RS-14-338, Byron/Braidwood Nuclear Stations, Updated Final Safety Analysis Report (Ufsar), Revision 15, Appendix C - Turbine Missile Study
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B/B-UFSAR C-i APPENDIX C - TURBINE MISSILE STUDY TABLE OF CONTENTS
PAGE C.0 ABSTRACT C.0-1 C.1 INTRODUCTION C.1-1 C.2 METHODOLOGY C.2-1 C.2.1 P 1 - Missile Generation Probability C.2-1 C.2.2 P 2 - Strike Probability C.2-2
C.2.3 P 3 - Penetration Probability C.2-11 C.3 PARAMETERS C.3-1 C.4 RESULTS C.4-1 C.5 CONCLUSION C.5-1 C.6 REFERENCES C.6-1 ATTACHMENT C.A: DETAILS OF PROBA BILITY CALCULATIONS FOR THE CONTAINMENT BUILDING C.A-1
B/B-UFSAR C-ii APPENDIX C - TURBINE MISSILE STUDY LIST OF TABLES
NUMBER TITLE PAGE C.0-1 Reliability Criteria C.0-3 C.3-1 Characteristics of Low-Pressure C.3-3 Turbine Missiles C.3-2 Critical Component Density Factors C.3-4 C.4-1 Summary of Results f or Byron/Braidwood C.4-2 C.A-1 Probabilities for Containment Building C.A-4 Wall C.A-2 Approximate Computation of P 3 for C.A-5 Regions B and C
B/B-UFSAR C-iii APPENDIX C - TURBINE MISSILE STUDY LIST OF FIGURES
NUMBER TITLE C.2-1 Assumed Coordinate S ystem for the Model C.2-2 Transformed Two-Dimens ional Coordinate System C.2-3 Exit Dynamics Sp ace of the Point Target C.2-4 Strike Geometry in Two-Dimensional -Z Plane C.2-5 The Band of Allowed Values in the -V Plane C.2-6 Strike Geometry in X-Y-Z Plane C.2-7 Relationship Between D isc Plane and Exit Direction C.2-8 Limits of Integration of the Integral (24) or Integral (30) and the Relationship Between and V C.3-1 Plant Arrangement C.A-1 Containment Auxiliary and Turbine Building Roof Plan C.A-2 Locations of Regions A, B, C, and D on Containment Building Wall C.A-3 P 3 vs. Thickness
B/B-UFSAR C.0-1 REVISION 3 - DECEMBER 1991 C.0 ABSTRACT This appendix discusses the analyses that have been performed and inspection criteria which have been developed to show that the Byron/Braidwood Stations are acceptably safe against postulated turbine missi le damage. These mi ssiles result from a postulated high pres sure turbine rotor f racture and a low-pressure turbine disk fracture at design and destructive overspeeds.
C.0.1 Current Approach Byron/Braidwood currently use the probabilit y values outlined in Reference 6 and reproduced in Table C.0-1 for the minimal acceptable range which will allow unit s tartup or continued operation. The statio ns fall into the U nfavorably Oriented category. To ensure the Byron
/Braidwood turbine rotors maintain their integrity and unit operation is mainta ined within the SER limits a probabilistic program based on the manufacturers' methodology has been implemented.
The method uses manu facturer supplied missile generation probability values, P 1 , for each low pressur e turbine rotor.
The missile generation p robability values ar e provided f or both rated speed and overspeed conditions for dif ferent operational lengths of time. For each individual tu rbine rotor the overspeed and rated speed probab ility values are added together, giving the total probabi lity of a missile ge neration based on time in operation.
This information is generally displayed in graphical form. Each time a rot or disc inspecti on is performed and the results are satisfactory (no indicatio ns found within the rotor disc which c ould lead to d isc rupture) the operational point on the time vs missile g eneration curve is set back to zero hours of operation.
At each refueling outage a cal culation for tot al unit missile generation probability is made. To make this calculation the operational hours on each of the low pressure turbines is gathered. The missile generation probability for each of the LP turbine rotors is taken from the individual rotor's graph based on the operational time on the rotor. The values for the three rotors are then added together to determ ine the current missile generation probability for the unit. Th is value must be below 1.0E-05 to allow loading the tur bine and bringing the unit on line. In addition, a calculation is made to determine when the unit missile generation p robability will drop below the point at which action (rotor in spection) must be take
- n. This calculation is made using the three individual r otor curves and the operation hours on e ach of the turbine r otors. A curve is usually generated. From thi s combined curve the total
B/B-UFSAR C.0-1a REVISION 3 - DECEMBER 1991 length of operational ti me allowable before ac tion must be taken is determined. This value is compared a gainst the duration of the next fuel cycle to ensure a forced shutd own will not occur.
If a turbine rotor is replaced, or if indications during disc inspections are found wh ich require replacement or maintenance, new probability values will be supplied by the rotor manufacturer. The p robabilistic determinati on method described above would then be performed to ensure missile generation probabilities are within an acce ptable range and that no forced shutdown would occur in the next fuel cycle.
This approach focuses on the probability of turbine missile generation, P 1 , which is consistent with the recommendations provided in Reference 6. The emphasis was s hifted from determining strike and damage probabilities (P 2 and P 3), which involved elaborate and ambiguous analyses, to the probability of turbine failure resulting in the ejection of turbine disc (or internal structure) fragments th rough the turbine casing (P 1). The NRC has since reviewed a nd approved the manufacturer's (Westinghouse) methodo logy which provides procedures for estimating crack growt h, missile generation (P 1), and volumetric inspection intervals (Reference 8). T he following is a discussion of previous approaches used to satisfy turbine missile protection requirements.
C.0.2 Previous Approach According to Bush (Reference
- 1) the probability per year (P
- 4) of turbine missile damage m ay be expressed as P 4 = P 1 . P 2 . P 3 where: P 1 = Probability of turbine failure resulting in the ejection of a missil e, per year. P 2 = Probability that a mis sile will strike a barrier which houses a critical plant component, given that a missile has been ejec ted from the turbine; and P 3 = Probability that a mis sile will perforate a barrier, thus damaging a critical plant component, given that a missile has been ejected from the turbine and has struck the barrier. Based on studies conducted by Tw isdale et al. (Reference 5), the product of (P 2)(P 3) can be taken as 10
-3 or 10-2 depending upon favorable or unfa vorable turbine orientat ion, respectively.
Thus, the probability, P 1 , of a turbine failure
B/B-UFSAR C.0-1b REVISION 1 - DECEMBER 1989 resulting in ejection of a mis sile must meet the guidelines given in Table C.O-1 tak en from Reference 3.
The methodology for evaluation of P 1 values at that time had been submitted to but not yet reviewed by the NRC.
It is also specified in Reference 6 that until approval of the methodology two criteria must be met regardless of turbine orientation. These criteria are:
- a. Having an inservice insp ection program of the steam turbine rotor acceptable to the NRC that will provide assurance that disk flaws having potential for brittle failure of a disk at speeds up to design speed will be detected.
