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I Docket No. 50-346 h f%- License No. NPF-3 Serial No. 588 February 7, 1980 POTENTIAL REACTOR SYSTEM VOIDING DURING ANTICIPATED TRANSIENTS | I Docket No. 50-346 h f%- License No. NPF-3 Serial No. 588 February 7, 1980 POTENTIAL REACTOR SYSTEM VOIDING DURING ANTICIPATED TRANSIENTS PREPARED BY BABC0CK & WILC0X NUCLEAR POWER GENERATION DIVISIO.? | ||
LYNCHBURG, VIRGINIA JANUARY, 1980 8002120 5%l | |||
PREPARED BY BABC0CK & WILC0X NUCLEAR POWER GENERATION DIVISIO.? | |||
LYNCHBURG, VIRGINIA JANUARY, 1980 | |||
8002120 5%l | |||
CONTENTS 1.0 Problem Introduction and Summary 1.1 Introduction 1.2 Summary 2.0 Analysis, Assumptions and Event Descriptions 2.1 Analysis of Steam in the Upper Vessel Plenum 2.1.1 Stagnant " Hot" Water 2.1.2 Residual Heat Stored in Metal 2.1.3 Conclusion 2.2 Analysis of Steam in the Candy Cane 2.2.1 Pressurizer Outsurge Water Mixing in Hot Leg Flow 2.2.2 Residual Heat Stored in Metal 2.2.3 Conclusion 2.3 Event Description for Mass / Volume Balance 2.3.1 Description of Analysis 2.3.2 Derivation of Equations Used 2.3.3 Mass / Volume Analysis 2.3.3.1 Davis Besse 9/18/79 Trip 2.3.3.2 Davis Besse 10/15/79 Trip 2.3.3.3 Davis Besse 9/26/79 Trip 2.3.3.4 Oconee I 10/8/79 Trip 2.3.3.5 Oconee II 1/4/74 Trip 3.0 Conclusion 4.0 References h | |||
CONTENTS 1.0 Problem Introduction and Summary 1.1 Introduction 1.2 Summary 2.0 Analysis, Assumptions and Event Descriptions 2.1 Analysis of Steam in the Upper Vessel Plenum 2.1.1 Stagnant " Hot" Water 2.1.2 Residual Heat Stored in Metal 2.1.3 Conclusion 2.2 Analysis of Steam in the Candy Cane 2.2.1 Pressurizer Outsurge Water Mixing in Hot Leg Flow 2.2.2 Residual Heat Stored in Metal 2.2.3 Conclusion 2.3 Event Description for Mass / Volume Balance 2.3.1 Description of Analysis 2.3.2 Derivation of Equations Used 2.3.3 Mass / Volume Analysis 2.3.3.1 Davis Besse 9/18/79 Trip 2.3.3.2 Davis Besse 10/15/79 Trip 2.3.3.3 Davis Besse 9/26/79 Trip 2.3.3.4 Oconee I 10/8/79 Trip | |||
2.3.3.5 Oconee II 1/4/74 Trip 3.0 Conclusion 4.0 References h | |||
List of Figures 2.2.1 Column Whldment Flow Paths 2.2.2 Upper Plenum Flow Paths 2.3.1 RC Volume Breakdown 2.3.3.1 TECO 9/18/79 Trip 2.3.3.2 TECO 10/15/79 Trip 2.3.3.3 TECO 9/26/79 Trip 2.3.3.4 Oconee 1 10/8/79 Trip 2.3.3.5 Oconee II 1/4/74 Trip A-1 Pressurizer level 52. corrected pressure tap measurements (320" pressurizer) | List of Figures 2.2.1 Column Whldment Flow Paths 2.2.2 Upper Plenum Flow Paths 2.3.1 RC Volume Breakdown 2.3.3.1 TECO 9/18/79 Trip 2.3.3.2 TECO 10/15/79 Trip 2.3.3.3 TECO 9/26/79 Trip 2.3.3.4 Oconee 1 10/8/79 Trip 2.3.3.5 Oconee II 1/4/74 Trip A-1 Pressurizer level 52. corrected pressure tap measurements (320" pressurizer) | ||
A-2 Pressurizer level vs. corrected pressure tap measurements (400" pressurizer) | A-2 Pressurizer level vs. corrected pressure tap measurements (400" pressurizer) | ||
| Line 42: | Line 28: | ||
A-4 Error in level indication vs. indicated level (320" pressurizer) | A-4 Error in level indication vs. indicated level (320" pressurizer) | ||
AttacNnents Pressurizer Level Error | AttacNnents Pressurizer Level Error | ||
l.0 PROBLEM INTRODUCTION AND | l.0 PROBLEM INTRODUCTION AND | ||
| Line 56: | Line 38: | ||
