Paper SNI 6/26 A PARAMETRIC STUDY ON REACTOR CONTAINMENT RESPONS E TO FUELSODIUM INTERACTIO N TAKASHI SAWAD A YASUO HASEGAWA ASAKO NISHIMUR A


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1 Paper SNI 6/26 A PARAMETRIC STUDY ON REACTOR CONTAINMENT RESPONS E TO FUELSODIUM INTERACTIO N TAKASHI SAWAD A YASUO HASEGAWA ASAKO NISHIMUR A Mitsubishi Atomic Power Industries, Inc
2 A Parametric Study on Reactor Containment Respons e to FuelSodium Interaction Takashi Sawada, Yasuo Hasegawa, Asako Nishimur a Mitsubishi Atomic Power Industries, Inc. 61, Ohtemachi 1chom e Chiyodaku, Tokyo ABSTRAC T Evaluations have been made on the effects of FSI parameters whic h affect dynamic responses of reactor containment structures. A couple d computer code FI II/ASPRINII has been employed in this study. The FCIII code is based on a modified ratelimited model originally devel  oped by Cho, Ivins and Wright. The ASPRINII code is a modified version of the reactor containment response analysis code ASPRIN originall y developed by G. L. Fox. Coupling between an FSI region and its surround  ings is determined by FSI zone pressure, P(V,t), as well as by FSI zone volume which is a function of constraint conditions. A spherical PSI zone in the core of a demonstration plant is assume d in this study. 1000Kg of molten fuel at 3338 K is mixed with 105Kg o f sodium coolant at 900 K. The parameters changed are constraint condi  tions and FSI parameters such as a fuel particle size, a rate of fragmen  tation and mixing, a fuelsodium mixing ratio and a twophase heat transfer coefficient at a fuel particle surface
3 I. INTRODUCTION In the course of LMFBR. safety assessment, consequences of molte n fuels released into sodium coolant must be evaluated in a hypothetica l core disruptive accident (HCDA). Design measures must be established t o assure safety without undue economic penalties. Although much effort s have been devoted to clarify mechanisms of FSI, there remain many uncertainties. It is necessary for reactor designers to evaluat e consequences of such uncertainties and to evaluate the effects of design changes on the dynamics of PSI process and containment response. This work is directed toward providing guidance for evaluating such parameter variations. A fast structural response analysis code ASPRINII, which is couple d with the FSI analysis code ICIII, has been developed to accomplish a quick design survey. The FCIII code is based on a modified ratelimited model originall y developed by Cho, Ivins and Wright (. l) This code has been verified b y analyzing the H2 experiment in TREAT. The analytical results reasonably reproduced the experimental voiding history. The ASPRINII code is a modified version of the quasi twodimensional reactor structural respons e analysis code ASPRIN originally developed by G. L. Fox (. 2) The code has been evaluated with some simulation experiments using chemical explosives. The analysis has shown good agreement with experiments in predicting the maximum deformation of the reactor vessel. Couplings between an FSI region and its surroundings are determined by FSI zone pressure, P(Y,t ) and zone volume, which is a function of constraint conditions. A spherical FSI zone in a core of a demonstration plant was assumed. In this study, 1000Kg of molten fuel at 3338 K was mixed with 105Kg of sodium coolant at 900 K. The structural response was investigated b y 683
4 changing FSI parameters and constraint conditions. These include th e strength of reactor vessel and those include a fuelsodium mixing ratio, a rate of fragmentation and mixing and a twophase heat transfer coeffi  cient at fuel particle surfaces
