Improvement and Verification of Steam Explosion Models and Codes for Application to Accident Scenarios in Light Water Reactors Z

Institut für Kernenergetik IKE und Energiesysteme

Improvement and Verification of Steam Explosion Models and Codes for Application to Accident Scenarios in Light Water Reactors

Zoran Vujic

Dezember 2008 IKE 2-154

Universität Stuttgart

Institut für Kernenergetik IKE und Energiesysteme

Improvement and Verification of Steam Explosion Models and Codes for Application to Accident Scenarios in Light Water Reactors

von der Fakultät Energie-, Verfahrens- und Biotechnik der Universität Stuttgart zur Erlangung der Würde eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Abhandlung

vorgelegt von Zoran Vujic Geboren in Zrenjanin/Serbien

Hauptberichter: Prof. G. Lohnert, Ph.D

Mitberichter: Prof. Dr.-Ing. Eberhard Göde

Tag der Einreichung: 06. Oktober 2008

Tag der mündlichen Prüfung: 22. Dezember 2008

ISSN – 0173 – 6892

Dezember 2008 IKE 2-154

Universität Stuttgart

…dedicated to my beloved parents

Abstract

Steam explosions can occur during an accident with core melting in Light Water Reactors (LWR) as a consequence of the interaction between molten core material with the water inside the Reactor Pressure Vessel (RPV) or, if RPV failure cannot be excluded, due to the release of melt from the RPV into water in the cavity. Generally, steam explosions progresses through two distinct phases, characterized by different time scales for the dominant processes i.e. the premixing and explosion phase. The objective of this thesis is to evaluate critical conditions and the resulting damage potential of steam explosions under real reactor conditions. As a basis, models for simulation of the premixing and the explosion phase of steam explosion are already available as IKEJET/IKEMIX and IDEMO codes, currently under development at IKE. A status in the development is to be reached, where the existing models and corresponding computer programs can be applied for risk analysis and for accident management. A major limitation in obtaining strong steam explosions has been determined to be the mass of melt available to be mixed with water without too high a void during the premixing phase. The mass in the mixture is limited by the rate of melt mass plunging into the water (pours diameter, melt velocity) and by the break-up of the melt flow which may be assumed to take form as jets. This break-up yields the mass which can be intermixed with water to form an explosive mixture. Steam production under film boiling may produce a highly voided mixture which limits heat transfer from melt to coolant, and thus decreases the possibility of a strong steam explosion. It additionally affects the fragmentation processes. During the explosion phase, a high void yields dampening effects due to the high compressibility of the coolant, which in turn reduces the possibility of developing strong pressure waves. In order to capture essential features decisive for the explosion strength and to check the capabilities of the models to reproduce them sufficiently, verification of the codes against specified and qualified experiments is required. First calculation attempts performed with IKEJET/IKEMIX code for the experiment FARO L-28 showed significant void overestimation. A reasonable explanation for such a strong steam accumulation in the mixture was found in the used friction models yielding too high interfacial friction between steam and water which as a consequence suppresses fast steam escape from the mixing zone. A new model which considers different vapour velocities for both liquid and steam continuous regimes in the transition range (0.3 < α < 0.7) has been developed and implemented in the IKEJET/IKEMIX code. Calculations with the improved model provided good agreement with the experimental data for the pressure development, the energy release, jet break-up

and void in the mixture. Verification of the IDEMO code has been performed taking the experiments FARO L-33 and KROTOS K-44 as a basis for this validation with the aim of creating a unique model description for the different cases in order to be able to extrapolate the results to reactor conditions. Calculations for reactor conditions are carried out in order to asses the capabilities of the codes and to get a perspective of the limiting effects on explosion strength and the resulting loads. It was attempted to reach the most challenging conditions by considering conditions with highest amounts of melt in the mixture in the frame of the underlying scenario conditions. This has been accomplished by varying the melt composition, the melt diameter, the flow rate, the water level, the possible lateral extension of the mixture and the trigger time. It appeared that the limitations to strong steam explosions due to water depletion and in addition, partial jet break-up, strongly reduce the damaging potential of steam explosion, at least in saturated conditions, much more than it had been assumed earlier.

Kurzfassung

Bei schweren Störfällen in Leichtwasserreaktoren (LWR) mit Auftreten von Kernschmelze können Dampfexplosionen als Folge von Wechselwirkungen zwischen geschmolzenem Reaktorinventar und Wasser innerhalb des Reaktordruckbehälters (RDB) oder, bei Versagen des RDB durch Einströmen von Schmelze in die wassergefüllte Reaktorgrube, nicht ausgeschlossen werden. Beim Ablauf von Dampfexplosionen können zwei verschiedene Phasen identifiziert werden, die sich durch verschiedene Zeitskalen für die sie dominierenden Prozesse charakterisieren lassen: Die Vorvermischungs- und die Explosionsphase. Das Ziel dieser Arbeit ist die Bestimmung von kritischen Bedingungen für das Auftreten von Dampfexplosionen und das daraus resultierende Zerstörungspotenzial unter realen Reaktorbedingungen. Als Grundlage hierfür werden die Rechenprogramme IKEJET/IKEMIX für die Vorvermischungs- und IDEMO für die Explosionsphase verwendet, die sich am IKE in der Entwicklung befinden. Es soll ein Stand erreicht werden, der eine Verwendung der existierenden Modelle und der korrespondierenden Rechenprogramme für Risikoanalyse und Risikomanagement erlaubt. Als begrenzender Faktor, der das Ausmaß der Dampfexplosion wesentlich bestimmt, wurde die Masse der Schmelze, welche mit Wasser ohne größeren Dampfanteil vermischt wird, identifiziert. Die Schmelzemasse in der Mischung wird sowohl durch die in Form von angenommenen Schmelzestrahlen ins Wasser fallende Schmelzemasse (Durchmesser des Schmelzestrahls, Strömungsgeschwindigkeit der Schmelze), als auch durch die Zerteilung der Schmelze-Strömung bestimmt. Diese Zerteilung der Schmelze bei zusätzlicher Durchmischung mit Wasser kann möglicherweise zu explosionsfähigen Mischungen führen. Dampfproduktion durch Dampffilmsieden kann zu dampfreichen Mischungen führen, mit einem stark erniedrigten Potenzial für Dampfexplosionen, da der Wärmeübergang von Schmelze auf Kühlmittel stark reduziert wird. Außerdem beeinflusst der Dampfanteil selbst auch den Fragmentierungsprozess. Ein hoher Dampfanteil in der Mischung führt durch die resultierende Kompressibilität des Gemischs zur Dämpfung der Druckwelle einer Dampfexplosion während der Explosionsphase. Um die für die Explosionsstärke wesentlichen Größen sowie die Aussagekraft der Modelle ausreichend zu überprüfen, müssen die entwickelten Rechenprogramme einer Plausibilitätsprüfung unterzogen werden. Dazu werden geeignete und genau beschriebene Experimente nachgerechnet. Resultate erster, für das Experiment FARO L-28 mit IKEMIX/IKEJET durchgeführte Rechnungen, wies starke Überschätzung des Dampfanteils in der Vorvermischung auf. Als Ursache für die überhöhte, simulierte Dampfakkumulation in

III

der Mischung wurde die mit herkömmlichen Modellen berechnete zu hohe Interphasenreibung zwischen Dampf und Wasser ausgemacht. Diese verhindert eine schnellere Dampfflucht aus der Mischungszone. Ein neues Modell für die Interphasenreibung im Übergangsbereich zwischen wasserkontinuierlichem und dampfkontinuierlichem Bereich wurde entwickelt. Die zugrunde liegende Annahme hierfür ist die Existenz von vertikalen Dampfkanälen mit eigenen Dampfgeschwindigkeiten im Übergangsbereich (0.3 < α < 0.7), gegenüber dem wasserkontinuierlichen Bereich des Übergangsbereichs. Dieses Modell wurde in IKEJET/IKEMIX implementiert. Rechnungen mit dem verbesserten Modell zeigen gute Übereinstimmung mit den experimentellen Daten für den Druckanstieg, die Energiefreisetzung, den Strahlzerteilung und den Dampfanteil in der Mischung. Verifikationsrechnungen mit dem Explosionscode IDEMO wurden für die Experimente FARO L-33 und KROTOS K-44 durchgeführt mit dem Ziel einer allgemein gültigen Modellierung zur Beschreibung dieser Experimente mit verschiedenen

Schmelzematerialien (Corium vs. Al2O3), um einen auf Reaktorbedingungen extrapolierbaren Code zu bekommen. Rechnungen für Reaktorbedingungen werden durchgeführt, um die Fähigkeiten der Codes im Allgemeinen abzuschätzen und um eine Perspektive der die Explosionsstärke und resultierenden Belastungen begrenzenden Effekte zu erhalten. Es wurde versucht für die zugrunde liegenden Szenarien die Bedingungen herauszuarbeiten, bei denen die höchsten Schmelzemasse in der Mischung erreicht werden. Hierzu wurde die Schmelzezusammensetzung, der Schmelzestrahldurchmesser, der Schmelzemassenstrom, der Wasserspiegel, die mögliche laterale Ausdehnung der Mischung und der Triggerzeitpunkt variiert. Die Resultate weisen auf eine Limitierung von starken Dampfexplosionen hin aufgrund von wasserarmen Mischungsverhältnissen und zusätzlich wegen des partiellen Strahlaufteilung/-zerteilung ein - gegenüber früheren Annahmen - stark reduziertes Schädigungspotential von Dampfexplosionen bei gesättigten Bedingungen.

Table of Contents

Abstract ...... I

Kurzfassung...... III

Table of Contents ...... V

Nomenclature...... VIII

1 Introduction...... 1

1.1 Steam explosion as a subclass of fuel-coolant interactions in nuclear reactor safety considerations...... 1

1.2 Main limitations to steam explosion strength ...... 3

1.3 Objectives of the present work...... 5

1.4 Approach and outline of the present work...... 8

2 Investigation of steam explosion phenomena - State of the art ...... 9

2.1 Possible accident scenarios leading to steam explosion in LWRs ...... 9 2.1.1 In-vessel phenomena...... 9 2.1.2 Ex-vessel phenomena ...... 12

2.2 History of investigation and resolving of the so-called “alpha-mode containment failure” ...... 13

2.3 Current understanding of steam explosion phenomena...... 16

2.4 Modelling approaches for steam explosion analyses codes ...... 17 2.4.1 Premixing...... 17 2.4.2 Melt jet fragmentation ...... 19 2.4.3 Triggering ...... 21 2.4.4 Fine fragmentation ...... 22 2.4.5 Heat transfer between fine fragmented melt and coolant ...... 23

3 Description of the premixing model IKEJET/IKEMIX ...... 24

3.1 Jet model and melt break-up ...... 24

3.2 Melt drops in mixture...... 27 3.2.1 Dynamics ...... 28 3.2.2 Heat transfer...... 29

3.3 Two phase-description of coolant ...... 30 3.3.1 Conservation equations...... 30 3.3.2 Constitutive laws ...... 32 3.3.2.1 Exchange with melt ...... 32

3.4 Improvements of the model for interfacial friction between steam and water...... 35

3.5 Numerical method ...... 39

4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 ...... 40

4.1 Experimental database ...... 40

4.2 Results of IKEJET/IKEMIX calculations performed for the experiment FARO L-28...... 44

4.3 Additional investigations related to the initial phase of the FARO L-28 experiment...... 52

5 Verification of the IDEMO code with explosion experiments ...... 57

5.1 Experimental database ...... 57

5.2 Explosivity of corium versus alumina in KROTOS and FARO experiments...... 60

5.3 Results of IDEMO calculations performed for KROTOS K-44 and FARO L-33 experiments...... 62

6 Application to reactor conditions ...... 67

6.1 Premixing calculations ...... 67 6.1.1 Modelling suppositions ...... 68 6.1.2 Results of the premixing calculations ...... 70 6.1.2.1 Metallic melt jet outflow from the RPV ...... 73

6.2 Explosion calculations ...... 82 6.2.1 Initial conditions and modelling suppositions ...... 82 6.2.2 Results of the explosion calculations ...... 84 6.2.2.1 Consideration of a triggering time later than at MBC...... 85 6.2.3 Discussion...... 86

7 Summary and conclusion...... 95

8 References ...... 101

A. Description of the explosion model IDEMO ...... 108

A.1. Conservation equations...... 108 A.1.1. Mass conservation equations ...... 108 A.1.2. Momentum conservation equations...... 108 A.1.3. Energy conservation equations ...... 108 A.1.4. Droplet length scale equation ...... 109 A.1.5. Volume conservation equation...... 109

A.2. Constitutive laws ...... 110 A.2.1. Mass transfer between melt drops and fragments...... 110 A.2.2. Mass transfer to micro-interactions field...... 112 A.2.3. Heat transfer from melt ...... 113 A.2.4. Interfacial friction ...... 113

B. Initial conditions for verification of the IDEMO code...... 115

VII

Nomenclature

Latin symbols A m2 cross section of jet B - function depending on droplet volume fraction or void C - coefficient

cpv J/(kgK) heat capacity, heat capacity of vapour at const. pressure

cd, cj - drag coefficient of drops or jet

ci m/s imaginary part of phase velocity D m diameter d m distance, thickness 1 E J/kg specific total energy, E = e + v 2 2 e J/kg thermal energy F(B) - function for drag coefficient depending on B r F, F N force f - factor g m/s2 gravitational acceleration (= 9.81 m/s2) h J/kg specific enthalpy 2 hfilm,hbh W/(m K) heat transfer coefficient to vapour film or to hot part of the coolant 1 H J/kg specific total enthalpy, H = h + v 2 2 K kg/(m3s) friction coefficient K* kg/m4 modified friction coefficient k 1/m wave number L m jet length l m (characteristic) length M& kg/(ms) source line fragmentation rate m kg mass

Nfr - product of wave number and wave amplitude n 1/m3 number of drops per unit-volume

nd number of drops in representative particle group,

3 md nd = 3 4 πRd ρm p N/m2 pressure

VIII

Q W/m3 heat flux density q J/(m2s) heat flux R m radius T K temperature t s time * t fr - dimensionless fragmentation time, * t fr = (v rel ⋅t / D ) ⋅ ρf / ρm u m/s growth rate of wave, radial velocity V m3 volume v m/s axial velocity 3 2 vfr m /(m s) fragmentation rate v m/s average axial velocity x - exponent on pore fraction in friction coefficient

Zlt, Zvt water resp. steam continuous volume parts in transition region z m co-ordinate (direction of gravity)

Greek symbols: α α - void, α = v αv + α l

αk - volume fraction of k (k = m, l, v, b, c, h) Γ kg/(m3s) evaporation/condensation rate 3 Γfr kg/(m s) fragmentation rate 3 Γe kg/(m s) entrainment rate η m wave amplitude κ m2/s thermal diffusivity

λfr m wavelength of dominant wave on jet µ Pa S dynamic viscosity λ W/(mK) thermal conductivity ν m2/s kinematic viscosity ρ kg/m3 density ρ kg/m3 average density σ N/m surface tension ζ - fitting factor on steam velocity profile

Indices: a ambient b debris/fragments

bulk vapour/liquid part in vapour/liquid continuous regimes, respectively c cold conv convective d drop e entrainment f fluid (debris, cold and hot coolant) fb film boiling film film fr fragmentation h heated (hot) part of coolant htc heat transfer coefficient int interface intfric interface friction j jet k index for phase l, v KH Kelvin-Helmholtz l liquid lt liquid-transition / liquid continuous in transition regime lv liquid-vapour (interaction) m melt p particle rel relative s stripping sat saturation t transition v vapour vt vapour-transition / vapour continuous in transition regime 0 initial value

Dimensionless numbers: 2 Bo - Bond number, Bo = ρ ⋅v& ⋅ l / σ h ⋅ l Nu - Nusselt number, Nu = conv λ ν Pr - Prandtl number, Pr = κ v ⋅ l Re - Reynolds number, Re = ν

ρ ⋅v 2 ⋅ l We - Weber number, We = σ

Abbreviations: ABWR Advanced Boiling Water Reactor BWR Boiling Water Reactor CANDU CANada Deuterium Uranium DCH Direct Containment Heating EPR European Pressurised Reactor FCI Fuel-Coolant Interaction IKE Institut für Kernenergetik und Energiesysteme JRC Joint Research Centre KH Kelvin-Helmholtz LWR Light Water Reactor MBC Melt-Bottom Contact NRC Nuclear Regulatory Commission OECD Organisation for Economic Co-operation and Development PWR Pressurised Water Reactor RBMK Реактор Большой Мощности Канальный RDB Reaktordruckbehälter RPV Reactor Pressure Vessel SBWR Simplified Boiling Water Reactor SERENA Steam Explosion REsolution for Nuclear Applications SERG Steam Explosion Review Group SKI Swedish Nuclear Inspectorate TMI Three Mile Island

1 Introduction

1.1 Steam explosion as a subclass of fuel-coolant interactions in nuclear reactor safety considerations

A large part of electrical energy to-date is produced by controlled nuclear fission in nuclear reactors. The benefit of electrical energy produced in this way is mainly that the technology emits no greenhouse gases, which is a key issue considering the consequences of global warming. Larger commercial use of nuclear energy is suppressed mostly by controversial discussions about potential risk of nuclear reactors on both the public and the environment. In order to best consider the potential risks, nuclear reactor safety is of tantamount importance for the construction and operation of nuclear power plants. Nuclear reactors operate under extreme heat generation and transport conditions involving in particular, high pressures, high heat fluxes and the possibility of power excursions. Even after shutdown of a reactor, either by means of a regular or emergency stop, heat is further produced by the radioactive decay of the fission products i.e. decay heat. The decay power drops from about 6 % of the heat operating power directly after shutdown to approximately 1 % after one hour. From then, it continues to decay at a slower rate. As long as a nuclear core remains covered (flooded) with water, it cannot suffer damage due to the decay heating. In the commonly used various types of Light Water Reactors (LWR), this flooding is done by pumping cooling water via the primary circuit through the core, just as in normal operation. In spite of high safety standards, very unlikely failures considering the defect of all normal and emergency cooling systems may still occur. A prolonged lack of cooling would lead to the loss of core geometry and result in fuel melting, leading to severe situations. During a severe reactor accident, a molten core material could relocate in the lower plenum of the Reactor Pressure Vessel (RPV) or, in the case that a failure of the RPV cannot be excluded, it could be released from the RPV into the containment cavity. Taking into account the presence of water in the degraded/molten core or in the reactor cavity, this could lead to one or more energetic Fuel-Coolant Interactions (FCI). In safety studies of nuclear reactors, FCIs consider all the phenomena occurring after a contact of a molten core material with a much colder coolant. Steam explosions have been classified as a subclass of FCI. During a FCI, a huge amount of heat might be transferred from the molten material to surrounding water on a time scale of a few milliseconds or seconds, and

1 1 Introduction sometimes even hours. If the interactions occur in the millisecond range, it can lead to energetic steam explosions. During steam explosions, the heat transfer between molten material and water is so intense and rapid that the timescale for heat transfer is shorter than the timescale for pressure relief. This can lead to the formation of shock waves which can damage the RPV and containment integrity thereby producing a significant risk of release of fission products into the environment which is why these phenomena have been so widely analyzed in the past. The strength of steam explosions and resulting loads depend on the time in which energy transfer occurs, as well as on the amount of energy released in this time. Rapid heat transfer requires a rapid increase of the heat exchange surface (i.e. fine fragmentation of the melt) and a high energy release means that large masses of melt must be involved in this process. Rapid fine fragmentation of large masses cannot occur in a one-step process. Essentially, a large scale steam explosions progresses through two distinct phases, characterized by different time scales for the dominant processes i.e. the premixing and explosion phases. During the premixing phase the core melt flows into the water in the form of jets and is progressively transformed into droplets (in a range from a few millimetres to centimetres) which are dispersed into the two-phase coolant. The melt vaporises part of the coolant during this contact and stable vapour film boiling develops around the droplets. Due to relatively slow heat transfer between melt drops and water, such a mixture can be considered as stable against interactions (no liquid-liquid contact). All these major processes take place in a time scale from a few tenths of a second to several seconds. The explosion phase can be initiated by the destabilisation of the vapour film around the melt drops, leading to rapid heat transfer, a local pressure rise and fine fragmentation. This can generate shock waves which propagate at supersonic speed through the multiphase mixture producing further fine fragmentation (to sizes in order of some ten microns) of the melt inside the wave and corresponding increased heat transfer, thus supporting an escalation of the waves. A time scale characteristic for the explosion phase has an order of magnitude of a few milliseconds. In order to quantify the effects and strength of steam explosions, large experimental programs (e.g. FARO (Magallon et al., 1997), KROTOS (Hohmann et al., 1994)) and numerous small-scale and separate effect tests have been carried out. The results of these tests have been used for developing analytical simulation tools. Among them are IKEJET/IKEMIX and IDEMO computational codes developed at the “Institut für Kernenergetik und Energiesysteme” (IKE) in Stuttgart. IKEJET/IKEMIX simulates a break-up of melt jet coupled with a three-phase flow modelling of a particle–water–steam mixture in a 2D cylindrical geometry i.e. the

2 1 Introduction premixing phase of a steam explosion. On the other hand, the IDEMO code is a 2D, transient multi-phase model based on a thermal detonation concept developed in order to simulate the explosion phase with a primary emphasis on escalation and propagation. The overall objective is to reach a status in development of these codes which enables their application in obtaining a reliable estimation of the magnitude of FCI loads. The special emphasis is on understanding the key processes and energetics that are relevant for reactor applications.

1.2 Main limitations to steam explosion strength

Main limitations in obtaining vigorous steam explosions have already been identified to be established during the premixing phase. Namely, in realistic scenarios, the melt content in the mixture is already limited by the coarse jet break-up process, i.e. the amount of melt available for rapid heat transfer in an explosion (see e.g. Vujic et al., 2007). For example: a large melt pour (large diameter, high velocity) into water delivers a large amount of melt to the coolant, and thus yields the potential of extended and melt-rich mixtures. However, only partial melt break-up will occur by stripping of fragments and a higher release velocity will further limit this mass via means of a more rapid penetration to the bottom. It will promote the formation of smaller droplets from the higher steam velocity reached along the longer melt jet. The smaller the melt jet break-up droplets, the higher the heat transfer and evaporation will be, due to an increased interfacial area. There is a strong tendency towards void buildup in premixing due to high heat transfer from the hot melt (from radiation) and a limited steam removal from the mixture and water (due to interfacial friction). With a high void in an extended region around the inflowing melt, jet break- up will be less effective. Thus, strong void buildup additionally reduces a potential melt mass in the premixing phase. Additionally, during the premixing phase, formation of crusts at the surface of the falling drops of melt under film boiling is to be expected, especially for oxidic corium melt (i.e. oxidic corium melt is a mixture formed during a severe accident in nuclear reactors following core melting and composed mainly from UO2 (70 - 80 wt%) and

ZrO2 (30 - 20 wt%)). Low thermal conductivity of this material suppresses heat transfer from the inside of the droplet to the surface, supporting fast solid crust formation. Moreover, with relatively small melt drops from corium jet break-up, as obtained in the KROTOS experiments (Huhtiniemi et al., 1999) in comparison with alumina melt (Al2O3) and in strong subcooling conditions, the solidification effect is additionally emphasized. Solidification and crust formation at the surface of the falling melt droplets further limit heat transfer between melt and water and significantly decrease the possibility of fine fragmentation during the explosion phase. Already frozen melt is not able to participate in an explosion.

3 1 Introduction

During the explosion phase a major limitation to steam explosion strength is again given by a large void fraction in the mixture. Firstly, it limits the triggering potential by preventing direct melt/water contact. More important, the high compressibility of a mixture with a large void reduces the potential for escalation and propagation of explosion waves. In an explosion wave, according to the thermal detonation concept (see Chapter 2.3), the volume occupied by the steam first has to be compressed at the shock front before direct melt/water contact enables fine fragmentation and fast heat transfer from the fragments. This lowers the shock front pressure. In order to have a sustained or even escalating pressure wave it has to be driven from behind. This driving occurs within a self-escalating process, produced by the fine fragmentation and heat transfer in the wave, attached to the leading pressure peak or shock front. Since a higher void with a fixed shock front pressure yields a larger velocity difference between water and melt, thus producing a stronger hydrodynamic fragmentation, a higher void could even promote the escalation. However, the reduction of the shock front pressure due to high compressibility acts against it. It could only be maintained by additional driving from behind with unrealistically strong triggers.

4.0

3.5

3.0

Mixture 2.5 (melt droplets +steam+water)

2.0 Height / m

1.5

1.0 Pressure transducers Trigger 0.5

0.0 0.0 0.2 0.4 0.6 0.8 1.0 Radius / m

Fig. 1. Calculation domain used in IDEMO calculations for an assumed in-vessel case considering the given premixture with the different void concentrations of α = 0.3 and α = 0.7.

An example of the influence of a high voiding mixture on explosion strength is shown here by comparing two IDEMO explosion calculations for a given premixture with

4 1 Introduction different void concentrations considering an in-vessel case (see e.g. Fig. 3).

Homogenous mixtures are assumed with a melt volume fraction of α m = 0.03 and void volume fractions of α = 0.3 in the first, and α = 0.7 in the second case, concentrated in the central part of the calculation domain (Fig. 1). Fig. 2 shows pressure pulses obtained at different elevations (20 mm, 740 mm and 1488 mm, measured from the bottom of the RPV) along the side RPV wall versus time. In the first case with the smaller void concentration (Fig. 2a), escalation and propagation of the explosion pressure wave starting from the bottom (where triggering occurs) towards the side and upwards can be observed. Maximum pressure peaks are in a range of 25 MPa, with the relatively long duration of ~5 ms. In the case with the high void concentration (Fig. 2b), significantly smaller propagation velocities are obtained. Here the pressure wave approached the side wall first after ~6 ms as compared with ~3 ms in the previous case. Additionally, the higher compressibility of the mixture strongly counteracts to escalation and propagation of the explosion wave. Maximum pressures obtained are in the range of ~3 MPa. Explosion venting is another important limitation to explosion strength which has to be considered for the explosion phase. Firstly, it addresses pressure relief to lateral regions of the premixture through which the pressure wave is propagating and possibly escalating, or pressure relief by 2D/3D propagation and expansion of the wave (cylindrically or spherically). Secondly, reflections at free boundaries yield dilatation waves and weakening in the continued propagation and escalation itself or at least in the resulting pressure buildup.

1.3 Objectives of the present work

The central aim of the present work is the assessment of the knowledge on steam explosions and thus of the methods for the reliable prediction of loads under realistic reactor conditions. As a basis for present investigation, models for simulation of the premixing and the explosion phase of steam explosion are already available in IKEJET/IKEMIX and IDEMO codes, being under development at IKE. The objective is to reach a status, where the existing models and corresponding computer programs can be applied for risk analysis and management. Estimation of the potential pressure loads and resulting damage on reactor structures is to be made irrespective of the likelihood of such an accident having the potential for strong steam explosions. The emphasis here lies on the key FCI processes which are decisive for steam explosion strength, i.e. jet fragmentation under film boiling conditions, drag laws in a three-phase flow (melt, water and steam) and heat transfer from very hot melt to water in the premixing phase and fine fragmentation and rapid heat transfer in the explosion phase of steam explosion. In order to capture the essential features decisive for the explosion strength and to check the capabilities of the models to

5 1 Introduction reproduce them sufficiently, verification of the codes against specified and qualified experiments is to be performed. The task also considers improvements of the deficits in the existing models, observed during verification, in order to be able to extrapolate the achieved results to real accident scenarios in LWRs.

