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Experimental investigation of corium quenching at elevated pressure
Nuclear Engineering and Design 236 (2006) 2271–2280
Experimental investigation of corium quenching at elevated pressure S. Lomperski a,∗ , M.T. Farmer a , S. Basu b a
b
Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, USA U.S. Nuclear Regulatory Commission, 11545 Rockville Pike, Rockville, MD, USA
Received 1 January 2004; received in revised form 27 May 2005; accepted 20 March 2006
Abstract This paper describes the results of experiments designed to quantify the cooling rate of corium by an overlying water pool. The experiments are intended to provide fundamental information on the ability of water to ingress into cracks and fissures that form in the debris during quench, thereby augmenting the otherwise conduction-limited heat transfer process. This information is being used to assess the effectiveness of a water pool in thermally stabilizing a molten-core/concrete interaction and cooling of ex-vessel core debris. The experiments involved corium inventories of 75 kg with a melt depth of 15 cm and diameter of 30 cm. The corium was composed of UO2 /ZrO2 /concrete to simulate mixtures of molten reactor core components and either siliceous or limestone/common sand (LCS) concrete. Initial melt temperatures were of the order of 2100 ◦ C. The heat transfer rate from the corium was determined through measurements of the vapor production rate from the water pool. The melt was quenched at atmospheric pressure for the first two tests and at 4 bar for the two subsequent tests. Preliminary data analysis indicates that the overall heat transfer rate exceeded the conduction-limited rate for the three melts containing 8 wt.% concrete, but not for the fourth, which had 23 wt.% concrete. Also, the quench rate of the 8 wt.% concrete melts did not vary appreciably with pressure. © 2006 Published by Elsevier B.V.
1. Introduction The ability to adequately cool molten-core material (“corium”) by an overlying water layer, whether located within the reactor pressure vessel or on the containment building floor, remains an unresolved issue. For “ex-vessel” accident sequences, in which the RPV fails and corium is released into the containment, sufficient cooling would halt erosion of the basemat and prevent fission product release into the environment. Because of the complexity of the interactions, the quenching of ex-vessel melts is a process that is not yet well-understood. Experiments are being performed as part of an OECD-sponsored program to quantify the cooling rate of ex-vessel melts flooded from above and to measure concrete basemat ablation rates under prototypical conditions. The quenching of corium involves removal of both the melt sensible energy and the fission product decay heat. The most
∗
Corresponding author. Tel.: +1 630 252 1144. E-mail addresses: [email protected] (S. Lomperski), [email protected] (M.T. Farmer). 0029-5493/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.nucengdes.2006.03.041
effective source of cooling is water. However, the mode of contact between water and the melt strongly influences the corium cooling rate. A variety of mechanisms exist through which the surface area available for heat transfer is increased and the cooling rate enhanced. Such mechanisms include: (i) the formation of cracks and fissures in the solidified, insulating “crust” that forms as the corium cools, (ii) crust breaches, in which the crust ruptures to such an extent that water and melt are brought back into direct contact, and (iii) melt eruptions, where gas entrains melt up through the crust into direct contact with coolant. This paper describes the results of experiments concerned with the first mechanism. Specifically, the experiments were designed to detect and measure the enhancement of heat transfer due to crack formation within the crust of an ex-vessel corium melt. The tests described in this paper investigated how the cooling rate is affected by the concrete mass fraction of the melt, the concrete composition, and the system pressure. They will be used as a baseline for comparison of future tests with melts of differing concrete composition and mass fraction. This paper begins with a brief discussion of the water ingression phenomenon, followed by a description of the test apparatus and experimental results.
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Nomenclature Ac Act cp g hfg m ˙ P q qc Q t
surface area of corium (m2 ) cross-sectional area of condensate tank (m2 ) specific heat (J/kg K) gravitational constant (9.8 m/s2 ) heat of vaporization of water (J/kg) mass flow rate (kg/s) pressure (N/m2 ) heat flux (W/m2 ) corrected heat flux (W/m2 ) dimensionless dryout heat flux time (s)
Greek letters κ permeability (m2 ) µ viscosity (N s/m2 ) ρ density (kg/m3 ) Subscripts dry dryout f fluid g gas HL heat losses str structures sen sensible heat 1.1. The water ingression phenomenon One approach to cooling an ex-vessel melt deposited upon the containment basemat is to flood it from above. Initially, energy is removed from the melt via bulk cooling, which is characterized by heat transfer to the overlying water layer through both convection and radiation with mixing of the melt by natural convection. With further cooling, precipitates form within the melt so that the bulk cooling involves a mixing of both solids and liquids. Eventually, either a critical solid fraction or surface temperature is reached and a crust forms at the melt surface. The crust then divides the water from the yet-molten corium below. Because of its low conductivity, the crust can restrict heat transfer between the melt and water layer and greatly retard further cooling. The minimum, conduction-limited heat transfer rate through the crust can be calculated from a well-known analytical solution. However, the actual heat transfer rate from the melt to the water layer is expected to be greater than the conductionlimited rate due to cracks and voids that form within the crust as it cools. Such a porous crust provides pathways for liquid to penetrate downwards, where it can provide additional cooling through a boiling mechanism. This liquid transport through a permeable crust towards the freezing front is known as “water ingression”. The degree of enhanced heat transfer due to water ingression is difficult to predict analytically because of the strong dependence of the water ingression rate on the crust morphology. The percolation of water down through the cracks and voids coin-
Fig. 1. Elapsed time to quench corium at various heat fluxes.
cides with a counter current steam flow generated by boiling. The water flow and effective heat removal rates vary strongly with the crust morphology, which is determined by the chemical composition, cooling rate, and mixing mechanisms such as sparging by concrete decomposition gases. Thus it is critical to use prototypical materials so that the quench process forms a crust having a realistic permeability and cooling rate. Sparging gases are, however, excluded from the experiments described in this paper so that water ingression and enhanced cooling due to thermallyinduced cracking can be studied in isolation. Sparging gases may have either a positive or negative influence on heat removal rates and their study is left to future experiments.The basic premise of the current experiments is to measure the heat flux from the melt to the overlying water layer, compare it to the analytical solution, and then determine the extent to which water ingression enhances cooling of the melt. Fig. 1 is a plot of the analytical solution for transient cooling of a semi-infinite slab by conduction following a step change in surface temperature (Ozisik, 1980). In this case, the initial slab temperature is 2100 ◦ C and the transient is initiated by setting the surface temperature to 100 ◦ C. The model is one-dimensional and so multi-dimensional effects such as heat losses are disregarded. The relevant thermo-physical properties for this calculation are the corium thermal conductivity, density, and specific heat, which were set to 1.5 W/m K, 7000 kg/m3 , and 660 J/kg K, respectively. Fig. 1 shows how the conduction-limited heat flux drops rapidly during the early phase of the transient and then, at a reduced rate, diminishes asymptotically towards zero. In contrast, for a porous crust, the heat transfer rate may at some point exceed that given by the conduction solution and thus diverge from the conduction-limited curve after initially tracking it. The divergence is a consequence of enhanced heat removal via the vaporization of liquid that has percolated down through pathways within the crust. The point where the two cooling rates diverge can be thought of as the limiting heat removal rate from the porous material though the boiling process. This limit is often referred to as the “dryout” heat flux and it has been studied experimentally for porous media such as particle beds (see, for example Atkhen and Berthoud (2003), Hu and Theofanous (1991) and Miettinen et al. (2002)). The three dashed curves in
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Fig. 1 represent hypothetical levels of the dryout heat flux. Such plateaus would be observed if the rate of heat removal from the melt remained fixed at the dryout heat flux level. In practice, however, even with water ingression-enhanced cooling, the heat removal rate is expected to decline over time as the melt cools and the crust thickens. The decline is due, in part, to diminishment of the rate of convective heat transfer between the melt and crust as the former cools. There may also be a decline in the effectiveness of the water ingression mechanism over time since pathways for water percolation to the melt quench front lengthen as the crust thickens. These phenomena are excluded from the idealized curves in Fig. 1, which are intended only to illustrate the enhanced cooling that might be achieved through the water ingression mechanism and the associated acceleration of the quench process. The end points marked for each curve indicate the approximate time at which a 15 cm deep melt is entirely quenched, i.e. cooled to 100 ◦ C, for the selected dryout heat flux levels. The calculation considered the energy removed from the melt up to the moment when the heat flux departed from the conduction-limited solution. The length of the dashed line represents the time necessary to remove the residual energy of a 15 cm melt at the given dryout heat flux. The graph illustrates the extent to which differing levels of dryout heat flux shorten the time to quench compared to conduction-limited cooling. Many models and correlations have been developed to predict dryout heat fluxes for porous beds. Some of the models presume dryout limits to be governed by a counter-current flow limitation in which the drag forces between vapor and liquid limit the cooling rate of the bed (Ostensen and Lipinski, 1981). Other models are based on Darcy’s law, which describes flow that is limited by drag forces between the particles of the bed and the gas and vapor. One such model provides an expression for the dryout heat flux of a deep bed in terms of a dimensionless dryout heat flux Q (Jones et al., 1984): qdry =Q
κρg hfg (ρf − ρg )g µg
(1)
where hfg is the latent heat of vaporization, ρ the density, µ the viscosity, g the gravitational constant, and κ is the permeability of the porous medium. The dimensionless heat flux is a function of the kinematic viscosity ratio of the vapor and liquid along with the model chosen for the specific permeabilities of the liquid and vapor. For water and steam in the pressure range of 1–4 bar, the range of interest for this study, estimates of the dimensionless heat flux cited in the Jones study vary between roughly 0.1 and 0.8. Though this wide range for Q produces a correspondingly wide range of estimates for the dryout heat flux, the Jones model clearly illustrates some trends expected for the experiments. From the above relation it is seen that an increase in the crust permeability augments the dryout heat flux, which in turn increases the melt quench rate. The Jones model also predicts an increase in heat flux with pressure due to an increase in steam density that permits higher mass flow rates through cracks and pores. Other, more sophisticated dryout models, as well as experimental findings, also indicate that the dryout heat flux increases with pressure (see, e.g. Jakobsson et al. (1983)).