5 II. ANALYTICAL MODEL 1) General Description The coupled computer code PCIII/ASPRINII is capable of evaluatin g reactor structural response due to the pressure loading in I. The PCIII code is an PSI analysis code, which performs heat transfer an d pressure transient calculations using a ratelimited model originall y developed by Cho, Ivins and Wright. The ASPRINII code is a contain  ment response analysis code which performs spherical onedimensional hydrodynamics analysis and quasi twodimensional containment respons e analysis of the ASPRIN code originally developed by G. L. Fox (. 2 ) In PSI, the coolant is heated rapidly by the fuel, increasing a pressure in the PSI zone. The.FSI zoné then expands against a constraint induced by the surroundings. A time history of pressure and coolan t expansion in the FSI zone is determined by an interaction between tw o competing processes ; heating of the coolant which is computed with PCII I and an expansion of the heated liquid against the surrounding constraint s which is computed with ASPRINII. The F3I zone is represented by a spherical mixture of fuel and sodium in PCIII/ASPRINII. If the volume change of molten fuel is neglected, the expansion of the mixing zone is due only to the volume change of the heated coolant. It is also assumed that the heated coolant is in unifor m.thermodynamic equilibrium throughout the mixing zone and that the mixin g zone does not exchange mass with the surroundings. A change in volume, V, of the heated coolant is related to a change in enthalpy H and pressur e P. They are given by the first law of thermodynamics ; d  it& + qdp (1 )
6 and by the equation of state of the coolant, H = H(P,V), (2, where dqjdt denotes an overall heating rate of the coolant in the mixing zone. Thermodynamic properties in ANL809 (5 3) was used for sodium. The term dq/dt depends on the process of fragmentation and mixing as well a s on heat transfer mechanisms. An additional relationship between P anc:. V is given by considering a dynamics of a constraint induced by th e surroundings ; P = f( V, dt' ) (3) dt Equation (3) represents the constraining effects of the surroundings c n the expansion of the mixing zone. The surroundings include unheate d coolant, reactor internal structures, reactor vessel and reactor head. In this study, the quasi twodimensional model of constraint is furnished by the ASPRINII code. In obtaining the pressure exerted on the internal structures and th e vessel wall, the hydrodynamic equations are solved in the spherical one  dimensional Lagrangian coordinate system. The quasi twodimensiona l Newtonian model of the ASPRIN code is utilized in simulating the contain  ment response. The elasticplastic deformation is taken into account in calculating the mechanical behavior of the internal structures, th e reactor vessel and the holddown bolts. 2) Heat Transfer Approximatio n A spherical mixing zone in the core was considered where spherica l fuel particles are uniformly dispersed in the coolant. Since details of fragmentation and mixing are not well understood, the fuel particle siz e and mixing time constant were regarded as characteristic constants which express the rate of fragmentation and mixing
7 When the sodium is in liquid phase, the heat transfer is assumed t o be limited only by the thermal conductive resistance of the fuel. When the sodium is in twophase or in vapor phase, the heat transfer wa s assumed to be limited by both the thermal conductive resistance of the fuel and twophase heat transfer coefficient, at the fuel surface, htwo, by taking account of sodium vapor blanketing. For the heating rate, dqfdt, of the sodium in the fuelcoolant interaction zone, the following form was assumed ; da _ dq..n dqout dt dt dt (4) where dq. /dt is the heating of sodium with fuel and dqout/dt is the heat dissipation to the surroundings. The former is given by d dtn ha ( Tf  T ) (5) with A = OC ( 1cxp(t) ) (6) 1 1 _ r hf two (7) Effective heat transfer coefficient, h f, due to heat conduction resistance of fuel is determined from the transient conduction approximation developed by Cho, Ivins and WrightP ) The twophase heat transfer coefficient, is an input parameter, htwo, which may be changed in time and in sodium vapor fraction. 3) Hydrodynamics and Structural Response Model The analytical model of ASTh INII is shown in Fig. 1. The FSI exert s pressure over the core region, while deforming the core Barrel and reactor vessel radially, accelerating the coolant slug upward and the vessel