3.0*107 IDEMO/PT/Wall/20mm IDEMO/PT/Wall/740mm 2.5*107 IDEMO/PT/Wall/1488mm

2.0*107

1.5*107

7 Pressure / Pa / Pressure 1.0*10

5.0*106

0.0*100 0.0 0.005 0.01 0.015 Time / s

(a) 3.0*107 IDEMO/PT/Wall/20mm IDEMO/PT/Wall/740mm 2.5*107 IDEMO/PT/Wall/1488mm

2.0*107

1.5*107

7 Pressure / Pa 1.0*10

5.0*106

0.0*100 0.0 0.005 0.01 0.015 Time / s

(b)

Fig. 2. Pressure-time histories obtained at different elevations along the side RPV wall for the given premixture with void concentrations of α = 0.3 (a) and α = 0.7 (b)

Special importance is given to verification of the models describing the jet break-up and void formation during premixing, being identified as dominant limiting effects to strong steam explosions. Correct prediction of the void formation in the mixture during the premixing phase is required in order not to underestimate the danger of strong steam explosions. First IKEJET/IKEMIX calculations performed on the 6 1 Introduction experiment FARO L-28 (Silverii et al., 1999) showed a significant overestimation of the void in comparison with experimental data (see Chapter 4.2). The reason was identified as a deficit in steam release, due to the modelling of interfacial friction, depending on the flow pattern. Namely, an average steam velocity is used for both partial patterns in a transition regime (i.e. in a water continuous and steam continuous range), thus not allowing more rapid release via the steam continuous part (steam channels). Therefore, present modelling efforts required an improvement in order to allow for a more rapid steam release from the mixture. The correction itself is based on an assumption that separate steam velocities in both of partial patterns exist and have since been implemented in the IKEJET/IKEMIX code. After improvement, comparison calculations with regard to FARO L-28 experiment are to be carried out. Furthermore, the thermal detonation code, IDEMO, is to be verified before code application to reactor conditions and detailed estimation of explosion loads can be carried out. The main uncertainties with this respect are related to different explosivity between prototypic and simulant materials obtained from FARO and especially KROTOS experiments (Huhtiniemi and Magallon, 2001). While experiments using corium melt only weak explosions have been observed, tests with alumina showed strong explosions with clearly detectable escalating and propagating waves. This difference can be attributed to specific experimental conditions (low melt mass, high melt entrance velocity) accentuating differences in break-up related to the melt density. They lead to a significantly different premixing behaviour with much smaller droplets with corium and consequently much higher void buildup. First IDEMO calculations, performed for the given premixtures on the experiments FARO L-33 (Magallon and Huhtiniemi, 2001), with corium, and KROTOS K-44, alumina experiment (Huhtiniemi et al., 1999), showed the inability of the model to reproduce the differences in explosion loads using the same set of numerical parameters (see Chapter 5.3). Experimental results could be reached by assuming slower heat transfer from fragments to coolant. The difference could be explained considering that partial freezing of melt droplets during the premixing phase was not taken into account. Assuming that no additional differences than those already included in the modelling exist between different materials during the explosion phase (i.e. especially concerning fine fragmentation), the capability of the code to reproduce this different behaviour using unique descriptions is to be aspired. After the verification of the models and setting up the numerical parameters, calculations are to be carried out considering a realistic accident scenario. The aim is to investigate the most challenging case with a potential for the most vulnerable steam explosion under the given conditions. With this respect, different parameters as the melt flow rate, the melt diameter, the water level, the possible lateral extension of the mixture and the time of explosion triggering are to be varied

7 1 Introduction according to realistic boundary conditions during severe accidents in LWRs.

1.4 Approach and outline of the present work

First, an overview of the state of art is given. The possible scenario of a severe accident in an LWR is described which could result in one or more strong steam explosions (both in-vessel and ex-vessel). Furthermore, a short history of steam explosion investigation, as well as modelling approaches followed in computer codes for simulation of FCIs, are given as a closure of Chapter 2. In Chapter 3, the IKEJET/IKEMIX model, which describes the processes of the break- up of a molten jet falling into a water pool, stripping of melt particles, their cooling and formation of a premixture, is presented. The resulting governing equations are given together with a description of the numerical solution methods. Additionally, detailed description of the improvements of the model for interfacial friction between steam and water as well as its comparison with previous modelling approaches is presented. In the next chapter, the validation of improved models with the experiment FARO L- 28 is shown, considered as adequate to describe the void effect without overestimation as well as pressure buildup, heat transfer and jet break-up. Chapter 5 is devoted to verification of the 2D-thermal detonation model, IDEMO, especially regarding the different explosivity between alumina and corium melts obtained in the selected experiments. Calculations have been performed for the FARO L-33 and KROTOS K-44 tests. Chapter 6 contains applications of the verified models (both IKEJET/IKEMIX and IDEMO) to an in-vessel case assuming sideways jet outflow from the reactor core into saturated water in the cavity. Calculations are carried out in order to gain a perspective of the limitations to explosion strength and additionally on the resulting loads due to void production and jet break-up. It was attempted to estimate as strong as possible steam explosions under given conditions and to assess the resulting pressure loads. Finally, in the summary and conclusion, the major results are discussed with respect to the main limiting effects for obtaining strong steam explosions. Further perspectives for improvement and completion of modelling are outlined. Appendix A contains a detailed description of the models which are implemented in the thermal detonation code, IDEMO. In Appendix B initial conditions - estimated from the experimental data and used for verification calculations of the IDEMO code - are presented.

8 2 Investigation of steam explosion phenomena - State of the art

2 Investigation of steam explosion phenomena - State of the art

2.1 Possible accident scenarios leading to steam explosion in LWRs

The emphasis here is mainly on LWRs, considering two major reactor designs i.e. the Pressurised Water Reactor – PWR and the Boiling Water Reactor – BWR, which are nowadays the most common types of nuclear reactors worldwide. The Canadian CANDU reactor and the Russian RBMK designs are not considered, taking into account their different design and specific construction. According to the place of occurrence, the description of a severe accident can be roughly divided into in-vessel and ex-vessel phenomena. Here, accident scenarios are presented which may yield a potential for an energetic FCI, together with accident management procedures foreseen in order to prevent such accidents or to decrease their consequences for both PWRs and BWRs alike.

2.1.1 In-vessel phenomena

A very unlikely severe accident may occur in the case that all normal and emergency cooling systems fail. If the core is not sufficiently cooled by water, the decay power of the fission products in the fuel can heat up the reactor core and evaporate the water causing a decrease of water level in the RPV. Depending on the accident development and reactor design, the core will dry out after one to several hours, beginning at its upper regions. At low system pressure the core would heat up in an essentially adiabatic fashion, whereas under high pressure high density of steam supports redistribution of heat (by natural circulation) inside the core and the other parts of a primary system. Cladding at temperatures higher than ~1200 C reacts with steam in a highly exothermic manner that will further accelerate the rate of heating. Other low melting components, such as the control rod materials (silver, indium, cadmium, boron) and stainless steel, behave in the same manner, leaving behind the stack of uranium dioxide pellets which are readily reduced to rubble. Several other processes, such as candling of melt (i.e. downflow of melt along the rods under repeated freezing and melting) or the dissolution of fuel by metallic melt, occur in this stage. They are described in details by Buck (2007). The core in this stage of a severe accident may still be coolable if the cooling systems of the reactor can be re-established. However, in the continued absence of water, the temperature of the dry portions of the core will continue to increase, resulting in the melting of the core materials themselves. Molten material can

9 2 Investigation of steam explosion phenomena - State of the art relocate axially under gravity within the available open spaces, which are of a very small characteristic dimension, equal to the initial coolant channel (~1 cm). Due to later dryout and additional heat sinks provided by structural materials (mainly steel), the temperatures in lower core regions are expected to be significantly smaller in comparison with the upper parts of the core. This gives the opportunity for freezing and plugging of the relocated melt. The stability of a resulting crust configuration depends on the cooling from below by conduction, radiation and steam flow. In principle, two different scenarios may be considered. At one extreme, no cooling from below will prevent crust formation and a gradual relocation of the molten material (as it melts) into the lower plenum will occur. At the other, excessive cooling from below provides the potential for accumulation of large quantities of melt in the core region (i.e. a melt pool will be formed), supported by a crust, as in the case of the Three Mile Island (TMI-2) accident (Akers, 1992). The stability of the crust depends on the heat flux distribution at the pool inner boundaries and the extent of external heat removal. However, if the thermal loads are high enough to fail the support of melt pool, depending on the type and location of the failure, three major modes of melt release from the melt pool to the lower head of RPV are possible: melt outflow in the form of several jets through the lower grid plate due to crust failure in the bottom central part of the pool, a massive splash of melt due to an extended failure of the lower grid plate and other lower core support structures and a sideways melt release due to crust failure in the upper region, provided by natural convection in the melt pool, yielding highest temperatures at the top (Buck, 2007). When melt is released from the PWR core, it interacts with residual water in the lower head resulting in jet fragmentation, yielding droplets in the order of magnitude from 1 to 10 mm (according to FARO and KROTOS experiments). There are two main points of concern here. The first addresses the formation of a debris configuration (e.g. particulate debris) due to fragmentation and quenching of the melt. Only part of the total mass of the core can be quenched by the residual water in the lower head. If additional water cannot be supplied, or a configuration which is established during melt inflow into water can not be cooled (e.g. large unfragmented parts or small particles yielding a small dryout heat flux), the water will boil off and the debris will re-melt and relocate, resulting in a melt pool. The vessel wall will be attacked and weakened by the hot melt, leading to a lower head failure. The coolability of debris bed is discussed in details by Schmidt (2004). The other point of concern is the possible occurrence of energetic FCIs provided by an interaction between melt and water. Considering the safety of nuclear reactors, the primary concern of such an “in-vessel steam explosion” (see Fig. 3) is whether

10 2 Investigation of steam explosion phenomena - State of the art such explosions can generate missiles, destroy the upper head of the reactor vessel and be energetic enough to cause a containment failure. This, so-called α -mode containment failure issue has been successfully resolved. However, concern about strong steam explosions which could fail the RPV still exists. The intensity of steam explosion depends on several parameters (e.g. melt flow rate, water level, water temperature, system pressure etc.) which determine the way of premixing between melt and water. As it is mentioned above, strong limitations to steam explosion loads are identified to be provided already in the premixing phase, limiting the mass of molten material which can be mixed with water without too high a void. It is stil unclear if these limitations could suppress strong steam explosions and avoid loads which could damage the RPV. As an accident management procedure foreseen to prevent a lower head failure, cooling of the vessel together with an inner melt pool from outside is considered, by immersing it in water i.e. “in-vessel retention”. Such external flooding can be assured by proper arrangement of the containment volumes and ensuring that sufficient quantities of water are available. In the absence of ex-vessel cooling the lower head will fail thermally in any case, leading to melt outflow from the RPV.

Fig. 3. Scheme of a potential in-vessel steam explosion scenario with a sideways melt jet outflow.

Considering boiling water reactors (BWR), large melt accumulations in the core region could be excluded unless a metallic or ceramic blockage occurs. The possibility of an energetic in-vessel steam explosion is significantly reduced due to automatic depressurisation system which will result in core dryout prior to any large melt relocation. In addition, a densely packed lower plenum has a certain suppression

11 2 Investigation of steam explosion phenomena - State of the art effect on energetic steam explosions. However, explosion intensity could be supported due to chemical energy release produced by the interaction between metallic melt and water.

2.1.2 Ex-vessel phenomena

If a failure of RPV occurs under high system pressure conditions (e.g. by a station blackout accident where the coolant gradually boils off through the safety valves, which cycle around their set point, thus maintaining the reactor at a pressure somewhat higher than the normal operating level), melt ejection could be rapid and followed by very intense steam blowdown. In the relatively confined space of a reactor cavity this would give rise to velocities high enough to atomize and entrain the melt, thus opening a number of serious containment loading mechanisms. They include dispersed flow with liquid films along the walls, heat transfer and exothermic chemical reactions that have significant influence on further processes and eventually on the discharge and thermal/chemical interactions with the atmosphere and hydrogen combustion. Combined, these phenomena are known as Direct Containment Heating, or DCH. It is to be mentioned that these high pressure scenarios can and must be avoided by safety systems which consider depressurisation of the RPV well before any significant core degradation, as for example in the advanced passive plants e.g. AP-1000, SWR-100 and AB-1600.

Fig. 4. Scheme of a potential ex-vessel steam explosion scenario with a sideways melt jet outflow.

12 2 Investigation of steam explosion phenomena - State of the art

If pressures inside and outside the RPV are equal at the moment of RPV failure, the melt relocation in the “reactor cavity” will occur by gravity. The outflow will most likely be in a form of a sideways jet in an upper region of the melt pool, caused by natural circulation that yields highest temperatures on the top. The reactor cavity, i.e. the volume below the RPV in an LWR can be placed low in the reactor containment and, by this, the external flooding required for the in-vessel retention is relatively easy achievable. This is straightforward in some of PWR designs, as in the case of Loviisa (a Russian PWR in a Westinghouse ice condenser containment) currently operating in Finland, and AP-1000 (an advanced passive PWR in a large dry containment) designed by Westinghouse. On the other hand, BWRs, due to bottom inserted control rods, have RPV placed at much higher position above the floor and they are quite variable in this aspect of their containment designs. In some, the cavity is separated into a drywell, and the volume below is part of the pressure suppression pool, while in others this pool is found around the lower drywell volume. This lower drywell volume, however, depending on the design and accident, may or may not be flooded at the time when melt is released into it. For example, in BWR with Mark-I type containment, cavity flooding (relatively shallow) is recommended to prevent an early failure of the containment liner. The Swedish Nuclear Inspectorate (SKI) has adopted deep water cavity flooding as an accident management strategy for operating BWRs in Sweden. In Advanced Boiling Water Reactors (ABWR), deep water cavity flooding is a design feature to prevent or to mitigate the consequences of melt-concrete interactions. The presence of water within the reactor cavity significantly increases the possibility for occurrence of energetic steam explosions (i.e. “ex-vessel steam explosions”, see Fig. 4). Such strong explosions could destroy the containment or the supporting structures and allow release of fission products to the environment. Again, as in the in-vessel case, major uncertainty is related to the existence of mixtures which include large quantities of melt mixed with water under limited void, providing a potential for vigorous steam explosions.

2.2 History of investigation and resolving of the so-called “alpha-mode containment failure”

The history of investigations on the risk of steam explosions in LWRs has been summarised in detail by Speis and Basu (1997). First identification of an in-vessel steam explosion in LWRs as a potential cause of an early containment failure was provided more than 30 years ago in Reactor Safety Study (U.S. Nuclear Regulatory Commission, 1975). It was roughly estimated that kinetic energy produced during an intensive in-vessel steam explosion could be sufficient to breach the upper head of the RPV and to yield an upward missile which could penetrate the containment. This

13 2 Investigation of steam explosion phenomena - State of the art potential early containment failure was designated in the Reactor Safety Study as the alpha-mode (α -mode) containment failure. Following the Reactor Safety Study, main efforts have been focused on investigation and better understanding of the α -mode failure, in particular, in relation to containment failure probability. Early steam explosion studies performed by Henry and Fauske (1981) and by Corradini and Swenson (1981) were used for the Zion and Indian Point plant risk assessment (Meyer et al., 1981). They concluded very low likelihood of an α -mode failure for these plants. On the other hand, the first thermodynamic evaluation of steam explosion has been reported much earlier by Hicks and Menzies (1965). They estimate the maximum work potential available when a certain mass of melt at very high temperature interacts with a certain mass of water at low temperature. This gave an upper bound for the work potential of an explosion and the theoretical conversion ratio of about 0.3. It was estimated under the assumptions that a steam explosion is ideally composed of two steps: an ideal mixing (i.e. instantaneous and without heat losses) of two materials leading to temperature equilibrium and to a high–equilibrium pressure for the mixture, and an isentropic expansion of the mixture in which the temperature equilibrium is maintained. Thus, taking into account an ideal thermodynamic conversion estimated by Hicks and Menzies and considering mixing of 20 tons core debris (quantity relocated during TMI-2) with an equal quantity of water, the mechanical energy which could be released is in the order of magnitude of around 7 GJ. It is estimated also that the energy necessary to fail the upper head bolts is in a range between 1 and 2 GJ (Speis and Basu, 1997). Considering no dissipation of energy and if only axial motion occurs (i.e. doing work in one direction), the possibility of a missile formation from vessel upper head impact becomes evident. On the other hand, if only part of the released melt is mixed with the water and if the thermodynamic conversion is less than ideal, the threat for the vessel or containment integrity is significantly reduced. Hence, the probability of α -mode failure depends very much on the extent to which “ideal” premixing and “ideal” thermodynamic conversion are achievable. In WASH-1400, the α -mode failure probability (i.e. conditional probability of containment failure from an in-vessel steam explosion, given a core melt accident) is conservatively estimated to be in the order of 10-2. Moreover, a later study of PWR steam explosions performed by Berman et al. (1984) proposed that the probability of such events must be considered to span the entire range between zero and one. In order to clarify the potential risk of α -mode failure, a first Steam Explosion Review Group (SERG-1) workshop was held in 1985 in the United States. The aim of this 14 2 Investigation of steam explosion phenomena - State of the art workshop was to evaluate more systematically the α -mode failure issue. Experts contributing to this workshop have summarized present knowledge on steam explosion phenomena and have concluded that α -mode failure has very low probability despite all uncertainties related to this topic. However, they recommended additional research in order to decrease identified uncertainties and to achieve high confidence level in the assessment of the probability. After the SERG-1 workshop, it became evident that a proper assessment of the α - mode failure requires a proper understanding and quantification of melt/water configurations during pouring of melt into water (i.e. premixing), as well as better estimation of released mechanical energy (estimation of a conversion ratio). Since the SERG-1 workshop, the aim of investigations on steam explosion phenomena have mainly focused on understanding of the fundamental processes involved in energetic FCI (i.e. premixing, triggering, propagation and escalation, see below). Numerous experiments and theoretical investigations have been performed in order to achieve a better understanding of the α -mode failure issue under reactor safety perspective. In order to summarise achieved knowledge on steam explosion phenomena and to discus remaining uncertainties, the Nuclear Regulatory Commission (NRC) convened the second Steam Explosion Review Group (SERG-2) workshop, held in June, 1995 in the United States. A group of eleven experts from academia, industry and the research community have concluded that the α -mode failure issue is “essentially” resolved considering a very low probability of such an event. Furthermore, it was agreed that α -mode failure is of little or no significant importance on nuclear power plant safety and that remaining uncertainties can’t change the probability in an appreciable manner. The consensus opinion of the experts was that the combination of events leading to α -mode failure would be highly unlikely taking into account fuel/coolant mixing, steam voiding and water depletion phenomena (i.e. high void in the mixture). It was also concluded that conversion ratios obtained in experiments (0.3 to 3 %) are much lower than ideal thermodynamic conversion ratio of approximately 30 %, estimated by Hicks and Menzies (1965). Though the current understanding of steam explosion phenomena was sufficient to exclude the possibility of an α -mode failure, an improvement in the understanding is required with respect to other FCI issues. It is still unclear whether an energetic in- vessel steam explosion could produce a failure of reactor pressure vessel and whether ex-vessel steam explosions could produce shock loading of the cavity support structures and containment failure, thus giving the possibility for the release of fission products into the environment. For final clarification, a further development of multidimensional, multifield FCI codes and assessment of these codes against experimental data are required.

15 2 Investigation of steam explosion phenomena - State of the art

2.3 Current understanding of steam explosion phenomena

Current understanding of the steam explosion phenomena is based on the achievements of Board and Hall (1976), known also as “thermal detonation” concept, being nowadays widely accepted in the FCI community. It considers steam explosion progress through two distinct phases, characterised by different time scales for the dominant processes: premixing and explosion phase. In the premixing phase, where the major processes take place in a time range of few tenths of seconds to several seconds, the melt is premixed with water on a relatively coarse scale, yielding pre-fragmented melt droplets in the range of few millimetres to centimetres. High heat transfer from the melt to the water produces a vapour film around the melt droplets. These vapour films reduce heat transfer between two liquids and delay quenching of the melt and formation of crusts on the droplets. In this stage, the mixture is quasi-stable.

Fig. 5. Schematic sketch of a thermal detonation model.

In the explosion phase (see Fig. 5), a large part of the internal energy stored in the melt is transferred to the coolant in a time scale of few milliseconds and a length

16 2 Investigation of steam explosion phenomena - State of the art scale of meters. Concerning the explosion processes, triggering, escalation/propagation and the expansion phase can be distinguished. Triggering is an event which causes the destabilisation of the vapour film around melt droplets allowing direct liquid-liquid contact. Such events may be due to different mechanisms, as for example pressure pulses caused by impact (e.g. when the melt touches the bottom of the vessel) or from entrapment of water in the melt. Direct liquid-liquid contact allows high heat transfer rates yielding a local rapid pressure rise, followed by fine fragmentation of the melt. It is thought that with relatively small triggers at first, fine fragmentation results mainly from the above mechanism, also known as thermal fragmentation. Later, when the pressure pulses increase, the fine fragmentation is driven directly by the relative motion between the melt and the coolant induced by their different densities and compressibilities i.e. by hydrodynamic fragmentation. The debris produced by such fine fragmentation processes is in a size range of 100 µm. Due to larger melt surface area, the heat transfer rates increase strongly. As the energy of melt is rapidly transferred to the coolant by this mechanism, high pressure is built up and finally high-pressure steam results in the expansion process, yielding damaging work to surrounding structures.

2.4 Modelling approaches for steam explosion analyses codes

Numerous computational codes have been built in the past and they are still under development in order to improve the understanding of basic processes related to steam explosion phenomena. Overviews of the models used for simulation of key processes during steam explosion have been given by many authors (e.g. Berthoud, 2000, Meignen and Magallon, 2005, etc.). Here, the key physics for the different phases of a steam explosion, as used by most computational codes nowadays, will be presented.

2.4.1 Premixing

It has long been recognised that premixing is necessary for steam explosions involving tons of melt. There are three main modes of contact between melt and water: the melt can be poured into the coolant in the form of jets, which is the most common situation, the coolant can be injected into the melt, which is less probable to yield a large mixture, considering thermal and density effects (melt is denser than coolant) and melt and coolant can exist in a stratified geometry.

17 2 Investigation of steam explosion phenomena - State of the art

From a reactor safety point of view, bringing large quantities of already prefragmented melt into a contact with water and their mixing under limited void provides the largest potential for the most vigorous steam explosions. Thus, the emphasis here is on the first mode of contact. The problem of premixing between melt and water has been treated in two different ways which, taking into account that this is the initial phase of FCI, could have significant influence on subsequent behaviour of steam explosions. One is based on the consideration of pouring of already pre-fragmented particle clouds with certain melt volume fractions, particle diameters and particle velocities into water. Leading numerical tools in this approach are: PM-ALPHA (Amarasooriya and Theofanous, 1991), CHYMES (Fletcher and Thyagaraja, 1991), TEXAS (Tang and Corradini, 1993) and EVA (Jacobs, 1993). The opposite point of view is based on the jet break-up behaviour in a quasi-two-dimensional treatment. The most representative codes concerning this approach are: THIRMAL (Sienicki et al., 1993), IKEJET (Bürger et al., 1993), MC3D (Berthoud and Brayer, 1997), VESUVIUS (Vierow et al., 1997) and JASMINE (Moriyama et al., 1996). Promoters of the purely drop flow argue that the melt break-up is caused mainly due to fragmentation at the leading edge through Rayleigh-Taylor mechanisms. With this hypothesis, the use of drops is legitimate and leads to a leading edge fragmentation (Meignen and Magallon, 2005). On the other hand, modelling of jet break-up is based on assumption that fragmentation takes place all along the melt jet, mainly due to Kelvin-Helmholtz instabilities. The different approaches of melt break-up lead also to a different drop size distribution and melt particles dispersion which could be decisive for formation of “explosive premixtures”. It is to be mentioned that jet break-up models also consider radial dispersion of melt particles, which is not taken into account in the other approach. Moreover, leading edge fragmentation can be introduced in jet models. However, both methods of melt break-up modelling are still lacking in both formulation and in their constitutive laws. Considering extrapolation and code application to realistic accident scenarios, the understanding of melt jet break-up together with premixing behaviour between melt droplets and water could be crucial in assessing the limitations to strong steam explosions. As it was already mentioned previously (Chapter 1.2), incomplete jet break-up is one of the main limiting effects (besides partial freezing and high void) to the formation of large explosive mixtures e.g. as in the case of increased melt flow rates due to larger jets and higher outflow velocities. Therefore, the description of premixing has to provide a good basis for estimation of melt jet break-up and coarse mixing (i.e. spatial distribution of melt, steam and water).

18 2 Investigation of steam explosion phenomena - State of the art

2.4.2 Melt jet fragmentation

A review on possible jet break-up mechanisms can be found, e.g. in (Ginsberg, 1985, Bürger et al., 1995 or Vierow et al., 1997). Ginsberg’s review was the first one performed to evaluate jet break-up specifically for severe accidents applications and is used as a standard reference for many jet break-up models. The different jet break-up mechanisms in isothermal conditions are classified in terms of their dependence on ambient Weber numbers. According to Ginsberg (1985), the jet might be fragmented by following mechanisms: for low We numbers (We < 0.4), fragmentation of the jet takes place in Rayleigh regime. Shear forces may be neglected due to the low relative velocity and surface tension is the primary force governing break-up (varicose type, Fig. 6). Increasing of the We number (0.4 < We < 1), fragmentation takes place in a transition regime in which the effect of surrounding fluid becomes important. Behaviour in this regime is governed by the balance between surface tension and viscous shear forces yielding drops in order of magnitude of the jet diameter (sinous type, see Fig. 6). For high We numbers (1 < We < 100), fragmentation of the jet takes place in a turbulent regime. General characteristic of this regime is that instead of only coarse, core break-up, surface break-up is also evident. Also the grater inertia of the jet promotes further penetration into the surrounding fluid (see Fig. 6) An ambient We of ~100 may be taken as a condition for entering the atomization range with intense spray production just beginning at the outlet (see Fig. 6). As another possible jet break-up mechanism, Taylor instabilities at the leading edge, due to deceleration of the jet in the surrounding medium, may also be considered (Wang, 1988). In comparison with the stripping along the jet surface which is mainly dependent on existence of strong relative flows parallel to the jet, the effectiveness of Taylor instabilities depends on the occurrence of strong deceleration effects. While both mechanisms may act in a combined manner, phases with strong relative flows may persist longer than phases with strong decelerations. Thus, Taylor instabilities can be decisive for the jet break-up only during the short, initial phases of melt- coolant interactions. Additional aspects with respect to the differences between experimental conditions and real accident conditions must be taken into account. In the real severe accident scenario, corium will be superheated and at extremely high temperatures. Therefore, a thick vapour film formation around the jet is to be expected. Furthermore, the

19 2 Investigation of steam explosion phenomena - State of the art break-up regimes will be determined by the vapour flow, and according to estimations of Ginsberg (1985) the atomization regime may be established for conditions relevant during core-melt accident. The first model describing the melt jet fragmentation by the stripping of Kelvin-Helmholz instabilities along the jet tail, which takes into account the thickness of vapour film was developed by Epstein and Fauske (1985). They derived correlations for the jet penetration distance in the limits of thin and thick vapour films. In other words, they showed that in the thin film case, the water density determines the behaviour, whereas in the thick film case, melt jet break-up is determined by the vapour properties. On the other hand, during the melt jet penetration into water, also thermal interactions may occur due to local film collapses, especially at the leading edge of the jet. This can be caused by the thinning of the film at the leading edge due to increased pressure and especially by Taylor instabilities at the water/steam interface in this regime. However, no clear experimental indications about significant importance of thermal fragmentation effects in the conditions of thick vapour film exist (Bürger et al., 1995). Thus, the emphasis here with respect to governing jet break-up mechanism is mainly on hydrodynamic fragmentation models.

Fig. 6. Classical jet break-up types (Bürger et al., 1995).

Concerning the modelling used in IKEJET/IKEMIX code, different mechanisms of break-up of melt jets in water were discussed in the past and were also described in the IKEJET break-up model. Major approaches concerned are, firstly, the leading edge break-up by Rayleigh-Taylor instabilities of stripping of material after vortex formation, and secondly, stripping of waves at the lateral jet surfaces produced by Kelvin-Helmholtz instabilities in the parallel fluid flow. Comparison of calculations on 20 2 Investigation of steam explosion phenomena - State of the art the different mechanisms (e.g. Bürger et al., 1995 and Hohmann et al., 1995), taken separately and in an integrated model, have shown the mechanism based on Kelvin- Helmholtz instability as most effective, thus largely determining the break-up. Lateral stripping based on Kelvin-Helmholtz instabilities must essentially occur in the upwards stream of mixture fluid (mainly steam) around the melt jet produced rapidly. In initial stages, with strong jet deceleration and vortex formation at the leading edge, although less pronounced with high-density melts as corium, Rayleigh- Taylor instabilities and vortex stripping may contribute. However, modelling based on this was not able to adequately describe the continued pressure development as in FARO L-28 (see Chapter 4). Thus, the present break-up modelling in IKEJET is solely related to the lateral stripping based on Kelvin-Helmholtz instability in thick vapour film conditions. A detailed description of the jet break-up model is given in Chapter 3.1.