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Experimental investigations of dryout heat flux typically involve measurements of cooling limits for columns of heated particles or small spheres imitating, in part, core material debris beds that may exist following a hypothetical reactor accident. Test data for particle beds can be represented by a variety of models, such as those based on Darcy’s law (e.g. Hardee and Nilson (1977) or Jones et al. (1984)) or counter current flow limitations (Ostensen and Lipinski, 1981). However, some reactor accident scenarios involve a generally contiguous melt rather than a collection of particles. In this case, mechanisms that create porous structures within the melt can determine the limit of melt coolability and so, ideally, the processes of melt cooling and pore formation would be combined in the study of dryout heat flux and the limits of corium cooling. A relevant and comprehensive study of the cooling of hot rock by water penetration was conducted by Lister (1974), who examined cracking mechanisms that open up pathways for water percolation down into geological formations. His model envisions a cracking front that advances downwards as molten rock solidifies and then fractures under stresses generated by thermal contraction. The amount of cracking, and hence the rock permeability and rate of advance of the front, is dependent upon thermo-physical properties of the rock and temperature gradients in the region near the cracking front. Lister’s view of the cooling of molten rock appears compatible with the quenching of a contiguous corium melt. The experiments reported here are used to examine the influence of corium thermo-physical properties on cracking behavior and permeability, and how they influence the melt cooling rate. The properties are varied by altering the amount and type of concrete in the melt, which corresponds to variations in the elapsed time after a melt enters the reactor cavity and different reactor containment basemat compositions. Other trends, such as the predicted increase in dryout heat flux with pressure, are examined by conducting selected experiments with system pressures above ambient pressure. 2. Test apparatus A facility was constructed for the purpose of producing corium melts with a precisely-defined geometry and chemical composition while ensuring confinement during quenching at elevated pressure. The reaction vessel (RV) lower plenum consists of a 67 cm long, 46 cm (18 in.) outer diameter carbon steel pipe (Fig. 2). The pipe is insulated from the melt by a 6 cm thick liner of cast MgO. An MgO “basemat” insulates the RV lower flange and spans the entire inner diameter of the pipe. The MgO liner sits on top of the basemat and the two insulators form the crucible that holds the corium. This geometry produces a 30 cmdiameter melt (surface area of 707 cm2 ). The system is designed to produce melts of up to 100 kg at 2500 ◦ C and the RV is rated for a pressure of 7.7 bar. This small-scale facility has been designated SSWICS (small-scale water ingression and crust strength). The latter portion of the term refers to complementary tests in which the solidified corium ingot is mechanically loaded to measure the fracture strength of the crust. The corium itself is produced by an exothermic chemical reaction of a powder comprised of oxides and metals that react
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Fig. 2. Reaction vessel (dimensions in mm).
with an oxidizer (collectively referred to as thermite). The thermite consists mainly of U3 O8 , zirconium metal and the oxidizer CrO3 , which react together to produce the UO2 and ZrO2 that are the main components of a corium melt. It also includes other materials, such as silicon and aluminum, to produce the desired corium/concrete mixture. The thermite components are apportioned by considering both the net heat of reaction and the final melt composition. The chemical reaction generating the melt must produce both the desired corium composition and the target initial temperature. For the first three tests, the thermite was formulated to produce corium containing 8 wt.% concrete constituents, which accounts for the concrete erosion expected during the corium spreading phase after a breach of the RPV (Sienicki and Spencer, 1986). The RV upper plenum consists of a second section of pipe with inlets for the water supply and an outlet for steam produced by the quenching process. The outlet leads to a 10 cm diameter line that transports steam from the quenching melt to a tube-intube heat exchanger (Fig. 3). The water-cooled heat exchanger condenses the steam, which is collected within a 200 cm high, 20 cm diameter condensate tank (CT). Measurements of the time-varying CT inventory provide an indirect measurement of
the steam flow rate from the RV, which is then used to determine the corium cooling rate. Melt temperatures are obtained with tungsten–5% rhenium (type-C) thermocouples mounted on the RV flange below the basemat. Two single-junction thermocouples with tantalum sheathes were used in the first pair of tests. The measurement junctions were located 20 mm above the bottom of the melt. In tests 3 and 4, multi-junction (4) thermocouples were employed and they were enclosed in tungsten thermowells to prolong their operating lives and allow them to extend further into the melt (100 mm). For all tests, two type-C thermocouples in the basemat were positioned near the bottom of the melt to detect arrival of the quench front, which is indicated by temperatures falling to the steam saturation temperature. The tips of these thermocouples rested against the underside of a ZrO2 insulating board that was protected from direct contact with the corium by a thin tungsten plate (see Fig. 2). The melts for tests 3 and 4 were quenched at a pressure of 4 bar absolute to study the effects of pressure on cooling rate. A control valve in the steam line was used to regulate the RV pressure. The RV structures and quench water supply were preheated to ∼100 ◦ C to reduce the effects of heat sinks early in the quench
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Fig. 3. Schematic of water ingression test facility.
process (these preheating systems were not yet in place for the first two tests at ambient pressure). 3. Test results 3.1. Overview Four water ingression experiments with the SSWICS facility have been completed. For the first three tests, the melt mass was 75 kg and composed of a fully oxidized PWR melt containing 8% concrete decomposition products. The amount of concrete was increased for the fourth test to 23 wt.%. Three of the melts contained limestone/common sand concrete and the fourth was made with siliceous concrete. The melt depth for all tests was about 150 mm. Water injection into the RV typically began about 2 min after thermite ignition and lasted less than 10 min, producing an initial water layer of about 0.5 m. A summary of the test parameters is provided in Table 1. Figs. 4–7 are plots from selected tests (2 and 3) intended to illustrate the typical course of both low and high pressure tests. Fig. 4 shows the measured melt temperatures. In the legends, TM indicates that the thermocouple was within the melt while TI refers to those near the interface between the melt and base-
mat. The term H# signifies the height above the bottom of the melt (in mm) and the remaining term corresponds to the radial position. For all plots, the time t = 0 is defined as the moment when thermite ignition was first detected by an initial rise in the gas temperature of the RV upper plenum. The plotted data for some sensors does not extend the full length of a test due to corrosion-induced failure. Such data has been truncated at the points where sensor failures were evident. The pyrometer trace ends where the sensor reached its lower range limit of 1200 ◦ C. Once the thermite was ignited, the chemical reaction proceeded quickly through the entire charge and the measured melt temperatures peaked within about 10 s of their initial rise. The temperatures then fell as energy was lost to the MgO crucible and subsequently recovered as conductive and convective heat transfer from the center of the melt reheated the periphery. The measured temperatures plateaued for several minutes before declining as the melt was quenched. The plateau is used to establish the initial bulk melt temperature, the accuracy of which is estimated to be of the order of 100 ◦ C. The pyrometer readings in test 2 confirm that this is a satisfactory method for establishing an initial melt temperature. The pyrometer, which was located near the melt center (H100 and depth of 50 mm), peaked
Table 1 Selected test parameters Parameter
1
2
3
4
Test section i.d. (cm) Melt composition (UO2 /ZrO2 /Cr/concrete) (wt.%) Concrete type Melt mass (kg) Melt depth (cm) Initial melt temperature (◦ C) System pressure (bar) Water injection flowrate (l/m) Water injected (l) Initial water/structure temperature (◦ C)
30.5 61/25/6/8 LCS 75 15 ∼2300 1 4 55 ∼20
30.5 61/25/6/8 SIL 75 15 ∼2100 1 4 39 ∼20
30.5 61/25/6/8 LCS 75 15 ∼2100 4 12 34 ∼100
30.5 48/20/9/23 LCS 60 15 ∼2100 4 13 40 ∼100
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Fig. 4. Melt temperatures for (a) test 2 at 1 bar and (b) test 3 at 4 bar. Fig. 5. Liquid inventories for (a) test 2 at 1 bar and (b) test 3 at 4 bar.