8 downward. In obtaining the pressure exerted on the core barrel and th e middle portion of the vessel (midvessel), the hydrodynamic equation s are solved in spherical onedimensional coordinate. The quasi two  dimensional Newtonian model of the ASPFIN code is utilized in simulating the slug motion and containment response. The élastoplastic deforma : ion is considered in calculating the mechanical behavior of the interna l structure, the reactor vessel and reactor head holddown bolts. In investigating the pressure wave propagation, hydrodynamic equations and equations of states are expressed in spherical onedimensiona l Lagrangian formulation, which is written in explicit finite differenc E form s (. 4) Shock discontinuities are eliminated by using the von Neumar n  R.i.chtmyer pseudviscosity, q (s ) The radial deformations of the core barrel and the reactor vesse l are represemted by where FB 2 d FB K ( P, (t)  p ' (n) J (FB  1/4) (0) dt 2 R 2 f s 0 = the vessel inside radius/initial radius t = time K = strain hardening coefficient, (stress) = N (strain) K r = material density P'(t) = dimensionaless pressure exerted on the vessel wall P'(FB) = dimensionless pressure retaining ability of the vesse l wal l The wall motion is retarded by the tangential strength of the reacto r vessel wall which increases in an exponential strain hardening law. The downward acceleration' of the reactor vessel due to FSI pressur e is expressed in
9 .d2y3 dt 2 = ( P.A + R3A  M2.G )/M2 (9 ) where R3A G = force from longitudinal stress in vessel wal l = gravity M2 = lower vessel mass. The motion is restrained by the elastoplastic deformation of th e vessel wall with linear strain hardening. The coolant slug continues accelerating while decreasing FSI pressur e until it impacts with the vessel cover, whose equation of motion is give n by d2 X1 P.A dt 2 M3  G (10 ) where M3 is equal to the mass of coolant in slug. Up to this time, the slug may have received a considerable portio n of the PSI energy, and this energy must be conserved during the collision process. The impact pressure was assumed to depend on increase i n coolant density during impact. The upper vessel zone was considered a fixed region where a coolant mass balance is equated. The mass flow into the region depends on the slug velocity ; while the mass flowing ou t from the region depends on upward cover movement and radial wall movement. The rate of mass increase then determines the rate of impact pressure. buildup which is integrated obtaining the value of impact pressure. Equating a pressuretime relationship for the impact, it is possibl e to determine the upper vessel wall response ; d2 FT 2TrFT 0= (PI+PPW) TM where FT P I = upper vessel radius/initial radiu s = PSI pressure
10 = pressure retaining ability of upper wal l TM = effective mass of vessel wall and coolan t The upper vessel radial expansion is restricted by the strength o f the wall, which increases in accordance with a linear strain hardenin g law. The reactor cover is accelerated by the impact pressure and restraine d by holddown bolts secured to a building foundation ; d 2 23 = ( PI + P) A  R3 M1,G) / Ml (12 ) d t where R3 Ml = cover restraining force of holddown bolt s = slug and cover mas s 4) Verification of the Code s Calculations of the inpile test using FCIII code showed goo d agreement with the experimental result. The calculations of a scale tes t with chemical explosives using ASPRINII showed good agreement with th e experimental results. These calculations indicate that the modelin g techniques and parameters used in describing the reactor containmen t responses due to FSI pressure must be adequate. A. FCIII Code Comparisons of analytical results with experiments have been under  taken in establishing the validity of the FCIII code and parameter s used in the code. Experimental voiding history of the H2 experiment in TREAT (6) was analyzed using MIII code, as performed by Cronenberg Ç? ) The analysis has successfully reproduced the experimental voidin g history with following input parameters ; tm t txo = 20 msec = 0.1 w/cm 2 C
