ML20027D036

Structural Analysis of Peach Bottom Units 2 & 3 Reactor Pressure Vessel Head Drop,Shroud Head Assembly Drop & Steam Dryer Assembly Drop Conditions.

ML20027D036
Person / Time
Site:	Peach Bottom
Issue date:	08/31/1982
From:	Marisa Herrera, Mok G GENERAL ELECTRIC CO.
To:
Shared Package
ML20027D035	List: ML20027D034 ML20027D036 ML20027D039 ML20027D044
References
REF-GTECI-A-36, REF-GTECI-SF, RTR-NUREG-0612, RTR-NUREG-612, TASK-A-36, TASK-OR 82-32, DRF-137-0010, DRF-137-10, NUDOCS 8210280198
Download: ML20027D036 (38)

Text

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. REPORT NO. 82-32 DRF 137-0010

' AUGUST 1982 STRUCTURAL ANALYSIS OF PEACH BOTTOM 2/3 REACTOR PRESSURE VESSEL HEAD DROP, SHROUD HEAD ASSEMBLY DROP, AND STEAM DRYER ASSEMBLY DROP CONDITIONS PREPARED BY: 8/27/.fd M.L. HERRERA 'DAT E'

(& A $/O S/fb G. M0K DATE REVIEWED BY: _b , S 'G OL-H.S. MEHTA ~.) ATE APPROVED BY: P Ff 23/82 DATE l S. RANGANATH oetnu- rNw

~0 ATE F

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0AT 5 NUCLEAR POWER SYSTEMS ENGINEERING DEPARTMENT GENERAL ELECTRIC COMPANY, SAN JOSE, CALIFORNIA kggok!ac O!$00b7 p PDR

TABLE OF CDNIDFIS SDMAIN 1.9 INDGUCTION 2.0 VESSEL HEAD IBOP 2.1 MASS AE VEIDCITY OF VESSEL HEAD 2.2 VESSEL HEAD IIOP RESULTS 2.3 neGY ABSORBED IN VESSEL FLANGE REGION 3.0 SHROUD HEAD ASSEMBLY IEOP 3.1 VEIDCITY OF SHROUD HEAD 3.2 MASS OF SHROUD HEAD 3.3 SHROUD HEAD IEOP RESULTS 4.0 SIEAM DRYER ASSDELY IBOP

5.9 CONCLUSION

S APPENDIX A VESSEL SUPPORT SKIRE STABILITY ANALYSIS APPENDIX B SiROUD HEAD VELOCITY UNDER SUBMERGED ONDITIONS

_i.

S2mnary A detailed finite elenent elastic plastic analysis was performed to evaluate the effects of the vessel head drop, shroud head drop and steam dryer assembly drop for the Peach Bottan 2/3 plants. The results of the analysis show that structural integrity of the vessel and shroud is maintained, although same yielding does occur in the vessel flange regimi.

Further, no damage to the fuel is predicted since the couponent geometry precludes damage to the fuel. In view of the fact that there is no significant damage to the reactor conponents or the fuel, no release of radioactivity is expected as a result of the drop.

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1.9 INDGUCTION The purpose of this analysis is to evaluate the structural consequences of dropping the Peach Bottom 2/3 reactor pressure vessel head, steam dryer, and steam separator (shroud head assenbly) during maintenance cperations. The vessel head was assumed to be dropped resulting in inpact on thg reactor vessel flange. It is conservatively asstuned that the head rotates 99 during the drop, producing local point inpact between the vessel flange and the head. The shroud head and dryer were assmed to drop from a height sufficient to generate the steady state velocity of the two assenblies as they move through water and are tr. der the action of the fluid drag forces. In reality the dryer assembly inpacts the shroud head assenbly. However, it is conservative to assme the impact with the main body of the shroud since no credit is taken for energy absorbed by the shroud head assembly.

An elastic-plastic dynamic analysis was performed for both the vessel head drop and shroud head drop. Stress and displacements following impact were plotted. The results show that the structural integrity of the vessel and shroud are maintained and therefore there will not be any significant release of radioactivity.

2.9 VESSEL HEAD DROP A finite elenent analysis was performed to determine the vessel response when impacted by the vessel head. The ANSYg ccmputer code (Ref.1) was used for the analysis. Due to synmetry, only a 189 segment of the vessel body between the vessel-head flange and the bottczn of the support skirt was modelled. The plane stress isoparametric quadrilateral element from the ANSYS elenent library was used to model the reactor vessel body. The model reflects the longitudinal and lateral, extensional and inextensicnal effects. Transverse effects are considered negligible and therefore the use of the plane stress option is justified. The model contains 43 nodes and 31 elements. To simulate the inpact of the vessel head with the vessel, the ANSYS gap element was used. Figure 1 shows the modelling of the vessel and vessel head used in the analysis. The botton row of elements represents the reactor vessel skirt. Nodes 6 and 43 define the gap element.

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• %f0DgEgHEAD c 403.8"

• CAP ELEMENT e IMPACT POINT N0DE 6 n

SA533 Gr B' MATERIAL PROPERTIES:

E=26.4E+06 psi e,=70KSI G=10.2E+06 psi

@ @ @ @ G @ Element numbers are circled 3 All Vessel Data 04 Obtained From

>d Reference 2 I @ @ @ @

N0DE 2 t u

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at o RN @ @ @ @ @ @

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FIGURE 1 Vessel finite Element Model O

2.1 Mann Ard Velocity Of Pallina Hand ,

ne actual height of drop for the vessel head was specified as 24 feet (Ref. 3).'

he weight of the head is 96 tons and the weight of the strongback and crane book is approximately 28 tons. Since the information of the drop height and the weight of the strongback was not available at the time the analysis was performed, it was asstaned that the drop height was 48 ft. and the drop weight was 96 tons (Figure 2). h is is coprvative since the total energy of inpact as analyzed, is 96 (2000)(40) = 7.68 X le ft-lb.6 Se actual inpact energy in a postulated drop is (96 +29) (2000) (24) =

5.568 X 19 ft-lb. S e results of the analysis presented here are conservative and can be used to evaluate the structural consequences of the vessel head drop.