2140 ◦ C.
40 ◦ C
at This is within of the temperature estimated with the thermocouples. Fig. 5 provides plots of the liquid inventories of the RV and condensate tank along with the amount of water injected into the RV. The latter was calculated by integrating the measured injection flow rate (F-quench in Fig. 6). The RV liquid inventory was calculated with a mass balance using the integrated flow and the measured CT inventory. Calculations confirm that for each test the melt was water-covered for the entire test duration. Fig. 6 shows the measured total pressure in the reaction vessel (PA-RV) and also the injection flow rate (F-quench). For the low pressure tests, the flow rate is lower and the injection period longer than for the high pressure tests. However, the total amount of water injected is similar for all tests. In the low pressure tests, the RV pressure began near ambient and then was pulled slightly below atmospheric pressure by the heat exchanger. The set-point pressure for the high pressure tests was 4 bar, which was maintained within 0.1 bar after the initial rise to the set point and a short settling period. The dip in pressure at 6000 s is due to a second, brief water injection. The flow rate was below the flow meter threshold and does not appear in the trace of F-quench. 3.2. Corium heat flux The main objective of each water ingression test is to determine the heat flux through the corium surface. A first order
estimate of the heat flux can be obtained by assuming that all cooling contributes directly to the production of steam, all of which reaches the heat exchanger, is condensed, and then deposited within the condensate tank. In this case, the heat of vaporization is used to directly calculate the heat flux through the melt surface: q =
m ˙ g hfg Ac
(2)
where m ˙ g is the steam mass flow rate out of the RV, hfg the heat of vaporization of water, and Ac is the surface area of the corium (0.071 m2 ). The steam mass flow rate is equal to the condensate collection rate, which is determined through P measurements, and so the heat flux can be written as: q =
Act ∂ P hfg Ac ∂t g
(3)
where Act is the cross-sectional area of the CT, P the measured differential pressure, and t is the time. The derivative was calculated with pairs of averaged P readings (an average of five measurements recorded at 0.5 Hz) centered around a t of 60 s. The averaging and large t are necessary because the water level in the CT increases slowly and even small fluctuations in the P produce large changes in the calculated heat flux.
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Fig. 7. Corium heat flux as measured by rate of condensate collection for (a) test 2 at 1 bar and (b) test 3 at 4 bar. Fig. 6. RV pressure and injection flow rate for (a) test 2 at 1 bar and (b) test 3 at 4 bar.
The heat flux determined with Eq. (3) is plotted in Fig. 7 for tests 2 and 3 (key data from these tests is protected by a proprietary agreement, which requires use of an arbitrary heat flux scale). The vertical scale limits are the same for each plot so that the magnitude of the heat fluxes can be directly compared. The off-scale peaks early in the test are due to strong heat transfer and steam production when water initially meets the yet-molten surface of the corium. The steam flow rate subsequently declines as the surface cools and the water pool depth increases. The continued addition of subcooled water eventually suppresses boiling towards the end of the injection phase, which, using Eq. (3), appears as a drop to near-zero heat flux. Once water injection is completed, boiling resumes and steam flow reaches a second, lower peak and gradually declines as the melt cools. The comparatively large heat flux oscillations of the high pressure test are due to pressure variations produced by position adjustments of the pressure regulating valve. Though the pressure fluctuations were small, the constantly changing valve position produced variations in the steam flow rate to the heat exchanger, which appear as substantial swings in the measured heat flux. Eq. (3) provides only a first order estimate of the heat flux because energy transfer to several heat sinks has been neglected. During the water injection phase of a test, energy is absorbed by the coolant as it is heated to the saturation temperature. Also, early in the transient, steam condenses on relatively cold
RV structures until they reach the saturation temperature. Both these effects reduce the amount of steam reaching the condenser and thus the apparent heat flux. Heat losses from the RV to the ambient also reduce steam flow to the condenser. The following expression provides the corrected heat flux qc , which accounts for the heat sinks: qc =
1 [m ˙ g hfg + Qsen + Qstr + QHL ] Ac
(4)
where Qsen is the rate of sensible energy deposition into the coolant, Qstr the rate of energy absorption by the RV structures due to steam condensation, and QHL represents heat losses from the RV. Steam superheating, which may occur in the first seconds of water injection, has been neglected. The corrections for structure and coolant sensible heat are significant only during the early phase of the transient. The heat flux is corrected using the net energy absorbed by the structures and coolant in heating them to the saturation temperature. The heat transfer rate from the melt to the heat sinks was approximated with a simple linear function that distributes the net energy absorbed by the heat sinks over the course of the injection phase. Measurements of structure temperatures indicate that heating is spread over a somewhat longer period, but this approach has the advantage of clarity since it restricts all corrections to the period before steam flow recovery. The net energy deposition into the structures was calculated using the total heat capacity of the test vessel structures and the difference between the ambient and steam saturation temperatures. The sensible energy added to the
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calculated using the difference between the initial melt temperature and the saturation temperature, and by assuming a mean heat capacity of 660 kJ/kg K. This measure of melt energy is most accurate after a short period following water injection, when heat transfer rates to the heat sinks are insignificant. The plots show the melt energy at test end to be near zero for both tests, as expected. Note that even though test 3 was considerably longer than test 2, a similar amount of energy was removed after an elapsed time of 4300 s, which marked the end of test 2. The length of a particular test is not a good indicator of the average heat removal rate because the basis for terminating a test (thermocouples beneath the melt reaching the saturation temperature) envisions a one-dimensional system with a quench front propagating down towards the bottom of the melt. In actuality, the melt cools from all sides so that at test-end the hottest region may be closer to the center of the corium than the bottom. Thus a temperature sensor near the base of the melt can provide only an approximate indication of when the melt has been fully quenched. 4. Comparisons with conduction-limited cooling
Fig. 8. Corrected heat flux and net melt energy for (a) test 2 and (b) test 3.
water was calculated in a similar fashion using the integrated flow and measured liquid temperature near the injection point. The function is defined so that heat transfer to the sinks reaches zero as steam flow recovers, and it is scaled using the corium sur , has face area. The heat flux associated with the heat sinks, qsink been plotted to mark the interval defined as the injection phase and to allow a comparison between dissipated melt energy associated with steam flow to the HX and energy absorbed by the heat sinks. The correction has been treated in an approximate fashion because the heat sink effects are significant only early in a test, which is not the period of focus for these experiments. Moreover, an accurate determination of heat transfer rates to the heat sinks requires substantially more temperature sensors than were available for these tests. The main purpose of correcting for the heat sinks is to provide an indication of the melt energy during the intermediate and late phases of the test. The thermal energy available for steam production declines towards zero as the melt temperature approaches the saturation temperature and so a plot of melt energy versus time serves as a crosscheck of the calculations. The corrected heat fluxes for tests 2 and 3 are shown in Fig. 8 (the vertical scale ranges again match for direct comparisons). The corrected heat flux was integrated and subtracted from the initial melt energy to obtain the net melt energy versus time, which is included in the figures. The initial corium energy was
The existence of enhanced cooling due to water ingression is identified by comparing the measured corium heat flux with the conduction-limited solution. The one-dimensional model described earlier provides a rough estimate of the conductionlimited heat flux through the corium surface. However, such a model fails to account for the lateral and axial heat losses that are present during the experiment. Inclusion of these heat losses is necessary to find the conduction-limited heat flux that corresponds to the actual experimental conditions so that a meaningful comparison between the measured and conduction-limited heat fluxes can be made. A 3D model of the RV lower plenum was constructed using the graphical modeler SINDA/3D (Network Analysis Inc.), which is a CAD-type program for creating models and a processor for the finite-difference analysis thermal analyzer SINDA/G. Fig. 9 depicts the model created for the RV, which has been reduced to a 1/8th-size slice of the lower plenum using symmetry. The model was simplified further by omitting regions that have little influence on heat losses, such as the mating lower flange (welded around the pipe) and all portions of the lower plenum that are more than 50 mm above the corium surface. The corium itself was treated as a solid block of material that excludes the effects of convective heat transfer from mixing during the bulk cooling phase, and also later in the transient when the corium consists of a stable crust overlying a liquid or slurry mixed by natural convection. Mixing enhances heat transfer to the underside of the crust thereby increasing the overall corium cooling rate compared to the conduction solution. However, this is expected to have a 2nd order effect on the cooling rate because of the high thermal resistance of the crust. In addition, natural convection mixing below the crust is thought to have a much smaller influence on the corium cooling rate than the lateral conduction losses that are being calculated with this 3D model. A representative calculation is presented here for comparison with the measured heat fluxes of all four tests. The initial melt
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Fig. 10. Measured heat fluxes and calculated conduction-limited heat flux.
