The impact of thermal non-equilibrium and large-scale 2D/3D effects on debris bed reflooding and...

The 11th International Topical Meeting on Nuclear Thermal-Hydraulics (NURETH-11)Popes’ Palace Conference Center, Avignon, France, October 2-6, 2005

Paper: 095

THE IMPACT OF THERMAL NON-EQUILIBRIUM ANDLARGE-SCALE 2D/3D EFFECTS

ON DEBRIS BED REFLOODING AND COOLABILITY

FICHOT, Florian 1, DUVAL, Fabien, TREGOURES, NicolasInstitut de Radioprotection et de Surete Nucleaire, Cadarache, Franceflorian.fichot@irsn.fr, fabien.duval@irsn.fr, nicolas.tregoures@irsn.fr,

QUINTARD, MichelInstitut de Mecanique des Fluides de Toulouse, France, michel.quintard@imft.fr

ABSTRACT

During a severe nuclear accident, a part of the molten corium resulting from the core degradation mayrelocate down to the lower plenum of the reactor vessel. The interaction with residual water in the lowerplenum leads to a fragmentation of the corium and formation of particles (order of magnitude : 1-5mm ). In order to predict the safety margin of the reactor under such conditions, the coolability of thisporous heat-generating medium and the possibility to reflood the particle bed are studied in this paperand compared with other theoretical or experimental results.

The detailed description of two-phase flow in a debris bed is addressed in the French Institut deRadioprotection et de Surete Nucleaire (IRSN) by a special module of the ICARE/CATHARE code.This thermalhydraulic module is three-dimensional and is able to deal with a non-homogeneous debrisbed. Calculations of one-dimensional reflooding are compared with two-dimensional calculations. Asexpected, water supply is greater considering multi dimensional flow in the bed and the dryout heat fluxis larger than predicted by 1-D modelling. Conditions for reflooding are also more favourable if large-scale non homogeneities exist in the debris bed. This leads to a flow pattern where steam can exit thedebris bed in preferential channels and there is no limitation by counter-current flow. The results alsoshow the importance of using a non-equilibrium model for temperatures. The impact of metallic debrisoxidation during reflooding is also presented.

KEYWORDS

reflooding, debris bed, severe accident.

1 INTRODUCTION

In case of a hypothetical severe accident in a pressurized water reactor (PWR), the destruction of fuelrods and melting of materials lead to the accumulation of core materials, which are commonly, called”debris beds”. There are two main possible configurations of debris beds. The first configuration of thedebris bed may result from the quenching of very hot rods during the reflooding of the core: this wasobserved in TMI-2 reactor above the core molten pool, with debris size of the order of several millimeters(Broughton et al. , 1989). The second configuration may result from the fragmentation of a jet of moltenmaterial falling through water in the lower plenum of the vessel: this was observed in many experimentalfacilities, and the average debris size is of the order of a few millimeters (Magallon, 1997).

The coolability of debris beds has been the subject of numerous questions and studies in the last thirtyyears. Indeed a non-coolable debris bed is assumed to quickly rise in temperature, due to the residualdecay heat, melt and form a large molten pool that would expand even when surrounded by water, andthreaten the integrity of the vessel. Many experimental studies and theoretical models have focused onthe determination of the ”critical” heat flux and the maximum volumetric power that can be removed from

1Corresponding author

2/18 The 11th International Topical Meeting on Nuclear Thermal-Hydraulics (NURETH-11)Popes’ Palace Conference Center, Avignon, France, October 2-6, 2005

a debris bed by water. In most cases, one-dimensional debris beds were considered (Lipinski, 1984). Afew interesting experimental studies of two-dimensional effects were done in parallel (Lee & Nilson,1977), (Hardee & Nilson, 1977). Recently, two-dimensional effects have been studied in more details,either experimentally (Decossin, 2000), (Atkhen & Berthoud, 2003) or numerically (Mayr et al. , 1998)(Bechaud et al. , 2001). It appears that the counter-current flow limitation, which is always present inone-dimensional situations, can be avoided in some two-dimensional configurations, leading to a highercritical heat flux. It has also been observed that local thermal equilibrium may not exist everywhere inthe debris bed, even for heated debris covered by water at saturation temperature (Atkhen & Berthoud,2003). The flow of overheated steam through the bed appears as a relatively important process to coolthe ”dry” debris.

On the other hand, the reflooding of hot debris beds has received less attention. Some experimentalstudies are available ( (Armstrong et al. , 1982), (Armstrong et al. , 1981), (Cho et al. , 1984), (Ginsberg,1982), (Ginsberg, 1985), (Ginsberg et al. , 1986), (Tutu et al. , 1984), (Konovalikhin et al. , 2000) )and a few models have been proposed ((Petit et al. , 1999), (Sozen & Vafai, 1990)). The existenceof temperature differences between the solid particles, the water and the steam makes modeling andexperimental measurements more difficult. Furthermore, flow patterns are complex since, for very hightemperature particles, steam becomes the ”wetting” phase due to the presence of a stable steam filmaround the particles. This was observed experimentally, on single spheres, by Dhir and Purohit (Dhir& Purohit, 1978) who proposed a theoretical model for heat transfer around spheres under film boilingregime. However the results obtained for spheres are difficult to apply to particle debris beds. Becauseof the lack of experimental data on real debris beds, models must rely on several assumptions.