4--- Ve :el Head J 4>

h=40 feet

[ u u

Vessel

,, ~~,

Figure 2 Drop Height 2

%e impacting mass is: M = %(2000)/386.4 = 496.9 lbf-sec/in Since cnly one half of the vessel is being modelled due to synmetry, a value of W 2 is used in the analysis.

We effective travel, asstuning that the head rotates 90 such that a point impact occurs is h=480" - 139.625" = 348.4". Figure 3 shows the impact configuration.

We velocity at impact is :

V, = /2gh = /2(386.4) (340.4")

V, = 512.9 ir/sec

I W

i 139.625"

(

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,-s Figure 3 Inpact Configuration In simulating the head drop, node 43 of the finite elenent model is given a velocity of 512.9 irv'sec just before closure of the gap. At the same time node 43 is subjected to a downward force equivalent to its weight.

'Ihe material behavior is taken to be perfecty plastic with a yield strength of 70 Ksi (Reference 4) .

2.2 vessel Haad Droo Panalts Figures 4 and 5 show the axial stress at elements 1 and 5, and deflections at nodes 2 and 6 respectively (See Figure 1). 'Ibe wave propagation, is clearly evident from the figures takes approximately .903 seconds to reach the top of the support skirt. 'Ihe maximum deflection at the point of impact and top of the support skirt is 1.65 and .35 inches respectively.

Yielding occurs rapidly at element 5 which is the location of inpact. Yielding occurs in the support skirt .877 seconds into the transient. 'Ihe yielding in the support skirt indicates that buckling should be considered.

'Ihe results of the finite elenent analysis indicate extensive inelastic yielding in the inmediate element at the point of inpact, and throughout the reactor support skirt. Subsequent analyses with a more refined model confirmed that the yielding in the region of impact is localized.

1 A more detailed analysis (Appendix A) was performed to determine if buckling occurs, taking into consideration dispersion of the travelling wave at the vessel-skirt junction, and reflection of waves at the skirt-foundation junction. 'Ihe analysis confirms that buckling of the support skirt will not occur as a result of the inpact.

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2.3 Enerav Annrbed in Vammal F1anoe Reaien Due to local yielding in the vessel flange regicm, not all of the energy transferred by the inpact of the vessel head with the vessel will be transmitted into the remainder of the vessel. Se energy dissipated at the point of impact can be determined by taking into account the plastic strain pro &ced & ring the loading. Se energy dissipated is given by:

U fr dE (Voltane) d y

] element 5 2 1s may be approximated by:

U d =r y (Voltane of element 5) E,ff Where E,pp is the average Von Mises effective plastic strain for elenent 5 when the maxinaan cerlection of the impact node occurs. Substituting in the appropriate values from the finite element analysis give:

Ud = 70000 (42801.79)(.0072196) 6 U

d

= 2.16 X 10 in-lbf = 1.8 X 10 ft-lbf Thus the plastic yielding in the vessel flange region dissipates approximately 47% of the energy transferred &e to inpact of the vessel head and vessel.

3.0 SHROUD HEAD ASSEMBLY IBOP Dynamic response of the shroud and shroud support legs to an accidental drop of the shroud head assenbly is found by a finite element analysis. The dropped shroud head is assumed to impact axisymetrically on the upper flange of the top guide shroud.

As a result, the loads are transferred through the top guide shroud to the lower shroud, and subsequently to the vessel shell through the shroud support legs and attactment ring. Se mcnents developed &e to eccentricities in the load path are asstned to be carried by the top guide assernbly and core support plate, where the eccentricities exist.

Figure 6 shows the model used in the finite elenent analysis. Se model is axisynnetric using isoparametric quadrilateral elenents. S e core plate and top guide are simulated in the analysis by modifying the density of the elenents respresenting then. Se structure is fixed at the vessel attachments. Since the core plate is relatively stiff, the elenent representing it is not allowed to move radially. ' Bro analyses were performed to determine the behavior of the shroud structure with and without the shroud support legs. In the first analysis an effective thickness was determined asstaning the legs were fully circumfermtial. his results in a thickness of .44" alcng the legth of the reinforcenents, and .29" below the reinforcenents. In the subsequent analysis the shroud support legs were not included in the finite elenent model to determine if the structural integrity of the shroud can be assured even without including the load carrying capability of the shroud support legs. This traabnent of the shroud support legs is more applicable in the areas where no legs are present. Se attachnent ring is 1 inch instead of the actual 2 inches thick to conpensate for the cutouts.

To simulate the drop, two gap elenents are used as shown in Figure 6. Se mass of the falling head is divided evenly between the two point masses shown.

S e material behavior is taken to be perfectly plastic with a yield strength of 30 Ksi (Reference 4) .

1 3.1 Velocity of aroud had At Tmnact ne geanetry and weight data for Peach Bottan 2/3 vessel and shroud head are as follows:

Vessel I. D. = 251.375" Ref. 2 Shroud Head O. D. = 220"

[ GE Drawing 729E476 Weight = 13 %89 lbs As the shroud head drops through the vessel the downward motion is resisted by the pressure drop due to water flow through the annulus between the shroud head and the vessel inside diameter and by the flow thrcugh the standpipes. Se terminal velocity that the shroud head attains is therefore dependent on the overall pressure drop. In this analysis, it is assumed that the shroud head has attained the steady state terminal velocity prior to inpact.

