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Dynamic structural response of LMFBR head closures to hypothetical core disruptive accidents
Nuclear Engineering and Design 49 (1978) 119-129 © North-Holland Publishing Company
119
DYNAMIC STRUCTURAL RESPONSE OF LMFBR HEAD CLOSURES TO HYPOTHETICAL CORE DISRUPTIVE ACCIDENTS * R.F. KULAK Engineering Mechanics Program, Reactor Analysis and Safety Division, Argonne National Laboratory, Argonne, Illinois, USA
Presented here is an investigation of the dynamic structural response of the primary vessel'shead closure to a hypothetical core disruptive accident (HCDA). Two head-closure designswere considered: the first represents a loop-type design and the second represents a pool-type design. Using representative configurations of liquid metal fast breeder reactors (LMFBR), independent models were used (1) to derive loading pressure histories and (2) to study the structural response of the head closures. Results for loading pressures, displacement histories, deformed prof'des, stress magnitudes and plastically deformed regions are presented.
1. Introduction Under normal operating conditions the head closure of a liquid metal fast breeder reactor's vessel provides support for suspended components. However, during a core disruptive accident (CDA) it must also provide topside containment of radioactive core materials and coolant. During this accident the sodium above the core is propelled upward until it impacts against the vessel's head. The dynamic loading of the head could produce structural failure and/or sodium leak paths. Therefore, it is of vital importance that the dynamic response of the vessel's head closure be performed in the safety analysis of LMFBRs. There are essentially two basic system approaches that have been taken in designing liquid metal fast breeder reactors (LMFBRs); the loop and the pool. In the loop system, which has been the choice for the Fast Test Reactor (FTR) and Clinch River Breeder Reactor (CRBR) in the United States, the reactor core, fuel handling machinery and instrument tree are contained within the reactor vessel while the other coolant system components, such as pumps and * Some of the results contained in this paper were presented at the Fourth International Conference on Structural Mechanics in Reactor Technology,San Francisco, August 1977, and appeared in a greatly condensed form in Paper E 1[7 of the Transactions of that conference.
heat exchangers, are connnected outside of the reactor vessel. In contrast, the pool-type design has all primary system components enclosed within a comparatively large diameter tank and shield deck. Several reactors of the pool-type design are currently operational, under construction, or being designed worldwide. Operational pool LMFBR systems include the Experimental Breeder Reactor-II (US), the Phenix Reactor (France) and the Prototype Fast Reactor (UK). Currently under construction is the BN-600 (USSR), a 600 MW(e) plant, while the French are currently designing a 1200 MW(e) plant at Creys-Malville named Super Phenix I. In the United Kingdom a commercial sized LMFBR is also being designed based upon the pool concept. At this time we must point out that there are basic differences in vessel closure design between loop and pool systems as well as differences between various designs of the same system. In this paper we will not consider all the major variations but instead concentrate on one design from each system. The key features and analysis of the selected loop and pool designs are described in sections 2 and 3, respectively.
2. Loop-type LMFBR head closure analysis Presented below is a preliminary investigation of the transient structural response of a loop-type head
120
R.F. Kulak/Dynamic structural response o f LMFBR head closures to HCDA s
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closure to a hypothetical core disruptive accident (HCDA). A finite-element model is presented that accounts for the important structural features of the head-closure assembly. The transient response of the head is studied using the SADCAT code [ 1]. Results for plug-displacement histories, deformed profiles, and plastically deformed regions are presented.
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2.1. Reference cover description The head structure studied was of a triple, rotating-plug design (see figs. 1 and 2). The small plug is supported by the intermediate plug; the intermediate plug is supported by the large plug; and the large plug is supported by the concrete ledge via the vessel flange and stationary ring. Under normal operating conditions the load (gravity) acts in the downward direction and the supporting system consists of riser and bearing sets (see fig. 2). However, during a core-disruptive accident the load (slug pressure) acts in the upward direction and the supporting structures are the segmented shear rings. These rings are located at the interfaces between the small and intermediate plugs, between the intermediate and large plugs, and between the large plug and vessel flange. Each plug supports its respecitve shielding and crush tubes (see fig. 2) from the underside. In addi-
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tion, the intermediate rotating plug provides support for the upper internal structure (UIS) support columns. The plugs are all plate-type structures with a nominal thickness of 53 cm. The large plug has a nominal outside diameter of 653 cm and a large eccentric hole (nominal diamter of 434 cm). Also, there are penetrations for the ex-vessel transfer mechanism (EVTM) and the liquid-level monitors. The nominal od of the intermediate plug, which has several penetrations is 434 cm. A large 152 cm nomi-
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R.F. Kulak/Dynamic structural response of LMFBR head closures to HCDAs
121
Table 1 Material properties
Young's modulus Poisson's ratio Yield stress Ultimate stress Tangent modulus
Carbon steel grade 508, class II
T1 steel
206 0.3 345 311 552
206 GPa 0.3 620 MPa
GPa MPa (room temp.) MPa (204°C) MPa
724 MPa 620 MPa
nal hole is located offcenter, in addition to penetrations for the UIS support columns and control rod drive mechanism (CRDM). The small rotating plug has an od of 152 cm (nominal) and a 46 cm od eccentric penetration for the invessel transfer mechanism (IVTM). The plug material is taken to be carbon steel, grade 508, class II, with the material properties given in table 1. The minimum yield stress of 311 MPa was used in this study. The associated biological shield and crush-tube assemblies are suspended from each plug. The top, middle, and bottom shield plates are nominally 25.4, 25.4, and 23 cm thick, respectively. The total weight of the closure head assembly is 6.89 MN. Although the closure head has a nonuniform weight distribution, it was assumed to be uniformly distributed for our simple model. The above description summarizes the relevant design features of this loop-type head closure.