In this paper, we intend to provide a multi-dimensional model for two-phase flow in a porous debrisbed, having the capability of dealing with the large temperature differences that may exist among thethree phases during quenching (but also in dry-out situations). Flow patterns are assumed and theirimpact on heat transfer taken into account. At present, no attempt was made to describe the effect offlow patterns on momentum transfer. The model is implemented in the ICARE/CATHARE code whichis a mechanistic code developed by the French Institut de Radioprotection et de Surete Nucleaire (IRSN)and devoted to the calculation of severe accident scenarios in PWRs, (Guillard et al. , 2001). Severalapplications to a debris bed in a PWR lower plenum are shown. Comparisons between 1D and 2Dcalculations show that the critical heat flux is increased as soon as the liquid water penetration is enhancedby a 2D circulation. The two-dimensional effects in reflooding situations are studied numerically, in alarge debris bed, as expected in a reactor core. The progression of water and the timing of quenchingare compared with the one-dimensional configurations. Finally, the impact of a possible oxidation of thedebris bed is studied in situations where a fraction of the debris consists in metallic Zircaloy.

2 ICARE/CATHARE MODELLING

ICARE/CATHARE is developed by IRSN to be used as a tool for severe accident analysis in IRSN andother foreign institutes. Its range of applicability covers all kinds of accident sequences, from the initialphases (for instance a break in the primary circuit) to the LOCA phase and eventually to the core degra-dation and melting, and possible vessel failure. For that purpose, several models have been included inthe code to deal with the different physical and chemical processes involved during an accident sequence.

In particular, IRSN has developed a model for the three-dimensional two-phase flow in a heat-generating porous medium. The extension of Darcy’s law for each fluid phase to describe the momentumbalance equations is used. Unlike many previous models, the present one is able to take into account tem-perature differences between the three phases.

It is also designed to calculate the flow outside of the porous medium. Therefore, the tricky problemof the conditions to be applied at the boundaries of the bed is solved by using a generalized set ofequations. The volume averaging method used to derive the conservation equations also provides closureproblems for the heat transfer coefficients between phases, as well as for the effective diffusivity anddispersion coefficient in each phase.

2.1 Momentum balance equations

Among all the theoretical models which have been developed at that time, Lipinski’s model ((Lipinski,1982)) has been widely used because it is able to predict the critical heat flux for a wide range of param-eters (particle diameter, bed height, ...) in a one-dimensional debris bed. One advantage of Lipinski’smodel is that it does not need a large number of parameters. However, it is based on several assumptionswhich may limit its range of applicability. First, all phases, including the solid debris, are assumed tobe in thermal equilibrium at the saturation temperature. This assumption is rather justified in the boilingregions, but it cannot be retained to extend the model to reflooding situations, or even post-dry-out situa-tions, where the flow of overheated steam must be calculated accurately. This point will be discussed inthe next subsection.

Second, the friction forces on the fluid phases are taken into account by using the classical extensionof Darcy’s law to two-phase flows. This means that viscous and inertial drag forces are calculated withrelative permeabilities and passabilities coefficients, depending mainly on the void fraction. There isno explicit interfacial drag force between the liquid and gas phases. This may be a lack in the model,as it was demonstrated by (Schulenberg & Muller, 1987) and by (Buck et al. , 2001). More important,the extension of Darcy’s law, as it is used in most models (including the model derived in the presentpaper) is based on a single correlation for the relative permeability and a single correlation for the relativepassability : this implies that a single flow regime is assumed, whatever the thermalhydraulic parameters(void fraction, debris temperature, etc...). This may not be justified when there is a stable steam filmaround the debris. In such a case, liquid water is not the ”wetting” phase, and most classical correlationsmay not apply since they were generally determined for water-air flows, with water being the wettingphase. Unfortunately, no experimental studies have been able, up to now, to clearly identify the possibleflow regimes that could exist in a self-heated debris bed. It is a serious limitation to further progress onmodelling and, as a consequence, the same ”simple” friction models have been used for more than thirtyyears now. It should be noted that several authors have proposed improved formulations of friction forcesbetween phases, but no consensus has been reached up to now. It appears clearly that the form of themomentum equation for a two-phase flow in a porous medium is still a matter of investigations. Morestudies are necessary, both theoretical and experimental, to take into account both co-current as well ascounter-current flows and to deal with a non-wetting liquid.

One of the first forms of momentum balance equations for debris beds was proposed by (Hardee &Nilson, 1977). Modifications were introduced by several authors to take into account additional effects.In this study, a classical extension of Darcy’s law for one-phase flow was simply used for each phase, asfollows:

α〈ρg〉g(

∂〈vg〉g

∂t+ 〈vg〉

g.∇〈vg〉g)

= −α∇〈pg〉g + α〈ρg〉

−εα2(

Kkrg〈vg〉

g + εα〈ρg〉

ηηrg〈vg〉

∣〈vg〉g∣

(1 − α) 〈ρ`〉`

∂〈v`〉`

∂t+ 〈v`〉

`.∇〈v`〉`

= − (1 − α)∇〈p`〉` + (1 − α) 〈ρ`〉

−ε (1 − α)2(

Kkr`〈v`〉

` + ε (1 − α)〈ρ`〉

ηηr`〈v`〉

∣〈v`〉

In these equations, 〈pβ〉β , 〈ρβ〉

β , µβ and 〈vβ〉β are respectively the average pressure, density, dynamic

viscosity and velocity of the β-phase (β = g, `). These variables are defined as volume averages overa representative volume including all phases (however, for each phase, averaging is made only over thefraction of volume occupied by the phase). The void fraction of the gas phase, α, is related to the liquidsaturation S by:

α = 1 − S (3)

For uniform spherical particles, the intrinsic permeability and passability are correlated with theparticle diameter dp and the porosity ε by the Carman-Kozeny relation (Carman, 1937) and Ergun law(Ergun, 1952):

180 (1 − ε)(4)

η =dpε

1.75 (1 − ε)(5)

The relative permeability and the relative passability for spherical particles have been chosen fromBrooks and Corey relation (Brooks & Corey, 1966):

krg = (1 − S)3 and kr` = S3 (6)

ηrg = (1 − S)3 and ηr` = S3 (7)

Several simplifications have been made deliberately, compared to previous works. The exponents forthe relative permeability and passability were chosen equal, as recommended by several authors ((Saez& Carbonnell, 1985), (Lee & Catton, 1984), (Lipinski, 1982), see above discussion). The interfacialdrag terms were omitted because no formulation of that term has proved to be valid over the wholerange of flow parameters that may be found in our studies. As it was mentioned in the previous section,we are aware that our model cannot be predictive without a proper expression for the interfacial dragterms. The capillary pressure is introduced in the equations to represent macroscopically the effect ofthe pressure jump across the non-wetting/wetting phase interface. It is generally modeled as a functionof the saturation.

pc = 〈pg〉g − 〈p`〉

` = σ cos θ(

ε (K)−1)1/2

J (S) (8)

where J is the Leverett function expressed in this study according to (Turland & Moore, 1983).

2.2 Energy balance equations

Macroscopic energy conservation equations of the three phases are obtained by averaging the local en-ergy conservation equations ((Duval et al. , 2004), (Duval, 2002), (Quintard et al. , 1997)). In thismethod, local thermal non-equilibrium between the three phases is considered.For further details on the averaging process, the reader may refer to (Quintard et al. , 2000, Quintard &Whitaker, 1994). The complete set of closure problems is presented in (Duval, 2002).The averaged equations are simplified following (Petit et al. , 1999), where heat transfers occuring inthe porous medium are expressed according to temperature differences between the phase temperatureand the saturation temperature. In order to be compatible with ICARE/CATHARE existing thermalhy-draulics modeling, an arithmetic transformation provides a new expression of the heat transfer termswhich exhibits explicitely the thermal exchanges between fluid phase and solid phase (Qpβ), fluid phaseand interface (Qβi), solid phase and interface (Qpi).

Qβi = hβi

〈Tβ〉β − Tsat

Qpβ = hsβ

〈Ts〉s − 〈Tβ〉

hpβ , hβi are the heat transfer coefficients. The expression of the energy balance equations usingQpl, Qpg, Qpi, Qgi and Qli exchange terms is then formally identical to the one used in the standardthermalhydraulic model of CATHARE2 code. The resulting macroscopic energy conservation equationsare expressed as follows:

- gas phase:

αε〈ρg〉g〈hg〉

∂t+ ∇ ·

αε〈ρg〉g〈vg〉

g〈hg〉g) = ∇ ·

g.∇〈Tg〉g)

+.mg hsat

g + Qpg + Qgi

- liquid phase:

(1 − α) ε〈ρ`〉`〈h`〉

∂t+ ∇ ·

(1 − α) ε〈ρ`〉`〈v`〉

`〈h`〉`)

= ∇ ·(

` .∇〈T`〉`)

+.m` hsat

` + Qpl + Qli

- solid phase:

∂ ((1 − ε) 〈ρs〉s〈hs〉

∂t= ∇ · (K∗

s .∇〈Ts〉s) − Qpl − Qpg − Qpi + $s (13)

In these equations, 〈hβ〉β and 〈Tβ〉

β are the macroscopic enthalpy and the temperature of the β-phaserespectively (β = g, `, s for the gas, the liquid and the solid phases respectively). K∗

β is the effectivethermal diffusion tensor.The phase change rate, which is obtained by adding the three phase equations and neglecting diffusionterms, is then given by the relation

Qpi − Qgi − Qli

hsatg − hsat

The macroscopic two-phase flow model is solved numerically on a two-dimensional meshing.The space discretization of the equations is based on a finite volume approach, with structured meshes.A staggered mesh grid is used with a main grid for scalar transport equations (mass and energy) and threeother grids for momentum balance equations (one for each velocity component). The discretization is offirst order in space and time and is based on the upwind scheme. The resolution scheme is semi-implicit.

3 APPLICATIONS TO 2D DRY-OUT AND REFLOODING

Several applications of the model have been done with ICARE/CATHARE. First, these applicationswere done with the aim of assessing the model by comparing with experimental data, mostly in 1Dconfigurations. The model was also used on reactor scale debris beds to try to identify some importantprocesses that may be expected during the dry-out or the reflooding. The most instructive applicationsare presented in this section.

