Validation and application of the WABE code: Investigations of constitutive laws and 2D effects on debris coolability

Nuclear Engineering and Design 236 (2006) 2164–2188

Validation and application of the WABE code: Investigations of constitutive laws and 2D effects on debris coolability Manfred B¨urger ∗ , Michael Buck, Werner Schmidt 1 , Walter Widmann 2 Institute of Nuclear Technology and Energy Systems (IKE), University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany Received 1 January 2004; received in revised form 15 March 2006; accepted 20 March 2006

Abstract The WABE-2D model aims at the problem of coolability of degraded core material during a severe accident in a light water reactor (LWR) and describes the transient boil-off and quenching behavior of debris beds. It is being developed in the frame of the KESS code system, which is considered to describe the processes of core heatup, melting, degradation and relocation to the lower plenum as well as the subsequent behavior. The models developed in this frame are being integrated in the German system code ATHLET-CD. An emphasis of the present contribution lies on multidimensional aspects of the cooling behavior. From multidimensional features a significant improvement of overall coolability is expected compared to what is concluded based on classical one-dimensional analyses. Such analyses – also mainly oriented at top cooling conditions – additionally miss the expected importance of interfacial drag which should support coolability in co-current flow situations due to bottom flooding. The latter situation plays a role in the multidimensional behavior expected under realistic conditions. Thus, a further emphasis in the present contribution lies on the constitutive drag laws and their effects in such configurations. Calculations comparing top and bottom flooding and the influence of interfacial friction are presented. An explanation for effects observed in related experiments at Forschungszentrum Karlsruhe is provided based on this influence. The significant increase of dryout heat flux with water inflow from below, driven by a lateral water column, is reproduced and understood. Enhanced cooling due to this and in general by lateral inflow is also demonstrated for reactor scenarios, considering particulate debris in the lower head of the reactor pressure vessel (RPV) of a LWR or in a deep water pool in the reactor cavity of a boiling water reactor (BWR). Cooling by steam flow through local dry zones can establish under lateral water supply to regions below and yield a further extension of coolability. Quenching of hot material is also analyzed. Finally, cases with loss of coolability, dry zone formation and melting are considered, especially in the perspective to analyze melt pool formation in the lower head of the RPV and the history of thermal interaction with the lower head wall. The latter will determine failure possibilities and modes of the RPV. © 2006 Elsevier B.V. All rights reserved.

1. Introduction Considerations on severe accidents with core melting in LWRs finally yield the question whether and by which means even such events can be managed and safely cooled states can

Abbreviations: BWR, boiling water reactor; CCFL, counter-current flow limitation; DHF, dryout heat flux; LWR, light water reactor; PWR, pressurized water reactor; RPV, reactor pressure vessel ∗ Corresponding author. Tel.: +49 711 685 62368; fax: +49 711 68562010. E-mail address: [email protected] (M. B¨urger). 1 Present address: AREVA NP GmbH, Erlangen, Germany. 2 Present address: Westinghouse Electric Germany GmbH, Mannheim, Germany. 0029-5493/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2006.03.058

be reached. In the last years, mainly ex-vessel options as deep water pools in BWR or core-catcher concepts especially with respect to the European pressurized water reactor (EPR), were under discussion, as well as the concept of external flooding of the RPV for cooling a melt pool inside the vessel considered to be applicable to reactor types with lower power. In the latter case, not considering the coolability of corium states before reaching the final pool situation means to neglect the potential of coolability and reaching safe states before running into the ultimate condition. This becomes especially problematic if coolability for this condition cannot be guaranteed. The concept as single measure appears especially not to be feasible for most existing reactors, due to higher power than allowable and specific design problems (e.g. insulation around the RPV hindering heat

M. B¨urger et al. / Nuclear Engineering and Design 236 (2006) 2164–2188

Nomenclature dp F j K Kr p p* s z

particle diameter (m) volumetric drag force (N/m3 ) superficial velocity (m/s) permeability, K = ε3 d2p /(150(1 − ε)2 ) (m2 ) relative permeability (−) pressure (Pa) dimensionless pressure gradient, p* = −(dp/dz)/(g(ρl − ρg )) (−) liquid saturation (−) height (m)

Greek symbols α void fraction (−) ε porosity (−) η passability, η = ε3 dp /(1.75(1 − ε)) (m) ηr relative passability (−) µ dynamic viscosity (kg/m/s) ρ density (kg/m3 ) Γ vapor production rate (kg/m3 /s) Subscripts i interface l liquid p particle s slip sat saturated g gas, steam

removal). The EPR concept yields no solution for existing reactors. However, basic aspects of melt cooling are also addressed in this context. As could be seen in the TMI-2 accident (Broughton et al., 1989; Reinke et al., this issue; M¨uller, this issue), a non-coolable situation with a melt pool – under water – in the core became coolable again after relocation of the melt to the lower head, with even only partial breakup and gap formation between a cake of low-porosity material and the RPV wall. Under different, perhaps more typical conditions of melt relocation in the form of jets released to the water-filled lower head (without intermediate water injection as in TMI-2, which yielded melt outflow under water and partly flow along cold structures), more significant breakup can be expected, as e.g. obtained in the FARO experiments (Magallon, this issue). Coarse particles (diameters in the range of few millimeters) can then be expected. Similar situations and resulting particulate configurations may be anticipated for ex-vessel situations in reactors with a water-filled cavity after RPV failure. This is especially envisaged for BWRs, with intentional flooding of the cavity or water in the cavity as a consequence of severe accident sequences. In deep water pools in the cavity of BWR, the applied safety concept relies on the expectation of more significant breakup and quenching, see e.g. Lindholm et al. (this issue).

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Therefore, the coolability of such particulate debris is a major issue for managing severe accidents in existing reactors. Further, it is also considered as an essential part in cooling spread melt in evolutionary reactor concepts. For example, in the COMET core catcher concept (Alsmeyer et al., 2000; Widmann et al., this issue), water injection from below yields a porous frozen structure which is coolable by the water flow. Certainly, the knowledge about these coolability features also helps to understand and evaluate measures and cooling options for existing reactors. In earlier investigations on particulate or porous debris coolability for LWRs (with larger particles than in the area of liquid metal fast breeder reactors, where the topic was originally investigated), mainly one-dimensional situations with top flooding have been considered, i.e. a water pool above a particulate debris bed. These conditions yield practically a homogeneous inflow of water from above against the upward steam flow. Partially, investigations on situations with water fed from the bottom have also been carried out, which indicated a significant increase of the power which can be removed from the debris bed before reaching dryout (Hofmann, 1984). However, only rarely conclusions have been drawn, pointing out a significantly improved coolability under realistic multidimensional conditions due to this effect. Under such conditions, the effect is e.g. provided by lateral inflow of water into bottom regions driven by lateral pressure differences from regions where water penetration is favored (smaller heights of particle beds, larger particles, higher porosity, unheated parts). This may be due to the fact that multidimensional models were just in the early stages of development when the emphasis in reactor severe accident research switched to other fields and safety concepts indicated above. With emphasis on experimental work and also extended modeling using multidimensional codes such investigations on multidimensional coolability of particulate debris beds have been restarted in the last years, e.g. in the frame of the development of the codes MC3D (Berthoud, this issue) and ICARE/CATHARE (Fichot et al., this issue). However, analyses are still limited, concerning code validation as well as application to reactor cases. The role of interfacial drag between vapor and liquid in this context has not yet been sufficiently investigated and estimated. Constitutive laws, as the friction laws of Tung and Dhir (1988) (see also Chu et al., 1983) or of Schulenberg and M¨uller (1984) considering interfacial drag explicitly, have not or only rarely been applied for such analyses. In order to check the expectations of strongly improved coolability under realistic multidimensional situations, calculations with the code WABE-2D (see Section 2) have been performed for the present contribution. The emphasis here is firstly on checking the modeling with respect to integral experiments on coolability under top and bottom flooding conditions, especially the experiment performed by Hofmann (1984) and available multidimensional experiments, especially the SILFIDE experiments (D´ecossin, 2000; Athken and Berthoud, this issue), then on application to reactor-related cases. Another line specifically addresses checking of the constitutive laws, especially with respect to the DEBRIS experiments at IKE, University of Stuttgart. These investigations are presented in the contribution

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of Sch¨afer et al. (this issue) in the present issue. Extended validation of the constitutive laws, especially the friction laws is still necessary. Nevertheless, first reactor-related cases are considered by WABE-2D calculations. The main aim here is to check the potential effects on coolability for more realistic conditions, expected to strongly favor the overall coolability. Quenching of hot debris is also considered, at first again with respect to integral quenching experiment, e.g. the experiment of Tutu et al. (1984), then for reactor related cases. Again, first analyses of DEBRIS experiments with top and bottom quenching have been performed applying WABE-2D. These are reported in the paper of Sch¨afer et al. (this issue). 2. Features of WABE-2D The WABE-2D model describes the boil-off and quenching of particulate or porous debris beds. It is being developed in the frame of the KESS code system (see e.g. B¨urger et al., 2004). Models developed in this frame are also being integrated in the German system code ATHLET-CD (Trambauer et al., 2004). The aim is to describe the processes of core heatup, melting, degradation and relocation to the lower plenum as well as the subsequent behavior until RPV failure. Only a short description of WABE-2D is given here, emphasizing the relation to the lines pursued in this paper. An extended description will be available in the frame of the KESS documentation and in subsequent publications. In WABE-2D, the transient behavior of the debris bed is modeled in two dimensions with cylindrical or Cartesian geometry using a quasi-continuum approach. Three separate phases, solid particles, liquid coolant (water) and gas (vapor), are considered. The solid matrix is assumed to be fixed. The mass conservation equations of the fluids are ∂t εαρg + ∇ρg jg = Γ,

(1)

∂t ε(1 − α)ρl + ∇ρl jl = Γ,

(2)

where ε is the porosity, α the void fraction, and jg and jl are the superficial velocities of gas and liquid. Under the assumption of dominant friction between the particles and the fluids, temporal and spatial derivatives of the velocities are neglected leading to the simplified momentum conservation equations: −∇pg = ρg g + −∇pl = ρl g +

F pg F i + , εα εα F pl F i − . ε(1 − α) ε(1 − α)

(3) (4)

For the particle–fluid drag forces the model of Ergun (1952) is adopted, which is extended to the present situation with two separated fluids by the introduction of relative permeabilities and passabilities (e.g. Lipinski, 1982): 
µg ρg       Fpg = εα (5) j g jg , jg + KKrg ηηrg 
µl ρl       Fpl = ε(1 − α) (6) j l jl . jl + KKrl ηηrl

The relative permeabilities and passabilities are based on dryout measurements. The most common approach is Krg = αn , m

ηrg = α ,

Krl = (1 − α)n , m

ηrl = (1 − α) .

