ML19308C831

Draft of Preliminary Analysis of Containment Failure Probability by Steam Explosions Following Hypothetical Core Meltdown in Lwr

ML19308C831
Person / Time
Site:	Crane
Issue date:	03/28/1979
From:	Michael Corradini, Voelker L, Woodfin R SANDIA NATIONAL LABORATORIES
To:
References
CON-FIN-A-1030, TASK-TF, TASK-TMR NUREG-CR-1104, NUREG-CR-1104-DRFT, SAND79-2002, NUDOCS 8002070582
Download: ML19308C831 (136)

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{{#Wiki_filter:god @f 't 4 9a NUREG/CR-1104 SAND 79-2002 Preliminary Analysis of the Containment Failure Probability by Steam Explosions following a Hypothetical Core Meltdown in a LWR E. Voelker M. L. Corradini, R. L. Woodfin, L. Prepared for Division of Reactor Safety Research Office of Nuclear Regulatory Research U. S. Nuclear Regulatory Comission Washington, DC 20555 Under Interagency Agreement DOE 40-550-75 NRC FIN No. A-1030 l 80020705 M L ~ /

T 1.0 Introduction ~ Sandia The purpose of the steam explosion phenomena program at To identify experimentally the trigger energy, is twofold: (1) sary to trigger . impulse and other initial conditions which are neces lten and propagate explosive interactions between water and mo ~ to develop criteria light water reactor *(LWR) materials; and (2) losions to assess the probability and consequences of steam exp during a hypothetical core meltdown accident in an LWR. t This report describes the models used in analyzing the even s f leading to containment failure and offers a preliminary set o criteria to assess containment failure probability. (1) assessed 'n 1975 the Reactor Safety Study (WASH-1400) l ion as the probability of containment failure via a steam exp os one of the many physical processes that could occur during a The probability of this event was hypothetical core meltdown. subdivided into three factors a g = 10-2, P, = Pgy sxs a e where probability that 20% or more of the molten core 1= Pfy = contacts a similar mass of water. probability of fuel fragmentation (< 4000 pm)

.1

asxs when fuel falls into the water. fraction of steam explosions leading to a f =.1 = c containment failure. the In particular, containment failure analysis indicated that li a fuel containment could be breached for an interaction invo v ng

mass of more than 20% of the core and final fragment diameters less The reactor vessel is predicted to fail by brittle than 4000 um. This results f ailure in the elastic regime of strain in WASH-1400. in negligible energy expended and failure is predicted to occur below The whole upper head is then accelerated upward the vessel flange. and if it rises to an elevation equal to or greater than the contain-ment walls it is asumed to have penetrated the containment structure. Large uncertainty bands (more than an order of magnitude) were attached to these probabilities and subsequent research has Buxton (2) concluded that attempted to reduce the uncertainty. indeed the probability of molten core / water contact for at least 20% of the core is nearly one. Also experiments at small and intermediate scale (4,5,6) and subsequent analysis (3) has indicated that a steam explosion event with fuel fragments smaller than 4000 um in diameter is quite likely. In the final area of containment failure probability, a f' c analysis of the main portions of the event for an invessel explosion has been in three areas: Expansion phase of the steam explosion when the high (i) pressure coolant vapor accelerates the coolant slug above it up to reactor vessel head impact. Structural analysis of shock wave effects and reactor (ii) vessel head impact when the slug fails the head and generates a missile. Dissipation of missile energy by impact with obstructing (iii) structures and subsequent impact of the missile with the i l containment structure. e s ilure In the following sections each portion of the containment fa l event is addressed by examining (1) what models are used to ana yze t It the transient, and (2) what is the probable course of even s. should be emphasized that much of the physics of these processes is still not well understood and research is still underway. E 2.0 Expansion Phase transfer event which The vapor explosion is the rapid heat ih converts molten fuel thermal energy into mechanical work, wh c dynamic shock may breach the integrity of reactor vessel by (i) acceleration of a slug of water which impacts over-pressure or (ii) (Figure 1). The the vessel head and thereby generates a missile vessel structural response to overpressure and head impact are In this section we will address addressed in the next section. h the expansion phase and the heat transfer which may re3uce t e Heat kinetic energy of the slug after the propagation phase. l t transfer to the solid structure and to the cold liquid coo an will both be considered. It should be emphasized that the amount of heat transfer is ' dependent upon the geometry within the vessel for coolant vapor In fact, expansion which in turn is accident scenario dependent. -3o steam explosion occurs within the reactor if it is postuPted ths- ~ heat vessel but only below in the reactor cavity area, then some initial con-transfer processes will still occur but with different ditions and geometry. Because of this dependence on the accident scenario, which at i ily directed this time includes many alternatives, research was pr marf r phenomena, i toward identifying the key fluid mechanics and heat trans e i I 'U OOOE GG *6$66 6

and performing parametric calculations to determine the possible range of effects ci the expansion work of the interaction. The geometry within the interior of the reactor vessel will The presumably be quite distorted due to the meltdown sequence. amount and location of fuel and cladding which would be melted E Some bounds, however, before fuel-coolant contact is not well known. can still be proposed. If the molten core remains above the lower core grid plate for a long time (~ 1-2 hrs.) before failure, then a substantial fraction (50-100%) and would be intermixed of the fuel would be molten (2) In addition oxidation of with the zirconium and stainless steel. i the metallic components (Zr and Fe) will continually be occurr ng. Thus it seems likely that a substantial portion of the core would In fact the core barrel wall may also be be melted out radially. Additionally the radiant heat flux upward under thermal attack. from the core melt could severely weaken or melt some portion of \\ The dhckbody the upper internal structure or the upper head region. heat flux from a molten corium pool through the steam to the cold Thus when the lower grid plate 2 walls is of the order of 2 MW/m. the expansion path to failure occurs and fuel and coolant meet, There still may be the reactor head & hould be essentially clear. Cae amount is a matter of some upper inter'nal structure left, but speculation. Conversely if the meltdown has not proceeded for very long (30-60 min.) when grid plate failure occurs then substantially There will then be a larger less core would be molten (5-50%). amount of resolidified and relocated core materials through which