2.4.3 Triggering

The trigger is the event that induces the transition between the premixing and the explosion phases due to rapid heat transfer and local pressure rise which will eventually escalate during its propagation through the mixture. It is associated with the local collapse of the vapour film surrounding a melt droplet, followed by rapid fragmentation of the droplet. Two principal mechanisms as well as several variations of these two have been proposed for triggering (see e.g. Corradini et al., 1988). Firstly, it may occur if the melt surface temperature falls below the minimum film boiling temperature, resulting in vapour film instability. This mechanism has been observed in several experiments using simulant materials (e.g. Dullforce, 1976), but this hypothesis may not be applicable to reactor cases since the melt remains at relatively high temperatures during interaction with the coolant. In reactor situations, the interfacial instability is more likely to be caused by a pressure perturbation, a flow perturbation or a local coolant entrapment. Numerous events can contribute to such actions (e.g. when melt touches the bottom of RPV/cavity, sudden valve closure, pump cavitation, collapsing structures, condensation etc.). Pressure and water perturbations may induce motions inside the mixture that result in vapour film instability. This may lead to direct contact between melt and water and thus the triggering occurs. In the case that the water is entrapped within the melt or against the vessel wall its temperature rises to the homogeneous nucleation temperature, at which point it flashes into steam, throwing the surrounding melt into contact with water. Explosions which result from a known trigger are usually known as triggered explosions while those occurring due to some uncontrolled event are usually referred to spontaneous explosions. If the trigger is provided by some artificial means (e.g. a

21 2 Investigation of steam explosion phenomena - State of the art detonator, release of compressed gas), the explosion is said to be externally triggered (as often applied in steam explosion experiments). As a dominant mechanism during this phase, a thermally induced fragmentation is considered. Nevertheless, the key physics describing a collapse of the vapour film and further fragmentation of melt droplets is still not completely clear. Taking into account the complexity and uncertainties related to the triggering process, it becomes clear how difficult is to model and quantify it. Therefore, from the reactor safety standpoint, there is a consensus to support a conservative approach for triggering i.e. that trigger would be available under accident conditions of interest and that an explosion would be triggered at the worst time during a premixing transient. With regard to modelling of steam explosions it is assumed that sufficiently strong trigger is applied to induce an explosion. After “successful” triggering of a steam explosion, the escalation and propagation phase takes place. The pressurisation caused by the trigger will destabilise vapour film around the melt droplets and induce more fine fragmentation, followed by increased heat transfer and consequential vaporisation. The key processes describing this are then the identity and kinetics of fine fragmentation mechanisms during escalation and propagation and heat transfer from the fragmented debris to the liquid coolant into which they are ejected.

2.4.4 Fine fragmentation

It is accepted, in general, that initiation (i.e. triggering and early phase of escalation stage), when the pressures are not too high, are dominated by thermal fragmentation. In the later phase of FCI, when the shock wave is fully developed (propagation stage), hydrodynamic fragmentation is considered as a driving mechanism. Hydrodynamic fragmentation is caused by the difference in relative velocities between melt drops and coolant, induced by strong pressure waves. Once again, there are different opinions about dominant hydrodynamic fragmentation mechanism. Two, widely accepted approaches are: Rayleigh-Taylor instabilities on the windward side of the melt drops due to the acceleration by the ambient coolant flow (if the melt has a higher density than the surrounding coolant), proposed by Chen et al. (1995). The leading numerical tools using this model are ESPROSE and TEXAS (Tang and Corradini, 1993), and stripping of fine droplets by boundary layer effects and surface instabilities (Kelvin-Helmholtz type), based on Pilch’s (1987) correlation. The most representative codes using this approach are: MC3D (Berthoud and Brayer, 1997), CULDESAC (Fletcher, 1991), IFCI (Young, 1987) and

22 2 Investigation of steam explosion phenomena - State of the art

IDEMO (Buck and Bürger, 1997). Detailed descriptions of the fine fragmentation model based on Kelvin-Helmholtz instabilities, as proposed by Bürger et al. (1986) and implemented in IDEMO, as well as its variations, which are used in the other numerical tools, are given in Appendix A.

2.4.5 Heat transfer between fine fragmented melt and coolant

In order to obtain rapid escalation after “sufficiently strong” triggering, it is necessary to achieve high heat transfer rates. They are partly produced by large surface area given by fine fragmentation of melt droplets. Also, considering the ongoing production of new melt-coolant contacts, it is expected that transiently high heat transfer coefficients can be obtained. Taking into account this transient aspect, it is assumed that the coolant temperatures in the interaction zone may not be uniform. The two most commonly used approaches are based on this assumption. They are the non-equilibrium concept proposed by Berthoud and Brayer (1997) and the so- called micro-interaction concept proposed by Chen et al. (1995) and Yuen and Theofanous (1993). In the first approach, the fuel drops give heat to the coolant in a finite time scale according to the local conditions. This heat is further transferred into vapour generation either by a non-equilibrium balance at the coolant interface, or by a parametric partition. The pressure buildup here is linked to the phase change. A heat transfer coefficient between fuel drops and interface and between interface and bulk coolant has to be provided. They are deduced from the experiments in which the transient quenching of a hot material in water is investigated (Inouse, 1982, Derewnicki and Hall, 1982 and Honda et al., 1993). The second approach is based on the conceptual picture that the heat of the fragments is transferred only to a part of the coolant in a “micro-interactions” zone surrounding the fuel drops, while the other “cold” part, which is “too far outside”, is not heated. The micro-interactions zone grows with time as cold coolant is entrained into it, due to mixing. Transferring the heat of the fragments to only a part of the coolant will yield a stronger heat-up of this part, with correspondingly stronger increase of specific volume (even much stronger in case of phase change), which in turn leads to larger pressures. This concept has also been adopted for IDEMO. A detailed description of this model is provided in Appendix A.

23 3 Description of the premixing model IKEJET/IKEMIX

3 Description of the premixing model IKEJET/IKEMIX

The model IKEJET/IKEMIX is being developed at IKE in the scope of the KESS code system. The KESS system consists of several modules developed in order to simulate the processes of core melting, relocation of core material to the lower head of the RPV and its further heatup as well as modelling of fission products release and coolability of the core material. Several of these modules are also included in the German system code ATHLET-CD. The integral module IKEJET/IKEMIX describes the break-up of a molten jet plunging into a water pool, the cooling of fragments and the formation of particulate debris beds. In the present study emphasis is layed on the processes related to jet break- up, the falling of stripped melt particles into water, their cooling and the formation of a premixture, rather than on formation of a debris bed. These processes have been calculated by two coupled modules. Mixing of melt and water is simulated with IKEMIX in a two-dimensional, cylindrical geometry. Here, three phases are considered: melt drops, liquid water and steam, each having separate velocities and temperatures. In IKEMIX, the jet is treated as a line source of drops of melt. On the other hand, the coherent jet length and the local rate of mass release as well as the sizes of released drops are determined separately in the module IKEJET; they depend on the conditions around the jet calculated with IKEMIX. Thus, feedback is accounted for the jet break-up process which determines the drops of melt of the resulting mixture and the mixture conditions, which then are used to determine the jet break-up. The coolant phases are modelled according to the quasi-continuum Eulerian approach, while the drops have been described by the discrete Lagrangean method. In the latter, the behaviour of characteristic particles is modelled, which are representative for a group of particles with similar properties (size of particles, initial conditions). These particles are subject to body and friction forces as well as heat transfer in the coolant flow. Feedback to the coolant is provided by considering the transferred momentum and heat in the respective conservation equations of the coolant phases.

3.1 Jet model and melt break-up

The jet behaviour is described by a separate model for a representative jet, which yields the jet penetration in water (jet diameter vs. length, coherent jet length) and the fragmentation rate as well as drop sizes along the jet. Actual jet lengths and the local distribution of fragmentation rates, together with resulting drops sizes along the

24 3 Description of the premixing model IKEJET/IKEMIX jet are transmitted to IKEMIX as a line source of fragments. Fragmentation is mainly modelled due to steam flow along the jet. A separate steam flow description is applied, for which in the present simplified approach a hydrostatic head of a water- vapour mixture close to the jet is considered to yield the driving forces. By balance with the inertial forces of the steam, the steam velocity is determined (see Eq. (4)). An alternative approach is also used, in which averaged steam velocities around the jet are calculated directly by IKEMIX. Present difficulties with the latter approach are related to the possible determination of the flow field close to the jet and to fluctuations in these regions. Only the heat transfer from the resulting particles is considered. The energy equation of the jet is neglected. The 1D calculation of jet dynamics is based on the conservation equations for mass and momentum:

∂A ρ ∂ j m + (A ρ v ) = −M& (1) ∂t ∂z j m j

∂v j ∂v j 1 ∂ pa K j +v j = − ⋅ + (vv −v j ) + g , (2) ∂ t ∂ z ρm ∂ z ρm

2 with a jet cross section area Aj = π ⋅ R j and a local source line fragmentation rate

M& = 2πR jv fr ⋅ ρm (fragmented mass per jet length unit and time).

Here, the z-direction is downwards (in direction of gravity) and the axial velocities (v ) are to be taken positive in this direction. The pressure gradient term is replaced ρ g by − a assuming the hydrostatic head of the ambient mixture as decisive. At ρm present, friction is approximately considered as determined by the surrounding vapour, i.e. by the vapour density and by the relative velocity v rel between falling jet v j and upwards directed vapour flow vv . The friction coefficient K j is given by:

1 K j = c j ⋅ ρv ⋅ v rel , (3) R j where the constant c j is taken to be c j = 0.1.

3 2 The fragmentation rate v fr (m /(m s)) in IKEJET, which can be interpreted as a mean velocity of mass outflow from the jet per unit surface area, is based on the Kelvin-Helmholtz (KH) model of wave growth. As indicated above, a simple balance approach may be applied to yield the steam velocity vv along the jet:

ρa v v = ζ ⋅ g (L − z ) . (4) ρv

25 3 Description of the premixing model IKEJET/IKEMIX

Here, ρa gL represents the driving head of the mixture around the jet of length L .

ρa is the mean density of the mixture ambient to the jet. It contains the feedback of the resulting mixture with jet break-up. The KH model yields the imaginary part of the phase velocity

ρv c i = v rel ⋅ , (5) 3ρm which gives the growth rate u of wave amplitude η :

dη u = = k ⋅ c ⋅η , (6) dt i for waves of wave number k . The wavelength of maximum amplitude growth λfr is expected to dominate the growth and the stripping processes and is therefore selected. Here, the fragmentation rate can be concluded to be proportional to the growth rate of waves at maximum amplitude ηs (i.e., where stripping occurs):

v fr = ffr ⋅u fr = ffr ⋅ k ⋅c i ⋅ηs = ffr ⋅N fr ⋅c i . (7)

The factor f fr indicates the part of the wavelength over which separation occurs.

N fr = k ⋅ηs relates the wave amplitude of separation ηs to the wavelength. The drop radius after stripping of the wave crest from the jet surface is assumed to be proportional to the wavelength. This approach assumes that the steam flow around the jet, under conditions of a thick film or a steam continuous zone, essentially determines the wave growth and stripping of fragments. The factor ζ in Eq. (4) for the decisive steam velocity can be fitted to gain the characteristic L /D values of jet break-up. The above approach yields for constant jet velocity and fragmentation rate (applying an average 2 v = v (z = 0) ): v 3 v

2 / 3 L ⎡ 3 3 ρ v j ⎤ = ⎢ ⋅ m ⋅ ⎥ , (8) D ⎣⎢4 ffr ⋅ N fr ⋅ ζ ρa gD ⎦⎥ based on

L v = j . (9) D 2v fr

The choice of values for ffr and N fr can partly be related to geometrical arguments as indicated above. Choosing one-quarter of a wavelength to define the separation area on the jet gives f fr = 0.25. With one-quarter of a wavelength also for the 26 3 Description of the premixing model IKEJET/IKEMIX

separation amplitude, one gets N fr = π / 2. Then, fitting to L /D = 20 with v j = 5 m/s, D = 3.5 cm (approximate values for jet entry in water in the experiment FARO L-28 (see Bürger et al., 2004 and Magallon, 2002), and with assumed ρa = 0.5 ⋅ ρl yields ζ = 1.3 for the stationary phase of jet break-up, i.e., the established state with constant jet length. The radial velocity of fragments leaving the jet is assumed to be determined by the wave growth at the separation amplitude. E.g., with the above approach and data, a value of c i = 0.3 m/s is derived for characteristic conditions in FARO L-28, yielding ud = 0.47 m/s. The initial axial velocity v d of the released drops is taken equal to the local jet velocity. From the above approach, also a characteristic size of fragments from the jet can be derived. A basis is given by the wavelength of the maximum growing waves:

3πσ 3πσ λfr = 2 = 2 . (10) ρvvv ζ ρa g (L − z ) Related to this, smaller or larger fragment sizes may then be assumed depending on the separation process.

Using an average steam velocity vv and an average ambient density ρa yields

−1 27πσ ⎛ L ⎞ λfr = 2 ⋅ ⎜ ⎟ . (11) 4ζ ρa gD ⎝ D ⎠

With one-half of the water density taken for ρa , as a first approach, about 2 mm results for λfr with characteristic data of FARO L-28. This is somewhat smaller than the mass averaged diameter of around 3 mm, resulting from the experiment. For adaptation to the experimental results, the drop diameter is taken to be

Dd = 1..5 ⋅ λfr

The above chosen parameters, adapted with respect to FARO L-28 in an integral way, are applied in the model for the local, instantaneous conditions at the jet, according to Eqs. (4), (7) and (10).

3.2 Melt drops in mixture

Within the 2D Lagrangean description of the melt drops, the so-called representative drops are traced representing the groups of drops with similar properties e.g. size, temperature etc. For usual applications, the number of groups of particles can be chosen large enough to avoid the necessity of redistribution of groups of particles. This allows following in detail the development of properties of representative

27 3 Description of the premixing model IKEJET/IKEMIX particles. For momentum and heat transfer to the coolant, the contributions of all different groups with respective representative drops in a mesh are added. Groups are generated as follows: initially, each computational cell along the jet line (centreline) is divided axially into a certain number of intervals (given via input) with axial length ∆z . Each timestep ∆t generates for each interval on the jet, for which fragmentation takes place, a group of particles being initially in a volume of the size

2 2 Vd = π ⋅ [(R j + ud ⋅ ∆t ) − R j ]⋅ ∆z (12) where the stripped-off mass is given by:

md = M& ⋅ ∆z ⋅ ∆t . (13)

3 md The number of drops in such a representative particle group is nd = 3 . Each 4 πRd ρm group has its own velocity, temperature, diameter and porosity.

3.2.1 Dynamics

For such a group of representative drops, the equation of motion is given by

r dv d ρa r r md = md (1 − ) ⋅ g + nd F p , (14) dt ρm r where the drag force on a single spherical particle Fp is essentially the hydrodynamic r drag, based on the pressure influences from the surrounding flow. Fp is given in general form as

r 1 F = c ⋅ πR 2 ⋅ ρ vr (vr −vr ) . (15) p d 2 d a rel a d r Mixture densities and velocities of the ambient coolant phases ( ρa , v a ) are used in the water and steam continuous regimes, thus yielding an influence of void within these regimes. Water and steam continuous regimes denote the regimes with steam bubbles in water for lower void (or steam volume part) and with water droplets in steam for high void. In the transition range, assumed between these flow patterns, the above mixture values as well as mean values of physical properties, such as friction and heat transfer, are derived from the respective values at the chosen boundaries (void α = α lt and αvt as lower and upper values of the transition range between the liquid and vapour continuous regimes, for default chosen as 0.3 and 0.7), according to their volume partition. This corresponds to the approach chosen in MC3D (Berthoud and Valette, 1999). The underlying idea is that the transition states are composed of water-rich as well as of steam-rich patterns, at the conditions of the

28 3 Description of the premixing model IKEJET/IKEMIX boundaries of the transition regime, respectively. Practically, linear interpolation is carried out between the transition boundaries. Due to the innacuracies found by the present model observed during verification, modifications of this description in IKEMIX are done as described in Chapter 3.4.

For the drag coefficient c d , the same relations are applied as given by Berthoud and Valette (1999):

1 2 2 ⎡g ()ρm − ρa ⎤ c d = ⋅ Dd ⎢ ⎥ ⋅ F (B ) (16) 3 ⎣ σ ⎦ with

2 ⎡1 + 17.6B 6 / 7 ⎤ F (B ) = ⎢ ⎥ (17) ⎣ 18.6B ⎦ and

x B = (1 − α m ) , (18) with x = 2.25 in water continuous and x = 3 in steam continuous regime as well as taking the water and the steam densities for ρa , respectively. This description is considered valid for a melt volume fraction of αm < 0.3. Multi-particle effects are contained in these correlations.

Correlations for the dense particle regime (αm > 0.4) and a transition description are also included in IKEMIX. These are mainly relevant after settling has occurred, and hence they are not taken into account in the present study. The models for friction in particulate debris are defined according to relative permeabilities and passabilities for the linear and non-linear parts of the Ergun equation as has been implemented in the WABE code (see Bürger et al., 2006).

3.2.2 Heat transfer

Heat transfer from the drops is also treated depending on the flow patterns, in a similar way as for friction. The energy conservation equation for a single spherical particle is

de m p = q ⋅π ⋅D 2 (19) p dt p with heat flux q and thermal energy e p . The latter corresponds to the mean temperature T p .

29 3 Description of the premixing model IKEJET/IKEMIX

In the continuous regime of the water, the heat flux is taken according to the description of Epstein and Hauser (1980) for forced convection film boiling. For the ambient velocity and properties, the water values have been used. An extension has been made for subcooling, through the use of a correlation for forced convection heat transfer into subcooled water and a factor adapted to experimental results (see Chapter 3.3.2.1). In the steam continuous range, forced convection heat transfer is described according to the classical Ranz-Marshall correlation (Ranz and Marshall, 1952) for an infinite flow and Reynolds number 10 < Re < 2000:

1 1 2 3 Nu = 2 + 0.6 Rep Pra . (20) Radiation heat transfer to the coolant is taken into account as an additional contribution in both flow regimes. The emissivity of corium is taken as 0.7. A decrease of radiation heat transfer from the drops has been described with decreasing water volume content. This has been done independently from the above modeling of transition. A factor of (1 − α ) has been used as by Theofanous et al. (1996). Radiation heat transfer beyond local meshes is presently not taken into account in IKEMIX. Thus, radiation heat transfer from the drops in a cell is only considered if sufficient water is contained. Certainly, for high voided regions this approach is highly controversial because, in reality, the radiation should be transferred beyond these regions. However, concerning a main interest here in major limiting effects to steam explosion strength, highly voided regions will anyway imply to a large extent the exclusion of strong steam explosions.

3.3 Two phase-description of coolant

3.3.1 Conservation equations

The conservation equations for the coolant phases are: Mass:

∂ ()α ρ + ∇ ⋅ ()α ρ vr = Γ , (21) ∂t k k k k k k with:

αk = volume parts of fluid phases, k = l (liquid), v (vapour), with αl + αv = 1,− αm

Γv and Γl = evaporated and condensed mass per unit volume and time with

Γl = −Γv = Γ .

30 3 Description of the premixing model IKEJET/IKEMIX

Different processes are considered for phase change: evaporation due to hot melt droplets under film boiling (fb) and evaporation/condensation at the water/steam interfaces (bulk) of bubbles and water droplets, thus Γ = Γfb + Γbulk .

Momentum:

∂ ()α ρ vr = −α ∇p + α ρ gr − K (vr −vr ) − []K ()vr −vr , (22) ∂t k k k k k k dk k d ik k i i ≠k where the term with K dk denotes friction at the melt drops and that with K ik denoting the interfacial friction between steam and water, K dk and K ik being the respective friction coefficients (see Chapters 3.3.2.1 and 3.4). Convection of momentum and momentum transfer by phase change are presently not taken into account. The former implies the neglect of inertial effects and the assumption of rapid establishment of balanced forces according to local conditions. Energy for the vapour:

∂ α ρ ⋅ e + α ρ (vv ⋅ ∇) ⋅e = Q − Q + Γ ()h − h , (23) v v ∂t v v v v v dv v ,int v v ,int v Energy for the liquid:

∂ α ρ ⋅ e + α ρ (vv ⋅ ∇) ⋅e = Q − Q + Γ (h − h ) (24) l l ∂t l l l l l dl l ,int l l ,int l where Qdk and Qk ,int are the volumetric heat transfer rates from melt to coolant phase k and from coolant phase k to the steam/water interface. Last terms in the energy equations refer to energies connected with heat-up of masses from phase transition. Evaporation/condensation is defined by:

Qd ,int (Qv , int + Ql ,int ) Γv = −Γl = fb fb + bulk bulk . (25) h v ,int − h l ,int h v ,int − h l ,int

Where Qd ,int denotes the heat transfer from melt drops to the fluids directed to the interface of steam and water via conduction over the steam film. It considers heating up of water up to Tl ,sat (in subcooling conditions) and it also contains heat input into

fb fb the steam film until Tv ,film is achieved. Thus, h v ,int and h l ,int correspond to hv ,film and hl , respectively. Qdl characterizes the heat directly transferred from melt into subcooled water e.g. from film boiling and/or radiation. Qdv denotes the direct heat transfer from the melt to the steam via radiation, and due to convection, at present it is set to zero. Qv ,int and Ql ,int concern the other exchanges between the phases, not connected with the film boiling mode. The enthalpies in the last term of

Eq. (25) correspond to hv ,sat for bubbles and hl ,sat for water droplets, respectively.

31 3 Description of the premixing model IKEJET/IKEMIX

3.3.2 Constitutive laws

3.3.2.1 Exchange with melt

According to Chapter 3.2, the drag between melt and coolant phases is obtained from Eq. (15) by multiplying with the respective number of particles in a cell (per volume) for every Lagrangean group and by summing over the different groups in a cell. This sum replaces the representation in Eq. (22) written for groups with identical conditions. The coefficients K dk for a certain group are defined by

r ⎛ 6α r ⎞ K (vr −vr ) = n ⋅ F ⎜= d ⋅ F ⎟ , (26) dk k d p ⎜ 3 p ⎟ ⎝ πD p ⎠ with n = number of particles of this group per unit volume. The partitioning of this momentum transfer into the coolant phases of the water as well as in steam continuous regimes has been chosen according to the volume parts of phases. In the transition range, the composition by the bounding conditions follows the interpolation according to the void. Heat transfer from the melt drops is already described in Chapter 3.2. The partitioning into evaporation, steam heat-up and water heat-up remains to be described. It depends on the flow regimes. Some specific features are to be remarked: Radiation: The dependence of heat release from the melt drops on the flow patterns, especially the void, has already been discussed in Chapter 3.2. Parts of this heat transfer can be attributed parametrically to either evaporation or water heat-up. As default and for present calculations, 10 % into evaporation and 90 % into water heat-up have been chosen. This relation was motivated by the significant absorption length of high temperature radiation in water (Jacobs et al., 1997). It also corresponds to the default choice in MC3D (Valette et al., 2001). Presently, absorption by steam is not considered. Convective heat transfer in the steam continuous range according to Eq. (20): This has been neglected in the present calculations. Radiation heat transfer to water droplets appears to be the mode contributing most to steam production, thus also contributing to the maintenance of a high void. The latter essentially decides about quenching options. These will be, in any case, small with high void. Heat transfer at film boiling in the water continuous range: Besides radiation, this is considered as most important. Heat transfer from the melt drops is described according to Chapter 3.2 by the film boiling model for forced convection of Epstein and Hauser (1980). The 32 3 Description of the premixing model IKEJET/IKEMIX

partitioning is done as follows: • A mean temperature in the steam is assumed according to

Tv ,film = C film ⋅T sat + (1 − C film ) ⋅T d . A value of C film = 0. 9 has been chosen for the calculations to get temperatures close to saturation (see also Valette et al., 2001). An argument for this choice is that under film boiling at high temperatures strong turbulent mixing in the steam film should occur, thus tending to establish a mean temperature close to that of the steam producing surface, i.e. saturation temperature. Fluctuations between evaporation and condensation are hereby avoided. • The balance of heat fluxes at the steam/water interface determines the evaporation according to Eq. (25). The heat transfer to

subcooled water (Qdl ) is still to be defined. While the effect of subcooled water is included in the model of Epstein and Hauser for the heat release from a spherical body in forced-convection film boiling, a separation of the heat flux into subcooled water cannot directly be gained from their results. This is due to the close coupling of the processes (heat transfer to water reduces the film thickness, thus increasing the heat transferred to the interface) and the dependence of the heat transfer into water on the interface boundary conditions. Thus, a separate correlation of the heat transfer from the steam/water interface into water was at first chosen according to the forced convection around a solid sphere at saturation temperature, which was also done e.g. in MC3D (Valette et al., 2001). In other words, while the heat release from the melt drops under the subcooled forced convection film boiling is taken from the correlation result of Epstein and Hauser, a different approach is used to gain the heat transfer to subcooled water and from this the corresponding reduction of evaporation according to Eq. (25) is gained. However, the latter approach involves difficulties. For example, an increased evaporation with subcooling may result, if the heat transfer to water obtained in this way is smaller than that implicitly calculated in the correlation of Epstein and Hauser. Such an increased evaporation with subcooling would not be physically reasonable. In fact, such effects were obtained in the calculations and from separate evaluations. Also, from basic considerations, it is a problem to apply a correlation gained from forced convection heat transfer at solid bodies to heat transfer from film interface into water. It has been shown (e.g. by Bürger and Unger, 1985) that the difference of boundary conditions (solid surface vs. film interface) causes strong differences in

33 3 Description of the premixing model IKEJET/IKEMIX heat transfer; i.e. a much higher heat transfer in the film case must be expected. This is also indicated by Epstein and Hauser (1980) and is a reason for their coupled description. Thus, higher heat fluxes from the interface to water can be expected (in the natural convection case more than 3 times higher values have been derived for some cases by Bürger and Unger, 1985). In addition, large disturbances in the agitated system may yield further increases. Thus, it was considered as problematic to choose a separate model for heat transfer at the steam water interface. However, the heat transfer from the film interface to water (ql ) should approximately be independent from the sphere temperature, if the influences of turbulence and the effects of the wake region of the drop are not taken into account, as done in the model of Epstein and Hauser (of course this needs further consideration anyway). Then, in the correlation of Epstein and Hauser, found to be

1 1 2 4 κ Re 2 Pr h ⎡A 3 ⎛ 2 ⎞ ⎤ q = h ()T −T = 2.5 ⋅ v ⋅ l ⋅ v lv ⋅ ⎢ + ⎜ ⎟ B 4 ⎥ , (27) film film d sat D β c 24 π pv ⎣⎢ ⎝ ⎠ ⎦⎥

with

c (T −T ) T −T 1 pv d sat κ l sat l 2 A = , B = β c pv Prl , hlv = hv,sat − hl,sat , Prv hlv κv Prv hlv

1 1 2 ⎡ 2 ⎤ r r ⎛ ρ ⎞ ν v d −v l D β = ⎢⎜ l ⎟ ⋅ v ⎥ , Re = , ⎢⎜ ρ ⎟ ν ⎥ l ν ⎣⎝ v ⎠ l ⎦ l

A can be considered as tending to zero for getting the limiting case q l ≈ q film , thus yielding

1 2 1 1 λl ⎛ 2 ⎞ 2 2 q l = ()Tsat −Tl ⋅ 2.5⎜ ⎟ ⋅ Rel ⋅ Prl (28) D ⎝ π ⎠ or as Nusselt relation for the heat transfer from the interface to water:

1 2 1 1 1 1 ⎛ 2 ⎞ 2 2 2 2 Nu l = 2.5 ⋅ ⎜ ⎟ ⋅Rel ⋅ Prl ≈ 1.99 ⋅ Rel ⋅Prl . (29) ⎝ π ⎠ This yields a factor ≥ 3 as compared to the classical correlations for solid spheres. In general, increased heat transfer from drops and from the interface to water is plausible considering interface instabilities, turbulence and wake effects (e.g. separation of bubbles). On the other hand, a reduced heat transfer may be caused

34 3 Description of the premixing model IKEJET/IKEMIX by the breakdown of thin film assumptions at high drop temperatures. Furthermore, if more significant evaporation due to radiation must be considered, it will reduce the convective portion of heat transfer at film boiling due to the produced increase in film thickness. Presently such additional effects are not included in the model. Radiation heat transfer is considered separately.