Fig. 9. Model of reaction vessel lower plenum (dimensions in cm).
and structure temperatures were set to 2100 and 20 ◦ C, respectively. The thermodynamic properties used for the corium are the same as those described for the 1D model in Section 1. The heat capacity of 660 kJ/kg K is an average value calculated from the enthalpy change between the initial and final melt temperatures, which therefore incorporates the heat of fusion. The melt depth is 15 cm and the heat transfer coefficient from the surface of the corium to the water pool was set to 10 kW/m2 K. The latter parameter is not critical because, soon after the transient begins, heat transfer through the corium surface is limited primarily by the poor conductivity of the corium rather than the heat transfer coefficient. The boundary conditions at the outer surface of the RV wall and flange are of particular importance because they control the lateral and axial heat losses. These are significant since the associated surface area is greater than that of the corium/water interface while the thermal conductivities of the MgO and corium are comparable. During the experiment, the outer surface of the RV lower plenum is uninsulated and so specifying a natural convection heat transfer coefficient could be expected to suffice. However, the actual construction of the lower plenum differs slightly from that of the simple model shown in the figure: a narrow gap exists between the liner and the RV wall. An examination of measured structure temperatures suggests that water and/or steam is present within the gap and so the outer surface of the liner is cooled by water and/or steam. Some water may also seep between the basemat and the flange. For the present calculations, the heat losses through the liner are modeled by assuming a vessel wall heat transfer coefficient of 1 kW/m2 K to a sink temperature of 100 ◦ C (cooling of the liner by steam and saturated water). Heat losses through the basemat are assumed to be caused primarily by conduction to the flange (water seepage is neglected) and are modeled with a flange heat transfer coefficient of 2.5 W/m2 K to a sink temperature of 20 ◦ C.
Fig. 10 shows the result of the calculation, which is plotted along with heat flux data from all four tests for comparison. The data is uncorrected and plotted on an expanded vertical scale that omits the early peak in heat flux after quenching is initiated. Attention is directed to the period after about 1000 s, when energy loss to heat sinks is minor. Based on this collection of data, the following four observations relevant to the water ingression cooling mechanism are drawn: 1. For tests 1–3, the measured heat flux exceeds the conduction limit during the early and intermediate phases of each test. Towards the end of a test, the measured heat flux fell below the conduction limit, which would be expected since most of the melt energy was removed earlier. In addition, plateau-like features are evident in the curves for tests that used corium with 8 wt.% concrete, as would be expected if water ingression was active during the quench process (see Section 1.1 and Fig. 1). This collection of information indicates that water ingression is an active cooling mechanism for corium containing nominally 8 wt.% concrete. 2. Based on the consistency of the peak heat fluxes after 1000 s, the water ingression cooling rate for corium containing either siliceous and limestone/common sand concretes appears to be similar under the condition in which the corium concrete content is the same. 3. Comparison of the results for tests 1 and 3, in which the melts were of the same composition but quenched at different pressures, indicates that system pressure has little effect on the water ingression rate. This is an unexpected finding since, according to Eq. (1), the dryout heat flux is expected to increase with pressure by roughly a factor of two. Other studies, both analytical and experimental, have predicted significant increases in the dryout heat flux with pressure (Jakobsson et al., 1983). The increase, however, is less pronounced for the beds with smaller particle size, which may indicate that the effective pore size within the corium for the water ingression experiments is very small. If so, the dryout
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heat flux is likely to be set by flow resistance of the crust rather than a counter current flow limitation. 4. For the fourth test, which had the highest melt concrete fraction, there is no apparent plateau in the heat flux, as would be expected if water ingression contributed significantly to cooling. Moreover, the overall asymptotic decline in the heat flux is quite similar to the conduction-limited solution. Finally, the heat flux exceeds the calculated conduction limit by only ∼40%, which aside from thermo-physical property uncertainties, could be accounted for by uncertainty in the lateral heat losses through the MgO crucible. This collection of information indicates that water ingression does not significantly augment the debris cooling rate for corium containing around 23 wt.% limestone/common sand concrete.
sured heat flux of the melt containing 8 wt.% limestone/common sand concrete is similar to that of the melt containing the same amount of siliceous concrete. The effect of pressure on heat flux was also investigated and it was observed that the there is little difference between the melts quenched at 1 bar and at 4 bar. The melt with 23 wt.% concrete, quenched at 4 bar, cooled more slowly than the melts with less concrete. The SINDA/G calculations with a model of the RV indicate that the melt with 23 wt.% concrete cooled at a rate that is close to the expected rate for conduction-limited cooling. In contrast, the three melts with 8 wt.% concrete cooled at a rate that is significantly higher than the conduction-limited rate.
Note that the comparison between the data and the calculated conduction-limited heat flux is inexact because some boundary conditions required for the thermal model are not well known. The existence of a gap between the liner and the RV wall results in uncertainty in the heat transfer rate at the liner surface and the corresponding lateral heat losses. Heat losses are greatly increased when the liner is cooled by surface boiling rather than pure conduction through the RV wall and natural convection air cooling at the RV surface (the ideal case without a gap). In addition, such boiling would add to steam production and, through the collected condensate, contribute to the apparent heat flux. Supplementary instrumentation in subsequent tests and additional calculations will be used to determine the appropriate boundary conditions for a more accurate calculation of the conduction-limited heat flux. Nevertheless, despite this uncertainty in the heat losses, these test results provide an indication of the range and extent to which water is able to ingress into corium during cool-down and augment the conduction-limited cooling rate. They also furnish clear comparisons of the relative melt cooling rates for various corium compositions and system pressures. As part of the program, models are being utilized to assess the extent to which the water ingression cooling mechanism, as well as the other mechanisms under investigation in the program, are able to mitigate (and possibly terminate) the course of core–concrete interaction (e.g. see Farmer et al. (2000)).
This work has been sponsored by the Organization for Economic Cooperation and Development (OECD). Participating countries include Belgium, Czech Republic, Finland, France, Germany, Hungary, Japan, Norway, South Korea, Spain, Sweden, Switzerland, and the United States of America. This support is gratefully acknowledged.
5. Conclusion The first four tests with the SSWICS water ingression facility have been successfully completed. The experiments were used to measure the quench rates of fully oxidized PWR melts containing 8 and 23 wt.% concrete at pressures of 1 and 4 bar absolute. The melts were 15 cm deep, ranged in mass from 60 to 75 kg, and had an initial temperature of the order of 2100 ◦ C. The mea-
Acknowledgements
References Atkhen, K., Berthoud, G., 2003. Experimental and numerical investigations on debris bed coolability in a multidimensional and homogeneous configuration with volumetric heat source. Nucl. Technol. 142, 270–282. Farmer, M.T., Spencer, B.W., Kilsdonk, D.J., Aeschlimann, R.W., 2000. Results of MACE corium coolability experiments M0 and M1b. In: Proceedings of the Eighth Conference on Nuclear Engineering (ICONE-8), Baltimore, MD, April 2–6. Hardee, H.C., Nilson, R.H., 1977. Natural convection in porous media with heat generation. Nucl. Sci. Eng. 63, 119–132. Hu, K., Theofanous, T.G., 1991. On the measurement and mechanism of dryout in volumetrically heated coarse particle beds. Int. J. Multiphase Flow 17 (4), 519–532. Jakobsson, J.O., Catton, I., Squarer, D., 1983. The pressure dependence of dryout heat flux. In: International meeting on light-water reactor severe accident evaluation, Cambridge, MA, USA, pp. 18.4.1–18.4.7. Jones, S.W., Epstein, M., Bankoff, S.G., Pedersen, D.R., 1984. Dryout heat fluxes in particulate beds heated through the base. J. Heat Transfer 106, 176–183. Lister, C.R.B., 1974. On the penetration of water into hot rock. Geophys. J. Roy. Astron. Soc. 39, 465–509. Miettinen, J., Sairanen, R., Holmstrom, S., Lindholm, I., 2002. Experimental study and analytical methods for particle bed dryout with heterogeneous particles and pressure variation. In: Proceedings of the 10th International Conference on Nuclear Engineering (ICONE10), Arlington, VA, April 14–18. Ostensen, R.W., Lipinski, R.J., 1981. A particle bed dryout model based on flooding. Nucl. Sci. Eng. 79, 110–140. Ozisik, M.N., 1980. Heat Conduction. John Wiley and Sons, New York, USA. Sienicki, J.J., Spencer, B.W., 1986. OECD CSNI Specialist Meeting on Core Debris/Concrete Interactions, Palo Alto, CA, USA.