2.2 Analytical model The finite-element model of the triple rotatingplug head is shown in fig. 3. This is a simple model which encompasses the gross features of the head. The plugs were subdivided into 148 triangular plate elements. The following boundary conditions were used. The outer periphery of the large plug was treated as simply supported in the usual manner. The large-tointermediate plug and the intermediate-to-smaU plug boundaries were treated as modified simple supports, the modification being that these boundaries were allowed to translate in space. This type of boundary does not permit the transfer of moments or membrane forces from plug to plug, but it does allow transfer of the transverse force.
\~~lnterme~,o*e \ Pil Fig. 3. Finite-element mesh of a representative loop-type head closure.
The localized mechanics of the plug-to-plug boundaries was not treated here (1) because it was dependent'upon the details of a specific design and (2) we are mainly interested in the global behavior of the head. A finite-element computer code SADCAT (Structural Analysis for 3-D Core Assembly Transients) is the analytical tool used to calculate plug response. SADCAT is a computer code developed at ANL for the three-dimensional dynamic or static structural analysis of reactor components. The version used for this study is based upon an explicit, temporal, integration scheme. The code can economically solve large scale, nonlinear (geometric and material) problems. Built-in material laws can model elastoplastic behavior with a multi-linear stress-strain curve. A fiat triangular plate element is used to model the plugs. The plate element is formulated using a corotational coordinate system which enables the use of simple strain-nodal displacement and nodal forcestress relations. This plate element can be subjected to linear in-plane displacements and cubic transverse displacements. The orientation of lumped masses is described by unit vectors so that arbitrarily large rotations can be treated.
R.F. Kulak / Dynamic structural response o f LMFBR head closures to HCDAs
122 30
2.3. Results and conclusions
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A brief description of the dynamic loading conditions is presented below. During a core disruptive accident, the closure head is dynamically loaded by the UIS column-support loads and the sodium-slug impact. Relative to the sodium-slug load, the UIS column-support load is small and can be neglected. The hypothetical accident used as a basis for the calculations corresponds to an end of excursion average fuel temperature of 4527°C and a base temperature of 2727°C. These data were used in a thermodynamic model to describe the core expansion to obtain a PV relationship for use as REXCO [2] input. The sodium-slug pressure on the closure head as calculated with REXCO is shown in fig. 4. It must be pointed out that the REXCO model does not treat the UIS so the derived sodium-slug pressures would be on the high side and therefore conservative. A modification of the applied slug loading was necessary for the sake of tractability. The actual pressure was applied to the bottom shield plates via the thermal reflector plate. Since our simple model does not include the shield plates, the slug pressure w a s assumed to act on the bottom of the large, intermediate, and small plugs.
Of concern in the safety evaluation of the head closure are the deformations and the resulting stresses. By use of the finite-element model described above the following results were determined. Fig. 5 depicts the vertical displacement histories of nodes 116/117 which lie on the diametral symmetry line. These nodes are at the plug-to-plug boundary. The peak displacements occurred at 30.6 msec after slug impact, which is 98.6 msec from the beginning of the accident. Fig. 6 shows the deformed profile of the closure head along the diametral symmetry line;the largest deformations occur in the large rotating plug. The outer-to-inner periphery deformation (i.e. node 65 to node 116 of fig. 6) is 6.76 cm at the left side. The darkened areas in fig. 7 indicate the finite elements within each plug that underwent plastic deformation. It is seen that the entire large rotating plug experienced plastic behavior. The plastic behavior was found to be primarily the result of the bending behavior of the plugs; thus, through the plate thickness there is an upper plastic layer, a central elastic core, and a lower plastic layer. In contrast to the large plug, only part of the intermediate plug experienced plastic deformation. Fig. 7 shows that the plastic region is located at the thinner side of the annular-shaped intermediate plug. This area is subjected to the small plug load at its inner periphery and the restraining load of the large plug at its outer periphery. Finally, it is seen that the small rotating
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R.F. Kulak / Dynamic structural response of LMFBR head closures to HCDAs
123
HCDA energy release. Maximum absolute plug displacements were under 7 cm. Although the peak von Mises stress (381 MPa) did exceed the material's initial yield stress 311 MPa, it was well below the ultimate stress 552 MPa. The above study treated the global response of a representative, loop-type head closure. For a final analysis it may be necessary to consider localized responses, such as the mechanics of the plug-to-plug boundaries, before we can assess the safety of a specific design.
3. Pool-type LMFBR deck structure analysis
Fig. 6. Deformed profile of triple-rotating plug. plug does not undergo any plastic deformation. It was noted that the largest yon Mises stress was 381 MPa, occurring in the large rotating plug. The initial yield stress was taken to be 311 MPa. Based on the above calculations of the dynamic response of a loop-type head closure, the following conclusions can be drawn. This type of head closure can maintain its structural integrity under the given
Fig. 7. Location of plastic regions.