Presumably this solid material the vapor expansion must proceed. will be attached to the grid plate and to the inner wall of the The material will serve to retard the expansion and core barrel. Additionally more uppe.r structure break up the liquid water slug. will remain intact and not be as severely weakened by the thermal I Thus the mechanism and time of grid plate failure are radiation. important but not well known. The location of the lower grid plate and the resolidified If the fuel, steel and ziQconium can affect the vapor explosion. grid plate f alls to the bottom of the vessel and the explosion If occurs above it then it may not participate in the explosion. the explosion occurs below it, two possibilities exist: {1) the grid plate, if totally free, would become part of the internal (2) the grid plate, if slug being thrown toward the vessel head; could reduce the liquid slug attached to a core barrel support, At this time uncertainty about the meltdown process acceleration. does not make one of these alternatives morc likely than another. After the explosion has occured, the high pressure vapor will (Figure begin to expand, accelerating the water above it as a slug. If The compressibility of this water slug is not well known. 1) the fraction of vapor is small and the acceleration process does its outer edges along the vessel walls, not break up the slug at If the converse is true, then it could be considered quite rigid. the slug may actually be a series of separate liquid water masses that may or may not behave coherently as they impact the vessel To date no conclusive experimental evidence structure and head. in a has borne out either possibility. Experiments by Buxton (6) Oteel tank demonstrated that the water above the fuel-coolant The relative interaction zone contains vapor and noncondensible gas. amount of these gases is not exactly known but is dependent on the As subcooling increases, vapor initial experimental conditions. Gases from is partially condensed before emerging from the top. I However in all the tests a metallic oxidation are always present. In fact, in test 42, somewhat coherent slug of water is expelled. + this slug expelled a cover plate 70-80 meters in the air while breaking the steel cable tie down. Heat transfer to solid structures in the core is very scenario dependant because the geometry remaining after the accident dictates Therefore, this the surface area available for heat transfer. question cannot be adequately addressed at this time other than to assume either of two O extreme,d cases; all the upper vessel structure The heat transfer ccefficient has melted out or all is still in place. for this process is complicated by the fact that, as the high pressure coolant vapor from the interaction expands, it pushes the liquid coolant slug upward exposing solid structure with a liquid water film remaining (Fiaure 2). Depending on the liquid film thickness, l the heat transfer process may be dominated by transient condensatiron ) A, on the liquid film or a combination of condensation and conduction f into the solid. Ozgu and Chen (7) indicate the ratio of A to the is on the average 0.1 for hydraulic diameter of a channel, D H, 1 sur case, the driving pressure driving pressures of a few bars. Thus, a very rough extrapolation is an order of magnitude higher. of the film thickness would be.01 < A/DH < .1. The hydraulic if we choose the diameter is again dependent on the geometry but l

~7-Possible and the film is thicker than the thermal smallest DH f penetration length (a > /a Twexp)wherea,isthethermaldiffusivity then liquid film controlled condensation would appear to be the is in.the fission The smallest DH dominant heat transfer process. <.11 cm. The gas plenum, with DH ~ 1.1 cm; therefore,.011 < A thermal penetration thickness is found by evaluating the characteristic This time can be expansion time, texp, through the structure. estimated to be l (1) , ' 2aL ' s exp ,a and (2) AP a= b Pw w where < 3 meters A L, length of the structure pressure pulse due to interaction = 10MPa AP - L, - thickness of coolant slug = 1 meter =.005 cm. Thus This gives t exp = 20 msec and /a t w exp and liquid film controlled condensation is the A > /a t y,xp expected mode of heat transfer. Heat transfer to the cold liquid coolant should also be con-This process takes place between the hot vapor and the sidered. interaction zone during its accelera-liquid above the fuel-coolant The surface area for this tion by the coolant vapor expansion. heat transfer would be increased by fluid instabilities which cause Then the liquid coolant to become entrained in the hot vapor.

condensation heat transfer similar to that expected with the liquid film on the solid structure would occur. Liquid coolant extrainment into the expanding hot vapor may be caused by a number of mechanisms. Some that have been proposed are: l ~ Taylor instability entrainment would be caused by the (i) less dense vapor accelerating the nnre dense liquid. Corradini (B) has proposed a model for this entrainment This mechanism was originally suggested by mechanism. Cagliostro (9) for small scale SRI tests. Hemil.Oltz instability entrainment would be caused by (ii) vapor flow over a liquid film and the induced shear stresses. Cagliostro et al (9) have also suggested the mechanism but no transient models have been proposed. has recently suggested that neither of the (iii) Theofanous (10) hydrodynamic entrainment mechanisms previously described Rather it may dominate in a condensing vapor expansion. has been suggested that a condensation shock occurs at the vapor-liquid interface entraining the liquid coolant. No mathematical model has been proposed. Work All these mechanisms may be operative during the expansion. At this point, however, is continuing on these entrainment models. analysis based on Taylor instability entrainment alone is presented We feel that this mechanism and applied to the accident situation. is dominant throughout the expansion because 'saj:or is accelerating the liquid coolant for most of this time, ?V<~;odel to be presented SRI performed l has been compared to small scale integcal experinents at

A more detailed description of the model is by Cagliostro (9). given in Appendix A. The Taylor instability entrainment model is based on simple hydrodynamic experiments (8). These planar quasi two-dimensional experiments were used to determine the non-linear growth rate of Based upon the the Taylor instability at a water-air interface. results,avolumetricentrainmentrate,h,,isproposed: (4) h = dVe = 4.6 A [a1 e dt p c (5) 8 A = 2w C (p -py)a g is the is the critical Taylor wavelength, and Ap where A c projected area. The surface area, Ad, of the entrained liquid is 0Y (6) e Ad =~3] is the characteristic entrained drop diameter thought to lie where Dd It should be noted here that this between A and A, = / 3 Ac. c heat transfer area exceeds that of the upper internal structures by is felt to an order of magnitude. This characteristic diameter, Dd, because this is the probable size of the entrained be near Ac Further droplet breakup due droplets when they are being formed. and if the breakup time is to Weber forces may occur if We > Wecrit smaller than the time scale of the transient. The condensation heat transfer coefficient for these processes can be approximated by a combination of three heat transfer resistances J

(Figure 3); (i) interfacial resistance to condensation, h, (ii) g 6 condensate film heat transfer resistance, hg, (iii) heat transfer resistance in the coolant droplet or the film on solid structures, Note that both the drop and the film can be treated as semi-h. y infinite because a > /a t or Dd > /*w. The interfacial t I w resistance is negligible for these processes in comparison to the is other resistances and thus the heat transfer coefficient (7) TOT /wa t g y E[ + 2k, is the condensate film thickness and k, is the water where 6 thermal conductivity. For the case of liquid heat transfer, the heat transfer rate, combining egns. 4-6, becomes, 6V (8) ji h T) TOT (T q=-D v c d where T is the vapor temperature and T is the liquid coolant c y temperature. expansion is modeled by a one-dimensional momentum The vapes equation.and the expanding vapor volume is modeled by a lumped parameter energy equation including this heat transfer model. This model can be applied to vapor source expansion of a full scale LWR interaction or to the tests of Buxton (6), given the initial conditions after the propagation phase is completed. In the experiments performed by Buxton the thermite mixture was poured into water (~ 850 kg) and the explosion usually occurred j i I

near the bottom of the steel tank. An analysis to determine the effect of heat transfer was done. The coo.act slug kinetic energy exiting the steel tank was compared for isencropic and heat transfer The results are shown in Figure 4 where the model assumptions. in the interaction zone is assumed to be nearly saturated coolant I quali i ~.04) giving a mass of coolant of about 25 kg. water (X = c The initial vapor explosion pressure was varied over the range of The results indicate values observed in the open geometry tests. that heat transfer significantly reduces the slug kinetic energy and gives mechanical-thermal conversion ratios similar to those As another experimentally determined by Buxton (= 0.5-1.5%). (TEST indication of the effect of heat transfer one specific test, 43), was compared to the analytical model of the expansion (Fig. 5). Here again the transient pressure data during the expansion match transfer is reasonably well with the analytical model when heat included. Parametric calculations of the full scale expansion were also done assuming no core structure is present, where the physical It is assumed in picture of the expansion is given in Figure 1. the analysis that the hot two-phase coolant in the interaction thereby zone accelerates the cold coolant transferring energy to it, For the full reducing the vapor pressure and slug kinetic energy. scale hypothetical accident the initia2 conditions are not well the amount of coolant participating in the inter-kn.own, i.e., (a) the average coolant thermodynamic state after the action, M r (b) e propagation phase (P and X ); (c) the cold coolant slug mass c c For the parametric above the propagation interaction zone, Malug. i l m e