3.4 Improvements of the model for interfacial friction between steam and water

The description of interfacial friction between steam and water follows the flow patterns. Steam bubbles in the water continuous regime result from film boiling.

Water droplets are assumed in the steam continuous regime. αlt = 0.3 and

αvt = 0.7 are taken as the respective boundaries. Between, interpolation is applied according to respective parts of the limiting configurations. The same friction relations are applied as given by Berthoud and Valette (1999), based on the Ishii-Zuber models for bubbles in water continuous and droplets in steam continuous regimes. These laws correspond in principle to Eqs. (15) – (18) applied for the melt drops, if the drop diameter is replaced either by bubble or water droplet values, and likewise the velocity difference, (ρm − ρa ) in Eq. (16) is replaced by (ρl − ρv ) in both cases. B in Eq. (18) is also changed:

B = ()1 − α 1.5 for bubbles, (30)

B = α 3 for water droplets, (31) with α being the void, i.e. α = αv /(αv + αl ) . The first calculations performed for FARO L-28, generally yielded a strong void buildup in the mixture, which was considered as too high compared to the experimental results and also counteracted the pressure build-up (see Bürger et al., 2004). Especially, the practically constant pressure rise over about 5 s was interrupted due to this void build-up. It could only approximately be obtained by additional measures promoting steam production in the steam continuous regime, which were considered as not realistic. Furthermore, with such strongly voided mixtures sufficient quenching for the formation of particle debris appears to be questionable. Thus, it is important to check other possibilities in view of the modelling uncertainties. Since in FARO L-28 at least a partial bed of particles was obtained in only about 1.5 m initial water depth, this gives a further indication of an exaggerated void resulting from the modelling. On the other hand, a high steam production is required to reproduce the pressure increase. Thus, only more rapid steam removal from the

35 3 Description of the premixing model IKEJET/IKEMIX mixture could be an explanation; i.e. reduced friction would then result from the applied correlations, especially the interfacial friction between steam and water in the water continuous and transition regimes. Assuming steam bubble formation from film boiling and therefore upward motion of bubble assemblies as the steam removal rate in the water continuous regime, a significant reduction of friction is not visible. However, the boundaries of the flow patterns as well as the transition behaviour from the water continuous to the steam continuous regime involve significant uncertainties. Especially in extended regions and in a three-phase mixture of melt drops, water and steam (as compared to rather 1D-like configurations and two-phase mixtures in the experiments on which the basic laws are based), spatially inhomogeneous patterns may develop on a local scale, i.e. not resolved in present codes. Such non-homogeneities may include the formation of steam channels within a still water-homogeneous surrounding which would promote steam removal. Also, an intermittent behaviour can occur in which rapid voiding would due to the strong steam production, yield strong release paths as well as heat transfer reduction, thus again causing the collapse of such patterns. Presently, the experiments which clearly identify such patterns are lacking. There are only indications from the problems of calculating the integral experiments mentioned above, as well as some observations indicating channelling effects, e.g. by Zeisberger and Mayinger (2006) with respect to particulate debris and by Moriyama (see Pohlner et al., 2006), who observed increased gas removal and a limited void beyond a certain rate of gas injection into a water pool from the bottom. The present approach in dealing with these problems refers to the formal approach and the underlying physical idea of describing the transition range in MC3D (Berthoud and Valette, 1999 and Valette et al., 2001). As already outlined above, it is assumed that both, the water continuous and steam continuous regimes, co-exist in the transition range with varying partitions. However, different velocities of steam in the respective parts are not considered. As an averaging approach, mean steam velocities (and also water velocities) for the combined pattern are assumed. The interfacial term in transition regime can be generally written as:

* 2 Flv = K lv vv (32) In view of the non-linearity of dependencies, this may strongly reduce the potential of steam removal. The general strength of reduction of interfacial friction between the water continuous and steam continuous regimes can be realized from the density factor in the friction laws, either from the water around steam bubbles or the steam around water droplets. Thus, proper weighting in combining the different regimes is very important. Furthermore, the boundaries of the transition range may also be questioned, which was e.g. done by introducing variants in MC3D. In a first step, a reduction factor on interfacial friction was introduced to explore 36 3 Description of the premixing model IKEJET/IKEMIX improved options to reproduce the experimental results, especially FARO L-28. With a strong reduction factor of 0.001, a significant improvement could indeed be obtained due to a more rapid steam removal and the resulting smaller void in the mixture. Thus, in order to proceed in a more mechanistic way, an extension of the above model is attempted, introducing in principle different steam velocities in the transition range for the respective flow pattern parts. Here, the boundaries have not been changed from their original values. In a simplified approach, a relation between the two steam velocities in the respective regimes can be derived from strongly simplified momentum equations:

∂p − α Z = K * v 2 (33) lt lt ∂z lv lt v lt

∂p − α Z = K * v 2 (34) vt vt ∂z lv vt v vt

Here, αlt and αvt denote the boundary values of the transition regime since the respective states are taken at these boundaries. Z lt and Zvt are the volume parts of water and steam continuous parts in a certain mixture state with the void α of the transition regime, i.e.:

αvt − α Z lt = (35) αvt − αlt

α − αlt Zvt = (36) αvt − αlt and α = Z lt ⋅αlt + Zvt ⋅αvt . The steam velocities vv vt and vv lt in each regime are related to an averaged velocity of water (which may be as problematic as taking an averaged steam velocity, but especially the steam removal is under question, here). * For simplification, the friction coefficients K lv of quadratic velocities are used here, corresponding to K lv with omitted products of absolute velocity value. Then, by pressure elimination, assuming the same pressure drop in the different parts, a coupling between the two vapour velocities vv vt and vv lt will result:

1 ⎡ * ⎤ 2 αvt Zvt K lv lt vv vt = vv lt ⋅ ⎢ ⋅ * ⎥ . (37) ⎣⎢αlt Z lt K lv vt ⎦⎥ This coupling occurs due to the strong coupling effect by the pressure terms in the simplified momentum equations. It may be considered as a first approach, in the spirit of a drift flux approach. The composed interfacial friction term in the transition regime can generally be

37 3 Description of the premixing model IKEJET/IKEMIX written as a sum of the respective friction terms:

* 2 * 2 Flv = K lv ltvv lt + K lv vtvv vt . (38) Then, for further use of the momentum equation for the composed states, i.e. a mean momentum equation for the steam, a mean steam velocity has to be considered, defined as

(Z α v + Z α v ) v = lt lt v lt vt vt v vt . (39) v α Together with the above coupling of velocities, the respective velocities can be written as

−1 vv lt = α ⋅vv ⋅ ()Z lt ⋅αlt + Zvt ⋅αvt ⋅ ft (40)

−1 vv vt = α ⋅vv ⋅ ft ⋅ (Z lt ⋅αlt + Zvt ⋅αvt ⋅ ft ) , (41) where the factor ft is given by

1 v ⎛ α ⋅ Z ⋅K * ⎞ 2 f = v vt = ⎜ lt lt lv lt ⎟ (42) t ⎜ * ⎟ vv lt ⎝αvt ⋅ Zvt ⋅ K lv vt ⎠ and can be introduced in Eq. (38), yielding the final form of the interfacial friction term for the momentum equation

2 ⎛ α ⎞ ⎜ ⎟ * * 2 2 Flv = ⎜ ⎟ ⋅ ()K lv lt + K lv vt ⋅ ft ⋅vv (43) ⎝ Z lt αlt + Zvt αvt ⋅ ft ⎠ In the present calculations, both the first approach with a reduction factor f intfric = 0.001 on Flv as well as this extended approach (in the following referred as the “New model”) have been used for FARO L-28. The reduction with the extended approach approximately met the factor reduction. Presently, heat transfer from steam bubbles to water as well as from superheated steam to water droplets have both been reduced strongly. This has been motivated by concentrating on the major effects that will reveal decisive mechanisms and deficits in their description. Since high voids are being questioned (see above), the emphasis was not posed on details of this regime. The regime determining void buildup (water continuous regime) was considered more important. In a view of the complex processes, the parametric parts in the modelling can not be presently avoided. In order to reach nevertheless a firm basis for extrapolating application, it is important to concentrate on major processes and their mutual dependencies. As outlined, this is in principle concerned with e.g. getting the

38 3 Description of the premixing model IKEJET/IKEMIX feedback of the mixture produced by jet break-up and getting a realistic perspective on the void build-up by emphasising the major production processes of radiation and film boiling in the water continuous regime (with simplifications concerning evaporation-superheating-condensation interplay) and the steam removal process.

3.5 Numerical method

For the spatial discretisation of the partial differential equations, i.e. the conservation equations of the Eulerian fields (liquid and vapour), a finite volume method is applied. For the temporal discretisation, backward differences (implicit scheme) are used. The non-linear coupled system of equations resulting from the discretized conservation equations is solved with a segregated procedure. From the momentum equations, the steam and water velocities are expressed in terms of pressure and void. Linearization has to be done with respect to non-linearities in the friction laws and coefficients containing α . Substitution in the mass conservation equation and further linearization finally yield a linear system of equations, from which the pressure and void fraction corrections are calculated simultaneously. After the update of pressures and void fractions, the energy equations of liquid and vapour are solved separately. Linearization with respect to the respective temperatures yields linear systems, from which temperature corrections are calculated. Due to non-linearities and coupling between equations, an iterative procedure is required. The above steps of the segregated solution procedure are therefore repeated within the actual time step until sufficient convergence is reached. The coupling between the Eulerian fields and the Lagrangean description for the melt droplets is done explicitly. At the beginning of a new time step, the states of the different droplet groups advance in time, taking into account the state of the continuous fields known either from initial conditions or the previous time step. The new state of the melt drops is then used to derive the volume averaged quantities in order to calculate heat transfer and friction, partly in an implicit way within the above described two-phase solution for the coolant.

39 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

4.1 Experimental database

Quenching and fragmentation of prototypic melt jets were investigated experimentally in the FARO experimental facility (Hohmann et al., 1986) at the Joint Research Centre (JRC), Ispra. Tests were performed by releasing melt jets of 5- 10 cm diameter with about 5 m/s initial penetration velocity into 1-2 m deep water. The diameter of the test vessel was 0.7 m. Up to 177 kg of melt mass was released, mostly into saturated water under different system pressures from 0.2-5 MPa. In cases with low system pressure (0.2–0.4 MPa), subcooling of water of ∼100 K was also applied. The test facility (see Fig. 7) was composed of five main components i.e. the furnace for melt generation, the intersection valve unit which isolates the furnace from the test section, the release vessel which holds up the melt temporarily for operational reasons, the melt-water interaction test vessel and the venting system for accommodating overpressures in excess of the design pressure (8 MPa). All tests were started by melting of corium inside the furnace. After melting, corium was relocated to the release vessel where it remained until the balance between the release vessel and the test vessel pressures was achieved. This was carried out in order to ensure gravity release of the melt. When all the melt had settled in the release vessel and the pressures were equalised, a release valve was opened letting the melt into water in the test vessel. At the end of mixing with water, corium was then collected in the debris catcher. During the melt-coolant interactions, pressures, temperatures and water level swells were measured. Additionally, some of the tests were filmed using high speed video cameras. Debris analyses considered visual recordings and sieving of the debris in order to determine the particle size distributions. A major outcome of these experiments was that a significant break-up occurs with corium melt jets flowing under realistic conditions into water. Rather similar particle size distributions were obtained for the fragmented parts, under a wide range of initial conditions (see Fig. 8). The mass averaged particle size is between 2.6 and

40 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

4.8 mm, which indicates a similar break-up process. In all FARO tests, except the final FARO experiment (i.e. FARO L-33) no artificial trigger was applied, hence no steam explosions were obtained. In FARO L-33 (Magallon and Huhtiniemi, 2001), in spite of high subcooling applied to avoid extensive void formation, only a rather weak explosion occurred (maximal pressures up to 10 MPa).

Release tube FARO furnace closing disc (W)

Lower electrode

γ detectors 1, 2

Release tube Mirror system drive (Ø 50 mm, h= 2.5 m)

Videocam

Depressuriser V420 Protection valve S01 Pressure equalisation (Ar) for melt release Vx Main isolation valve S02

Lateral flap for pressure equalisation Dome during quenching

Release vessel

Melt Release orifice Release valve S05 elevation 2330 mm Instrumentation ring Overflow elevation 1835 mm Release orifice (Ø 50 mm) Water initial level 1440 mm FAT vessel (Øint 1494 mm)

Internal cylinder (Øint 710 mm)

Annular space

Water

Instrumentation rack

Debris catcher Elevation 0.00 mm (Ø 660 mm h=250 mm)

Bottom plate Elevation -260 mm (thickness = 40 mm)

Fig. 7. FARO test facility.

FARO L-28 has been selected for calculations to validate the IKEJET/IKEMIX code, since relatively detailed results, which allow critical checking, exist from this experiment. The establishment of clear conditions is enabled, especially, due to a long lasting pour of melt of ~5 s and an initial jet diameter of 5 cm. These conditions can also be considered as relevant for reactor cases with respect to the long pour,

41 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 the high temperatures, the diameter of the melt jet and also the oxidic corium material used in the FARO test. A perfectly constant pressure increase over 5 s (after an initial phase with a stronger increase) indicates a steady state behaviour; i.e. essentially constant mixture conditions (especially void), constant rates of jet fragmentation and settling of fragments, constant steam production and release from the mixture. Thus, as it was already seen in the first calculation attempts, it is quite a challenge for the models and codes to provide understanding of these features and to reproduce the experimental results. Hence, this experiment is well qualified for the validation of premixing codes.

L-06 L-08 L-11 (4% Zr) L-14 1 L-19 L-20 L-24 L-28 Particle size Particle size (mm) L-31 L-33 (S.E.)

0.1 0.1 1 10 30 50 70 90 99 99.9 Mass less than indicated size (%)

Fig. 8. Particle size distribution in FARO tests (Magallon, 2006).

According to post-test debris analyses, the agglomerated (“cake-like”) part of debris was most likely formed from earlier separated particles which had stuck together (see Pohlner et al., 2006). This provides indication that a complete jet break-up occured in this test. A further support for complete jet break-up in L-28 can be drawn from results on melt front progression in the water (Magallon et al., 2000). A significant decrease of melt front velocity about 70 cm below the initial water surface can be taken as an indication of a coherent jet length of 70 cm, although this is strictly valid only for the initial conditions of melt inflow. During the 5 s long steady state period mentioned above, it can be estimated that roughly 30 kg of fragmented melt are always in falling state in water. These unsettled fragments in the mixture have a characteristic drop diameter of about 3 mm and their melt surface is about 8 m2. With the melt temperature of 3050 K and an emissivity of 0.7, heat transfer by radiation could explain approximately 28 MW energy input into the water, i.e. about 42 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

150 MJ in 5 - 6 s, as detected from the experiment. This may be considered to be independent of the void build-up, but taking into account that it requires assumed break-up, it becomes clear that it must depend also on mixture conditions, especially on the void. Since there are no indications of significant steam superheat or water subcooling in the experiment from the thermocouples, the pressure buildup may directly be estimated from the estimated heat input to the water under the assumption of saturation states. This yields, starting from initially 8.4 kg of steam in the gas volume at 0.51 MPa system pressure (only initially superheated by 40 K, at 465 K), a steam mass of about 27 kg at the final pressure of 1.68 MPa, i.e. an evaporation of 18.6 kg. This corresponds to an energy input of about 37 MJ for evaporation and 117 MJ for heatup of water to saturation, i.e. 154 MJ in total, corresponding to the experimental detection. These estimations indicate a consistent picture with steady state behaviour over about 5 s, supported by the constant pressure increase. As a main task for code validation, it remains to be shown by the calculations that the modelled processes interactions also support these estimations. The emphasis is especially on pressure and void buildup, fragmentation and heat transfer which are to be checked. Radiation is not the only factor that will contribute to the latter, especially during cooling. Both, the fragmentation and the heat transfer depend on the mixture conditions i.e. especially on the void development. Thus, the establishment of a nearly constant void should also be a necessary feature of the process.

3.0 2.8 2.6 2.4 Melt inlet 2.2 2.0 Overflow 1.8 opening 1.6 Initial water 1.4 height [m]height level 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.1 0.2 0.3 radius [m]

Fig. 9. FARO L-28 discretisation used for IKEJET/IKEMIX calculations. 43 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

Furthermore, it is difficult to conceive that under high void, even in the steam continuous range, this behaviour can be supported, especially concerning the necessary break-up, as well as falling of fragments and heat transfer. Based on the experimental data collected for the level swell and water overflow, a limited void of 20 – 40 % was concluded. From this, the validation tasks for the code application can be stated more precisely, namely to check and explain the relation between 28 MW energy input rate and the maintained void of 20 – 40 % (Magallon et al., 2000). Additionally, the relations to other key processes such as fragmentation, heat transfer to water and evaporation, falling of the fragments (all depend on the mixture conditions and produce them likewise) are to be considered as well.

4.2 Results of IKEJET/IKEMIX calculations performed for the experiment FARO L-28

Calculations for the experiment FARO L-28 are performed with IKEJET/IKEMIX code in 2D cylindrical geometry assuming an idealised geometrical configuration. This and the numerical discretisation are shown in Fig. 9. The heights are chosen according to the experiment, while the outer annular gas space is not modelled directly. The corresponding gas volume is taken into account by a point model, linked to the overflow opening. Gas exchange between this outer and the inner volume, the latter directly modelled as shown in Fig. 9, is regulated by the pressure boundary condition. The outflow of water in the first approach is described according to a Torricelli outflow from a (collapsed) water column above the outflow opening (if establishing) and the outflow of water droplets, included in the two-phase steam/water mixture (local mixture conditions at outlet). The outside steam is modelled by the ideal gas law. The chosen experimental conditions and the scheme of the test facility are given in Table 1 and in Fig. 7, respectively. In first calculations with the standard formulation of the constitutive laws, the pressure increase was much smaller than the one obtained in the experiment (see Fig. 10, f_intfric = 1.0). A parametrical increase of heat transfer helped only in a limited fashion. Obviously, a high void ~70 % with the standard formulation (see Fig. 15a and 15d), limits the heat transfer. This can also be seen in Fig. 11 (f_intfric = 1.0), giving the energy release to the water, which, by far, does not reach the experimentally detected values. In the cases with parametrically increased heat transfer, an even increased void counteracts even more, thus preventing sufficient heat transfer and resulting pressure build-up to explain the experimental results. Fig. 10 to Fig. 12b (f_htc = 3.0) presents the calculation results obtained by multiplying the heat transfer coefficient by a factor of 3 in comparison with the standard formulation, whilst keeping other numerical parameters unchanged.

44 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

Experiment FARO L-28

Melt and composition 80 wt% UO2

20 wt% ZrO2 Melt mass released [kg] 175 Melt temperature [K] 3053 Melt superheat [K] 203 System pressure [Mpa] 0.51 Water temperature [K] 424 Water subcooling [K] 0 Release diameter [m] 0.05 ∆p melt delivery Gravity Free fall in gas space [m] 0.89 Water depth [m] 1.44 Water pool diameter [m] 0.71 Free-board [m3] Closed volume - 3.5 Trigger No

Table 1. Experimental conditions of the test FARO L-28.

In spite of the higher energy input, no increase in the pressure development nor in the energy release is achieved (see Fig. 10 and Fig. 11, f_htc = 3.0). On the other hand, a significantly stronger steam production and accumulation in the mixture is obtained, counteracting to further heat transfer from melt to the coolant. Fig. 12 provides the calculation results with respect to void development given by fragmented melt masses in regions with void less than a certain value (obtained by integration over the premixing zone below the water level). A significant increase of the mass in high void regions can be observed with parametrically increased heat transfer in comparison with the standard formulation (especially remarkable is the increase of the mass surrounded by void between 60 % and 80 %, see Fig. 12b). Only with a modelling which drives heat transfer under high void in a way considered as unrealistic, the experimental results could be reached. The reduction effects of a high void on heat transfer may, however, be questioned as a global effect in the whole mixture with respect to long-range radiation. In the present model (as in most other existing models), radiation is only considered to contribute to water heatup and evaporation inside a certain cell. If the water content becomes too small, a reduction of radiation heat transfer is considered. This implies that practically only redistribution of heat between melt drops by radiation can further take place in this mesh. This feature is certainly not realistic and must be improved by taking into account radiation heat transfer beyond the boundaries of numerical meshes (as by Theofanous et al., 1996).

45 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

1.6E+06 Experiment 1.4E+06 f_intfric=1.0 f_htc=3.0

1.2E+06

1.0E+06 Pressure [Pa]

8.0E+05

6.0E+05

01234567 Time [s]

Fig. 10. Calculated pressure increase for experiment FARO L-28 obtained with standard formulations of interfacial friction and heat transfer (f_intfric=1.0) and with parametrically varied heat transfer coefficient (f_htc=3.0) in comparison with the experimental result.

1.5E+08 Experiment f_intfric=1.0 f_htc=3.0

1.0E+08

Energy Release [J] 5.0E+07

0.0E+00 01234567 Time [s]

Fig. 11. Energy release for experiment FARO L-28 obtained with standard formulations of interfacial friction and heat transfer (f_intfric=1.0) and with parametrically varied heat transfer coefficient (f_htc=3.0) in comparison with the experimental result.

On the other hand, such high voids as obtained from the calculations must at least reduce other contributions of heat transfer (especially film boiling), which come into play and which may even dominate at least after some cooling has taken place. Significant heat transfer via radiation by itself brings into play these other heat transfer modes, due to a reduction of surface temperatures.

46 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

100 100 1% void < m-% <= 20% void 20% void < m-% <= 40% void 40% void < m-% <= 60% void 80 80 60% void < m-% <= 80% void 80% void < m-% <= 100% void total mass in mixture 60 60

40 40 Mass in mixture [%] in mixture Mass Total mass in mixture [kg] 20 20

0 0 01234567 time [s] (a)

100 100 1% void < m-% <= 20% void 20% void < m-% <= 40% void 40% void < m-% <= 60% void 80 80 60% void < m-% <= 80% void 80% void < m-% <= 100% void total mass in mixture 60 60

40 40 Mass in mixture [%] Total mass in mixture [kg] inTotal mass mixture 20 20

0 0 01234567 time [s] (b)

Fig. 12. Comparison between fragmented melt masses in regions with different void concentration for experiment FARO L-28 obtained with standard formulations of interfacial friction and heat transfer (a) and with parametrically varied heat transfer coefficient (b).

Based on the aforementioned discussion, especially the obtained high void is questionable. From the experimental data, rather a lower void of 20 – 40 % was concluded (see above). Since the evaporation is required to yield the pressure buildup (see also the above estimates), only a more rapid steam outflow from the water region to the cover gas region remains as possibility. This essentially throws the friction laws into doubt, primarily the role of interfacial friction between steam and water. The respective discussion and alternative modelling attempts are described in Chapter 3.4. In a first approach, parametric reductions of interfacial friction (factor f_intfric) have been carried out to check the effects. The major

47 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 question is whether a balance of sufficiently rapid steam production is able to explain the pressure increase and steam removal, under establishment of a void which supports the heat transfer required for evaporation and for water heatup over 5 s.

1.8E+06

Experiment 1.6E+06 f_intfric=0.001 New model 1.4E+06

1.2E+06

1.0E+06 Pressure [Pa] Pressure

8.0E+05

6.0E+05

01234567 Time [s]

Fig. 13. Calculated pressure increase for experiment FARO L-28 obtained with parametrically reduced interfacial friction (f_intfric=0.001) and with the new interface friction model (New model) in comparison with the experimental result.

Furthermore, a high void is considered to reduce the jet break-up, thus not yielding sufficient fragmentation to explain the heat transfer. Approaches to model such a feedback are important to explore such behaviour. Presently, the expected behaviour is that with limited void in the mixture region around the jet, the driving forces for the steam or mixture fluid flow adjacent to the jet may be close to the water head. 2 Then, the jet break-up may essentially be determined by the water head since ρvvv of the fluid (steam) flow along the jet is determined by it. Only a weak dependence of the fragmentation rate on the surrounding mixture data could be explained under these conditions by the 1/3 power in the L/D relation (see Eq. (8) and Bürger and Berthoud, 2006). By such effects, the apparent independence of the particle distributions in the FARO experiments on the system pressure and subcooling (Magallon, 2006) may be explained. Only with very high and radially extended void, significant restrictions in break-up may result. The present approach for the FARO L-28 calculations derives the driving mixture head around the jet from the determination of a mean mixture density ρa within a radius range of < 15 cm around the jet. Furthermore, the steam velocities calculated in IKEMIX close to the jet have been directly applied in an alternative approach, in spite of remaining questions concerning numerical resolution of the decisive velocities adjacent to the jet (see Chapter 3.1). For both approaches, the effect on

48 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 reducing jet break-up was less pronounced than expected with the high void calculated. Also, the pressure head in this mixing region was not reduced that significantly. This is due to friction forces on the steam flow from the melt and water droplets, obviously sufficient to balance the outer water head. Underestimation of transient effects (downflow of the outside water and its effect on lateral pressure distribution) may also be a reason and requires further specific checking of the IKEMIX modelling itself.

1.5E+08 Experiment f_intfric=0.001 New model

1.0E+08

Energy Release [J] Energy Release 5.0E+07

0.0E+00 01234567 Time [s]

Fig. 14. Energy release for experiment FARO L-28 obtained with parametrically reduced interfacial friction (f_intfric=0.001) and with the new interface friction model (New model) in comparison with the experimental result.

time t = 1.50089 s time t = 1.50016 s time t = 1.50377 s

3.0 3.0 3.0 Void averaged Void averaged Void averaged

over r=0.15m over r=0.15m over r=0.15m 2.5 2.5 2.5

2.0 2.0 2.0

1.5 1.5 1.5 Height [m] Height [m] Height Height [m] Height

1.0 1.0 1.0

0.5 0.5 0.5

0.0 0.0 0.0 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0 Void [-] Void [-] Void [-] (a) (b) (c) 49 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

time t = 5.00172 s time t = 5.00029 s time t = 5.00081 s

3.0 3.0 3.0 Void averaged Void averaged Void averaged

over r=0.15m over r=0.15m over r=0.15m 2.5 2.5 2.5

2.0 2.0 2.0

1.5 1.5 1.5 Height [m] Height Height [m] Height [m] Height

1.0 1.0 1.0

0.5 0.5 0.5

0.0 0.0 0.0 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Void [-] Void [-] Void [-] (d) (e) (f)

Fig. 15. Radially averaged void distribution (over radius r = 0.15 m) for time of 1.5 and 5 s from FARO L-28 calculations obtained with classical interfacial friction modelling (f_intfric=1.0, a and d), parametrically reduced friction (f_intfric = 0.001, b and e) and the new interface friction model (New model, c and f).

In the first attempt of reducing interfacial friction by applying a factor f_intfric = 0.001 (see above), a strongly improved approximation to the experimental pressurisation and energy release is obtained (see Fig. 13 and Fig. 14, f_intfric = 0.001). Furthermore, a significantly smaller void (radially averaged over a radius of 0.15 m), mainly below 50 %, in lower regions even smaller, has been obtained here (see Fig. 15b and 15e), corresponding also to the lower mixture level compared to the one with unreduced interfacial friction (Fig. 15a and 15d). Good agreement with experimental data has been concluded also considering the jet break-up i.e. resulting jet length and mass mean fragment diameter (see Fig. 16, f_intfric = 0.001). Further steps have been done by applying the improved model for interfacial friction between water and vapour in a transition regime, reducing it in a more mechanistic and sophisticated manner (see Chapter 3.4). The experimental pressure buildup and energy release are reproduced with a reasonable accuracy (see Fig. 13 and Fig. 14, New model). The void in the mixture (radially averaged over a radius of 15 cm) is of the same order of magnitude as in the case having a parametrical reduction (see Fig. 15c and 15f). Results obtained with the new model for interfacial friction, considering distributions of fragmented melt mass in regions with different void concentration, are presented in Fig. 17. The fragmented masses are presented relative to the total 50 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 fragmented mass and they were obtained by integration over the premixing zone below the water level. A clear difference can be seen in comparison with the previous results obtained with standard modelling, where the majority of the fragmented mass was in high void regions, mostly having a void between 40 % and 80 % (see Fig. 12a).