(7) (8)

Lipinski (1982) originally assumed n = 3 and m = 3. Increasing the dependence on the void, Reed (1982) and later also Lipinsky (1984) used m = 5. This is the most commonly used approach that fits experimental dryout data well. Hu and Theofanous (1991) criticized that according to the measurement procedure the experimental values are too high, and consequently proposed an exponent m = 6 in the relative passability, based also on own measurements, see also the discussion by B¨urger and Berthoud (this issue). Based on isothermal air/water experiments, where air is injected into the bottom of a water saturated particle column, Schulenberg and M¨uller (1984) used the measured pressure gradient to determine a formulation for the interfacial friction, not included in the above models (see also the discussion by B¨urger and Berthoud, this issue): F i = 350(1 − α)7 α

  ρl K (ρl − ρg )g jr  jr , ησ

(9)

where jr is the relative velocity, given by jr =

jg jl − . α (1 − α)

(10)

Based on this formulation Schulenberg and M¨uller fitted the relative passability of the gas by  0.1 α4 : α ≤ 0.3, ηrg = (11) α6 : α > 0.3. The other expressions are taken as in the formulation proposed by Reed. A more detailed description according to Tung and Dhir (1988), also based on measurements of pressure gradients in air/water experiments, includes flow patterns for bubbly, slug and annular flow. Their expressions for the gas phase in the bubbly and slug flow regime are

 1 − ε 4/3 4 1 − ε 2/3 4 Krg = α , ηrg = α , (12) 1 − αε 1 − εα and in the annular flow regime:

  1 − ε 4/3 3 1 − ε 2/3 3 Krg = α , ηrg = α . 1 − εα 1 − εα

(13)

For the liquid phase: Krl = ηrl = (1 − α)4

(14)

is applied in all flow patterns. Interfacial friction F i between the liquid and the gas is included in the form:   F i = A(α)jr + B(α) jr  jr . 1−α

(15)

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Details on the formulations for the different flow patterns are to be taken from (Tung and Dhir, 1988). With respect to capillary effects various forms of Leverett functions can be applied. For larger particles (≥3 mm), the influences remain small, if not sharp transitions between layers of significantly different particle size are considered. These could lead to strong gradients in the liquid volume part (“saturation” s = 1 − ␣), thus in effects of capillary pressure. Heat transfer and evaporation are in principle based on a thermal non-equilibrium between the phases. Superheated particles, subcooled water and superheated steam are taken into account. A strongly simplified boiling curve description is presently used for the heat transfers. Due to the lack of data, a major assumption is to take the heat transfer from a single sphere in an infinite liquid coolant medium as a basis, only modified by the factor of the liquid part (1 − α) and an additional factor accounting for the modifications in the bed of particles (presently taken as 1). A corresponding approach has been assumed by Tutu et al. (1984). The Rohsenow correlation (Rohsenow, 1952) is taken for nucleate boiling up to the critical heat flux. A 100 K superheat above saturation is presently assumed to yield vapor film boiling, for which a correlation of Lienhard (1987) is used, taking also into account a radiation part. In the intermediate range, the heat flux from the particles is calculated by linear interpolation as a function of the temperature difference between particle and saturation temperature. For the splitting of the heat transfer from the particles into the fluid parts, also simple approaches are presently applied. In film boiling, a forced convection correlation is taken for the heat transfer from the fluid interface to water, thus yielding the difference of arriving heat flux and the heat flux to subcooled water for evaporation. The part going into steam heatup is taken from a parametric approach yielding practically rapid adaptation of the steam temperature to the local sphere temperature. The modeling of heat transfer based on the thermal nonequilibrium of phases becomes important for regions with developed or developing dryout as well as naturally for quenching of hot debris. For analysis of long-term coolability assuming an initially quenched bed heated by decay heat, it suffices to assume thermal equilibrium. Usually, only small superheats of the particles of few degrees will be required to transfer decay heat to surrounding water. Thus, limitations of cooling do not occur by this process but by limitations of steam removal and especially water access. For this, the friction forces can be considered as responsible (see B¨urger and Berthoud, this issue). 3. Dryout heat flux with top and bottom flooding Classical analyses of coolability have mainly been based on dryout heat fluxes under boiling conditions, especially under top flooding (upper water pool) in 1D-like columns. Then, as discussed above, friction forces can be considered to determine the coolability. The dryout heat flux (DHF) gives the limiting heat flux per cross-section leaving the particle bed at top, for which still steady states can be maintained, i.e. removal of produced steam and access of water, see also the discussion by B¨urger and Berthoud (this issue). Dryout heat fluxes have been

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Fig. 1. Dryout heat flux for top fed beds vs. particle diameter: comparison of predictions using classical friction models with experimental measurements.

determined experimentally and by models corresponding to that described above. Adaptation of the models mainly to top flooding experiments has been reached by adaptation of the exponents in Eqs. (7) and (8) as indicated above. The model of Reed with n = 3 and m = 5 is usually taken as a standard model with best adaptation, although objections remain and may need further clarification, see e.g. Hu and Theofanous (1991). The critical condition is reached when the accumulated upwards vapor flow hinders water to penetrate the bed sufficiently and compensate the evaporated water. The DHF was measured for pure 1D top fed configurations by many authors. A comparison of results of various authors with theoretical predictions is given in Fig. 1 for different particle diameters. The model of Reed may be considered as best adapted of the classical models, while the earlier Lipinski model with m = 3 in Eq. (8), later adapted to m = 5 as used by Reed (Lipinsky, 1984) gives too high values and the Hu and Theofanous model appears to give too low values. The experimental results have in general been questioned by Hu and Theofanous (1991) concerning principal deficits yielding an overestimation of dryout heat fluxes. Main points were a too small vessel to particle (sphere) diameter ratio and especially too short times taken for checking occurrence of dry zones. They also express some general questioning concerning the scattering of experimental data and the surpassing of the flat plate CHF (critical heat flux) by the data with increasing particle sizes beyond 5 mm. Based on own experiments, however with stone gravel, Hu and Theofanous propose a corrected value m = 6 of the exponent in Eq. (8). This yields the lower critical heat fluxes (DHF) in Fig. 1.The experimental data of Hu and Theofanous are also given in Fig. 1. However, these data indicate the problem of defining an appropriate characteristic diameter for the nonspherical gravel, see also the discussion by B¨urger and Berthoud (this issue). The smaller diameter in Fig. 1 is an equivalent particle diameter based on equal permeability of a bed of spheres,

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Fig. 2. Comparison of model predictions with experimental measurements of the dryout heat flux for top fed beds with particle diameters in a range relevant for severe accident conditions.

while the larger one is based on an equal-volume sphere. From sieve analysis the non-spherical particles of stone gravel have been characterized by 7–9 mm sieve pass (heating was by resistance elements of layers of aluminum balls of 1.25 cm diameter). It appears, that clarification by additional experiments is required, at first for spherical particles of uniform size. First results from the DEBRIS experiments at IKE, University of Stuttgart (Sch¨afer et al., this issue) with spheres of 3 and 6 mm diameter are also included in Fig. 1. These data appear rather to confirm the model of Reed. The value of 813 kW/m2 for 3 mm lies close to the experimental results of Hofmann (1984) and Squarer et al. (1982), the value of 1330 kW/m2 for 6 mm also close to respective results of Squarer et al. (1982) and in the range of the data of Catton et al. (1983) and Barleon and Werle (1981). In the DEBRIS experiments special care was taken to control the time delay of onset of dryout. Further, the bed is with 60 cm height deep enough and with 12.5 cm diameter wide enough as compared to maximum 6 mm diameter spheres, to largely exclude boundary effects (see Sch¨afer et al., this issue for further details). Results from the above presented models of Tung and Dhir (1988) and Schulenberg and M¨uller (1986) which include explicitly interfacial friction, in contrast to the models of Lipinski, Reed and Hu and Theofanous, are included in Fig. 2. Fig. 2 reproduces a part of Fig. 1, without the data on very large diameters, in an enlarged representation. The omitted single data of large diameters are considered as rather uncertain (see above). Further, the range of most interest for reactor applications with respect to severe accidents in LWR lies rather within 1–6 mm diameters. While the values from the Tung/Dhir model lie significantly below the data, especially for sphere diameters smaller than 5 mm, the Schulenberg/M¨uller model appears to be more appropriate in this range of smaller diameters. The experiment of Hofmann takes a special place due to the careful checking of time delays of dryout inception, as also mentioned by Hu and

Theofanous. Thus, the agreement with this experiment gives also some confirmation for the DEBRIS experiment and the resulting data. From this comparison, the Schulenberg/M¨uller model, together with the Reed model, may be considered as most appropriate in the relevant range. The conclusion then would be to favor the Schulenberg/M¨uller model, at least as a basis, due to the extended description with explicit interfacial friction. However, the interfacial friction model of Schulenberg/M¨uller appears to be questionable. In contrast to the basic physical argumentation that interfacial friction yields the limitation of water inflow and steam release, its influence vanishes in the model rapidly with increasing void (due to the factor (1 − α)7 , see Eq. (9)), thus towards the top of the debris bed where the restriction in the sense of counter-current flow limitation (CCFL) should occur. As discussed by B¨urger and Berthoud (this issue), the assumption in the approaches without explicit interfacial friction is that the effect can be included in the relative friction contributions of the phases with the solid, essentially addressing the effects of their volume parts. Finally, an adaptation to the experimental data is to be done. However, this cannot work as a general description for all situations. Especially, top and bottom flooding cannot be adapted likewise if interfacial friction plays a role, since its influence is in opposite directions (against or with water flow). This causes the need for an explicit formulation of interfacial friction. But then, this formulation should be in accordance with the physical considerations on CCFL. In contrast, it appears that in the Schulenberg/M¨uller approach the disappearing interfacial friction towards the top (high void) saves the adaptation of the classical approach without interfacial friction for the top flooding situation. The additional term coming into play at bottom then yields a correction option, there. Even if less adapted to the top flooding results according to Fig. 2, the Tung/Dhir approach appears in principle to be physically more appropriate. Like the other forces on the liquid phase, the interfacial friction per (total) volume only vanishes according to the liquid volume part, see Eqs. (4) and (15). This means that the forces on the remaining liquid could even increase with increasing steam flow (higher void) and thus strongly influence the remaining water, eventually yielding separation of water droplets and entrainment. In spite of this more physical character than disappearance of interfacial friction for small liquid parts, also the Tung/Dhir approach appears to suffer from principal deficits. Especially, still the interfacial friction term appears not to finally determine the flow limitation yielding DHF. Although it acts against water inflow under top flooding, there is no drastic effect visible causing the limitation. Rather, this appears still to be contained in the liquid particle friction with remaining (1 − α)-terms in the denominator from the choice of relative permeabilities and passabilities, still in contrast to the physical mechanism (CCFL) usually claimed. Furthermore, under the present conditions of heated particles, the assumption of liquid at the solid surface as a basis for the existence of liquid/solid friction becomes questionable, in contrast to the experimentally investigated cases with isothermal gas/water cases. Thus, fundamentally improved laws will be required along the above discussion lines. Experimentally,