analysis, the range of these three values are taken to be 0 1000 kg < Mc < 2000 kg = 0. 5 MP, <Pc < 20 MPar for Xe / 1400 kg > Malug < 72000 kg is based on 5-100% of the water in the lower plenum The range on Mc on the range of initial vapor pressures observed in of a PWR, Pc on the water height of the lower plenum Buxton's tests, and Mslug to 50% of the active core height. The results of the analysis are given in Figures 6 to 9. Figure 6 illustrates the significant effect of heat transfer in reducing the slug kinetic energy for one set of initial conditions as a function of the expansion volume. The final volume (av = 120 m) corresponds to the slug entering 3 the upper head region where upper internal structure may be present even after the core meltdown. Figures 7 and 8 indicate the effect of the initial coolant vapor and M pressure on the slug kinetic energy for two values of M c slug

• Some observations can be made from these results:

(i) The slug mass does not appreciably affect the kinetic This is due to two counter balancing effects; energy. increases the expansion time increases allowing as Mslug more heat transfer yet the heat transfer area decreases, due to an increase in the entrained droplet size. (ii) The percentage reduction in slug kinetic energy due to when M heat transfer is not drastically affected by Pc c is held constant. The percentage reduction in slug kinetic energy is strongly (iii) i dependent on'the mass of coolant, M ' Participating in c ~~ ~~ s the explosion; for Mc=1000kgfK.E.HT/K.E.ISEN =.25 S This effect is while for Mc " 4000 kg K.E.HT/K.E.ISEN. more graphically demonstrated in Figure 9 for a given f value of P ' c Based on this analysis, the mass of the coolant involved in the interaction is thN most crucial parameter in accurately determining the reduction in the kinetic energy of the coolant slug due to heat transfer after the propagation phase. Once the coolant slug enters the upper vessel head region the analysis becomes more complex because a number of physical effects may occur due to fluid-upper internal structure interactions: deformation or failure of internal structure reducing the 1) overall slug energy 2) breakup and deceleration of the coolant slug due to passage through the upper internal structure breakup and deceleration of the coolant slug due to Taylor 3) instabilities and the compression of steam vapor and non-condensible gas above the slug as it nears vessel impact. The amount of upper internal structure and its geometry following the accident is not known accurately. Qualitatively though the BWR with its internal steam separators and dryers in the upper vessel head region would represent more of a structural barrier than the PWR. The approach taken at present is not to quantitatively estimate the reduction in slug kinetic energy directly because the uncertainties Rather, we intend to bound the effects of at present are large. In the following section the modelling the upper internal structure. of the structural response of the vessel is presented. I

-le-Reactor Pressure Vessel Structural Response 3.0 in structural details of LWR Because of the wide diversit W- ~ (ktMitC & pressure vessels, no. ..r....c; statement is possible en their' $P" By its otructural response for a hypothesized steam explosion.. structural response is design dependent and most often is EE

nature, in a controlled by details which are not the first things noticed is possible, of course, to generically It look at the design.

ider discuss some effects, but for a dependable result one must cons a specific design. The In this section discussion will center on one design. (PV) at the Zion Power Plant example chosen was the pressure vessel Since more detailed drawings were not (Commonwealth Edison Co.). d The available, the drawings in the FSAR for the plant were use. specific in the results are then both specific and generalized: lized sense that application to other designs is limited and genera in the sense that they are not based on blueprints and were done An in the manner of a preliminary design analysis for a PWR. h blem additional attempt was made to consider one aspect of t e pro in a generic sense, exclusive of the Zion design. basic The question of structural response was divided into two The early time domain is the time after time domains for the study. through the steam explosion during which the motion of stress waves This was studied in a generic the vessel dominate the response. The later time domain is that way, independent of the Zion design. d entrained time during which a slug of material composed of water an of bits of the core structure strikes the upper internt1 structure f Consideration of other dissipative effects the PV and the PV head. is left for future work and the existence of some core structure is ignored in this analysis. 3.1 Early Time Domain In the early time domain two possible failure mechanisms were i One is sufficiently general in character to allow a identified. generic analysis, the other is so specific that even the choice of an example is difficult. The former is the case of the stress wave propagating through the water surrounding the explosion to the vessel walls and then A generic analysis indicated up the walls toward the flange area. (a spalling that the potential failure mechanism in this process, type tensile failure at a reflection point), was precluded by the In effect, the rise time slowness of the steam explosion event. of the pressure pulse produced by the steam explosion is so long that no shock wave is,)roduced and the combined reflected wave is not short enough to cause spall. Both 1-D and 2-D generic models 21 The basic conclusion is that using the HONDO code were run. the water has time to flow aside in this slow explosion event, mitigating the level of the pressure transmitted to the vessel and causing complex rather than simple stress wave interactions. These interactions cannot combine in the simple way required to Even if a local tensile stress sufficient to produce a missile. cause vessel failure were produced, it would be a local effect and Thus, no potential containment incapable of producing a missile. breaching mechanism can be found in this part of the time domain. Now consider the case of a perforation of the bottom of the This vessel as the direct effect of an adjacent steam explosion.

._ t, ? 4 Therefore, no general possibility is design and event specific. case is thought to be representative, but it is also clear that this mechanism can never produce missiles which might breach con-tainment because any missile would be directed into the reactor cavity. Therefore, this mechanism was not considered further. 3.2 Late Time Domain Most of the efforts in this analysis were directed toward the remaining, late-time domain. The assumption was made that the energy of the postulated steam explosion was available in the form of kinetic energy of a s1 g of water. This water was taken to be initially in a compact configuration or " slug" for each case con-This slug was then allowed to impact the upper internal sidered. } structura for one case and the vessel head for three other cases. j I -d>- An intermediate case considering the diss/ pative effects of the upper internal structure was identified and will be analyzed in the toere s 'by future. y presentative calculationSwas performed for an energy of 300 MJ. This is representative of that calculated in the previous section. Three basic analyses were conducted with one variation. The first analysis considers that the water arrives at the vessel head with no obstructions and that the water forms a compact Two voidless slug with the volume determined by the mass chosen. combinations of slug mass and velocity were used based on considera-tions discussed in the previous section. Figure 10 illustrates the finite element model used for both water slug configurations. Figure 11a illustrates the model using the small water slug; Figure 12a, the 4 l \\ l