(1) Minimum RC pressure after trips occurs about the same time as the minimum coolant temperature (as expected) and not because of a primary system " Steam Pocket" restricting a further pressure decrease. These minimum temperatures errelate with secondary side steam pressures. | (1) Minimum RC pressure after trips occurs about the same time as the minimum coolant temperature (as expected) and not because of a primary system " Steam Pocket" restricting a further pressure decrease. These minimum temperatures errelate with secondary side steam pressures. | ||
(2) With the most conservative assumptions steam pockets are virtually impossible during transients where minimum measured pressure is greater than 1740 psig. | (2) With the most conservative assumptions steam pockets are virtually impossible during transients where minimum measured pressure is greater than 1740 psig. | ||
Specific concern per reference 1 \3 | |||
(3) Using more realistic assumptions regarding potential steam production, it is unlikely that any net steam production can occur at measured pressures greater than 1500 psig. | (3) Using more realistic assumptions regarding potential steam production, it is unlikely that any net steam production can occur at measured pressures greater than 1500 psig. | ||
2.0 Analysis, Assumotions and Event Descriotions 2.1 Analysis of Steam in the Vocer Vessel Plenum 2.1.1 Stacnant " Hot" Water Typically, the hottest bundle in a 2772 MWT core is a 1.5 relative peaked bundle. This localized power could conservatively result in localized stagnant water temperatures | 2.0 Analysis, Assumotions and Event Descriotions 2.1 Analysis of Steam in the Vocer Vessel Plenum 2.1.1 Stacnant " Hot" Water Typically, the hottest bundle in a 2772 MWT core is a 1.5 relative peaked bundle. This localized power could conservatively result in localized stagnant water temperatures of s 620*F in the upper control rod guide (column weldment). | ||
For this situation to occur, at least 53 in of flow area in the column weldment (see flow path 2 on figure 2.1.1) would have to be blocked. If this blockage could occur, then the following statement can be made: Any B&W reactor trio resulting in minimum RC tao pre.ssures less than 1740 psig (the tap pressure 1.s s 40 psid lower than core plenum pressure) voiding may occur. | For this situation to occur, at least 53 in of flow area in the column weldment (see flow path 2 on figure 2.1.1) would have to be blocked. If this blockage could occur, then the following statement can be made: Any B&W reactor trio resulting in minimum RC tao pre.ssures less than 1740 psig (the tap pressure 1.s s 40 psid lower than core plenum pressure) voiding may occur. | ||
Since this blockage is highly unlikely, a somewhat more realistic hot spot assumption would be localized maximum temperatures of 610*F (instead of 620') in the upper vessel plenum. This assumption is based on (1) water stagnating (or having an extremely low flow rate) in the upper plenum (per Fig. 2.1.2) | Since this blockage is highly unlikely, a somewhat more realistic hot spot assumption would be localized maximum temperatures of 610*F (instead of 620') in the upper vessel plenum. This assumption is based on (1) water stagnating (or having an extremely low flow rate) in the upper plenum (per Fig. 2.1.2) and acquiring the steady state enviromental temperature of the 59 column weldment flow temperatures and (2) plugged return holes (per figure 2.1.2, Flow Path 3). This condition would not allow flashing until the pressure decreases to 1660 psia, i.e.,1605 psig at the pressure tap. | ||
