Simulation of Ex-Vessel Steam Explosion in PWR Reactor Cavity

Transcription

1 International Conference Nuclear Energy for New Europe 005 Bled, Slovenia, September 5-8, 005 Simulation of Ex-Vessel Steam Explosion in PWR Reactor Cavity ABSTRACT Matjaž Leskovar, Boštjan Končar, Leon Cizelj Jožef Stefan Institute Jamova 9, SI-000 Ljubljana, Slovenia An ex-vessel steam explosion may occur when during a severe reactor accident the reactor vessel fails and the molten e pours into the er in the reactor cavity. A steam explosion is a fuel coolant interaction process where the heat transfer from the melt to er is so intense and rapid that the timescale for heat transfer is shorter than the timescale for pressure relief. This can lead to the formation of shock waves and production of missiles at later times, during the expansion of the highly pressurized er our, that may endanger surrounding structures. The purpose of the paper is to give an insight of the steam explosion phenomenon in a typical PWR cavity, to provide a rough estimation of the expected pressure loadings on the cavity structures during a steam explosion, and to assess the vulnerabilities of the cavity structures to steam explosions. To achieve this a fit-for-purpose steam explosion model was developed, followed by a comprehensive and reasonable conservative analysis. The multiphase flow in the reactor cavity during the high-pressure premixture expansion was simulated with the CFD code CFX-5.7. and the stresses in the reactor cavity walls were determined with the stress analysis code ABAQUS/Explicit. INTRODUCTION One of the most important remaining issues in e melt progression during a severe accident in a nuclear power plant are the likelihood and the consequences of a steam explosion, which may occur when the hot e melt comes into contact with the coolant er. A steam explosion is a fuel coolant interaction process where the heat transfer from the melt to er is so intense and rapid that the timescale for heat transfer is shorter than the timescale for pressure relief. This can lead to the formation of shock waves and production of missiles at later times, during the expansion of the highly pressurized er our, that may endanger surrounding structures [,, ]. A steam explosion is a complex, highly nonlinear, coupled multi-component, multi-phase, multi-space-scale and multi-time-scale phenomenon. Consequently modelling of steam explosions is a difficult task and the uncertainties of reactor simulations performed with steam explosion codes based on modelling fundamental steam explosion processes are still large. Therefore for assessing the vulnerability of reactor cavity structures to an ex-vessel steam explosion a parametric approach capturing the uncertainties in steam explosion understanding and modelling is needed. For this purpose a simple, easy to apply parametric steam explosion model was developed, which can be straightforwardly implemented also in the general CFD codes. The main purpose of the performed study is to give an insight of the steam explosion 0.

2 0. phenomenon in a typical PWR cavity, to provide a rough estimation of the expected pressure loadings on the cavity structures during a steam explosion, and to assess the vulnerabilities of the cavity structures to steam explosions. The steam explosion was modelled as an expanding high-pressure premixture of dispersed molten fuel, liquid er and our in the partially flooded reactor cavity. The multiphase flow during the high-pressure premixture expansion was simulated with the CFD code CFX-5.7. [4] and the stresses in the cavity walls were determined with the stress analysis code ABAQUS/Explicit [5]. STEAM EXPLOSION PHENOMENON Steam explosions are a subclass of what is called Fuel Coolant Interactions (FCI) in safety studies of nuclear reactors. Based on the phenomena occurring during a steam explosion it can be divided into four consecutive phases: the premixing phase, the triggering phase, the propagation phase and the expansion phase (see Figure ). Coolant Premixing phase Triggering phase Propagation phase Expansion phase Vapour film Molten fuel Figure : Schematic presentation of the four consecutive phases of the steam explosion. In the premixing phase a coarsely mixed region of molten ium and coolant er is formed. The melt and er are separated by a our film, so the heat transfer between the melt and er is relatively low. The premixing phase is characterized by a steam production rate at a timescale of the same order as the timescale of the melt pouring rate. It results in a slow pressurization of the system, or even not, if condensation is able to balance orization. The system can remain in this metastable state till the melt is quenched or till a steam explosion is triggered if the conditions are appropriate. The timescale of the premixing process is in the range of seconds, and the length scale of melt particles is in the range of centimetres. In the triggering phase the steam explosion is triggered. The triggering event is a disturbance, which destabilizes the our film around a melt particle allowing liquid-liquid contact, which leads to locally enhanced heat transfer, pressurization and local fine fragmentation. Many reasons can cause the our film destabilization, including pressure pulses resulting from different impacts (in experiments interactions are often triggered when the melt reaches the bottom of the tank), transition from film boiling to nucleate boiling, and er entrapment at melt-structure contact. During the propagation phase, there is an escalation process resulting from the coupling between pressure wave propagation, fine fragmentation, and heat transfer after the trigger event. The pressurization induced by the trigger destabilizes the surrounding our films, leading to the fine fragmentation of the surrounding melt. Early in the process fine fragmentation results from local liquid-liquid contacts after the our film destabilization. Locally, some coolant is rapidly heated and pressurized, and this causes some fine fragmentation of the surrounding melt. This type of fragmentation is often called thermal fragmentation. Later, when the pressure is already high, the fine fragmentation is believed to be of a hydrodynamic nature owing to the relative motion between the melt and the coolant induced by their different densities and compressibilities. The fine fragmentation propagates at a velocity, which depends on the