B/B-UFSAR C.0-2 REVISION 8 - DECEMBER 2000 b. Having an inservice insp ection and test program for the governor and overspeed p rotection system that is acceptable to the NRC for detection of f ailures that can lead to overspeed condit ions above the design overspeed.
The inspection program to meet these two cri teria was submitted in Reference 7 for review. Until a program was approved, volumetric inspection of all low pressure turbine rotors was required to be performed every third refueli ng outage and an acceptable turbine valve inspe ction program was incorporated Technical Requirements Manual 3.3.g. Subseq uently, the NRC has reviewed and approved a program as outli ned in Section C.0.1.
C.0.3 Original Approach The remainder of this appendix discusses the original approach where the strike and d amage probabilities, P 2 and P 3 , were calculated. This work has been superse ded by the approach summarized in Section C.0.1. The following sect ions of this appendix are included for historical purposes.
B/B-UFSAR
C.0-3 TABLE C.0-1 RELIABILITY CRITERIA
PROBABILITY, YR
-1 FAVORABLY ORIENTED UNFAVORABLY ORIENTED REQUIRED LICENSEE ACTION A. P 1 < 10-4 P 1 < 10-5 This is the general, minimum reliability requirement for loading the turbine and bringing the system on line.
B. 10-4 < P 1 < 10-3 10-5 < P 1 < 10-4 If during operation th is condition is reached, the turbine may be kept in service until the next scheduled outage, at wh ich time the licensee is to take ac tion to reduce P 1 to meet the appropriate A criterion (above) before returning the t urbine to service.
C. 10-3 < P 1 < 10-2 10-4 < P 1 < 10-3 If during operation th is condition is reached, the turbine is to be i solated from the steam supply within 60 days, at which time the licensee is to take ac tion to reduce P 1 to meet the appropriate A criterion (above) before returning the t urbine to service.
D. 10-2 < P 1 10-3 < P 1 If at any time during operation this condition is reached, the turbine is to be isolated from the steam supply within 6 days, at which time the licensee is to take action to reduce P 1 to meet the appropriate A criterion (above) before returning the t urbine to service.
B/B-UFSAR C.1-1 C.1 INTRODUCTION This report examines the Byr on/Braidwood Stations for susceptibility to dama ge due to a catast rophic failure of the turbine generator, resul ting in the ejection of high-speed rotor fragments, hereafter c alled "turbine missiles." The probability is calculated of turbine missiles causing damage that interferes with normal safe shutdown or d amage that results in environmental releases beyond the limits specified by 10 CFR 100 during normal operating or safe shutdown conditions.
In Section C.2, the me thodology used to determine the probability of turbine missile damage is presented. In Section C.3, numerical values are assigned to the parameters of the analysis, and features unique to the Byron/Braid wood Stations are discussed. The resu lts of the analysis and a summary are presented in Sections C.4 and C.5, respectively.
B/B-UFSAR C.2-1 REVISION 1 - DECEMBER 1989 C.2 METHODOLOGY The probability of turbi ne missile damage is expressed (after Bush, Reference
- 1) as: P 4 = P 1 . P 2 . P 3 (C.2-1) where: P 4 = probability of turbine m issile damage, per year; P 1 = probability of turbine failure resulting in the ejection of a missil e, per year; P 2 = probability that a m issile will strike a barrier which houses a critical plant component, given that a missile has been ejected from the turbine; and P 3 = probability that a mis sile will penetrate a barrier, thus damaging a cri tical plant component, given that a missile has bee n ejected from the turbine and has stru ck the barrier.
P 1 , P 2 and P 3 are evaluated using a met hod which considers turbine characteristics, turbine failure mechanisms, plant layout, barrier types, and the inherent variabil ity of the parameters influencing missile pene tration. A descript ion of the method follows.
C.2.1 P 1 - Missile Gen eration Probability The general process for the generati on of a missile begins when the generator separates from the system and because of a succession of malfunctions in the protection system, the steam supply to the turbines is not properly inter rupted. The turbine is subsequently driven to an overspeed condi tion at which one of the discs breaks into several pieces, some of which perforate the turbine housing and beco me known as missiles.
In general, two specif ic overspeed condition s are of interest:
- a. Design Overspeed
- This is 120% of rated speed and is based on the precept that should the turbine speed governing system be incapacita ted so that the turbine is tripped by the over speed trip mechanism, the calculated speed attained wi ll not exceed 120% of rated speed.
- b. Destructive Overspeed
- The bursting speed of each shrunk-on disc is ca lculated. The cri terion used is that the disc will fail when the average tangential stress equals the maximum ultimate tensile
B/B-UFSAR C.2-2 strength of the disc materia
- l. Disc No. 3 is the most highly stressed dis c, with a calculated failure speed of 182% of rat ed speed. Upon failure of disc No. 3, f urther acceleration of the unit is assumed to halt, and for the purpose of analysis, all other discs have been as sumed to fail at 182%
of rated speed.
At either overspeed co ndition, it is assumed that the rupture of one disc will do su fficient damage to the unit such that further overspeeding a nd additional missile generation will not occur. It is further assumed that the d isc will rupture into four quadrants, of which two will be projected downward into the turbine foundation, one will be projected toward the plant, and one will be projec ted away from the plant. If the disc ruptures into fewer than four pieces , the probability that one of the pieces will be projected towa rd the plant will be less than unity. If the disc ruptures into m ore than four pieces, each piece will have proportionately less mass and, therefore, less potential for damage.
The determination of the probabi lity of generati ng a turbine missile is an extremely complex problem that can be, and has been, stated in various ways with a resu lting variety of answers.
For further discussion of th is problem, see Reference 2.
C.2.2 P 2 - Strike Probability
The method of determining th e strike probability, P 2 , has been adopted from Ref erence 2 and is summarized here.
If a missile is produced by a rupturing disc, it will leave the turbine with a g iven speed and direction, where the direction can be defined in terms of two angles, i.e., the angle from the horizontal plane and the angle of the horizontal component from the turbine axis. This three-di mensional space (speed and two angles) is called the exit dynamics space.
A given target has an "image" in the exit dynam ics space which co nsists of all points, i.e., initial sp eed and direction, w hich result in the missile hitting the targ et. The basic problem is to describe this image in terms of the target posi tion, orientation, and size. This is done on ly for plane targe ts, since any target can be subdivided into "subtargets" which ar e small enough to be approximated by plane targets.
The first problem cons idered is that of finding the image of a given point target. T his result is extended to the case of a target consisting of a short line passing through the point at an arbitrary angle in the plane of the traject ory, and then to the case of a plane target with an arbitrary o rientation. The final result is an e xpression for the im age of a plane target of given orientation and size located at a given position.