Typical outlet temperatures were verified from TMI-2 pre March, 1979 100". power outlets thermocouple data. | |||
and acquiring the steady state enviromental temperature of the 59 column weldment flow temperatures and (2) plugged return holes (per figure 2.1.2, Flow Path 3). This condition would not allow flashing until the pressure decreases to 1660 psia, i.e.,1605 psig at the pressure tap. | |||
} | } | ||
The most realistic assumption is the desian condition of s 5% core flow through the guide tubes into the upper pl enum. Following a reactor trip, the coolant temperature in this region will decrease rapidly to below 600F as core outlet temoerature-eliminating the potentid for " hot" water pockets at arty pressures above HPI injection levels. | The most realistic assumption is the desian condition of s 5% core flow through the guide tubes into the upper pl enum. Following a reactor trip, the coolant temperature in this region will decrease rapidly to below 600F as core outlet temoerature-eliminating the potentid for " hot" water pockets at arty pressures above HPI injection levels. | ||
2.1.2 Residual Heat Stored in Metal After a trip, the metal in the upper vessel will be conservatively assumed to remain at 610 F until a minimum pressure is reached. | 2.1.2 Residual Heat Stored in Metal After a trip, the metal in the upper vessel will be conservatively assumed to remain at 610 F until a minimum pressure is reached. | ||
| Line 81: | Line 52: | ||
Stored Energy = Cp x Mass x AT m m Cpm = .11 BTU /lh, F AT = 610 - 575 = 35 F Mass s 5x10' lbm = total mass of metal above the outlet hot leg piping including reactor vessel Stored Energy = 1.925x10 BTU's The amount of water in this region is 1366 ft. | Stored Energy = Cp x Mass x AT m m Cpm = .11 BTU /lh, F AT = 610 - 575 = 35 F Mass s 5x10' lbm = total mass of metal above the outlet hot leg piping including reactor vessel Stored Energy = 1.925x10 BTU's The amount of water in this region is 1366 ft. | ||
* 3 4 1366 ft.3 x 44.5 lbm/ft = 6.08x10 lb of water Conservatively assuming this energy is instantly released to the water, the water temperature will increase from 575 F to s 601 - | * 3 4 1366 ft.3 x 44.5 lbm/ft = 6.08x10 lb of water Conservatively assuming this energy is instantly released to the water, the water temperature will increase from 575 F to s 601 - | ||
The pressure required for flashing at this temperature is s 1505 psig (at the pressure tap). Therefore, in order to fill this region with | The pressure required for flashing at this temperature is s 1505 psig (at the pressure tap). Therefore, in order to fill this region with This is water density at 575 F, 1600 psia. | ||
**l.925x106BTU's/6.08x1041b = 32 BTV/lb or s 26 F temperature increase. | **l.925x106BTU's/6.08x1041b = 32 BTV/lb or s 26 F temperature increase. | ||
950 078 | 950 078 | ||
steam (to cause spillover into the hot legs) from just residual heat, 20 times more mass of hot metal would be required. (s 10 BTU /lb are needed to reach Tsat and another 533 BTU /lb to vapori7.e the water. This equals 543 BTU required to convert a pound of water to lb a pound of steam). | steam (to cause spillover into the hot legs) from just residual heat, 20 times more mass of hot metal would be required. (s 10 BTU /lb are needed to reach Tsat and another 533 BTU /lb to vapori7.e the water. This equals 543 BTU required to convert a pound of water to lb a pound of steam). | ||