Appendix B shows the calculation of an equivalent drag coefficient and the associated terminal velocity. In calculating the drag forces, it is asstuned that the flow through the stan@ipe is negligible since the presence of the turning vane in the

, stan@ipes makes the flow tortuous. Also the effect of any small flow in the j stan@ipes is more than made tp by the pressure drop due to friction on the outside

! surface of the pipe. Se following analysis denonstrates the calculation of the I steady state terminal velocity.

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M/2,V M .0 O H

]J T' 2 Gap Elements 41.6" ll  ;-; Top Guide Shroud Data From GE Drawing 729E458 173.5"

--. 4--

2" i f n .-; Core Plate 58.71" i

O Vessel a o Shroud Support Ring Shroud Support Ring and Shroud Support 0.5" Leg Data From Ref. 2 t------

Shroud Support Leg v

1. 8 Vessel Figure 6 Shroud Head Drop Axisymmetric finite Element Model

he shroud head projected area is:

1 A = I (220)2 = 38013.3 in 2 )

l 4

h e vessel projected area is: f

.i (251.375)2 = 4%28.81n 4 = 4 he annulus area is:

2 A =

4 - A = 49628.8 - 38013.3 = 11615.5 in f

he drag coefficient is given by (Appendix B):

2 Ay C " -

1 d -

f -

Where C = .8 for the geanetry considered.

C = -1 = 18.85 d

.8(11615.5) .

We steady state terminal velocity (derived in Appendix B) is:

,, =/ ~<- w (m. 3-1.u 4Cd

-5 Where to = mass density of water = 9.36 x 10 lb/in

-4 3 b = mass density of steel = 7.246 x 10 2/6 Substituting into equation 3-1.1 gives:

.9 6 = 52.9 iry'see 2(13 9600) (1- 7, 6 )

y ,

t 9.36 x 10' (49628.8)(18.85) 3.2 14 ann of Shroud % d h e mass of the falling shroud head is:

80 2 M = = 361.28 lbf sec /in 386.4 Since the analysis is axisynnetric, the mass per radian is:

361.28 2 M = = 57.5 lbf sec /im rad 2w i

Half of this mass is applied at each gap elenent.

3.3 Mhroud Hand Dron Dann1ts Results of the analysis indicate no inelastic behavior in the shroud. However yielding does occur in the shroud support legs. S e yielding in the shroud support l legs may be overly conservative due to the axisynnetric treatment of the legs. To

! determine if the shroud support legs were required for structural integrity of the shroud, an analysis was performed of the shroud head drop excluding the shroud support legs. S e model used is shown in Figure 7. Results from the modified model analysis shows no inelastic behavior in the shroud or shroud support ring. Figure 8 shows the '

deflectica at the point of inpact and shroud - shroud support ring junction up to the l time when peak deflections are reached. The maximian deflection at both locations is approximately .86 inches. S e significance of this analysis is that the integrity of ,

the shroud can be shown without taking credit for the load capability of the shroud '

support legs.  !

Se main conclusion from tte shroud head drop analyis is that the associated deformations are not' excessive and that structural integrity and stability of the shroud are maintained. S us no release of the coolant or radioactivity is expected.

4.0 STEAM DRYER ASSDELY DEOP An accidental drop of the steam dryer assembly is asstuned to produce an inpact on the shroud flange. Se dryer assenbly would first inpact the steam dryer support brackets. It is conservatively asstaned that these brackets do not ingede the motion of the falling dryer assenbly, the assembly would then inpact upon the shroud head assenbly. Se impact would be absorbed by the same structure that would absorb the shroud head assenbly drop. If it can be shown that the mass and kinetic energy of the steam dryer assenbly are less than those of the shroud head, then no additional analysis is required since the conclusions from the shroud head drop analysis apply to the steam dryer assenbly drop.

Se weight of the steam dryer assenbly is 45 tons which is less than the weight of the shroud head assembly. (Ref. GE Drawing 9 731E711)

To determine if the kinetic energy of the steam dryer is less than the shroud head upon inpact, the velocities may be ccupared.

M/2,V C M/2,Vo O

H TT *- 2 s., tiements 41.6" ll la Top Guide 173.5"

--+ +--

2" if

.4 Core Plate 58.71" 1"

1P Vessel o

Shroud Support Ring MM/ VESSEL Figure 7 Shroud Head Drop Axisymmetric finite Element Model

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Using the same equation as for the velocity of the shroud head assembly (E4 3-1.1) .

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'Ihis is less than 52.7 irv'sec which is the terminal velocity for the shroud head assenbly.

'1herefore since the mass and velocity of the steam dryer assembly is less than that of the shroud head assenbly, the conclusions from the shroud head assenbly drop analysis apply to the steam dryer assembly drop.

5.9 CCNCLUSION A detailed finite elenent elastic-plastic analysis was performed to evaluate the effects of the vessel head drop, shroud head drop and steam dryer assenbly drop for the Peach Bottom 2/3 plants.

Structural integrity of the vessel and shroud is maintained even though some local yielding occurs following inpact. Specifically, yielding occurs in the vessel flange to vessel junction area following vessel head drop and in the shroud support legs following the scroud head drop.

No damage to the fuel is predicted since the conponent geometry precludes direct impact on the fuel. In view of the fact that there is no significant damage to the reactor components or the fuel, no release of radioactivity is expected as a result of the drop.

