Meguro-ku, Tokyo, Published online: 07 Feb 2012.

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1 This article was downloaded by: [ ] On: 24 March 2014, At: 15:32 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Journal of Nuclear Science and Technology Publication details, including instructions for authors and subscription information: Modeling for Evaluation of Debris Coolability in Lower Plenum of Reactor Pressure Vessel Yu MARUYAMA a, Kiyofumi MORIYAMA a, Hideo NAKAMURA a, Masashi HIRANO a & Kengo NAKAJIMA b a Japan Atomic Energy Research Institute, 2-4 Shirakata-shirane, Tokai-mura, Naka-gun, Ibaraki, b Research Organization for Information Science and Technology, Naka-Meguro, Meguro-ku, Tokyo, Published online: 07 Feb To cite this article: Yu MARUYAMA, Kiyofumi MORIYAMA, Hideo NAKAMURA, Masashi HIRANO & Kengo NAKAJIMA (2003) Modeling for Evaluation of Debris Coolability in Lower Plenum of Reactor Pressure Vessel, Journal of Nuclear Science and Technology, 40:1, 12-21, DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 40, No. 1, p (January 2003) Modeling for Evaluation of Debris Coolability in Lower Plenum of Reactor Pressure Vessel Yu MARUYAMA 1,,, Kiyofumi MORIYAMA 1, Hideo NAKAMURA 1, Masashi HIRANO 1 and Kengo NAKAJIMA 2 1 Japan Atomic Energy Research Institute, 2-4 Shirakata-shirane, Tokai-mura, Naka-gun, Ibaraki Research Organization for Information Science and Technology, Naka-Meguro, Meguro-ku, Tokyo (Received September 19, 2002 and accepted in revised form November 18, 2002) Effectiveness of debris cooling by water that fills a gap between the debris and the lower head wall was estimated through steady calculations in reactor scale. In those calculations, the maximum coolable debris depth was assessed as a function of gap width with combination of correlations for critical heat flux and turbulent natural convection of a volumetrically heated pool. The results indicated that the gap with a width of 1 to 2 mm was capable of cooling the debris under the conditions of the TMI-2 accident, and that a significantly larger gap width was needed to retain a larger amount of debris within the lower plenum. Transient models on gap growth and water penetration into the gap were developed and incorporated into CAMP code along with turbulent natural convection model developed by Yin, Nagano and Tsuji, categorized in low Reynolds number type two-equation model. The validation of the turbulent model was made with the UCLA experiment on natural convection of a volumetrically heated pool. It was confirmed that CAMP code predicted well the distribution of local heat transfer coefficients along the vessel inner surface. The gap cooling model was validated by analyzing the in-vessel debris coolability experiments at JAERI, where molten Al 2 O 3 was poured into a water-filled hemispherical vessel. The temperature history measured on the vessel outer surface was satisfactorily reproduced by CAMP code. KEYWORDS: severe accident, in-vessel debris coolability, lower head, volumetrically heated pool, turbulent natural convection, CAMP code, gap cooling I. Introduction The molten debris composed of core component materials may relocate into the lower plenum of a reactor pressure vessel (RPV) during a severe accident of a light water reactor (LWR) as occurred in the accident of Three Mile Island Unit 2 (TMI-2). 1, 2) The molten debris imposes a significant thermal load onto the lower head of the RPV due to the volumetric decay heat generation if cooling is insufficient. The thermal load could cause the failure of the RPV lower head, resulting in the release of the molten debris into a reactor containment vessel (RCV). A threat to the RCV integrity by phenomena that occur outside the RPV (ex-vessel phenomena), including interactions of the molten debris with the concrete structure and water, is one of safety concerns for commercial LWRs. In order to exclude the threats of the ex-vessel phenomena onto the RCV, mitigative accident management measures have been proposed for in-vessel retention of the molten debris. A typical measure of the in-vessel retention is to externally cool the RPV lower head by flooding the RCV volume below the RPV. 3, 4) With an assumption that the RPV lower head is flooded prior to debris relocation from the core region to the lower plenum, the effectiveness of the external cooling is evaluated by the balance between the thermal load onto the lower head wall and the cooling capability of the external Corresponding auther, Tel , Fax , maruyama@nupec.or.jp Present address: Nuclear Power Engineering Corporation, Fujita-kanko Toranomon Bldg., Toranomon, Minato-ku, Tokyo water. Therefore, many experimental studies have been performed for natural convective heat transfer of volumetrically heated pools, 5 9) and also for critical heat flux on downwardfacing hemispherical surfaces ) Those studies on natural convection were performed at internal Rayleigh numbers up to approximately expected during the LWR severe accident, and furnished valuable outcome to evaluate the feasibility of the external cooling. It is supposed that, however, material properties of the molten debris vary widely, depending on LWR types and sequences of accident progression. Additionally, immiscible two liquid layers may appear, causing the density stratification where lighter metallic layer is placed above heavier oxidic one. 3) Considering limitations in the experimental approach, the application of analytical codes well validated with appropriate experiments is suitable to deal with the diversity and complexity of the phenomena during severe accidents. One of the findings from the TMI-2 accident was that the water addition into the RPV during an early stage of core degradation could reduce the amount of debris relocated to the lower plenum, resulting in the increase in the possibility for the in-vessel debris cooling if the RPV internal water acts as a sufficient heat sink. The OECD (Organization for Economic Cooperation and Development) TMI-VIP (Vessel Investigation Project) identified that approximately 19 t of debris was accumulated on the lower head during the accident. 1, 2) However, the lower head was maintained intact, which could be due to the existence of inherent cooling mechanisms. The metallurgical examinations in the TMI-VIP showed that the temperature of the lower head wall was locally elevated up to 12