2.1.3 Conclusion The previous calculations and discussion basically show that it is impossible to produce steam in the upper head above a measured pressure of 1740 psig, highly improbable above 1620 psig, and highly .unlikely above 1500 ps.ig. (Very few . transients have ever gone below 1600 psig .) This statement assumes no primary system breaks. | 2.1.3 Conclusion The previous calculations and discussion basically show that it is impossible to produce steam in the upper head above a measured pressure of 1740 psig, highly improbable above 1620 psig, and highly .unlikely above 1500 ps.ig. (Very few . transients have ever gone below 1600 psig .) This statement assumes no primary system breaks. | ||
| Line 95: | Line 62: | ||
Qh | Qh | ||
The saturation pressures for these temperatures is well below 1500 psig. | The saturation pressures for these temperatures is well below 1500 psig. | ||
2.2.2 Residual Heat Stored in Metal The residual heat stored in the hot leg metal is conservatively 5 | 2.2.2 Residual Heat Stored in Metal The residual heat stored in the hot leg metal is conservatively 5 | ||
calculated to be s 1.89x10 BTV's. This calculation is based on (1) hot leg piping temperature remains at s 605 F for 60 seconds after the trip and (2) the residual heat is dumped instantaneously into the hot leg flow volume at the RTD indicated temperature | calculated to be s 1.89x10 BTV's. This calculation is based on (1) hot leg piping temperature remains at s 605 F for 60 seconds after the trip and (2) the residual heat is dumped instantaneously into the hot leg flow volume at the RTD indicated temperature of s 550 F and 1600 psia. | ||
of s 550 F and 1600 psia | |||
Hot leg metal volume = 70.45 ft 3 3 4 Hot leg metal mass = 70.45 ft x 490 lb = 3.45 x 10 lbm ft* | Hot leg metal volume = 70.45 ft 3 3 4 Hot leg metal mass = 70.45 ft x 490 lb = 3.45 x 10 lbm ft* | ||
The AT driving function will be 605 - 555 or 50 AT. | The AT driving function will be 605 - 555 or 50 AT. | ||
| Line 114: | Line 74: | ||
197x10 lb This is equivalent to s 8 F in temperature addition. | 197x10 lb This is equivalent to s 8 F in temperature addition. | ||
Therefore, the saturation pressures for 551oF* + 8oF = 559 F and 5810F + 80F = 5896 F are below 1500 psig. | Therefore, the saturation pressures for 551oF* + 8oF = 559 F and 5810F + 80F = 5896 F are below 1500 psig. | ||
Per previous calculation O | |||
. . Column Wddgart Flow Path 7 Fig. 2.1.1 | . . Column Wddgart Flow Path 7 Fig. 2.1.1 | ||
/ | / | ||
\ ' | \ ' | ||
/ | / | ||
/ | / | ||
r | r | ||
/ | / | ||
/ -PLEN UM s COVER t+t t t +tt A | |||
/ -PLEN UM | |||
s COVER | |||
t+t t t +tt | |||
A | |||
Flow Path - | Flow Path - | ||
d 2 | d 2 | ||
s | s | ||
<' _ o | <' _ o | ||
; p, 7 | ; p, 7 | ||
' / | ' / | ||
d d. | d d. | ||
t | t 4 | ||
I i | |||
e (' | |||
f | f | ||
+-LEAD | +-LEAD | ||
' SCRCW l, | ' SCRCW l, | ||
[ - | [ - | ||
i - | i - | ||
| Line 182: | Line 103: | ||
// r rr-i ~ | // r rr-i ~ | ||
T-in // ~ ' | T-in // ~ ' | ||
b \ \/ | b \ \/ | ||
f | f | ||
,/ | ,/ | ||
U | U | ||
)*l u t *.* | )*l u t *.* | ||
' ' I s- | ' ' I s- | ||
) l U | ) l U | ||
l C # _ _ _-[- .::- r | l C # _ _ _-[- .::- r | ||
~ ~~ | ~ ~~ | ||
w ~ | w ~ | ||
U U J-U PPE R EN D FITTING p_ _s < | |||