I REFERENCES

1. AIEYS Ehgineering Analysis Systen, Swanson Systems, Inc., March 1975 l

2. Final Design Docunent For General Electric - IED Peach Bottom III General Electric Order No. 285-Bil56, Babcock & Wilcox Contract No. 618-8146-51 Vol. 1

3. General Electric Engineering Work Authorization No. EhF 93-CM Issued June 7, 1982

4. ASME Boiler And Pressure Vessel Code,Section III, Sub-section NA,1988 Ed.

9

--;-_W A - Shhility Analyn{ n of sar4 rt I

A-1 Yntrnaw+ fan he result of the inpact study of Section 2 indicates high stress and i plastic defonnation in the skirt. mis observation raises the concern about the stability of the skirt under the impact load. To overcome this concern, the result of the impact study is exanined herein to detennine the cause of the high stress in the skirt. It is concluded that the high ctress in the skirt is mainly due to simplifications of the structural model at the tcp and botta of the skirt. Sese simplifications, which are acceptable in detennining the gross structural response of the vessel, unfortunately induce unrealistic dynanic stress concentration in the skirt. Specifically, the simplifications are: (i) at the top of the i, ckirt the downward branch of the vessel is not modelled (ii) at the botte

of the skirt the concrete foundation is modelled as an infinitely rigid and fixed body. %ese simplifications cause the stress wave generated by the impact to be " trapped" in the skirt and the stress in the skirt to be '

much higher than actual stress. A stress wave analysis described later in  !

this section shows that the actual stress level in the skirt is probably i cs low as 50 to 60% of the value given by the inpact analysis. Based on this result, the skirt is shown not to buckle under the impact load.

Details of the stress wave and the buckling analysis are described in the renainder of this section.

A-2 Strann Wave Analynin Figure A-1 shows the axial stresses obtained in the inpact study for locations in the vessel and the skirt, respectively. In the figure, the times for the stress wave generated by the inpact to travel from the vessel top to the top and bott e of the skirt are also given. Se times are calculated using the elastic wave speed in a slender rod, c which is an approximation of the actual wave speed in the vessef, wall.

Sese time values indicate that the rise and fall of stresses at various locations of the vessel and skirt are strongly related to wave propagation. Fbr example, the result shows that the compressive axial stress at the vessel top is released when the reflected stress wave peak reaches the vessel top, and that the stress in the skirt starts to rise when the wave front reaches its top. Accordingly, the causes for the high stress level in the skirt should be identifiable by studying the wave propagation between the vessel and the skirt.

j Reviewing the structural model for the inpact study in light of wave propagation, one can inmediately identify two possible explanations for the high stress level in the skirt. First, at the top of the skirt the lower portion of the vessel is not included in the structural model.

Bus, the entire wave energy is channelled into the skirt to cause high stress. Secondly, at the bott e of the skirt, the boundary is assumed to be infinitely rigid in the structural model. Consequently, a capressional wave will be reflected as a cmpressional wave of the same amplitude, and the reflected wave will then be added to the inoming wave

-Al-

to double the stress level. If these conservative approximations had not been used in the structural =rdal, the stress level obtained for the skirt would have been much less than the value given by the impact analysis. To provide a quantitative estimate of the conservatism of the predicted stress level in the skirt, a simple analysis of the transmission and reflection of stress wave at the top and botta of the skirt is presented herein. A detailed finite elenent wave analysis of the skirt is also conducted to confirm the results of the single analysis.

Se reflection and transnission of waves at a structural interface occur when the wave ingedance of the joining structures are different. At the top of the skirt, the impedance of the vessel and skirt are different because there is a change in cross-sectional area. At the bottan of the skirt, a difference exists due to both changes of area and material properties. A stress wave passing through these interfaces can be partly l transnitted and partly reflected. Se amplitudes of the transnitted and reflected waves are dependent on the wave ingedance (product of the

- density and the wave speed =pc) on both sides of the interface.

Considering the simplified case of the interface of two slender bars of different cross-aectional areas and materials (Figure A-2), the stress amplitude of the transnitted wave, 9;. and the reflected wave, q can be related to the amplitude of the incident wave, 9. By equating the normal forces and velocities on both sides of the interface, the following relations are obtained.:

2(F'22 /f',c,) (A-la)

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Y Y 0 2N Y k '2I0 Y i

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O- Q

/ + (A,/A, )(Qc,/g c,)

where the subscripts 1 and 2 denote properties on the incident wave and transnitted wave sides of the interface, respecitvely; f is the mass density and c the elastic wave speed of the materials; A is the cross-sectional areas of the joining structural couponents. Rese

- equations can be used as approximate formulas to estimate the stress level in the skirt due to stress wave propagation.

In th ctnictural model for impact study, since the lower portion of the vessel is omitted at the top of the skirt, the wave propagation only occurs between the skirt and the upper portion of the vessel (Figure A-3).

= 0.204, Using Equations (A-la) and (A-lb), and settingfc3=fc, r r on of the wherethesubscripts1and2denotepropertiesbfthe vessel and of the skirt, respectively, the stress level in the skirt due

-A2-

. \

to stress wave propsgation can be shwn to be 4.88 times of that of the

. vessel when the stress wave propsgates fra the vessel into the skirt. At ,

the botta of the skirt, since the support is modelled as rigid; i.e.,

fc =ce, Equation (A-lb) shes that a stress wave in the skirt will be reflected undanged at the rigid support. B us the stress level in the skirt will be twice the anplitude of the incident stress wave. Taking into consideration the effects of both the vessel skirt interface and the rigid styport, one can expect stress level in the skirt to be approximately 10 (2x4.88) times that of the vessel. Bis rough estimate appears to agree with the results of the inpact study shwn in Figure A-1, i.e., the stress of finite element 1 (representing the skirt) is about 8 times of the stress in elenent 2 (representing the vessel location imediately above the vessel).