3 0. conditions in the premixing region. It can be governed by timescales responding to the propagation of disturbances in the premixing region, resulting in sequential ignition of the mixture. Typical velocities in this case are of the order of some tens of meters per second. In this case, the pressurization of the system is relatively limited, slow and uniform, without generation of shock waves. But the fine fragmentation can escalate also up to reaching supersonic velocities in the premixture and quasi steady state propagation. Depending on the conditions, the premixture can burn more or less completely before the system can expand, thus creating a zone of high pressure. During the propagation phase the thermal energy of the melt is converted into thermal energy of the coolant. The timescale of the explosion propagation process is in the range of milliseconds, and the length scale of the fine fragmented particles is in the range of hundreds of micrometers. During the expansion phase the thermal energy of the coolant is converted into mechanical energy. The expansion of the high-pressure premixture of dispersed molten fuel, er and our against the inertial constraints imposed by the surroundings determines the damage potential of the steam explosion. If the locally high pressures are quickly relieved, then they may not damage the surrounding structures, but the kinetic energy transmitted to the materials around the interaction zone may be the damaging agent. MODEL. Steam Explosion Model To be able to treat the steam explosion with a general CFD code, an appropriate fit-forpurpose analytical model of the steam explosion was developed. In general, the model is based on the Hicks-Menzies thermodynamic approach [] taken into account the microinteraction zone concept [6]. Acding to the microinteraction zone concept not all coolant thermally participates in the explosion, but only the coolant, which is in the surrounding of the melt particles. In Figure the steam explosion model is schematically presented. The ium phase is denoted with the red color and the superscript, the or phase with the light blue color and the superscript and the liquid er phase with the blue color and the superscript. It was assumed that all phases share the same velocity field and the same pressure. In the presented control volume each phase is described with the phase volume fraction, volume V, density and temperature T. The microinteraction zone is denoted with the dotted blue color and the index MI. In the model it was assumed that all heat transfer from the molten fuel to the coolant occurs during the first three steam explosion phases and that during the expansion phase the generated our, which is at high pressure, adiabatically expands. An important parameter of the steam explosion is the steam explosion energy conversion ratio, which is quantified also in steam explosion experiments and reflects how much internal energy of the melt is transformed into mechanical energy of the explosion. In our model the steam explosion energy conversion ratio was used as the basis for the calculation of all other steam explosion parameters. After the conditions during the premixing phase are chosen, the pressure at the start of the expansion phase can be calculated by iteratively solving the equation p sat ( κ ) c ( T T ), p = η () κ κ p p where η is the steam explosion energy conversion ratio, κ the ratio of the or specific heat sat at constant pressure and at constant volume, c the ium specific heat, the er T

4 saturation temperature and microinteraction zone the expansion phase MI p 0.4 the containment pressure. The volume fraction of the, which determines the or volume fraction at the beginning of = + MI, was chosen so that the pressure at the start of the expansion phase p was maximized, considering the physical feasibility of the process. Due to the assumption of the adiabatic or expansion, the density of the premixture during the mix expansion process can be calculated solely as a function of pressure as where mix mix mix ( p) =, κ p + p is the premixture density at the start of the expansion phase. a) Premixing phase (index ) () b) Triggering and Propagation phase MI,V MI c) End of Triggering and Propagation phase and Start of Expansion phase (index ) d) End of Expansion phase (index ) Figure : Schematic presentation of steam explosion model (red molten e, light blue our, dark blue liquid er, dotted blue liquid er in microinteraction zone). With the developed analytical steam explosion model the initial conditions at the start of the expansion phase are determined, whereas the expansion phase itself has to be simulated with the CFD code taking into account the derived equation of state of the premixture (). A drawback of our parametrical steam explosion model is that the calculated premixture highpressure p at the start of the expansion phase depends on the chosen premixing conditions, since the same steam explosion energy conversion ratio η can be obtained with different combinations of the premixture or fraction and premixture pressure p (lower results in higher p ). But since the destructive consequences of an explosion depend mainly on the pressure impulse of the explosion (integral of pressure over time), this property of our model does not present a severe weakness for our study, since at lower due to the