B/B-UFSAR C.2-3 Consider the coordinate system shown in Figure C.2-1. The origin is the center of the disc which r uptures, the x-axis corresponds to the tur bine axis, and the disc rotates in the y-z plane. The missile will leave the o rigin with an initial speed v and initial di rection defined by o and o (see Figure C.2-1). For a given point (x o , y o , and z o) the objective is to find the co mbinations (v, , ) which will result in the trajectory of the missile passing through the point.
Since the only force a cting on the missile is that of gravity (air resistance is ignored), the trajectory will lie in the plane = o , where )y/x ( tan = o o-1 o (C.2-2) and the original problem reduces to a two-dimens ional problem.
If is the distance from the or igin along the intersection of the x-y plane and the = o plane, then the pr oblem is as shown in Figure C.2-2, y + x = 2 o 2 o o (C.2-3) The equation of the trajectory in the -z plane is
)cos v/2 (g - tan = z 2 2 2 (C.2-4)Where g is the accel eration of gravity.
For a given ( o , z o) the equation can be solved for v as a function of obtaining
)z - tan (cos g/2 = v o o 2 o (C.2-5)and from this it follows that is restricted to the range 90 < < z tan o o 1- (C.2-6)It can also be shown that v is restricted to the range
)z + + z ( g v 2 o 2 o o (C.2-7)Figure C.2-3 is a graph of v vs. . This is the image in the exit dynamics space of the point target.
Next, consider a sma ll line target centered at ( o , z o) of length 1 at an angle with respect to the horizontal
B/B-UFSAR C.2-4 )2 2 (- as shown in Figure C.2-4.
For each value of satisfying Equation C.2-6 in Figure C.2-3 th ere will be a range of v alues for v which will result in the line target being hit by the miss ile. Using a differential argument wi th Equation C.2-5, the range in v, dv, is given by 1 3/2 o o o o 2 )z- tan ( 2) cos 2z - ) tan cos + sin ( cos 2 g= dv (C.2-8)In the - v plane the l ine of allowable values in Figure C.2-3 for a point target becomes a band of allowable values for the line target, as show n in Figure C.2-5. Equa tion C.2-8 is an approximation whose accu racy is a function of the size of 1. The less the expression in square brackets in Equation C.2-8 changes over the line, the more accurate is the approximation.
Because of the natur e of the physical problem, only those trajectories are of inte rest which result in the missile hitting the target from the posi tive side, i.e., the side from which the upward pointing normal vector N = ( -sin , cos ) extends. This condition is stated mathematical ly by requiring that the dot product of t he velocity v and N be negative.
This leads to the restriction:
) tan - 2z ( tan > o o 1- (C.2-9)If tan z o/ o then Equation C.2-9 is less restrictive than Equation C.2-6 and has no effect on the allowable range of . Next consider an are a centered at (x o , y o , z o), or equivalently at
( o , z o , o), whose orientation is def ined by its normal vector N = (cos , cos , cos), where , , and are the dir ection cosines of N, as shown in Figure C.
2-6. The line of intersection of the target area and the -z plane, L 1 , is the line which corresponds to the line 1 in Figure C.2-4. It can be shown that the slope of this line in the -z plane is given by cos)cos cos + cos sin ( - = tan (C.2-10)
B/B-UFSAR C.2-5 With this angle, Equation C.2-8 can be used to calcu late the band of allowed values in the -v plane, as shown in Figure C.2-5.
Let L 2 be the line in the target plane which is perpendicular to L 1. The extent of the target in this direction must be covered by varying through an angle d. If n = (cos , -sin , 0) is the normal to the -z plane then L 2 is a scalar multiple of
), n x N ( x N where cos - cos cos sin[- = )n x N ( x N i)]cos + cos ( 2 2 + )cos + cos ( sin[ +2 2 j ]cos cos cos + k )] cos sin - cos cos ( cos[ + (C.2-11) and k , j , i are the unit vectors in the x, y, and z directions, respectively.
L is defined to be the unit vector in this direction
ll)n x N ( x Nll)n x N ( x N = L (C.2-12) and the projection of L onto N is to be found.
ll)n x N ( x Nllcos-cos cos-cos sin-cos cos cos sin 2- = n.L 2 2 2 2 2 (C.2-13) If the dimension of the target area along L 2 is 2 then d must satisfy 2 oln.Ll = d (C.2-14) or o 2ln.Ll = d (C.2-15) If Fig. C.2-5 is exten ded to three dimensions by letting the -axis come out of the page, the shaded area of allowable values takes on a thickness in the -direction of d given by Equation C.2-15.
B/B-UFSAR C.2-6 The above projection r eplaces the original t arget area by its projection on the pl ane determined by L 1 and n, and to this extent it is an approximation. Thi s should be a reasonable approximation as long as and do not change a ppreciably over the area.
Now assume that the init ial velocity and directi on of the missile are random variables.
The initial veloc ity and direction are specified by three independent random va riables: the random variable v representing the initial velocity, the random variable 1 representing the angle of the vertical com ponent (i.e., the projection on disc plane) from the horizontal plane, and the random variable 2 representing the a ngle from the disc plane (see Figure C.2-7). Assume that:
- a. The initial velocity v is uniformly distributed between v 1 and v 2 , where v 1 < v 2. b. The angle 1 is uniformly distrib uted between 0 and /2 for one quadrant.
- c. The angle 2 is uniformly distr ibuted between -o and + o. (If 2 is uniform between min and max , the strike probability can be obtained by u sing the following formula:
] P[ - - ] P[ - = P min min max min max min max max 2 where P [max] and P[min] are the strike probabilities obtained based 2 uniform between -max and + max and 2 uniform between - min and + min , respectively.)
The probability of a m issile having the initial velocity and direction within a specified ran ge R (R is such that the missile will strike the target) can formally be written as:
1 2 2 1 R)v , , (2 1 2 d dvd)v , , (f)R)v , , ( ob Pr= P 2 1 (C.2-16)
B/B-UFSAR C.2-7 where the probability density f( 1 , 2 , v) has the form
, otherwise , 0 ,< <,-2<<,0 v<v<v if , )v - v ( )(2 2 1 = v), , f(2 1 2 1 1 2 2 1 (C.2-17) since the random variables v, 1 and 2 were assumed to be uniformly distributed between v 1 and v 2 , 0 and /2, and - and +, respectively. The d istributions and Equation C.2-16 are expressed in terms of 1 , 2 , and v, which are hereafter called the distribution space, but the target, the missile trajectory, and its "image" are all expressed in the exit dy namics space.
The exit dynamics space consists of the exit v elocity v, the angle from the horizontal pl ane, and the angle of the horizontal component from the disc plane.
The relationship between the distribution space and the exit dy namics space is given in Figure C.2-7.