%e above estimate of stress in the skirt is drastically reduced, if ,

the presence of the lower portion of the vessel and of the' flexibility of l the skirt styport is included. In this case, an incident wave fra the upper part of the vessel will be transnitted into not only the skirt but also the lower part of the vessel (Figure Ar-3). Similar calculations can be carried out as before, using =Ag+Ag in B3uation (A-la) and (A-lb), where the subscript Lv tes Efea value of the lwer vessel and S the area of the skirt. Se new calculations show that the stress level in the skirt is only 0.83 times the stress in the upper vessel. Bis value i is substantially lower than the 4.88 obtained for the case of omitted lower vessel. Similar reduction of stress level can be shown at the skirt support if the stpport is asotned to be non-rigidg AssQ pe stpport to be made of concrgte (mass density = 2.25 x 10 lb-sec /in and Young's modulus = 3.33 x 10 psi) and iporing the effect of area change, Bguation (A-lb) shows that the reflected wave due to an incident cmpressional wave in the skirt is a tensile wave whose anplitude is 0.92 times of that of the incident wave. Accordingly, in the actual structure, the dynamic i

stress in the skirt will probably be quickly released rather than be amplified by the reflected wave as shown earlier for the rigid support 3

model. Before unloading, the stress level in the skirt would be about the see as in the vessel.

l To confirm the foregoing observations concerning the sipificant effects of the presence of lower vessel and support flexibility on the dynamic stress in the skirt, a special finite element dynamic analysis of the skirt is carried out. Se finite element model used in this analysis is given in Figure A-4. It is a detailed model of the skirt and its surrounding structures; it includes the entire skirt, a portion of the concrete styport and a portion of the upper and lower vessel located near the top of the skirt. With negligible effects on the usefulness of the results, the model is taken to be a plane strain model with thickness of unity. %e model is supported at its boundary nodes by springs and dampers in the global x and y directions. Sufficient damping is assigned to the depers to absorb all the incident wave energy at the model boundary, so that the analysis results will not be affected by reflected waves fra the boundary. Se model initially at rest is subjected to a suddenly applied constant pressure pulse at the upper end of the vessel.

-A3-

In general agreement with the results of the foregoing wave study, the finite el ment results sh w that the maximia stress in the skirt is only 1.3 times of the stress in the vessel. Morewer, the dynmic stress in the skirt is quickly released although it takes more than a few traverses of the stress wave in the skirt to accomplish it.

Fr a the foregoing results, one can conclude that to determine the stress in the skirt, it is essential to include in the model the lwer portion of the vessel and the flexibility of the skirt stpport. Se results also shw that the maximum magnitude of the actual stress in the skirt is about the same as that of the vessel. Accordingly, for the buckling analysis, we can use as the skirt stress the average of the stresses obtained in the inpact study for the vessel and the skirt; i.e.,

stresses in Elements 2 and 1 in the finite elenent model for the impact study. Se maximum skirt stress obtained in this way is about 45 kai (see Figure 1). his stress value is instead used in the buckling analysis of the skirt.

A-3 Vanaal Prt sadrt m-irlina Analyala A conservative elastic-plastic buckling analysis is performed to evaluate the stability of the skirt under the inpact loading follwing the head drop. %e dynanic stress in the skirt is asstaned to be uniform around the ciretaference of the skirt, and the stress is applied statically. Since the inertia of the material tends to help prevent buckling at the beginning stage, it is conservative to ignore the inertia in the estimate of buckling load. S me experimental data have been l published in the literature shwing that cylinders buckle.at higher stresses under dynaric than static loads.

'Ib determine the buckling stress, it is necessary to first identify the governing mechanisms. Past research has shwn that two gemetric ing load of paraneters circular cylinder are particularly under axialhelpful load; in i.e.,

determining the,byep/gt, r/t and (1-if) L where r is the radius, t is the thickness, and L is the length (or height) of the cyclinder; y is tihe2Poisson's ratio of the material. For the skirt r/t =

91 and 2 = 1-tr)L /rt = 32.7. Se r/t value indicates that the skirt is a moderaky(thick cylinder whose buckling stress is not very sensitive to randely-distributed geanetric imperfections, if it buckles at stress above the proportional limit where the material ceases to be linear elastic. % e value 2 of the skirt shows that it is an " intermediate-length" cylindcr whosh buckling stress and deformation are strongly affected by the length and end condition of the cylinder. An analytical prudiction of the buckling stress is difficult. Gerard provided a conservative enpirical formula for the prediction of the buckling stress l

for cylinders with clamped ends (Reference A-1).

2 2

~

• c 7c Et (A-2a) i 12 (1 - v') L '

l t

-A4-

k, + ( o. ssi C 2, )2/kp (n-2b) k, =

where k is the buckling coefficient for a flat plate and C is a function of r/t.e For r/t = 91, C = 0.43, and k p = 4.0. Substituting appropriate values in (h-2a) and A-2b), the elastic buckling stress of the skirt is obtained to be 158 kai. Since this value exceeds the yield stress of the material (assumed to be 60 kai for this analysis), the skirt will buckle plastically. To find the buckling stress, a plasticity-reduction factor ofgcanbeused;i.e.,

g(g) (A-3) where the subscripts p1 and el denotes elastic and plastic buckling stresses, and the elastic buckling stress is obtained using Equation (A-2a). %e formula for y of a flat plate is used herein, since for this case it gives a slightly more conservative result than the foonula for a long cylinder. For a flat plate,

• 3&

/-v i Ez

~

, ,a 2 IE IE 1/2 - (1/2 -F)Ef;Fand E are Poisson's ratio and Young's where modulus o the skirt material, respectively; E =f/Eis the secant modulus p =f and E, = d7/dE is the tangent modulus of the sEress-strain curve of the material. %e E and E corresponding to the buckling stress can be conveniently evafuated bsing the Ranberg-Aa7vvl representation of the stress-strain curve of the skirt material (Figure A-6):

97/

EE P /, / 2 (A-5)

-/.