11 t'loss = 0.8 ^1.2 w/cm 2 C where tm is the fragmentation and mixing time constant, is the two  htwo phase heat transfer coefficient at the fuel particle surface which i s estimated from the experiments by Faraha t (, 8) and hloss is an effectiv e heat transfer coefficient between the PSI region and cold surroundings. Analytical results, in which the parameters tm and hloss being varied are shown in Figs. 2 and 3 compared with the experimental voiding history. A more systematic effort in code development and verification i s being planned in the following areas ; (i) (ii) (iii) fragmentation and mixing mode l two phase heat transfer mode l a model which evaluates heat dissipation to cold surrounding s and its applicability to HCDA conditions. B. ASPRINII Code To establish validity of the ASPRINII code, comparisons of analyti  cal results with experiments, as well as with twodimensional hydro  dynamic calculations have been undertaken. The analysis has been successful in predicting the experimental maximum deformations at a middle and a upper vessel. Comparisons o f the calcu.'_ational results with experiments as well as twodimensiona l calculations are shown in Tables 1 and 2. The MONJU E3 experimen t (g ) was performed in Japan by Nuclear Safety Association using a 1/7.5 scal e model which was constructed from SUS3O4, and using water as test fluid. Core pressure was simulated by explosions of Pentolite. As shown in Table 1, a good agreement was obtained at the midvesse l region. As for the upper vessel region, discrepancies in. the ASPRINI:L analysis and the experiments are partly due to a lack of detailed data. In Table 2, deviations of the ASPRINII results showed effects of
12 uncertainties of input parameters and experimental conditions. A more systematic effort to establish validity of the ASPRINII code is being performed under contract between PNC and.mapi
13 III. CONDITIONS OF ANALYSI S A spherical FSI zone was assumed in which 1000Kg of molten fuel at 3338 K was mixed with 105Kg of sodium at 900 K. Table 3 shows the reactor geometrics studied for the reference case. In Table 4, materia l strength data are shown. In these data, the effects of temperature, irradiation and strain rate (15)(18) have been taken into account a t each part of the reactor structure. Table 5 shows, for the referenc e case, the initial conditions and the parameters of PSI analysis. The fuel particle radius, R f, was Latent heat of fusion of the fue l was taken into account, using the equivalent temperature differenc e methodt l9) Twophase heat transfer coefficient, was assume d htwo, 0.]. w/cm 2 C referring to the experimental results by Farahat.a) Fragmentation and mixing time constant, t m, was set 20 msec being obtained from the analysis of the H2 experiment in TREAT
14 IV. RESULTS AND DISCUSSIO N 1) Boundary Condition s A. Radial Constrain t The analytical model used here consists of two spherical zones, th e inner F51 zone and the surrounding zone of unheated sodium. The hydro  dynamic equations are solved for the surrounding zone as employed it th e ASPRINII code using the following boundary conditions : Case A : Free surface ; P = 0 Case B : Fixed surface ; R = 0 Case C : Deformable vessel ; equation (8). The FST parameters were as shown in Table 5. Outer radius of th e surrounding zone was the same as the midvessel inner radius in Table 3. The thickness of the vessel in Case C was assumed 40mm. Some of the results are shown in Figures 4 to 8. Pressure and vclume transients for three different boundary conditions are obtained. The results indicate a little difference in pressure but a substantial di'fer  ente in volume. A pdv work with the fixed boundary is substantiall y lower than that fcr free boundary. For the case with free boundary, cos t of the work done by FSI zone is converted to kinetic energy. Wherea s for the case with fixed boundary, a significant fraction of the work i s converted to internal as well as kinetic energy of unheated sodium. B. Vessel Mode l The analytical model used here is the same as the reference cas e except for the effect of the core barrel, which was being neglected. The following two cases were analyzed : Case C : Deformable vesse l Case D : Rigid vesse l
