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Multiphase Flow Phenomena in SGTR:

Importance Ranking and Scaling

Nam Dinh

Division of Nuclear Power Safety

Royal Institute of Technology (KTH)

Stockholm, Sweden

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Outline

Multiphase Flow Phenomena in SGTR Context - Revisited

Pressure Shock Wave

Concluding Remarks

Sloshing

Steam Explosion

Transportability of Steam Bubbles to the Reactor Core

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SGTR

EFIT

15..25 MPa, 350..500 oC

LFR 2000 MWth

0.3 MPa, 500..600 oC

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Economy

Risk

Eliminate the intermediate

HLM loop

Risk of SGTRR = 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?

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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

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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

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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)

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Water14 MPa335 oC

14 mm

Liquid Lead (Pb)

Gas Space 0.1MPa,

Void fraction: 10% --85%

Normal Operation

Steam Generator Tube Rupture

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Water14 MPa335 oC

Rupture site

10…50 mm

Accident Initiation: Tube Rupture

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Water14 MPa335 oC

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

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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,Again, … Bubble and Droplet Sizes (Length Scales) are Key … Bubble and Droplet Sizes (Length Scales) are Key

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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!

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EFIT – AnsaldoNucleare

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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 RaTa/Pa)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 h0a = M (h0 – ha);

with h0 and ha being the initial (pre-BLEVE) mixture (liquid) enthalpy and mixture enthalpy after flash evaporation (at ambient condition), respectively.

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Primary Side – Pressure Wave

The ambient mixture enthalpy is ha related to the saturation enthalpies of liquid and vapor as

ha = xv hv,a + (1- xv)hl,a ,

where xv is the mass fraction of vapor after flash evaporation of a superheated liquid. xv can be determined from the isentropic expansion as

xv = (sl,0 – sl,a)/(sv,0 – sl,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 m3).

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Primary Side – Pressure Wave

The pressure wave magnitude can be predicted and shown to be negligible (say 0.1Pa) for structures in a distance equal to a so-called energy-based radius r* determined as r* = (E/Pa)1/3.

The value h0a 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 m3) 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.

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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 oC) 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

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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

34 6. "( ) ( ).(1 )

3 . .V V VP L LV

qR G t x dt G t x dt

d H

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 dp.

fast slow

Compensating factors

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Beznosov et al, 2005

Steam Bubble Size Distribution

Water: 22-24 MPa, 150-250 oC

14x2 mm tube

10 mm discharge

2000 mm depth

52 mm

Short wavelength due to high-pressure discharge.

2CAP g

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Size distributions of water drops

92% does not boilBeznosov et al, 2005

x7 final bubble radius

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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

, ,[ ]CCI P L SUB LV L DROPE C T H m

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m-FLUID PREMIXTURE

vO, PO

COOLANTVAPORFUEL(melt)

NON-PARTICPATING COOLANT

Multiphase Thermal DetonationMultiphase Thermal Detonation

,0 ,[ ( ) ]FCI P M C A FUS DROPE C T T H m

22KTH MISTEE synchronized video and Xray images.

“Anatomy” of Explosion

0.2 ms interval

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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

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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

,0 ,[ ( ) ]FCI P M C A FUS DROPE C T T H m

, ,[ ]CCI P L SUB LV L DROPE C T H m

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CCI – Limiting Mechanisms – Macro-Level

Short-lived “premixture”: short time window for steam explosion.

The characteristic time period tEVA during which a water droplet (1 mm) is 60 s.

/EVA D EVAt R V 2

,

2

( )

4M L SAT D

EVALV W D

h T T RV

H R

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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

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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) UC,DOWN ? UB,TER.

Forces (depth of mixture)

Bubble Size (Length Scale) is KeyBubble Size (Length Scale) is Key

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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 ExperimentsNext Step: Scaling Support for SGTR Experiments