Among the design features of the pool-type LMFBR system which can have an impact on safety are: (1) a highly reliable, simple, low pressure, primary coolant boundary embodied in a single primary tank enclosing all primary system components; (2) a large heat capacity of the primary coolant system and large reactor inlet and outlet volumes which can provide margins for decay heat removal and protection o'f components from rapid thermal transients; (3) since in many designs the only piping necessary is a relatively short length between the pump and reactor core inlet, the operating pressures are low, the pipe is isothermal, and there is a low probability of occurrance, as well as severity of consequences, for a loss of piping integrity (LOPI) event; and (4) the large overall cross-sectional area of the primary tank can provide for the dissipation of sodium-slug impact forces in the event of a HCDA as well as provide for the dispersion of fuel particles resulting from such an event. Because of the large shield deck necessary to enclose the primary system the question has arisen as to the ability of the deck to resist the forces generated by an energetic HCDA. The purpose of this study has been to address specifically this question in connection to the overall structural design of the deck. The results presented here were part of a study, conducted at Argonne National Laboratory (ANL) for the Energy Research and Development Administration (ERDA), to determine the overall characteristics and concerns of commercial size ["1200 MW(e)] pool-type LMFBR systems [3]. These results are based on a reference reactor system design which was
124
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3.1. Reference reactor description Fig. 8 is a schematic elevation view of an 1200 MW(e) pool-type reference system. The reactor core A
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region was designed to provide 3000 MW of thermal power with sodium entering at about 371°C and leaving at about 538°C. The main components of the pool-type LMFBR system are shown: reactor core region, intermediate heat exchangers (IHXs), primary pumps, core support structure, primary and secondary tanks, and the shield-deck structure. The instrument tree and fuel handling machinery are not shown. Fig. 9 shows the plan view of the reference reactor. The primary vessel contains three primary pumps, six IHXs and two storage baskets. The basic dimensions of the pool reactor used in this preliminary study are shown in fig. 10. The shield deck itself is an annular structure which is supported by steel columns embedded in the surrounding concrete, radial biological-shield. The major structural components of the deck are the radial I-beams, the bottom annular plate and the inner ring which supports the rotating plugs. The radial beams form a 'spoked' type of structure with the central inner ring being the hub. The deck is, in general, a concretefilled, beam-plate composite structure which provides,
R.F. Kulak / Dynamic structural response of LMFBR head closures to HCDAs
in most designs, support for the pumps and heat exchangers, primary and guard tanks, and sufficient radiation shielding. 3.2. Analytical methods and models
The pressure loadings used in this study were obtained from output of the REXCO-HEP containment code. The mathematical model used in the REXCO-HEP calculations is shown in Fig. 10. A description of this model and the assumptions employed is presented below. The reactor region includes representations of the core, axial reflectors and blankets, radial reflectors and blankets, fissiongas plenum, core support structure, and reactor vessel. Between the top of the sodium pool and the bottom of the shield deck and plug structure, there is a cover-gas volume 50.8 cm (20 in.) deep. Although the plug and shield deck are included in fig, 10, they were assumed to be rigid in the REXCO calculational model. The plug is shown attached to the shield deck by a set of hold-down bolts. Although the REXCO-HEP code would, in general, be capable of calculating the effect that the plug motion has on the shield deck and wall loadings, it was felt to be conservative to ignore this effect for this study. The main tank is assumed to be rigidly attached to the shield deck so that neither axial nor radial movement is permitted at this point. From a practial point of view this is a reasonable assumption. The pressure-volume curve used to describe the core region expansion after an HCDA is shown in 280
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125
fig. 11. This curve represents an adiabatic expansion of fuel vapor; it has been normalized to the final volume expected in the core expansion which is an input requirement for the REXCO code. The initial core volume (It), at the start of the disassembly was assumed to be 10.34 m 3. Based on this volume, the V / V F ratio is 0.0022, where VF is the final volume of the expanded core. This particular p - V curve is representative of a core with an average temperature of 4800 K at the time of disruption. The total energy available in expanding the core to the final, quasiequilibrium, pressure of the containment vessel is about 1400 MW-sec; if the expansion were continued down to one bar, the total energy available would be about 2720 MW-sec. There were several conservatisms inherent in this analysis. These should be mentioned in order to put the following results into proper perspective. The conservatisms were dictated both by time and analytical limitations, but were felt not to affect the general conclusions which could be drawn for the deck structure. Among the conservatisms were (a) the rigid shield deck-and-plug assembly; (b) neglect of internal shrouds, skirts, baffles, and liners; and (c) neglect of pumps, IHXs, instrument trees, and other energyabsorbing structures. Neglect of the energy-absorbing capability of the deck-and-plug assembly has essentially two effects on the calculational results. The first is that, since the assembly is considered rigid, the loadings during impact are somewhat overestimated. Secondly, when performing independent, decoupled, calculations on the plug and shield deck, there is again a tendency to overestimate stresses and deflections because of the higher force loadings. Furthermore, the energy absorbed by the plug and shield deck is neglected. Based on the above model the pressure loading on the deck structure shown in fig. 12 was obtained. It must be pointed out that the 'zero' time shown on fig. 12 is referred to the beginning of slug impact. Relative to the beginning of the accident, slug impact occurs at about 95 msec. The peak pressure was 104 MD/cm ~ and occurred at 9.7 msec. The pressure decreases in an oscillatory manner to a quasi-equilibrium pressure at the end of the calculations. A finite-element model was designed to assess the ability of a pool-type LMFBR shield deck to sustain an energetic HCDA. From the plan view of a concep-
R.F. Kulak /Dynamic structural response o f LMFBR head closures to HCDAs
126
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tual representation of an expanded EBR-II type deck, it was determined that there is a reasonable amount of symmetry in the structure, and that an initial model would consist of a 12 ° sector encompassing
Fig. 13. Finite-element model of 12° shield-deck segment used for deck response calculations.