to)"# material model used is a bi[ linear /elasticq2 large water slug. Th pohL strain-hardening-pJjiA approx'. mating ASTM SA533 with ultimate tensile strength = 552 MPa (80 Ksi), yield strength = 344 MPa (50 Ksi), maximum elongation (assumed at ultimate) = 18%, and Young's 5 6 modulus = 2.07 10 MPa (30.10 pai). The HONDO code was used in The initial conditions are given on the figure in each both cases. case and apply to the entire mass of water. 3.85 ms Figures 11b and 12b illustrate the deformed condition at and 8 ms, respectively. These times represent the times of maximum stress to the head and the water slug may be seen in a rebounding condition, i.e., moving away from the head in each case. Even though the deformation appears greatest at the bolt ring, the peak stress occurs at the " top" of the hemisphere, i.e., on the axis. A close examination or overlay will confirm that the deformations at the top of the PV are greatest also. This conclusion is largely dictated by the loading condition. However, it is representative of any readily conceivable loading system in that some local stress will always be the highest;and when that stress reaches the ultimate . 3) of the material / a local failure may be expected. This local , 77 failure is not a missile generating failure, but a crack which emits a jet or a plane sheet of water at a velocity cc.nsiderably ) below that of the slug. J Postulating the water to be ejected upward at 100 m/sec., the t stream only barely reaches the inside of the containment ceiling l (by equating energies) even neglecting drag and instability in the 1 Therefore, the impact on the vessel appears to pose no threat flow. i to the containment. l l The second analysis is for a water jet or narrow, high velocity slug impacting the vessel head. This is based on a hypothesis of the slug being forced through a narrow opening in the remaining gi a efic e weeg y undisrupted core z.tructure with the full tel;;ity-of th.e entire ~s j slug. l The computer model for the water jet problem is shown in Figure 13 with a vertical column of water 10 cm in diameter and 3.2 m long. The water jet problem uses two different impact velocities 21s for the water column in the analysis by CSOy. The lower velocity of 0.5 km/s is based on the physical restrictions satic by equating eW kinetic energy and strain energy to get 2 = 2c t/(pr) v y higher velocity of 1.11 km/s corresponds to the sonic velocity The in the water column which approximates a choked flow condition. The Figure 14a shows a closeup view of the original configuration. two final configurations (14b and c) of fast and slow jet impacts at the time of-maximum vessel stress indicate that no penetration of the steel shell has occurred. The final analysis done in this series considers whether a con-trol rod assembly might be ejected. Again the full kinetic energy was attributed to the slug and uniformly distributed to each of the 53 control rod assemblies. In this case an energy of 400 MJ was used for further conservati E 9 In order to estimate a force on the control rod assembly, a The change force time history was postulated as shown in Figure 15. in esse;:nt was equated to the impulse, i.e., N'MtMm l

) '. tp (mv)t - ("V)o = f p t o i P subject, of course, to a tacit one-dimensional modelling assumption. The peak load is thus obtained, " 2amv t ~Y f A crude estimate for the factor tg is the time required for This a particle to travel the length of the slug at v = v. o resultf in a very long time of 50 ms. Shorter times will result in -_9p higher peak loads. While that may seem unconservative, it is notj _g=, since this assumption results in a peak load of about 6 MN which is essentially equal to the highest estimated Euler buckling load of 6.6 MN. Any higher peak loads will surely cause buckling and result in no missile generated. Actually the estimated Euler load it is itself conservatively high, Icading to the conclusion that is difficult to conceive of a loading condition of this type which does not buckle the control rod mechanism. Nevertheless, assuming that no buckling occurs and that ejec-tion is possible, the characteristics of the missile generated are explored. By evaluating the strain energy required to break loose i the control rod assembly, it is seen to be insignificant relative to the kinetic energy available, assuming no dissipation. This permits the assignment of the full proportion of the kinetic energy to t ae assembly, 7.0 MJ, and results in a missile velocity of 275 m/ set. ( f It is apparent from this preliminary investigation that more wock ~ so that the needs to be done in formulating the real problem (s) 1 While there does not analyses can be conducted in more detail. appear to be a serious question of any of the above accident l environments endangering the integrity of the containment vessel, that of the pressure vessel is not so well assured and further investigation may be warranted.* The rough nature of these calcula-I tions precludes any definite conclusions but does indicate the areas which could be investigsted. 4.0 Assessment of Containment Failure The primary concern in regard to vapor explosions is that they produce a leak path to the environment early in the meltdown for The possible radiological releases from a hypothetical accident. failure of containment by a missile is the primary way this could Overpressurization of the containment by this interaction occur. does not seem possible because the amount of steam needed to generate a missile would not significantly contribute to any overpressurization by its free expansion into the containment volume. To assess the possibility of containment failure by a missile, the approach taken has been to identify the obstacles to a missile coming from the reactor vessel and to assess the containment-missile interaction by empirical concrete penetration formulas. Previous analysis to answer this question was done in the Reactor Safety Study (WASH-1400) where the missile was assumed to be The obstacle for the missile in the PWR the reactor vessel head. was the control rod shield block which became part of the missile is recognized that these tentative conclusions are at variance 1 with the events during the SL-1 accident and research is being "It j directed to resolve this. i l l.-

it was assumed that afteraninelasticcollis/ionand,intheBWR, the upper internal structure was part of the missile. The ability to penetrate the containment was determined by calculating the maximum hiight the missile rose against the force of gravity; if this distance exceeded the height of the containment then the con-tainment structure was considered to have failed. The obstacles which a missile from the reactor vessel say encounter depend essentially on the type of reactor, PWR and BWR, For the and on each individual design for primary containment. analysis done in this section, the reactors ured in the Reactor Safety Study are considered; Surrey Power Station (PWR)(15) and Peach Bottom II Stat' ion (BWR).(16) There are two reasons for using these reactor plants:

1) consistency is maintained with the Reactor Safety Study analysis, and 2) detailed information about the contain-ment design is readily available for these two plants.

For the BWR, the primary containment is small and is in the If a missile is generated shape of an inverted light bulb (Figure 16). from the reactor vessel head, no major obstacles are between it and The control rod the primary containment and reinforced concrete. drive mechanisms and associated instruments enter from the bottom. There is a relatively short distance between the vessel and the If the missile penetrates the barrier, primary containment (~ 1 m). The reason for a radiological leak path has been established. this is that the secondary containment is not designed to maintain a low leak rate since it is a sheet steel structure similar to the Thus, even if the missile did not penetrate the turbine building. secondary containment, a leak path would sti11 exist.