In order to be c onsistent, Equation C.2-16 is rewritten using the co ordinates of the exit dynamics space: d dvd J v), , g( = ]R v), ,[( Prob = P R v), , (2 (C.2-18 where g( , ,v) = f[ 1 ( ,), 2 ( ,),v] (in this particular case, g( , ,v) = f( 1 , 2 ,v) since f( 1 , 2 ,v) of Equati on C.2-17 is independent of 1 and 2), R' in the e xit dynamics space corresponds to R in the dist ribution space, and J is the Jacobian of transformation:
), ( ) , ( = v) , , (v), , ( = J 2 1 2 1 The expressions for J, 1 ( ,) and 2 ( ,) can be ob tained from the relationships between ( 1 , 2) and ( ,): tan 1 = tan sec , sin 2 = cos sin . (C.2-19)
The Jacobian of transf ormation has the form:
sin cos-1 )sec tan + (1 cos)tan sin + (1 = J 2 2 2 2 2 2 (C.2-20)
B/B-UFSAR C.2-8 Suppose that the turbine disc is located at the origin and the disc plane coincides with = 0 plane and th at a target plane of dimensions 1 by 2 is specified by the location of its center
( o , o , z o) in cylindrical c oordinates and its orientation is specified by its normal vector N = (cos , cos , cos). The ranges of v, and which will hit the target can then be determined based on the relationships obtain ed earlier in this section. The probability of h itting the above specified target is given by the integr al of the form in Equa tion C.2-18 with the proper limits of integ ration, which are dete rmined by the location of the target, its size, and its or ientation. In order to evaluate the integral of Equa tion C.2-18, t he inner double integral of Equation C.2-18 is replaced:
, v J v), , g( with dvd J v), , g(v), ( (C.2-21) where
, )z-tan ( 2) cos 2z - )tan cos + sin ( cos 2 g= v 1 3/2 o o o o 2 from Equation C.2-8, and 2 oln.Ll = (C.2-22) from Equation C.2-15 with
)n.L ( given by Equation C.2-13. The angle in Equation C.2-21 is given by E quation C.2-10:
cos)cos cos + cos sin ( - = tan o o (C.2-23) Now, the multiple integral of Eq uation C.2-18 can be replaced by the following si mple integral
, d vlJl )]v(, , g[ = P 2 (C.2-24)
B/B-UFSAR C.2-9 where )z-tan (cos 2 g = )v( o o 2 o (C.2-25) and is restricted to the range 2 < < z tan o o 1- (C.2-26) Since only those traject ories which result in the missile hitting the target from above are of interest, there is another restriction on (from Equat ion C.2-9): tan z 2 tan o o 1- (C.2-27) The fact that the random variable 2 is uniformly distributed between - and + , i.e., - 2 + , places another restriction on , which depe nds on the values, 2 < <)h( (C.2-28) where - if , 0 ,- 2 - or 2 < if , tan sin - cos sin = )h(2 2 2 1- The limits of integration for the integral of Eq uation C.2-24 can now be obtained from the fact that the random variable v is uniformly distributed between v 1 and v 2 , i.e., v 1 v v 2 , and the restrictions of Equati ons C.2-26 through C.2
-28 on the allowed values. Defining
)}, ( h ), tan - 2z (tan ), z (tan{max = O o o 1-o o 1-min (C.2-29)
B/B-UFSAR C.2-10 then the integral of Equatio n C.2-24 can be rewritten as
}d v J )]v(, , {g[ = P u 2 2 u 1 1 2 (C.2-30)With an addition al restriction > min. In the integral of Equation (C.2-30, u 1 and 2 are obtained by solving Equation C.2-25 for with v = v 1 and 1 and u 2 are obtained by solving Equation C.2-25 for with v = v
- 2. In general, there are two values of satisfying E quation C.2-25 for e ach v (see Figure C.2-8); 1 is the smaller of the two values corresponding to v 2 and u 1 is the smal ler of the two values corresponding to v
- 1. For a given value of v, one value satisfying E quation C.2-25 is given by A) sin + ( 2 1 = 1- (C.2-31) where 2 o 2 o o 1 2 o 2 o o 2 2 o z)z (sin z z v g A and the other value is given by A) sin - + ( 2 1 = 1- (C.2-32) if 1> A for some v, then there exists no solution for , and in particular if 1 A for some v 1 , we set .2 1 + 4 = = 2 1 u In summary, the prob ability of hitting a target plane of small area 1 x 2 , whose center is located at ( o , o , z o) with its orientation given by its normal vector N = (cos , cos , cos), is given by the integral of Equation C.2-30 with the limits of integration 1 , u 2 and 2 determined from Equations C.2-29, C.2-31, and C.2-32.
B/B-UFSAR C.2-11 If the area of a target is large, the differ ential approximation form of Equations C.2-8 and C.2-15 cannot be used for the entire area. Therefore, the probability of hit ting the target can be obtained by first dividing the target area into small targets, for each small target ev aluating the integral of Equation C.2-30 in order to obtain the probability of hittin g a small target, and then finally summing up all the probabil ities of hitting small targets. C.2.3 P 3 - Penetration Probability The probability of penetration, P 3 , is calculated using Petry's formula: )215,000 S + (1 log A W K = D 2 10 p (C.2-33) where D = depth of penetration i nto "infinitely" thick concrete (ft), K p = penetration coefficient (ft 3/lb), W = missile weight (lb), A = cross-sectional area of missile (ft 2), and S = missile strike speed (ft/sec).
For a finite thickness of concrete, T(ft
), the depth of penetration, D' (ft), is given as
)]D 4T - (8 exp + D[1 = D (C.2-34)
Assume that "dam age" occurs if T C > D 1 (C.2-35) or T C > D 2 (C.2-36) where C 1 , C 2 are constants, and are rela ted to each other through Equation C.2-34.
B/B-UFSAR C.2-12 The variables in Equation C.2-33 (i.e., K p , W, A, S), are random; hence, for any g iven thickness of concre te, there is a finite probability, P 3 , that the missile may damage the enclosed components. This prob ability is calculated as:
T] C > [D P = P 2 3 (C.2-37) It is assumed that K p is normally dist ributed, with mean m K and coefficient of variation V K = 0.10. Similarly, it is assumed that W is normally distri buted with mean m W and coefficient of variation V W = 0.10. Then, for given values of S and A, the mean and coefficient of v ariation of D are approximately:
]215,000 s + [1 log A m m = m 2 10 W K D (C.2-38) V + V = V 2 W 2 K 2 D (C.2-39) Assuming that D is nor mally distributed, P 3 for a given T, S, and A is ] V m m - T C [- F = P D D D 2 U 3 (C.2-40) where F U denotes the cumulative dist ribution function of the standardized normal variate with zero mean and unit standard deviation.