5 0.5 premixture equation of state () also the duration of the pressure impulse is lower, and so the effect of the increased pressure peak is compensated. In any case, due to the large uncertainties in steam explosion understanding and modeling, enough conservatism has to be introduced in any approach. The detailed description of the steam explosion model is provided in [7].. Computational Fluid Dynamics Model The multiphase flow during the steam explosion expansion phase, consisting of three phases the premixture phase (mixture of dispersed molten fuel, liquid er and our), the liquid er phase and the air phase was simulated by the CFX-5.7. code. To simulate the pressure waves, all three fluids were treated as compressible and were modelled by the homogeneous Eulerian model, which assumes that all phases share a common velocity field. The effect of turbulences was taken into account with the k-ε turbulence model. The energy equation was not solved since the heat transfer during the steam explosion was considered already in the initial conditions, and the premixture or cooling during the expansion process was taken into account already within the adiabatic premixture equation of state (). The equation of state for er was determined using the standard er steam tables and air was treated as an ideal gas. For other material properties the default values as provided by the CFX-5.7. code were used. Since the CFD calculation did not converge on a relatively coarse numerical grid appropriate from the physical point of view, and since the required CPU times for the D calculation on a refined grid are much too long, the calculations were performed in D geometry. To assure that the D simulation results would be qualitatively and quantitatively valid also for the real D reactor cavity, the D geometry and the initial conditions had to be appropriately selected. Therefore the simulations were performed using two different D models of the D reactor cavity: the axisymmetric model, which is limited to axisymmetric phenomena in the cylindrical part of the reactor cavity directly below the reactor vessel and around it, and the D cavity model, which treats the whole reactor cavity but does not take into account the D geometry of the cavity and the D nature of the phenomena. The geometry and mesh of the D cavity model is presented in Figure. The detailed description of the computational fluid dynamics model is provided in [7].. Structural Model Based on the geometry of the problem, it is deemed sufficient to develop two models: an axisymmetric model of the cylindrical part of the reactor cavity and a D model of the ine instrumentation access. The models properly take into account the fact that the cavity walls are to a significant height embedded by the foundation of other containment structures. All the walls potentially affected by the steam explosion in the typical PWR reactor cavity are made of heavily reinforced concrete. The minimum required compressive strength of the concrete was assumed to be 0 MPa. The minimum required yield strength of the reinforcement steel was assumed to be 400 MPa. The material model used in the simulations is simplified to a significant extent and is aimed at detection of significant damage rather than to give an accurate account on the deformation history of the complex and non-homogeneous reinforced concrete. A homogeneous and essentially elastic response was therefore assumed both in tension and compression. The main effective parameters of the homogenous model assuming about 0 % (volume) of reinforcement steel were: density of 945 kg/m, Young s modulus of 45 GPa and Poisson s ratio of The yield strength of 50 MPa was arbitrarily assumed beyond the loading regime experienced in the simulation. The main

6 0.6 purpose was to enable the use of approximate damage models, which are built in the ABAQUS/Explicit code. The damage was assumed to occur with (tensile or compressive) hydrostatic pressure exceeding 50 MPa. Rector vessel L4 Opening Instrumentation part Cylindrical part L L L6 L5 L CFX Mesh of Reactor Cavity ABAQUS Mesh of Reactor Cavity Wall Figure : Geometry and mesh of CFX computational fluid dynamics D cavity model (black) and ABAQUS structural axial symmetric model (green). Loads include dead weight and pressure histories obtained from the CFX results. The variations of pressures in time and space are modelled using the FORTRAN subroutine VDLOAD. Linear interpolation between data points was used both in space and in time. The finite element model of the cavity walls for the axial symmetric model is presented in Figure. The detailed description of the structural model is provided in [7]. 4 RESULTS 4. Steam Explosion Scenario To get an insight of the steam explosion phenomenon in a typical PWR cavity, to provide a rough estimation of the expected pressure loadings on the cavity structures during a steam explosion, and to assess the vulnerabilities of the cavity structures to steam explosions, a comprehensive, reasonably conservative, parametric analysis considering different steam explosion scenarios has been performed [7]. In this paper only two typical cases differing in the location of the melt pour (side and central) are presented in some detail. In the presented cases the common assumptions are the following: Containment pressure:.5 bar, Cavity er temperature: 4 K, Water level in cavity: m, Corium temperature: 800 K, Melt pour