3 Modeling for Evaluation of Debris Coolability in Lower Plenum 13 approximately 1, K and cooled down with a temperature decrease rate of 10 to 100 K/s after the highest temperature was sustained for approximately 30 min. 13) A hypothesis was proposed by Henry and Dube, 14) in which a gap as a path for the water penetration was formed between the debris and the lower head wall. The hypothesis was qualitatively confirmed by several experiments, in which high temperature melts were slumped into water-filled hemispherical or cylindrical vessels ) As regards the experiments on the gap cooling, however, there were shortcomings that the experimental scale was rather small and the decay heat was not simulated. Phenomenological modeling on the gap cooling is necessary in order to evaluate its effectiveness of the gap cooling in reactor scale and to assess the in-vessel debris coolability by the RPV internal water. With the background mentioned above, an analytical code for thermo-fluiddynamics of debris in the lower plenum, 19, 20) CAMP (Coolability Assessment for Melt Pool), has been developed at Japan Atomic Energy Research Institute (JAERI). Models for the gap cooling, including gap growth and water penetration into the gap, were developed and incorporated into CAMP code for transient thermo-fluiddynamics together with one for turbulent natural convection. The objective of the present study was to assess predictive capability of CAMP code for important phenomena related to the in-vessel debris cooling by analyzing the experiments on natural convection of volumetrically heated pool and gap cooling. Simplified steady-state calculations were also performed prior to transient analysis with CAMP code to estimate the effectiveness of the gap cooling in reactor scale. II. Estimation of Effectiveness of RPV Internal Water on Steady Debris Cooling In order to assess the potential cooling capability of the RPV internal water, simplified steady-state calculations in reactor scale were performed. In the present calculations, the maximum coolable debris mass was examined by comparing critical heat flux in narrow gaps with natural convective heat flux at the surface of a volumetrically heated pool. 1. Critical Heat Flux in Narrow Gap A correlation for critical heat flux was derived taking into account the counter-current flow limitation (CCFL) of a gasliquid two-phase flow. 21) The general form of CCFL correlation is expressed as, jg 1/2 + mj 1/2 l = C, (1) where jg and j are defined as follows, jg = v g l ρ g gd e (ρ l ρ g ), (2) jl ρ l = v l gd e (ρ l ρ g ). (3) The CCFL correlation below was formulated from the experiments by Park et al. for a vertical annulus with an outer diameter of 0.5 m, 22) which were large scale experiments in terms of a peripheral length of narrow gap, jg 1/ j 1/2 l = (4) Considering the flow inclination at the gap entrance in a hemispherical geometry, Eq. (4) is transformed to the following equation with constant C, jg 1/ j 1/2 l = C(cos φ) 1/4. (5) Mass and energy conservations at the gap entrance are expressed as, ρ g v g = ρ l v l, (6) q b A dos = A gap ρ g v g h fg. (7) With Eqs. (2), (3) and (5) through (7), the following correlation for critical heat flux in narrow gaps is obtained, q chf = C 2 (cos φ) 1/2 h fg A gap A dos gde (ρ l ρ g ) (ρg 1/ ρ 1/4 l ). (8) 2 The constant C was evaluated through the comparison of Eq. (8) with the experimental results on critical heat flux in narrow gaps. The experiments had geometries of vertical annuli (Koizumi et al.), 23) vertical rectangular plates (CTF experiments) 24) and hemispherical gap (CHF experiments). 22) These experiments covered an ambient pressure from 0.1 to 8.0 MPa, a gap width from 0.5 to 5.0 mm and Bond number (Bo) from 0.16 to 98.0 as shown in Table 1. Since surface tension was expected to strongly influence critical heat flux in narrow gaps, Bo was chosen as a key parameter for a variation of the constant C. Influence of Bo on the constant m pointed out by Sudo and Kaminaga 25) was neglected in the present approach. The relationship between the evaluated constant C and Bo is plotted in Fig. 1. The following regression forms were derived from the plot, C = 1.21Bo (Bo < 2.5), (9) C = 1.05Bo (Bo > 2.5), (10) where Bo is defined as, Bo = gd2 e (ρ l ρ g ). σ (11) For Bo larger than 2.5, the constant C with Eq. (10) is close to values for rectangular gaps and annuli proposed by Mishima and Nishihara. 26) Table 1 Major conditions of experiments on critical heat flux in narrow gaps Pressure (MPa) Gap width (mm) Koizumi et al CTF CHF Bo VOL. 40, NO. 1, JANUARY 2003