The primary contain-For the PWR, the situation is different. ment is normally large in relation to the reactor vessel and many large components are located within it. (Figure 17); e.g., steam Also, the reactor vessel is l generators, polar crane, pressurizer. The control red drive located within the fuel transfer pool area. I mecha#sms, ventilation system and a control rod shield block are i A missile from the vessel may located directly above the vessel. Collision with the collide with any of these large components. is very control rod shield block, the heaviest structure above it, likely because id lies only 5-10 meters above the vessel head. 1 (1) inelastic The possible consequences of such a collision are: (2) collision, missile and shield block both projected upward; elastic collision, where the shield block becomes the missile, and (3) penetration of the shield block, the missile proceeding upward. Which of these actually would occur depends upon the details of For this analysis, the collision and the missile size and shape. the elastic collision case is neglected because the shield block has the larger mass and the final velocity of it or the combined masses is not significantly different. Collision with the steam generators and the pressurizer does not seem likely because they are located outside the vertical missile shield barrier and, with the vessel at the bottom of the fuel transfer pool, a missile from the vessel is not likely to have a trajectory toward them without being stopped Even if a collision could occur, first by the walls of the fuel pool. penetration or movement of these structures is not likely for two the masses of these components are a factor of three to reasons: (1) l five greater than the largest missile and (2) all the components have seismic restraints which add to their rigidity and strength. Collision with the polar crane is possible as the missile Penetration of the crane is the only approaches the containment. possible way the missile can reach the containment because of its The probability of colliding with it would be the large mass. ratio of its projected area to that of the containment ceiling A determination of whether the missile could penetrate the area. crane is difficult. The problem is one of armor penetration in a ballistic velocity range (100 < v < 1000 m/sec). There are many i empirical correlations available (7) for hypervelocity impact, none of which are completely suitable for use here because of the Based on a static calculation, limited experimental test range. the energy required for penetration of the steel appears negligible for the small missiles while low velocity large mass missiles may ) not penetrate it. Current work is underway to survey the large Jata base on ballistic armor penetration to obtain a more realistic f assessment of the energy required for penetration. To assess the containment failure capability a parametric analysis was done for two extremes of missile sizes using empirical concrete penetration and perforation formulas (18, 19, 20). Rep-resentative formulas used in this analysis are given in Table 1. l The empirical formula by Young (18) was originally developed from earth penetrator tests. Projectiles were directed into a large target which was essentially infinite in depth in comparison to l the projectile size. Penetration distances (X,,) were then con-f (P). verted to a perforation depth of a finite concrete thickness 1l1_.. l.._1

Perforation denotes a hole formation in a finite thickness wall, whereas penetration is applied to distance traveled into an infinitely thick target. The formula of the CEA (19) in France was especially developed for low speed impact (20 < V < 200 m/s) The of large missiles into finite reinforced concrete walls. o4 e coe,el d h cntainment of y 5e original -;;;1_cstier.3was +egmissile hazards te th cadaA4wEd The final two a nuclear power planggcaused by an airplane crash. empirical formulas are the result of high speed projectile tests into concrete by the Army Corps of Engineers and the Ballistic These two formulas are representative of a Research Laboratory. by family of empirical correlations for concrete penetration (20) high speed missile impact. The range of validity for all of these formulas are listed in Table 1. It should be noted that all the formulas are for head on impacts, i.e., little deviation from a perpendicular collision. The possible missiles that could be generated by an impact on the reactor vessel head range from the entire reactor vessel head and upper internal structure to a single control rod drive assembly. The missiles considered are the bounds on this range. (i) control rod drive assembly for the PWR (ii) reactor vessel head and shield block for PWR (iii) reactor vessel head with and without the upper internal structure for BWR These missiles bound the relative masses and sizes that could be The characteristics of each missile are listed in Table generated. The approach taken is to parametrically vary the velocity of 2. impact using these empirical correlations to predict the maximum l

l - 9 concrete perforation thickness attainable. In this way a graph is generated which can subsequently be used when the missile velocity is determined by a more realistic analysis of the coolant slug expansion and impa t on the vessel head. The results of this parametric analysis are given in Figures 18-20. In Figure 18 the predicted concrete perforation thickness is presented for the PWR vessel head (= 148 metric tons) using the four empirical correlations. The velocity range chosen for the parametric analysis corresponds to thermal-mechanical conversion ratios for the vapor explosions up to 8% for 20% of the core par-ticipating in the interaction. Thi As felt to be a sufficient range to cover the expected results. The BRL and ACE predictions bound the range of values while the correlations by Young and CEA-EDF show agreement at velocities near 100 m/s. The BRL and ACE correlations have been applied here outside of their range of applicability to illustrate that widely different predictions can be obtained when data are extrapolated. The most reliable correla-tion for this low velocity region is the CEA-EDF correlation (19). Young's formula was developed for penetration of a nearly infinite target rather than the perforation of a finite concrete thickness. Thus, it can underpredict the perforation thickness for low velocity as Figure 18 indicates. The CEA-EDF correlation was used for all the low velocity large mass missiles and the results are shown in Figure 19. For the BWR missiles (m = 162 and 298 at) the effect on perforation distance depends on the relative ratio of m/d. If the missile has a lower mass with the same diameter the perforation thickness decreases (m = 162 at, d = 6.7 m). As the mass increases, the energy increases However, for and perforation thickness increases (m = 298 mt). the whole range of possible large missiles the predicted concrete perforation thickness does not vary more than + 15% because P is a function of (m/d)1/2, i The predicted results for the small missile are given in Figure All the correlations used show good agreement over this high 20. The CEA-EDF correlation was not used here because velocity range. it is only valid for the lower velocity values. The key point to note here is that a small missile with a large 1 MJ) to penetrate L/D ratio requires significantly less energy (= although the hole will, of course, be much smaller. the containment, The possible f ailure of the primary containment for a PWR or BWR using these empirical correlations depends on the specific containment design. For the PWR the containment is made of reinforced concrete (= 1 m) thick with a thin steel plate (= l-2 cm) on the inner surface. with For the BWR the primary containment is a steel liner (= 2-4 cm) Reinforced it being free standing at the top of the containment. is built around this structure with a gap of concrete (= 1 m thick) approximately 1 meter at the top. This is done to allow removal of the concrete and upper part of the primary containment for refueling. The resistance that these steel liners present to the missile pene-tration is unclear at this time. Based on a static calculation the However, this resistance to penetration appears to be negligible. problem is similar to the polar crane question, in that the body of literature on ballistic armor penetration is being searched to i l l e find more realistic empirical correlations to determine the energy dissipated in *fenetration of the steel. 5.0 Conclusions and Recommendations This report has presented methods of analysis which can be used to assess the possible consequences of a steam explosion within the reactor vessel. Although not specifically addressed, the damage potential from an ex-vessel steam explosion can also be assessed using these same methods. Thic research has improved j upon the approach used in WASH-1400, Appendix VIII because it has removed some conservatism from the analysis. However, because the physics of many phenomena is still not well understood, the analysis can only be viewed as preliminary with many factors identified but not satisfactorily included. When these factors arose, we have tended to be conservative and did not take credit for effects which might mitigate the explosion damage potential. l There are a number of tentative conclusions which can be reached at this time: After the steam explosion has occurred within the reactor l (i) vessel, an early time failure mode of the vessel might Based on be spallation due to propagating stress waves. our analysis, this failure mode is not likely to cause vessel failure, because of the slow rise time of the explosion, low peak pressures and the stress wave patterns in the vessel. If vessel failure did occur it would most likely happen near the instrumentation probes in the lower plenum where missile generation would not endanger the containment.