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one radial I-beam, and one-half of a typical in-tank component (e.g. intermediate heat exchanger, pump, or storage basket). The model is shown in fig. 13. The structural components modeled are the main radial I-beam, the component-support I-beam, the inner ring, and the in-tank component nozzles. The model acounts for the mass of the concrete, but ignores its structural effect. The concrete mass is distributed along the main radial I-beam, while the mass of a typical in-tank component is taken into account as a concentrated mass located at its attachment to the radial beam. Although the rotating plug is not modeled explicitly, its mass was taken into account by distributing it along the inner ring. Similarly, the pressure load acting on the plug assembly was treated as a vertical line-load acting on the inner ring of the deck. A variation of the above model which treates the structural effect of concrete is currently under development. Type T1 steel was chosen as the material for the radial beams, bottom plate, nozzles, and component support beam. This material combines toughness with a high yield strength and therefore it is well suited for shock type loading. The material properties are listed in table 1. The steel was assumed to follow a bilinear,
R.F. Kulak/Dynamic structural response of LMFBR head closures to HCDAs
universal stress-strain curve based upon the mechanical properties listed in table 1. The applied pressure loading is shown in fig. 12. This pressure was applied uniformly to the underside of the bottom annular plate. As mentioned above, the plug load was considered to be a line load acting on the inner ring. It was assumed that the in-tank component did not contribute to the loading, except for its mass effect. Also, an investigation of the effect of the inner and outer peripheral boundary conditions on the dynamic behavior of the deck was made using this model in order to assess (a) uncertainties in the design and (b) bounding values for maximum deck deformation. 3.3. Results and conclusions
Once the basic overall dimensions of the deck are determined, the dynamic response of the deck will be influenced by its inner and outer peripheral boundary conditions. For the purpose of ascertaining the effect that different types of boundary conditions have on the dynamic response of the deck, the following scoping study was performed. At the outer periphery the head closure is supported by vertical columns which connect directly to the radial I-beams. The beams and columns were considered to be connected by either a bolted joint or a welded, stiffened corner. The bolted joint corresponds to a 'pinned' type of boundary connection and the welded comer corresponds to a 'fixed-end' boundary condition. At the deck's inner periphery the choice of the boundary condition is not as obvious. Here the boundary condition is determined by the manner in which the rotating-plug assembly is connnected to the deck. The rotating-plug assembly would be connected to the top area of the inner ring with a substantial system of hold-down bolts. Because of this hold-down system and the large stiffness of the plug assembly, it is believed that there would be little radial differential movement between the plug assembly and the deck at the top of the inner ring. Therefore, it was assumed that the top of the inner ring can move vertically and that it was restricted from radial motion. This boundary condition corresponds to a 'pinned-end' condition in which vertical motion is permitted. The remainder of the inner ring is separated from the plug assembly by a relatively small
127
clearance gap. Depending on the size of this gap, the plug assembly may further restrict the inner ring from rotating during loading. This motion constraint would occur when the gap dimension is small. In contrast, if the gap is relatively large no restraint would occur.
An assessment of this constraint condition on the dynamic response of the deck was made by considering the following two types of boundary conditions. The small gap design was modeled by preventing the entire inner ring from rotating. Thus, for this condition the movement of the entire ring was restricted to vertical motion. When the gap dimension is large the plug assembly would not put any rotational restriction on the inner ring and the ring can rotate but would be restricted from radial motion at its top due to the previously discussed holddown bolting system. Table 2 identifies the various boundary condition combinations studied and also relates them to a case number. The vertical displacements of the radial I-beam at its connnection to the inner ring are shown in fig. 14 for the various boundary condition combinations. It is seen that the end conditions strongly influence the displacement magnitudes as well as the peak displacement times. The largest peak displacements occurred for case B which was the constrained inner ring and the pinned-end beam column joint; the smallest displacement for case A which was the constrained inner ring and the fixed-ended radial beam. It: was noted that the largest peak displacement (case B) was three times the smallest (case A). Table 3 summarizes the peak displacements and the time after slug impact at which they occur. From fig. 14 it is seen that for cases A and B, both of which have a fixed inner ring, the inital displacements are nearly identical for the first 18 msec after slug impact and thereafter they differ markedly. A comparison between cases A and C, which differ only in the inner ring support connection, shows that the simply-supported inner ring Table 2 Deck boundary conditions Case
Inner
Outer
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fixed fixed pinned
fixed pinned fixed
128
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model initially deflects more than the fixedsupported model. Therefore, it appears that the initial displacements are governed to a certain extent by the inner-ring support connection and that the maximum displacement is influenced by both the innerring and radial I-beam support methods. Thus, the choice of the support connections for the deck are important considerations in the design of the deck. The following is a description of the deck's energy partitioning for the case of a pinned inner ring and a fixed-end radial beam. At slug impact some of the axial kinetic energy of the sodium is transferred to strain and kinetic energy in the deck. The deck's Table 3 Peak vertical displacements Case
Displacement (cm)
Time (msec)
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kinetic energy and strain energy histories are shown in fig. 15. The kinetic energy reaches a peak value of 21 MJ at 0.0142 s after slug impact and then decreases to a small value. The strain energy peaks out at a level of 76 MJ at 0.035 s after slug impact. In ref. [2] it was reported that the maximum main tank strain energy for this reactor configuration was 1114 MJ. Therefore, it is seen that the strain energy of the deck is about one-fifteenth that of the main tank. This preliminary study of the dynamic response of a pool-type deck structure indicates that this structure can maintain its structural integrity under the given energy release.
4. Summary A preliminary study of the dynamic response of the primary vessel's head closure to an energetic core disruptive accident was performed. This investigation considered representative designs for both loop and pool type LMFBR systems. The analysis proceeded as two independent, decoupled calculations: containment calculations and head-closure response calculations. The containment calculations were performed mainly to derive a loading pressure history for the head-closure. In this part of the study, the head closure was considered
R.F. Kulak / Dynamic structural response of LMFBR head closures to HCDAs
rigid so the derived loading pressures were conservative. In the second part of the study a set of independent deck response calculations were performed using the above derived loading pressure history as input. Finite-element models that incorporated the main structural components of the head closure were constructed. A preliminary study of the dynamic response of the closures was performed using these models.
Acknowledgement The author wishes to thank Drs. S.H. Fistedis and T.J. Marciniak for their guidance and support during
129
the performance of this work. The computer assistance of Mr. C. Fiala is greatly appreciated. This work is part of the Engineering Mechanics Program of the Reactor Analysis and Safety Division, Argonne National Laboratory and it was supported by the US Department of Energy.
References [1 ] A.H. Marchertas and T.B. Belytschko, ANL-8104, June (1974). [2] Y.W. Chang and J. Gvildys, ANL-75-19, June (1975). [3] A. Amorosi, E. Hutter, T.J. Marciniak, H.O. Monson, R.W. Seidensticker and W.R. Simmons, ANL-76-61, May (1976).