U U J-U PPE R EN D FITTING | |||
p_ _s < | |||
_ - - - _s - | _ - - - _s - | ||
_- _f k | _- _f k | ||
\9 | \9 | ||
Upper Plenum Flow Path Fig. 2.1.2 ' | Upper Plenum Flow Path Fig. 2.1.2 ' | ||
~ | ~ | ||
t 9 | t 9 | ||
,m, = ^ | ,m, = ^ | ||
l} !!yj{2 column X -- _ , | l} !!yj{2 column X -- _ , | ||
weldment : | weldment : | ||
| Line 226: | Line 127: | ||
dCD CD CD G ,: | dCD CD CD G ,: | ||
' t ji | ' t ji | ||
. lj ll H l' Top view of upper plenum | |||
. lj ll H l' | |||
Top view of upper plenum | |||
[ cover for 177 FA Plants , | [ cover for 177 FA Plants , | ||
l | l b | ||
N, Flow Path Flow Path ,\ | |||
s x 9 , o c o m o , Ji N s | s x 9 , o c o m o , Ji N s | ||
,5%,S U[ $lj[$R | ,5%,S U[ $lj[$R | ||
/// : w ( | /// : w ( | ||
e | e W: | ||
W: | |||
?e/ | ?e/ | ||
a , | a , | ||
~ | ~ | ||
/ j - | / j - | ||
#4 i. ( )< ! | #4 i. ( )< ! | ||
P oxx . | |||
P | |||
oxx . | |||
.. . 20 - | .. . 20 - | ||
:W . - | :W . - | ||
g . - | g . - | ||
// 2- , | // 2- , | ||
: . . _ _ ._. . _ ~ _. :_._ | : . . _ _ ._. . _ ~ _. :_._ | ||
nf 9 h t ) 7 % | |||
nf | |||
9 h t ) 7 % | |||
3 | 3 | ||
\ j li g $' N N 1 id . h'N g9SD g@:i | \ j li g $' N N 1 id . h'N g9SD g@:i | ||
2.2.3 Conclusion Using the conservative as'umptions on residual stored heat and hot leg - pressurizer outsurge mixing, the RC pressure which would allow fla.shing is below 1500 psig. This low pressyre ,. | 2.2.3 Conclusion Using the conservative as'umptions on residual stored heat and hot leg - pressurizer outsurge mixing, the RC pressure which would allow fla.shing is below 1500 psig. This low pressyre ,. | ||
snould not ce reacned during normal transients. | snould not ce reacned during normal transients. | ||
2.3 Evt.nt Description For Mass / Volume Balance 2.3.1 Description of Analysis A mass volume balance on the RC system before and after trips was analysed for five cases. These cases were chosen because of their abnormally low pressuri:or level, low RC pressure, or | 2.3 Evt.nt Description For Mass / Volume Balance 2.3.1 Description of Analysis A mass volume balance on the RC system before and after trips was analysed for five cases. These cases were chosen because of their abnormally low pressuri:or level, low RC pressure, or were referred to in reference 1. | ||
were referred to in reference 1. | |||
The method of analysis was basically: | The method of analysis was basically: | ||
(1) To break the RC system down into 4 different temperature / | (1) To break the RC system down into 4 different temperature / | ||
| Line 290: | Line 159: | ||
(4) Subtract this volume of water from the initial pressurizer volume to get " level 1". | (4) Subtract this volume of water from the initial pressurizer volume to get " level 1". | ||
(5) Calculate the amount of water that would have flashed in the pressurizer due to the lower pressure condition. | (5) Calculate the amount of water that would have flashed in the pressurizer due to the lower pressure condition. | ||
This is " level | This is " level 2". - | ||
2". - | |||
. (6) Fine.lly, calculate the pressurizer level error per attacnment 1. This is " level 3". | . (6) Fine.lly, calculate the pressurizer level error per attacnment 1. This is " level 3". | ||
(7) Subtract level 2 and 3 from level 1 to get level 4. If | (7) Subtract level 2 and 3 from level 1 to get level 4. If | ||
| Line 298: | Line 165: | ||