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friction (pressure drop) measurements with heated particles and evaporation are necessary, as performed in the DEBRIS experiments (Sch¨afer et al., this issue). Nevertheless, at present state, it appears to be best to use the Tung/Dhir model as a basis for improvements. Some attempts have been undertaken at IKE, University of Stuttgart. The latest attempt by Schmidt (2004) has meanwhile also been questioned since it follows in essential parts the line of the Schulenberg/M¨uller approach. Instead, an earlier approach (to be further improved) is favored again. As a cause for the too low dryout heat fluxes under top flooding from the original Tung/Dhir model according to Fig. 2, a too high interfacial friction may be considered acting against the water inflow from top. Then, this friction is to be reduced. Presently, a reduction factor of 0.4, used already earlier, is adopted in all flow regimes. This may be questioned and separate corrections may be required for the separate flow regimes in the Tung/Dhir model. Especially, the question remains whether this reduction is compatible with the data on bottom flooding and of course also with the original data from separate measurements with gas/water flows on which the modeling was based. With respect to top flooding, a significantly improved result is obtained with the modified Tung/Dhir correlation (factor 0.4 on interfacial friction), as is shown in Fig. 2. But, for smaller diameters (<3 mm) the resulting DHF values are still too low. For diameters of about 1 mm and smaller, effects of capillary pressure must also be taken into account, not included in the present calculations. Since a significant increase of coolability with increasing ambient pressure may be expected, it is important to check this effect. Data with this respect are rather limited, especially in the diameter range of interest. Thus, only a comparison with a diameter of 1.4 mm from DCC-2 experiments (Reed et al., 1985) and a comparison with data from the experiments of Hu and Theofanous (1991) are given here, taking an equivalent diameter of 4.5 mm for the latter experiments. Fig. 3a shows that over the large pressure range considered the Reed model gives the best agreement with the experimental data. In the lower pressure range (Fig. 3b) being most relevant (up to about 1 MPa), the uncertainties appear to be largest due to the strong increase of dryout heat fluxes detected there. With higher pressures, the Hu/Theofanous and Schulenberg/M¨uller models deviate strongly. For an even lower pressure range up to 0.25 MPa, the data from the experiments of Hu/Theofanous lie significantly below most models, besides those of Tung/Dhir and their own (Fig. 4) Thus, no final decision appears to be possible, especially not for the most relevant regions of low ambient pressures. Further experimental data are required. Extended analyses on the pressure are planned in the DEBRIS experiments at IKE, University of Stuttgart. A major interest with respect to coolability of real configurations lies in different inflow modes of water. Thus, data on bottom inflow are of special interest in the 1D experiments, in addition to top flooding. Such data are again hardly available, especially in the range of particle diameters of interest. Mainly the experiment of Hofmann (1984) may be considered, in which both top and bottom flooding have been investigated. Inductive heating has been applied, with steel spheres of 3 mm

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Fig. 3. Dryout heat flux for top fed beds vs. system pressure: comparison with measurements from DCC-2 experiments (Reed et al., 1985); (a) complete experimental pressure range; (b) pressure range relevant for severe accident conditions.

Fig. 4. Dryout heat flux for top fed beds vs. system pressure: comparison with data from (Hu and Theofanous, 1991).

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diameter in a cylindrical vessel of 6 cm diameter, filled with the particles to about 49 cm height (porosity 0.4, 0.1 MPa system pressure). Extensive tests have been done concerning the influences of experimental conditions as bed height, water submergence, dependence on filling conditions and vibrating before new experiments, etc. Also, the inception of dryout has been analyzed with great care, e.g. by checking the influence of heating power on the development towards dryout, especially the incipient dryout location. For realistic conditions with respect to water injection from the bottom, a similar height of a lateral water column driving the water inflow at the bottom of the bed may be assumed. This is approximately established in the experiments of Hofmann by a surrounding vessel forming an annulus of 7.5 mm diameter around the inner vessel. Other results of experiments of Stevens and Trenberth (1982) have also been taken into account, although some questions remain concerning these experiments, partly due to missing information. For example, there may be effects of the special heating method (heating by electric current through the bed, provided from plates at the sides), of the slice-like vessel of 3–4.5 cm thickness (10 cm along main side), of the height of particle bed of only 20 cm, of the water submergence by only 6 cm water above the bed, of the water passage from top to bottom in case of a permeable bottom plate (bottom inflow) via holes and a passage of 1.5 cm width at back of the vessel (passage effects may in general need checking, also with the experiments of Hofmann) and of the dryout detection for which application of different methods is claimed (however not clearly indicated which is applied for specific tests). An advantage of these experiments is that several particle sizes (of tin-plated iron shot) have been used, of diameters from 0.22 to 5 mm, while in the experiment of Hofmann only 3 mm diameter steel spheres were applied. For the porosity, Hofmann gives a measured value of ε = 0.405. Stevens and Trenberth (1982) give no value, but one may assume the usual value of about 0.4 for spherical bodies of uniform size in natural arrangement. Stevens and Trenberth also investigated both, top and bottom flooding. In the case of top flooding, their data for larger particles from 3 to 5 mm diameter lie below the other data and the trend of their lower diameter data, as can be seen from Figs. 1 and 2. They state that the reason of the latter is not known, but exclude walleffects due to experiments with beds of different thickness. Other effects from relatively low bed height or water submergence should rather yield higher dryout heat fluxes. The dryout heat flux data for the aforementioned experiments are given in Fig. 5, together with different correlations. The results of the Stevens and Trenberth experiments also show in the case with bottom injection a deviation behavior with larger particles from 2 to 5 mm, as compared to the trend with smaller particles. Further, no clear trend with increasing particle sizes can be seen, although these data lie in the range of the spread of the classical correlations of Lipinski, Reed and Hu/Theofanous, with Lipinski being too high. Even higher values result with the correlations which include interfacial friction terms, especially with the Tung/Dhir variants. Only the original version of the latter reaches the high result of Hofmann for 3 mm diameter (Fig. 5). Thus, the data of Stevens and Trenberth are further

Fig. 5. Dryout heat flux versus particle diameter for beds with injection at the bottom from a lateral water column: comparison of model predictions with experimental data of Hofmann (1984) and Stevens and Trenberth (1982).

questioned by the experiment of Hofmann and also by the correlations with interfacial friction. It is to be remarked further that even beds with lower height of 6–15 cm have been used in these experiments. However, again one would rather expect higher dryout heat fluxes from this. Another explanation of the differences may be related to differences in the lateral driving column, compared to the height of the bed and water or water/steam mixture above. In the experiment of Hofmann, these heights are established by overflow over the inner vessel, while connecting holes are used in the experiment of Stevens and Trenberth. Differences in water level above the debris may play a role. In order to further clarify such influences and effects, dryout heat flux measurements under bottom inflow are also foreseen in the DEBRIS experiments (Sch¨afer et al., this issue), with variants of the lateral water column and resulting inflow conditions. Table 1 specifically gives results of the different models for the experiment of Hofmann. As already to be seen from Figs. 2 and 5, but now more directly visible for the specific experiment, bottom flooding increases the dryout heat flux in comparison to top flooding. However, the increase is significantly smaller from the classical models without explicit interfacial friction term (L, R, T in Table 1) than from those including this term (TD variants, S), especially the original Tung/Dhir model. However, it must also be taken into account that in the latter the top flooding DHF is much too low. With the modified variants, at present only from reduction of interfacial friction by a factor, the latter adaptation of the DHF value for top flooding yields too low values for bottom flooding, at least with respect to the Hofmann experiment. If the latter is taken as the measure, this indicates the need of more specific improvements than by a factor on interfacial friction, as also discussed above. The result of a much too low DHF for top flooding from the original Tung/Dhir model, but a good agreement for bottom flooding, may be taken to indicate that the interfacial drag is especially overpredicted for the flow regime responsible for DHF under top flooding. This

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Table 1 Comparison of dryout heat flux for top and bottom fed configurations (dp = 3 mm) measured in the experiment of Hofmann (1984) with predictions using different friction models: L: Lipinski (1982); R: Reed (1982); H/T: Hu and Theofanous (1991); T/D: Tung and Dhir (1988); S/M: Schulenberg and M¨uller (1986)

DHF (top fed) (MW/m2 ) DHF (bottom fed) (MW/m2 ) DHFbottom /DHFtop Flow rate from below (mm/s) Level fed from bottom (%) Maximum void (top) Maximum void (bottom)

Experiment

L

R

H/T

T/D

Mod. T/D (0.4)

Mod. T/D (0.25)

S/M

0.93 2.10 2.25

1.22 1.48 1.21 0.563 0.825 0.795 0.864

0.90 1.22 1.35 0.453 0.807 0.770 0.849

0.71 1.01 1.42 0.374 0.801 0.742 0.820

0.60 2.00 3.34 0.927 0.999 0.758 0.991

0.75 1.83 2.46 0.847 0.999 0.744 0.999

0.80 1.72 2.14 0.794 0.999 0.740 0.959

0.82 1.58 1.94 0.724 0.990 0.784 0.935

is the annular flow regime in the approach of Tung and Dhir, but may rather be an inverted annular flow regime under boiling conditions (see the discussion above and below about boiling versus isothermal experiments). In general, the increased DHF by bottom instead of top inflow can be explained by inflow over the water rich regions at the bottom instead of inflow through the region with accumulated steam at top. This is in principle also described by the friction correlation without explicit interfacial friction term. The interfacial friction additionally facilitates the water inflow from bottom by the up-flowing steam (co-current mode), while it additionally hinders inflow from top (counter-current mode). Thus, it is understandable that an interfacial friction term is required to adequately describe the increase of DHF from top to bottom inflow. However, the influences may be different in different flow patterns, especially bubbly steam flow in the water-rich bottom region as compared to possibly steam-rich annular flow at top. Thus, modifications should be performed specifically for the different flow patterns instead of the present use of general factors. In this context it is also of interest to consider the maximum void values which are reached at top for the occurrence of DHF. These are given in Table 1 and generally show that DHF occurs already with still significant liquid parts of about 20–25% for top flooding with all correlations and still with liquid parts of about 15–20% for bottom flooding with the classical correlations. In contrast, those with explicit interfacial friction term closely approach 100% void, especially the original Tung/Dhir correlation. Obviously, in these approaches, the steam draws the water practically to the top. This is also confirmed by the heights shown in Table 1, up to which the water is fed from below. Practically no water is required from above according to these results.