119
DYNAMIC STRUCTURAL RESPONSE OF LMFBR HEAD CLOSURES TO HYPOTHETICAL CORE DISRUPTIVE ACCIDENTS * R.F. KULAK Engineering Mechanics Program, Reactor Analysis and Safety Division, Argonne National Laboratory, Argonne, Illinois, USA
Presented here is an investigation of the dynamic structural response of the primary vessel'shead closure to a hypothetical core disruptive accident (HCDA). Two head-closure designswere considered: the first represents a loop-type design and the second represents a pool-type design. Using representative configurations of liquid metal fast breeder reactors (LMFBR), independent models were used (1) to derive loading pressure histories and (2) to study the structural response of the head closures. Results for loading pressures, displacement histories, deformed prof'des, stress magnitudes and plastically deformed regions are presented.
1. Introduction Under normal operating conditions the head closure of a liquid metal fast breeder reactor's vessel provides support for suspended components. However, during a core disruptive accident (CDA) it must also provide topside containment of radioactive core materials and coolant. During this accident the sodium above the core is propelled upward until it impacts against the vessel's head. The dynamic loading of the head could produce structural failure and/or sodium leak paths. Therefore, it is of vital importance that the dynamic response of the vessel's head closure be performed in the safety analysis of LMFBRs. There are essentially two basic system approaches that have been taken in designing liquid metal fast breeder reactors (LMFBRs); the loop and the pool. In the loop system, which has been the choice for the Fast Test Reactor (FTR) and Clinch River Breeder Reactor (CRBR) in the United States, the reactor core, fuel handling machinery and instrument tree are contained within the reactor vessel while the other coolant system components, such as pumps and * Some of the results contained in this paper were presented at the Fourth International Conference on Structural Mechanics in Reactor Technology,San Francisco, August 1977, and appeared in a greatly condensed form in Paper E 1[7 of the Transactions of that conference.
heat exchangers, are connnected outside of the reactor vessel. In contrast, the pool-type design has all primary system components enclosed within a comparatively large diameter tank and shield deck. Several reactors of the pool-type design are currently operational, under construction, or being designed worldwide. Operational pool LMFBR systems include the Experimental Breeder Reactor-II (US), the Phenix Reactor (France) and the Prototype Fast Reactor (UK). Currently under construction is the BN-600 (USSR), a 600 MW(e) plant, while the French are currently designing a 1200 MW(e) plant at Creys-Malville named Super Phenix I. In the United Kingdom a commercial sized LMFBR is also being designed based upon the pool concept. At this time we must point out that there are basic differences in vessel closure design between loop and pool systems as well as differences between various designs of the same system. In this paper we will not consider all the major variations but instead concentrate on one design from each system. The key features and analysis of the selected loop and pool designs are described in sections 2 and 3, respectively.
2. Loop-type LMFBR head closure analysis Presented below is a preliminary investigation of the transient structural response of a loop-type head
120
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closure to a hypothetical core disruptive accident (HCDA). A finite-element model is presented that accounts for the important structural features of the head-closure assembly. The transient response of the head is studied using the SADCAT code [ 1]. Results for plug-displacement histories, deformed profiles, and plastically deformed regions are presented.
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2.1. Reference cover description The head structure studied was of a triple, rotating-plug design (see figs. 1 and 2). The small plug is supported by the intermediate plug; the intermediate plug is supported by the large plug; and the large plug is supported by the concrete ledge via the vessel flange and stationary ring. Under normal operating conditions the load (gravity) acts in the downward direction and the supporting system consists of riser and bearing sets (see fig. 2). However, during a core-disruptive accident the load (slug pressure) acts in the upward direction and the supporting structures are the segmented shear rings. These rings are located at the interfaces between the small and intermediate plugs, between the intermediate and large plugs, and between the large plug and vessel flange. Each plug supports its respecitve shielding and crush tubes (see fig. 2) from the underside. In addi-
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tion, the intermediate rotating plug provides support for the upper internal structure (UIS) support columns. The plugs are all plate-type structures with a nominal thickness of 53 cm. The large plug has a nominal outside diameter of 653 cm and a large eccentric hole (nominal diamter of 434 cm). Also, there are penetrations for the ex-vessel transfer mechanism (EVTM) and the liquid-level monitors. The nominal od of the intermediate plug, which has several penetrations is 434 cm. A large 152 cm nomi-
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R.F. Kulak/Dynamic structural response of LMFBR head closures to HCDAs
121
Table 1 Material properties
Young's modulus Poisson's ratio Yield stress Ultimate stress Tangent modulus
Carbon steel grade 508, class II
T1 steel
206 0.3 345 311 552
206 GPa 0.3 620 MPa
GPa MPa (room temp.) MPa (204°C) MPa
724 MPa 620 MPa
nal hole is located offcenter, in addition to penetrations for the UIS support columns and control rod drive mechanism (CRDM). The small rotating plug has an od of 152 cm (nominal) and a 46 cm od eccentric penetration for the invessel transfer mechanism (IVTM). The plug material is taken to be carbon steel, grade 508, class II, with the material properties given in table 1. The minimum yield stress of 311 MPa was used in this study. The associated biological shield and crush-tube assemblies are suspended from each plug. The top, middle, and bottom shield plates are nominally 25.4, 25.4, and 23 cm thick, respectively. The total weight of the closure head assembly is 6.89 MN. Although the closure head has a nonuniform weight distribution, it was assumed to be uniformly distributed for our simple model. The above description summarizes the relevant design features of this loop-type head closure.