During the expansion phase of the explosion heat transfer (ii) between hot vapor and cold liquid water would significantly reduce the work potential before coolant impact on the The kinetic energy of the head (by a factor of 1.5 to 4). slug at impact depends upon the mass of water involved in Based on parametric the explosion and its energy content. analyses, slug kinetic energy can range from 50 - 800 MJ depending on initial conditions. The coupling of the liquid coolant slug impact to possible (iii) vessel failure and missile generation is a complex problem. Preliminary structural analysis indicates that it would be difficult to make the reactor vessel head a missile. Even if the upper core structure is neglected, vessel failure is predicted to occur locally near the top of the head which would cause water ejection and preclude the possibility of a coherent failure of the head. To form a missile, more energy would be needed (1 300 MJ) to overcome these dissipative effects and those of the Another missile source would be upper core structure. Analysis the ejection of a control rod drive assembly. indicates that this type of missile is also questionable, because as the upper core structure is impacted by the coolant slug control rod, buckling may be more likely than its ejection as a missile. The analysis is still crude and small missile generation cannot be precluded. l (iv) When a missile is formed, it must penetrate the concrete Empirical correlations for concrete penetra-containment.

tion indicate that both large and small missiles can penetrate the containment with little energy expended (= 100-200 MJ); about 5-10% of the reactor core thermal energy for a 14 explosion. However, in light of the past analyses, consideration of only small missiles may be prudent. For a small missile (Figure 20) the contain-ment can be penetrated for velocities greater than ~50 2 m/s. This, though, would cause a small hole (~ 10 cm ) and leakage from containment would be small (~ 10% vol/ day). A number of physical effects have also been identified which, although not accounted for in this analysis, may mitigate the explosion damage potential. They are: (i) The rigidity of the liquid coolant slug will be affected by its vapor or gas fraction. (ii) The remaining core or upper internal structure could break up the slug before it impacts the head. (iii) The energy of the coolant slug at impact could be dissipated by crushing the upper internal structure and buckling the control rod drives. (iv) The penetration resistance of steel walls to a missile may be significant (e.g., polar crane) and could reduce the containment failure possibility. Future analyses will attempt to include th'se effects although fluid-structural experiments may provide a more definitive answer.

32 Appendix A - Models for the Expansion Phase Vapor-Liquid Heat Transfer Model The heat transfer model used in this analysis is based on the view that the energy is transferred from the hot coolant vapor to the cold liquid coolant as it is entrained into the expanding vapor volume. To determine the rate of heat transfer three parameters must be known 1) the volume of liquid entrained in the vapor 2) the size of the liquid drops entrained the heat transfer coefficient between the vapor and liquid 3) The dominant mechanism for liquid entrainment into the vapor volume we believe is due to Taylor instabilities. The reason is that the vapor is accelerating the liquid and this is a hydro-dynamically unstable condition. The liquid coolant will become entrained in the vapor as it is accelerated upward. The rate of entrainment is based on the model (8) for Taylor instability growth given by v = 4.6 Valc (AI) r where the Taylor critical wavelength is = 2w.[ (A2) 1c y a(pg -py) is the relative velocity of liquid penetration by the and v r velocity a is the acceleration e is the interfacial tension is the density of the liquid (1) and vapor (v) p -w

33 This correlation for relative velocity is based on experiments It with air and water over an acceleration range up to 1000 g. physically represents the rate of penetration of the gas into the liquid due to the instability in its final stages of growth. j Taylor and Lewis (11) originally identified three growth stages, I (for a the final one being a non-linear constant velocity stage constant acceleration). Birkhoff (1) subsequently expanded this view and proposed that a five stage growth process occurs where the final three stages are basically different phases of the He characterized constant velocity growth observed by Lewis. these stages as the time when the instability takes on a turbulent mixing characteristic where the fluid instabilities entrain the The volumetric rate of more dense fluid into the less dense. entrainment, V4, based on this physical picture is dV (A3) gf=vA i is the projected area of the expansion. where Ap The size of the entrained liquid droplet is thought to be initially between the critical Taylor instability wavelength, A c' After it is and the fastest growing wavelength, A,= /3 A c. entrained it can become smaller by hydrodynamic breakup if the characteristic Weber number is greater than the critical Weber r is much less than i number (7-20) and if the time for breakup, tb, The breakup time is approximately the time scale of the transient. given by (13,14) 1/2 3 rd_ ((b for Bo < 10 (g4) 1 [{u t =c rell (Dv/ l b l

34 \\ y rd fh. 1/2 ) I 3 (AS) Bo @ for Bo > 10 t =c b 2 urel)(PVj where cy = 3 to 6 l c2 = 65 rd is the drop radius; rd " D /2 d is the relative velocity of the drop urel and Bo is the Bond number; Bo = 3/8 We for droplet drag coefficient of Cd=2 D (A6) 8v rel d and We = l 8 i i l If these two criteria are not met, then the drop does not break up l but remains at Dd"Ac* The heat transfer coefficient was described in detail in the main report. It is composed of the heat transfer resistance due to the condensed water and the thermal resistance of the liquid drop. For analysis considered here, the liquid drops are large t The heat enough to be considered semi-infinite, Dd>2/aw. transfer coefficient for the drops at any time, t, is then 1 h (A7) = TOT g f,, t K" 2% 1 where the condensate thickness is t -T ) dt) - (A8) [hg (T 6(t) = y g W =W 4 W r@ eam e -=g u'= 4

35 As equation A3 suggests the heat transfer coefficient is found by iterating on the size of the condensate film at any time. The heat transfer rate then for all the entrained drops is i i given by 6V (^9) -T ) e hTOT(T q = <D > v 1 d where <D > is the average drop diameter for all the drops entrained. d This average drop size is necessary because during the expansion the acceleration changes thereby changing the size of drops entrained. The average size is given by L.h No (Axg) Dd (AXi) (A10) g <D>= d %sgt No (Axi)

1. i where No(Axi) is the number of drops in an axial increment, Axi, and is given by V,(Axi)

(#*i' "w 3 (Ax g) (All) D g d Figure Al illustrates pictorially how the expansion is modeled. Two lumped parameter volumes are utilized to model the two-phase volume, one for the coolant slug and one for the expanding bubble. The assumptions utilized in this analysis are: The thernophysical properties of water are assumed to be 1. constant. Tt.e water vapor can be modeled as a perfect gas. 2. A one-dimensional momentum equation is used. 3.