1.0 f_intfric=1.0 f_intfric=0.001 0.9 New model

0.8

0.7 Elevation [m] Elevation

0.6

0.5 01234567 Time [s]

(a)

7.0E-03 f_intfric=1.0 6.0E-03 f_intfric=0.001 New model 5.0E-03

4.0E-03

3.0E-03 Diameter [m] Diameter

2.0E-03

1.0E-03

0.0E+00 01234567 Time [s] (b)

Fig. 16. Calculated jet lengths (a) and mean particle diameter (b) for experiment FARO L-28 obtained with standard interfacial friction formulation (f_intfric=1.0), parametrically reduced interfacial friction (f_intfric=0.001) and the new interface friction model (New model).

Applying the new model, the majority of the fragmented melt mass (around 50 %) is in the regions with void concentration between 20 % and 40 % (see Fig. 17). By this smaller void, a continued heat transfer at high level is obviously supported, in contrast to the standard friction formulation yielding high void. Concerning the break-up process, it can be seen from Fig. 16 that the resulting jet length is smaller 51 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 with the less voided mixture by about 20 %. The mean mass fragment diameter develops to about 3 mm in the case with reduced friction and to about 4.5 mm in the case with the previous modelling. These feedback effects appear not to be sufficient to explain the large differences in pressure rise and energy release presented in Fig. 10, Fig. 11 and Fig. 13, Fig. 14, respectively. The present calculations show that by applying the new model with reduced interfacial friction, a significant improvement between calculated and experimental data has been achieved, considering a constant pressure buildup, heat transfer, void distribution in the mixture and jet break-up. However, the calculated heat transfer underestimates the experimental values which require further analyses. Moreover, it appears that the reduction of heat transfer in regions of high void plays a major role in the cases utilizing present approaches. These approaches still require further improvement, especially concerning the deficits in the radiation description and the modelling of jet break-up considering feedback with mixture conditions. Concerning the latter, a stronger effect with high void may also result, if the driving head based on the mixture density is determined in a smaller region around the jet or, correspondingly, if the calculated steam velocities close to the jet are directly applied.

100 100 1% void < m-% <= 20% void 20% void < m-% <= 40% void 40% void < m-% <= 60% void 80 80 60% void < m-% <= 80% void 80% void < m-% <= 100% void total mass in mixture 60 60

40 40 Mass in mixture [%] inMass mixture Total mass in mixture [kg] in mixture mass Total 20 20

0 0 01234567 time [s]

Fig. 17. Fragmented melt mass in regions with different void concentration for experiment FARO L-28 obtained with the new interface friction model (New model).

4.3 Additional investigations related to the initial phase of the FARO L-28 experiment

In the initial phase of the FARO L-28 experiment, a stronger pressure increase, in comparison with the later, quasi-steady period can be observed (see e.g. Fig. 18, Experiment). Pressurization increases from the jet-water contact up to the estimated

52 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 time for melt-bottom contact (~1.2 s) in a nearly linear way. It is characterized by a stronger, probably non-steady evaporation rate and heat input into water (see Silverii et al., 1999). The time of the subsequent decrease of the pressurization rate also corresponds to the time of start of water overflow. Although it is difficult to say whether the decrease is due to a change of heat transfer mechanisms or simply due to water depletion, the fact that the pressurization rate decreases far more rapidly than the water level, gives an indication in support of the first mechanism. Furthermore, the rise of the water level can be taken as a result of an increased void, marking the transition to a finally established, quasi-steady behaviour. Taking into account the safety issue and the assumption that triggering of steam explosion will most likely occur at the time of first melt-bottom contact (MBC), the initial phase (up to MBC) might be of special importance. With respect to the possible mechanism explaining this sharp pressure increase at the beginning of melt water interaction, two different views exist, discussed also in the scope of SERENA phase 1 (Bürger and Buck, 2005). According to Corradini, this phase is characterized by a specific mechanism of fragmentation at the jet leading edge, based on Rayleigh- Taylor instabilities and associated with direct melt-water contact. After that, fuel- coolant mixing is considered to be mainly a process on the chamber base i.e. fuel- melt accumulation, associated melt-water mixing and quenching in water at the chamber base. However, even if it is sufficient to reproduce the strong pressure increase in the initial phase, leading edge fragmentation cannot explain the later, quasi-steady phase of mixing which is decisive for understanding the mixing processes of melt and water, considering several important implications on the flow patterns, melt fragmentation, evaporation processes etc. (see above). After reaching the sharp pressure increase in the initial phase, the energy release and pressure stagnate or decrease already after about 2 s, due to strong counteraction of high void to effective heat transfer from melt to coolant (OECD Nuclear Energy Agency, 2006). On the other hand, it is very likely that most of the aspects related to the mixing during the long, quasi-steady phase are also effective during the first initial step, even if it is not possible to precisely determine their exact influence. Also, it must be considered that in this initial period, additional uncertainties about processes exist, as e.g. the initial distortion of jet or the initial break-up processes at impact on the water surface. This does not mean that these processes dominate the phase, but they certainly contribute. Furthermore, it does not appear probable that an initially overwhelming break-up mechanism (Rayleigh-Taylor) is after the first fall replaced by a totally different mechanism supporting the pressure rise at a similar rate (approximately 60 % of initial rate). Thus, this seems to indicate that there is a transition to this behaviour, certainly with additional effects. A transition from a phase of jet instabilities and break-up by Kelvin-Helmholtz like stripping under thin film boiling (i.e. instabilities and fragmentation determined by jet velocity and density

53 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 of water; see Epstein and Fauske, 1985) to stripping under steam flow in the developed multiphase environment may be expected if the latter process is considered to dominate. This will then result in shorter jet lengths and smaller particles in the initial phase (in comparison with the quasi-steady phase) which would lead to stronger evaporation rates and pressurisation.

1.6E+06 Experiment void criteria = 30% void criteria = 40% 1.4E+06 void criteria = 50% void criteria = 60% 1.2E+06 void criteria = 70%

1.0E+06 Pressure [Pa] Pressure

8.0E+05

6.0E+05

01234567 Time [s]

Fig. 18. Calculated pressure increase for experiment FARO L-28, considering transition between thin to thick fragmentation models, obtained by varying void criteria between 30 %, 40 %, 50 %, 60 % and 70 %.

In the model proposed by Epstein and Fauske (1985), two different types of jet break-up are considered, based on the conditions of the coolant surrounding the jet. If the coolant is mostly liquid, the conditions are considered as a thin film i.e. only a very thin vapour film over the surface of the melt jet exists. In such case, the fragmentation is driven by the liquid itself. In the simplified approach used in the

IKEJET/IKEMIX code, in Eq. (4), Eq. (8) and Eq. (10) instead of ρa and vv (ambient properties of jet surrounding mixture), ρl and vl are assumed (vl considered to be zero due to small motion of water). On the other hand, if the coolant is a mixture of vapour and liquid, then the fragmentation is driven by thick film conditions i.e. by properties of ambient fluid estimated around the jet, as it is presented in Chapter 3.1. The jet break-up under thin film conditions as well as transition between two fragmentation models according to void criteria have been implemented in the IKEJET/IKEMIX code. The calculations for the FARO L-28 are carried out assuming the same set of numerical parameters as in the previous simulations, also considering the new model for interfacial friction. Taking into account that no modelling of vapour film thickness around the jet exists in the present version of IKEJET/IKEMIX, the averaged void in the mixture over the radius of 15 cm is

54 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28 integrated along the jet under the water surface. This is taken as the criteria for transition between the two fragmentations mechanisms. This value also corresponds to estimations of Epstein and Fauske (1985) for thicknesses of vapour films around a corium jet at ~3000 K. When the averaged void exceeds certain value, assuming that a thick vapour film around the jet is established, the fragmentation is changed from thin to thick film conditions. Calculations are performed by varying transition criteria between several values (i.e. averaged void around the jet more than 30 %, 40 %, 50 %, 60 % and 70 %). In Fig. 18, calculated pressure increases are shown in comparison with the experimental measurement obtained for switching between two fragmentation models. The sharp pressure increase in the initial phase for the void transition criteria between 30 % and 60 % is reproduced with a good accuracy, but only for a very short duration. After the thick film fragmentation took a place, the pressure buildup underestimated experimental data i.e. transition between two fragmentations models occurred too early. Assuming that fragmentation driven by thick film conditions first occurs when averaged void around the jet reaches 70 %, much better agreement with the experimental data is achieved for both, the initial and the later, quasi-steady phase (see Fig. 18, void criteria = 70 %). Due to higher density of water, taken as an ambient medium during the initial phase, shorter jet length and smaller mean particle diameters are obtained in the first ~1 s (Fig. 19). The average particle diameter during the initial phase is approximately 0.6 mm, while after transition to thick film conditions it increases up to 2.3 mm (somewhat smaller in comparison with the previous calculations (Fig. 16b) due to longer falling time of smaller particles). The respective jet length at the beginning of melt-water interaction is ~30 cm in comparison with ~70 cm obtained during longer quasi- steady period of mixing.

1.0 void criteria = 70%

0.8

0.6

0.4 Elevation [m] Elevation

0.2

0.0 01234567 Time [s] ´

(a)

55 4 Verification of the IKEJET/IKEMIX code with the premixing experiment FARO L-28

4.0E-03

void criteria = 70%

3.0E-03

2.0E-03 Diameter [m] Diameter

1.0E-03

0.0E+00 01234567 Time [s]

(b)

Fig. 19. Calculated jet length (a) and mean particle diameter (b) for experiment FARO L-28 obtained by assuming that transition from thin to thick fragmentation models occurs when averaged void surrounding the jet reaches 70 %.

The obtained results indicate a possibility of a consistent description of both (initial and quasi-steady) phases of the FARO L-28 experiment, based on break-up by Kelvin-Helmholtz like stripping for thin and thick film boiling. Although the initial phase of melt-water interaction could be important due to a high likelihood that triggering occurs at the time of the first MBC, additional uncertainties exist with respect to jet break-up behaviour (initial jet distortion, effects of the initial melt- water impact etc.). Also, only few experimental data about this phase are available, therefore it is hard to judge if stronger pressurisation obtained in the initial phase is a result of these effects or of some different fragmentation mechanism (e.g. leading edge fragmentation based on Rayleigh-Taylor instabilities, Kelvin-Helmholtz thin film stripping etc.). Thus, a later quasi-steady phase appears as more valuable considering the understanding of basic features related to mixing between melt and water, supported by constant pressurisation, heat transfer, void development and jet break-up. However, a consistent explanation could be provided by transition from the jet break-up fragmentation for thin to thick film conditions, after sufficiently thick vapour film around the jet is established. This would yield smaller particles and consequently a higher void, supported with stronger pressure increase at the beginning of melt- water interaction. Considering the reactor conditions, this would result in even stronger counteraction of high voiding mixture to vigorous steam explosions. Therefore, when considering an application of the models to reactor conditions, it is a conservation feature to neglect these additional contributions yielding finer break- up in the premixing phase.

56 5 Verification of the IDEMO code with explosion experiments

5 Verification of the IDEMO code with explosion experiments

5.1 Experimental database

Another experimental program carried out in order to investigate melt-coolant premixing, as well as the propagation and energetics of spontaneous and externally triggered steam explosions, is the KROTOS experiment (Huhtiniemi, 1999) performed at JRC Ispra. This program was carried out in support of the large scale FARO experimental program and was used for back-up and fundamental research testing in the field of FCIs. A compromise between 1-D and 2-D geometry of the interaction region (smaller radius of the test vessel in comparison with the FARO experiment) was chosen in order to adjust experimental conditions so that proper premixing could be achieved as well as to maintain the experimental data required for a 1-D computer model validation. Tests were performed with prototypic (corium) and simulant material (alumina) pouring melt with jet radius of 3 cm into a 1.1 m deep water pool inside a test vessel having a diameter of 0.2 m. Achieved melt temperatures were around 3200 K. Up to 5.5 kg of melt mass was released, into saturated or, up to 120 K, subcooled water under different system pressures from 0.1–0.36 MPa. The test facility contained three main components: the radiation furnace on the top, the release tube connecting the furnace to the pressure vessel, and the test section below (see Fig. 20). The applied test procedure was the same as in the FARO experiments (see Chapter 4.1). First, material was heated in the furnace and discharged into the 5 m release tube. The tube was then broken at the bottom by a puncher, providing the release of the melt to the test vessel filled with water. In some tests, when the jet penetrated sufficiently deep into the water column (without exploding spontaneously), an external trigger was applied. Pressure, temperature and water level swell were the main experimental parameters measured during melt-coolant interactions in the KROTOS experiments. Additionally, some tests have been captured by high speed video camera. Debris analysis mainly consisted of visual recordings of the debris bed during removal, scanning electron microscopic analysis and determining the particle size distributions by sieving. Major outcomes from these tests are very strong explosions that have been observed with alumina melt, achieving pressure peaks up to 100 MPa, dependent neither on

57 5 Verification of the IDEMO code with explosion experiments water subcooling nor on spontaneous/external triggering. On the other hand, for the KROTOS tests with corium, only moderate explosive interactions have been obtained (maximal measured pressures up to 10–22 MPa), under a wide range of initial conditions. Moreover, visual observations, as well as post-test debris analyses from experiments without explosion, showed different jet break-up behaviour between corium and alumina melts. Generally, alumina melt fragments into larger particles, yielding a coarse mixture with water. For example, in the test K-57 with alumina melt, performed at system pressure of 0.1 MPa and water subcooling of 83 K, no coherent melt jet exists. The melt is broken up into relatively large particles distributed over the whole test cross section, as can be seen in Fig. 21. Debris analyses showed that more than 70 % of particles were above 10 mm (Huhtiniemi et al., 1998).

Fig. 20. KROTOS test facility.

Conversely, it was found that for the experiment KT-1 performed at ambient pressure of 0.37 MPa and with 123 K water subcooling, the corium falls in form of the jet concentrated in the central part of the test vessel. Also, a stripping of relatively small fragments from the jet can be observed (see Fig. 21). Debris

58 5 Verification of the IDEMO code with explosion experiments analyses after the experiment showed that 70 % of fragments were less than 1 mm (Magallon et al., 2000). Although the KROTOS alumina experiments are not prototypic with respect to melt material and their quasi-1D character, they are of major importance for the validation of steam explosion codes with respect to the inherent wave dynamics and associated models for fine fragmentation and rapid heat transfer. Among them, especially suitable is a test K-44 (Huhtiniemi et al., 1999) with relatively well defined conditions and detailed measurements, showing clearly detectable escalating and propagating waves. Estimated propagation velocities are within the range from 450 m/s to 1000 m/s, with pressure escalation up to ~50 MPa. With regard to modelling, the IDEMO code must be able to reproduce this very strong explosion under the given experimental conditions. Being able to demonstrate this, credible applications can be done for prototypic reactor case.

Fig. 21. Visual observations of corium melt mixing from KT-1 (left) and alumina melt mixing from K-57 (right) tests.

Alternately the test FARO L-33 (Magallon and Huhtiniemi, 2001) is currently the only “integral” (premixing and explosion) large scale experiment relevant for reactor conditions, as well as the only one among FARO test series which has resulted in explosion, albeit a weaker one. It involved a relatively large corium mass (100 kg, with 40 kg released at the time of explosion triggering) heated up to 3070 K. Also, the large test vessel used in FARO tests (70 cm diameter, 1.7 m height, see Fig. 7) features the formation of a non-homogeneous mixture and a 2D behaviour during premixing and also explosion phase. The trigger characteristics (intensity, time and location) are known with precision as being externally activated. Instrumentation allows a good characterisation of the explosion propagation. Thus, among the experiments performed with prototypic material and in prototypic reactor conditions,

59 5 Verification of the IDEMO code with explosion experiments this test is chosen as the most suitable for validation of the thermal detonation model. The main uncertainties with respect to the explosion model validation are related to different explosivity between alumina and corium melt, obtained in the relevant experiments. It is to be tried to understand and to explain these differences as well as to reproduce them with the models, especially having on mind an unique description for the different cases in order to be able to extrapolate it to reactor conditions.

5.2 Explosivity of corium versus alumina in KROTOS and FARO experiments

Taking into account nuclear reactor safety, vulnerable explosions with corium cannot be excluded in general, just based on the experiences from KROTOS and FARO tests, although this would be the easiest and the clearest way to gain surety. Better understanding of this different behaviour is certainly required in order to achieve a sufficient level of conservativity concerning reactor application. Through visual observation from the KROTOS experiments, as well as according to fragment size distributions in experiments that resulted with no explosions, it was estimated that the average fragment size obtained in the premixing phase was much smaller with corium compared to alumina (Magallon, 2006). No differences were considered to exist in the process of melt release to the water. According to visual observations (see Leskovar et al., 2007), a strong break-up of alumina melt in KROTOS tests may occur already before or upon impact with the water surface. High impact velocities at the intermediate catcher could result in even more increased outflow velocities of the melt jet producing strong disturbances of melt and partial mass accelerations and break-up. Such strong leading edge disturbances of jets have also been observed with corium. However, these effects should be much more pronounced with the low density alumina. For such a case, melt enters into the water not in the form of compact jet but rather as already broken parts which then result in large melt particles and consequently lower voids that support strong steam explosions. On the other hand, the higher density of corium strongly affects jet break-up (yielding higher Weber numbers), resulting in smaller fragments and high voiding mixture. High void also resulted from hydrogen production by corium. Such increased void shelters the melt from contact with water, reducing heat transfer and also increasing the compressibility of the system. Additionally, smaller fragments associated with lower thermal conductivity and lower melt superheat in FARO and KROTOS experiments make a crust formation more pronounced with corium. A low

60 5 Verification of the IDEMO code with explosion experiments superheat of melt results with high viscosity and rapid formation of a solid crust. A low thermal conductivity has the same effect at the melt surface with water. This rapid development of solid crust on melt surface is especially emphasized in subcooling conditions.

100

FARO L-14 FARO L-19 Particle Diameter [mm] Diameter Particle 0.1 FARO L-20 KROTOS 37 KROTOS 45

0.01 0.01 0.1 1 10 30 50 70 90 99 99.9 99.99 Mass Fraction Less than Indicated Diameter [%]

Fig. 22. Particle size distributions of FARO and KROTOS non-explosive tests with corium (Magallon, 2006).

It is also to be mentioned that somewhat larger particles were obtained for FARO than for the KROTOS corium experiments (both non-explosive, see Magallon, 2006). This is valid over a wide range of conditions in these experiments. The fragment distributions from several (non-explosive) experiments are given in Fig. 22. These differences may be attributed to different experimental conditions, i.e. melt velocity at water surface (larger in KROTOS than in FARO at the very beginning of the injection) and jet diameter (30 mm in KROTOS against 50 or 100 mm in FARO tests), yielding different jet break-up behaviour. However, in view of the detected importance for understanding the corium-alumina difference in KROTOS experiments, a different jet break-up yielding somewhat larger particles in FARO tests required also further investigation. Besides particular uncertainties related to jet break-up, the resulting smaller fragments appear to be the key to understand weaker corium interactions. Of course, the effects of solidification, inert gas and low superheat may separately play a role and limit the strength of explosions also in cases with break-up of melt into larger drops. In addition, no specific material influences could be identified in the fine fragmentation process in the explosion (i.e. different than ones already taken into account in fragmentation models as in IDEMO). In SERENA Phase 1 (see e.g. OECD Nuclear Energy Agency, 2006), some participants have used different parameters for fine fragmentation of corium than of alumina in order to account for the weaker 61 5 Verification of the IDEMO code with explosion experiments explosion results with corium. However, this is stated as problematic since different material behaviour in fine fragmentation has not been explained or phenomenologically shown. The difference would then be attributed to the wrong process which would yield problems for understanding and extrapolating to other conditions. Thus, although a general argument about different explosivity of corium versus alumina cannot be drawn from the KROTOS and FARO experiments, it appears that major differences in these experiments regarding explosion energetics occur already during premixing.

5.3 Results of IDEMO calculations performed for KROTOS K-44 and FARO L-33 experiments

First calculations carried out with IDEMO code showed that experimental results cannot be reproduced adequately with the same set of parameters for both experiments, considering decisive processes in the pressure wave. Although extensive validation work has been performed covering also e.g. axial and radial variations of mixture conditions, variations of trigger strength etc. (see Bürger et al., 2004), only selected results for the tests K-44 and L-33 are presented here. Calculations are done for the given premixtures, estimated from the experimental data (see Appendix B). For the test K-44, the reference initial conditions seem to give a reasonable representation of the results of premixing, which is also largely in agreement with measurements obtained during premixing and wave dynamics during explosion in the experiment. Visual observations available from later KROTOS experiments suggest that the premixing zone extends over the whole cross section, in contrast to the premixing behaviour obtained in experiments with a larger diameter of the test section, as in FARO L-33. Therefore, additional variations in mixing properties are not required. Assuming a very rapid heat transfer from fragments to coolant, with heat transfer coefficient of 5x105 W/ (m2K), relatively close agreement with experimental results for pressure levels, wave propagation speed and duration of pressure pulses has been obtained. In Fig. 23, calculated pressure pulses are shown in comparison to values obtained by pressure transducers at different elevations (350 mm (K2), 550 mm (K3), 750 mm (K4) and 950 mm (K5), see Fig. 20) along the test vessel wall. In the next approach, calculations have been performed for the experiment FARO L- 33 for the given premixture (see Appendix B, Table B-2), using same set of numerical parameters. According to experimental observations, it was assumed that mixing only took place in an inner region of the test section, while an outer annular zone contained only water not participating in mixing. Calculated pressure pulses have, by far, overestimated experimental values. Good agreement with experiment could be achieved by assuming a smaller heat transfer coefficient e.g. by factor 10 in

62 5 Verification of the IDEMO code with explosion experiments comparison with K-44 calculations (i.e. 5x104 W/ (m2K)), keeping other parameters unchanged. Also, taking into account the given mixture conditions, additional variations of mixture properties have been performed considering void fractions in inner mixing region, assumed initially to be 5 % (see Appendix B, Table B-2). Namely, first calculations using smaller heat transfer coefficient of 5x104 W/ (m2K) showed escalation and propagation of an explosion wave, starting from the external trigger with maximum and long-term pressure beyond, but approximately in the range of the experimental measurements (see Bürger et al., 2004). However, the calculated propagation speed of the pressure wave was faster than in the experiment which implies that the assumed vapour volume fraction was too low.

5,0*107 6,0*107 EXP/PTK2.0350 EXP/PTK3.0550

7 7 IDEMO/PT/Wall/348mm 5,0*10 IDEMO/PT/Wall/548mm 4,0*10

4,0*107 3,0*107

3,0*107 2,0*107 2,0*107

7 Pressure / Pa 1,0*10 Pressure / Pa 1,0*107

0 0,0*10 0 0,0*10

-1,0*107 -1,0*107 1,499 1,5 1,501 1,502 1,503 1,504 1,499 1,5 1,501 1,502 1,503 1,504 Time / s Time / s 7,0*107 6,0*107 EXP/PTK4.0750 EXP/PTK5.0950 7 6,0*10 IDEMO/PT/Wall/748mm 5,0*107 IDEMO/PT/Wall/948mm

5,0*107 4,0*107

4,0*107 3,0*107 3,0*107 2,0*107 2,0*107 Pressure / Pa Pressure / Pa 1,0*107 1,0*107

0 0,0*100 0,0*10

-1,0*107 -1,0*107 1,499 1,5 1,501 1,502 1,503 1,504 1,499 1,5 1,501 1,502 1,503 1,504 Time / s Time / s Fig. 23. Comparison of pressure histories at pressure transducer locations measured in the experiment KROTOS K-44 and calculated with IDEMO assuming a heat transfer coefficient of 5x105 W/ (m2K).

Therefore, void fractions in the mixture were varied between 5 % and 60 %, associated with respective water volume fractions. For vapour fractions between 20 % and 40 % only a small effect has been observed concerning the magnitude of the pressure waves, giving a similar pressure level, somewhat lower than in the 5 % case and thus closer to the experiment. This can be explained by counter-acting effects of stronger hydrodynamic fragmentation versus larger compressibility with increasing void. For a vapour volume fraction of 60 % and above, no further pressure escalation has been obtained. In Fig. 24, calculated pressure pulses are given in comparison to corresponding experimental data measured at different

63 5 Verification of the IDEMO code with explosion experiments elevations (490 mm, 715 mm, 940 mm and 1165 mm) along the wall of test vessel. The results have been achieved assuming heat transfer coefficient of 5x104 W/ (m2K) and void fraction in the mixture of 30 %.

6,0*106 EXP/PT.05.337.0490.245_YUW EXP/PT.05.337.0715.245_YUW 6 6 5,0*10 IDEMO/PT/Wall/486mm 6,0*10 IDEMO/PT/Wall/710mm

4,0*106

4,0*106 3,0*106

2,0*106 2,0*106 1,0*106 Pressure / Pa Pressure / Pa

0,0*100 0,0*100

-1,0*106

-2,0*106 -2,0*106 1,125 1,13 1,135 1,14 1,125 1,13 1,135 1,14 Time / s Time / s

6,0*106 EXP/PT.05.337.0940.245_YUW EXP/PT.05.337.1165.245_YUW 6,0*106 5,0*106 IDEMO/PT/Wall/934mm IDEMO/PT/Wall/1158mm

4,0*106 4,0*106

3,0*106

6 2,0*106 2,0*10 Pressure / Pa Pressure / Pa 1,0*106 0,0*100 0,0*100

-1,0*106 -2,0*106 1,125 1,13 1,135 1,14 1,125 1,13 1,135 1,14 Time / s Time / s

Fig. 24. Comparison of pressure histories at pressure transducer locations measured in the experiment FARO L-33 and calculated with IDEMO assuming a heat transfer coefficient of 5x104 W/ (m2K).

Other participants in SERENA either failed at reproducing the experimental results or found good agreement via choosing different parameters (OECD Nuclear Energy Agency, 2006). Good agreement with experimental data could be achieved by varying the heat transfer coefficient, as in IDEMO or e.g. by varying parameters in correlation with the fine fragmentation (see e.g. Bürger et al., 2007). As was previously discussed concerning differences between KROTOS experiments with alumina and corium, there are already obvious differences in the coarse break-up in premixing and thus in the mixing process as well. Thus, to simply replace these effects by a reduction factor in the fine fragmentation correlations appears to be false. On the other hand, assuming slower heat transfer from melt to coolant in calculations with corium melt can be explained by not taking into account partial freezing of melt droplets during the premixing phase. However, concerning reactor application, explanations with rather unique parameter sets are to be searched for. Such an explanation, which indeed finally influences the amount of fine fragmentation, may be related to the differences in solidification of melt droplets

64 5 Verification of the IDEMO code with explosion experiments partly due to material effects (e.g. low heat conductivity of corium, low superheat etc.), but mainly given already by different break-up. Furthermore, significantly higher subcooling in the FARO L-33 experiment (124 K in comparison with 10 K in K- 44) makes crust formation especially pronounced. In general, it would be important to gather a perspective on the solidification during premixing in order to explain the differences and to justify the reduced amounts involved in fine fragmentation.

6.0*106 7.0*106 EXP/PT.05.337.0490.245_YUW EXP/PT.05.337.0715.245_YUW 6 6 6.0*10 5.0*10 IDEMO/PT/Wall/488mm IDEMO/PT/Wall/713mm

5.0*106 4.0*106

4.0*106 3.0*106 3.0*106 2.0*106 2.0*106 1.0*106 6 Pressure / Pa Pressure / Pa Pressure 1.0*10

0.0*100 0.0*100

6 -1.0*10 -1.0*106

-2.0*106 -2.0*106 1.125 1.13 1.135 1.14 1.125 1.13 1.135 1.14 Time / s Time / s

7.0*106 8.0*106 EXP/PT.05.337.0940.245_YUW EXP/PT.05.337.1165.245_YUW 6 6.0*10 IDEMO/PT/Wall/938mm IDEMO/PT/Wall/1163mm 6.0*106 5.0*106

6 4.0*10 6 4.0*10

3.0*106

6 6 2.0*10 2.0*10 Pressure / Pa Pressure / Pa Pressure

1.0*106 0.0*100 0.0*100

-1.0*106 -2.0*106 1.125 1.13 1.135 1.14 1.125 1.13 1.135 1.14 Time / s Time / s

Fig. 25. Comparison of pressure histories at pressure transducer locations measured in the experiment FARO L-33 and calculated with IDEMO assuming that only 15% of the prefragmented melt droplets participate in the explosion (heat transfer coefficient of 5x105 W/ (m2K)).