2.2 Analytical model The finite-element model of the triple rotatingplug head is shown in fig. 3. This is a simple model which encompasses the gross features of the head. The plugs were subdivided into 148 triangular plate elements. The following boundary conditions were used. The outer periphery of the large plug was treated as simply supported in the usual manner. The large-tointermediate plug and the intermediate-to-smaU plug boundaries were treated as modified simple supports, the modification being that these boundaries were allowed to translate in space. This type of boundary does not permit the transfer of moments or membrane forces from plug to plug, but it does allow transfer of the transverse force.
\~~lnterme~,o*e \ Pil Fig. 3. Finite-element mesh of a representative loop-type head closure.
The localized mechanics of the plug-to-plug boundaries was not treated here (1) because it was dependent'upon the details of a specific design and (2) we are mainly interested in the global behavior of the head. A finite-element computer code SADCAT (Structural Analysis for 3-D Core Assembly Transients) is the analytical tool used to calculate plug response. SADCAT is a computer code developed at ANL for the three-dimensional dynamic or static structural analysis of reactor components. The version used for this study is based upon an explicit, temporal, integration scheme. The code can economically solve large scale, nonlinear (geometric and material) problems. Built-in material laws can model elastoplastic behavior with a multi-linear stress-strain curve. A fiat triangular plate element is used to model the plugs. The plate element is formulated using a corotational coordinate system which enables the use of simple strain-nodal displacement and nodal forcestress relations. This plate element can be subjected to linear in-plane displacements and cubic transverse displacements. The orientation of lumped masses is described by unit vectors so that arbitrarily large rotations can be treated.
R.F. Kulak / Dynamic structural response o f LMFBR head closures to HCDAs
122 30
2.3. Results and conclusions
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A brief description of the dynamic loading conditions is presented below. During a core disruptive accident, the closure head is dynamically loaded by the UIS column-support loads and the sodium-slug impact. Relative to the sodium-slug load, the UIS column-support load is small and can be neglected. The hypothetical accident used as a basis for the calculations corresponds to an end of excursion average fuel temperature of 4527°C and a base temperature of 2727°C. These data were used in a thermodynamic model to describe the core expansion to obtain a PV relationship for use as REXCO [2] input. The sodium-slug pressure on the closure head as calculated with REXCO is shown in fig. 4. It must be pointed out that the REXCO model does not treat the UIS so the derived sodium-slug pressures would be on the high side and therefore conservative. A modification of the applied slug loading was necessary for the sake of tractability. The actual pressure was applied to the bottom shield plates via the thermal reflector plate. Since our simple model does not include the shield plates, the slug pressure w a s assumed to act on the bottom of the large, intermediate, and small plugs.
Of concern in the safety evaluation of the head closure are the deformations and the resulting stresses. By use of the finite-element model described above the following results were determined. Fig. 5 depicts the vertical displacement histories of nodes 116/117 which lie on the diametral symmetry line. These nodes are at the plug-to-plug boundary. The peak displacements occurred at 30.6 msec after slug impact, which is 98.6 msec from the beginning of the accident. Fig. 6 shows the deformed profile of the closure head along the diametral symmetry line;the largest deformations occur in the large rotating plug. The outer-to-inner periphery deformation (i.e. node 65 to node 116 of fig. 6) is 6.76 cm at the left side. The darkened areas in fig. 7 indicate the finite elements within each plug that underwent plastic deformation. It is seen that the entire large rotating plug experienced plastic behavior. The plastic behavior was found to be primarily the result of the bending behavior of the plugs; thus, through the plate thickness there is an upper plastic layer, a central elastic core, and a lower plastic layer. In contrast to the large plug, only part of the intermediate plug experienced plastic deformation. Fig. 7 shows that the plastic region is located at the thinner side of the annular-shaped intermediate plug. This area is subjected to the small plug load at its inner periphery and the restraining load of the large plug at its outer periphery. Finally, it is seen that the small rotating
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R.F. Kulak / Dynamic structural response of LMFBR head closures to HCDAs
123
HCDA energy release. Maximum absolute plug displacements were under 7 cm. Although the peak von Mises stress (381 MPa) did exceed the material's initial yield stress 311 MPa, it was well below the ultimate stress 552 MPa. The above study treated the global response of a representative, loop-type head closure. For a final analysis it may be necessary to consider localized responses, such as the mechanics of the plug-to-plug boundaries, before we can assess the safety of a specific design.
3. Pool-type LMFBR deck structure analysis
Fig. 6. Deformed profile of triple-rotating plug. plug does not undergo any plastic deformation. It was noted that the largest yon Mises stress was 381 MPa, occurring in the large rotating plug. The initial yield stress was taken to be 311 MPa. Based on the above calculations of the dynamic response of a loop-type head closure, the following conclusions can be drawn. This type of head closure can maintain its structural integrity under the given
Fig. 7. Location of plastic regions.