4 14 Y. MARUYAMA et al. Constant C (-) C =1.21Bo ( Bo< 2.5) Koizumi, et al. CTF (one side heating) CTF (both sides heating) CHF C =1.05 Bo ( Bo> 2.5) Bond Number (-) Fig. 1 Dependence of constant C in CCFL correlation on Bond number 2. Natural Convective Heat Flux Based on experiments on natural convection of volumetrically heated pools, 5 9, 27 29) the following correlations for upward and downward heat fluxes were applied in the present calculations, Nu up = 0.345Rai (10 8 <Ra i <10 14 ), (12) Nu up = 0.383Rai (10 14 <Ra i <10 17 ), (13) Nu dn = 0.54Rai 0.18 (l/r) 0.26 (10 8 <Ra i <10 14 ), (14) Nu dn = 0.131Rai 0.25 (l/r) 0.19 (10 14 <Ra i <10 17 ), (15) where Nu and Ra i are defined as, Nu = ql λ T, (16) gβ Ql5 Ra i = ανλ. (17) Discontinuity is found in Eqs. (12) through (15) at Ra i of due to the limitation in applicable range of each equation. Therefore, those equations were combined to derive the following expressions, taking the minimum and maximum applicable values of Ra i, log Nu up = log Nu dn = log Ra i,max log Ra i log Ra i,max log Ra i,min log Nu up,(12) + log Ra i log Ra i,min log Nu up,(13), log Ra i,max log Ra i,min (18) log Ra i,max log Ra i log Ra i,max log Ra i,min log Nu dn,(14) + log Ra i log Ra i,min log Nu dn,(15), log Ra i,max log Ra i,min (19) where subscripts (12), (13), (14) and (15) indicate values calculated by Eqs. (12), (13), (14) and (15), respectively. Using Eqs. (18) and (19) together with the following energy balance, q up, q dn and T are obtained, A dus q up + A dos q dn = QV. (20) 3. Results of Estimation The maximum coolable depth of debris in the lower plenum was estimated as a function of gap width by comparing q chf with q dn. The comparison is plotted in Fig. 2 for a lower head radius of 2.0 m and an ambient pressure of 10 MPa, which simulates the situation of the TMI-2 accident. The debris depth at the intersection between q chf and q dn gives the maximum coolable depth for a specific gap width. The plot indicated a strong influence of the gap width on the maximum coolable debris depth. Additionally, it was found that a gap width of 1 through 2 mm had a potential to remove the decay heat from the debris mass relocated to the TMI-2 lower plenum corresponding to a depth of approximately 0.4 m, but the significantly large gap width should be required in case of the relocation of a larger amount of debris. The dependence of q chf on the ambient pressure was examined and the results are shown in Fig. 3 for a gap width of 3 mm. As shown in the figure, a larger q chf was obtained for a higher ambient pressure. This tendency implies that the maximum coolable depth decreases in case that core degradation progresses at a low RPV pressure. Heat Flux (kw/m 2 ) q dn q chf (1mm) q chf (2mm) P amb : 10MPa q chf (3mm) q chf (5mm) Molten Core Depth (m) Fig. 2 Comparison of critical and natural convective heat fluxes in reactor scale Heat Flux (kw/m 2 ) Fig q dn q chf (0.1MPa) q chf (1.0MPa) q chf (10MPa) Gap width : 3mm Molten Core Depth (m) Influence of ambient pressure on critical heat flux in gap JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

5 Modeling for Evaluation of Debris Coolability in Lower Plenum 15 III. Overview of CAMP Code The simplified steady-state calculations described in the previous section provided findings on the maximum coolable debris depth, depending on the gap width and the ambient pressure. However, the gap width was assumed unchanged and water penetration into the gap was not considered in the calculations. The maximum coolable depth could be shallower than predicted if a long time is taken for the water penetration to the bottom of the lower head. On the other hand, the gap cooling becomes more effective when the gap width is enlarged as a consequence of thermal interactions between the debris and the lower head. In these respects, the gap growth and the water penetration transient were investigated by using CAMP code. 1. General Description Thermo-fluiddynamic behavior of debris pool accumulated in the lower plenum can be predicted by CAMP code in twodimensional axi-symmetric or three-dimensional geometry. It is capable of analyzing laminar and turbulent natural convection of single and stratified two-component fluids with the volumetric heat generation, solid-liquid phase change, heat conduction in the vessel wall, boiling heat transfer at the debris upper surface, the gap growth due to the thermal expansion and the elastic deformation of the vessel wall and the water penetration into the gap. Phenomena that are modeled in CAMP code are schematically illustrated in Fig. 4. The finite volume scheme and the simplified marker and cell (SMAC) method were employed for the spatial discretization and the time integration for the thermo-fluiddynamic part of CAMP code. The finite element method was used for the calculation of the vessel deformation, based on the temperature distribution of the vessel wall and a pressure load onto Fig. 4 Heat Transfer in Stratified Configuration Metallic Layer Oxidic Molten Debris Heat Conductionin Vessel Wall Gap Formation and Water Penetration Liquid-Solid Phase Change (Crust Formation) Turbulent Natural Convection of Volumetrically Heated Fluid Schematic diagram for phenomena modeled in CAMP code the vessel. It is noted that thermo-fluiddynamics were not coupled with the vessel deformetion. The gap growth was evaluated based on the predicted vessel deformation. That is, a profile of the gap width is obtained from the difference in the inner surface position between the initial and deformed lower head. It is assumed that contact of the debris with the lower head is kept at the bottom. 