Calculations for FARO L-33 have been performed excluding an amount of melt drops considered as sufficiently crusted by varying amount of mass participating in the explosion due to variations of melt volume fractions. This was carried out in order to check if a sufficient explanation for the differences in explosivity obtained by alumina and corium melts could be achieved by assuming certain part of the fragmented mass as frozen during premixing, Experimental results have been approximately approached assuming that just 15 % of fragmented mass participate in an explosion (see Fig. 25). The set of numerical parameters, especially considering heat transfer coefficient (i.e. 5x105 W/ (m2K)) were kept unchanged as in the K-44 calculations. Calculations were performed with a given premixture (Appendix B, Table B-2) assuming the void fractions in the mixing zone of 30 %. Approached results indicate the perspective of a unified modelling. However, further confirmation is required and

65 5 Verification of the IDEMO code with explosion experiments the modelling of solidification under premixing could play an important role in determining the differences in behaviour of the corium and alumina cases, in addition to different break-up. In view of the present uncertainties of the solidification description and evaluations of the required crust thickness for exclusion or significant reduction of fine fragmentation, the reduction effects on explosion strength due to solidification are not taken into account in the present study. For the explosion part of the reactor calculations (Chapter 6.2), the same parameters are used as applied in KROTOS-44, i.e. for the alumina case with strong pressure escalations. This is to be understood in a conservative sense. Major limitations to the explosions, at least under saturated conditions, are already considered to result from the limitations of the mixed mass by realistic scenario and break-up conditions as well as from high void with drop sizes from jet break-up.

66 6 Application to reactor conditions

6 Application to reactor conditions

Calculations for reactor conditions are carried out to assess the capabilities of the premixing and explosion codes in general and to get a perspective of the limiting effects to explosion strength and resulting loads. The assessment has been performed for an assumed in-vessel case considering the presence of water in the lower plenum of the RPV. The main aim of the numerical calculations is to investigate the largest possible steam explosions for the underlying scenario conditions as well as to estimate their loads and the potential damage to the RPV, irrespective of the likelihood of these events. Emphasis is given to the influence of jet break-up and water depletion, which have been identified as major limiting factors of steam explosion strength. The most challenging conditions have been assumed, considering the largest amounts of melt in mixtures, while taking into account realistic accident scenarios and assumed geometry. This is to be done by varying the melt material composition, the melt diameter, the melt flow rate, the water level, the possible lateral extension of the mixture and the time of explosion triggering.

Jet release = 2.3 m

Tmelt = 3050 K Djet = 10/ 20/ 40 cm

Water level = 2 m

Water level = 1 m Twater = 408 K System pressure = 0.2 MPa

Fig. 26. Schematic sketch of an assumed in-vessel case with a sideways melt jet outflow from the reactor core into the water in the lower plenum of the RPV used for premixing and explosion calculations.

6.1 Premixing calculations

Premixing calculations have been performed with the IKEJET/IKEMIX code in 2D cylindrical geometry addressing an accident scenario with a sideways jet outflow

67 6 Application to reactor conditions from the reactor core into the water of the lower head of the RPV (see Fig. 26). The melt composition and temperature, considered as prototypic for reactor conditions, correspond to the FARO L-28 experiment i.e. corium oxidic melt (80 wt% UO2 –

20 wt% ZrO2) with the temperature of 3050 K. The outflow of the melt jet from the reactor core is assumed to occur at the height of 2.3 m, measured from the bottom of the RPV. The leak size is varied between 10 / 20 / 40 cm diameter, covering range of melt flow rates between 188 / 754 / 3016 kg/s respectively, and considering an outflow velocity of 3 m/s. It is assumed that, at the time of melt outflow into the lower plenum of the RPV, the water is at saturation temperature. With an ambient pressure of 0.2 MPa, the temperature of water is estimated to 408 K For the present calculations, the water level has been varied between two values, representing the water surface under lower core support plate (1 m) and just below the jet outflow from the core (2 m). Regarding the premixing calculations, first indications about explosion strength can be taken by estimating of the amount of fragmented melt mass in the mixture in regions having a low void. In general, larger quantities of melt mixed with water/steam having low void fractions will result in an increase of the mixture’s explosivity. Previous investigations and IDEMO calculations (see Chapter 1.2 or e.g. Bürger et al., 2004 and Vujic et al., 2007) showed that voids in the mixture higher than a certain value (50 – 60 %) decrease the possibility of pressure wave escalations and propagations significantly, preventing strong steam explosions. Taking into account model uncertainties and dependences on calculation conditions (e.g. melt volume fractions in the mixture) this value shouldn’t be considered as a fixed boundary. As a tentative upper limit of void concentration in the mixture under which it is still possible to obtain strong steam explosions, here the void is taken to be 60 %.

6.1.1 Modelling suppositions

The numerical discretization and assumed geometry configuration are shown in Fig. 27. The specific geometry of the lower plenum is not modelled assuming that melt interaction with curving lower head boundary doesn’t have significant influence on mixing conditions. The configuration with the sideways outflow of a melt jet from the reactor core in the lower head of the RPV is predominantly non-symmetric (see Fig. 26). A symmetric behaviour around the jet of break-up, distribution of particles, void development etc. may be assumed in the water. However, constraints for these processes are to be expected close to the RPV wall, especially concerning the lateral expansion of the

68 6 Application to reactor conditions mixture, i.e. the fragments of melt and the produced void. Only an approximate description of this situation is possible when employing a 2D model. As outlined above, the major concern is the possible mass of melt in a mixture with low void, which is a key in determination of the possible explosion strength. Thus, the expansion of the mixture resulting in lower or higher melt volume fractions and the corresponding establishment of void are the key aspects of limitations given by the existence of the wall. In order to address these aspects within the 2D approach, a symmetrical development around the jet is considered, but under variation of a radial constraint (radius of domain), in order to take the wall into account.

3.5

3.0

2.5

Melt inlet 2.0 height [m] 1.5

1.0

0.5

0.0 0.00.20.40.60.81.0 radius [m]

Fig. 27. Numerical discretization used for premixing calculations performed with IKEJET/IKEMIX code.

Fig. 28 presents the results of calculations performed for the case with Dj = 10 cm and water level of 2 m, by varying the radius of the calculation domain between 0.5 m, 1 m and 1.5 m. Void fractions are given for the time of the first melt bottom contact estimated to occur at 0.71 s (see Table 2). It is shown that in the case with the smaller radius (0.5 m), void in the mixture is generally higher than in the corresponding cases with larger calculation domains, mainly due to melt-richer mixture yielded by insufficiently extended mixing zone. A larger radial extension allows an increased radial distribution of melt droplets in a larger water volume and tends to improve the distribution of the steam produced. This leads to a reduction of the void content of the mixture. With sufficiently large extension, the effect of the wall becomes negligible, hence results change little with further increase of the wall 69 6 Application to reactor conditions distance. E.g. no significant differences are obtained in the development of void fractions between the cases with radius of 1 m and 1.5 m (Fig. 28, b and c). Thus, the question whether limited expansion by a wall can produce more or less critical mixtures yielding higher or lower loads appears to be adequately addressed as a major question in this approach. Certainly, expansion towards or away from the wall are non-symmetrical effects which cannot be effectively simulated. Thus the non- symmetrical distributions and flows of particles and steam are also not fully accounted for. However, the expansion effects themselves are included in the consideration of symmetric regions around a jet with variable radii.

(a) (b) (c)

Fig. 28. Void fractions at the time of first melt bottom contact (t=0.71 s) for the case with oxidic jet of 10 cm diameter and 2 m water depth obtained by varying radius of calculation domain between 0.5 m (a), 1 m (b) and 1.5 m (c).

In the present calculations, the radius of the calculation domain was chosen to be 1 m. By varying the domain’s radius it can be shown that the extension of the calculation domain is large enough such that the expansion of the mixture is not hampered. Thus, the choice is conservative, considering that in real geometry parts of the outflowing melt jet will be close to the RPV side wall which will hinder steam release and lead there to an increased void.

6.1.2 Results of the premixing calculations

An overview of the obtained results is given in Table 2. Presented results are estimated at the moment of the first MBC, when triggering is considered to occur. It is assumed that a steam explosion will be most likely triggered when the melt stream

70 6 Application to reactor conditions comes into a contact with a cold RPV wall, resulting in direct contact between melt and water (see Chapter 2.4.3). Results are given for two different water levels and for three different melt jet diameters i.e. different melt flow rates. Table 2 shows the masses of droplets mixed with water and steam, up to certain void fractions (30 %, 40 %, 50 %, 60 %). In addition, the total fragmented melt mass in mixture (only melt droplets, not unfragmented jet) as well as mass flow rates and mean particle diameters are presented.

Water level = 1 m Water level = 2 m

Jet diameter [cm] 10 20 40 10 20 40 Melt bottom contact [s] 0.42 0.42 0.42 0.71 0.44 0.43 Mass flow rate [kg/s] 188 754 3016 188 754 3016 Mean particle diameter [mm] 3 3.1 3.1 3.2 2.3 2.5

Total mass in mixture [kg] 14 34 68 102 154 360

Mass in mixture with void 0.5 0.7 2.1 4.5 0.4 1.8 less than 30 % [kg]

Mass in mixture with void 0.5 1.1 3.9 6.2 0.7 3 less than 40 % [kg]

Mass in mixture with void 1.2 2.4 11.5 10 1.4 7 less than 50 % [kg]

Mass in mixture with void 2.5 8.1 18.2 21.5 4.7 28 less than 60 % [kg]

Table 2. Overview of premixing results obtained with IKEJET/IKEMIX code for oxidic melt jet outflow.

In general, the premixing results, summarized in Table 2, show that, except for a water height of 2 m and a jet of 10 cm diameter, only a portion of the inflowing melt jet is fragmented before reaching the bottom. For example, in the case of a 10 cm melt jet and an 1 m water level, around 76 kg of melt was released from the RPV at the time of MBC. From this, more than half has not yet entered below the water level. Assuming that ~35 kg of melt is already under the water, only 14 kg of this mass is fragmented and mostly in high void regions (e.g. ~11.5 kg in regions with void > 60 %). It is expected that a larger jet diameter with a correspondingly higher flow rate increases the amount of fragmented mass in the mixture due to a larger surface available for fragmentation. In fact, larger fragmented masses are obtained, but are at the same time surrounded by a high void. E.g. in the case with jet diameter of 40 cm, the amount of totally fragmented mass is 68 kg with approximately 50 kg surrounded by void > 60 %. Furthermore, it is also expected that a higher water level supports stronger fragmentation of melt jets due to a more

71 6 Application to reactor conditions complete jet break-up which increases the melt mass available for mixing with water. Again, as in the previous calculations, larger jets and higher water level produced larger amounts of fragmented mass, but higher melt volume fractions and consequently higher void tend to counteract the formation of more “explosive” mixtures. This can be observed for the case with a 40 cm jet diameter and a water level of 2 m. Here, the total fragmented mass is 360 kg, of which approximately 332 kg are surrounded by a void > 60 %. Fig. 29 to Fig. 42 provide more detailed evaluations of the specific premixing calculations. Fig. 29 shows the development of void and melt droplet volume fractions at the MBC during premixing of the 10 cm diameter jet in a water pool with 1 m depth. Fig. 30 gives the development of melt droplet masses mixed with water and steam up to certain void fractions. The respective masses are given relative to the total fragmented mass in the mixture. The premixing results for the case with an initial jet diameter of 10 cm and a water depth of 2 m are given in Fig. 31 and Fig. 32. As can be seen from Fig. 31, in the case with the higher water level, the jet breaks up completely before it reaches the bottom. Due to the longer falling time required for fragmented particles in comparison to a coherent jet, the first MBC appears later, at around 0.71 s (see Table 2). A longer premixing period and complete jet break-up support better mixing of melt with water yielding a relatively lean mixture and a lower void. Considering the mixing conditions, this may be a more challenging case, but due to small jet diameter and correspondingly low flow rate, the maximum melt mass available for explosion remains limited. Thus, the total fragmented mass in mixture, at the time of first MBC reaches 102 kg, of which 21.5 kg are in a void range less than 60 % (see Fig. 32). Also, excessive increases of the voided area can be seen from Fig. 31 and Fig. 32 with continuing melt pouring. Fig. 33 to Fig. 36 give the respective results for the cases with oxidic melt jet of 20 cm diameter with water levels of 1 and 2 m. Contrary to the case with 10 cm jet, parts of the melt reach the bottom as an unfragmented jet even in case of the deeper water level. Due to larger melt mass flow rate and larger surface available for stripping of droplets from the jet surface, the total fragmented mass in mixture is larger in the case with 20 cm jet compared to the 10 cm jet. However, as can be seen from Fig. 34 and Fig. 36, the increase of the fraction of melt in regions with excess void is also much more pronounced. E.g., in Fig. 34 at the MBC, the amount of melt in a region with void less than 60 % is about 8.1 kg of 34 kg totally fragmented mass i.e. ~75 % of the total premixed mass is in high void regions. In the case with the higher water level, high voiding area development is even more extreme due to more fragmented mass in the mixture and larger melt volume fractions on the one side and on the other side, due to smaller mean particles diameter yielded by longer jet and higher relative velocities between melt jet and

72 6 Application to reactor conditions surrounding mixture. The estimated mean particle diameter is 2.3 mm in comparison to 3.1 mm obtained in corresponding case with the 1 m water level (see Table 2). This also leads to the result that in the case with 20 cm jet and 2 m water depth, the mass in void below 60 % at melt-bottom contact is much smaller than in the corresponding case with 10 cm jet, although the total premixed mass is larger. It can be explained by the complete jet break-up in the case with the 10 cm jet, yielding a larger mean particle diameter, longer time for settling and better radial distribution of the melt with consequently lower void. Fig. 37 to Fig. 40 give the respective premixing results for the cases with 40 cm jet diameter and water levels of 1 and 2 m. Due to larger total melt mass flow rate and larger surface available for stripping of droplets from the jet surface, the total fragmented mass in mixture is larger comparing it with the case with 20 cm jet. However, more fragmented mass in the mixture again yields larger melt volume fractions, making the excessive void production more pronounced. As can be seen from Fig. 40, the total premixed masses increase up to and beyond MBC. After MBC the mass of melt in void below 60 % still increases, but not as much as the amount of melt droplets in an excessive void range (above 60 %). This can also be seen from Fig. 39, which gives the development of the vapour and melt volume fraction distributions. At 1 s, most of the mixture containing melt droplets is strongly voided. It can also be seen that the largest part of the inflowing melt reaches the bottom unfragmented. The mixing region around the jet extends to about 80 cm, i.e. the radius of 1 m for the calculation domain is sufficient not to impose radial constraint on the mixing. Nevertheless, due to the large mass involved, the case with 40 cm jet and 2 m water level has the largest potential for a strong explosion yielding 28 kg of prefragmented mass in low void regions (i.e. less than 60 %) at the moment of a first MBC.

6.1.2.1 Metallic melt jet outflow from the RPV

According to potential development of severe accidents, the formation of a metallic melt layer at the top of melt pool, due to the lower density of metallic materials in comparison to oxidic corium, is possible (see Buck, 2007). Experimental observations (see e.g. Evans et al., 1982 and Mitchell and Evans, 1986) also showed more energetic interactions with water obtained by metallic melt than by oxidic. Therefore, in order to take into account the possibility of more vulnerable steam explosions, calculations for reactor conditions assuming metallic melt jet outflow into water of lower plenum are also performed. They are carried out for the case estimated as the most challenging for the oxidic melt, considering the largest amount of fragmented mass in lower void regions (Dj = 40 cm, water level = 2 m). The metallic melt assumed as prototypic in reactor conditions is Fe 70 %, Cr 20 %,

73 6 Application to reactor conditions

Ni 10 % (wt.) alloy, which corresponds to composition of austenitic steel in metallic structures inside the RPV. It is considered that the melt is superheated 200 K, i.e. the melt temperature is estimated to 1920 K (Tliquidus = 1720 K). Except for the material properties, all other initial conditions and numerical parameters remain unchanged, as in the calculations performed for the oxidic melt. The premixing results of calculations performed with metallic melt are given in Fig. 41 and Fig. 42. Again, no complete jet break-up has been obtained. First melt droplets come into contact with the bottom of the RPV after approximately 0.45 s. In Fig. 42 it can be seen that the total fragmented mass in the mixture at the time of first MBC is ~290 kg. From this mass, approximately 41 kg are in the region with voids less than 60 %. As in the previous calculations, a similar trend could be observed i.e. more fragmented mass in the mixture results in higher melt volume fractions yielding as a consequence high voiding mixtures. However, due to the lower melt temperature, a void buildup in the mixture is not as excessive as in the corresponding case with the oxidic melt.

Fig. 29. Development of void and melt droplet volume fraction during pre-mixing of oxidic melt (10 cm jet diameter) in water pool with 1 m depth.

74 6 Application to reactor conditions

55 m-kg <= 30% void 50 m-kg <= 40% void m-kg <= 50% void 45 m-kg <= 60% void 40 total fragmented mass in mixture 35 30 25 20

Mass in mixture [kg] 15 10 5 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 30. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with oxidic melt jet of 10 cm diameter and 1 m water depth.

75 6 Application to reactor conditions

Fig. 31. Development of void and melt droplet volume fraction during pre-mixing of oxidic melt (10 cm jet diameter) in water pool with 2 m depth.

170 160 m-kg <= 30% void 150 140 m-kg <= 40% void m-kg <= 50% void 130 120 m-kg <= 60% void 110 total fragmented mass in mixture 100 90 80 70 60 50 Mass in mixture [kg] mixture in Mass 40 30 20 10 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 32. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with oxidic melt jet of 10 cm diameter and 2 m water depth. 76 6 Application to reactor conditions

Fig. 33. Development of void and melt droplet volume fraction during pre-mixing of oxidic melt (20 cm jet diameter) in water pool with 1 m depth.

100 95 90 m-kg <= 30% void 85 m-kg <= 40% void 80 m-kg <= 50% void 75 m-kg <= 60% void 70 65 total fragmented mass in mixture 60 55 50 45 40 35 30

Mass in mixture [kg] mixture in Mass 25 20 15 10 5 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 34. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with oxidic melt jet of 20 cm diameter and 1 m water depth.

77 6 Application to reactor conditions

Fig. 35. Development of void and melt droplet volume fraction during pre-mixing of oxidic melt (20 cm jet diameter) in water pool with 2 m depth.

450

400 m-kg <= 30% void m-kg <= 40% void 350 m-kg <= 50% void m-kg <= 60% void 300 total fragmented mass in mixture

250

200

150 Mass in mixture [kg] mixture in Mass 100

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 36. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with oxidic melt jet of 20 cm diameter and 2 m water depth.

78 6 Application to reactor conditions

Fig. 37. Development of void and melt droplet volume fraction during pre-mixing of oxidic melt (40 cm jet diameter) in water pool with 1 m depth.

250

m-kg <= 30% void m-kg <= 40% void 200 m-kg <= 50% void m-kg <= 60% void total fragmented mass in mixture 150

100 Mass in mixture [kg] mixture in Mass 50

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 38. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with oxidic melt jet of 40 cm diameter and 1 m water depth.

79 6 Application to reactor conditions

Fig. 39. Development of void and melt droplet volume fraction during pre-mixing of oxidic melt (40 cm jet diameter) in water pool with 2 m depth.

80 6 Application to reactor conditions

900

800 m-kg <= 30% void m-kg <= 40% void 700 m-kg <= 50% void m-kg <= 60% void 600 total fragmented mass in mixture

500

400

300 Mass in mixture [kg] mixture in Mass 200

100

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 40. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with oxidic melt jet of 40 cm diameter and 2 m water depth.

Fig. 41. Development of void and melt droplet volume fraction during pre-mixing of metallic melt (40 cm jet diameter) in water pool with 2 m depth.

81 6 Application to reactor conditions

1,100

1,000 m-kg <= 30% void m-kg <= 40% void 900 m-kg <= 50% void 800 m-kg <= 60% void total fragmented mass in mixture 700

600

500

400

300 Mass in mixture [kg] mixture in Mass 200

100

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Time [s]

Fig. 42. Mass of prefragmented melt droplets surrounded by a mixture with certain void fraction range in the case with metallic melt jet of 40 cm diameter and 2 m water depth.

6.2 Explosion calculations

6.2.1 Initial conditions and modelling suppositions

The premixing results at the time of MBC from the above seven cases (also considering the premixing results obtained from the metallic melt) have been used for explosion calculations performed using the IDEMO code. The volume fractions of melt, water and vapour are transformed to the cylindrical shell geometry used for the explosion calculations, in order to yield the same melt masses and void in the mixing region. Unfragmented parts of melt are not assumed to participate in fine fragmentation during the explosion. Partial solidification of melt droplets as indicated by the IKEJET/IKEMIX calculation is not taken into account, i.e. the total fragmented melt mass is considered to participate in the interaction. Since the fuel droplet temperature is assumed to be constant in the present IDEMO version, average fuel temperatures of 2950 K and 1850 K are determined for oxidic and metallic melts, respectively, taking into account the total energy of the melt. No special material effects, except for those already included in material properties and fragmentation models (see Appendix A), concerning different explosivity between oxidic and metallic melt, are taken into account. Thus, the same calculation parameters have been applied for both melt compositions as they have been used in verification calculations yielding the strongest explosions with alumina melt i.e. KROTOS K-44 experiment (see Chapter 5.3). 82 6 Application to reactor conditions

6.0

5.5

5.0

4.5

4.0

3.5

3.0

Height / m Height 2.5

2.0 Pressure transducers

1.5

1.0

0.5

0.0 0.0 0.1 0.2 0.3 0.4 Radius / m

Fig. 43. Numerical discretization used for explosion calculations performed with IDEMO code.

From the reactor safety standpoint, there is a conservative approach which considers a trigger strong enough to initiate an explosion without a likelihood assessment of such an event occurring (see Chapter 2.4.3). Moreover, the influence of the trigger on the explosion strength was also investigated in the scope of the OECD program SERENA (Bürger et al., 2004). It was concluded that escalation and propagation of steam explosion is practically independent on the trigger strength, once the trigger is strong enough to induce an explosion. Furthermore, it is also shown that imposing of a pressure of 10 MPa and steam volume fractions of 99 % at the bottom in the most inner cell (such that the trigger is not located just inside the jet) is sufficient to initiate an explosion. Accordingly, the same manner of explosion triggering is applied in the present calculations. The numerical discretization used in the IDEMO calculations is shown in Fig. 43. In order to reproduce a constraint geometry between the reactor core and the RPV in a 2D cylindrical geometry, calculations were carried out with a domain radius of 0.4 m. In this way, strong steam explosions are supported due to less pronounced venting effects. Also, high loads with maximums in the vicinity of the mixture are expected to decay with increasing distance from the mixture. Therefore, with respect to maximum pressure loads on the RPV walls, this choice is assumed as the most challenging.

83 6 Application to reactor conditions

6.2.2 Results of the explosion calculations

Fig. 44 shows the pressure versus time at different heights along the RPV side wall for the case of sideways oxidic melt outflow from the RPV with a diameter of 10 cm into a water pool with 1 m height. As can be seen from Fig. 44, the maximum pressure loads are obtained where the mixture region is closest to the bottom RPV wall. Pressure pulses with maximum values of ~12 MPa and a short width of about 0.2 ms are obtained between 0.075 and 0.325 m in elevation. At the higher elevations where the void in mixture is also higher, maximum pressures are in the range of 4 and 6 MPa, but over a longer time period (~2 ms). After the pressure wave reaches the upper surface of the mixture, it vents towards the void region above. In Fig. 45 are presented pressure pulses over time for different elevations along the RPV side wall obtained for the case with 10 cm oxidic jet diameter and 2 m water level. By the premixing calculations, complete jet break-up has been obtained yielding a longer fall time for fragmented particles and results in a consequently later triggering (see above). The effect of the higher water level, providing complete jet break-up, is to yield more melt mass in the mixture and will additionally increase the distance for the explosion escalation and propagation. This can be clearly seen in the significantly higher maximum pressures and longer duration of pressure peaks. Maximum achieved pressures are again in the vicinity of bottom RPV wall (between 0.075 m and 0.325 m heights) in ranges of around 15 MPa and width of ~1 ms. At higher elevations, pressures are rather moderate with maximum values between 10 and 12 MPa, but with longer duration of about 2 ms. Explosion results for the cases with the oxidic melt jet of 20 cm diameter into 1 and 2 m deep water pools are given in Fig. 46 and Fig. 47. A similar trend can be observed, considering the higher pressures obtained with the higher water level, yielded more fragmented melt mass in the mixture. Maximum pressures for the cases with 1 m and 2 m pool depths are in ranges of 12 MPa and 14 MPa, respectively, over approximately 0.2 ms. Similar behaviour can be observed in the cases with 40 cm jet of oxidic melt given in Fig. 48 and Fig. 49. Due to larger amount of premixed melt mass, stronger explosions are obtained with the higher water level. In the case with the 40 cm jet and a water level of 2 m, the largest explosion is expected due to the large premixing potential, even though the pressure loads remain relatively low. Maximum values reach up to 25 MPa at 0.725 m elevation. Maximum estimated pressures near the bottom RPV wall are somewhat lower (~22 MPa), but have longer duration of pressure pulses of almost 1 ms. Approximately 8 ms after triggering, the first pressure wave reaches the upper surface of the mixture and it starts to vent. In the case with metallic melt, the lower melt temperature leads to lower void

84 6 Application to reactor conditions buildup during premixing i.e. more melt mass in lower void regions (see above). On the other hand, there should be a trend towards weaker explosions due to smaller internal energy stored in the metallic melt (1100 K lower melt temperature). The results of the explosion calculations given in Fig. 50 show a somehow weaker explosion with the metallic melt. Maximum values, obtained at the 0.975 m elevation, are in a range of about 17 MPa having a short duration of ~0.2 ms. It appears that the lower energy content has stronger influence on the resulting explosion strength in comparison to the lower voiding. Here, it has to be kept in mind that no special “material effects” have been assumed, giving metallic melt a higher explosivity than oxidic melt, i.e. the same calculation parameters have been applied for both metallic and oxidic melts as they have been used in the validation calculations for the K-44 experiment. Also, crust formation, impending fine fragmentation during explosion, is not considered, which means that a stronger weakening effect on the explosion strength is to be expected with oxidic melt due to larger heat losses, a smaller heat conductivity and a lower superheat. Since melt solidification was not considered in the analyses, the present results depend on the initial melt temperature and composition only with respect to the heat content (superheat, heat capacity etc.), which is an almost linear effect.

6.2.2.1 Consideration of a triggering time later than at MBC

Taking into account fluctuations in void production during premixing, oscillations of the fragmented masses in low void regions could be significant considering the time shortly before and after the first MBC. Namely, after MBC the total fragmented mass continues to increase monotonically until quasi-equilibrium between incoming and fragmented mass in the mixture (not yet settled at the bottom of RPV) has been established. At the same time, the fragmented mass in lower void regions is extended, but not as much as the melt mass surrounded by the high void. The exceptions are the peaks caused by already mentioned fluctuations. For example, in the most “explosive” case with 40 cm oxidic melt jet and 2 m water level, the mass surrounded by void < 60 % is estimated to be ~28 kg at the time of MBC. At 0.7 s (approximately 0.27 s after the first MBC), this mass increases up to ~65 kg and remains steady for a very short time, after which it decreases and remains relatively constant until the next increase occurs at approximately 0.93 s (see Fig. 40). In order to consider the possibility of later triggering, explosion calculations have been performed assuming the triggering of an explosion at 0.7 s, when the melt mass in lower void regions is more than twice when compared to the time of first MBC. Melt and void fractions at the time of second triggering are given in Fig. 51. It could be seen that most of the mixture is highly voided, except the regions close to the bottom. Pressure pulses versus time, at different elevations along the RPV wall are

85 6 Application to reactor conditions presented in Fig. 52. Maximum achieved pressures are obtained practically at the bottom RPV wall in ranges of about 25 MPa. At higher elevations, pressures are lower due to a higher void concentration, associated with larger melt mass in the mixture. The pressure field is shown in Fig. 53. After triggering, the pressure wave propagates rapidly vertically and laterally. After 0.9 ms it reaches its maximal value at the side RPV wall of around 25 MPa. Afterwards, it continues to propagate upwards and after approximately 4 ms, it approaches the mixing zone with higher void concentration. Due to the high void, propagation velocities are significantly reduced. Moreover, the high compressibility of the mixture counteracts to further pressure escalation and propagation. After ~9 ms, the pressure front achieves the upper bound of the mixture and venting occurs. With larger masses available for a steam explosion, as comparing with the reference case triggered at the time of MBC, higher loads on the RPV wall were expected. However, the maximum obtained values were in the same range, but with shorter duration of the pressure pulses. More fragmented mass in the mixture resulted in higher melt volume fractions and consequently in a more depleted mixture. The increase of the fragmented mass in the lower void regions did not yield a stronger explosion, rather it appears that higher steam accumulations in the mixture produced by higher melt volume fractions strongly limit escalation and propagation of the pressure waves. Calculations concerning premixing conditions beyond 0.7 s have not been performed assuming that a more voided mixture, associated with more fragmented mass, would prevent triggering of an explosion (i.e. suppressing direct contact between melt and water) and would also more effectively dampen the explosion strength due to the mixture’s higher compressibility.