3.1 Dry-out of a particle bed : comparison of 1D and 2D cases

One-dimensional dry-out results were first calculated with the model to show its validity by compari-son with theoretical and experimental results found in the literature. Those results were presented in(Bechaud et al. , 2001) and will only be summarized here. The dryout of a submerged bed occurs whenthe coolant can no longer reach some parts of the bed. As the heating debris power increases, the vaporfraction within the bed increases. For a certain value of the power, the vapor flow is large enough toreduce the downward flow of the liquid to the point where it all evaporates before it reaches the bottomof the bed. The power at which this condition is just met is called the incipient dryout power and thecorresponding heat flux, the critical dryout heat flux (DHF). It should be noted that the transition to DHFis not smooth but rather shows a sharp transition when the saturation decreases to a value that is still farfrom zero. For such saturation, it is likely that an unstable process leads to a sharp increases of frictionon the liquid phase which causes a local dry out. The coolant countercurrent flow also depends on thelocal properties (porosity, particle diameter, permeability, capillary pressure, ...). In (Bechaud et al. ,2001) the critical dryout heat flux was determined for beds with different heights and particle diameters.To summarize the results, we may mention that the one-dimensional calculations well predict the dryoutcritical heat flux trends with respect to the particle diameter and the bed height. The countercurrent floweffect is the main process governing the critical flux in 1D configurations. It is reminded here that con-clusions on the critical heat flux are limited because of the remaining uncertainties on the friction model

(in particular interfacial drag). The critical dryout heat flux is independent of the bed height when thisone is higher than a minimum value. This minimum bed height depends on the particle diameter and thepressure. The same phenomenon was experimentally observed by (Catton & Jakobsson, 1987).

As noticed by several authors, the 1D configuration may not be representative of the actual flowpattern that would occur in a large debris bed, at the reactor scale. To check the relevance of the 1Drepresentation, a comparison was made between two debris beds characterized by identical parameters(particle diameter, porosity, power) but different geometries: a 1D debris bed and a 2D hemi-sphericaldebris bed (as it is expected in the lower plenum). Both beds have the same height (1.5 m). The power waschosen so that it leads to dry-out in the 1D configuration (330 W/kg of fuel). The void fraction profilesin the center of the debris bed are compared on Figure 1. The differences are rather obvious. Contrary tothe 1D situation for which dry-out starts at the bottom of the bed because liquid water cannot penetratedeeper into the bed, the 2D situation shows an accumulation of steam at the top of the bed because ofgravitational effects. Such a profile may also be observed in 1D (for a lower power) but the flow patternis completely different as it can be seen on Figure 2: liquid water flows downwards along the vessel wallwhereas steam accumulates in the upper-central region where it flows upwards. As a consequence, thereare no regions with strong counter-current flow which could limit water penetration into the debris bed. Itmust be noted that the bed is perfectly homogeneous in porosity, particle diameter and volumetric power.The flow pattern and distribution of phase is only the consequence of the hemispherical geometry : theheight of debris is more important in the center than on the side, therefore there is more steam generatedin the center, which leads to a lower pressure in the center and a movement of the liquid towards thecenter, along the vessel wall. In their experimental study, (Horner et al. , 1998) have observed the samephenomenon.

0 0.2 0.4 0.6 0.8 1Void Fraction

2D case1D case

ICARE/CATHARE V2.0 - Debris Bed Dry-outP = 60bars, Dp = 1mm, Poro = 0.4

Figure 1: Comparison of axial void fraction profile for 1D and 2D debris beds

The consequence of that flow pattern is a higher dry-out heat flux than for the 1D configuration.This had already been predicted by other authors (see (Buck et al. , 2001) for example). In fact, (Tsaiet al. , 1984) have demonstrated experimentally that there is no limitation of the heat flux that can beremoved from a debris bed as long as a sufficient liquid mass flow can enter the bed from below. Theconclusion is that the accurate determination of the critical heat flux in large debris bed depends on thecorrect prediction of the 2D/3D two-phase flow that can be established in the debris bed. In that respect,

Figure 2: Void fraction and velocity fields in 2D configuration (no dry-out) - Vector scale : 1cm for 5cm/s (gas) or 2.5cm/s(liquid)

the proper estimation of drag forces between phases becomes essential. Since we have deliberatelyneglected the interfacial drag force in our model (because no validated formulation was available), theresults presented in this section have only a qualitative value.

Most of the models derived to predict dry-out in 1D situations are not able to predict the post dry-outevolution of the debris. However, dry debris can be cooled by overheated steam, which will delay thetime to reach debris melting. Figure 3 shows what happens for a 2D dry-out : the flow pattern is similarto the one observed before dry-out, but one region of the bed is filled with steam. This ”dry” region isswept by a strong steam flow which results from the evaporation of water throughout the bed and theaccumulation of steam towards the dry pocket. That steam flow is sufficient to cool the debris bed andreach a stable temperature, well below the melting point of debris. Without such cooling, the debris bedwould heat up almost adiabatically, at a much faster rate as can be seen on Figure 4.

As a conclusion to those studies of dry-out, it should be emphasized that the prediction of the 2D/3Dflow is essential to estimate the time to reach the dry-out and the heat-up of the debris bed after dry-out.The main flow regime across the debris bed is characterized by a co-current flow of steam and water.After dry-out, a complex process of latent heat transport through the dry part of the debris bed leads toan efficient cooling of the debris which may remain overheated without melting. As observed by (Lee &Nilson, 1977), there is a partial condensation of steam at the top part of the dry bubble.