and the void fraction in the bed may be determined, e.g. by the change of the water level on the top. With the fixed flow rates, both data are determined and can also be calculated. Thus, they can be used to check the modeling approach, here especially the friction modeling. However, as discussed by Fichot et al. (this issue), Berthoud (this issue) and B¨urger and Berthoud (this issue), the gas/water/particle configuration may differ from a water/steam/particle configuration expected in water-filled beds with heated or even hot particles. This may also yield substantial differences in the friction laws. Thus, investigations under the latter conditions are additionally necessary, as performed in the DEBRIS experiments (Sch¨afer et al., this issue). A comparison of model results with experimental air/water data measured by Tutu et al. (1984) is shown in Fig. 6. A zero net water flow was chosen for a particle bed consisting of stainless steel spheres with a diameter of dp = 6.35 mm. Air was injected into the bottom of the column. The superficial velocity of the air, corresponding to the mass flux through the test column, was varied. For the established steady states the pressure gradient was measured by the difference of two pressure taps, one in the lower and one in the upper bed region. Additionally, the void fraction in the bed was determined by the rise of the liquid level

4. Comparison of the friction laws with isothermal air/water experiments Isothermal air/water experiments have mainly been performed for direct investigation of the friction laws of two-phase flow in porous media, based on measurements of the pressure drop over test sections. By fixing the water and air flow rates through a vertical test column filled with particles, defined steady state conditions, either for co- or for counter-current flow are established. The pressure gradient in the test column is measured

Fig. 6. Comparison of friction models with data for the dimensionless pressure gradient and the void fraction from isothermal water/air experiments (particle diameter 6.35 mm, porosity 0.38, zero net water inflow) of Tutu et al. (1984).

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above the bed. In Fig. 6, the normalized pressure gradient: p∗ =

−dp/dz g(ρl − ρg )

(16)

is given versus the superficial velocity of the gas. The classical models, without explicit consideration of the interfacial friction, cannot reproduce the experimentally obtained decrease of p* , i.e. of the absolute value of the pressure gradient (negative gradient in upwards (z-) direction). This can directly be seen from the z-component of the momentum equation of the liquid phase, Eq. (4). The superficial velocity of the liquid jl , thus the friction force Fpl , is usually very small. Since in these models the interfacial friction Fi is zero too, this immediately yields ρ* = ρl /(ρl − ρg ) ∼ = 1, independent of the gas mass flux. Thus, in these models the pressure field must always be equal to the hydrostatic one for pure liquid, not influenced by the gas flux. This is in contrast to the experimental data. According to Fig. 6, the measured pressure p* first decreases with increasing gas flow rate. This behavior can only be reproduced by including the drag of the up-flowing gas on the liquid. The models of Schulenberg/M¨uller and Tung/Dhir, including this interfacial friction, qualitatively show this characteristics. This result clearly shows the necessity for the explicit consideration of the interfacial drag in the models. The experimental results also clearly show a minimum in the p* (jg ) curve. This can again be explained by the behavior of interfacial friction alone (still without net water flow, only flow on a micro-scale to be considered as result of interfacial friction). It indicates a reduction of interfacial friction to be explained by a change of flow pattern. With increasing steam flow and resulting void, the bubbly flow transforms to gas or steam slugs and finally gas or steam channels develop (annular flow with water films at the solid to be considered with isothermal gas/water flows). Thus, the subtracted Fi -term in Eq. (4) becomes smaller and a minimum occurs. This is reproduced in principle by both approaches with explicit interfacial friction term, the Tung/Dhir as well as the Schulenberg/M¨uller models. However, the latter yields for larger jg an increase of p* beyond the experimental data, while the former yields lower values and even a flat maximum. The versions with reduced interfacial friction by a factor in the Tung/Dhir model yield more pronounced minima than the original Tung/Dhir model, as can be seen for factor of 0.4 and 0.25 in Fig. 6 and is also indicated by the experiment. However, the p* curves are significantly above the data in the latter cases. Again, this indicates the need for more specific improvements. The same factors applied only to the annular flow regime in the Tung/Dhir model yield an improved agreement with the experiment, as can be seen in Fig. 6. Corrections with respect to the original Tung/Dhir model then only occur at higher jg . The further course of the p* curves beyond the minima is strongly different, especially between the Schulenberg/M¨uller approach and the Tung/Dhir variants. While, with increasing gas flow, p* tends to 1 in the Schulenberg/M¨uller model, maxima with subsequent continued decrease occur in the Tung/Dhir variants. Obviously, the latter behavior has to do with the transition to annular flow, thus also the difference in the course specifi-

cally in this range (with voids above 70%) between Tung/Dhir variants of Fig. 6. As an explanation, an increase of interfacial friction may occur again in this flow pattern, due to increasing steam flow, produced waviness and finally even entrainment of water droplets. Schmidt (2004) favors the behavior according to the Schulenberg/M¨uller model, even fundamentally requiring that p* should approach 1 with the void approaching 1, i.e. with disappearing liquid phase. However, this requirement appears not to be justified. Rather, an increase of interfacial friction with increasing steam flow may yield breakup of the remaining liquid and entrainment processes. After the disappearance of the liquid phase, the gas friction at the particles will determine the pressure gradient. No decision about the further course can be drawn from the experimental results which are missing in the corresponding higher ranges of jg . Tung and Dhir (1988) even limit their results to a lower range of jg -values for the case of a net zero liquid flow rate, since they conclude that steady-state operation at zero liquid flow rate is possible only up to the onset of annular flow. Then, liquid flow at macro-scale may necessarily occur. A further case from Tutu et al. (1984), with 3.18 mm diameter spheres, is considered in Fig. 7. Here, the initial decrease of p* is less pronounced. Astonishingly, the void dependence on jg is rather similar, in contrast to the differences in p* . This smaller sensitivity for α than for p* was already apparent in Fig. 6. Differences between the models can less clearly be seen in the limited jg -range. Further, more detailed analyses about the influences of single forces depending on jg are still to be done. The initial decrease of p* with increasing jg has been explained rather formally from the liquid momentum Eq. (4), based on the interfacial drag force. This can be understood more fundamentally by considering that the up-flowing gas relaxes the hydrostatic liquid pressure. Another picture can be gained from summing the z-components of Eq. (3), multiplied by εα, and Eq. (4), multiplied by ε(1 − α). This yields, with pg = pl , a

Fig. 7. Comparison of friction models with data for the dimensionless pressure gradient and the void fraction from isothermal water/air experiments (particle diameter 3.18 mm, porosity 0.38, zero net water inflow) of Tutu et al. (1984).

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Fig. 8. Comparison of friction models with experimental data from isothermal water/air experiments of (Chu et al., 1983) with particles of 9.9 mm diameter: dimensionless pressure gradient and void fraction vs. superficial gas velocity for: (a) zero net water inflow and (b) co-current flow with jl,0 = 9.15 mm/s.

mixture momentum equation (in 1D) in which Fi is eliminated: −

  dp = ε (1 − α) ρl + α ρg g + Fpg + Fpl . dz

(17)

Then, the rapid decrease of p* with increasing jg or void ␣, respectively, can be explained by the reduction of hydrostatic head in the mixture according to the first term in Eq. (17). This corresponds to the relaxing effect of Fi (which is required for this by consistency, although Fi disappeared in Eq. (17)). Then, from Eq. (17), the counter-effect against the decrease of p* yielding the minimum is due to the increasing drag mainly of the gas flow at the particles. In cases with fixed upwards net water flow (co-current), Tung and Dhir (1988) even obtain positive p* values for higher jg , i.e. the upwards pressure drop becomes larger than the hydrostatic head of water. In the interpretation picture related to Eq. (4), this means that via the corresponding force balances the drag of liquid at the particles (depending also on α) must come into play. A comparison of results for this situation is given in Fig. 8. The case is taken from Fig. 4 of (Tung and Dhir, 1988) and concerns a particle diameter of 9.9 mm. Besides the case with no net water flow (jl = 0 mm/s, Fig. 8a), an upwards water flow rate of jl = 9.15 mm/s (Fig. 8b) is considered. p* and α dependencies