15 In both cases, the reactor geometries and PSI parameters are the same as those for the reference case. For the case with rigid vessel, fictitious rigid material data were used. As shown in Table 6, for the deformable vessel, the twophase pressure and the slug collision pressure are lower than those with the rigi d vessel because a vessel deformation relieves the pressure rise. Higher pressure in slug collision yields substantially larger deformation for plug holddown bolts with the rigid vessel. 2) Design Parameter s Effects of structural design parameters on containment response wer e investigated. The structural design parameters varied were, thickness, tv, of upper vessel wall, plug mass, Mp, holddown bolts length, LB, and cross section area, AB. The analytical model and the parameters use d were the same as those for the reference case except for the parameter s mentioned above. Some of the results are shown in Table 7 to 9. These parameters e o not give much influence on the pressure transient of the FSI region. An increase in the upper vessel thickness decreases an upper vessel deformation yielding a slight increase in bolt deformation. An increase in slug mass yields a slight decrease in bolt deformation giving less effect c n the upper vessel deformation. An increase in bolts area decreases bol t deformation, which results in a slight increase in the upper vesse l deformation. The cross sectional area of bolts give an inverse effect, because the deformation of the bolts are in the elastic region in thes e cases. 3) FSI Parameter s A. Fuel and Sodium Mass 695
16 While keeping the fuel/sodium mass ratio constant, the total mass. MT, was varied. As shown in Figure 9, an increase in fuel and sodium mass yields an increase in work, especially work done after slug collision. The twophase peak pressure is not much influenced by increasin g fuel and sodium mass while single phase peak pressure increases significantly as fuel and sodium mass were increased. B. Sodium Mas s Keeping fuel mass, Mf, constant, mass, M8, of sodium interacting with fuel was varied. As shown in Figure 11, a peak pressure decreases as the sodium mat s increases. The work done varies only about 15% as the sodium mass wa t changed as shown in Figure 12. This variation in work gives much effec t on upper portion of the vessel deformation. The lower vessel as well a s barrel deformations decrease as sodium mass increases, as shown in Figur e 13. It is because these deformations are influenced by single phas e pressure rather than total work done. C. Fragmentation and Mixing Time Constant As the fragmentation and mixing time constant, tm is increased, the peak pressure is. decreased, and the rise time becomes longer as shown i n Figures 14 and 15. Deformations increase much as tm decreases for the midvessel and for the core barrel, while the upper vessel deformation is not much influenced by t m, as shown in Figure 16. D. TwoPhase Heat Transfer Coefficient Parametric calculations were performed for some values of twophas e heat transfer coefficient, htwo, which was kept constant during FSI process. As shown in Figures 17 and 18, the work done, as well as twophas e peak pressure, increases as the twophase heat transfer coefficien t
17 increases. An increase in twophase pressure makes the slug velocit y larger and causes larger deformation in the upper vessel. Twophas e heat transfer coefficients give less effect on deformations at the lowe r vessel and the core barrel as shown in Figure 19. E. Fuel Particle Radiu s Figure 20 shows the fuel surface area as a function of time. Prou this figure, it will be clear that the fuel particle radius, R f, has similar effect on pressuretime histories as the fragmentation and mi ;in g time constant, t m, and an inverse effect on that of the twophase hea t transfer coefficient, htwo, because the heat transferred to the sodiu n depends on fuel surface area, A f, and htwo. As shown in Figure 21 to 23, work done by FSI and the peak pressur e decrease with increasing fuel particle size. The twophase peak presfur e does not vary much when the fuel particle radius is greater than 100/ 1.. The vessel deformation decreases as the fuel particle radius increase ;, as shown in Figure 24. F. Heat Loss to the Surrounding s An evaluation has been made on the effect of heat loss from the FE I zone to the cold surroundings during a pressure transient and containnen t response. Heat transfer coefficient was assumed 0.3 cal/seccm2  C according to the analysis of the H2 experiment in TREAT. Heat transfe r area was assumed to be equal to the surface area of a spherical PSI zcne. Temperature of the cold boundary was assumed to be equal to the reactc r.outlet coolant temperature which is kept constant during the FSI process. As shown in Table 10, a heat loss to the surroundings has negligibl e effects on the results under the abovementioned assumptions. In th e actual HCDA conditions, the heat transfer area might be greater than th e above assumption, if cold structural materials around the FSI zone ar e