3.2 2D reflooding of a particle bed

(Tregoures et al. , 2003) have applied the model to 1D reflooding configurations and compared theresults with experimental data obtained by (Tutu et al. , 1984) for bottom reflood conditions and by(Ginsberg, 1982, 1985, Ginsberg et al. , 1986) for bottom reflood conditions. The results show that thephenomenology of the quenching of a debris bed under bottom flood conditions is described reasonablywell by our model. The transition from a slowly rising quench front for low inlet liquid velocities toa more complex quenching process for high liquid inlet velocities is reasonably well captured. For thehighest velocities, a more accurate description of liquid entrainment is probably necessary to achieve abetter agreement, but such description is not included in the model and further work will be necessary.The model is also able to predict a transition in the reflooding mechanism for debris bed quenchingunder top-down conditions. The particle diameter at which the transition occurs does not agree with theexperimental data but, to some extent, this is not surprising. As outlined in section 2, expressions for therelative permeability, relative passability and interfacial friction (absent in our model) are questionable,especially when the gas is the ”wetting” phase.

3.2.1 Reflooding without oxidation

Figures 5 and 6 show the reflooding of a debris bed made of 2mm particles, with a power of 200 W/kg offuel and a porosity of 0.4. The pressure is 60 bar. The initial temperature is 1050K, which correspondsapproximately to 500K above the saturation temperature. Water comes from above the debris bed. Thecharacteristic features of the transient flow are summarized below.

Figure 3: Temperature, void fraction and velocity fields for stable dry-out - Vector scale : 1cm for 5cm/s (gas) or 2.5cm/s(liquid)

• Because of the slope of the lower head, water can flow along the wall without any counter-currenteffect and steam escapes through the upper part of the debris bed. Moreover, the colder tempera-tures along the vessel wall favor a faster quenching of that region and, as it can be seen on Figure6, the main liquid flow path is located along the bottom wall.

• Penetration of water from the top of the bed is limited by the strong steam flow resulting fromevaporation of water at the bottom. As a result, a liquid pool forms above the debris bed, anda dry ”bubble” appears in the center part of the bed, where the temperature keeps increasing.This bubble is progressively quenched by water, as water is continuously driven into the bed byhydrostatic pressure difference.

• It appears that there is no sharp quench front but a rather continuous transition from the dry over-heated region to the saturated and cooled region. It is reminded here that the numerical schemeis only of order one in space and diffusive because of the adopted upwind scheme. Therefore,the accuracy on the location and progression of the quenched front should be further analyzed(sensitivity to the mesh size for example).

• No comparison was made with 1D reflooding, but it was shown in (Tregoures et al. , 2003) thatthe quenching time is significantly lower than for an assumed 1D reflooding from the top, becauseof the easier penetration of water into the bed. The time of quenching strongly depends on theparticle size, as expected.

0 200 400 600 800 1000Time (s)

TsatCooling, z = -1.0mCooling, z = -0.9mCooling, z = -0.7mNo cooling

ICARE/CATHARE V2.0 - Debris Bed Dry-outP = 60bars, Dp = 1mm, Poro = 0.4

Figure 4: Comparison of temperature evolution in the dry-out zone : the saturation temperature is shown, as well as thecalculated evolution in the dry debris bed without steam flow (almost adiabatic) and the other curves correspond to variouslocations in the dry bubble

On Figure 7, it is possible to compare the void fraction distribution at the same instant of refloodingfor 1mm and 2mm particles. For 2mm particles, the major part of water injected from the top has migratedinto the debris bed whereas for 1mm particles, the debris bed is less permeable and the major part of waterinjected still remains above the bed, forming a pool. As for 2D dryout, it appears that 2D reflooding ismainly driven by gravity and that the total quenching time depends on the maximum mass flow of waterthat can penetrate into the debris bed. Water penetration is not strongly limited by steam counter-currentbecause steam is driven out of the debris bed far from the location of water penetration.

For a non homogeneous debris bed, the same process would result in the formation of dry pocketsin areas with smaller particles or low porosity, while water would saturate the regions of higher perme-ability. If a significant fraction of the debris consists in metals (Zr or steel mainly), the quench frontvelocity and the flow path followed by steam will have a strong influence on the debris oxidation duringquenching. This process is briefly studied in the next paragraph.

3.2.2 Reflooding with Zr oxidation

Reflooding has two opposite effects with respect to oxidation. On one hand, it brings an additionalsupply of steam to the hot metallic debris which prevents steam starvation and enhances oxidation. Onthe other hand, it quickly cools the particles which reduces the rate of oxidation. Both effects are actuallysequential at a given location. First, the particles will be swept by an increased steam flow and later, theywill be quenched. The time interval between the two processes depends mainly on the quench frontvelocity. The intensity of oxidation during that time interval depends on the debris temperature. Becauseof that sequence of events, the accurate prediction of the steam flow path through the debris bed andof the quench front progression is essential for the calculation of oxidation. A model for oxidationof Zr particles was introduced. It follows the standard approach used for the oxidation of fuel rodcladdings. The growth of the zirconia ( ZrO2 ) layer and the total amount of oxygen taken by themetal both follow parabolic kinetic laws. The standard correlation of Urbanic was selected. From athermalhydraulic point of view, the oxidation results in a production of hydrogen and a consumption ofsteam. An oxidation power, proportional to the hydrogen production, is added as a source term to thesolid phase energy equation. The oxidation behaviour is illustrated on Figure 8 where the total hydrogenproduction resulting from Zr oxidation is compared for two different initial temperatures : 1050K and1350K. The initial debris bed composition is : 75% UO2, 15% ZrO2 and 10% Zr. Other conditions arethe same as in the previous cases. Reflooding starts after 300s. The temperature evolutions in the centerof the bed (and at the elevation of −1.2m) is shown on Figure 9