' VA o

% Q 3

where ,= 60 ksi, and E = 30x10 kai.

By trial and error, the plastic buckling stress of the skirt under Bis value is greater synmetric axial load can be obtained as 54 kai.

than 45 kai which was determined in the foregoing stress wave analysis to be the maximum dynanic stress generated in the skirt by the shroud head impact. Consequently, the skirt will be able to withstand the inpact load without buckling.

-AS-

30 : _ :.g gg. . g.. g3x 3... , . .up n =3 3 ..

. g .:.;". , , x-gun q : ;3.g T'"  :.i:,. ....

p=: :j;  : .::n:-

. gu.. . 1:a_

gp.p.3:ggg:: :: .q:p.3.; . ,, :;jiiinuppg- .

t 3!i:= di!:: ~ ' "I  !!!

tg .:::! ~4.4 H.in' U .,.;

. r . ur:i:Tld$.....

, ...:.---- ..p m)!i"fi ii. ~;.3~:g :,- .. ,.

. .i . , . , ug.

Z. :3- -4  : 5:: 6i 8- i9 '10" 11. .  : .. 13:!. --14 i:iE

' d' i. ~

' m'

^ ~ '

0 , m . . . .

3 K -

) -

~ ~ ' - -- 4" t -Ett 2-(VESI;EL ON TOP

_ 10 t

1 0F $KIRT) g,

-- -~ - - - - - - - - -

0 -- -- --- - - -

a: ~

J.

,-30 -

---

=----: - - - - i--:-==--=----

4 e-o u Ei.. 5- (TOP OF VESSELP

< -40 - --

-:--+-- - --

-50 - ---

3

-60 - .

1

-70 -

-8J --

b - EL. 1 (SKIRT) t i 2- 3

-90 -

l-i t0  :. . Time of initiab impact : - :-

tg: Time when wave front reaches.. bottom

. . . . . . . - - - . .of - .skirt- . . . . . - .

t2: : Time when wave peak reaches . bottom of skirt t .L. Time when reflected was front reaches top- of skirt.- --

3 14  :- Time when reflected wave peak reaches top -. of vessel; --- -

.._2..._..__-...._. 2 .- .

- - n= =. . :- : - - - - -.

Note: All times are. calculated using the elastic wave speed in a

- =- : barr-en (-E]f } k. ;--1.96 N 10 in/secr -- - -

2. . . .. .n.:.i. ..;...

ci

2 2 u-

..id:92i

iH:-

.-i{F'iiiii:.. . ~.  !:h M'

' . :- . .. .. b.. . .

1. i: . ...,..=lt.. .....;-  :

i T .i.:525.1.:. ?. .i.l5i.i.;.!.!.!!S-i.}3..

.g. - -~=-~ -

E 5 ~5.E...E.3!.I.$.=$.15.5.5...

.t . .......-...,; .  : ..:: .

.=.-...--.m--

.at.;.u..nn :an.4 n n;a;..:....

i5-:d.

--. r .. :

iS.5.n..: .u.iiEUE!iin.n.unsa

.:u.

. x:.. ... :n.= =:n: ... -n nu: . - - - --" - - - - w n . :. n =. : - n u.-.

.r.=.un x*u . . . . . . .. . . :. .n

.:. ~~~~-

.::: ...=: un =n

=:::it::Eith="iii.'!. - i:iiEEdii -EiEEE-EijEEi n;ihi: T-iE-iT.il . EE"iEi!EEli::

nt----- .n n: =n - . ne i"!!....

n - - .. ~~  :.-

. :u=nl :---in=:=: - = 4a :cc.t:2: _-.-=: == c:.ur rat -

! FIGURE A-1 CORRELATION OF AXIAL STRESSES FROM It' PACT STUDY WITH WAVE PROPAGATION PHENOMENA

-A6-

n __ - _ _ -

k d IR g,c,A3 y Y

INTERFACE U f2'*2'^2

&T 1

l h

FIGURE A-2 WAVE PROPAGATION ACROSS A STRUCTURAL INTERFACE 1

i

-A7-

UPPER VESSEL

~

UPPER VESSEL d

h PR = -0.66 g q q=0.09y u

. I U

cr7 = 1.ss q U 7e 'i q=0.91%

F I

. SKIRT LOWER VESSEL

- SKIRT 7; 7"b T 0i i l  %=-0.92%

U CONCRETE RIGID & FIXED BASE BASE 7T= 0.0 7=1.92%

T SIMPLIFIED MODEL COMPLETE MODEL FIGURE A-3 SCliEMATIC OF SIMPLIFIED AND COMPLETE SKIRT MODELS FOR WAVE PROPAGATION STUDY

-A8-

FIRURE A-4 FINITE ELEMENT MODEL FOR WAVE PROPAGATION STUDY h

p=1 ksi 1

0.011 "t

@ 0 UPPER VESSEL 4

3 6

@- h Damper Elements g h- h Damper Elements LOWER VESSEL 20 - 19 y

12, b n 11 SKIRT EE 2I 6

15 17 16 24 -

23 46 39 31 27 26 25 30 34 38 b@*'

• • (V

.5 g voy g e eN e

@ 7 3

- 44 41 0 0 @. U 43 42

-A9-

i  ::iB#-! MINI $55!i=!!E EFiir'il5IiIiEE58!5555 Ss.'i$Ni"E$E i !5i!005!! Mi!!$1555!SEid5

p s m s = E s : s : ~rm .:i-- - 5:is== ==+ - - di =:::==iir == - E::T n!== : . = -- ~

1.2: -J 1::i..Z :Zr L - -- WE.l.f. M ,- SMR. . T'f a::r : : :ai:==  :: Z:

... .;=. = i, .:t. .. ;_.. =... .@ . : .g :. . =. . =. =. ..=_ ..:. . . : . . . = - . : :i. =z .