However, S, and A are random variables, and Equation C.2-40 represents the probability of damage, given the values of S and A. Equation C.2-40 mu st be multiplied by the probability density functions of S and A, and th en integrated ov er the possible regions of S and A. Thus, dads (s) f (a) f ]V m m - T C [- F = P S A D D D 2 U A S 3 (C.2-41)
Since A is taken to be uniformly distributed between the minimum missile area (A 1 in ft 2) and the maximum missile area (A 2 in ft 2), the probability density function of A is
B/B-UFSAR C.2-13 A - A 1 = (a)f 1 2 A (C.2-42) with the limits of int egration on A from A 1 to A 2. The strike speed is derived from the principle of conservation of energy, and is f ound to be gz 2 - V = S o 2 (C.2-43) The probability density function of S can now be obtained from Equation C.2-43, from the probabilit y density function of V, and from the relation f(y) dy = f(x)dx, and is
]gz 2 + s s[ V -V 1 = (s)f o 2 1 2 S (C.2-44) The integration limits on S are obtained fro m the integration limits on used in Equation C.2-30 by finding t he equation for S as a function of . Combining equatio ns C.2-43 and C.2-25, we obtain z 2g - )z - tan ( cos 2 g = S o o o 2 o 2 (C.2-45) The limits of integration over S in Equation C.2-41 can be obtained as the two intervals 1 S to S u 1 , and 2 S to S u 2 , where these limits are obtained by substituting the values of u1 , 1 , 2 , and 2 u , respectively, into Equation C.2-45.
Furthermore, the probabi lity of penetration, P 3 , is calculated using the correction for the ang le of impact of the missile with the barrier. Bush (Reference 1) suggests that the actual thickness divided by the square of the cosine of the angle of impact gives the effecti ve thickness to be p enetrated. The angle of impact, i.e., the angle bet ween the velocity vector at impact and the normal to th e target area, is easily determined. If S is the velocity at impact and is the angle of impact, then
B/B-UFSAR C.2-14 REVISION 1 - DECEMBER 1989 llS llS N- = cos (C.2-46) where the negative sign is i ncluded because N is defined to be the upward pointing norm al. Upon substitution and simplification Equation C.2-43 becomes 2 o o o o tan - 2z + 1 cos )tan - 2z ( + cos cos + sin cos = cos (C.2-47)
B/B-UFSAR C.3-1 REVISION 3 - DECEMBER 1991 C.3 PARAMETERS Westinghouse Electric Co rporation has calculat ed the probability, P 1 , of turbine failure resulting in the ejec tion of a missile as 9.5 x 10-11 per year for design o verspeed and 1.7 x 10
-6 per year for destructive overspeed (Reference 2).
The characteristics of the missiles were determ ined in Reference 3, and are given here in Table C.3-1, where the missile velocities are assumed to be uniformly distributed wi th 10% of the value given in the table.
The critical plant r egions in this ana lysis are the auxiliary building, the fuel h andling building, the reactor containment buildings and the pu rge rooms. The location s of these buildings with respect to the turbines are sho wn in Figure C.3-1.
The moisture separator r eheaters (MSR; 153 inch OD x 1-1/2 inch shell thickness) partly shield the wall of t he auxiliary building from low-trajectory miss iles. The shielding effect of the MSR is taken into account by calculating whether or not the postulated missiles perforate the M SR, and if so, the r esidual velocities of the missiles are determined using the methods of Reference 4 (Stanford Research Institute For mula). There is a 1-foot, 8-inch structural concrete wall in front of the auxiliary building wall (L row) enclosing pl ant office services area. The residual velocity of the missile, V r , as it perforates through this wall is calculated using modified Petr y's formula as follows:
]1}- 10{ [215000 - v= V 2 W)K 2 (TA/2 m r p This residual velocity of the missile, V r , is used for impact on the auxiliary building wall.
In addition to the shielding provided by the MSR and the 1-foot, 8-inch wall in front of L row, the s tructures on the roof of the auxiliary building which house t he diesel exhaust silencers provide partial shielding against low trajectory missile strikes on the containme nt building wall. The effect of this shielding is explained in deta il in Attachment A.
The properties of th e target structu res are as follows:
K p = 0.00325 ft 3/lb for the r eactor containment buildings. (This value is obtai ned by increasing the 5500-psi design strength of the containment conc rete by 25% to account for added strength due to both aging and the overdesign associated with the basic mix design).
K p = 0.00405 ft 3/lb for all o ther buildings.
(3500-psi concrete, incr eased 25% as above).
B/B-UFSAR C.3-2 C l = 0.667 for nonmetal-backed concrete, namely the auxiliary building walls.
C l = 0.715 for concrete roo fs supported by metal decking.
C l = 0.800 for the containment co ncrete, which is backed by the containment liner.
The calculation of the strike probabilities was performed for small areas (10 ft x 10 ft maximum size) within each critical plant region, and the results we re added to give the total strike probability for the region. The strike and penetration probabilities were cal culated for the exteri or walls and roofs only. In order to a ccount for the fact that the safety-related components housed inside the S afety Category I structures were not individually and s eparately modeled, the strike probability for the region has been multiplied by the critical component density factor assigned for the region to obta in the value of P 2. The criteria for assigning a critical com ponent density factor were relative a rea (volume) of the safety-related components to the ar ea (volume) of the r egion, redundancy of components, location of the components, direction of the missile, and importance of the components as to their safety function. With thes e considerations a nd after a detailed review of the layout drawings for piping, cable and ducts, a single value of the critical component density factor was assigned for the region. Ta ble C.3-2 shows the critical component density factors for different regions.
B/B-UFSAR
C.3-3 TABLE C.3-1 CHARACTERISTICS OF LOW-P RESSURE TURBINE MISSILES (Shear and Rot ation Modes)
MISSILE WEIGHT W (lb) DEFLECTION ANGLE 2 DESIGN OVER-SPEED EXIT VELOCITY (ft/sec) DESTRUCTIVE OVERSPEED EXIT VELOCITY (ft/sec) MAXIMUM AREA, A 2 (ft 2) MINIMUM AREA, A 1 (ft 2) Disc No. 1 Quadrant 3095
+/- 5° Contained 262 5.60 2.60 Blade Ring No. 1 Fragment 4200
+/- 5° Contained 262 11.62 3.34 Disc No. 2 Quadrant 3501
+/- 5° Contained 405 6.70 3.00 Blade Ring No. 2 Fragment 2174
+/- 5° Contained 405 6.84 1.90 Disc No. 3 Quadrant 4229
+/- 5° Contained 440 6.70 3.30 Blade Ring No. 3 Fragment 2843
+/- 5° Contained 440 9.55 2.61 Disc No. 4 Quadrant 3380
+/- 5° 370 704 3.50 2.00 Disc No. 5 Quadrant 3459
+/- 5° 156 518 3.72 1.36 Disc No. 6 Quadrant 3503
+/- (5°-25°) 268 542 4.50 1.38
B/B-UFSAR
C.3-4 TABLE C.3-2 CRITICAL COMPONENT DENSITY FACTORS
ELECTRICALMECHANICAL HVAC REGION S/S* S/S R/R* S/S TOTAL Aux. Bldg. Region 1 0.08 0.10 0.18 Aux. Bldg. Region 2 0.09 0.10 0.19 Aux. Bldg. Region 3 0.0 Aux. Bldg. Region 4 0.11 0.11 Aux. Bldg. Region 5 0.11 0.11 Aux. Bldg. Region 6 0.0 Aux. Bldg. Region 7 0.09 0.10 0.19 Aux. Bldg. Region 8 0.08 0.10 0.18 Aux. Bldg. Region 9 0.03 0.10 0.03 Aux. Bldg. Region 10 0.15 0.10 0.25 Aux. Bldg. Region 11 0.15 0.34 0.49 Aux. Bldg. Region 12 0.30 0.37 0.67 Aux. Bldg. Region 13 0.30 0.37 0.67 Aux. Bldg. Region 14 0.15 0.34 0.49 Aux. Bldg. Region 15 0.15 0.10 0.25 Aux. Bldg. Region 16 0.03 0.03 Aux. Bldg. Region 17 0.05 0.11 0.16 Reactor Bldg. Unit 1 1.00 1.00 Reactor Bldg. Unit 2 1.00 1.00 S. Purge Room-S. Section 0.02 0.02 S. Purge Room-N. Section 0.05 0.08 0.13 N. Purge Room-S. Section 0.05 0.08 0.13 N. Purge Room-N. Section 0.02 0.02 Fuel Handling Bldg. 0.10
___________________
- S/S: Equipment requir ed for safe shutdown R/R: Radioactive release in excess of 10 CFR 100 limits
B/B-UFSAR C.4-1 C.4 RESULTS The results of the ana lysis are summarized in Table C.4-1.