Experimental investigation of corium quenching at elevated pressure S. Lomperski a,∗ , M.T. Farmer a , S. Basu b a
b
Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, USA U.S. Nuclear Regulatory Commission, 11545 Rockville Pike, Rockville, MD, USA
Received 1 January 2004; received in revised form 27 May 2005; accepted 20 March 2006
Abstract This paper describes the results of experiments designed to quantify the cooling rate of corium by an overlying water pool. The experiments are intended to provide fundamental information on the ability of water to ingress into cracks and fissures that form in the debris during quench, thereby augmenting the otherwise conduction-limited heat transfer process. This information is being used to assess the effectiveness of a water pool in thermally stabilizing a molten-core/concrete interaction and cooling of ex-vessel core debris. The experiments involved corium inventories of 75 kg with a melt depth of 15 cm and diameter of 30 cm. The corium was composed of UO2 /ZrO2 /concrete to simulate mixtures of molten reactor core components and either siliceous or limestone/common sand (LCS) concrete. Initial melt temperatures were of the order of 2100 ◦ C. The heat transfer rate from the corium was determined through measurements of the vapor production rate from the water pool. The melt was quenched at atmospheric pressure for the first two tests and at 4 bar for the two subsequent tests. Preliminary data analysis indicates that the overall heat transfer rate exceeded the conduction-limited rate for the three melts containing 8 wt.% concrete, but not for the fourth, which had 23 wt.% concrete. Also, the quench rate of the 8 wt.% concrete melts did not vary appreciably with pressure. © 2006 Published by Elsevier B.V.
1. Introduction The ability to adequately cool molten-core material (“corium”) by an overlying water layer, whether located within the reactor pressure vessel or on the containment building floor, remains an unresolved issue. For “ex-vessel” accident sequences, in which the RPV fails and corium is released into the containment, sufficient cooling would halt erosion of the basemat and prevent fission product release into the environment. Because of the complexity of the interactions, the quenching of ex-vessel melts is a process that is not yet well-understood. Experiments are being performed as part of an OECD-sponsored program to quantify the cooling rate of ex-vessel melts flooded from above and to measure concrete basemat ablation rates under prototypical conditions. The quenching of corium involves removal of both the melt sensible energy and the fission product decay heat. The most
∗
Corresponding author. Tel.: +1 630 252 1144. E-mail addresses: [email protected] (S. Lomperski), [email protected] (M.T. Farmer). 0029-5493/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.nucengdes.2006.03.041
effective source of cooling is water. However, the mode of contact between water and the melt strongly influences the corium cooling rate. A variety of mechanisms exist through which the surface area available for heat transfer is increased and the cooling rate enhanced. Such mechanisms include: (i) the formation of cracks and fissures in the solidified, insulating “crust” that forms as the corium cools, (ii) crust breaches, in which the crust ruptures to such an extent that water and melt are brought back into direct contact, and (iii) melt eruptions, where gas entrains melt up through the crust into direct contact with coolant. This paper describes the results of experiments concerned with the first mechanism. Specifically, the experiments were designed to detect and measure the enhancement of heat transfer due to crack formation within the crust of an ex-vessel corium melt. The tests described in this paper investigated how the cooling rate is affected by the concrete mass fraction of the melt, the concrete composition, and the system pressure. They will be used as a baseline for comparison of future tests with melts of differing concrete composition and mass fraction. This paper begins with a brief discussion of the water ingression phenomenon, followed by a description of the test apparatus and experimental results.
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Nomenclature Ac Act cp g hfg m ˙ P q qc Q t
surface area of corium (m2 ) cross-sectional area of condensate tank (m2 ) specific heat (J/kg K) gravitational constant (9.8 m/s2 ) heat of vaporization of water (J/kg) mass flow rate (kg/s) pressure (N/m2 ) heat flux (W/m2 ) corrected heat flux (W/m2 ) dimensionless dryout heat flux time (s)
Greek letters κ permeability (m2 ) µ viscosity (N s/m2 ) ρ density (kg/m3 ) Subscripts dry dryout f fluid g gas HL heat losses str structures sen sensible heat 1.1. The water ingression phenomenon One approach to cooling an ex-vessel melt deposited upon the containment basemat is to flood it from above. Initially, energy is removed from the melt via bulk cooling, which is characterized by heat transfer to the overlying water layer through both convection and radiation with mixing of the melt by natural convection. With further cooling, precipitates form within the melt so that the bulk cooling involves a mixing of both solids and liquids. Eventually, either a critical solid fraction or surface temperature is reached and a crust forms at the melt surface. The crust then divides the water from the yet-molten corium below. Because of its low conductivity, the crust can restrict heat transfer between the melt and water layer and greatly retard further cooling. The minimum, conduction-limited heat transfer rate through the crust can be calculated from a well-known analytical solution. However, the actual heat transfer rate from the melt to the water layer is expected to be greater than the conductionlimited rate due to cracks and voids that form within the crust as it cools. Such a porous crust provides pathways for liquid to penetrate downwards, where it can provide additional cooling through a boiling mechanism. This liquid transport through a permeable crust towards the freezing front is known as “water ingression”. The degree of enhanced heat transfer due to water ingression is difficult to predict analytically because of the strong dependence of the water ingression rate on the crust morphology. The percolation of water down through the cracks and voids coin-
Fig. 1. Elapsed time to quench corium at various heat fluxes.