then a viable explanation would be potential " steam pockets" h | then a viable explanation would be potential " steam pockets" h | ||
in the RCS. | in the RCS. | ||
The results of this study show that the :ndicated pressurizer level (level 5) is less than or equal to the calculation of level 4 and therefore a steam pocket occurring in the RCS is highly unlikely. | The results of this study show that the :ndicated pressurizer level (level 5) is less than or equal to the calculation of level 4 and therefore a steam pocket occurring in the RCS is highly unlikely. | ||
| Line 313: | Line 177: | ||
For raised loop plants (TECO) | For raised loop plants (TECO) | ||
V 5 | V 5 | ||
(APl } + ( 2 3}+ (P 4 1 + 3.207 (level)] p 5 1 | |||
(APl } + ( 2 3}+ (P 4 1 + 3.207 (level)] p 5 | p 5 9' For lowered loop plants V | ||
5 9' For lowered loop plants | |||
V | |||
= 3800(ao)) + 887(ap 2 ) + 3197 (ap3) + 2774 (ap4) + [A) + 3.207 (level)] p 5 1 | = 3800(ao)) + 887(ap 2 ) + 3197 (ap3) + 2774 (ap4) + [A) + 3.207 (level)] p 5 1 | ||
P5 Eq.2 h | P5 Eq.2 h | ||
RC. VOLUME BREAFDOWN e~ Fig. 2.3.1 if*m\,'ftao | RC. VOLUME BREAFDOWN e~ Fig. 2.3.1 if*m\,'ftao | ||
,'f ',, | ,'f ',, | ||
. v | . v m i er. | ||
m i er. | |||
He en | He en | ||
) | ) | ||
p | p | ||
'e I .2 'u je e , | |||
'e I .2 'u | |||
je e , | |||
/' | /' | ||
p ,- 7 c* g | p ,- 7 c* g | ||
, ,, e , n | , ,, e , n | ||
) '' | ) '' | ||
,e i | ,e i | ||
, D, e j ,' e 'l ) | , D, e j ,' e 'l ) | ||
-- ,, i ,, .e ,' *- Tube Sheet t | |||
lt , c' , | |||
-- ,, i ,, .e ,' *- Tube Sheet | i # #, e ,. ,, f' b / O ? $ :5* W '') % / | ||
b / O ? $ :5* W '') % / | |||
t | t | ||
, ,k . , , | , ,k . , , | ||
l , . ,. ;,t ,/ | l , . ,. ;,t ,/ | ||
. , i_, | . , i_, | ||
i 's .. , | i 's .. , | ||
./ / | ./ / | ||
,i " , | ,i " , | ||
,. , '., . [il/ | ,. , '., . [il/ | ||
/ . | / . | ||
/ .. x s, K / | / .. x s, K / | ||
e_' . ". | e_' . ". | ||
.%. < '.. il' / / | .%. < '.. il' / / | ||
1..,. u. | 1..,. u. | ||
p; \;w, | p; \;w, | ||
.. . i.t . . . . .; | .. . i.t . . . . .; | ||
m....,, | m....,, | ||
r . . . .. . | r . . . .. . | ||
., y , .. | ., y , .. | ||
O - | O - | ||
Raised Looo Lowered Loro | Raised Looo Lowered Loro | ||
.. 177 NSS (ft3 ) 177 NSS (ftJJ V) | .. 177 NSS (ft3 ) 177 NSS (ftJJ V) | ||
= | = | ||
f ,' ,'*.l .' = Cold Water Volume = | f ,' ,'*.l .' = Cold Water Volume = | ||
, 3739 3800 | , 3739 3800 | ||
, .6 | , .6 V | ||
2 i ', = Core Water Volume = 887 887 | |||
.--,..a V = | |||
i ', = Core Water Volume = 887 887 | |||
.--,..a | |||
V = | |||
'3 e = Hot Water Volume = 3062 3197 3 , 3 , | '3 e = Hot Water Volume = 3062 3197 3 , 3 , | ||
: i. --, | : i. --, | ||
V = 2774 2774 4 { = Steam Generator Water Volume = | V = 2774 2774 4 { = Steam Generator Water Volume = | ||
e .- e | e .- e | ||
| Line 428: | Line 241: | ||
P4=P tap 0 5 = f(P5, Tsat) p5ptap g 395B | P4=P tap 0 5 = f(P5, Tsat) p5ptap g 395B | ||
2.3.3.1 Davis Besse 9/18/79 Trio At 12:43 on September 18, 1979, while operating at s 100% | 2.3.3.1 Davis Besse 9/18/79 Trio At 12:43 on September 18, 1979, while operating at s 100% | ||