6.2.3 Discussion

Premixing and explosion calculations are performed for an assumed in-vessel case considering sideways melt jet outflow from the core into water in the lower head. Earlier calculations on the risk of steam explosions dealt with melt masses of several tons of corium in the lower head yielding mixtures of void less than 50 % and not being able to fail the lower head (e.g. Abolfadl and Theofanous, 1987). In later analyses performed on the AP600, Theofanous et al. (1998) obtained only a few tens of kilograms as available for steam explosions, based on the limited outflow from the core. On the other hand, an initially complete break-up with parameterized particle sizes has been assumed. Locally, high (a few hundred MPa) but very short pressures (about 0.1–0.3 ms) were obtained. Here, it was attempted to reach the most challenging conditions by considering conditions with the highest amounts of melt in the mixture in the frame of the underlying scenario conditions. This has been done by varying the melt composition,

86 6 Application to reactor conditions the melt diameter, the flow rate, water level, the possible lateral extension of the mixture and the time of triggering. On the other hand, break-up of the melt has been taken into account, which may restrict the available melt for mixing, especially with thick jets, but may also reduce void buildup during the phase of break-up and mixture formation. In all considered cases, the fragmented mass in lower void regions (here, a void less than 60 % is tentatively taken as marking a limit of explosive mixtures) was estimated to be in the range of a few tens of kilograms due to an incomplete jet break-up and high melt volume fractions with a consequently high void. The results of explosion calculations showed relatively moderate pressures. Maximum pressure loads along the RPV wall, in the case selected as the most challenging, considering the largest melt masses in lower void regions, are in ranges up to 25 MPa. It is to be noted that maximum loads obtained in the corresponding case with metallic melt are lower (~17 MPa) although generally lower void in the mixture. This can be explained by smaller internal energy stored in metallic melt which obviously has stronger influence on the resulting explosion strength than low void obtained during premixing. Also, no crust formation is taken into account in this investigation which could be considered as an additional limitation for obtaining strong explosions, especially with the oxidic corium (due to its material properties). Assuming a possibility of triggering of explosions later than at MBC, calculation for the most challenging case was triggered at 0.7 s, when the mass in the lower void regions was estimated to be close to its maximum, obtained during this calculation. Nevertheless, maximum pressures on the RPV wall remain in the same order of magnitude (up to 25 MPa), but with shorter duration of the maximum pressure peaks. Calculations assuming later triggering are not performed, considering that high void associated with more melt mass in the mixture would even stronger counteract to explosion triggering as well as to escalation and propagation of pressure waves. Thus, the result is that significantly smaller melt masses in the mixture and lower pressures are obtained than in the previous investigations. As compared to the results of Theofanous et al. (1998) for AP600, the question about the origin of high local pressures (although of small duration) obtained in those calculations arises, in contrast to the present calculations. Based on closer inspection it is concluded here, that the reason is not in a larger melt mass in mixture (based on complete break- up), but in a frontal zone of the downwards falling melt with only small void. This is a likely result from neglecting net steam production around drops in a region with subcooled water, related to local pressure, in contrast to the net steam production assumed in the present model also under such conditions. However, in the major mixture region the pressures are also moderate in the AP600 calculations with values of only a few tens of MPa and the difference by the short high pressure peaks resulting from small regions appears to be marginal.

87 6 Application to reactor conditions

1,2*107 IDEMO/PT/Wall/75mm IDEMO/PT/Wall/325mm IDEMO/PT/Wall/725mm 1,0*107 IDEMO/PT/Wall/975mm IDEMO/PT/Wall/1980mm

8,0*106 IDEMO/PT/Wall/4020mm

6,0*106 Pressure / Pa 4,0*106

2,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s Fig. 44. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic melt with a diameter of 10 cm into a water pool with 1 m height

1,6*107 IDEMO/PT/Wall/75mm 7 1,4*10 IDEMO/PT/Wall/325mm IDEMO/PT/Wall/725mm 1,2*107 IDEMO/PT/Wall/975mm IDEMO/PT/Wall/1975mm 1,0*107 IDEMO/PT/Wall/4100mm

8,0*106

6,0*106 Pressure / Pa Pressure

4,0*106

2,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s

Fig. 45. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic with a diameter of 10 cm into a water pool with 2 m height

88 6 Application to reactor conditions

1,2*107 IDEMO/PT/Wall/75mm IDEMO/PT/Wall/325mm 1,0*107 IDEMO/PT/Wall/725mm IDEMO/PT/Wall/975mm

6 IDEMO/PT/Wall/1980mm 8,0*10 IDEMO/PT/Wall/4020mm

6,0*106

6 Pressure / Pa Pressure 4,0*10

2,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s Fig. 46. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic melt with a diameter of 20 cm into a water pool with 1 m height

1,4*107 IDEMO/PT/Wall/75mm 1,2*107 IDEMO/PT/Wall/325mm IDEMO/PT/Wall/725mm IDEMO/PT/Wall/975mm 1,0*107 IDEMO/PT/Wall/1975mm IDEMO/PT/Wall/4100mm 8,0*106

6,0*106 Pressure / Pa Pressure 4,0*106

2,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s Fig. 47. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic melt with a diameter of 20 cm into a water pool with 2 m height

89 6 Application to reactor conditions

1,6*107 IDEMO/PT/Wall/75mm 7 1,4*10 IDEMO/PT/Wall/325mm IDEMO/PT/Wall/725mm 1,2*107 IDEMO/PT/Wall/975mm IDEMO/PT/Wall/1980mm 1,0*107 IDEMO/PT/Wall/4020mm

8,0*106

6,0*106 Pressure / Pa Pressure

4,0*106

2,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s Fig. 48. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic melt with a diameter of 40 cm into a water pool with 1 m height

3,0*107 IDEMO/PT/Wall/75mm IDEMO/PT/Wall/325mm 2,5*107 IDEMO/PT/Wall/725mm IDEMO/PT/Wall/975mm

7 IDEMO/PT/Wall/1975mm 2,0*10 IDEMO/PT/Wall/4100mm

1,5*107

7 Pressure / Pa Pressure 1,0*10

5,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s Fig. 49. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic melt with a diameter of 40 cm into a water pool with 2 m height

90 6 Application to reactor conditions

7 1,6*10 IDEMO/PT/Wall/75mm IDEMO/PT/Wall/325mm 7 1,4*10 IDEMO/PT/Wall/725mm IDEMO/PT/Wall/975mm 7 1,2*10 IDEMO/PT/Wall/1975mm IDEMO/PT/Wall/4100mm 1,0*107

8,0*106

Pressure / Pa Pressure 6,0*10

4,0*106

2,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s

Fig. 50. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of metallic melt with a diameter of 40 cm into a water pool with 2 m height

Fig. 51. Void and melt droplet volume fractions for the case of sideways outflow of oxidic melt with a diameter of 40 cm into a water pool with 2 m height, at the time of later triggering at 0.7 s.

91 6 Application to reactor conditions

3,0*107 IDEMO/PT/Wall/75mm IDEMO/PT/Wall/325mm 2,5*107 IDEMO/PT/Wall/725mm IDEMO/PT/Wall/975mm

7 IDEMO/PT/Wall/1975mm 2,0*10 IDEMO/PT/Wall/4100mm

1,5*107

7 Pressure / Pa / Pressure 1,0*10

5,0*106

0,0*100 0,0 0,002 0,004 0,006 0,008 0,01 0,012 0,014 0,016 Time / s Fig. 52. Pressure vs. time at different heights along the RPV side wall for the case of sideways outflow of oxidic melt with a diameter of 40 cm into a water pool with 2 m height, triggered at 0.7 s.

92 6 Application to reactor conditions

93 6 Application to reactor conditions

Fig. 53. Pressure development for the case of sideways outflow of oxidic melt with a diameter of 40 cm into a water pool with 2 m height, triggered at 0.7 s.

94 7 Summary and conclusion

7 Summary and conclusion

The central aim of this thesis was the assessment of the knowledge on steam explosions and thus of the methods for the reliable prediction of loads under realistic reactor conditions. As a basis, models for simulation of the premixing and the explosion phase of steam explosion were already available in IKEJET/IKEMIX and IDEMO codes, being under development at IKE. The objective was to reach a status, where the existing models and corresponding computer programs can be applied for risk analysis and for accident management. Special emphasis was given to key FCI processes decisive for steam explosion strength i.e. jet fragmentation under film boiling conditions, drag laws in a three-phase flow and heat transfer from very hot melt to water in the premixing phase and fine fragmentation and rapid heat transfer in the explosion phase of steam explosion. In order to capture the essential features decisive for the explosion strength and to check the capabilities of the models to reproduce them sufficiently, verification of the codes against specified and well qualified experiments was required. The task also considered improvements of the deficits in the existing models, observed during verification, which were performed in order to be able to extrapolate the achieved results to real accident scenarios in LWRs. Calculations for reactor conditions are carried out to asses the capabilities of the codes in general, and to get a perspective of the limiting effects on explosion strength and the resulting loads. The major limitation for strong steam explosions regarding reactor scenarios is given by the mass of melt which can be mixed with water without creating too high a void. Limitations of masses available for mixing are given by the rate of melt plunging into the water (pours diameter, melt velocity) and by the break-up of this melt flow which may be assumed to take form as jets. The break-up yields the fragmented mass which may be intermixed with water to form an explosion mixture. Steam production under film boiling may produce a highly voided mixture. Such high void reduces the heat transfer from melt to coolant and thus decreases the possibility of a strong steam explosion. It also affects jet break-up, making fragmentation less effective. Furthermore, high void limits the triggering potential of the mixture by preventing direct melt/water contact. During the explosion phase, high compressibility of the water depleted mixture significantly reduces the potential for escalation and propagation of explosion waves. In addition, crust formation on the melt surface could further limit the potential of obtaining more explosive mixtures, especially in subcooling conditions. Melt droplets with already formed crust are not able to participate in fine fragmentation. However, modelling of partial freezing is not considered in the present investigation assuming that main limitations to explosions, at least in saturation conditions, are already given by the limited mixed mass from 95 7 Summary and conclusion realistic accident scenario and break-up conditions as well as by high void with drop sizes from jet break-up. Concerning the validation of the IKEJET/IKEMIX code, calculations on the experiment FARO L-28 are carried out. The experiment performed with prototypic corium oxidic melt and in relevant conditions resepecting reactor scenarios was especially suitable for this task due to the long melt inflow and mixing time of about 5 s. A significant overestimation of void which reduces heat transfer from melt to coolant has been concluded from earlier simulation attempts not only with IKEJET/IKEMIX, but also with other codes (OECD Nuclear Energy Agency, 2006). Even with parametrically increased heat transfer, experimental data were not achieved due to strong counteraction of a corresponding production of higher void. Thus, the only reasonable explanation for such a strong steam accumulation in the mixture was seen as being the result of an overestimation of the interfacial friction between steam and water. This may suppress faster steam escape from the mixing zone due to so-called channelling like flow patterns. In order to allow faster steam release, it was necessary to improve the present models. A major deficit of earlier modelling efforts was found while observing the behaviour of the transition regime between water and steam continuous flow patterns. Here, no different, but averaged steam velocities have been considered, although combining it by parts of both patterns. In view of the non-linearity of dependencies, this may strongly reduce the potential of steam removal. A new model, considering different vapour velocities in liquid and steam continuous parts in the transition range has been developed and implemented in the IKEJET/IKEMIX code (see Chapter 3.4). Applying the new model for interfacial friction, a strongly improved approximation to the experimental data was obtained. Furthermore, in the initial phase of the FARO L-28 experiment (up to ~1.2 s, when approximately melt-bottom contact occurs), a stronger pressure increase in comparison to the later, quasi-steady, period was observed. Taking into account the safety issue and the assumption that the triggering of steam explosions will most likely occur at the time of first MBC, this phase might be of special importance. Although uncertainties related to jet break-up behaviour in this phase exist (e.g. initial distortion of jet, initial break-up processes at impact on the water surface etc.), this could indicate a different fragmentation mechanism when comparing it to a later break-up by Kelvin-Helmholtz like stripping at thick film boiling. The increased evaporation rate estimated during this phase can be obtained only by smaller melt particles produced by stronger fragmentation. According to Corradini (Bürger and Buck, 2005), this stronger fragmentation rate is due to Rayleigh-Taylor instabilities at the jet leading edge associated with direct melt-water contact. However, even if it is sufficient to reproduce the strong pressure increase in the initial phase, this mechanism cannot explain the later, almost constant pressure build-up. Taking into account a consistence with the later, quasi-steady phase, as a driving mechanism in

96 7 Summary and conclusion the initial phase could be rather assumed fragmentation based on Kelvin-Helmholtz instabilities under thin film conditions (i.e. water as an ambient medium). This will then result in shorter jet length and smaller particles yielding stronger pressure increase. A consistent description of both phases of the experiment FARO L-28 is obtained by assuming a transition from thin to thick film fragmentations when the averaged void surrounding the jet reaches 70 % (Chapter 4.3). With respect to reactor application, smaller melt particles yield higher evaporation, meaning that an increased void produced in the initial phase will counteract even stronger the explosion strength (if triggering of steam explosion occurs at the time of MBC or before). In the present investigation, thin film fragmentation is not taken into account considering as a conservation feature to neglect these additional contributions yielding finer break-up in the premixing phase. As a basis for validation of IDEMO code, the experiments KROTOS K-44 with alumina and FARO L-33 with prototypic corium melt were chosen. With respect to reactor application, the IDEMO code must be able to reproduce the strong steam explosions obtained in the K-44 test. On the other hand, FARO L-33 is currently the only large scale experiment performed in prototypic conditions which has resulted in a steam explosion, albeit a rather weak one. The point here is to understand the differences in explosivity between alumina and corium melt obtained in the relevant experiments as well as achieving a unified modelling concept for different cases in order to extrapolate the results to real reactor conditions. First calculation attempts showed that by using the same set of parameters is not possible to describe both of these experiments. In order to reproduce experimental results obtained in the FARO L-33 test, it was necessary to decrease the heat transfer coefficient from 5x105 W/(m2K) (as used in K-44 calculations) to 5x104 W/(m2K). This can be explained by not taking into account partial freezing of melt droplets during premixing phase. Good agreement with experimental data is possible to achieve also when a slower fine fragmentation of the corium melt was assumed (Bürger et al., 2007). However, taking into account that different material behaviour in fine fragmentation is not explained nor phenomenologically shown, this could yield problems for understanding and extrapolation the results to other conditions. On the other hand, according to both the KROTOS and FARO experiments, obvious differences exist in the coarse break-up in premixing, and thus in the mixing process between corium and alumina melt. Jet break-up by corium melt yields significantly smaller particles than alumina, which associated with specific material properties of corium (low heat conductivity, low superheat etc.) strongly pronounce crust formation at the melt surface, especially in high subcooling conditions as e.g. in FARO L-33 experiment. In order to check if sufficient explanation for a different explosivity obtained by alumina and corium melts in these tests could be achieved by assuming certain part of the fragmented mass already frozen during premixing (i.e. not able to participate in fine

97 7 Summary and conclusion fragmentation), calculations for the experiment FARO L-33 are performed excluding an amount of droplets considered as sufficiently crusted. Good agreement with experimental data is achieved assuming that just 15 % of fragmented mass participated in the explosion. The set of numerical parameters was kept unchanged in comparison to K-44 calculations especially considering the heat transfer coefficient of 5x105 W/(m2K). Approached results indicate the perspective of a unified modelling concept. However, further confirmation is required and the modelling of solidification under premixing could then become important to account for different behaviour of the corium and alumina cases, in addition to different break-up. The main aim of premixing and explosion calculations performed for an in-vessel case was to assess the ability of the codes to predict potential explosion loads in the underlying scenario conditions and also to investigate the main limiting effects to vulnerable steam explosions. For these reactor oriented calculations a scenario with a sideways jet outflow from the reactor core into the saturated water of the lower plenum is chosen. In order to achieve as strong as possible steam explosions the melt composition, the melt diameter, the melt flow rate, the water level, the possible lateral extension of the mixture and the time of explosion triggering were varied. Results of the premixing calculations showed that the total amount of molten material available in the core is not directly relevant for the strength of a potential steam explosion, since it is impossible to premix very large melt masses with water. Under the conditions of a realistic scenario i.e. outflow of melt (assumed in the form of a jet) from the core into water of the lower plenum, limited melt mass flow rates (leak size and velocity) and limited jet break-up will allow only a small amount of the melt mass to form an “explosive premixture” with the coolant. Consideration of higher outflow melt jet velocity would lead to an increase of the melt flow rate but would also limit the amount of mass available for explosion due to more rapid penetration to the bottom. Additionally increasing the diameter of pours yields a larger amount of melt delivered to the coolant, but is only partially broken up. For example, in cases with larger leak sizes (20 to 40 cm diameter), the melt jets break up only partly, i.e. large portions of the melt arrive at the bottom unfragmented. Only for a water level just below the leak (2 m) and a jet of 10 cm diameter, is complete melt jet break-up obtained. However, for this case the melt mass delivered to the water was limited due to smaller mass flow rate. Furthermore, although reduced interfacial friction and faster steam escape from the mixing zone, strong void buildup during premixing is obtained. Variations of water pool depth resulted in larger masses in the mixture, but due to high melt volume fractions mostly in an environment with very large steam fractions (> 60 %). This is generally to be expected in cases with prototypical material and correspondingly high temperatures. In all considered cases, the fragmented melt mass in the lower void regions were estimated having an order of magnitude in the lower tens of kilograms. In addition,

98 7 Summary and conclusion calculations assuming metallic melt jet outflow from the RPV into water of the lower plenum were also carried out in order to consider a possibility of obtaining stronger steam explosions as it was indicated from several experiments performed with metallic materials (Evans et al., 1982 and Mitchell and Evans, 1986). In comparison to oxidic corium melt, somewhat larger melt masses in the lower void regions were obtained due to significantly lower melt temperatures. Explosion calculations showed that relatively small pressure loads (up to ~25 MPa) resulted from the calculated premixtures even for the best estimate case considering the largets amount of fragmented mass in lower void regions with oxidic melt (Dj = 40 cm, water level = 2 m). Achieved pressure loads for the metallic melt are even lower although generally lower void in the mixture was obtained. Except in lower void, lower melt temperatures resulted also in smaller heat capacity stored in metallic melt which effectively prevented enhanced pressure escalation and propagation. It is to be mentioned that no special material effects concerning different explosivity between metallic and oxidic melt are considered except those already included in the fragmentation models. No solidification is taken into account as well. Assuming certain part of the fragmented melt already frozen during premixing would additionally limit explosion strength, especially with oxidic corium melt due to its lower superheat and lower heat conductivity. Moreover, in order to take into account possibility of later triggering, calculations for the most challenging case with oxidic corium melt (Dj = 40 cm, water level = 2 m) are performed assuming triggering of an explosion at 0.7 s, when the mass in lower void regions is more than doubled when compared to that within the MBC. Aside from the increased mass in the lower void regions, the obtained pressure peaks are in the same range as compared to the reference case, due to the strong counteraction of highly depleted mixture. Calculations assuming later triggering are not performed considering that an even higher void in the mixture will further counteract the steam explosion triggering as well as escalating and propagating an explosion pressure wave. Previous studies on the risk of steam explosions dealt with melt masses of several tones of corium in the lower head yielding mixtures of void less than 50 % and not being able to fail the lower head (Abolfadl and Theofanous, 1987). In later analyses for the AP600, performed by Theofanous et al. (1998), only some tens of kilograms were estimated to be available for steam explosion. This was based on limited outflow from the core (melt mass flow rate up to 400 kg/s) and assuming initially complete break-up with parameterised particle sizes. Comparing the masses able to participate in steam explosions estimated in the present study to Theofanous et al. (1998), they are approximately in a same range, but with higher mass flow rates assumed here. Thus, as a main result of this thesis, it can be concluded that much stronger limitations to formation of explosive premixtures are obtained as were

99 7 Summary and conclusion assumed earlier, mainly due to incomplete jet break-up and a high void in the mixture. Concerning explosion calculations, locally high (a few hundred MPa) but very short pressure peaks (with duration of 0.1 to 0.3 ms) are obtained by Theofanous et al. (1998). They are most likely generated by neglecting net steam production around drops in a region with subcooled water, related to local pressure. In the major mixture region, the pressures are also moderate having values of only a few tens MPa and the difference by the short high pressure peaks resulting from small regions appears to be marginal. However, these loads are estimated as insufficient to produce failure of RPV in the AP600 cases. Thus, considering the maximum achieved pressure peaks of ~25 MPa, loads obtained in this thesis can also be considered as benign. In general, the results of this study can be extrapolated to both, in-vessel and ex- vessel cases, considering similar conditions with relatively shallow water levels and saturated or low subcooling water temperatures. As it is shown here, the main limiting effects for obtaining strong steam explosions are given already by incomplete jet break-up and high voiding mixture resulting in low melt masses available for steam explosions and consequently moderated pressure loads. It remains to be checked if under high subcooling conditions and with deeper water pools (as e.g. in BWRs) stronger steam explosions can be obtained. More complete jet break-up resulting from an increase in the water level, and a smaller void due to high subcooling are to be expected. On the other hand, an increase in crusted mass during premixing due to the extended falling time of particles and a lower water temperature may be presumed as well. Therefore, in addition to jet break-up and void formation, the proper modelling of solidification during the premixing phase may play a decisive role in the assessment of potential loads under subcooling conditions. It is to be investigated if the limiting effects given by interplay between void and solidification are sufficient to suppress vulnerable steam explosions which could lead to damage of nuclear reactor’s structures and to release of fission products in the environment. Solidification, as indicated in Chapter 5, could also explain differences between alumina and corium explosivity obtained in the experiments. With respect to nuclear reactor safety, this would be the next step required before the remaining uncertainties related to the steam explosion phenomena can be fully resolved.

100 8 References

8 References

Abolfadl, M.A., Theofanous, T.G., 1987. An Assessment of Steam-Explosion-Induced Containment Failure. Part II: Premixing Limits. Nuclear Science and Engineering 97, 282-295. Akers, D.W. et al., 1992. TMI-2 Examination Results from the OECD-CSNI Program. OECD Report NEA/CSNI/R(91)9. Alsmeyer, H., Tromm, W., 1995. Concept of a Core Cooling System and Experiments Performed. Nuclear Engineering and Design 154, pp. 69-72. Amarasooriya, W.H., Theofanous, T.G., 1991. Premixing of Steam Explosions: A Three Fluid Model. Nuclear Engineering and Design 126, pp. 23-29. Annunziato, A., Addabbo, C., Magallon, D., 1999. FARO Test L-31 Quick Look Report, Technical Note No.I.99.193, Institute for System, Informatics and Safety, Ispra, December. Berman, M., et al., 1984. An Uncertainty Study of PWR Steam Explosions. NUREG/CR-3369, SAND81-1092, Sandia National Laboratories. Berthoud, G., 2000. Vapour Explosions. Annual Review of Fluid Mechanics, Vol. 32, pp. 573-611. Berthoud, G., Brayer, C., 1997. First Vapor Explosion Calculations Performed with the MC3D Code. In: Proceedings of the OECD/CSNI Specialists Meeting on Fuel-Coolant Interactions, Tokai-Mura, Japan, May 19-24. Berthoud, G., Valette, M., 1999. Description des lois Constitutives de la Version 3.2 du Logiciel de Prémélange MC3D. SMTH/LM2/99-39, CEA Grenoble. Board, S.J., Hall, R.W., 1976. Recent Advances in Understanding Large Scale Steam Explosions. In: Proceedings of the 3rd Specialist Meeting on Sodium-Fuel Interactions in Fast Reactors, Tokyo, PNC N251, 76-12, pp. 249-283. Buck, M., 2007. Modelling of the Late Phase of Core Degradation in Light Water Reactors. PhD Thesis, Institute of Nuclear Technology and Energy Systems (IKE), University of Stuttgart. Buck, M., Bürger, M., 1997. IDEMO - A Thermal Detonation Model of Vapor Explosions: Multi-Fluid Model, Constitutive Laws and Verification Lines. In: Proceedings of the 2nd Japanese-German Symposium on Multi-Phase Flow, Tokyo, September 25-27.

101 8 References

Bürger, M., et al., 1995. Break-up of Melt Jets as Pre-condition for Premixing: Modeling and Experimental Verification. Nuclear Engineering and Design 155, pp. 215-251. Bürger, M., Buck, M., 2005. OECD Programme SERENA (Steam Explosion Resolution for Nuclear Applications), Analyses of Task 2 Calculation Results, Internal Report. Bürger, M., Buck, M., Schatz, A., 1996. Experimental and Theoretical Investigations on the Fragmentation of Melt Drops in Relative Flows. IKE Universität Stuttgart, Report: IKE 2-135. Bürger, M., Buck, M., Schmidt, W., Widmann, W., 2006. Validation and Application of the WABE Code on Coolability of Particle Debris: Influence of 2D Effects and Friction Laws. Nuclear Engineering and Design 236, pp. 2164–2188. Bürger, M., Buck, M., Vujic, Z., 2004. Stand der Arbeiten zur Explosion. Zwischenbericht zum Vorhaben BMWA 150 1266, IKE Universität Stuttgart, Report: IKE 2-153. Bürger, M., Buck, M., Vujic, Z., 2007. Stand der Arbeiten zur Explosionsphase. Zwischenbericht zum Vorhaben BMWA 150 1266, IKE Universität Stuttgart, Report: IKE 2-155. Bürger, M., Carachalios, C., Cho, S.H., v. Berg, E., Kim, D.S., Unger, H., 1987. Theoretische und Experimentelle Untersuchungen zur Eingrenzung von Dampfexplosionen im Rahmen von Sicherheitsbetrachtungen bei Leichtwasserreaktoren. Abschlußbericht zum Forschungsvorhaben BMFT 1500 639 90, IKE Universität Stuttgart, Report: IKE 2 TF-77. Bürger, M., Carachalios, C., Kim, D.S., Unger, H., 1986. Theoretical Investigations on the Fragmentation of Drops of Melt with Respect to Description of Thermal Detonations and Their Application in the Code FRADEMO. Commission of the European Communities, Report: EUR 10660, Brussels. Bürger, M., Cho, S. H., Berg, E. v., Schatz, A., 1993. Break-up of Melt Jets as Pre- Condition for Premixing: Modeling and Experimental Verification. In: Proceedings of the CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8. Bürger, M., Pohlner, G., Vujic, Z., 2004. Stand der Arbeiten zur Vorvermischung. IKE Universität Stuttgart, Report: IKE 2-161. Bürger, M., Unger, H., 1985. Theoretical Investigations on Vapour Film Boiling at Small Spheres and Horizontal Cylinders under Natural Convection. Symposium zur Wärmeübertragung in Kryosystemen, Kharkow, September 24–27.