cides with a counter current steam flow generated by boiling. The water flow and effective heat removal rates vary strongly with the crust morphology, which is determined by the chemical composition, cooling rate, and mixing mechanisms such as sparging by concrete decomposition gases. Thus it is critical to use prototypical materials so that the quench process forms a crust having a realistic permeability and cooling rate. Sparging gases are, however, excluded from the experiments described in this paper so that water ingression and enhanced cooling due to thermallyinduced cracking can be studied in isolation. Sparging gases may have either a positive or negative influence on heat removal rates and their study is left to future experiments.The basic premise of the current experiments is to measure the heat flux from the melt to the overlying water layer, compare it to the analytical solution, and then determine the extent to which water ingression enhances cooling of the melt. Fig. 1 is a plot of the analytical solution for transient cooling of a semi-infinite slab by conduction following a step change in surface temperature (Ozisik, 1980). In this case, the initial slab temperature is 2100 ◦ C and the transient is initiated by setting the surface temperature to 100 ◦ C. The model is one-dimensional and so multi-dimensional effects such as heat losses are disregarded. The relevant thermo-physical properties for this calculation are the corium thermal conductivity, density, and specific heat, which were set to 1.5 W/m K, 7000 kg/m3 , and 660 J/kg K, respectively. Fig. 1 shows how the conduction-limited heat flux drops rapidly during the early phase of the transient and then, at a reduced rate, diminishes asymptotically towards zero. In contrast, for a porous crust, the heat transfer rate may at some point exceed that given by the conduction solution and thus diverge from the conduction-limited curve after initially tracking it. The divergence is a consequence of enhanced heat removal via the vaporization of liquid that has percolated down through pathways within the crust. The point where the two cooling rates diverge can be thought of as the limiting heat removal rate from the porous material though the boiling process. This limit is often referred to as the “dryout” heat flux and it has been studied experimentally for porous media such as particle beds (see, for example Atkhen and Berthoud (2003), Hu and Theofanous (1991) and Miettinen et al. (2002)). The three dashed curves in
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Fig. 1 represent hypothetical levels of the dryout heat flux. Such plateaus would be observed if the rate of heat removal from the melt remained fixed at the dryout heat flux level. In practice, however, even with water ingression-enhanced cooling, the heat removal rate is expected to decline over time as the melt cools and the crust thickens. The decline is due, in part, to diminishment of the rate of convective heat transfer between the melt and crust as the former cools. There may also be a decline in the effectiveness of the water ingression mechanism over time since pathways for water percolation to the melt quench front lengthen as the crust thickens. These phenomena are excluded from the idealized curves in Fig. 1, which are intended only to illustrate the enhanced cooling that might be achieved through the water ingression mechanism and the associated acceleration of the quench process. The end points marked for each curve indicate the approximate time at which a 15 cm deep melt is entirely quenched, i.e. cooled to 100 ◦ C, for the selected dryout heat flux levels. The calculation considered the energy removed from the melt up to the moment when the heat flux departed from the conduction-limited solution. The length of the dashed line represents the time necessary to remove the residual energy of a 15 cm melt at the given dryout heat flux. The graph illustrates the extent to which differing levels of dryout heat flux shorten the time to quench compared to conduction-limited cooling. Many models and correlations have been developed to predict dryout heat fluxes for porous beds. Some of the models presume dryout limits to be governed by a counter-current flow limitation in which the drag forces between vapor and liquid limit the cooling rate of the bed (Ostensen and Lipinski, 1981). Other models are based on Darcy’s law, which describes flow that is limited by drag forces between the particles of the bed and the gas and vapor. One such model provides an expression for the dryout heat flux of a deep bed in terms of a dimensionless dryout heat flux Q (Jones et al., 1984): qdry =Q
κρg hfg (ρf − ρg )g µg
(1)
where hfg is the latent heat of vaporization, ρ the density, µ the viscosity, g the gravitational constant, and κ is the permeability of the porous medium. The dimensionless heat flux is a function of the kinematic viscosity ratio of the vapor and liquid along with the model chosen for the specific permeabilities of the liquid and vapor. For water and steam in the pressure range of 1–4 bar, the range of interest for this study, estimates of the dimensionless heat flux cited in the Jones study vary between roughly 0.1 and 0.8. Though this wide range for Q produces a correspondingly wide range of estimates for the dryout heat flux, the Jones model clearly illustrates some trends expected for the experiments. From the above relation it is seen that an increase in the crust permeability augments the dryout heat flux, which in turn increases the melt quench rate. The Jones model also predicts an increase in heat flux with pressure due to an increase in steam density that permits higher mass flow rates through cracks and pores. Other, more sophisticated dryout models, as well as experimental findings, also indicate that the dryout heat flux increases with pressure (see, e.g. Jakobsson et al. (1983)).
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Experimental investigations of dryout heat flux typically involve measurements of cooling limits for columns of heated particles or small spheres imitating, in part, core material debris beds that may exist following a hypothetical reactor accident. Test data for particle beds can be represented by a variety of models, such as those based on Darcy’s law (e.g. Hardee and Nilson (1977) or Jones et al. (1984)) or counter current flow limitations (Ostensen and Lipinski, 1981). However, some reactor accident scenarios involve a generally contiguous melt rather than a collection of particles. In this case, mechanisms that create porous structures within the melt can determine the limit of melt coolability and so, ideally, the processes of melt cooling and pore formation would be combined in the study of dryout heat flux and the limits of corium cooling. A relevant and comprehensive study of the cooling of hot rock by water penetration was conducted by Lister (1974), who examined cracking mechanisms that open up pathways for water percolation down into geological formations. His model envisions a cracking front that advances downwards as molten rock solidifies and then fractures under stresses generated by thermal contraction. The amount of cracking, and hence the rock permeability and rate of advance of the front, is dependent upon thermo-physical properties of the rock and temperature gradients in the region near the cracking front. Lister’s view of the cooling of molten rock appears compatible with the quenching of a contiguous corium melt. The experiments reported here are used to examine the influence of corium thermo-physical properties on cracking behavior and permeability, and how they influence the melt cooling rate. The properties are varied by altering the amount and type of concrete in the melt, which corresponds to variations in the elapsed time after a melt enters the reactor cavity and different reactor containment basemat compositions. Other trends, such as the predicted increase in dryout heat flux with pressure, are examined by conducting selected experiments with system pressures above ambient pressure. 2. Test apparatus A facility was constructed for the purpose of producing corium melts with a precisely-defined geometry and chemical composition while ensuring confinement during quenching at elevated pressure. The reaction vessel (RV) lower plenum consists of a 67 cm long, 46 cm (18 in.) outer diameter carbon steel pipe (Fig. 2). The pipe is insulated from the melt by a 6 cm thick liner of cast MgO. An MgO “basemat” insulates the RV lower flange and spans the entire inner diameter of the pipe. The MgO liner sits on top of the basemat and the two insulators form the crucible that holds the corium. This geometry produces a 30 cmdiameter melt (surface area of 707 cm2 ). The system is designed to produce melts of up to 100 kg at 2500 ◦ C and the RV is rated for a pressure of 7.7 bar. This small-scale facility has been designated SSWICS (small-scale water ingression and crust strength). The latter portion of the term refers to complementary tests in which the solidified corium ingot is mechanically loaded to measure the fracture strength of the crust. The corium itself is produced by an exothermic chemical reaction of a powder comprised of oxides and metals that react
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Fig. 2. Reaction vessel (dimensions in mm).
with an oxidizer (collectively referred to as thermite). The thermite consists mainly of U3 O8 , zirconium metal and the oxidizer CrO3 , which react together to produce the UO2 and ZrO2 that are the main components of a corium melt. It also includes other materials, such as silicon and aluminum, to produce the desired corium/concrete mixture. The thermite components are apportioned by considering both the net heat of reaction and the final melt composition. The chemical reaction generating the melt must produce both the desired corium composition and the target initial temperature. For the first three tests, the thermite was formulated to produce corium containing 8 wt.% concrete constituents, which accounts for the concrete erosion expected during the corium spreading phase after a breach of the RPV (Sienicki and Spencer, 1986). The RV upper plenum consists of a second section of pipe with inlets for the water supply and an outlet for steam produced by the quenching process. The outlet leads to a 10 cm diameter line that transports steam from the quenching melt to a tube-intube heat exchanger (Fig. 3). The water-cooled heat exchanger condenses the steam, which is collected within a 200 cm high, 20 cm diameter condensate tank (CT). Measurements of the time-varying CT inventory provide an indirect measurement of
the steam flow rate from the RV, which is then used to determine the corium cooling rate. Melt temperatures are obtained with tungsten–5% rhenium (type-C) thermocouples mounted on the RV flange below the basemat. Two single-junction thermocouples with tantalum sheathes were used in the first pair of tests. The measurement junctions were located 20 mm above the bottom of the melt. In tests 3 and 4, multi-junction (4) thermocouples were employed and they were enclosed in tungsten thermowells to prolong their operating lives and allow them to extend further into the melt (100 mm). For all tests, two type-C thermocouples in the basemat were positioned near the bottom of the melt to detect arrival of the quench front, which is indicated by temperatures falling to the steam saturation temperature. The tips of these thermocouples rested against the underside of a ZrO2 insulating board that was protected from direct contact with the corium by a thin tungsten plate (see Fig. 2). The melts for tests 3 and 4 were quenched at a pressure of 4 bar absolute to study the effects of pressure on cooling rate. A control valve in the steam line was used to regulate the RV pressure. The RV structures and quench water supply were preheated to ∼100 ◦ C to reduce the effects of heat sinks early in the quench
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Fig. 3. Schematic of water ingression test facility.