Details of the analy sis for the reactor containment building for the destructive over speed condition are gi ven in Appendix C.A. Since the results are tabulated by tar get, the values of P 2 and P 3 are the average values of all the mis siles striking the target at differ ent locations and different angles of incidence.
Taking full advantage of the geometric symmetry of t he problem, the analysis is perfor med for the complete set of target regions, but only one of the t wo turbine units is used to send missiles to the targ et structures.
The values of P 2 , P 3 and P 4 for individual targets are the probabili ties due to turbine Unit 1.
The individual probabili ties due to turbine Unit 1 are summed at the bottom of Tab le C.4-1 and then multiplied by 2 to account for turbine Unit 2.
The bottom values of P 4 labeled "TOTAL" are the total probabilities of damage to the plant per yea
- r. The notation in Table C.4-1, 4.294-08, means 4.294 x 10
-8.
B/B-UFSAR
C.4-2 REVISION 1 - DECEMBER 1989 TABLE C.4-1
SUMMARY
OF RESULTS FOR BYRON/BRAIDWOOD CONCRETE THICKNESS DESIGN OVERSPEED DESTRUCTIVE OVERSPEED TARGET NAME (in.) P 2 P 3 P 4 P 2 P 3 P 4 Aux. Bldg. Roof Region 1 24 1.953-04 2.022-02 3.753-16 3.050-05 7.814-02 4.052-12 Aux. Bldg. Roof Region 20 24 2.721-04 2.019-02 5.219-16 4.243-05 7.814-02 5.636-12 Aux. Bldg. Roof Region 3 24 0.000-00 0.000-00 0.000-00 0.000-00 0.000-00 0.000-00 Aux. Bldg. Roof Region 4 24 3.972-05 6.151-02 2.321-16 1.892-05 7.790-02 2.506-12 Aux. Bldg. Roof Region 5 24 7.317-06 3.340-00 2.321-16 1.892-05 7.774-02 2.506-12 Aux. Bldg. Roof Region 6 24 0.000-00 0.000-00 0.000-00 0.000-00 0.000-00 0.000-00 Aux. Bldg. Roof Region 7 24 8.779-06 6.432-01 5.364-16 3.728-05 8.893-02 5.637-12 Aux. Bldg. Roof Region 8 24 7.693-06 5.571-01 4.071-16 1.988-05 1.199-01 4.052-12 Aux. Bldg. Roof Region 9 24 2.654-05 2.043-02 5.150-17 4.183-06 7.822-02 5.562-13 Aux. Bldg. Roof Region 10 24 2.918-04 2.040-02 5.655-16 4.594-05 7.821-02 6.107-12 Aux. Bldg. Roof Region 11 24 5.155-04 2.627-02 1.287-15 1.046-04 7.812-02 1.389-11 Aux. Bldg. Roof Region 12 24 1.990-04 6.158-02 1.164-15 9.481-05 7.798-02 1.257-11 Aux. Bldg. Roof Region 13 24 3.687-05 3.324-01 1.164-15 9.501-05 7.782-02 1.257-11 Aux. Bldg. Roof Region 14 24 1.953-05 6.939-01 1.288-15 1.048-04 7.800-02 1.390-11 Aux. Bldg. Roof Region 15 24 9.506-06 6.435-01 5.811-16 4.038-05 8.898-02 6.108-12 Aux. Bldg. Roof Region 16 24 1.055-06 5.575-01 5.587-17 2.729-06 1.199-01 5.562-13 Aux. Bldg. E. Wall Region 9 20+ 36 0.000-00 0.000-00 0.000-00 4.226-03 1.497-01 1.076-09 Aux. Bldg. E. Wall Region 10 20+ 36 0.000-00 0.000-00 0.000-00 4.069-02 1.442-01 9.979-09 Aux. Bldg. E. Wall Region 11 20+ 36 0.000-00 0.000-00 0.000-00 6.280-03 6.899-02 7.365-10 Aux. Bldg. E. Wall Region 12 20+ 36 0.000-00 0.000-00 0.000-00 7.965-06 0.000-00 0.000-00 Aux. Bldg. E. Wall Region 13 20+ 36 0.000-00 0.000-00 0.000-00 3.659-06 0.000-00 0.000-00 Aux. Bldg. E. Wall Region 14 20+ 36 0.000-00 0.000-00 0.000-00 2.056-06 0.000-00 0.000-00 Aux. Bldg. E. Wall Region 15 20+ 36 0.000-00 0.000-00 0.000-00 4.988-07 0.000-00 0.000-00 Aux. Bldg. E. Wall Region 16 20+ 36 0.000-00 0.000-00 0.000-00 3.084-08 0.000-00 0.000-00 Aux. Bldg. Roof Region 17 14 1.472-04 1.572-01 2.198-15 1.206-04 2.276-01 4.668-11 Fuel Handling Bldg. Roof 14 1.339-04 1.430-01 1.818-15 9.958-05 2.296-01 3.887-11 S. Purge Room - Southernmost Roof Portion 14 8.525-05 1.135-02 9.191-17 3.611-05 2.251-02 1.360-12 S. Purge Room - Northernmost Roof Portion 14 3.713-04 4.544-02 1.603-15 7.362-05 2.308-01 2.889-11 N. Purge Room - Southernmost Roof Portion 14 1.371-05 9.975-01 1.299-15 7.372-05 2.299-01 2.881-11 N. Purge Room - Northernmost Roof Portion 14 7.013-07 9.737-01 6.487-17 2.742-06 2.672-01 1.245-12
B/B-UFSAR
C.4-3 TABLE C.4-1 (Cont'd)
CONCRETE THICKNESS DESIGN OVERSPEED DESTRUCTIVE OVERSPEED TARGET NAME (in.) P 2 P 3 P 4 P 2 P 3 P 4 Reactor Bldg. Unit 1 - Vertical Walls 42 7.061-02 1.120-07 7.511-19 9.079-02 6.010-02 9.276-09 Reactor Bldg. Unit 1 - Dome 36 1.365-02 1.186-04 1.538-16 1.762-03 1.961-02 5.873-11 Reactor Bldg. Unit 2 - Vertical Walls 42 2.285-06 0.000-00 0.000-00 1.949-05 0.000-00 0.000-00 Reactor Bldg. Unit 2 - Dome 36 3.880-04 4.139-03 1.526-16 1.393-03 2.481-02 5.875-11 For one turbine unit 1.584-14 = 2.147-08 Total for two turbine units x 2 = 3.168-14 x 2 = 4.294-08
B/B-UFSAR C.5-1 REVISION 12 - DECEMBER 2008 C.5 CONCLUSION The total probability of turbi ne missile damage is 4.3 x 10
-8 per year, which is less th an the acceptable value of 2.0 x 10
-7 per year for the two units.