. u = = i. - - -.r z

.g;: -yur;;

. . . =

= . . . . . .==

r r-

.. u: 1g;" - ; . ; .3.;: =y- p----- ;;;= t f " ;,j,

~~

" Z ~i 1.0 -

- .j? ~

• :w.gjp : p 2 o=

0.8 ' - - - - - ' - " - -  ;;_ --* L---;- - -- -

K .  ; ..

. -  : = .:

^

'-- =

0.6 - - - - - - - - -

^5"':

. . . . . .* t. ...

=-;... t

.. { .-. x..r g. . . . '

- ;.t: . . _

. ..-=x.=.. .

0.4 - 9 -- -:--------=3 ~r u . . . --+'---i

.- ~

- - .c.

. 1- . :. - ._

.0 0.2 4 1 - - - - - - " - -

== ~ " - - " - = ~ - - - - -

_" [_ h.

II . . . . . . . .

m 0.0 . . . . . . . .

1 g 1 2 3 4 5 6- 7 8 9 10 TIFE(10-3 sec} }

-0.2 - --- - - - - - - - - - - -

c x

0.4 -

l

-0.6 -

1

-0.8 - - - - - - - - - - - - - -- - - - - - - - - - - - - - - -

- - -i

-1.0 - -

EL.1 (UPPER VESSEL):

-1.2 -

h __

., } ,4 . g . . . . . . . ._ ._:_ .._.:[f. _*-  ;-.-[ . . . . .._.-.a..- . _ . - . . -

- -----,-:~

z - a- --n -- . ;_ c- ..

.m.-

. .

= .. =

. h. ..

.f.

'_. - l . f _

-+ - - . -tps--Time when wave- front- reaches top of skirt" --  :---

. --i+.. . - .. -+-i. . . . - .

'.;:...-.:'.1......=..-*... .:-'.'--.  :*--

.n.iu i.. .J. : 1:. . . t 2-.-"

Time when wave front 11 reflected' to top of?

~

• Ents-E!Mi[.i"R:lii: skirt by- concrete ' support - -

= .. J..: . : . . . . . ~ ~ :i= . . . . . . . . . . . . . . .. .

=E l ;5=il!$$5!i!55 -Y; "-$hn .[h:,jiiU'NI$FEiNi!!NEM Hit ' . . . .T:"E5E =' i'= "i" ~~-'i'

u. . : =.. =...=..::.-=...

=.a=...:.:=..n.,............:=.-,:.....=:.=..-...

~~ - "'

I- fiE} '

b N 3 .

I. ..I 5.5 .- -..L---

=

.u e=3. =:=Es 1. ---- === :5=siesi=L=ss :=*E.:E,=1:.n=Em==

- : : = - - - - -- u = : ~-=C .-==a====.:= ===f=e:==--- -- - =: =. =.c=u : =:= ===:: :

==: .

FIGURE A-5 AXIAL STRESS IN SKIRT DUE TO WAVE PROPAGATION (FINITE ELEMENT MODEL IN FIGURE A-4)

-A10-l

10 0 i l i l

A533-B STEEL (200'F) 90 -

0 EXPERIMENTAL DATA 3

80 -

i = g [ F._ )" F IT 60 70 u>

m c o= 60 ksi M 70 E = 30 x 103ksi Eo = co /E = 0.002 0 = 1.12 '

60 11 -

n = 9. 7 I I I I I I 50 0 0.05 0.10 0.15 0.20 0.25 0.30 PLASTIC STRAIN Figure A-6. Stress-strain curve for A5338 steel at 200'F and its representation by the Ramberg-Osgood law.

1

- Al 'l -

Reference A-1 Gerard, G., and Becker, B., "Harubook of Structural Stability, Part III - Buckling of Curved Plates and Shells," NACA TN 3783, August 1957.

I

-A12-

. \

AFFENDII B SHROUD HEAD VELOCITY UNDER SUBMERGED CONDITIONS l

\

/

$ vf

/

REACTOM / p "'""%

PRES $URE $ ll ,#'~ '"k VESSEL j b

$ if 4

Figure B 1. Schematic of Shroud Head Drop Define:

V = shroud head velocity a = shroud head mass A = projected area of the shroud head normal to V V = flow velocity relative to the shroud head (neglect friction f

and assume that velocity through the steam separators is negligible).

l A

g

= total flow area = A, - A Ay = vessel cross-section area p = mass density of water 6 = mass density of steel l S = displacement coordinate with S = 0 when V = 0 l

CD = dras coefficient in equation drag force -a c . p . d . area l

l 2

-B1-t i

o CALCUI.ATION OF THE DRAC COEFFICIENT C7AND THE DRAG FORCE CONTROL VOLUME RELATIVE TO g y l STATIONARY g l RELATIVE TO VESSEL i PLATE g l

Vf vn- v, - v 'V f 'h d ^ '

a htN ;l R

s n, , s i P'. ATE

>>l I N

N N N s Ify

% 4  ; 'I l ts s N s

~ I l N w  % h v i lL*' J A00 S76 Figure B 2. Relative Velocities in the Shroud Heed Drop The actual situation is shown in the figure above on the left hand side. A plate with projected area A (representing the shroud head) moves downwards with velocity V. Shown on the right hand side above is the same system with the plate made stationary by adding a velocity component V, to the vessel.