process (these preheating systems were not yet in place for the first two tests at ambient pressure). 3. Test results 3.1. Overview Four water ingression experiments with the SSWICS facility have been completed. For the first three tests, the melt mass was 75 kg and composed of a fully oxidized PWR melt containing 8% concrete decomposition products. The amount of concrete was increased for the fourth test to 23 wt.%. Three of the melts contained limestone/common sand concrete and the fourth was made with siliceous concrete. The melt depth for all tests was about 150 mm. Water injection into the RV typically began about 2 min after thermite ignition and lasted less than 10 min, producing an initial water layer of about 0.5 m. A summary of the test parameters is provided in Table 1. Figs. 4–7 are plots from selected tests (2 and 3) intended to illustrate the typical course of both low and high pressure tests. Fig. 4 shows the measured melt temperatures. In the legends, TM indicates that the thermocouple was within the melt while TI refers to those near the interface between the melt and base-
mat. The term H# signifies the height above the bottom of the melt (in mm) and the remaining term corresponds to the radial position. For all plots, the time t = 0 is defined as the moment when thermite ignition was first detected by an initial rise in the gas temperature of the RV upper plenum. The plotted data for some sensors does not extend the full length of a test due to corrosion-induced failure. Such data has been truncated at the points where sensor failures were evident. The pyrometer trace ends where the sensor reached its lower range limit of 1200 ◦ C. Once the thermite was ignited, the chemical reaction proceeded quickly through the entire charge and the measured melt temperatures peaked within about 10 s of their initial rise. The temperatures then fell as energy was lost to the MgO crucible and subsequently recovered as conductive and convective heat transfer from the center of the melt reheated the periphery. The measured temperatures plateaued for several minutes before declining as the melt was quenched. The plateau is used to establish the initial bulk melt temperature, the accuracy of which is estimated to be of the order of 100 ◦ C. The pyrometer readings in test 2 confirm that this is a satisfactory method for establishing an initial melt temperature. The pyrometer, which was located near the melt center (H100 and depth of 50 mm), peaked
Table 1 Selected test parameters Parameter
1
2
3
4
Test section i.d. (cm) Melt composition (UO2 /ZrO2 /Cr/concrete) (wt.%) Concrete type Melt mass (kg) Melt depth (cm) Initial melt temperature (◦ C) System pressure (bar) Water injection flowrate (l/m) Water injected (l) Initial water/structure temperature (◦ C)
30.5 61/25/6/8 LCS 75 15 ∼2300 1 4 55 ∼20
30.5 61/25/6/8 SIL 75 15 ∼2100 1 4 39 ∼20
30.5 61/25/6/8 LCS 75 15 ∼2100 4 12 34 ∼100
30.5 48/20/9/23 LCS 60 15 ∼2100 4 13 40 ∼100
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Fig. 4. Melt temperatures for (a) test 2 at 1 bar and (b) test 3 at 4 bar. Fig. 5. Liquid inventories for (a) test 2 at 1 bar and (b) test 3 at 4 bar.
2140 ◦ C.
40 ◦ C
at This is within of the temperature estimated with the thermocouples. Fig. 5 provides plots of the liquid inventories of the RV and condensate tank along with the amount of water injected into the RV. The latter was calculated by integrating the measured injection flow rate (F-quench in Fig. 6). The RV liquid inventory was calculated with a mass balance using the integrated flow and the measured CT inventory. Calculations confirm that for each test the melt was water-covered for the entire test duration. Fig. 6 shows the measured total pressure in the reaction vessel (PA-RV) and also the injection flow rate (F-quench). For the low pressure tests, the flow rate is lower and the injection period longer than for the high pressure tests. However, the total amount of water injected is similar for all tests. In the low pressure tests, the RV pressure began near ambient and then was pulled slightly below atmospheric pressure by the heat exchanger. The set-point pressure for the high pressure tests was 4 bar, which was maintained within 0.1 bar after the initial rise to the set point and a short settling period. The dip in pressure at 6000 s is due to a second, brief water injection. The flow rate was below the flow meter threshold and does not appear in the trace of F-quench. 3.2. Corium heat flux The main objective of each water ingression test is to determine the heat flux through the corium surface. A first order
estimate of the heat flux can be obtained by assuming that all cooling contributes directly to the production of steam, all of which reaches the heat exchanger, is condensed, and then deposited within the condensate tank. In this case, the heat of vaporization is used to directly calculate the heat flux through the melt surface: q =
m ˙ g hfg Ac
(2)
where m ˙ g is the steam mass flow rate out of the RV, hfg the heat of vaporization of water, and Ac is the surface area of the corium (0.071 m2 ). The steam mass flow rate is equal to the condensate collection rate, which is determined through P measurements, and so the heat flux can be written as: q =
Act ∂ P hfg Ac ∂t g
(3)
where Act is the cross-sectional area of the CT, P the measured differential pressure, and t is the time. The derivative was calculated with pairs of averaged P readings (an average of five measurements recorded at 0.5 Hz) centered around a t of 60 s. The averaging and large t are necessary because the water level in the CT increases slowly and even small fluctuations in the P produce large changes in the calculated heat flux.
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Fig. 7. Corium heat flux as measured by rate of condensate collection for (a) test 2 at 1 bar and (b) test 3 at 4 bar. Fig. 6. RV pressure and injection flow rate for (a) test 2 at 1 bar and (b) test 3 at 4 bar.
The heat flux determined with Eq. (3) is plotted in Fig. 7 for tests 2 and 3 (key data from these tests is protected by a proprietary agreement, which requires use of an arbitrary heat flux scale). The vertical scale limits are the same for each plot so that the magnitude of the heat fluxes can be directly compared. The off-scale peaks early in the test are due to strong heat transfer and steam production when water initially meets the yet-molten surface of the corium. The steam flow rate subsequently declines as the surface cools and the water pool depth increases. The continued addition of subcooled water eventually suppresses boiling towards the end of the injection phase, which, using Eq. (3), appears as a drop to near-zero heat flux. Once water injection is completed, boiling resumes and steam flow reaches a second, lower peak and gradually declines as the melt cools. The comparatively large heat flux oscillations of the high pressure test are due to pressure variations produced by position adjustments of the pressure regulating valve. Though the pressure fluctuations were small, the constantly changing valve position produced variations in the steam flow rate to the heat exchanger, which appear as substantial swings in the measured heat flux. Eq. (3) provides only a first order estimate of the heat flux because energy transfer to several heat sinks has been neglected. During the water injection phase of a test, energy is absorbed by the coolant as it is heated to the saturation temperature. Also, early in the transient, steam condenses on relatively cold
RV structures until they reach the saturation temperature. Both these effects reduce the amount of steam reaching the condenser and thus the apparent heat flux. Heat losses from the RV to the ambient also reduce steam flow to the condenser. The following expression provides the corrected heat flux qc , which accounts for the heat sinks: qc =
1 [m ˙ g hfg + Qsen + Qstr + QHL ] Ac
(4)
where Qsen is the rate of sensible energy deposition into the coolant, Qstr the rate of energy absorption by the RV structures due to steam condensation, and QHL represents heat losses from the RV. Steam superheating, which may occur in the first seconds of water injection, has been neglected. The corrections for structure and coolant sensible heat are significant only during the early phase of the transient. The heat flux is corrected using the net energy absorbed by the structures and coolant in heating them to the saturation temperature. The heat transfer rate from the melt to the heat sinks was approximated with a simple linear function that distributes the net energy absorbed by the heat sinks over the course of the injection phase. Measurements of structure temperatures indicate that heating is spread over a somewhat longer period, but this approach has the advantage of clarity since it restricts all corrections to the period before steam flow recovery. The net energy deposition into the structures was calculated using the total heat capacity of the test vessel structures and the difference between the ambient and steam saturation temperatures. The sensible energy added to the
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calculated using the difference between the initial melt temperature and the saturation temperature, and by assuming a mean heat capacity of 660 kJ/kg K. This measure of melt energy is most accurate after a short period following water injection, when heat transfer rates to the heat sinks are insignificant. The plots show the melt energy at test end to be near zero for both tests, as expected. Note that even though test 3 was considerably longer than test 2, a similar amount of energy was removed after an elapsed time of 4300 s, which marked the end of test 2. The length of a particular test is not a good indicator of the average heat removal rate because the basis for terminating a test (thermocouples beneath the melt reaching the saturation temperature) envisions a one-dimensional system with a quench front propagating down towards the bottom of the melt. In actuality, the melt cools from all sides so that at test-end the hottest region may be closer to the center of the corium than the bottom. Thus a temperature sensor near the base of the melt can provide only an approximate indication of when the melt has been fully quenched. 4. Comparisons with conduction-limited cooling
Fig. 8. Corrected heat flux and net melt energy for (a) test 2 and (b) test 3.
