circuit forms a steam cavity (large bubble). We write mass balance for the steam bubble (of characteristic radius R) as Expanding Bubble where the first term in RHS is the steam supply rate from isentropic expansion, and the second term represents evaporation (by film-boiling heat flux q”) of water droplets of the same diameter d p. fastslow Compensating factors

18. 18 Beznosov et al, 2005 Steam Bubble Size Distribution Water: 22-24 MPa, 150-250 o C 14x2 mm tube 10 mm discharge 2000 mm depth 52 mm Short wavelength due to high-pressure discharge.

19. 19 Size distributions of water drops 92% does not boil Beznosov et al, 2005 x7  final bubble radius

20. 20 Can Explosion Occur? - Is pre-mixture triggerable and detonable? If yes, - What are ranges of pressure impulse? - What is post-explosion mixture? Primary Side – Coolant-Coolant Interactions CCI

21. 21 m-FLUID PREMIXTURE v O, P O COOLANTVAPORFUEL (melt) NON-PARTICPATING COOLANT Multiphase Thermal Detonation

22. 22 KTH MISTEE synchronized video and Xray images. “ Anatomy ” of Explosion 0.2 ms interval

23. 23 Micro-Interactions Dynamics in FCI Undisturbed molten droplet  Prior external trigger arrival 1st bubble expansion  melt non-uniform pre- fragmentation/ deformation Bubble collapse  water entrainment Explosive vaporization  fine fragmentation of the molten droplet 2nd bubble collapse  mixing Final Explosive vaporization  total fine fragmentation of the molten droplet KTH MISTEE Xray images

24. 24 For a postulated FCI with 1000 kg of oxidic corium in the pre-mixture, the total energy potential is 1.5GJ. Given triggerability and detonation, a typically small fraction  of this energy (10% and less), or 150 MJ mechanical energy. Analogy and Difference between FCI and CCI FCI For a postulated CCI with 10 kg of liquid water in the pre-mixture (self- limiting liquid inventory), the total energy potential is 20 MJ. Given triggerability and detonation, a typically small fraction  of this energy (0.1-1% and less), or 20…200 kJ mechanical energy. CCI

25. 25 CCI – Limiting Mechanisms – Macro-Level Short-lived “premixture”: short time window for steam explosion. The characteristic time period  t EVA during which a water droplet (1 mm) is 60 s.

26. 26 High contact (interface) temperature, forming stable vapor film Stable bubble-wall surface due to high density of HLM No phase-change occurs at bubble wall FCI CCI T >> CCI – Limiting Mechanisms – Micro-Level

27. 27 Transportability of Steam Bubbles to the Reactor Core and Reactivity Insertion depend on Primary Side – Core Voiding  Smaller bubbles are more easily trapped in HLM flow Steam dispersal during water discharge Bubble distribution and coalesence during transport Flow path geometry  Convection (velocity) U C,DOWN ? U B,TER. Forces (depth of mixture) Bubble Size (Length Scale) is Key

28. 28 Today Messages  Prediction of core voiding is subject to multiphase flow patterns dynamics governed by bubble length scale (steam dispersal & coalescence)  Initial-phase data exist but more are needed  New experiments in relevant flow regimes. Scaling.  Safety-by-design: Limiting design/operation conditions need to be established  High-fidelity 3D CFD simulation of (lead, water, vapor) system  Analytical experiments for constitutive relations  Integral experiments for validation  The mechanical effect of dynamic and energetic threats are expected to be insignificant  Careful treatment of the driving side (secondary loop) Next Step: Scaling Support for SGTR Experiments