It is, therefore, c oncluded that Byron and Braidwood are acceptably safe against postulated turbine missile damage.
The value of P 1 has been reduced based on the design of the digital EHC system. The probability per year for turbine missile damage has been reduced by an order of m agnitude. Revised probabilities are given in W estinghouse WNA-CN-00056-GEN, Revision 3, "Reliability Calculation of the Ovation DEH Overspeed Trip Function."
The values of P 4 shown in this attachment remain bounding.
B/B-UFSAR C.6-1 REVISION 1 - DECEMBER 1989 C.6 REFERENCES
- 1. S. H. Bush, "Proba bility of Damage to Nuclear Components Due to Turbine Failu re," Nuclear Safety 14 (3), pp. 187-201, May-June 1973.
- 2. Westinghouse Electric Co rporation, "Analysis of the Probability of the Gen eration and Strike of Missiles From a Nuclear Turbine," March 1974.
- 3. Westinghouse Electric Co rporation, "Turb ine Missile Information for Design Overspeed and Destructive Overspeed," Letter from L. K. Koering to G. C. Kuhlm an of Sargent & Lundy dated September 16, 1977.
- 4. "Interim Criteria for the Design of Structures f or Missile Impact Effects," Sargent & Lundy Report No. SDDA 136, March 1975.
- 5. L. A. Twisdale, W. L. Du nn, and R. A. Frank, "Turbine Missile Risk Methodolo gy and Component Code," EPRI Seminar on Turbine Missile Effects in Nuclear Pow er Plants, Palo Alto, California, October 25-26, 1982.
- 6. U.S. Nuclear Regulatory Co mmission, "Safety Evaluation Report Related to the Op eration of Byron Station, Units 1 and 2," NUREG-0876, Supplement N
- o. 5, October, 1984.
- 7. Letter from T.
R. Tramm of CECo to H.
R. Denton of NRC, "Byron Generating Stat ions Units 1 and 2, Braidwood Generating Stations, Units 1 and 2, Turbine Missiles," dated September 25, 1984. 8. Letter from B.
J. Youngblood of NRC to D. L. Farrar of CECo, "Byron Unit 1 License Condition on Turbine Missiles," dated May 20, 1985.
B/B-UFSAR
ATTACHMENT C.A DETAILS OF PROBA BILITY CALCULATIONS FOR THE CONTAINMENT BUILDING
B/B-UFSAR C.A-1 C.A DETAILS OF PRO BABILITY CALCULATIONS FOR THE CONTAINMENT BUILDING A detailed analysis for strike and penet ration probabilities for the containment wall is presented herein. It is shown that the probabilities for the co ntainment buildi ng wall in a destructive overspee d accident are P 2 = 1.8 x 10
-1 (for two turbine units)
P 3 = 6.0 x 10
-2 and P 4 = 1.86 x 10
-8/year A similar analysis was performed for t he design overspeed accident, the results of which a re given in Table C.A-1. A detailed description of the analysis for des tructive overspeed which was performed to obtain the above valu es is given below.
The method of analysis used in this attachme nt is identical to that used in Appendix C.
The portion of the containment building wall between el evations 497 feet 0 inch and 579 feet 0 inch is comprised of r egions A, B, C, and D of Figure C.A-2. A plan of this area is shown in Figure C.A-1.
Region A (Elevation 562 feet 0 inch to Elevati on 579 feet 0 inch)
In this region, P 3 is zero since none of the postula ted turbine missiles are capable of penetrating the effe ctive thickness of concrete in this region. Therefore, P 4 is zero for region A.
Region B (Elevation 539 feet 0 inch to Elevati on 562 feet 0 inch It is assumed that region B is not shi elded by other structures, and that missiles ejected fr om the turbine may strike this regi on directly.
Region C (Elevation 515 feet 6 inches to Ele vation 539 feet 0 inch) This region is partial ly shielded by str uctures (enclosing the diesel exhaust silence rs) on the roof of the auxiliary building. Of the 36 discs in the three LP sections of each turbine unit, only six are capable of striking and penetrating the containment building wall in region C. An analysis was performed for these six discs.
Region D (Elevation 497 feet 0 inch to Eleva tion 515 feet 6 inches)
This region is s hielded from dir ect impact by the wall (3 feet 0 inch) and roof (2 feet 0 inc h) of the auxiliary building.
B/B-UFSAR C.A-2 None of the postulated missiles is capable of penetrating the effective thickness of this dual barrier. Therefore, in this region P 2 is zero; hence, P 4 is zero also.
The probability values f or the above regions are tabulated in Table C.A-1. These va lues were computed on the basis of the assumptions discussed above, and utilizi ng the methodology described in the body of this re port. The cal culations were performed on MISLODS.
MISLODS is a computer program developed by Sargent & Lundy to compute the probability of damage from turbine missiles.
An approximate check on the values of P 2 and P 3 for regions B and C follows. Differences be tween the approximate values computed below and the v alues from MISLODS are due primarily to the effect of the curvature of the containment building which is not considered in the approximate calculation.
P 2 The probability that reg ion B will be struck by a missile is approximately equal to t he likelihood that a missile will be ejected into the 5.9 o angle which encloses region B times the number of missiles w hich are ejected.
For a single disc failure, the average number of missiles whic h will be ejected is 1.5 due to the fr agments which are al so ejected. Also one-third of the missiles or iginating from d ifferent LP sections of a turbine un it miss the containmen
- t. Therefore, P 2 for region B is approximately 10 x 6.55 = 90 5.9 x 1.5 x 2/3 2-°° which compares f avorably with the va lue of 4.85 x 10 2 computed by MISLODS.