36 w The volume of s#turated liquid water is assumed to be small 4. bubble. in comparison to the saturated vapor volume in tht; l The Clausius Clapeyron relation describes the slope of 5. the saturation line. A one-dimensional momentum equation is utilized to describe the bubble expansion given by 2 - P.) ggy3) dv lug, y, (P s dx y A P dt M alug where (A13) sat (T ) P =P v v The energy equation for the bubble is given by dVb d 2t "v v' " '9 ~ 'v dt (A14) where (A15) u = X' u fb + cy(T -Tref) + uref y and where PV (A16) V D is the water quality X= mRT cy y (A17) V3=Ap x The energy equation can be rearranged in terms of enthalpies to give (A18) v h(mh) -q + V = b l.. l

37 e where (A19) -Tref) + href h = X hgg + cy(Ty Simplifying the result is b (A20) ih+mb"~9+Yb y c c Now the derivative of pressure can again be approximated by the Clausius Clapeyron relation dP dP dT hg dT P hgg (g21) y y y y y 2 v 3t , dt de v T de p7 y g vv the energy equation is With these definitions for S, V, h, and Py, b and only a function of the bubble saturation temperature (T ) y Thus this set of nonlinear previously defined unknowns (x,q). ordinary differential equations in time is a complete system of equations to describe the transient expansion giventhe initial conditions (t=0). This system of nonlinear ordinary differential equations are The algorithm is in solved by a numerical integration technique. a subroutine which is part of a mathematics subroutine library available for the CDC computer system. l ' ' ~ ~ ". _ _. _ _

• L,, r_;,

i t. References ~ Reactor 9afety Etudy - WASH-1400, NUREG-75/0114, Appendix VIII, 1. 0:tober 1975. Bunton, L. D., " Molten Core / Water Contact Analysis for Fuel Melt Accidents," SAND 77-1842, NUREG/CR-0391, Feb. 1979. 2. l Corradini, M. "Phenomenological Modeling of the Small Scale Vapor Explosion Experiments," SANDIA TOPICAL REPORT, to be '3. publiched in 1979. S., Buxton, L. D., " Steam Explosion Triggering Stainless Steel and Corium - E Simulants Studies 4. Helson, L. NUREG/CR-Phenomena: with a Floodable Ar Melting Apparatus," SAND 77-0998, 0122, May 1978. S., et al'., " Steam Explosion Triggering Phenomena, 5. Nelson, L.Corium-A and Corium-E Stimulants and Oxides of Iron and Cobalt Studied with a Floodable Arc Melting Apparatus," Part 2: NUREG/CR-0633 to be published in 1979. SAND 79-0260, 6. Buxton, L. D., Benedick, W. B., " Steam Explosion Efficiency Scaling Experiments" SAND 79-0920, to be published in 1979.

Ozgu, R.,

Chau, J. C., " Local Film Thickness During Transient Voiding of a Liquid Filled Channel," ASME Winter Annual 7. Meeting, 75-WA/HT-27, 1975. Corradini, M. L., " Heat Transfer and Fluid Flow Aspects of Interacting," Ph.D. Thesis MIT-COO-2781-15TR, 8. Fuel-Coolant Sept., 1978. " Development and Characterization Cagliostro, D. J., et al., of a Liquid-Vapor Bubble Source for Modeling HCDA Bubbles," 9. SRI International, Tech. Rep. 2, PYU-2939, March 1977. "The Termination Phase of Core Disruptive Theofanous, T. G., Accidents in LMFBRS," Specialist's Workshop on Predictive 10. Analysis of Material Dynamics in LMFBR Safety Experiments, March 1979. J., "The Instability of Liquid Surfeces Taylor, G. I., Lewis, D. when Accelerated in the Direction Perpendicualar to their 11.

201, Planes, I and II," Proc. of the Royal Soc. of Lon. A,

p. 92 and 202, p. 81, 1950.

LA-1862, 1954.

Birkoff, G., Taylor Instability, LASL Report, 12.

R., Waldram, F., Proc. 34d Intern. Conf. of Rain Rienecke, W. 13. Erosion and Associated Phenomena, 1970. Simpkins, P. G., Bales, E. L., " Fragmentation of Water Drops 55, 1972. due to Sudden Acceleration," Int. of Fluid Mechanics, 14. l

15. FSAR, Surrey Nucle 0r Station, VEPCO FSAR, Peach Bottom II Nuclear Station, Philadelphia Gas and 16. Electric. " Survey of Hypervelocity Impact 17. Herman, W., Jones, A.,A.S.R.L. Report, No 99-1, Sept. 1961. Information," MIT, " Empirical Equation for Projectile Penetration in Young, C. W., SC-DR-72-0523, 18. Layered Earth Material and Concrete Penetration," Dec. 1972.. " French Program for the Study of the Effects of

Berriaud, D.,

le. Projectile Impacts on Reinforced Concrete Walls," 4th SMIRT Conference, CEA-EDF, 1976. Berriaud, C., " Rigid Missiel Penetration in Concrete REir. forced Prob. and Extreme Load Design 20. Wall," POST 4th SMIRT SEMINAR, of Nuclear Power Plants. E., and Krieg, R. D., SLA, Division 1281, Key, S. W., Beisinger, Z. 21. "HONDO II, A finite Element Computer Program for the Large Deformation Dynamic Response of Axisymmetric Solids," SAND 78-0422, October 1978. d54 'T SAJO 77- / 33 fy Fe4./T7f' 21. T s q S.L. j

Table 1 Empirical Concrete Penetration Formula Young [18] P = 2X= I* 2 in(1 + 2,2 -5); V<200 ft/sec 1 X,, (ft) =.53 SN y (1bm/m ) m X,, (ft) =.0031 SN (1bm/m-2)(V-100); V>200 ft/sec concrete.5<S<1 reinforced concrete flat plate.5<N<1 cone CEA-EDF [19] (p(kg/m))-1/8Mf(Vm/sec)3/4, 3 .82[o(Pa)]-3/8 P(m) = 20<V<200 m/s .3<P/d<4 ACE [20] P = 1.32d + 1.24X, V.5(m/s) +.5d, 150<V<900 m/s 1 X,, = 3.53 (10-4) M(kg) ' 3<P/d<18 d.785,) y,gp3) l g BRL [20] P = 1.3X, X,, =.00103 M(kg) V *33(m/s) Approximately same range l as ACE formula d.8(m) /o(Pa) l v is missile velocity a is missile mass d is missile diameter 7 7 o is the concrete compressive strength (3(10 ) - 5(10 )Pa) 3 is concrete density (2500 kg/m ) p

Table 2 Diameter Mass Missile l I 162 stons 6.7 m i BWR Read & 6.7 298 Internal Structure I PWR Heat & 4.85 m 148 mtons Shield Block PWR Control Rod .05 m Drive Assembly ,206jpf wh i l l i ( l

Flq uit E.:1. laA=u k / A ence.EmJ ff 5 ' Vessel Hea 4N

1. f" I

I Upper internal Structures ( Coolant Slug (Above The Fuel-Coolant Inter. Zone) Cold Coolant / Entrained I Hot Conlant e - s p* ,8 Vapor e o* p

eO e

o o O i g g o 8 O 0 (a oo O o \\ O SN Fragmented Fuel l Reactor Vessel (After Propagation Phase) l J ee. m e - e O* elm em ee -..e so e