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on jg are shown for both water flow rates. It is seen that the void does not differ that significantly between the water flow rates of 0 and 9.15 mm/s, whereas a significant difference occurs for p* , with the increase to p* > 1 with increasing jg for jl = 9.15 mm/s. The original Tung/Dhir model compares well with the measurements. For the Schulenberg/M¨uller model, the comparison in Fig. 8 shows approximate agreement for the void in both cases and for p* in the case with jl = 0 mm/s until the minimum, then however an increasing p* in contrast to the slight final decrease from the data. A strong deviation of p* from the experimental results occurs especially for jl = 9.15 mm/s. According to Fig. 8, the modified Tung/Dhir model with a general factor of 0.4 on interfacial friction yields still a good approach to the experimental data, although here with some difference in p* for the case with jl = 0 mm/s. In the case with jl = 9.15 mm/s (Fig. 8b), practically no differences are obtained between the original Tung/Dhir model and the modified versions with a reduction factor of 0.4 or 0.25 only in the annular flow pattern. With jl = 0 mm/s, these curves only differ a little for larger values of jg (voids α), see Fig. 8a, i.e. after reaching this flow pattern. Other comparisons with experimental data and calculations are given by Tung and Dhir (1988) for the counter-current flow situation, i.e. for an imposed downwards (counted negative) water flow. The cases correspond to Figs. 7–9 in Tung and Dhir (1988). Approximate agreement has been obtained with the experimental results using the original Tung/Dhir model (Fig. 9). No substantial differences in the range of experimental data are obtained with the modified versions using factors of 0.25 or 0.4 in the annular flow part of the Tung/Dhir model (and correspondingly the transition range from slug to annular flow). This range is again only reached for higher values of jg . However, a maximum with respect to jg is obtained for the α- and p* -curves from the models, in these cases of counter-current flow. This is indicated and discussed for the case with jl = −11.67 mm/s in (Tung and Dhir, 1988). It means that a limitation for steady states with the given jl in counter-flow to gas exists, i.e. a maximum possible gas flow under steady state conditions. This occurs significantly below α = 1, as known from DHF conditions discussed in the previous section. In the range of this maximum, the influence of the modeling of annular flow may become relevant. This is indicated in Fig. 9a by the versions of the Tung/Dhir model with reduction of interfacial friction in the annular flow range. This reduction directly yields an extension of possible jg -values, corresponding to higher DHF in top flooding situations. A decision cannot be made based on the present data. Experimental data are missing in the respective range of higher jg -values. In the case of Fig. 9, no difference of these versions as compared to the original Tung/Dhir model are obtained (Fig. 9b), obviously since the annular flow regime is not reached here. Similarly, a constant reduction factor on the interfacial friction in all flow patterns yields an increase of the maximum (possible jg -values), now also with changed results in the range with existing data. There, also differences between data and the calculation exist, which indicate that the modification only in the annular flow range is more appropriate. For the Schulenberg/M¨uller model, the comparison in Fig. 9 shows, in addition to deviations of the curves from the data, that the maximum gas

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Fig. 9. Comparison of friction models with experimental data from isothermal water/air experiments of (Chu et al., 1983) with particles of 9.9 mm diameter: dimensionless pressure gradient and void fraction vs. superficial gas velocity for counter-current flow with a) jl,0 = −3.89 mm/s and b) jl,0 = −11.67 mm/s.

Fig. 10. Comparison of friction models with experimental data from isothermal water/air experiments of (Chu et al., 1983) with particles of 5.8 mm diameter: dimensionless pressure gradient and void fraction vs. superficial gas velocity for counter-current flow with (a) jl,0 = −3.89 mm/s and (b) jl ,0 = −11.87 mm/s.

flow rate occurs already at significantly smaller values than with the Tung/Dhir model. This could be taken as an indication that the DHF from the Schulenberg/M¨uller model lies below that of the Tung/Dhir model, in contrast to the results for the Hofmann experiment. However, Fig. 2 shows that for small particle diameters the DHF is smaller with Tung/Dhir, while it becomes larger for larger diameters. The relation and transition will also depend on the gas properties, here air in contrast to steam with DHF. Further, steady states under boiling conditions require the validity of the relation jl = −ρg /ρl jg instead of independent establishment of jl and jg . Thus, a direct extrapolation of the relation of results for the DHF problem is not possible. However, for the experimental conditions corresponding to Fig. 9, the Schulenberg/M¨uller model does not yield good agreement, especially with respect to the limit (maximum) of jg for jl = −3.89 mm/s lying much below the maximum jg for which steady states were obtained in the experiment. Further comparisons with experimental data for a particle diameter of 5.8 mm, again in counter-current flow, are given Fig. 10. The predictions of the original Tung/Dhir model give an approximate agreement with the limited data (here less good for α), which especially here (but also in the above cases) do not allow to identify the limit for jg and the respective conditions. For the case with jl = −3.89 mm/s in Fig. 10a, the Schulen-

berg/M¨uller model yields a limitation of jg only little smaller than from the Tung/Dhir model, while the difference is larger for jl = −11.87 mm/s. The experimental data indicate existence of steady states at higher jg -values than the theoretical limit, also from the Tung/Dhir model. The present results with the modified Tung/Dhir model with reduction factors in the annular regime are identical to the original model and do not yield higher gas flow rates since the limitation occurs below the annular flow regime. As major conclusions of these comparisons, it must be noted that still significant uncertainties exist even with respect to the air/water flows. While it is clear that models without explicit interfacial friction cannot describe the measured pressure gradients and the different modeling approaches essentially reproduce the behavior for smaller gas flows, the differences become large in the range of higher jg -values which are most important with respect to a limiting behavior, either by hindering water to penetrate from top in counter-current mode or by restricting the flow pattern in which a limited void can be reached by pulling sufficient water in the co-current mode with the gas stream. Data in this higher jg and void ranges are missing and the modeling approaches differ significantly. However, from the available data and the present analyses it may be concluded that an extended description based on the Tung and Dhir approach distinguishing

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different flow regimes is most promising. Agreement is essentially obtained for the lower ranges of jg and α and adaptations to the annular flow regime by reducing interfacial friction appear to yield improvements with respect to extended applications, e.g. with respect to the experiments of Tutu et al. (1984), remaining likewise consistent with the original data given by Tung and Dhir (1988) with reference to experiments performed by Chu et al. (1983). This way to improve the description appeared also to be necessary and most promising from the analysis of DHF in the previous section. However, the present comparisons still indicate deficits concerning the present parametrical approaches. Since further questioning concerned the use of isothermal gas/liquid flow patterns instead of steam/water flows under boiling conditions, this remains as the next step of model checking and improvement. The DEBRIS experiments at IKE, University of Stuttgart serve for this purpose. Section-wise vertical pressure drops are measured under boiling conditions. Results are given by Sch¨afer et al. (this issue) for spherical particles of 3 and 6 mm diameter. Different local conditions of steam and water flow are considered. Comparisons with theoretical approaches are also given there. The present conclusions are similar to those above. Principal differences between the results under boiling conditions and the isothermal results could not yet be clearly found, besides perhaps more significant deviations of the Tung/Dhir model from the data for higher steam flow rates and the smaller particle diameter. Uncertainties remain especially for the higher steam flow rates, for which the difference between the isothermal and boiling flow patterns may become most significant (annular versus inverted annular flow). Further clarification is expected from continued experiments. A further step of model validation concerns the application to again more integral experiments, like the dryout experiments (DHF determination under top and bottom flooding), but now in the perspective of multidimensional effects to be expected under prototypic conditions. Another line concerns prototypic local compositions of particles, with respect to particle sizes and shapes, in contrast to spheres of uniform size. This is not pursued in the present contribution but will be a task for further DEBRIS experiments (see also the contribution by Lindholm et al. (this issue) and the discussion by B¨urger and Berthoud (this issue)). Concerning the multidimensional effects, the recent SILFIDE experiments have a special relevance. 5. Application to SILFIDE experiments Configurations to be expected in the frame of severe LWR accidents, in- or ex-vessel, favor coolability by multidimensional features. Debris beds in the lower head imply already by the RPV geometry smaller heights at the sides, thus facilitating water penetration from there. Furthermore, a mound shape of the particulate bed is more realistic than a flat surface. In such configurations, the easier inflow of water via regions of smaller height, thus against less steam production, yields a water flow from the sides predominantly to lower central regions. This is comparable to some extent with the bottom flooding case. The inflow from the sides, especially via bottom regions, is further promoted by the lateral pressure gradients inherently produced

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between central regions with high steam content and water-rich outer regions. The attainable improvement of coolability needs further investigations, firstly concerning the validation of codes such as WABE-2D, then on reactor-related cases. The SILFIDE experiments address the multidimensional aspects and the improved coolability expected hereby (Athken and Berthoud, this issue). The inductively heated steel spheres have sizes in a relevant diameter range from about 2 to 7 mm. The 0.6 m × 0.6 m slice geometry (thickness of 10 cm) of the vessel allows in principle to study various 2D configurations of debris beds in a flexible way. Onset of dryout and subsequent heatup are detected by an array of 26 thermocouples. However, in test series published up to now, the bed height was not varied laterally. Lateral and axial non-homogeneities of the bed were only produced by a locally non-uniform power distribution. This may not have produced as strong influences as to be expected for the realistic situations. Thus, the SILFIDE experiments have 2D features due to the spatial power distribution with in general higher power at the sides than in the middle of the 2D-like slice geometry. Therefore, the onset of dryout or hot spot formation naturally appears at the sides. Additional features are less evident: (i) such spots started to develop at the sides in the upper region, although in 1D configurations first dry spots occur at the bottom, at least with powers just slightly above the critical one, due to insufficient water inflow from above; (ii) the spots remained rather stable with increased temperature but stabilizing for a certain power level and not expanding spatially. The WABE calculations also yield these features which can be explained by water supply from the middle to the sides, especially to lower regions. This also supports steam flow through the more or less dry spots which is sufficient to keep the temperatures bounded by cooling in the steam flow. Results of a WABE calculation for a case with 4.76 mm particle diameter are given in Fig. 11. Fig. 11a shows the liquid saturation (volume part of liquid in the pores) together with the steam velocities for practically steady state conditions established about 80 s after the last power transient. Fig. 11b shows the temperature distribution together with the liquid velocities. The temperatures reached in the dryout regions appear to be higher and the extension of the practically dry and heated regions appears to be larger than indicated by Athken and Berthoud (this issue). Results from MC3D-REPO calculations for a particle diameter of 3.17 mm, given by Berthoud (this issue), also show a different distribution of the liquid saturation. In the WABE calculation, the liquid part forms a downwards pyramid in the center, surrounded by the dry regions. This indicates water downflow concentrating to the center which can also be seen from the water flow given in Fig. 11b. This flow then supports evaporation and steam flow through the dry regions from below. An inverse pyramid of liquid content is obtained by Berthoud (this issue), which may indicate water inflow from top via a small center region with flow enlargement downwards. These patterns may depend on the friction description. However, in both calculations the Reed description has

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Fig. 11. Results of a WABE-2D calculation for a SILFIDE experiment showing stabilized dry regions after increase of the heating power from 687 to 1168 W/kg; (a) liquid saturation and vapor velocity; (b) solid temperature and liquid velocity.

been used. The different diameters may also play a role, especially with this respect. More detailed analyses about the key phenomena (water inflow patterns, steam cooling, development towards steady state under steam cooling or continued dryout and heatup) depending on the conditions and different modeling approaches are required to reach better understanding and quantitative results. From the experiments, local dryout heat fluxes at the top of the bed have been derived, based on the power in the vertical columns at the side, where dry spots occur. These local values are much higher than the average values derived for the whole bed. They also exceed 1D model predictions for the top flooding situation, even by factors >1.5. With the WABE calculations this effect, attributed again to the two-dimensional behavior (lateral water flows), could only partly be reproduced, with the Reed as well as the Tung–Dhir friction laws (see Fig. 12). This can in principle be understood, concerning the Reed model, since

Fig. 12. Local and average dryout heat flux values derived from SILFIDE experiments with different particle sizes compared to the Reed 1D-correlation and WABE-2D calculations applying the Reed and Tung/Dhir friction models.