2. Turbulent Model One of crucial models for the in-vessel debris coolability is turbulent natural convection in a deep debris pool since the volumetric heat generation due to decay heat enhances the buoyancy driven convection. A simple way could be the combined use of low Reynolds number type k-ε twoequation model for flow and zero-equation model for heat transfer. Eddy viscosity and thermal eddy diffusivity are needed for the derivation of Reynolds stress and turbulent heat flux in Reynolds-averaged momentum and energy conservation equations, respectively. In k-ε two-equation model, the eddy viscosity is derived by solving transport equations for turbulent kinetic energy and its dissipation rate. The thermal eddy diffusivity is obtained in the zero-equation model by setting turbulent Prandtl number Pr t in advance, which is defined as, Pr t = ν t. (21) α t As pointed out by Dinh and Nourgaliev, 30) however, the combination of the above turbulent models showed the limited feasibility for evaluating heat transfer characteristics of natural convection of volumetrically heated pools. This implied that the spatial distribution of the thermal eddy diffusivity or Pr t should be properly estimated to predict heat flux from a volumetrically heated pool to boundaries under a variety of debris conditions. The two-equation turbulent model developed by Yin, Nagano and Tsuji 31) was incorporated into CAMP code. This model explicitly considers influences of the buoyancy force on the Reynolds stress and turbulent heat flux, being based on Nagano and Hishida model 32) and Nagano and Kim model 33) categorized in low Re k-ε two-equation model for flow and k θ -ε θ two-equation model for heat transfer, respectively. In k θ -ε θ two-equation model, thermal eddy diffusivity is derived by solving transport equations for temperature variance and its dissipation rate. The Yin-Nagano-Tsuji model assumes that velocity fluctuation is composed of two components being generated by shear stress and buoyancy force, u i = u i + u i, (22) u i = C b t m g i βθ. (23) The Reynolds stress and turbulent heat flux are expressed by the following equations, respectively, u i u j = u i u j + C b t m g i βu j θ, (24) u i θ = u i θ + C bt m g i βk θ, (25) where the first term of the right-hand side in both equations, corresponding to the Reynolds stress generated by shear VOL. 40, NO. 1, JANUARY 2003

6 16 Y. MARUYAMA et al. force, and t m are expressed as, ( u i u Ūi j = ν t + Ū ) j x j x i ( 2 3 δ ijk 1 + C bt m g i βu j θ 2k ), (26) u i θ = α T t, (27) x i k t m = ε k θ. (28) 2ε θ The spatial distribution of the eddy viscosity and the thermal eddy diffusivity are obtained as a function of fluid properties and turbulent flow characteristics. The validation of Yin-Nagano-Tsuji model was made with experiments on natural convection along a vertical flat surface. 34) In application to reactor scale, it is required to satisfactorily predict turbulence of the volumetrically heated debris in a hemispherical geometry. Specifically, capability of dealing with the debris cooled from the whole surfaces is necessary since crust (solidified debris layer) is formed at the top and bottom, resulting in density and temperature stratification in the debris. 3. Boiling Heat Transfer When water covers the debris upper surface in the lower plenum, Kutateladze correlation 35) and Berenson correlation 36) were employed to calculate nucleate boiling and film boiling, respectively. Thermal radiation from high temperature surfaces to the overlying water was taken into account in the film boiling. Critical heat flux was evaluated by Zuber correlation. 37) For the temperature at minimum heat flux, the smaller value between one from the Berenson correlation 36) and the thermodynamic upper limit temperature was used. Heat flux in transition boiling regime was derived by linearly interpolating the critical and minimum heat fluxes in a logarithmic plot. 4. Gap Cooling The model used to predict the water penetration into the gap was one-dimensional and based on CCFL phenomenon. The conceptual scheme for the gap cooling model is illustrated in Fig. 5. The following CCFL correlation was used to predict the amount of water penetrating into the gap, jg 1/ j 1/2 t = 1.226(cos φ) 1/4. (29) The above equation was obtained by modifying Eq. (4) to take into account expected flow characteristics in the gap and the gap inclination in a hemispherical geometry. It is noted that influences of Bo on the constant in the right-hand side of the CCFL correlation were ignored. The CCFL experiments performed by Park et al., 22) on which Eq. (4) was based, were under an isothermal air-water counter-current flow condition in a vertical annuli. In such a condition, water is considered to penetrate as a film flow along both surfaces of the gap, forming an annulus type separated flow. As illustrated in Fig. 6, however, a stratified flow would be developed in a hemispher- Crust Water Molten Debris Lower Head CCFL Nucleate Boiling (Kutateladze) Transition Boiling Film Boiling (Bromley and Radiation) Fig. 5 Conceptual scheme of analytical model for water penetrationintogap Water Air (a) Air-water CCFL experiments Crust Molten Debris Water Vapor (b) Expected situation in lower plenum Fig. 6 Difference in flow characteristics in narrow gap between vertical air-water CCFL experiments and debris cooling in hemispherical geometry ical geometry since the most of vapor is generated by boiling heat transfer to the penetrating water on the high temperature downward-facing debris surface. Assuming that the interfacial area for the momentum exchange in the stratified flow is a half of that in the annular type flow, the constant in the right-hand side of Eq. (4) is doubled. A depth of the water penetration into the gap is explicitly calculated in each time step so as to satisfy Eqs. (6), (29) and the following energy conservation equation at the gap entrance, q vw A vw + q dw A dw = A gap ρ g v g h fg. (30) As shown in Eq. (30), boiling heat flux to the penetrating water is necessary. A complete boiling curve for narrow gaps covering nucleate, transition and film boiling is currently unavailable. Therefore, the boiling curve the same as that for the debris upper surface was used except for film boiling regime where Bromley correlation for vertical surfaces 38) was applied. For an area deeper than the leading edge of the penetrating water, heat transfer from the debris to the vessel wall was calculated by heat conduction and thermal radiation JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