. a. -- e -)hf l l yh # -l

1. ^~

j &'/h V.A+:.v. W ' l / i \\ L-lG)UIT) C C OL 4 M T $0up i I

• iTQ.uCUE.1,

/, ~ +d upwMtp vz<.om h LXpMJptf f. V&PORIEEz? C@OL. W ) V" sof V N' k l RL5tvuM uO -l STRUCAVRE LIQUID PLnf 4 MFA*f" ~7X44V3FER. 141/T;W UgutO FLnt on.sw .I ~ ) % - M Q e M 9 g l fuk/ O % - W.,y e e<a + 9. A 4.3s e aw mwen win sou, srx.aeran.e u,r>.ugue e,w 05 AH W 'T(LAWSCSA RE..So3 T1%Jcg,, !*L T (_ = = =. _

i Ney 3. : ffs fA: M-9 k 9 /hd6"fW \\ } N f s ""- I a IV 3 (* DbT) v =... 7 com r U QUID T Tc 4 l 3 I / w_ -.-g c+ut.u.uJ<.bfm I f# = h.,7 IT[-T ) c '~l .L + -.L +I = h h h rur u z kw h" - Vra;c kw h= 4 5 4 r-h' RaCG_ f3 i Re (rv.) ____ i (K-T,) I?rRl Vn YTz 1- . _ _.... ~... -.... =

L t/- < AC da& URE 5I w +C ~C !sM;Jf n - a y Vf A 41 / ^'~. f/wy /Mr nd-ygO p -M J yG m^ i /m@w-s J. 3 I I 1 7 M iSENTROPIC SLUG - 850kg -- VAPOR - LIQUID H.T.' X .04 6 R c P. =.1MPa o. e;

l[

i g Too= 300 'K 5 z. 2 El 2 m 5 w 5

s. -

g 4 a o .i o b a z 2 u e i o 3 y 3 e-- m 8 3 D= a z 1 2 ~ ~ o z o c o x u$ 1 I I I O 5. 10. 15. 20. l INITI Al. COOLANT VAPOR PRESSURE (P -MPa) i b

~ 'n T. A T 3 H A A e~ DD 1 I L 0 U A 3 I QT ly/ cI N a l L a P k P E - M P M O w" = = E M 4 0 RRI3 R4 1 0 TO 5 0 r ET . 3 N P P S _W e = A XE e o VET S C C o b c I P X P n, O/ ~ I ~ sa I 4 %47'0 igm g= )c esm ( '"p od E M .~ s l T N 4-f'4 g ,+/, \\ { ,N 0 l 1 \\. 6~& \\ s \\ ' g\\ 2 :- I o \\- i gy \\ \\ \\ p \\ L o \\' . a,y ]< 0 l 4/.g y 5 4 3 2 1 2n.sCgMw:a" i i:i;!ii i I 4

9 5 ~ gf g e /, / LYN Yff -Y $ #$ $-- f-; 1 i 1 I I I I I I = 100 MPa ISENTROPIC c X m.05 --- VAPOR -1.1001D H.T. (Too= 373 *l0 c

---

VAPOR - LIQUID H.T.(Too= 300 *f0 -

s 200 M = 1000 kg c E Poo =. IMPa w 5 M =14000kg 150 SLUG o_ _b j E x i 3 100 O w M 3 o 8 50 [ ____ t i I i i i i 20 40 60 80 ~100 120 140 3 EXPANSION VOLUME (dV-m )

FIy. ] s. .pg4.;,,afn/L Aa-.Q n~.N M s.f am m.A s <9 ni, g > D i i i i .i i i X =.05 C M = 1M 4 250 c P =.1MPa .i "E T== 37k 'K p 3 200 >y

2s 150 ISENTROPlc e

g --- VAPOR - LIQUID H.T. - M =14000kg SLUG w . VAPOR - LIQUID H.T. - M = 72000kg o SLUG t; 100 E M e#, p amme # ss-p,, g:, 50 t I I i 50 100 150 200 INITl Al COOLANT VAPOR PRESSURE (P 2MPa) c

I se n - Jwe on 43 y w n$w dw*vy' W & t. //&n i f., / I I I I I I I l c' - ISENTROPlc c -- VAPOR - LIQUID H.T. - M -14000kg t c 600 SLUG y Poo =.1 MPa = VAPOR -LIQUID H.T. - M -72000kg i SLUG b= 373 'K ~ s e 5 i, 1 e 3 o x Q LAJ d',W' ,I u s W i E s x 6. - sp#- 25 200 P.. 8 o j> I I I I I I t 50 100 150 ,200 INITI Al COOLANT VAPOR PRESSURE (Pc - MPa 1

j s. Sh = LTi "sc ' -/y' ' g " " * '* ' */ Mr, a y.uwd s. -.., dL,, M. : .. s.... & -i e. i i iii11] i i I II 800 - P - 100 MPA c 600 - X =.05 c Po=.lMPA 400 Too= 373 *k / 3 / 0 m 4 o ISENTROPlc p .c --- VAPOR - Li@l0 H.T. - M "I g 100 ~ St.UG j g -[ VAPOR - Li@lD H.T. - M =72000kg ~ 80 3gg 60 # O__ f b i Z M i 20 l ) }Q t i i i l l Ii! 1 I i 1 i if j 1 10 100 - C001. ANT PARTICIPATING IN INTERACTION (M - 1000 kg) g

\\ 1 i I SODY i i e i i i i s.no A4 Y Axl5 m3 i a.co Stect Enclosure licsd 1 s i t ,s.so .co t 1 g ss -~~ 1 Head Studs .soo

---

,/

m ibe / J o .m e4g c. l 1. 1 I F f ',7 " l 'llK .. son b,:. !!!/Y Pressure Vessel Wall ..co ~

~I

..so ] l \\ \\A a e a v r Fi,xe d i i ..sco o. .soo a.co -.so r.co r.so 3 00 3 so X AX)S Z3DN PRESSURE VESSEL HEAU FOR INTERNAL ]MPACTS (BOLTS BY AREA R ATio) Figun 49 Finite Element Model of Reactor Vessel u

u s, \\ e .?. l I 4.9000 yettgago M9M r 3 -s.oooo r s 4' l l T ,,,:n ... = j), . 'I ' e i' in D' u .r.oooo s S ~ Water [1ug V = 200 m/s ...oo. a = 12600 kg 1 - asW ,,g i - Axis of Symmetry-j I .r.oo'oo ,,,4 e.como e,anoo EN s.eeno

g. asis en.s.as.een son. sus s

est untes sous room.tn 2nitial Configuration of Snall Water / lug Impacting Figurella. at 200 m/s. 8 s I {* i 1 9a ,a j 'i

e l l I I spetrengo usa a.gooo L I &1.; i -3 9000 ~ i l Waterflug s a l V = 113 m/s '::rw. a = 42530 kg ^ i s 1 > i - > 271 R7 j-r.o000 r I l r-e ? , p-i t.0000 ~ 1 1I__a t i I f, i 1 f o.e00c i f -i i f 1 Axis of Symmetry

• I-3,h 3,gidp0 1.30kpo 8.0000

.I.0000 3.as3 88tC setta 3LgG PeeBLtn en.S-as.es s 333. sus S Initial Configuration of Large Waterdlug Impacting Figure Ga. at 113 m/s. e .mo e * *.* 9

.g........_ .=. t

• e i

B -3. 000 -s ---j --"""*~ -W-+-4 T es s s i a I i i i x. '. '... ..wsus' / \\ / o m 1 s // / th) x I ,,t ss f! i1 .. /. b I M 7 1 1--i] i a Axis of Symmetry s.6 e.6 e..ain -..ain -t*** =a - S Small Water / lug at 3.85 as Figure lib. ) l t

• d

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