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this does not contain interfacial friction, which in the bottom area could play a role drawing the water towards the bottom of the dry zones with the steam moving upwards there and flowing into these zones. Concerning the original Tung/Dhir model, it has been concluded above that interfacial friction is overestimated in the upper void region thus yielding much too low DHF for top flooding. This means in the present case that it strongly acts against the water inflow from top. Thus, the interfacial friction (in this formulation) may here act overall in the direction of smaller local DHF, explaining the lower DHF values in Fig. 12 for the original Tung/Dhir model as compared to the Reed model. The conclusion is, in line with the considerations of the previous sections, that an improved description is required in the direction proposed by the modification of the Tung/Dhir model. Thus, further analyses with the improved modeling will be done. Further, comparisons between WABE and MC3D-REPO calculations for the whole bandwidth of experimental results and under variation of friction laws should be done to yield firmer conclusions. From SILFIDE experiments with bottom injection even higher values of the dryout heat flux (about twice those for top cooling) resulted. Analyses are still to be performed. Experiments with more pronounced multidimensional situations favoring coolability are unfortunately missing. Due to higher lateral driving forces under such conditions and water inflow via regions with lower height, more significant effects than in the present experiments, which only address non-uniform power distribution, should occur. Thus, experiments with such configurations emphasizing lateral water inflow (e.g. mound configurations or configurations with non-homogeneities favoring water access, such as gaps or regions with increased porosity) would be important for getting more insight into realistic coolability options. Partly, experiments in this direction, although not in the scale of the SILFIDE experiments, have been performed, as the LATTUM experiments (Zeisberger and Mayinger, this issue) or the POMECO experiments (Kazachkov and Konovalikhin, 2003; Nayak et al., this issue). Also, such investigations will be performed in smaller scale in future DEBRIS experiments. Analyses on these experiments with WABE are still to be performed. 6. Quenching of hot particle debris beds Already with heatup in dry zones developing from boiling conditions, the heat transfer description becomes important, in addition to friction. For the latter, additional needs may occur due to different flow patterns. The need for respective modeling and checking increases in the case of quenching of hot debris. In the limiting case of a slowly propagating water front due to high friction, the quenching will be rapid enough to occur in a thin front (“frontal type”). Then, the need for detailed heat transfer description is relaxed. However, if the water penetrates a significant distance without significant quenching, then the heat transfer description becomes important to determine quenching. Since both situations may occur, a sufficient description for both cases may be necessary. Nevertheless, there may be relaxing aspects. For example, with small particles friction can be considered to dominate, thus a more detailed heat transfer

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description may only be needed for larger particles. Top and bottom flooding may also yield different requirements, as above considered for friction. In order to check the present modeling, available experiments on bottom flooding from literature have been taken, at first. Calculations with WABE have already been presented in (B¨urger et al., 1998) on the experiments of Tutu et al. (1984), mainly concerning the temperature development. New calculations have meanwhile been performed with the further developed WABE code, addressing especially the experimental results on the steam or heat fluxes at top of the bed. In the experiment, a bed of steel spheres of 3.18 mm diameter and a height of about 42 cm within a cylindrical tube of 10.8 cm inner diameter has been used. The porosity is given as 0.39. After heating the bed to initial temperatures between 512 and 775 K, water at saturation temperature (0.1 MPa system pressure) was injected at the bottom with constant flow rates, given as superficial velocities of 1.01, 1.98, 4.42 and 7.4 mm/s in (Tutu et al., 1984). Major phenomena from the experiments are: • A frontal type water penetration results for small penetration velocities and lower temperatures with a relatively narrow (as discussed above) and also plane front. This yields constant steam flow rates at top due to a steady 1D quench front progression upwards. • An extended quenching zone establishes with higher water velocities and higher temperatures, due to inflow of water in regions remaining hot under film boiling. Under these conditions, no constant steam flow rate at top results. Due to the more rapid penetration of water and onset of quenching in a large zone, the quenching becomes overall more rapid and the steam flow rates at top reach higher values. Peaks of steam flow rate occur since an increasing region is involved in rapid heat transfer and quenching. Results for the highest experimental temperature of 775 K (Ts − Tsat = 402 K) as well as a lower one of 594 K and the different (superficial) velocities of water inflow at bottom are given in Fig. 13a and b, together with the results of WABE calculations. The heat transfer model described in Section 2 has been applied, but with a factor of 2 on the film boiling heat transfer. This may be justified by the inherent disturbances within the bed of particles as compared to single spherical bodies in a pool, further by the effect of relative water flow (although this is small, it may have some effect in the narrow pores). In the friction description, the Reed model was used, i.e. not yet a model including explicitly interfacial friction. In spite of these present restrictions of the calculations, the agreement with the experimental results appears to be rather well from Fig. 13. It shows the calculated results taking into account a delay required to fill the empty tube below the screen at bottom of the debris, i.e. taking the start of filling as time zero. Some evaporation may already occur during this phase, e.g. due to the heated tube wall. The magnitude and duration of heat fluxes is rather well met for the different water inflow rates, as well as the transition in behavior from the peaks at higher water inflow rates to the

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water column, i.e. under feedback with the pressure build-up in the bed. Difficulties arose to explain a significant slow-down of quenching propagation in the bed with temperatures above about 670 K. 7. Applications to reactor-related cases The WABE-2D calculations performed here are considered as first checks about the postulated strong effects favoring coolability under realistic conditions. While bottom flooding should yield much better coolability than top flooding alone, the realistic case with lateral water inflow may be somewhat in between or may even yield an increased coolability due to the lateral access of water. Lateral water inflow occurs when lateral water rich columns drive the water to the interior of the bed. In general, water access is strongly favored by laterally lower bed heights or paths of high porosity, large particles and unheated regions. Gaps have been investigated by Zeisberger and Mayinger (this issue), downcomer structures by Sehgal (this issue) and Nayak et al. (this issue). Detecting and investigating such favorable conditions by WABE calculations shall also give orientation for future experiments. 7.1. Decay heat removal for in-vessel debris configurations

Fig. 13. Comparison of measured and calculated heat fluxes at the top of the bed for quenching experiments of Tutu et al. (1984) with initial temperatures of 775 K (a) and 594 K (b) and different superficial water injection velocities at the bottom.

establishment of nearly constant steam flow rates, respectively, heat fluxes at top of the bed. In the simulation, the injection into the debris starts instantaneously, with the full value of the experimentally given injection rate. For the lower injection rates this yielded in the calculations according to Fig. 13 oscillations around the steady state. This can be understood by some initial over-“shooting” of water penetration, subsequently corrected by evaporation and back-pushing by pressure buildup. Due to the peaking behavior of quenching, which involves a larger region in the debris, this does not occur with the higher injection rates, at least not with the highest. Double peaks partly occurring in the model results, in contrast to the experimental results, may be explained by a too rapid quenching of an extended region, then yielding a new push with a newly involved region. Further analyses are required for clarification. But, due to the experimental uncertainties (also missing information), it may also not be that necessary to go further into details. Rather, the whole pattern of available conditions should be included in future analyses. Comparisons with the approaches and results of Fichot et al. (this issue) are considered most important. Quenching of hot beds of 6 mm diameter spheres in a temperature range of 500–700 K by water injection from bottom (as well as from top) has also been investigated in the DEBRIS experiments. The results and first comparison calculations with WABE are discussed in Sch¨afer et al. (this issue). In these experiments, the water was not injected in a fixed rate, but via a lateral

Two axis-symmetric in-vessel configurations (particle beds in the lower head of the RPV) are considered here, one with a flat top (Case 1), the other with a mound shape (Case 2), as sketched in Fig. 14. In the first case, the upper bed surface is assumed at about 1.6 m height. Further, a uniform particle diameter of dp = 3 mm, a system pressure of p = 0.5 MPa and a porosity of ε = 0.4 in the bed are assumed in both cases, with a total corium mass of 80 t in Case 1 and 86 t in Case 2. The calculations with WABE-2D are performed in cylindrical geometry, approximating the shape of the lower head by adopting a very low porosity (ε = 10−10 ) in the outer region. The calculation domain is continued into the surrounding free water range approximating it as unheated bed with a high porosity (ε = 0.8). Variations of this value between 0.6 and 0.8 showed only negligible influences, thus supporting the assumption that water penetration into the bed is not sensitive to details of outer water flow. Essentially, the outside vertical pressure distribution remains determined by the static water column and the inflow into the bed is determined by the pressure difference between this and the inner pressure build-up as well as the friction inside the bed. Since the main aim here is to get some impression on the strength of effects, the heat release in the bed has been varied in order to determine the onset of dryout. Realistic values of decay heat depending on the material composition and time yield a specific power between 200 and 300 W/kg. The variations have been performed with transient calculations until getting first dryout at any location. Below the related heat release, cooled steady states establish. The Reed friction law, without explicit interfacial friction, as well as the Tung/Dhir model, modified with a factor 0.4 on interfacial friction, have been applied. This corresponds to an earlier status of evaluations on the basic laws. According to the above analyses, rather a model modified only

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Fig. 14. Configurations considered for the analysis of the coolability of particulate debris beds in the lower head of a RPV: flat debris bed (Case 1, left) and mound-shaped debris bed (Case 2, right).

with respect to the annular flow pattern (high void) appears to be appropriate. Extended analyses will be done in future, based on firmer conclusions from the investigations on basic laws. The present calculations may give a perspective on the effects. Although the use of dryout heat fluxes to analyze coolability in a complex multidimensional case has been questioned (Section 1), determination of specifically defined values may still be useful for specific comparisons. Thus, dryout heat fluxes have been determined here from the axial integration of the volumetric heat release rates in the center where the first dryout appears. As reference values, the pure 1D top flooding dryout heat fluxes have also been calculated with WABE. Results are given in Table 2. As compared to the 1D top flooding values, the WABE-2D calculations with the Reed friction model (without interfacial drag) already yield significant increases of the dryout heat flux. Thus, the usual application of 1D DHF correlations related to top flooding is much too conservative. The coolability is significantly higher under realistic multidimensional conditions. A further increase of DHF is obtained with the modified Tung/Dhir model. This is higher in Case 2. It is to be remarked here that the DHF from the modified Tung/Dhir model is under pure top flooding smaller than from the Reed model. This result was already obtained for the experiment of Hofmann (Section 3, Table 1) and indicates that variants of the Tung/Dhir model should be better adapted to the basic results, probably with emphasis on the annular flow regime. Then, limitations to the inflow of water from top, perhaps relevant in upper regions of a deep bed, may Table 2 Comparison of calculated dryout heat fluxes and corresponding removable power with Reed (R) and modified Tung/Dhir (T/D) friction laws Case 1