For an initial temperature of 1050K, the chemical reaction is slower than the quench front progres-sion, and after a limited increase of the hydrogen production due to the increase of steam generation, thereaction is quickly stopped because of quenching. Oxidation occurs everywhere in the dry region, andthere is no starvation. For an initial temperature of 1350K, the chemical reaction is much faster and thebeginning of quenching is followed by a strong increase of the hydrogen production. On Figure 8, thefast rise of the hydrogen production is obvious. There is a delay with respect to the beginning of reflood-ing which corresponds to the time necessary to produce enough steam in the debris bed and the time toreach high temperatures (above 2000K) in the bed. One interesting point to notice is that, contrary tothe ”low” temperature case, this case leads to an intense localised oxidation front, just downstream ofthe quench front. The hydrogen production is so intense that all the region downstream of the oxida-tion front is filled with hydrogen (steam starvation conditions) and therefore, is not subject to oxidation.The different location of the oxidation regions for both cases can be observed also on the distribution ofoxidized metal.

On Figures 10 and 11, one can clearly identify the differences. For an initial temperature of 1050K,only a small part of the metallic debris has been oxidized after quenching, and a very limited region hasbeen almost fully oxidized. For an initial temperature of 1350K, at an intermediate stage of quenching,a fully oxidized region is already formed when the center remains unoxidized. Oxidation is completeand occurs in a narrow region (oxidation front) downstream of the quench front. Downstream of theoxidation front, the debris are surrounded by hydrogen (limited steam supply) and therefore they do notoxidize until the oxidation reaches them. The final state, for an initial temperature of 1350K, corresponds

to the full oxidation of the central part of the debris bed. The relocation of molten Zr (above 2100K)was not calculated. It might result in a reduction of the total amount of Zr oxidized. In both cases, itmay be observed that the debris near the vessel wall are quenched without being oxidized. The finaldistribution of oxidized metal is non uniform, which confirms the interest of using a 2D (or even 3D)model to compute such complex processes where the steam and liquid water flows are difficult to predictand where the heat and mass transfers are strongly coupled.

4 CONCLUSIONS

In this paper, we have presented a multi-dimensional three-temperature model for two-phase flow indebris beds. This model is implemented in the ICARE/CATHARE code developed by the French Institutde Radioprotection et de Surete Nucleaire to study severe accident scenarios in PWRs. The model isbased on two generalized Darcy momentum balance equations closed by empirical relations. The choiceof such relations, especially for the drag forces (solid-fluid and gas-liquid) is discussed. It appears thatthere is a need for complementary experimental and theoretical work to reach a consensus about theexpression for two-phase friction forces in a porous debris bed.

The extended 3D module of ICARE/CATHARE developped for this study can be activated during thecalculation of core degradation, and in particular the formation of debris beds. Thanks to this coupling,it will be possible to predict the transient formation of debris beds, their possible dry-out and refloodingin the course of realistic accident scenarios.

Comparisons with 2D calculations show that the 1D dry-out process may not be realistic as soonas water can penetrate into the particle bed from the top or from the side. In such cases, evaporationinduces a natural circulation of water through the bed, and this process supplies water to all parts ofthe bed. As a result, the critical heat flux may be much higher than predicted in 1D. Such a result wasconfirmed experimentally ((Konovalikhin et al. , 2000), (Atkhen & Berthoud, 2003)) and is of significantimportance for the safety evaluation of nuclear reactors under severe accident conditions. Our study alsoshows that, even after dry out, the strong steam flow generated by evaporation may be sufficient to coolthe dry debris and keep them at a low temperature, preventing the formation of a molten pool.

Two-dimensional reflooding simulations of an internally heated debris bed in a reactor vessel undertop flooding conditions were also presented. The calculations show that the water progresses throughthe debris bed mainly along the external side (water was initially injected in the downcomer, at theexternal side of the vessel). On the other hand, the steam flows out preferentially in the center part ofthe bed. Depending on the particle diameter, the water flow injected above the debris bed can eitherpenetrate quickly into the bed or penetrate slowly. In the latter case, the water which cannot enter thebed directly along the side spreads above it and wets the top part. A dry ”bubble” forms at the center ofthe bed and is progressively cooled by the progression of the surrounding quench front. It must be notedthat the quench front progresses mainly from the side and the bottom, although a top quench front alsoexists. Once again, the 2D situation appears as a complex combination of the processes observed in 1Dconfigurations.

Finally, the effects of debris oxidation were briefly studied. The strong evaporation leads to a sus-tained oxidation of metallic debris. Depending on the initial debris temperature and on the flow pattern,a part of the debris bed may be under steam-starvation conditions. In that case, oxidation is strong butlimited to a small region along the quench front, whereas the rest of the debris bed (central part), althoughvery hot, cannot be oxidized. This results in a limitation of the instantaneous total hydrogen generationduring the quenching. In any case, the bed is not completely oxidized after the quenching. The amountof oxidized debris depends on the quench front velocity and the initial debris temperature.

In conclusion, the results presented in this paper show the benefits of using a multi-dimensionaland three-temperature model. They also show that an improved modeling of the closure laws of themomentum equations as well as a more sophisticated flow regime map must be made as they are of crucialimportance in the modeling of debris bed reflooding. Such improvements will require new experimentaldata. It also appears that there is a lack of multidimensional experimental results providing a clear viewof the flow patterns and phases distribution in the course of either dry-out or reflooding transients.