7 0.7 size: 0.5 m, Depressurized primary system, Premixture volume fractions: ium 0., our 0., liquid er 0.8, Steam explosion energy conversion ratio % resulting in the premixture pressure 400 bar. At experiments with prototypic ium materials (UO+ZrO, ) the maximum obtained steam explosion energy conversion ratios are about 0.5% and the maximum measured peak pressures are about 00 bar, so the assumptions are conservative regarding to these small-scale experiments. In the performed comprehensive ex-vessel steam explosion analysis, which is presented in [7], also steam explosions with a still higher energy conversion ratio of 0 %, resulting in the premixture pressure of 500 bar, are treated. Some results of the analysis of the steam explosion scenarios with an energy conversion ratio of 0 % are given in [8]. Case presents a side melt pour resulting in a premixture of width 0.5 m at the cavity end side. Case presents a central melt pour resulting in a premixture with radius 0.8 m in the cavity centre. 4. Simulation Results and Discussion To get a qualitative and quantitative picture of the multiphase flow during the steam explosion in the reactor cavity, the basic results of the CFD simulation of the steam explosion expansion phase for the side melt pour (Case ) and the central melt pour (Case ), are presented in Figures 4 and 5. On the figures the time development of the pressure field, the phase volume fractions (mixture, er and air) and the velocity field is shown. For the simulation of Case (side melt pour; Figure 4) the D cavity model, treating the entire reactor cavity in D, was used. The origin of the steam explosion at the initial time (t = 0 seconds) is indicated by the red coloured high-pressure region and by the red coloured premixture region embedded on the right side below the reactor vessel. Due to the high pressure in the mixture caused by the generated our, the mixture phase expands and pushes the er and air out of the cavity through the annulus around the reactor vessel and through the instrumentation tunnel on the left side of the cavity. As the er level rises, the er eventually hits the bottom of the reactor vessel (t = 0.0 s) causing local pressure increase in this region, pressing the vessel side- and upwards. The mixture phase expands faster towards the air since the density of air is much lower than the density of er. After s the mixture phase hits the upper part of the cavity (point L in Figure ), where the narrow annular part of the cavity begins, and the pressure there locally increases. As the pressure rapidly decreases with time, the mixture phase expands further and pushes the er towards the instrumentation tunnel. After about half a second the er level in the instrumentation tunnel reaches the opening and is discharged into the containment. The maximum fluid velocities are above 00 m/s and are reached at the outlet of the annulus at about 0.05 s. Case (central melt pour; Figure 5) was simulated using the axisymmetric cavity model, where only the cylindrical part of the reactor cavity is treated. The area indicating the origin of the steam explosion is clearly shown with the red coloured high-pressure region and with the red coloured mixture region embedded below the centre of the reactor vessel. The high-pressure in the premixing zone in the central part of the cavity causes the expansion of the mixture, which pushes the er and air through the annulus around the reactor vessel. After 0.05 s the mixture is practically completely surrounded with er, as the er can be pushed only upwards (no openings in the side walls of the cylindrical part of the cavity are modelled). After s er hits the upper part of the cavity (L in Figure ) where the narrow annular part around the vessel begins. At later times, when the pressure is already low (a few bars), the er flows back into the cavity. The maximum fluid velocities, reached at the outlet of the annulus at about 0.05 seconds, are above 00 m/s.

8 0.8 Figure 4: Pressureolume fractions of fluid phases and Velocity field in reactor cavity for side melt pour (Case ) at different times.