18 taken into account. In addition to that, the FSI zone may not be a perfect sphere as assumed in the present model. Considering these conditions, results with greater surface areas are also shown in Table 10 :'or reference
19 V. CONCLUSION Using the experimentally verified code FCIII/ASPRINII, evaluaticns have been made on the effect of FSI parameters o n. structural response in HC])A. Radial deformation of upper portion of the vessel is much large r than those of mid portion of the vessel and core barrel. Therefore ora e of the most important safety concerns is the deformation at the uppe r portion of the vessel. In this point of view, the twophase heat transfer coefficient, and the fuel particle radius, R f are found most important among many FSI parameters. The fragmentation and mixing tim htwo e constant, t m does not give much effect on deformation at the upper portion of the vessel because the time constant considered is much less than th e time period in which sodium slug is accelerated
20 Reference s (1) D. H. Cho, R. O. Ivins and R. W. Right, "RateLimited Model o f Molten Fuel/Coolant Interactions : Model Development and Preliminary Calculations", March 197 2, ANL (2) G. L. Fox, "ASPRINA Computer Code for Predicting Reactor Vesse l Response to Hypothetical Maximum Accidents on Fast Reactors", December 1969, BNWL (3) A. Padilla, Jr., "HighTemperature Thermodynamic Properties o f Sodium", April 1974, ANL (4) R. D. Richtmyer, "Difference Methods for InitialValue Problems".. Interscience Publishers, Inc., New York, 1957 (5) J. von Neumann and R. D. Richtmyer, "A Method for the Numerica l Calculation of Hydrodynamic Shocks", J. Appl. Phys. 21, 3(1950 ) (6) A. B. Rothman et al., Trans. Am. Nucl. Soc., 13, 652 (1970 ) (7) A. W. Cronenberg, H. K. Fauske and D. T. Eggen, "Analysis o f Coolant Behavior Following Fuel Failure and Molten FuelSodium Interaction in a Fast Reactor", Nucl. Sci. Eng., 50, (1973 ; (8) M. M. K. Farahat, "TransientBoiling Heat Transfer from Sphere tc o Sodium", January 1972, ANL (9) K. Sasanuma, et al., "Analysis of Containment Experiments", 1973 Fall Meeting, Atomic Energy Society of Japan (10) D. D. Stepnewski, G. L. Fox, D. E. Simpson and R. D. Peak, "FFTF Scale Model Structural Dynamic Tests", April 1974., CONF (11) "PISCES, Structural Dynamics Test Analysis of MONJU Scaled Model " June 1974, PNC PISCES Report 3, ZN (unpublished )
21 (12) "A General Description of PISGE>2DL", August ]971, Physics Inte :.  national Company, California, US A (13) S. H. Fistedis, Y. W. Chang, T. J. Marciniak, G. Nagumo an d J. Gvildys, "Fast Reactor Containment Analysis, Recent Improvements, Applications and Future Development", April 1974, CONF (14) Y. W. Chang, J. Gvildys and S. H. Fistedis, "Analysis of the Priiiary Containment Response Using a Hydrodynamic ElasticPlastic Compute r Code", 2nd SMiRT, September (15) J. M. Steichen, "High Strain Rate Mechanical Properties of Type ;04 Stainless Steel and Nickel 200", September 1971, HEDLTME (16) J. J. Holmes, et al., "Effects of Fast Reactor Irradiation on th e Tensile Properties of 304 Stainless Steel", J. Nucl. Mat. 32 (1969 ) (17) J. M. Steichen, "Effect of Irradiation on the Strain Rate Dependhnc e of Type 304 Stainless Steel Mechanical Properties", Nucl. Tech. ] 6 (1972) (18) A. L. Ward and J. J. Holmes, "Ductility Loss in Fast Reactor Irrediated Stainless Steel", Nucl.. Appl. & Tech..2 (1970) (19) D. H. Cho, W. L. Chen, and R. W. Wright, "A Parametric Study o f Pressure Generation and SodiumSlug Energy from MoltenFuelCoolan t. Interactions", August 1974, ANL8105