water was calculated in a similar fashion using the integrated flow and measured liquid temperature near the injection point. The function is defined so that heat transfer to the sinks reaches zero as steam flow recovers, and it is scaled using the corium sur , has face area. The heat flux associated with the heat sinks, qsink been plotted to mark the interval defined as the injection phase and to allow a comparison between dissipated melt energy associated with steam flow to the HX and energy absorbed by the heat sinks. The correction has been treated in an approximate fashion because the heat sink effects are significant only early in a test, which is not the period of focus for these experiments. Moreover, an accurate determination of heat transfer rates to the heat sinks requires substantially more temperature sensors than were available for these tests. The main purpose of correcting for the heat sinks is to provide an indication of the melt energy during the intermediate and late phases of the test. The thermal energy available for steam production declines towards zero as the melt temperature approaches the saturation temperature and so a plot of melt energy versus time serves as a crosscheck of the calculations. The corrected heat fluxes for tests 2 and 3 are shown in Fig. 8 (the vertical scale ranges again match for direct comparisons). The corrected heat flux was integrated and subtracted from the initial melt energy to obtain the net melt energy versus time, which is included in the figures. The initial corium energy was
The existence of enhanced cooling due to water ingression is identified by comparing the measured corium heat flux with the conduction-limited solution. The one-dimensional model described earlier provides a rough estimate of the conductionlimited heat flux through the corium surface. However, such a model fails to account for the lateral and axial heat losses that are present during the experiment. Inclusion of these heat losses is necessary to find the conduction-limited heat flux that corresponds to the actual experimental conditions so that a meaningful comparison between the measured and conduction-limited heat fluxes can be made. A 3D model of the RV lower plenum was constructed using the graphical modeler SINDA/3D (Network Analysis Inc.), which is a CAD-type program for creating models and a processor for the finite-difference analysis thermal analyzer SINDA/G. Fig. 9 depicts the model created for the RV, which has been reduced to a 1/8th-size slice of the lower plenum using symmetry. The model was simplified further by omitting regions that have little influence on heat losses, such as the mating lower flange (welded around the pipe) and all portions of the lower plenum that are more than 50 mm above the corium surface. The corium itself was treated as a solid block of material that excludes the effects of convective heat transfer from mixing during the bulk cooling phase, and also later in the transient when the corium consists of a stable crust overlying a liquid or slurry mixed by natural convection. Mixing enhances heat transfer to the underside of the crust thereby increasing the overall corium cooling rate compared to the conduction solution. However, this is expected to have a 2nd order effect on the cooling rate because of the high thermal resistance of the crust. In addition, natural convection mixing below the crust is thought to have a much smaller influence on the corium cooling rate than the lateral conduction losses that are being calculated with this 3D model. A representative calculation is presented here for comparison with the measured heat fluxes of all four tests. The initial melt
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Fig. 10. Measured heat fluxes and calculated conduction-limited heat flux.
Fig. 9. Model of reaction vessel lower plenum (dimensions in cm).
and structure temperatures were set to 2100 and 20 ◦ C, respectively. The thermodynamic properties used for the corium are the same as those described for the 1D model in Section 1. The heat capacity of 660 kJ/kg K is an average value calculated from the enthalpy change between the initial and final melt temperatures, which therefore incorporates the heat of fusion. The melt depth is 15 cm and the heat transfer coefficient from the surface of the corium to the water pool was set to 10 kW/m2 K. The latter parameter is not critical because, soon after the transient begins, heat transfer through the corium surface is limited primarily by the poor conductivity of the corium rather than the heat transfer coefficient. The boundary conditions at the outer surface of the RV wall and flange are of particular importance because they control the lateral and axial heat losses. These are significant since the associated surface area is greater than that of the corium/water interface while the thermal conductivities of the MgO and corium are comparable. During the experiment, the outer surface of the RV lower plenum is uninsulated and so specifying a natural convection heat transfer coefficient could be expected to suffice. However, the actual construction of the lower plenum differs slightly from that of the simple model shown in the figure: a narrow gap exists between the liner and the RV wall. An examination of measured structure temperatures suggests that water and/or steam is present within the gap and so the outer surface of the liner is cooled by water and/or steam. Some water may also seep between the basemat and the flange. For the present calculations, the heat losses through the liner are modeled by assuming a vessel wall heat transfer coefficient of 1 kW/m2 K to a sink temperature of 100 ◦ C (cooling of the liner by steam and saturated water). Heat losses through the basemat are assumed to be caused primarily by conduction to the flange (water seepage is neglected) and are modeled with a flange heat transfer coefficient of 2.5 W/m2 K to a sink temperature of 20 ◦ C.
Fig. 10 shows the result of the calculation, which is plotted along with heat flux data from all four tests for comparison. The data is uncorrected and plotted on an expanded vertical scale that omits the early peak in heat flux after quenching is initiated. Attention is directed to the period after about 1000 s, when energy loss to heat sinks is minor. Based on this collection of data, the following four observations relevant to the water ingression cooling mechanism are drawn: 1. For tests 1–3, the measured heat flux exceeds the conduction limit during the early and intermediate phases of each test. Towards the end of a test, the measured heat flux fell below the conduction limit, which would be expected since most of the melt energy was removed earlier. In addition, plateau-like features are evident in the curves for tests that used corium with 8 wt.% concrete, as would be expected if water ingression was active during the quench process (see Section 1.1 and Fig. 1). This collection of information indicates that water ingression is an active cooling mechanism for corium containing nominally 8 wt.% concrete. 2. Based on the consistency of the peak heat fluxes after 1000 s, the water ingression cooling rate for corium containing either siliceous and limestone/common sand concretes appears to be similar under the condition in which the corium concrete content is the same. 3. Comparison of the results for tests 1 and 3, in which the melts were of the same composition but quenched at different pressures, indicates that system pressure has little effect on the water ingression rate. This is an unexpected finding since, according to Eq. (1), the dryout heat flux is expected to increase with pressure by roughly a factor of two. Other studies, both analytical and experimental, have predicted significant increases in the dryout heat flux with pressure (Jakobsson et al., 1983). The increase, however, is less pronounced for the beds with smaller particle size, which may indicate that the effective pore size within the corium for the water ingression experiments is very small. If so, the dryout
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heat flux is likely to be set by flow resistance of the crust rather than a counter current flow limitation. 4. For the fourth test, which had the highest melt concrete fraction, there is no apparent plateau in the heat flux, as would be expected if water ingression contributed significantly to cooling. Moreover, the overall asymptotic decline in the heat flux is quite similar to the conduction-limited solution. Finally, the heat flux exceeds the calculated conduction limit by only ∼40%, which aside from thermo-physical property uncertainties, could be accounted for by uncertainty in the lateral heat losses through the MgO crucible. This collection of information indicates that water ingression does not significantly augment the debris cooling rate for corium containing around 23 wt.% limestone/common sand concrete.
sured heat flux of the melt containing 8 wt.% limestone/common sand concrete is similar to that of the melt containing the same amount of siliceous concrete. The effect of pressure on heat flux was also investigated and it was observed that the there is little difference between the melts quenched at 1 bar and at 4 bar. The melt with 23 wt.% concrete, quenched at 4 bar, cooled more slowly than the melts with less concrete. The SINDA/G calculations with a model of the RV indicate that the melt with 23 wt.% concrete cooled at a rate that is close to the expected rate for conduction-limited cooling. In contrast, the three melts with 8 wt.% concrete cooled at a rate that is significantly higher than the conduction-limited rate.
Note that the comparison between the data and the calculated conduction-limited heat flux is inexact because some boundary conditions required for the thermal model are not well known. The existence of a gap between the liner and the RV wall results in uncertainty in the heat transfer rate at the liner surface and the corresponding lateral heat losses. Heat losses are greatly increased when the liner is cooled by surface boiling rather than pure conduction through the RV wall and natural convection air cooling at the RV surface (the ideal case without a gap). In addition, such boiling would add to steam production and, through the collected condensate, contribute to the apparent heat flux. Supplementary instrumentation in subsequent tests and additional calculations will be used to determine the appropriate boundary conditions for a more accurate calculation of the conduction-limited heat flux. Nevertheless, despite this uncertainty in the heat losses, these test results provide an indication of the range and extent to which water is able to ingress into corium during cool-down and augment the conduction-limited cooling rate. They also furnish clear comparisons of the relative melt cooling rates for various corium compositions and system pressures. As part of the program, models are being utilized to assess the extent to which the water ingression cooling mechanism, as well as the other mechanisms under investigation in the program, are able to mitigate (and possibly terminate) the course of core–concrete interaction (e.g. see Farmer et al. (2000)).
This work has been sponsored by the Organization for Economic Cooperation and Development (OECD). Participating countries include Belgium, Czech Republic, Finland, France, Germany, Hungary, Japan, Norway, South Korea, Spain, Sweden, Switzerland, and the United States of America. This support is gratefully acknowledged.
5. Conclusion The first four tests with the SSWICS water ingression facility have been successfully completed. The experiments were used to measure the quench rates of fully oxidized PWR melts containing 8 and 23 wt.% concrete at pressures of 1 and 4 bar absolute. The melts were 15 cm deep, ranged in mass from 60 to 75 kg, and had an initial temperature of the order of 2100 ◦ C. The mea-
Acknowledgements
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