The issue of debris coolability is essential for the evolution of the accident scenario and the possibility

to keep the fuel inside the vessel without external cooling. The beds formed during a possible accidentwould probably have various shapes, with heterogeneous porosity, particle size and volumetric power.The effect of the spatial variability of such parameters was out of the scope of this paper, but it is obviousthat it may be very important. The present study, although dealing with homogeneous beds, has shownthat such heterogeneities are also likely to induce water circulation in the bed and therefore enhance orreduce its coolability.

NOMENCLATURE

dp particle diameter, mh enthalpy per unit mass, J.kg−1

h effective heat exchange coefficient, W.K−1

〈hβ〉β β = g, `, s, intrinsic average enthalpy

for the β-phase, J.kg−1

K permeability, m2

Kβγ β, γ = g, `, s, effective thermaldispersion tensor, W.m−1.K−1

.m mass rate of evaporation, kg.m−3.s−1

p pressure, N.m−2

S saturation, S = ε`/εt time, sT temperature , K〈Tβ〉

β β = g, `, s, intrinsic averagetemperature for the β-phase, K

v velocity, m.s−1

〈vβ〉β β = g, `, intrinsic average velocity

for the β-phase, m.s−1

Greek symbolsα void fractionρ density, kg.m−3

µ viscosity, N.s.m−2

η absolute passability, mεβ β = g, `, s, volume fraction

of the β-phaseε porosity, ε = 1 − εs$s volumetric heat source, W.m−3

σ surface tension coefficient, N.m−1

Subscriptsg gas, vapor` liquids solid

ACKNOWLEDGEMENTS

The ICARE/CATHARE development and validation team is gratefully acknowledged for their help andsupport.

REFERENCES

Armstrong, D.R., Cho, D.H., Bova, L., Chan, S.H., & Thomas, G.R. 1981. Quenching of a high temper-ature particle bed. Transactions of the American Nuclear Society, 39, 1048–1049.

Armstrong, D.R., Cho, D.H., & Bova, L. 1982. Formation of dry pockets during water penetration intoa hot particle bed. Transactions of the American Nuclear Society, 39, 418–419.

Atkhen, K., & Berthoud, G. 2003. Experimental and numerical investigations on debris bed coolability ina multidimensional and homogeneous configuration with volumetric heat source. Nuclear Technology,142(June).

Bechaud, C., Duval, F., Fichot, F., Quintard, M., & Parent, M. 2001 (April). Debris bed coolabilityusing a 3-D two phase model in a porous medium. In: Proceedings of ICONE 9, 9 th InternationalConference on Nuclear Engineering.

Brooks, R. H., & Corey, A. T. 1966. Properties of porous media affecting fluid flow. J. Irrig. Drain. Div.Am. Soc. civ. Engrs IR2, 92, 61–89.

Broughton, J.M., Kuan, P., Petti, D.A., & Tolman, E.L. 1989. A scenario of the Three Mile Island unit 2accident. Nuclear Technology, 87, 34–53.

Buck, M., Schmidt, W., & Burger, M. 2001 (November). Multidimensional modelling of debris bedcoolability and quenching. In: First ICARE/CATHARE Seminar. IRSN, Cadarache, France.

Carman, P.C. 1937. The Determination of the Specific Surface Area of Powder I. J. Soc. Chem. Ind., 57,225–234.

Catton, I., & Jakobsson, J. O. 1987. The Effect of Pressure on Dryout of a Saturated Bed of Heat-Generating Particles. J. of Heat Transfer, 109(february), 185–195.

Cho, D.H., Armstrong, D.R., & Chan, S.H. 1984. On the pattern of water penetration into a hot particlebed. Nuclear Technology, 65, 23–31.

Decossin, E. 2000. Ebullition et Assechement dans un Lit de Particules avec Production Internede Chaleur : Premieres Experiences et Simulations Numeriques en Situation Multidimensionnelle.Ph.D.,Institut National Polytechnique, Toulouse, Fevrier.

Dhir, V.K., & Purohit, G.P. 1978. Subcooled film-boiling heat transfer from spheres. Nuclear Engineer-ing and Design, 47, 49–66.

Duval, F. 2002. Modelisation du renoyage d’un lit de particules : contribution a l’estimation des pro-prietes de transport macroscopiques. Ph.D. thesis, Institut National Polytechnique de Toulouse.

Duval, F., Fichot, F., & Quintard, M. 2004. A local thermal non-equilibrium model for two-phase flowswith phase change in porous media. International Journal of Heat and Mass Transfer, 47(3), 613–639.

Ergun, S. 1952. Fluid flow through packed columns. Chem. Eng. Prog., 48, 89–94.

Ginsberg, T. 1982 (August). Transient core debris bed heat removal experiments and analysis. In:International Meeting on Thermal Nuclear Reactor Safety.

Ginsberg, T. 1985 (August). Analysis of influence of steam superheating on packed bed quench phe-nomena. In: International Meeting on Heat Transfer Conference.

Ginsberg, T., Klein, J., Klages, J., Sanborn, Y., Schwarz, C.E., Chen, J.C., & Wei, L. 1986. An ex-perimental and analytical investigation of quenching of superheated debris beds under top-refloodconditions. Tech. rept. NUREG-CR-4493. Sandia National Labs.