22 Table 1 Coniparison o f AS?RINII and Other. Codes' Result : with Experiments (I ) MidVessel Mztximu:! Deformation ASPi',INI I Analytical 2D hydrodynamic s Analytical _._ * 1 f Experimenta l MONJU Scal e Test E % % (9 ) _. ~_ F1'1F CoT p] ( x Y 2 1. Mode l.2e$(cm301 test ) 1.3% 1.0% 1/30 Scale I.UE1 (CM302 te ; t) _ *1 Analytical result 11 by PISCES2DL code 1 2 *2 Analytical. result (11) by REXCO HEP code Table 2 Comparison o f ASI'RINII ; nd Other Codes' Result s with Experi!u nts (II ) Umor Ve.,sel Maximum Deformatio n FFPF Comple x Mode l 130 Sale FM =A Analysis ASPRINI I Analytical REXCO}tP Analytical Experimenta l 2.4 ~ 4.8% 3.4f (13) 2.2% (10 ) J 3.5(14).~
23 Table 3 Reactor Geometries of the Reference Cas e Core barrel ; inner radius 1850mm thi ckness t~ 40mm gridvessel ; inner radius 3550mm thickness Upper vessel ; inner radius effective thickness tu0 Cover gas gap Cover plug mass 40mm 3900mm 48.7mm 500mm 1600tons Plug holddown bolts ; length LB mm effective area ABo m 2 Table 4 Material Strength Dat a Core barrel Midvesse l Upper vessel 0.2% yield stre s Kg/mm ultimate stres s Kg/mm ultimate strai n %
24 Table 5 Initial. Cond.ition: and Farometerr of. FSI for the Reference Cas e Nass of molten fuel,?if 1000Kg Initial temperature of fuel 3338 K Fuel particle radius, R f 11.7 /4 Mass of sodium, Ms 105Kg Initiel temperature of sodium 900 K Fracmentation and mixint ; i,i_me constant, t m 20mse c Twophase heat transfer coefficient, htwo Heat transfer coefficient to th e Surroundings, hloss 0.1 w/cm 2 C 0.0 w/cm 2 C
25 Table 6 Effects of Vessel Mode l Deformabl e vessel Rigi d vesse l Two phas e peak pressur e (Kg/cm 2 ) Pressure pea k due of slu g collision (Kg/cm 2 ) Max. deformation of plug holddown bolts (%) ~
26 Table 7 Effect of Upper Vessel Thicknes s 0.8 x tj0 tu0 1.2 x tii0 Max. upper ver,e l deformation ( ;') Max. bol t defy ;. motion (â) tu0 = 48.7mm Table 8 Effect of Plug Ma s 0.5 x Mp0 Mp0 2 x Mp 0 tîax, upper ve.e : ;ei. deformation (%) Max. bol t deformation (~ ' ) Z C Mp0 1G00ton s Table 9 Effect of Bolt Area and Lengt h LB x 4B0 LB O LB 0 2 x ARO 0.5 x LB0 AB O ABO Max. upper vesse l deformation ( ; ) Max. bol t deformation () ' LB0 = 1950m m ABO = m
27 Table 10 Effect of heat Los3, to The Surroundings h loss_ 0 i1 loss JP ' loss F Two phase peak pressure (F:;;/ort ) Work k done before collision WeS) S Total work don e (K Max. upper vesse l deformation C) hloss = 0.3 cal/sco cm2 C AF = 47CR FSI ~F5I  rr:dius of KU zone
28 1.1 deformation at upper portion of vessel! I v I I IL  u'" plug motion Mug collision 1 1 I I holddown t ol t deformati c n coolant slug motion deformation I i at middle ``, 1I I portion of 1 vessel ~' PSI zon e U pressure wav e transfer vesse l downwar d motio n Figure 1 The Analytical Model of ASPRINI I
29 m =0 tm=1omse c / tm=20mse c 70 6o V''/ Experimental voiding histor y nf = 250 / A hioss = 0 htwo = 0.1 w/cm2 ' C mf/mi a = \ 10 1 t time (msec ) 40 Figure 2 Effect of the fragmentation and mixing time constant, t m, on the voiding history
30 loss= i / ' hloss=0.1 cal/seccm 2 C hloss=0. 2 cal/seccm2 C " experimental voiding histor y 50 hloss =0. 3 cal/seccm2 10 Rf = 250, tm = 20mse c htwo = 0.1 w/cm2 C Mf/Ms = time (msec) Figure 3 Effect of heat loss on the voiding history
31 1 Free boundary Fixed boundar y 1000 Deformable vessel H f = tm = 1171 t 20mse c htwo = 0.1 w/cm2 C Mf/Ms = 9.52 Mf = 1000Kg 100 (2 )  sec ) I i,! E time (m Figure 4 Effect of boundary condition on pressure transient
32 20 Free boundar y Fixed boundary Deformable vessel (1 ) Rf = 117 f tm = 20mse c htwo = 0.1 w/cm2 C Mf/Ms = f = 1000Kg (3) 10 c 5 (2 ) a time (msec ) Figure 5 Effect of boundary condition on volume change 712
33 8 7 5 Free boundary Fixed boundary Deformable vessel Rf = 117 tm = 20msec htwo = 0.1 w/cm2 C Mf/Ms = 9.52 Mf = 1000Kg (1 ) m 4 o N H a) o,ci 3 (3 ) s.i 0 2 I 0 5 time (msec ). 1, 10 Figure 6 Effect of boundary condition on work done by FSI zone 713
34 5 (1) Free boundary (2) Fixed boundar y (3) Deformable vesse l R f 11.7 (1 ) tr = 20msec 4 htwo = 0.) w cm2' C ISTf /1s = 9. ~i2 mf = 1000 K 'n \ ( 2) N time (mscc ) Figure 7 Effect of boundary conditions on kinetic energy cf the surrounding s
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