Among the design features of the pool-type LMFBR system which can have an impact on safety are: (1) a highly reliable, simple, low pressure, primary coolant boundary embodied in a single primary tank enclosing all primary system components; (2) a large heat capacity of the primary coolant system and large reactor inlet and outlet volumes which can provide margins for decay heat removal and protection o'f components from rapid thermal transients; (3) since in many designs the only piping necessary is a relatively short length between the pump and reactor core inlet, the operating pressures are low, the pipe is isothermal, and there is a low probability of occurrance, as well as severity of consequences, for a loss of piping integrity (LOPI) event; and (4) the large overall cross-sectional area of the primary tank can provide for the dissipation of sodium-slug impact forces in the event of a HCDA as well as provide for the dispersion of fuel particles resulting from such an event. Because of the large shield deck necessary to enclose the primary system the question has arisen as to the ability of the deck to resist the forces generated by an energetic HCDA. The purpose of this study has been to address specifically this question in connection to the overall structural design of the deck. The results presented here were part of a study, conducted at Argonne National Laboratory (ANL) for the Energy Research and Development Administration (ERDA), to determine the overall characteristics and concerns of commercial size ["1200 MW(e)] pool-type LMFBR systems [3]. These results are based on a reference reactor system design which was
124
R.F. Kulak /Dynamic structural response o f LMFBR head closures to HCDA s
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3.1. Reference reactor description Fig. 8 is a schematic elevation view of an 1200 MW(e) pool-type reference system. The reactor core A
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region was designed to provide 3000 MW of thermal power with sodium entering at about 371°C and leaving at about 538°C. The main components of the pool-type LMFBR system are shown: reactor core region, intermediate heat exchangers (IHXs), primary pumps, core support structure, primary and secondary tanks, and the shield-deck structure. The instrument tree and fuel handling machinery are not shown. Fig. 9 shows the plan view of the reference reactor. The primary vessel contains three primary pumps, six IHXs and two storage baskets. The basic dimensions of the pool reactor used in this preliminary study are shown in fig. 10. The shield deck itself is an annular structure which is supported by steel columns embedded in the surrounding concrete, radial biological-shield. The major structural components of the deck are the radial I-beams, the bottom annular plate and the inner ring which supports the rotating plugs. The radial beams form a 'spoked' type of structure with the central inner ring being the hub. The deck is, in general, a concretefilled, beam-plate composite structure which provides,
R.F. Kulak / Dynamic structural response of LMFBR head closures to HCDAs
in most designs, support for the pumps and heat exchangers, primary and guard tanks, and sufficient radiation shielding. 3.2. Analytical methods and models
The pressure loadings used in this study were obtained from output of the REXCO-HEP containment code. The mathematical model used in the REXCO-HEP calculations is shown in Fig. 10. A description of this model and the assumptions employed is presented below. The reactor region includes representations of the core, axial reflectors and blankets, radial reflectors and blankets, fissiongas plenum, core support structure, and reactor vessel. Between the top of the sodium pool and the bottom of the shield deck and plug structure, there is a cover-gas volume 50.8 cm (20 in.) deep. Although the plug and shield deck are included in fig, 10, they were assumed to be rigid in the REXCO calculational model. The plug is shown attached to the shield deck by a set of hold-down bolts. Although the REXCO-HEP code would, in general, be capable of calculating the effect that the plug motion has on the shield deck and wall loadings, it was felt to be conservative to ignore this effect for this study. The main tank is assumed to be rigidly attached to the shield deck so that neither axial nor radial movement is permitted at this point. From a practial point of view this is a reasonable assumption. The pressure-volume curve used to describe the core region expansion after an HCDA is shown in 280
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125
fig. 11. This curve represents an adiabatic expansion of fuel vapor; it has been normalized to the final volume expected in the core expansion which is an input requirement for the REXCO code. The initial core volume (It), at the start of the disassembly was assumed to be 10.34 m 3. Based on this volume, the V / V F ratio is 0.0022, where VF is the final volume of the expanded core. This particular p - V curve is representative of a core with an average temperature of 4800 K at the time of disruption. The total energy available in expanding the core to the final, quasiequilibrium, pressure of the containment vessel is about 1400 MW-sec; if the expansion were continued down to one bar, the total energy available would be about 2720 MW-sec. There were several conservatisms inherent in this analysis. These should be mentioned in order to put the following results into proper perspective. The conservatisms were dictated both by time and analytical limitations, but were felt not to affect the general conclusions which could be drawn for the deck structure. Among the conservatisms were (a) the rigid shield deck-and-plug assembly; (b) neglect of internal shrouds, skirts, baffles, and liners; and (c) neglect of pumps, IHXs, instrument trees, and other energyabsorbing structures. Neglect of the energy-absorbing capability of the deck-and-plug assembly has essentially two effects on the calculational results. The first is that, since the assembly is considered rigid, the loadings during impact are somewhat overestimated. Secondly, when performing independent, decoupled, calculations on the plug and shield deck, there is again a tendency to overestimate stresses and deflections because of the higher force loadings. Furthermore, the energy absorbed by the plug and shield deck is neglected. Based on the above model the pressure loading on the deck structure shown in fig. 12 was obtained. It must be pointed out that the 'zero' time shown on fig. 12 is referred to the beginning of slug impact. Relative to the beginning of the accident, slug impact occurs at about 95 msec. The peak pressure was 104 MD/cm ~ and occurred at 9.7 msec. The pressure decreases in an oscillatory manner to a quasi-equilibrium pressure at the end of the calculations. A finite-element model was designed to assess the ability of a pool-type LMFBR shield deck to sustain an energetic HCDA. From the plan view of a concep-
R.F. Kulak /Dynamic structural response o f LMFBR head closures to HCDAs
126
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tual representation of an expanded EBR-II type deck, it was determined that there is a reasonable amount of symmetry in the structure, and that an initial model would consist of a 12 ° sector encompassing
Fig. 13. Finite-element model of 12° shield-deck segment used for deck response calculations.