P 2 for region C may be computed in a similar manner. However, due to the relative po sitions of region C, t he structures on the roof of the auxiliary buildi ng, and the turbine discs, only six of the 36 discs can produce missiles which are capable of both striking region C and damaging the containment building.
These six discs are sh own in Figure C.A-
- 1. From Figure C.A-2, the missiles must be ejected into a 6.8 o "window" in order to strike region C.
The resulting P 2 for region C is approximately
, 10 x 1.259 = 90 6.8 x 36 6 2-°° which compares f avorably with the value of 1.072 x 10
-2 computed by MISLODS.
B/B-UFSAR C.A-3 P 3 Figure C.A-3 is a plot of P 3 versus concrete thickness for quadrants from discs numbers 4, 5, and 6 in a destructive overspeed turbine failure. The angle of impact of the missile with the target is taken as 0 o (i.e., direct impact). For oblique impact, the ac tual target thic kness divided by the square of the cosine of the angle of impact gives the effective thickness to be pene trated. This effe ctive thickness is taken as 4.81 feet for region B and 4.27 feet for region C. Knowing these effective thicknes ses, the value of P 3 for each missile striking regions B and C can be obtained from the curves in Figure C.A-3. Table C.A-2 shows the computation of P 3 for regions B and C. Th e values obtained are in reasonable agreement with the val ues given by MISLODS.
B/B-UFSAR C.A-4 TABLE C.A-1 PROBABILITIES FOR CONT AINMENT BUILDING WALL REGION P 1/yr P 2 P 3 P 4/yr A 1.7 x 10
-6
- 0 0 B 1.7 x 10
-6 8.007 x 10
-2 3.230 x 10
-2 4.4 x 10-9 C 1.7 x 10
-6 1.072 x 10
-2 2.704 x 10
-1 4.9 x 10-9 D 1.7 x 10
-6 0
- 0 9.3 x 10
-9 For two units, P 4 = 1.86 x 10
-8/year
- Not computed
B/B-UFSAR C.A-5 TABLE C.A-2 APPROXIMATE COMP UTATION OF P
3 FOR REGIONS B AND C MISSILE REGION B, T = 4.81 ft REGION C, T = 4.27 ftNUMBER i DESCRIPTION n i P 3 i n i P 3 i n i P 3 i n i P 3 i 1 Disc No. 1 Quadrant 6 0.000 0.000 0 0.000 0.000 2 Blade Ring No. 1 Fragment 6 0.000 0.000 0 0.000 0.000 3 Disc No. 2 Quadrant 6 0.000 0.000 0 0.000 0.000 4 Blade Ring No. 2 Fragment 6 0.000 0.000 0 0.000 0.000 5 Disc No. 3 Quadrant 6 0.000 0.000 0 0.000 0.000 6 Blade Ring No. 3 Fragment 6 0.000 0.000 0 0.000 0.000 7 Disc No. 4 Quadrant 6 0.330 0.909 2 0.530 0.779 8 Disc No. 5 Quadrant 6 0.130 0.566 2 0.235 0.414 9 Disc No. 6 Quadrant 6 0.125 0.551 2 0.217 0.387 54 6
___________________
P 3 AVE = (1/54) (0.909 + 0.56 6 + 0.551) = 3.75 X 10
-2 P 3 AVE = (1/6) (0.799
+ 0.414 + 0
.387) = 2.633 X 10
-1 Legend: n 1 = number of missiles of type i con sidered to be capabl e of striking the containment building wall in the region of interest.
P 3 i = P 3 for missile type i corresponding to t he effective t hickness of the containment building wall in the region of interest (o btained from curves in Figure C.A-3).
x BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2*1 ASSUMED COORDINATE SYSTEM FOR THE MODEL o f BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2*2 TRANSFORMED TWO-DIMENSIONAL COORDINATE SYSTEM v I I I I I I I I I I I I I I I I I I-----t----
I ,..--I I"'0 I I c:a.::..I+I 0 I I0"')I I....l:-0 TA..r l (qO@BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2*3 EXIT DYNAMICS SPACE OF THE POINT TARGET o p BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2-4 STRIKE GEOMETRY IN TWO-DIMENSIONAL p-Z PLANE v oBYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2-5 THE BAND OF ALLOWED VALUES IN THE PLANE L. ,i e)If(Jl&Q, eo)\...,.//y p BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2.6 STRIKE GEOMETRY IN X-Y-Z PLANE X A'tIST f-l E TUR BI t-JE A':<It;YZ*PLANE" rHE 015C PL.A-t-JE XV...PLAI-JE'T H E: H 0 RI'ZOtJTAL.
PlAkJ5 BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.2-7 RELATIONSHIP BETWEEN DISC PLANE AND EXIT DIRECTION v Vz.-----VI\, v (¢)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE LIMITS OF INTEGRATION OF THE INTEGRAL (24)OR INTEGRAL (30)AND THE RELATIONSHIP BETWEEN V
-I@e<::*o*@-r------'-""" t40'.O'I 14d.t'./I\FUEL I ReACYOR CONT1:"ENT
}-t-t"NOL.l"JG CONTAt MENT INI aUIL..DING H"02 I-r--1'1 i-0..4 5 7 IS't-o" r-@;,.'--<0BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.3-1 PLANT ARRANGEMENT
-t---I , I!------------r---------if----;,-.
UJ z ii a:.0*,00;'i3-J oJ..t on\A'".."-Ji......I I III i UJ III...----,I D 6 J,I: 8I J I;\L,...." r----I 8II IL__-, 1 I iI;I eII L J BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.A-1 CONTAINMENT AUXILIARY AND TURBINE BUILDING ROOF PLAN
<t.CONTA.INMENT I
CONTAIN!.1ENT 8UII..D:NG REGIOW D EL, REGION A_f-_-<_El...'2.'*0's..
I BLDG.: I I I SECTION I------------, I I I I TURBINE I B'JILDli"';G BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.A-2 LOCATIONS OF REGIONS A, B.C, AND D ON CONTAINMENT BUILDING WALL DESTRUCTIVE OVERSPEED 0.1 0.8 0.2 0.3'0.9 0.10 0.7 DISC NO.4 QUADRANT 5 DISC NO.5 QUADRANT0.6 DISC NO.8 QUADRANT to 0 a:: D.Z 00.5 lU z W D.C')0.4 D.6 5 4 3 2 1 0.0 I-----'-----'___I...L__......J o CONCRETE THICKNESS (FT)(Kp c 3.25 X 10-3 FT3/LB;C1-0.8)BYRON/BRAIDWOOD STATIONS UPDATED FINAL SAFETY ANALYSIS REPORT FIGURE C.A-3 P 3 VS.THICKNESS