9 0.9 Figure 5: Pressureolume fractions of fluid phases and Velocity field in cylindrical part of reactor cavity for central melt pour (Case ) at different times. The pressure histories at selected locations, which are of importance for the assessment of the cavity structures, are presented in Figures 6 and 7. These locations are denoted in Figure with L L6. In the D cavity model the pressure curves are given for all locations L to L6 (Figure 6), whereas for the axisymmetric model the pressure curves can be given only for locations L L4 due to the limited geometry. It can be seen that the pressure reaches the highest values during the premixture high-pressure relief in the first milliseconds of the transient when also pressure shocks propagate to the walls. The pressure loads on the cavity walls at later times, which are caused by the high kinetic energy of the fluids flow, are much lower. The ABAQUS structural analysis showed that the cavity walls will not be damaged if the pressure loads on the walls in the cylindrical part of the cavity and in the in-e

10 0.0 instrument part of the cavity are lower than 400 bar and 50 bar, respectively. From Figures 6 and 7 it can be established that these damage criteria are not exceeded, so one may conclude that the cavity walls at the considered steam explosion scenarios (Case and Case ) will not be damaged. This conclusion was confirmed also with dynamic ABAQUS structural mechanical simulations, where the calculated pressure histories from the CFD simulations were applied. Further details are available in [7]. Pressure [MPa] L L L L4 L5 L Time [s] Pressure [MPa] L L L L4 L5 L Time [s] Figure 6: Pressure at selected locations as a function of time (left side: initial part of simulation, right side: full simulation) for side melt pour (Case ). Pressure [MPa] L L L L Time [s] Pressure [MPa] L L L L Time [s] Figure 7: Pressure at selected locations as a function of time (left side: initial part of simulation, right side: full simulation) for central melt pour (Case ). The upward pressure force on the reactor vessel is presented in Figure 8. The upward pressure force was calculated as the integral of the relative pressure over the reactor vessel surface in upward direction. For a typical two loop PWR the reactor vessel total restraining force is about 0 MN, calculated conservatively from the reactor vessel mass, assuming that all e has left the vessel, and the force needed to shear the cold and hot legs. In Figure 8 we see that in both considered steam explosion cases the maximum upward pressure force on the reactor vessel is much lower (Case : 50 MN, Case : 4 MN) than the conservatively estimated reactor vessel total restraining force, so the reactor vessel would not be lifted in any of these steam explosions. Since in a severe accident, that results in an ex-vessel melt pour, the reactor vessel lower head would be weakened due to its heat up and failure, the reactor vessel lower head would probably deform at high pressure loads, and so the maximum upward pressure forces on the reactor vessel are expected to be even lower than presented in Figure 8.

11 0. Force [MN] Force Time [s] Force [MN] Force Time [s] Figure 8: Upward Pressure force on reactor vessel as a function of time for Case (left side) and Case (right side). 5 CONCLUSIONS A comprehensive analysis of the ex-vessel steam explosion in a typical PWR reactor cavity was done [7]. Two typical ex-vessel steam explosion cases, differing in the location of the melt pour (side pour and central pour), are presented in some detail in this paper. A fit-for-purpose parametric steam explosion model was developed in order to be able to perform the analysis with a general CFD code. A reasonable conservative ex-vessel melt pour scenario producing a large premixture region was selected. It was assumed that the steam explosion energy conversion ratio is % resulting in the premixture pressure 400 bar. The multiphase flow during the steam explosion expansion phase for both considered cases side melt pour and central melt pour was simulated by the CFX-5.7. code. The calculated pressure loads on the cavity walls were taken as the input for the ABAQUS simulation of the stresses in the cavity walls. The pressure loads on the cavity walls and on the reactor vessel were compared against the established damage criteria. The results of the performed CFD and structural analysis show that the damage criteria are not exceeded in any of the presented two steam explosion cases. That means that at an exvessel steam explosion with an energy conversion ratio %, following a reasonable conservative assumed ex-vessel melt pour at a depressurised primary system, the reactor cavity walls in the cylindrical and in-e instrumentation part of the reactor cavity would not be damaged and the reactor vessel would not be lifted. The complete ex-vessel steam explosion analysis, where also steam explosions with an energy conversion ratio of 0 % are treated, is presented in [7]. Some results of the analysis of the steam explosion scenarios with an energy conversion ratio of 0 % are given also in [8]. For a more detailed insight in the ex-vessel steam explosion phenomenon and its consequences more refined models would be needed. Future analyses should address the high-pressure melt ejection scenarios and the consequences of successive steam explosions. ACKNOWLEDGMENTS The authors acknowledge the support of the Ministry of higher education, science and technology of the Republic of Slovenia within the program P-006 and the research project J The Jožef Stefan Institute is a member of the Severe Accident Research Network of Excellence (SARNET) within the 6 th EU Framework Programme.

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