DHF (MW/m2 ) Spec. power (W/kg) Total power (MW)

1D WABE-2D 1D WABE-2D 1D WABE-2D

Case 2

R

T/D

R

T/D

1.87 2.64 245 345 18.5 26.1

1.66 2.85 217 372 16.4 28.1

1.87 2.34 141 175 11.1 13.7

1.66 3.01 124 225 9.7 17.7

be less strong, while the supporting effect of interfacial friction in lower bed regions with smaller void should be kept. Figs. 15 and 16 show for the Cases 1 and 2, with applications of the Reed and modified Tung/Dhir friction models, the spatial distributions of the liquid volume fraction in the pore volume (saturation), the pressure difference to the local hydrostatic water head and vapor or liquid velocity fields (superficial velocities) in steady states, just below the onset of dryout. While the saturation distributions demonstrate the cooled states (although an almost dry, but stable spot occurs at the top), the water flow fields indicate the reason for the increased coolability as compared to the top-fed 1D conditions. Water flows from the side can be seen penetrating down to the deeper central regions of the bed, then flowing upwards in this range, which is most sensitive to dryout occurrence since the bed is highest there. The water inflow to the bottom regions and the up-flow in the center is significantly stronger with the Tung/Dhir friction, for both cases. This results in hindering water inflow from top (Case 1) or from the cone sides (Case 2), while this still occurs with the Reed model. Correspondingly, the lowest relative pressures are at the bottom and the pressure differences are generally stronger in the Tung/Dhir calculations. Thus, under multidimensional conditions there may be counter-effects with respect to coolability. A strong water inflow to bottom and subsequent upflow may be favored by interfacial friction, but inflow from top in regions which are hardly reached by the flow from bottom may be hindered likewise. This may especially be indicated by the results on water flow and saturation in Case 2 with the high pyramidal configuration. This configuration should, on the one hand, favor the water inflow due to the height of water versus water/steam mixture columns. On the other hand, the large height makes water access to all regions of the bed more difficult. The final result of such counter-plays may depend on the modeling variants of friction, especially interfacial friction, as well as the cases considered. This is indicated by the results of Table 2 and the different phenomena in Figs. 15 and 16, especially the different water flow fields. As an important additional effect of the inflow of water via bottom regions, it is to be remarked that even dry regions in the bed could be cooled by steam flow supplied from evaporation in bottom regions. This is not further

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Fig. 15. Steady state results of the WABE-2D calculations on Case 1 with Reed (left) and modified Tung/Dhir (right) friction model. Top row: distribution of saturation and vapor velocities; bottom row: pressure field (reduced by the hydrostatic pressure of pure water) and liquid velocities.

investigated here, but in the context of quenching of hot debris below. 7.2. Decay heat removal for an ex-vessel debris configuration (BWR) A further reactor-related case under boil-off conditions is considered here with respect to an ex-vessel situation. A scenario for a large boiling water reactor is assumed, where the whole core and major parts of the structures have been destroyed and collected as particulate debris in the reactor pit. The chosen corium consists of about 150 t UO2 , 80 t Zircaloy and 210 t structure material yielding a total corium mass of 440 t. These values are typical for reactors of about 4000 MW thermal power. As the decay heat after some hours is about 1% of this value, about 40 MW have to be discharged from the particles in the reactor pit. This corresponds to a specific power of Q ≈ 90 W/kg. The geometry of the assumed configuration is shown in Fig. 17 (oriented at realistic configurations, the particle bed is assumed to be in mound shape). A porosity of ε = 0.4, a particle diameter of dp = 3 mm and a system pressure of about 0.3 MPa are chosen as parameters in the calculations. Here, only the influence of multidimensional effects will be demonstrated using the Reed friction model. With a one dimensional debris configuration of 2.8 m height, the Reed model

yields steady states for specific bed powers below 112 W/kg, corresponding to a DHF of 1.5 MW/m2 . Applying the mound configuration from Fig. 17, steady states up to a specific power of 146 W/kg are possible. The reason for this increased coolability can again be understood from the water flow (Fig. 18). Lateral water flows to the bottom of the debris driven by hydrostatic head differences support again the coolability. Along this flow path, the friction of the water flow at the particles is also smaller than in regions with high void at top. In general, with lateral coolant flow paths, only some part of the water inflow is via the top, and thus the limitation is reached for higher steam fluxes. But this influence strongly depends on the geometric configuration. Hence, the overall coolability has to be investigated for different configurations by calculations based on verified models instead of using DHF results. A further enhancement in coolabilitiy can be expected, if there is a direct flow path from the water pool surrounding the debris to lower bed regions. This may be via downcomer pipes, or, as assumed here, via the reactor sump. The sump is connected to the cavity and covered by a supporting grid. In the present calculation, such a flow path is applied by assuming a hydrostatic pressure of a water column of the bed height as boundary condition at the bottom over a radius of 0.6 m. The calculation results, again with the Reed model, are shown in Fig. 19. Now, steady states can be reached up to specific powers of 152 W/kg, thus the

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Fig. 16. Steady state results of the WABE-2D reactor related calculations on Case 2 with Reed (left) and modified Tung/Dhir (right) friction model. Top row: distribution of saturation and vapor velocities; bottom row: pressure field (reduced by the hydrostatic pressure of pure water) and liquid velocities.

coolability is further increased. As can be seen in Fig. 19, strong water inflow from below results. Integrating the water flow over the boundaries shows that about 20% of the water inflow is via the bottom. Again, more effective water distribution in the bed, thus further increased coolability, may be obtained by including interfacial friction. Comparing the calculated power limits with the expected decay heat of about 90 W/kg indicates the high margins and

chances for overall coolability. But, in the calculations presented here, only a homogeneous configuration with a large amount of structure material was assumed. Hindering effects, e.g. multigrain configurations or top layers of fine particles, have not been analyzed. On the other hand, also the additional cooling potential of steam flow in already formed dry zones (e.g. in higher locations or in regions with lower porosities) has not been included. This will be done now in the context of quenching analyses. 7.3. Quenching of hot debris in the RPV

Fig. 17. Configuration of the particulate debris in the reactor pit (BWR type).

Finally, in-vessel scenarios with hot debris will be considered to get a perspective on the quenching phenomena. In this context, also steady states with dry zones cooled by steam flow are analyzed. Cases with hot debris of initially 1273 K at system pressures of 6 and 0.3 MPa are chosen, the first similar to a case studied by Fichot et al. (this issue). The particle diameter is uniformly 2 mm, the porosity 0.4 and the height in the center of the axis-symmetric bed in the lower head is 1.3 m. Ceramic particles of 80 wt.% UO2 and 20 wt.% ZrO2 have been chosen and a decay heat of 160 W/kg in UO2 . It is assumed that water with saturation temperature is introduced via the downcomer and thus the particle bed is flooded from above. Figs. 20 and 21 show the time development in both cases, the development of saturation (water volume part in the

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Fig. 18. Results of a WABE calculation for a debris bed in the reactor pit according to Fig. 17 (no inflow via sump) at a power of Qmax = 146 W/kg still yielding a coolable steady state: distributions of liquid saturation and vapor velocity (top) as well as pressure field (reduced by the hydrostatic pressure of pure water) and water velocity (bottom).

Fig. 19. Results of a WABE calculation for a debris bed in the reactor pit according to Fig. 17 with open flow path via the sump at a power of Qmax = 152 W/kg: steady state distributions of liquid saturation and vapor velocity (top) as well as pressure field (reduced by the hydrostatic pressure of pure water) and water velocity (bottom).

pores), of the temperature and the water and steam velocities. The calculation has again been performed in cylindrical geometry. Multidimensional effects are also decisive in the transient quenching process. Due to the shape of the lower head, water can flow in predominantly along the wall, while the steam escapes upwards through the particle bed. This kind of water inflow is supported by the lower height of the bed at the sides (thus the smaller steam production), by the inclination of the wall of the reactor pressure vessel allowing water to flow into the bed along the wall without essential counter-flow of steam and by lower temperatures at the wall allowing more rapid quenching. In contrast, inflow directly from the upper surface of the bed is hindered by the steam flow resulting from the evaporation of water penetrating at bottom. The result is a dry zone in a central upper region of the bed. There, the temperature even increases due to decay heat. This zone is quenched successively by the surrounding water, flowing in the bed from the sides, partly also from above. About 900 s are required, until complete quenching to saturation temperature is reached in the case with 6 MPa system pressure (Fig. 20). In principle, also a non-coolable situation could establish if the temperature in the dry zone would increase until melting and relocation occurs. Since the assumed high system pressure of 6 MPa strongly favors quenching, also a case

with 0.3 MPa has been considered, in order to investigate a scenario with depressurization and low pressure injection. The results in Fig. 21 show a similar behavior as in the high pressure case, but a slower development. The produced steam can only escape more slowly due to its higher specific volume. Thus, the penetration of water and quenching occurs more slowly. As can be seen in Fig. 21, most of the bed is quenched after about 2000 s, but the complete cooling requires about 1.5 h. The continued heatup in the dry zone reaches in this case temperatures of up to 2000 K. 7.4. Cooling of dry zones in steam flow Quenching of dry zones occurred more rapidly than heatup due to decay heating in the above cases, thus finally leading to a completely quenched state at practically saturation temperature. Melting temperatures were not reached in the dry zone, although heat up occurred in parallel to progress of quenching. A stable situation can also be established if cooling by a steam flux through the dry zone is just sufficient to remove the decay heat at a certain temperature level below melting temperatures. This is finally explored here with the same configuration as above used for the quenching scenarios. Boil-off calculations with WABE have been performed with various specific powers at 0.3 MPa system pressure. The results are given in Fig. 22.

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Fig. 20. WABE-2D results at different times for quenching of hot debris (80 wt.% UO2 , 20 wt.% ZrO2 , initial temperature 1000 ◦ C, particle size 2 mm, porosity 0.4, specific power 160 W/kgUO2 ) in the lower head of an RPV at 6 MPa system pressure.