7 Modeling for Evaluation of Debris Coolability in Lower Plenum 17 through a superheated vapor layer. For simplification, it was assumed that the leading edge of the penetrating water moves only in the downward direction. That is, the drawback of the leading edge due mainly to the gap width reduction was not taken into account. Vessel E IV. Experiments for Validation and Analytical Models In order to validate predictive capability of CAMP code for natural convective heat transfer and the gap cooling in the lower plenum, a series of analysis was performed for one of experiments at University of California, Los Angeles (UCLA) 9) and in-vessel debris coolability experiments at JAERI. 15) The volumetric heat generation was simulated by microwave heating of Freon-113 filled in a hemispherical Pyrex glass vessel in the UCLA experiment. Inner diameter and wall thickness of the vessel were mm and 11 mm, respectively. A volumetric heat generation rate of 6.17 kw/m 3 was supplied to the mm deep fluid, which corresponded to Ra i of The vessel was put in a water pool at a constant temperature of K to establish an isothermal boundary. The fluid upper surface was cooled by cold air to keep almost constant. In the in-vessel debris coolability experiments at JAERI, 30 kg or 50 kg of molten Al 2 O 3 produced by a thermite reaction was gravitationally poured into a water-filled hemispherical steel vessel (designated as IDC001 and, respectively). The vessel had an inner diameter of 0.5 m and a wall thickness of 21 mm. A depth of the molten Al 2 O 3 was 114 mm or 160 mm, corresponding to external Rayleigh number, Ra e,of and , respectively. The definition of Ra e is expressed as, Ra e = gβ Tl3. (31) αν The vessel was covered with a layer of thermal insulator to develop a nearly adiabatic boundary. Initial water depth was 186 mm and 140 mm for IDC001 and, respectively. The temperature of the vessel wall immediately before the melt pouring was approximately 440 K, which was closed to the water saturation temperature at the ambient pressure (1.3 MPa). A typical spatial discretization in the CAMP analysis is schematically shown in Fig. 7. Fluid and vessel wall are divided into three and two regions, respectively. For the UCLA experiment, the fluid was discretized with 7,500 ( ) cells. The hemispherical part of the Pyrex glass vessel was constructed with 1,000 (10 100) cells. The cylindrical part of the vessel was not modeled and the upper boundary of the hemispherical part was assumed to be thermally insulated. The vessel outer surface was treated as a constant temperature boundary at the water pool temperature. Due to no description in Ref. 9), the fluid upper surface temperature was assumed to be K as the boundary condition, which was measured at the vicinity of the upper surface. Material properties of the fluid and the vessel wall were taken from Ref. 39). For the in-vessel debris coolability experiments, the total A B Fluid Fig. 7 Schematic illustration for spatial discretization of CAMP code cells of the molten Al 2 O 3, lower and upper regions of the steel vessel were 1,200 ( ), (10 40) and (10 40), respectively. The temperature at the vessel inner surface in contact with the overlying water pool was set at the water saturation temperature at 1.3 MPa. Other surfaces of the vessel were assumed to be thermally insulated. A thermal resistance between the molten Al 2 O 3 and the vessel wall was initially given so as to be consistent with a temperature increase rate of the vessel wall observed in the experiments. The initial temperature of the molten Al 2 O 3 was not measured but defined to be 2,500 K, employing the result of a separate measurement with a pyrometer using a 3 kg of thermite. 40) Material properties of Al 2 O 3 used in the analysis were the same as those listed in Ref. 15). C D V. Code Prediction and Discussions 1. Natural Convection of Volumetrically Heated Pool The comparison between the UCLA experiment and the analysis is summarized in Table 2 for the maximum fluid temperature, the temperature of the vessel inner surface, heat losses from the fluid upper surface and from the vessel outer surface. Except the heat loss from the fluid upper surface, the prediction agreed satisfactorily with the experimental results. The discrepancy in the heat loss from the fluid upper surface could have partly resulted from the uncertainty in the thermal boundary condition mentioned earlier. The predicted isotherms of the fluid are shown in Fig. 8. A flat temperature profile was predicted in the upper part of the fluid as also found in the experiment. This type of temperature Table 2 Summary of comparison between UCLA experiment and CAMP prediction Experiment Prediction Maximum fluid temperature (K) Vessel inner surface temperature at bottom (K) Upward heat loss (W) Downward heat loss (W) VOL. 40, NO. 1, JANUARY 2003