102 8 References

Bürger, M., Berthoud, G., 2006. Editorial Overview: Basic Laws and Coolability of Particulate Debris – Comments on the Status and Present Contributions. Nuclear Engineering and Design 236, pp. 2049-2059 Chen, X., Yuen, W.W., Theofanous, T.G., 1995. On the Constitutive Description of the Micro Interaction Concept in Steam Explosion. In: Proceedings of the Nuclear Reactors Thermal Hydraulics 5, Saratoga Springs, Vol. 1, pp. 1586-1606. Corradini, M.L., et al., 1988. Vapour Explosions in Light Water Reactors: A Review of Theory and Modeling. Progress in Nuclear Energy, 22(1), pp. 1-117. Corradini, M.L., Swenson, D.V., 1981. Probability of Containment Failure due to Steam Explosions Following a Postulated Core Meltdown in a LWR. NUREG/CR-2214, SAND-2132, Sandia National Laboratories. Derewnicki, K.P., Hall, W.B., 1982. Homogeneous Nucleation in Transient Boiling. In: Proccedings of the 7th International Heat Transfer Conference, Munich, Vol. 4, PB 2, pp. 9-14. Dullforce, T.A., Buchanan, D.J., Peckover, R.S., 1976. Self-Triggering of Small-Scale Fuel-Coolant Interactions: 1. Experiments. J. Phys. D: Appl. Phys. 9, pp. 1295-1303. Epstein, M., Fauske, H.K., 1985. Steam Film Instability and the Mixing of Core Melt Jets and Water. In: Proceedings of the National Heat Transfer Conference, Denver. Epstein, M., Hauser, G., 1980. Subcooled Forced-Convection Film Boiling in the Forward Stagnation Region of a Sphere or Cylinder. International Journal of Heat and Mass Transfer 23, pp. 179–189. Evans, M., Mitchell, D., Nelson, L., 1982. Recent Results from the Sandia Steam Explosion Program, SAND 82-2269 C, Sandia National Laboratory, Albuquerque, USA. Fletcher, D.F., 1991. An Improved Mathematical Model of Melt/Water Detonations – I. Model Formulation and Example Results. Int. Journal of Heat and Mass Transfer 34, No.10, pp 2435-2448. Fletcher, D.F., Thyagaraja, A., 1991. The CHYMES Coarse Mixing Model. Prof. Nucl. Energy 26, pp. 31-61. Ginsberg, T., 1985. Liquid Jet Break-up Characterization with Application to Melt- Water Mixing. ANS Proc. National Heat Transfer Conf., Denver, Co. Henry, R.E., Fauske, H.K., 1981. Required Initial Conditions for Energetic Steam Explosions. Fuel-Coolant Interactions, HTD-V19, American Society of Mechanical Engineers. Hicks, E.P., Menzies, D.C., 1965. Theoretical Studies on the Fast Reactor Maximum Accident. In: Proceedings of the Conference on Safety, Fuels and Core Design in Large Fast Power Reactors, October 11–15.

103 8 References

Hohmann, H., Magallon, D., Huhtiniemi, I., Annunziato, A., Yerkess, A., 1994. Advance in the FARO/KROTOS Melt Quenching Test Series. 22nd Water Reactor Safety Information Meeting, Bethesda, Maryland, USA, October 23-26. Hohmann, H., Magallon, D., Schins, H., Zeyen, R., Laval, H., Benuzzi, A., 1986. Contribution to FBR Accident Analysis: The FARO programme at JRC-Ispra. In: Proceedings of the Int. Conf. Science and Technology of Fast Reactor Safety, Guernsey, U.K., May 12-16, Vol. 2, pp. 139, British Nuclear Engineering Science. Hohmann, H., Magallon, D., Yerkess, A., Huhtiniemi, I., Corradini, M.L., Bürger, M., Buck, M., 1995. Escalating and Propagating Melt/Coolant Interactions in the KROTOS Experiments: Status of Knowledge, Proc. of Int. Symposium Heat and Mass Transfer in Severe Nuclear Reactor Accidents, Cesme, Turkey, May 22-26. Honda, H., Takamatsu, H., Yamashiru, H., 1993. Heat Transfer Characteristics During Rapid Quenching of a Thin Wire in Water. Heat Transfer Japanese Research 21(8):773-91. Huhtiniemi, I., Hohmann, H., Faraoni, R., Field, M., Gambaretti, R., Klein, K., 1996. KROTOS 38 to KROTOS 44 Data Report, Technical Note No.I.96.37, Institute for System, Informatics and Safety, Ispra, March. Huhtiniemi, I., Magallon, D., 2001. Insight Into Steam Explosions with Corium Melts in KROTOS. Nuclear Engineering and Design 204, pp. 391-400. Huhtiniemi, I., Magallon, D., et al., 1998. KROTOS Alumina Tests: K-49, K-50, K-51, K-57, Technical Note No.I.00.21, Institute for Systems, Informatics and Safety, Ispra. Huhtiniemi, I., Magallon, D., Hohmann, H., 1999. Results of Recent KROTOS FCI Tests: Alumina Versus Corium Melts. Nuclear Engineering and Design, Volume 189, Issues 1-3, pp. 379-389. Inoue, A., 1982. Study on Transient Heat Transfer of Film Boiling due to Arrival of a Pressure Pulse. In: Proccedings of the 7th International Heat Transfer Conference, Munich, Vol. 4, FB 39, pp. 403-408. Jacobs, H., 1993. Analysis of Large-Scale Melt-Water Mixing Events. In: Proceedings of the CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8. Jacobs, H., Väth, L., Thurnay, K., 1997. Constitutive Relations for Multiphase Flow Modelling. In: Proceedings of the OECD/CSNI Specialists Meeting on Fuel–Coolant Interactions, Tokai-Mura, Japan, May 19–21, pp. 205–219. Leskovar, M., Meignen, R., Brayer, C., Bürger, M., Buck, M., 2007. Material Influence on Steam Explosion Efficiency: State of Understanding and Modelling Capabilities. The 2nd European Review Meeting on Severe Accident Research (ERMSAR-2007), Karlsruhe, Germany, June 12-14.

104 8 References

Magallon, D., 2002. OECD Programme SERENA (Steam Explosion Resolution for Nuclear Applications) Task 2, Reference Data for Calculation of FARO Tests L-28, L- 31 and L-33. Internal Report. Magallon, D., 2006. Formation and Characterisation of Corium Debris Arising From Fuel–Coolant Interaction. Nuclear Engineering and Design 236, pp. 1998–2009. Magallon, D., et al., 2000. MFCI Project—Final Report. INV-MFCI(99)-P007, EUR 19567 EN. Magallon, D., Huhtiniemi, I., 2001. Energetic Event in Fuel-Coolant Interaction Test FARO L-33. ICONE-9 Conference, Nice, France, April 8-12. Magallon, D., Huhtiniemi, I., Hohmann, H., 1997. Lessons Learnt from FARO/THERMOS Corium Melt Quenching Experiments. In: Proceedings of the OECD/CSNI Specialists Meeting on Fuel Coolant Interactions, Tokai-Mura, Japan, May 19–21. Meignen, R., Magallon, D., 2005. Comparative Review of FCI Computer Models Used in the OECD-SERENA Program. Proceedings of ICAPP ’05, Seoul, Korea, May, 15-19. Meyer, J.F. et al., 1981. Preliminary Assessment of Core Melt Accidents at the Zion and Indian Point Nuclear Power Plants and Strategies for Mitigating Their Effects. NUREG-0850, U.S. Nuclear Regulatory Commission. Mitchell, D., Evans, N., 1986. Steam Explosion Experiments at Intermediate Scale: FITS B Series, NUREG/CR-3983, SAND 83-1057, R3, Sandia National Laboratory, Albuquerque, USA. Moriyama, K., Yamano, N., Maruyama, Y., Kudo, T., Sugimoto, J., 1996. Study of Premixing Phase of Steam Explosion with JASMINE Code in ALPHA Program. In Proceedings of 4th International Conference on Nuclear Engineering, New Orleans, volume 1B, pp. 903–915. OECD Nuclear Energy Agency, 2006. SERENA – Steam Explosion Resolution for Nuclear Applications - Final Report, Nuclear safety NEA/CSNI/R(2007)11. Pilch, M., 1987. Acceleration Induced Fragmentation of Liquid Drops, PhD Thesis, University of Virginia. Pohlner, G., Vujic, Z., Bürger M., Lohnert, G., 2006. Simulation of Melt Jet Break-up and Debris Bed Formation in Water Pools with IKEJET/IKEMIX. Nuclear Engineering and Design 236, pp. 2026-2048. Ranz, W.E., Marshall, W.R., 1952. Evaporation from Drops. Chem. Eng. Progress 48, pp. 141–146 and 173–180. Schmidt, W., 2004. Influence of Multidimensionality and Interfacial Friction on the Coolability of Fragmented Corium. PhD Thesis, Institute of Nuclear Technology and

105 8 References

Energy Systems (IKE), University of Stuttgart. Sienicki, J.J., Chu, C.C., Spencer, B.W., Frid, W., Löwenhielm, G., 1993. Ex-Vessel Melt-Coolant Interactions in Deep Water Pool: Studies and Accident Management for Swedish BWRs. In: Proceedings of the CSNI Specialists Meeting on Fuel-Coolant Interactions, Santa Barbara, CA, January 5-8. Silverii, R., Magallon, D., 1999. FARO LWR PROGRAMME, Test L-28 Data Report, Technical Note No.I.99.76, INV-MFCI(99)-D033, European Commission, Joint Research Centre, Ispra Site, April. Speis, P.T., Basu, S., 1997. Fuel-Coolant Interaction (FCI) Phenomena in Reactor Safety: Current Understanding and Future Research Needs. In: Proceedings of the OECD/CSNI Specialists Meeting on Fuel-Coolant Interactions, Tokai-Mura, Japan, May 19-24. Tang, J., Corradini, M.L., 1993. Modelling of the Complete Process of One- Dimensional Vapour Explosions. In: Proceedings of the CSNI-FCI Specialists Meeting, Santa Barbara, CA. Theofanous, T.G., Yuen, W.W., Angelini, S., 1996. Premixing of Steam Explosions: PM-ALPHA Verification Studies. DOE/ID-10504, UCSB. Theofanous, T.G., Yuen, W.W., Angelini, S., Sienicki, J.J., Freeman, K., Chen, X. and Salmassi, T., 1998. Lower Head Integrity under Steam Explosion Loads. Nuclear Engineering and Design 189, 7-57. U.S. Nuclear Regulatory Commission, 1975. Reactor Safety Study, WASH-1400, NUREG/75-0114. Valette, M., Berthoud, G., Meignen, R., Picchi, S., 2001. Description des Lois Constitutives de la Version 3.3 du Logiciel de PREMELANGE MC3D. Note SMTH/LDTA/2001-01, CEA Grenoble. Vierow, K., Nagano, K., Araki, K., 1997. Development of the VESUVIUS Module: Molten Jet Break-up Modelling and Model Verification. In: Proceedings of the OECD/CSNI Specialists Meeting on Fuel–Coolant Interactions, Tokai-Mura, Japan, May 19–21, pp. 541–566.

Vujic, Z., Bürger, M., Buck, M., Lohnert, G., 2007. Investigation of Limitations to Steam Explosions Strength due to Water Depletion. In: Proceedings of the 15th International Conference on Nuclear Engineering (ICONE15), Nagoya, Japan, April 22-26. Wang S.K., Blomquist, C.A., Spencer, B.W., Mc Umber, L.M., Schneider, J.P., 1988. Experimental Study of the Fragmentation and Quench Behaviour of Corium Melts in Water. 25th Nat. Heat Transfer Conf., Houston, Texas.

106 8 References

Young, M.F., 1987. IFCI: An Integrated Code for Calculation of all Phases of Fuel- Coolant Interactions. NUREG/CR-5084, SAND87-1048. Yuen, W.W., Theofanous, T.G., 1993. The Prediction of 2D Thermal Detonations and Resulting Damage Potential. In: Proceedings of the CSNI Specialists Meeting on Fuel- Coolant Interactions, Santa Barbara, CA, January 5-8. Zeisberger, A., Mayinger, F., 2006. Heat Transport and Void Fraction in Granulated Debris. Nuclear Engineering and Design 236, pp. 2117–2123.

107 A. Description of the explosion model IDEMO

Appendices

A. Description of the explosion model IDEMO

A.1. Conservation equations

A.1.1. Mass conservation equations

The following conservation equations for mass, momentum and energy can be applied. Conservation of mass applied to melt droplets (m ), debris (b ), cold (c ) and heated (h ) coolant gives:

∂ (α ρ ) + ∇ ⋅ (α ρ vr ) = −Γ , (A-1) ∂t m m m m m fr

∂ (α ρ ) + ∇ ⋅ (α ρ vr ) = Γ , (A-2) ∂t b b b b f fr

∂ (α ρ ) + ∇ ⋅ (α ρ vr ) = −Γ , (A-3) ∂t c c c c f e

∂ (α ρ ) + ∇ ⋅ (α ρ vr ) = Γ . (A-4) ∂t h h h h f e

In equations (A-1) and (A-2), Γfr is the mass transfer rate due to fragmentation and

Γe in equations (A-3) and (A-4) is the rate of entrainment of cold coolant into the micro-interaction zone due to mixing. The quantities are specified below.

A.1.2. Momentum conservation equations

Conservation of momentum for melt droplets and effective fluid (f ), the latter consisting of hot and cold coolant and debris, gives:

∂ r (α ρ vr ) + ∇ ⋅ (α ρ vr ⊗vr ) = −α ∇p − Γ ⋅vr + F , (A-5) ∂t m m m m m m m m fr m m ,f

∂ [][](α ρ + α ρ + α ρ ) ⋅vr + ∇ ⋅ (α ρ + α ρ + α ρ ) ⋅vr ⊗vr ∂t b b c c h h f b b c c h h f f . (A-6) r r = −(αb + αc + αh ) ⋅ ∇p + Γfr ⋅v m − Fm ,f

A.1.3. Energy conservation equations

For the melt droplets it is assumed that during the short time of the explosive

108 A. Description of the explosion model IDEMO interaction heat exchange between the droplets and the other fluid phases can be neglected compared to the heat transfer from the fragments (debris) yielded by the fragmentation of melt droplets. The droplet temperature is therefore assumed to be constant:

Tm = Tm ,0 = constant . (A-7) Energy conservation for debris, cold and hot coolant gives:

∂ ∂α (α ρ E ) + ∇ ⋅ (α ρ H vr ) = −p b + Γ H − Q , (A-8) ∂t b b b b b b f ∂t fr m bh

∂ ∂α (α ρ E ) + ∇ ⋅ (α ρ H vr ) = −p c − Γ H , (A-9) ∂t c c c c c c f ∂t e c

∂ ∂α r (α ρ E ) + ∇ ⋅ (α ρ H vr ) = −p ⋅ h + Γ ⋅ H + Q + F ⋅ (vr −vr ) ∂t h h h h h h f ∂t e c bh b ,m f m

(A-10) In the energy conservation equations the stagnation or total energies and enthalpies,

1 1 E = e + vr2, H = h + vr2 with k = b,c ,h (A-11) k k 2 f k k 2 f are used. This ensures that total energy is conserved.

A.1.4. Droplet length scale equation

A transport equation for the melt droplet length scale can be derived, assuming spherical droplets and considering changes in diameter only due to fine fragmentation (no coarse break-up):

∂ 4 (α ρ D ) + ∇ ⋅ (α ρ D vr ) = − Γ D . (A-12) ∂t m m m m m m m 3 fr m

A.1.5. Volume conservation equation

The volume fractions have to obey the volume constraint equation

αm + αb + αc + αh = 1 . (A-13)

109 A. Description of the explosion model IDEMO

A.2. Constitutive laws

A.2.1. Mass transfer between melt drops and fragments

As previously noted, fragmentation and heat-up of part of the water (“micro- interactions”) are central processes determining pressure build-up. Thermal and hydrodynamic fragmentation processes are usually distinguished. The latter denote processes due to relative velocities between melt drops and coolant in strong pressure waves, especially shock waves with relatively sharp leading edges. They are considered to dominate under such conditions, in contrast to initiation and first escalation stages of a steam explosion. Especially with spontaneously triggered melt/water contact, thermally driven processes must dominate, due to the lack of sufficiently high relative velocities. However, it may be sufficient for reactor safety analyses to consider within a conservative approach a sufficiently strong trigger. Thus, hydrodynamic fragmentation is of special interest here. In order to obtain the inherent restrictions to the hydrodynamic fragmentation process and thus also to thermal detonations, it is necessary to take into account the effects of the development of relative velocities (depending itself on the fragmentation process). Local, instantaneous descriptions of the fragmentation are required instead of laws depending only on initial conditions. It is difficult to derive such laws from experiments alone. Understanding and to some extent modelling is required to get adequate descriptions, even if formulated as correlations. Based on different assumptions on mechanisms, different laws have been constructed in more or less heuristic ways. Hydrodynamic fragmentation correlations used in MC3D (Berthoud and Brayer, 1997), CULDESAC (Fletcher, 1991), ESPROSE (Chen et al., 1995), TEXAS (Tang and Corradini, 1993), IFCI (Young, 1987) and IDEMO can all be written as

2 dmFr π ⋅ Dm ⋅v rel = * ⋅ ρf ⋅ ρm . (A-14) dt 6 ⋅t fr In IDEMO the relative velocity is taken to be the difference of the drop velocity and the velocity of the fluid composed of fragments, cold and hot coolant,

r r v rel = v f −v m , (A-15) with average density

α b ρb + αc ρc + α h ρh ρf = ,α f = α b + αc + α h . (A-16) α f The correlation (A-14) gives the rate of fragmented mass of a single drop for local, instantaneous conditions, i.e. values of relative velocity v rel , drop diameter Dm ,

110 A. Description of the explosion model IDEMO

* densities and the dimensionless fragmentation time t fr .The latter has still to be determined. The fragmentation rate does not depend on the history but only on instantaneous values. Just in this way, the dependence on the development of conditions is strongly accentuated.

Equation (A-14) is related to the mass transfer rate per volume Γfr by

dmfr 6 ⋅αm dmfr αm ⋅v rel Γfr = nm = 3 ⋅ = * ⋅ ρf ⋅ ρm . (A-17) dt π ⋅ Dm dt t fr ⋅ Dm

* Formulations for t fr differ, depending on the underlying hydrodynamic instability mechanism considered as dominant. IDEMO, MC3D, CULDESAC and IFCI (Pilch correlation) use

* t fr = constant , (A-18) assuming stripping of crests of shear-flow produced waves on the drop surface (due to shear flow instabilities, usually denoted as Kelvin-Helmholtz type instabilities). ESPROSE and TEXAS use correlations of the form

1 * − 4 t fr = C fr ⋅Bo (A-19) with the constant C fr and the Bond number

ρ ⋅v ⋅ R 2 Bo = m &rel m (A-20) σ m again related to local, instantaneous values. Here Rayleigh-Taylor instabilities produced at the windward side of the drop by relative flow acceleration are considered as dominant mechanism. For clarifying the questions of relative importance and interplay of different instability mechanisms, more detailed modelling has been pursued at IKE and incorporated in the steady state detonation code FRADEMO (Bürger et al., 1986). The models take into account drop deformation, drag depending on the instantaneous deformation state and the flow conditions, wave stripping, fine and coarse break-up due to Rayleigh-Taylor instabilities as well coarse break-up caused by deformation. A description of the essential modelling concepts is given in Bürger et al. (1986). According to FRADEMO calculations, fine fragmentation from wave stripping was concluded as most rapid and thus dominant mechanism. For a detailed discussion of different fragmentation mechanisms and comparisons with experiments on hydrodynamic drop fragmentation see (Bürger et al., 1996). By fitting the correlation (A-14) to results of various calculations with the wave stripping model in FRADEMO, values between 1.25 and 1.33 have been obtained for

111 A. Description of the explosion model IDEMO

* t fr and are used in IDEMO and MC3D. In IFCI a similar value of 1.36 is taken according to Young (1987).

ESPROSE assumes C fr = 9 in Equation (A-19), based on comparisons with SIGMA * experiments (Chen et al., 1995). This corresponds to t fr ≈ 1.3 for Bond numbers around 2300. For practical reasons, a modified definition of Bo given in Chen et al. (1995) is used in ESPROSE. It is derived from a simplified drift equation and gives

3 Bo = ⋅c ⋅ We (A-21) 8 d with Weber number

ρ ⋅v 2 ⋅R We= f rel m . (A-22) σ m

Bo ≈ We results for a typically assumed value c d = 2.5.

Both forms of correlations are available in IDEMO. A comparison of the fragmentation description by means of calculations with IDEMO for KROTOS alumina experiments is presented in Buck and Bürger (1997). The results show on the one hand significant quantitative differences in the obtained explosion strengths. On the other hand, also different trends result from the different correlations. Escalation of detonation waves starting from weaker triggers is favoured with the IDEMO correlation, while with strong triggers or established strong explosions finally higher pressures may be reached with the ESPROSE correlation due to the additional Bond number dependence.

A.2.2. Mass transfer to micro-interactions field

To derive a model for the entrainment of cold coolant into the micro-interactions field, a systematic procedure has been performed by Chen et al. (1995) to check the micro-interactions description in ESPROSE, using X-ray and visual high-speed film results from SIGMA single drop fragmentation experiments. First, the parameter βfr in the fragmentation correlation is fixed based on mfr (t ) detection from X-ray data. It is then assumed that the water entrained into the fragment cloud around the fragmenting drop, the latter observed in optical high-speed movies, can be taken as the part which participates in heat exchange. The entrainment rate Γe is taken to be proportional to the fragmentation rate Γfr  on a volume basis, i.e.

ρc Γe = fe ⋅ Γfr ⋅ . (A-23) ρm fe is an entrainment factor which needs to be varied parametrically. To fix this

112 A. Description of the explosion model IDEMO parameter, the cloud volume development is calculated assuming a certain fragmentation behaviour (i.e. C fr = 9). Then fe is chosen to fit the experimentally observed cloud volume development. Values of fe between 7 and 12 have been derived from first evaluations in Chen et al. (1995). fe ≈ 5 is considered as a conservative choice. The formulation (A-23) has also been adopted for IDEMO. Test calculations e.g. in Buck and Bürger (1997) show a strong dependence of the results on the entrainment factor. Peak pressures are getting higher with smaller fe (2-3 times higher peak pressures with fe = 5 compared to homogeneous heating, larger values of fe in between). This underlines the importance of the modeling of non-homogeneous heating and further improvements. The approach (A-23) can just be considered as a first rough approximation. Thermal boundary layers around the fragments should give a more realistic measure than the apparent cloud volume. On the other hand, mixing and turbulence include further parts. Comparison with other approaches on non-homogeneous coolant heating, especially the descriptions in MC3D and TEXAS based on heat transfer and pseudo-evaporation rather than fragment cloud volume development, must also be considered.

A.2.3. Heat transfer from melt

In the micro-interactions concept heat is transferred from the fragments only to the hot part of the coolant. This heat transfer rate is given by

6 ⋅αb Qbh = ⋅ hbh ⋅ (Tb −Th ) . (A-24) Db where spherical fragments with an average diameter of Db and an average temperature of Tb are assumed. The fragment diameters Db and heat transfer coefficients hbh are chosen parametrically at present in IDEMO. Typically fragment sizes of 10 to 100 µm and heat transfer coefficients from 106 to 104 W/(m2K) are used. Parametrical variations of these values in calculations with IDEMO showed that the heat transfer from fragments to coolant has a strong influence on the escalation velocity and also the finally reached explosion strength (see Chapter 5.3 and Bürger et al., 2004).

A.2.4. Interfacial friction

The interfacial momentum exchange between the melt droplets and the fluid is given by

113 A. Description of the explosion model IDEMO

r 3 ⋅αm ⋅ ρf ⋅c d r r r r Fm ,f = ⋅ v f −v m ⋅ (v f −v m ) . (A-25) 4 ⋅Dm In IDEMO, a fixed drag coefficient, typically 2.5, or a correlation derived for arrays of drops (Bürger et al., 1987) is used:

4 0.396 c d = ⋅ 0.05 (A-26) 3 ⋅αf Re' −1.20 with

α D ⋅v ⋅ ρ Re' = f ⋅ Re, Re = m rel f . (A-27) 1 − αf µf

114 B. Initial conditions for verification of the IDEMO code

B. Initial conditions for verification of the IDEMO code

Zone Quantity Value Comments

System Pressure at 0.15 MPa trigger time

Height 750 mm Based on (see Fig. 20):

- 124 mm level swell - Melt front had reached elevation 150 mm (K1) at

triggering

- Melt trail was in between K4 and K5 positions (average 850 mm) at triggering as inferred from pressure traces signals

Radial 200 mm Full test vessel diameter

extension (diameter)

Melt fraction 0.032-0.020 Linear variation from 0.032 at elevation 150 mm to radially 0.020 at elevation 850 mm, considering that melt averaged tends to accumulate as going downwards.

values by Gives an averaged value of 0.026, consistent within Pre-mixture level 3 % with all melt in 700 mm high column. Radial values must be adjusted to fit 1/r distribution

Void fraction 0.09 Considering 50 % steam quantity in pre-mixture and radially 50 % in plug. averaged Consistent with 124 mm level swell. value by level Radial values must be adjusted to fit 1/r distribution

Liquid coolant 0.878-0.890 Linear variation from 0.878 at elevation 150 mm to fraction radially 0.890 at elevation 850 mm, as deduced from melt averaged fraction distribution and void fraction distribution values by level

Melt 2673 K Initial temperature. temperature

Gas 1000 K As chosen for FARO L-33 simulation (see below) temperature

Liquid coolant 363 K Initial temperature temperature

Mean particle 15 mm From KROTOS 50 (no trigger, no explosion), which size was performed in similar conditions and exhibited almost same values for component fractions while the melt temperature was 2473 K (Huhtiniemi et al., 1996).

115 B. Initial conditions for verification of the IDEMO code

Zone Quantity Value Comments

Height from bottom 150 mm K1 position to bottom

Radial extension 200 mm Full test vessel diameter Below (diameter) Pre- Melt fraction 0 mixture Void fraction 0

Liquid coolant fraction 1

Liquid coolant 363 K Initial temperature temperature

Height 379 mm Based on 124 mm level swell and pre-mixture zone extension Radial extension 200 mm Full test vessel diameter (diameter)

Melt fraction 0

Above Void fraction 0.165 Considering 50 % steam quantity in plug pre- averaged Radial values must be adjusted to fit 1/r mixture value distribution

“Plug” Liquid coolant fraction 0.845 As deduced from void fraction distribution

averaged value

Liquid coolant 363 K Initial temperature temperature

Cover gas Cover gas 406 K As measured by the thermocouple in expansion temperature vessel TC8 (TF8 in database) at triggering

Position In centre of See details in data report (Huhtiniemi et al., bottom plate 1996) Trigger Peak pressure 14.8 MPa Pressure in gas chamber, resulting in ~5 MPa at transducer K1 in pure water.

Duration at half peak ~1 ms In pure water. See trigger characterisation details pressure in water in data report (Huhtiniemi et al., 1996)

Energy 222 J

Table B- 1. Given premixture conditions for the verification of the experiment KROTOS K-44 with IDEMO code.

116 B. Initial conditions for verification of the IDEMO code

Zone Quantity Value Comments

System Pressure at trigger 0.44 MPa time

Height from 1714 mm Average of the two level-meter signals at bottom triggering.

Radial extension 300 mm Based on the fact that thermocouples at radius (diameter) 150 mm exhibit an increase before triggering, (uniform) while those at radius 330 mm do not.

Melt fraction 0.026 Corresponding to 25 kg of melt and a density of liquid of 7960 kg/m3. (uniform)

Void fraction 0.05 Note that assigning this value to a cylinder Pre-mixture 300 mm in diameter is somehow inconsistent (uniform) with level swell measurements, from which ~0.05 void fraction is deduced if considering void uniformly distributed all over the cross- section area of the test vessel (i.e., 710 mm).

Liquid coolant 0.924 As deduced from other component fractions. fraction

Melt temperature 3070 K Initial temperature.

Gas temperature 1000 K

Liquid coolant 306 K Average of values at trigger time from non- temperature destroyed thermocouples at centreline and at radius 150 mm.

Mean particle size 3.6 mm Mass averaged.

From L-31 debris data (Annunziato et al., 1999).

Height from 1714 mm Idem as for pre-mixture. bottom

Out of Pre- Radial extension From mixture diameter 300 mm to

diameter 710 mm

Melt fraction 0

Void fraction 0

Liquid coolant 1

fraction

117 B. Initial conditions for verification of the IDEMO code

Melt temperature 3070 K Initial temperature. in cover gas

Out of Pre- Cover gas 418 K Saturation value at 0.43 MPa. temperature mixture Difficult to evaluate from thermocouple signals in gas space. Liquid coolant 297 K Average of values at trigger time from temperature thermocouples at radii 150 and 330 mm, and same angular positions.

Position Centreline, 5 mm above debris catcher bottom plate

Peak pressure 14 MPa As characterised in pure water.

Value at vessel wall and elevation 150 mm (from bottom plate).

Trigger Duration at half 20 µs In pure water. peak pressure

Energy ~1 kJ Estimated from formula: A E = (∆p)2dt ρc ∫

A: test vessel cross section area

ρ: density of water

c: speed of sound in water

Table B- 2. Given premixture conditions for the verification of the experiment FARO L- 33 with IDEMO code.

118

Institut für Kernenergetik und Energiesysteme Universität Stuttgart Pfaffenwaldring 31

D-70569 Stuttgart