Again, only the Reed model without explicit interfacial friction was used. The left column of Fig. 22 shows the saturation profiles in the bed. The power of 200 W/kg is the limit for which the decay heat can just be removed without formation of a dry zone. For comparison, it is to be remarked that the removable power according to the 1D model only is 141 W/kg. Thus, the improvement of coolability by multidimensional effects can again be seen. With

further increased power, extended dry zones develop, as can be seen in Fig. 22. However, these zones remain still stable and coolable up to a power of 300 W/kg, by cooling in the steam flowing through the dry zone, although with significant superheats of the particles. This cooling mode is only possible due to the inflow of water from the sides into regions below the dry zone. Expansion of the dry zone is thus stopped at bottom, limitation of superheats of the particles is reached by the resulting

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Fig. 21. WABE-2D results at different times for quenching of a debris bed (same configuration as in Fig. 20) at 0.3 MPa system pressure.

steam flow and additional evaporation at top of the dry zone can be balanced by water inflow from top. No steady coolable state is any more reached with the power of 350 W/kg, for which the situation reached 5000 s after starting of heating in the assumed cold, water-filled bed is shown in Fig. 22. With this power, the heatup and the extension of the dry zone continues. The right column of Fig. 22 gives the development of particle temperatures in the center (radius r = 0) at several heights z above the bottom,

from which the establishment of stable temperature levels in the bed, especially in the dry zone, or the continued heatup in the case of 350 W/kg, can be seen. It is finally to be remarked that, according to these investigations, the analyzed cooling mechanism provides coolability for more than twice the specific power than expected from the classical 1D analysis. Finally, it remains to indicate that cooling can even be reached with bed configurations which appear not to be coolable due to

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Fig. 22. Development of dry zones in a particulate debris bed on the lower head of the RPV (80 wt.% UO2 , 20 wt.% ZrO2 , particle size 2 mm, porosity 0.4, system pressure 0.3 MPa) at different specific powers; distribution of liquid saturation and water velocities at 5000 s (left column) and particle temperatures vs. time at radius r = 0 and different elevations (right column).

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reached. This is expressed by the fact that available modeling approaches were not able to yield adequate results for the top-fed as well as the bottom-fed cases, likewise. Secondly, the results have not been used to sufficiently investigate coolability options under realistic conditions related to reactor safety. Such conditions cannot be described by reduction to the idealized top and bottom flooding cases. They are rather characterized by a multidimensional situation with geometrical configurations providing lateral influences, especially inflow of water, e.g. by lateral variations of height of bed, by non-homogeneities with ranges of higher and lower porosity, larger particles and variations of volumetric heat release. Under such conditions, partly the bottom flooding case is approached due to lateral water inflow towards bottom regions of the bed. In addition, the inflow from the sides itself contributes to the coolability. In order to investigate the potential of coolability under such realistic conditions, multidimensional codes are required. WABE-2D is an approach in this direction. Such codes must be validated in two aspects, firstly concerning the constitutive laws, secondly with respect to the integral behavior which relates to the overall modeling approach. It is especially to be checked whether the most important features for the final aim, i.e. the understanding of coolability options, are captured sufficiently to allow conclusions. With this respect, three major tasks have been tackled in the present contribution: • Necessary revision and validation of constitutive laws, with emphasis on the bottom versus top flooding situations. • Examination of the calculated multidimensional behavior, for which support has been taken from the SILFIDE experiments. • Analysis of the possible improvement of coolability under realistic conditions, due to the multidimensional features as well as steam cooling as still relevant cooling mode beyond formation of dry zones. Fig. 23. Stabilization and cooling of a dense region (porosity 24%) inside a debris bed in the lower head of the RPV (configuration as in Fig. 22, specific power 200 W/kg): meshing and distribution of porosity (top), steady state distribution of liquid saturation and water velocities (middle) and particle temperatures versus time at radius r = 0 and different elevations (bottom).

non-homogeneities as dense regions with low porosity or superposed layers of very small particles. An example with a dense region (porosity 24%) inside the bed is given in Fig. 23. Although dryout develops rapidly in this zone, the presented steady state is reached for a specific power of 200 W/kg. Again, water flow from the sides to a region below this zone is essential, combined with cooling in the steam flow. 8. Conclusions The present contribution picks up earlier observations on significantly increased dryout heat fluxes, i.e. improved coolability, in the case of particulate debris beds provided with a water inflow from the bottom, as compared to the case of top-fed beds. It appears that these observations have not been sufficiently considered further, mainly in two respects. Firstly, sufficient quantitative as well as qualitative understanding has not been

The main present conclusions of these examinations are: • Earlier experiments of Hofmann at Forschungszentrum Karlsruhe, showing a strong increase of dryout heat flux with bottom versus top flooding, cannot be explained by the usually applied friction laws without explicit interfacial friction. A rather good agreement results by taking the more detailed, flow pattern dependent laws provided by Tung and Dhir based on gas/water experiments, but only after introducing a reduction factor on the interfacial drag. Interfacial drag appears to be the main physical feature, which is lacking in the usual friction laws and which can explain the results for top-fed as well as bottom-fed experiments. • No clear decisions on the different approaches of friction modeling can presently be made, based on the available data. However, also the available fundamental experiments with gas/water flows in co- and counter-current mode show that interfacial friction must be included as explicit term. From the comparisons shown in this paper, it is concluded that the Tung/Dhir friction model gives a reasonable basis, but must be modified with respect to interfacial friction. It appears to be most promising to introduce a reduced interfacial friction

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in the annular flow regime (high void), leaving the modeling for other flow regimes unchanged. Further uncertainties exist concerning the applicability to steam/water flow patterns under boiling conditions. Then, inverted annular flow may occur rather than annular flow patterns. There exists a lack of data for finally deciding about the models, especially for boiling conditions. The DEBRIS experiment at IKE, University of Stuttgart, aims to yield such data. • The SILFIDE experiments yield a significant increase of local DHF as compared to classical 1D top flooding models. Furthermore, they yield still relatively stable dry zones in upper regions after onset of dryout, due to cooling in the steam flow. From the calculations with WABE, this can in principle be explained by lateral water flows due to the non-homogeneous power distribution. Since water supply occurs from top via regions with lower, but still high power, the upwards steam flow hinders penetration. This may be the reason why the original Tung/Dhir model yields smaller DHF than the Reed model and the experiment. Final conclusions about the adequate modeling would be facilitated by experimental cases with more pronounced multidimensional effects, especially lateral water flows due to a variation of bed heights, not only heating power. • Comparison calculations with WABE have also been performed for experiments on quenching of hot debris by injection of water from bottom. The comparisons concern validation especially with respect to the boiling curve and friction models under these conditions. In view of the lack of knowledge, modifications of basic approaches by parametric choices were necessary. However, it was possible to get a rather good agreement with the experiments using a unique approach, even for the cases with higher temperatures and water inflow rates, for which the quenching process does not occur in a frontal type mode but in an extended quenching zone. • From the boil-off calculations on the reactor-related cases, it is concluded that indeed a strongly improved coolability of particle beds results under realistically assumed multidimensional configurations, as compared to the 1D situation usually taken as basis. In cases with a flat upper surface of a bed in the lower head of the reactor pressure vessel (RPV), the decisive lateral effects are already introduced by the geometry of the lower head. Here, already the Reed model yields a strong effect, which is somewhat surpassed by the Tung/Dhir model, in a first approach only modified by a general reduction factor on interfacial friction (adapted to the Hofmann experiment). A stronger effect from this modified Tung/Dhir model results in a second case for which – more realistically – a mound configuration of the bed in the lower head is assumed. This is considered to be caused by the stronger lateral head effects and the longer steam path in the bed emphasizing supporting interfacial drag effects in contrast to opposing effects against water inflow from top. Stronger effects supporting coolability may in general be expected by the envisaged improved friction description emphasizing modifications only in the annular flow regime. While reduced friction there may similarly act against top flooding, the favorable trends

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to support bottom flooding in the other flow regimes will then be kept. This approach appears to be most promising from the basic analyses but needs further confirmation (see above). • Quenching of hot particulate debris in the lower head of the RPV has also been investigated. Again, the importance of the multidimensional effects has been demonstrated with water penetration along the wall to the bottom and from there successive upwards quenching, including the cooling effects of steam flows through the hot dry zone. The competition of heatup by decay heat in the dry zone and quenching decides on the final success of quenching. • The importance of cooling steam flows through dry zones in improving coolability has also been shown by boil-off calculations for a lower head filled with debris (2 mm diameter, 0.3 MPa system pressure). As compared to classical 1D analyses with a resulting limitation of dry zone formation for a power of 141 W/kg, the 2D situation yields an increase for this to 200 W/kg and even an increase to 300 W/kg with steam cooling of dry zones enabled by the 2D pattern. In these calculations the model with interfacial friction has not yet been used which should yield further improvements. As a final major conclusion, the general importance of the multidimensional features for coolability must thus be underlined. This requires the need of multidimensional codes with validated constitutive laws, as outlined. Interfacial friction appears to be a necessary ingredient in the friction laws for adequate description. Overall, a strongly better coolability than assumed based on previous analyses can be concluded from these results. However, restrictions to coolability are also to be expected from particle mixtures with different particle sizes. Respective constitutive laws are still being investigated, see also the discussion by B¨urger and Berthoud (this issue). Thus, the present results can only be taken as first steps in the direction indicated. Further examination and confirmation is required along the lines described. Acknowledgements The work presented in this article was sponsored by the German Federal Ministry of Economics and Technology (BMWi). The authors, however, are responsible for the scientific content. References Alsmeyer, H., Albrecht, G., Fieg, G., Stegmaier, U., Tromm, W., Werle, H., 2000. Controlling and cooling core melts outside the pressure vessel. Nucl. Eng. Des. 202, 269–278. Athken, K., Berthoud, G., 2006. SILFIDE experiment: coolability in a volumetrically heated debris bed. Nucl. Eng. Des. 236, 2126–2134. Barleon, L., Werle, H., 1981. Dependence of dryout heat flux on particle diameter for volume- and bottom-heated debris beds. Technical report KfK 3138, Kernforschungszentrum Karlsruhe. Berthoud, G., 2006. Models and validation of particulate debris coolability with the code MC3D REPO. Nucl. Eng. Des. 236, 2135–2143. Broughton, J.M., Kuan, P., Petti, D.A., Tolman, E.L., 1989. A scenario of the TMI-2 accident. Nucl. Technol. 87, 34–53.

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