8 18 Y. MARUYAMA et al. profile is typical for volumetrically heated pools that convect in cooled boundaries. The depth of the fluid layer showing the flat temperature profile was well predicted by CAMP code, while the temperature of the lower fluid volume was slightly underestimated. The predicted distribution of local heat transfer coefficient along the vessel inner surface is compared with the measured data in Fig. 9. Two experiments with the same conditions were performed to confirm the reproducibility. The following equation was used to calculate local heat transfer coefficient in the same manner as that described in Ref. 9), h lcl = λ v δ v Tvis T vos T max T vis. (32) Though a slight difference was found at the top and bottom of the vessel, CAMP code well predicted the overall trend of the distribution of heat transfer coefficient. The profile of heat transfer coefficient was related to the spatial distribution of the fluid temperature shown in Fig. 8. Fig. 8 Predicted isotherms for UCLA experiment (unit in C) 2. Quench of Molten Al 2 O 3 with Gap Cooling The history of the vessel outer surface temperature obtained from the prediction is plotted in Fig. 10 for. The predicted temperatures started to increase soon after the initiation of the melt slump, and decreased to the water saturation temperature successively from the top of the melt pool to the bottom. This successive temperature decrease reproduced the observation in the experiment. The predicted temperature history of Al 2 O 3 at approximately 2 mm from the curved surface is shown in Fig. 11 for. In contrast to the vessel wall temperature, the Al 2 O 3 surface was maintained at much higher temperatures than the minimum film boiling temperature, indicating that the Al 2 O 3 surface was not wetted during the water penetration period. With the comparison between Fig. 10 and Fig. 11, the assumption of the stratified flow formation in the gap described earlier is supposed to be adequate. The comparisons for the temperature histories on the vessel outer surface between the prediction and the experiment are shown in Figs. 12(a) and (b) for. Latitudinal positions compared are at 30 degrees and 60 degrees from the vessel bottom. The experimental results are plotted for three Temperature (K) Degrees from Vessel Bottom Time (seconds) Fig. 10 Predicted temperature history on vessel outer surface for h lcl /h av (-) Experiment (1) Experiment (2) Analysis Angle from Vessel Bottom (degrees) Temperature (K) 3000 Degrees from Vessel Bottom Time (seconds) Fig. 9 Comparison of heat transfer coefficient distribution along vessel wall between UCLA experiment and CAMP prediction Fig. 11 Predicted temperature history of Al 2 O 3 at vicinity of curved surface for JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

9 Modeling for Evaluation of Debris Coolability in Lower Plenum 19 Temperature (K) Measurement (1) Measurement (2) Measurement (3) Analysis 30 Degrees from Vessel Bottom Temperature (K) IDC001 Measurement (1) Measurement (2) Measurement (3) Analysis 30 Degrees from Vessel Bottom Temperature (K) Time (seconds) (a) 30 degrees from vessel bottom Measurement (1) Measurement (2) Analysis 60 Degrees from Vessel Bottom Time (seconds) (b) 60 degrees from vessel bottom Fig. 12 Comparison of temperature history on vessel outer surface for or two different locations, respectively. The predicted vessel outer surface temperatures for IDC001 are compared with the experiment in Fig. 13 for a latitudinal position of 30 degrees from the vessel bottom. Applying the gap cooling model, the temperature histories observed in the experiment were reproduced by CAMP code. It was found that, however, CAMP code largely overestimated the temperature at the vessel bottom for both experiments. The predicted time-dependent profile of the vessel inner surface as a consequence of the vessel deformation is plotted in Fig. 14 for. For better understanding, the horizontal displacement of the vessel inner surface is multiplied by a factor of 10. The variation of the gap width can be evaluated by comparing the profile after deformation with the initial one. The gap width normal to flow direction at the entrance was predicted to be approximately 1.0 mm at maximum during the time frame indicated in Figs. 12(a) and (b). The plot also implied that, since the gap growth was mainly caused by thermal expansion of the vessel, the gap width became smaller with the temperature decrease of the vessel wall, resulting in the limitation of the water penetration into the gap. This was one of reasons why the present analysis overestimated the temperature on the vessel outer surface at vicinity of the vessel bottom. In addition to thermal expansion of the Time (seconds) Fig. 13 Comparison of temperature history on vessel outer surface at 30 degrees from vessel bottom for IDC001 Vertical Position (m) Fig Alumina Top Surface -0.2 Initial Profile 90 sec 180 sec 270 sec Horizontal Position (m) Predicted profile of vessel inner surface for vessel, other phenomena such as the shrinkage of debris due to the solidification and the temperature decrease should be taken into account for the improvement of predictive capability of CAMP code. VI. Concluding Remarks Phenomena associated with the in-vessel debris cooling were investigated through steady-state calculations and transient analyses for debris thermo-fluiddynamics. The steadystate calculations were conducted to estimate cooling capability of gap water between the debris and the lower head by comparing critical and turbulent natural convective heat fluxes. The calculated results indicated that the gap with a width of 1 through 2 mm enabled to cool the debris under conditions encountered during the TMI-2 accident. It was found that, however, a significantly larger gap width is needed to retain a larger amount of debris within the lower plenum. The model for turbulent natural convection developed by Yin, Nagano and Tsuji, categorized in low Re type twoequation model, were incorporated into CAMP code for transient analysis. The turbulent model was validated with the UCLA experiment on natural convection of a volumetrically heated pool with Ra i of The outputs from the ex- VOL. 40, NO. 1, JANUARY 2003