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one radial I-beam, and one-half of a typical in-tank component (e.g. intermediate heat exchanger, pump, or storage basket). The model is shown in fig. 13. The structural components modeled are the main radial I-beam, the component-support I-beam, the inner ring, and the in-tank component nozzles. The model acounts for the mass of the concrete, but ignores its structural effect. The concrete mass is distributed along the main radial I-beam, while the mass of a typical in-tank component is taken into account as a concentrated mass located at its attachment to the radial beam. Although the rotating plug is not modeled explicitly, its mass was taken into account by distributing it along the inner ring. Similarly, the pressure load acting on the plug assembly was treated as a vertical line-load acting on the inner ring of the deck. A variation of the above model which treates the structural effect of concrete is currently under development. Type T1 steel was chosen as the material for the radial beams, bottom plate, nozzles, and component support beam. This material combines toughness with a high yield strength and therefore it is well suited for shock type loading. The material properties are listed in table 1. The steel was assumed to follow a bilinear,
R.F. Kulak/Dynamic structural response of LMFBR head closures to HCDAs
universal stress-strain curve based upon the mechanical properties listed in table 1. The applied pressure loading is shown in fig. 12. This pressure was applied uniformly to the underside of the bottom annular plate. As mentioned above, the plug load was considered to be a line load acting on the inner ring. It was assumed that the in-tank component did not contribute to the loading, except for its mass effect. Also, an investigation of the effect of the inner and outer peripheral boundary conditions on the dynamic behavior of the deck was made using this model in order to assess (a) uncertainties in the design and (b) bounding values for maximum deck deformation. 3.3. Results and conclusions
Once the basic overall dimensions of the deck are determined, the dynamic response of the deck will be influenced by its inner and outer peripheral boundary conditions. For the purpose of ascertaining the effect that different types of boundary conditions have on the dynamic response of the deck, the following scoping study was performed. At the outer periphery the head closure is supported by vertical columns which connect directly to the radial I-beams. The beams and columns were considered to be connected by either a bolted joint or a welded, stiffened corner. The bolted joint corresponds to a 'pinned' type of boundary connection and the welded comer corresponds to a 'fixed-end' boundary condition. At the deck's inner periphery the choice of the boundary condition is not as obvious. Here the boundary condition is determined by the manner in which the rotating-plug assembly is connnected to the deck. The rotating-plug assembly would be connected to the top area of the inner ring with a substantial system of hold-down bolts. Because of this hold-down system and the large stiffness of the plug assembly, it is believed that there would be little radial differential movement between the plug assembly and the deck at the top of the inner ring. Therefore, it was assumed that the top of the inner ring can move vertically and that it was restricted from radial motion. This boundary condition corresponds to a 'pinned-end' condition in which vertical motion is permitted. The remainder of the inner ring is separated from the plug assembly by a relatively small
127
clearance gap. Depending on the size of this gap, the plug assembly may further restrict the inner ring from rotating during loading. This motion constraint would occur when the gap dimension is small. In contrast, if the gap is relatively large no restraint would occur.
An assessment of this constraint condition on the dynamic response of the deck was made by considering the following two types of boundary conditions. The small gap design was modeled by preventing the entire inner ring from rotating. Thus, for this condition the movement of the entire ring was restricted to vertical motion. When the gap dimension is large the plug assembly would not put any rotational restriction on the inner ring and the ring can rotate but would be restricted from radial motion at its top due to the previously discussed holddown bolting system. Table 2 identifies the various boundary condition combinations studied and also relates them to a case number. The vertical displacements of the radial I-beam at its connnection to the inner ring are shown in fig. 14 for the various boundary condition combinations. It is seen that the end conditions strongly influence the displacement magnitudes as well as the peak displacement times. The largest peak displacements occurred for case B which was the constrained inner ring and the pinned-end beam column joint; the smallest displacement for case A which was the constrained inner ring and the fixed-ended radial beam. It: was noted that the largest peak displacement (case B) was three times the smallest (case A). Table 3 summarizes the peak displacements and the time after slug impact at which they occur. From fig. 14 it is seen that for cases A and B, both of which have a fixed inner ring, the inital displacements are nearly identical for the first 18 msec after slug impact and thereafter they differ markedly. A comparison between cases A and C, which differ only in the inner ring support connection, shows that the simply-supported inner ring Table 2 Deck boundary conditions Case
Inner
Outer
A B C
fixed fixed pinned
fixed pinned fixed
128
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model initially deflects more than the fixedsupported model. Therefore, it appears that the initial displacements are governed to a certain extent by the inner-ring support connection and that the maximum displacement is influenced by both the innerring and radial I-beam support methods. Thus, the choice of the support connections for the deck are important considerations in the design of the deck. The following is a description of the deck's energy partitioning for the case of a pinned inner ring and a fixed-end radial beam. At slug impact some of the axial kinetic energy of the sodium is transferred to strain and kinetic energy in the deck. The deck's Table 3 Peak vertical displacements Case
Displacement (cm)
Time (msec)
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kinetic energy and strain energy histories are shown in fig. 15. The kinetic energy reaches a peak value of 21 MJ at 0.0142 s after slug impact and then decreases to a small value. The strain energy peaks out at a level of 76 MJ at 0.035 s after slug impact. In ref. [2] it was reported that the maximum main tank strain energy for this reactor configuration was 1114 MJ. Therefore, it is seen that the strain energy of the deck is about one-fifteenth that of the main tank. This preliminary study of the dynamic response of a pool-type deck structure indicates that this structure can maintain its structural integrity under the given energy release.
4. Summary A preliminary study of the dynamic response of the primary vessel's head closure to an energetic core disruptive accident was performed. This investigation considered representative designs for both loop and pool type LMFBR systems. The analysis proceeded as two independent, decoupled calculations: containment calculations and head-closure response calculations. The containment calculations were performed mainly to derive a loading pressure history for the head-closure. In this part of the study, the head closure was considered
R.F. Kulak / Dynamic structural response of LMFBR head closures to HCDAs
rigid so the derived loading pressures were conservative. In the second part of the study a set of independent deck response calculations were performed using the above derived loading pressure history as input. Finite-element models that incorporated the main structural components of the head closure were constructed. A preliminary study of the dynamic response of the closures was performed using these models.
Acknowledgement The author wishes to thank Drs. S.H. Fistedis and T.J. Marciniak for their guidance and support during
129
the performance of this work. The computer assistance of Mr. C. Fiala is greatly appreciated. This work is part of the Engineering Mechanics Program of the Reactor Analysis and Safety Division, Argonne National Laboratory and it was supported by the US Department of Energy.
References [1 ] A.H. Marchertas and T.B. Belytschko, ANL-8104, June (1974). [2] Y.W. Chang and J. Gvildys, ANL-75-19, June (1975). [3] A. Amorosi, E. Hutter, T.J. Marciniak, H.O. Monson, R.W. Seidensticker and W.R. Simmons, ANL-76-61, May (1976).