Now, consider a control volume of the fluid as shown by the dotted line. At For the time being, the bottom, the pressure is Pg and the velocity V.

neglect gravitational considerations. The fluid passes through the annular area, Af , with velocity V g. At some distance, the velocity V is regained, l

but due to enlargement of area, there is some head loss. Therefore, the pressure is only Pyat the upper and of the control volume.

The head loss due to the enlargement of the cross-sectional area to Ay is I

(" f

~

23 (Equation B-1)

The velocity Vfis at the vena contracta.

l t

f l

1 __________j

VESSEL WALL 1 i

///////////////////) ////////>

h VENA CONTRACTA A00 576 Figure 83. Vase Contracts for Fluid Flow The cross-sectional area at the vena co'ntracta is Cg Af , where Cc 18 the coefficient of' contraction. Values of Cc in the literature range from 0.5 to 1.0. For ideal flow through a rectangular sharp edged orifice classical hydrodynamics yields a value of 0 61.

Figure B-4 shows Cgy C for orifices with diameter ratios Dg /D,.

Since C ,is very close to 1.0, the value of C d C' c O yD in our case (i.e., A/A y) may vary from 0.8 to 0.9. Based on this, a conservative value of 0.8 is selected for C,. This value is considered to be reasonable since Reference El assumes a value of 0 66 forcC in the case of flow past an obstruction in a pipe. Note that it is conservative to use as large a value of Cc as is reas nable A C=C V = v V y f

NCAf ;

2 A (Equation B-2) h = V v -1 L

W .

Cn, _

• Hydraulics and Fluid Mechanics by E. R. Levitt, Publisher, Sir Isaac Pitman, London, 1958 edition, p. 112.

-B3-

now

' ' - 2 2 - 2 Av -1 (Equation 3-3)

Pg -F = p V_* A'v -1 =

,V 2 = 9h CAg 2 CA g 23 , ,

This is now in mass density units rather than weight units.

The f ree body diagram of the control volume shows the net reaction force on the fluid = (Fy-F)* A. This force is equal to the drag force on 2 v the shroud head.

FROM: PLUlO MECMANICS tWITM

• ENGINEERING APPUCATIONS.SV DAUGHEATV A80 FOANZINEl, to GRAW HILL,1986, EDITION p 3M 12 E

on i A K l l ea J

/  :

g g

e.,

- W ca - c.c, \

as (

em  % g N EAD poss (ORIFicEl } ,,, j w =

so s j NN g u A " J

%A 1 c.2

\

- ' NET HE AD LOSS (F LOW NOZZLE , E

' " I 20 0.1 M 5 o

'o 3 o 0.2 c.4 os os 1.o se DI AMETER RATIO Do /0, Figure 94. Coefficients for Sharp Edped Orifia with Preasure Differential Measured Either or the FWpar or at the Vene Contracts. Also Hand Loan Acrom Orifice and Flow Norrie. All Curwn are for Nn to,V, p,4) > td.

h 4 v a n, "p ,g From: FLUID MECHANICS ,, ~'j; ,

With Engineering App- ,  ; '

vgno o l l

lications, By Daugherty '

and FranZinei,McGRAW HILL,1965, Edition p 358. ,,fy l

I e

h[\ >

'3M b

L

__ o (Y4.?,?, >7 .

D, 1D eD 2  !- -'h n

" w .n w.s l

Ane4M fievre 95. ThiMare Orifice in a Pipe

-B5-

• ,. . . 2 Th3 Drcg forco =0*A 9 V

^

• .b -1 (Equatica B-5)

M i

2 '. . f .

. . s

• 9

• V .A

• then:

If the drag force is defined *as CD 9 7

= V - 1 (Equation B-6)

C D

CA g o Determination of Velocity V:

The equation of motion is as follows:

- F=a$ (Equation B-7)

Two forces on the decending body are:

Buoyancy force = as (1 - 0/6 ) (Equation B-8)

Drag force =C p

• V .A y a p (Equation B-9)

Therefore we have:

ag (1 8/6 ) - CD

• 2 b*'"

Since v = dv and V = ds de dt Then dc = ds and 1r = V dv V de Combining the above equations and solving for ds.

ag (1 9/ 6 ) ,CD *'*

• y" '

• e or ds = av dy .

og (1- p / 6 ) - C D b

[2 ,

- B6 -

~

(Equatics 5-11) cr ds = (2 V/8 C, AV ) dv 2 2as * (1 8/4 ) -V

pC A D y Define a = . 2ag * (1 8/d )

p= A C,*

Then.

5 Y

V dv (Equation B-12) 2a

- o / ds =PCDb , a-[

From standard integration formulas, we have

=-1 (Equation B-13)

V dy in (a-V )

2 2 a-V S= - a in (a - V )

DCD Ay ,,

o (Equation B-14)

=- a

• An (1 - V )

8CD ^v Solving for V ,

.b (Equation B-15) y2 , , y_,

An inspection of above equation shows that if the falling height, S through the liquid is large enough, then, the second term is essentially zero, therefore, 1

1 Terminal steady state velocity Vg = Va l

(Equation B-16)

=

I 2ag (1 P/6 )

l i pCD Ay

Conversely, we can also determine height, 5, through which a body has to fall before it essentially attains steady state terminal velocity. For exarple, let us determine the formula for drop height 'S' when shroud head attains 90%

of steady state velocity.

DAy C

• 2 D _

0.9 , y,,

or 9Ay C D

8/*

• 1*00 (Equation B-18) 5 " 1*66 8 90

- p%Cp Also, given a drop height, we can find what percentage of steady state I

velocity it will reach at the end Of this drop height.

1 1

a I A-

\

.