10 20 Y. MARUYAMA et al. periment were satisfactorily predicted by CAMP code except the heat loss from the upper surface of the pool. Most importantly, CAMP code reproduced quantitatively the spatial distribution of local heat transfer coefficients along the hemispherical vessel inner surface, which is of crucial importance for the feasibility evaluation of the in-vessel debris coolability. Models were developed and incorporated into CAMP code for the gap cooling. The gap cooling model deals with the enlargement of gap width due to thermal expansion and elastic deformation of a hemispherical vessel and the water penetration into the gap based on CCFL and boiling in the gap. The in-vessel debris coolability experiments performed at JAERI, where molten Al 2 O 3 was poured into a water-filled hemispherical vessel, were applied for the validation of the gap cooling model. It was confirmed that CAMP code had good capability of predicting the temperature transient of the vessel wall. However, CAMP code overestimated the wall temperature at the vicinity of the vessel bottom. This discrepancy implies that models on other phenomena such as the volumetric shrinkage of the crust due to temperature decrease should be added to improve the predictive capability of CAMP code. Nomenclature A: Surface area A gap : Cross-sectional area of gap entrance Bo: Bond number C: Empirical constant in CCFL correlation C b : Empirical constant in turbulent model D e : Hydraulic equivalent diameter of gap g: Gravitational acceleration h: Heat transfer coefficient h fg : Latent heat of vaporization j : Dimensionless velocity k: Turbulent kinetic energy k θ : Temperature variance l: Depth m: Empirical constant CCFL correlation Nu: Nusselt number Pr t : Turbulent Prandtl number q: Heat flux q chf : Critical heat flux Q: Volumetric heat generation rate Ra e : External Rayleigh number Ra i : Internal Rayleigh number Re: Reynolds number t m : Mixing time scale T : Temperature T : Average temperature T max : Maximum fluid temperature T : Temperature difference between fluid and wall u: Velocity fluctuation u : Velocity fluctuation caused by shear stress u : Velocity fluctuation caused by buoyancy force Ū: Average velocity v: Superficial velocity V : Volume x: Coordinate (Greek letters) α: Thermal diffusivity α t : Thermal eddy diffusivity β: Volumetric expansion coefficient δ: Thickness δ ij : Kronecker s delta ε: Dissipation rate of turbulent kinetic energy ε θ : Dissipation rate of k θ /2 φ: Gap entrance inclination from vertical line λ: Thermal conductivity ν: Kinematic viscosity ν t : Eddy viscosity θ: Temperature fluctuation ρ: Density σ : Surface tension (Subscripts) b: Boiling dn: Downward direction dos: Curved surface of debris layer dus: Upper surface of debris layer dw: Debris in contact with penetrating water g: Gas l: Liquid lcl: Local max: Maximum min: Minimum v: Vessel vis: Vessel inner surface vos: Vessel outer surface vw: Vessel in contact with penetration water up: Upward direction Acknowledgment Authors wish to gratefully acknowledge Dr. Jun Sugimoto and Mr. Kazuichiro Hashimoto of Japan Atomic Energy Research Institute for their kind assistance and valuable comments on the present work. References 1) J. R. Wolf, J. L. Rempe, L. A. Stickler, D. W. Akers, G. E. Korth, L. A. Neimark, D. R. Diercks, TMI-2 Vessel Investigation Project Integration Report, NUREG/CR-6197 TMI V(93)EG10 EGG-2734, U. S. Nuclear Regulatory Commission, (1994). 2) A. M. Rubin, E. Beckjord, Three Mile Island-New Findings 15 Years after the Accident, Nucl. Saf., 35, (1994). 3) T. G. Theofanous, C. Liu, S. Additon, S. Angelini, O. Kymalainen, T. Salmassi, In-vessel coolability and retention of a core melt, Nucl. Eng. Des., 169, 1 48 (1997). 4) O. Kymalainen, H. Tuomisto, T. G. Theofanous, In-vessel retention of corium at the Loviisa plant, Nucl. Eng. Des., 169, (1997). 5) T. G. Theofanous, S. Angelini, Natural convection for invessel retention at prototypic Rayleigh numbers, Nucl. Eng. Des., 200, 1 9 (2000). 6) J. M. Bonnet, J. M. Seiler, Thermal hydraulic phenomena in corium pools: The BALI experiment, Proc. 7th Int. Conf. on Nuclear Engineering, Tokyo, Apr , 1999, (1999). 7) B. R. Sehgal, V. A. Bui, T. N. Dinh, J. A. Green, G. Kolb, SIMECO experiments on in-vessel melt pool formation and heat transfer with and without a metallic layer, Proc. OECD/CSNI Workshop on In-Vessel Core Debris Retention and Coolability, Garching, Germany, Mar. 3 6, 1998, NEA/CSNI/R(98)18, p (1999). JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