Guillard, V., Fichot, F., Boudier, P., Parent, M., & Roser, R. 2001 (April). ICARE/CATHARE coupling: three-dimensional thermalhydraulics of LWR severe accidents. In: Proceedings of ICONE 9, 9 th

International Conference on Nuclear Engineering.

Hardee, H.C., & Nilson, R.H. 1977. Natural convection in porous media with heat generation. NuclearScience and Engineering, 63, 119–132.

Horner, P., Zeisberger, A., & Mayinger, F. 1998. Evaporation and Flow of Coolant at the Bottom of aParticle-Bed Modelling Relocated Debris. OECD/CSNI Workshop on In-Vessel Core Debris Retentionand Coolability, March.

Konovalikhin, M.J., Yang, Z.L., Amjad, M., & Seghal, B.R. 2000 (April). On dry-out heat flux of particledebris beds with a downcomer. In: Proceedings of ICONE 8, 8 th International Conference on NuclearEngineering.

Lee, D.O., & Nilson, R.H. 1977. Flow visualization in heat generating porous media. Tech. rept.SAND76-0614. Sandia National Labs.

Lee, H.S., & Catton, I. 1984. Two-phase flow in stratified porous media. In: 6th Information exchangemeeting on debris coolability.

Lipinski, R.J. 1982. A model for cooling and dryout in particle beds. Tech. rept. SAND 82-0765,NUREG/CR-2646. Sandia National Labs.

Lipinski, R.J. 1984. A coolability model for post-accident nuclear reactor debris. Nuclear Technology,65(April), 53–66.

Magallon, D. 1997 (May). The FARO program recent results and synthesis. In: Proceedings of CSARPMeeting.

Mayr, P., Burger, M., Buck, M., Schmidt, W., & Lohnert, G. 1998. Investigations on the Coolability ofDebris in the Lower Head with WABE-2D and MESOCO-2D. OECD/CSNI Workshop on In-VesselCore Debris Retention and Coolability, March.

Petit, F., Fichot, F., & Quintard, M. 1999. Ecoulement Diphasique en Milieux Poreux : Modele a Non-Equilibre Local. Int. J. Therm. Sci, 38, 239–249.

Quintard, M., & Whitaker, S. 1994. Convection, Dispersion, and Interfacial Transport of Contaminants: Homogeneous Porous Media. Advances in Water Resources, 17, 221–239.

Quintard, M., Kaviany, M., & Whitaker, S. 1997. Two-Medium Treatment of Heat Transfer in PorousMedia: Numerical Results for Effective Properties. Advances in Water Resources, 20(2-3), 77–94.

Quintard, M., Ladevie, B., & Whitaker, S. 2000 (January). Effect of Homogeneous and HeterogeneousSource Terms on the Macroscopic Description of Heat Transfer in Porous Media. Pages 482–489 of:Cheng, P. (ed), Symposium on Energy Engineering in the 21st Century, vol. 2.

Saez, A.E., & Carbonnell, R.G. 1985. Hydrodynamic parameters for gas-liquid co-current flow in packedbeds. AIChE Journal, 31, 52–62.

Schulenberg, T., & Muller, U. 1987. An improved model for two-phase flow through beds of coarseparticles. Int. J. Multiphase Flow, 13(1), 87–97.

Sozen, M., & Vafai, K. 1990. Analysis of the Non-Thermal Equilibrium Condensing Flow of a GasThrough a Packed Bed. Int. Journal of Heat and Mass Transfer, 33(6), 1247–1261.

Tregoures, N., Fichot, F., Duval, F., & Quintard, M. 2003. Multi-dimensional numerical study of coredebris bed reflooding under severe accident conditions. In: 10th International Topical Meeting onNuclear Reactor Thermal Hydraulics (NURETH-10).

Tsai, F.P., Jakobsson, J., Catton, I., & Dhir, V.K. 1984. Dry-out of an inductively heated bed of seteelparticles with subcooled flow from beneath the bed. Nuclear Technology, 65, 10–15.

Turland, B.D., & Moore, K. 1983. Debris bed heat transfer with top and bottom cooling. AIChE Sympo-sium Series, 79, 256–267.

Tutu, N.K., Ginsberg, T., Klein, J., Klages, J., & Schwarz, C.E. 1984. Debris bed quenching underbottom flood conditions. Tech. rept. NUREG/CR-3850. Sandia National Labs.

Figure 5: Temperature field during reflooding (at 100s, 300s, 400s and 500s)

Figure 6: Void fraction and velocity fields during reflooding (at 100s, 300s, 400s and 500s) - Vector scale : 1cm for 1cm/s

Figure 7: Comparison of void fraction at 300s after beginning of reflooding, for 1mm and 2mm particles

0 200 400 600 800 1000Time (s)

Tini = 1050KTini = 1350K

ICARE/CATHARE V2.0 - Debris Bed RefloodingP = 60bars, Dp = 2mm, Poro = 0.4

Figure 8: Comparison of Hydrogen production for initial temperatures of debris of 1050K and 1350K

0 200 400 600 800 1000Time (s)

Tini = 1050KTini = 1350K

ICARE/CATHARE V2.0 - Debris Bed RefloodingP = 60bars, Dp = 2mm, Poro = 0.4

Figure 9: Comparison of temperature evolutions for initial temperatures of debris of 1050K and 1350K (elevation −1.2m)

Figure 10: Fraction of initial Zr oxidized for Tini = 1050 K, at 900s

Figure 11: Fraction of initial Zr oxidized for Tini = 1350 K, at 500s

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