11 Modeling for Evaluation of Debris Coolability in Lower Plenum 21 8) M. Helle, O. Kymalainen, H. Tuomisto, Experimental data on heat flux distribution from a volumetrically heated pool with frozen boundaries, Proc. OECD/CSNI Workshop on In-Vessel Core Debris Retention and Coolability, Garching, Germany, Mar. 3 6, 1998, NEA/CSNI/R(98)18, p (1999). 9) F. J. Asfia, V. K. Dhir, An experimental study of natural convection in a volumetrically heated spherical pool bounded on top with a rigid wall, Nucl. Eng. Des., 163, p (1996). 10) F. B. Cheung, K. H. Haddad, Y. C. Liu, Critical Heat Flux (CHF) Phenomenon on a Downward Facing Curved Surface, NUREG/CR-6504 PSU/ME , U. S. Nuclear Regulatory Commission, (1997). 11) T. Y. Chu, J. H. Bentz, S. E. Slezak, W. F. Pasedag, Ex-vessel boiling experiments: Laboratory- and reactor-scale testing of the flooded cavity concept for in-vessel core retention Part II: Reactor-scale boiling experiments of the flooded cavity concept for in-vessel core retention, Nucl. Eng. Des., 169, (1997). 12) T. G. Theofanous, S. Syri, The coolability limits of a reactor pressure vessel lower head, Nucl. Eng. Des., 169, (1997). 13) D. R. Diercks, G. E. Korth, Results of metallographic examinations and mechanical tests of pressure vessel samples from the TMI-2 lower head, Nucl. Saf., 35[2], (1994). 14) R. E. Henry, D. A. Dube, Water in the RPV: A mechanism for cooling debris in the RPV lower head, Proc. Specialist Meeting on Selected Containment Severe Accident Management Strategies, Stockholm, Sweden, June 13 15, 1994, p (1994). 15) Y. Maruyama, N. Yamano, K. Moriyama, H. S. Park, T. Kudo, Y. Yang, J. Sugimoto, Experimental study on in-vessel debris coolability in ALPHA program, Nucl. Eng. Des., 187, (1999). 16) D. Magallon, A. Annunziato, M. Corradini, Debris and pool formation/heat transfer in FARO-LWR: Experiment and analysis, Proc. OECD/CSNI Workshop on In-Vessel Core Debris Retention and Coolability, Garching, Germany, Mar. 3 6, 1998, NEA/CSNI/R(98)18, p (1999). 17) J. H. Kim, K. H. Kang, R. J. Park, S. B. Kim, H. D. Kim, Experimental study on inherent cooling mechanism during a severe accident, Proc. 7th Int. Conf. on Nuclear Engineering, Tokyo, Japan, Apr , 1999, (1999). 18) S. Imai, K. Sato, R. Hamazaki, R. E. Henry, Experimental study on in-vessel cooling mechanisms, Proc. 7th Int. Conf. on Nuclear Engineering, Tokyo, Japan, Apr , 1999, (1999). 19) Y. Maruyama, K. Moriyama, H. Nakamura, K. Hashimoto, M. Hirano, K. Nakajima, Validation of CAMP code for thermo-fluiddynamics of molten debris in lower plenum, Proc. RASPLAV Semin. 2000, Munich, Germany, Nov , 2000, (2000). 20) Y. Maruyama, K. Moriyama, H. Nakamura, K. Hashimoto, M. Hirano, K. Nakajima, Modeling for water penetration into narrow gap in CAMP code, Proc. Workshop on Severe Accident Research, Tokyo, Japan, Nov. 8 10, 1999, JAERI-Conf , Japan Atomic Energy Research Institute, p (2000). 21) K. Mishima, H. Nishihara, The effect of flow direction and magnitude on CHF for low pressure water in thin rectangular channel, Nucl. Eng. Des., 86, (1985). 22) R. J. Park, S. J. Lee, K. H. Kang, J. H. Kim, S. B. Kim, H. D. Kim, An experimental study on critical heat flux in a hemispherical narrow gap, Proc. Workshop on Severe Accident Research, Tokyo, Japan, Nov. 8 10, 1999, JAERI-Conf , Japan Atomic Energy Research Institute, p (2000). 23) Y. Koizumi, T. Watanabe, Y. Anoda, Critical heat flux of counter-current two-phase flow in vertical-narrow-gap annular passages, Trans. 34th Natl. Heat Transfer Symp. Jpn., Sendai, Japan, May 21 23, 1997, (1997), [in Japanese]. 24) V. Asmolov, L. Kobzar, V. Nickulshin, V. Strizhov, Experimental study of heat transfer in the slotted channels at CTF facility, Proc. OECD/CSNI Workshop on In-Vessel Core Debris Retention and Coolability, Garching, Germany, Mar. 3 6, 1998, NEA/CSNI/R(98)18, p (1999). 25) Y. Sudo, M. Kaminaga, A CHF characteristic for downward flow in a narrow vertical rectangular channel heated from both sides, Int. J. Multiphase Flow, 15[5], p (1989). 26) K. Mishima, H. Nishihara, Effect of channel geometry on critical heat flux for low pressure water, Int. J. Heat Mass Transfer, 30[6], (1987). 27) R. R. Nourgaliev, T. N. Dinh, B. R. Shegal, Effect of fluid prandtl number on heat transfer characteristics in internally heated liquid pools with Rayleigh numbers up to 10 12, Nucl. Eng. Des., 169, (1997). 28) U. Steinberner, H. H. Reineke, Turbulent buayancy convection heat transfer with internal heat sources, Proc. 6th Int. Heat Transfer Conf., Toronto, Canada, Vol. 2, p (1978). 29) F. Mayinger, M. Jahn, H. H. Reineke, V. Steinberner, Examination of thermalhydraulic processes and heat transfer in a core melt, BMFT RS 48/1, Institut fur Verfahrenstechnik der T. U. Hanover, FRG, (1976). 30) T. N. Dinh, R. R. Nourgaliev, Turbulence modeling for large volumetrically heated liquid pools, Nucl. Eng. Des., 169, (1997). 31) Y. Yin, Y. Nagano, T. Tsuji, Numerical prediction of turbulent natural convection boundary layers, Trans. JSME, Series B, 55, (1989), [in Japanese]. 32) Y. Nagano, M. Hishida, Improved form of the k-ε model for wall turbulent shear flows, Trans. ASME, J. Fluids Eng., 109, (1987). 33) Y. Nagano, C. Kim, A two-equation model for heat transport in wall turbulent shear flows, Trans. ASME, J. Heat Transfer, 110, (1988). 34) T. Tsuji, Y. Nagano, Characteristics of a turbulent natural convection boundary layer along a vertical flat plate, Int. J. Heat Mass Transfer, 31, (1988). 35) S. S. Kutateladze, Heat Transfer in Condensation and Boiling, AEC-Translation-3770, USAEP Tech. Info. Service, (1952). 36) P. J. Berenson, Film boiling heat transfer from a horizontal surface, J. Heat Transfer, 83, (1961). 37) N. Zuber, M. Tribus, AECU-2931, (1958). 38) L. A. Bromley, Chem. Eng. Prog., 46[5], 221 (1950). 39) Japan Society of Mechanical Engineering, JSME Data Book: Heat Transfer, 4th Ed., (1986), [in Japanese]. 40) Y. Maruyama, N. Yamano, H. Itoh, K. Komori, H. Sonobe, R. Yagioka, J. Sugimoto, Evaluation of Specific Heat and Temperature of Thermite Melt Used in Melt Coolant Interaction Test of ALPHA Program, JAERI-M , Japan Atomic Energy Research Institute, (1993), [in Japanese]. VOL. 40, NO. 1, JANUARY 2003