power a test was in progress on the main steam turbine Electro Hydraulic Control System (EHC) at Davis Besse 1. While transferring EHC pumps a low pressure signal in the EHC initiated a turbine trip. The Anticipatory Reactor Trip on Turbine Trip tripped the reactor s 0.4 seconds after the turbine trip. | power a test was in progress on the main steam turbine Electro Hydraulic Control System (EHC) at Davis Besse 1. While transferring EHC pumps a low pressure signal in the EHC initiated a turbine trip. The Anticipatory Reactor Trip on Turbine Trip tripped the reactor s 0.4 seconds after the turbine trip. | ||
The reactor trip caused the RC pressure, RC T average and pressurizer level to decrease rapidly. The pressurizer level indication dropped off scale.some 50 seconds a,fter the reactor | The reactor trip caused the RC pressure, RC T average and pressurizer level to decrease rapidly. The pressurizer level indication dropped off scale.some 50 seconds a,fter the reactor trip, remained down scale for some 50 seconds and then slowly increased. The RC pressure reached a minimum of about 1710 psig at 1 minute after reactor trip and recovered. RC T reached a minimum of 546 F following the trip and stabilized at 550 F. | ||
The initial conditions prior to the trip are listed below. | The initial conditions prior to the trip are listed below. | ||
Reactor Power s 100% Rated Power RC Temperature (T,y,): 582 F R.C.S. Pressure: 2200 psig R.C.S. Flow: 4 pumps operating Pressurizer Level: 202 inches | Reactor Power s 100% Rated Power RC Temperature (T,y,): 582 F R.C.S. Pressure: 2200 psig R.C.S. Flow: 4 pumps operating Pressurizer Level: 202 inches Tests in Progress: EHC Test The pertinent data during the transient is shown on figure 2.3.3.1. The data analysis is as follows. | ||
Tests in Progress: EHC Test The pertinent data during the transient is shown on figure 2.3.3.1. The data analysis is as follows. | |||
h | h | ||
- Davis Besse 9/18/79 | - Davis Besse 9/18/79 | ||
, Reactor Trip Time (0) Initial Conditions T = | , Reactor Trip Time (0) Initial Conditions T = | ||
| Line 448: | Line 255: | ||
= | = | ||
46.24 p = 44.64 p = 42.57 p = 44.60 4 | 46.24 p = 44.64 p = 42.57 p = 44.60 4 | ||
p5" | p5" Time (1) = 42 sec | ||
* w T = 557 T = 550 p = 1740 psia hot cold tap Therefore p' = 46.40 p/ = 46.27 2 | |||
Time (1) = 42 sec | |||
* w T = 557 T = 550 p = 1740 psia hot cold tap Therefore p' = 46.40 | |||
p/ = 46.27 2 | |||
3 p'= E 97 3 | 3 p'= E 97 3 | ||
1, pi = 46.23 4. | 1, pi = 46.23 4. | ||
| Line 463: | Line 265: | ||
4037 lb. The final mass of steam is 1214 ft x 4.37 lb/ft or 5304 lb. This additional 1267 lb (5304 - 4037) of steam will come from s 10" of water . (level 2). | 4037 lb. The final mass of steam is 1214 ft x 4.37 lb/ft or 5304 lb. This additional 1267 lb (5304 - 4037) of steam will come from s 10" of water . (level 2). | ||
Therefore, level 1 - level 2 - level 3 = level 4 = 47.5-14-10 = 23.5". Level 4 is slightly great:r than level 5; therefore, the proba,bility of steam pockets is low. | Therefore, level 1 - level 2 - level 3 = level 4 = 47.5-14-10 = 23.5". Level 4 is slightly great:r than level 5; therefore, the proba,bility of steam pockets is low. | ||
A 4 second hot and cold leg RTO response time delay is incorporated. | |||
Note: Where possibic, data used in thc:e analyses is based on ccmputer print cut. | Note: Where possibic, data used in thc:e analyses is based on ccmputer print cut. | ||
The graphs arc representati ns of this data. | The graphs arc representati ns of this data. | ||
| Line 469: | Line 271: | ||
.. . - - . . __ . - . .. ~ | .. . - - . . __ . - . .. ~ | ||
Fig. 2.3.3.1 m es ed .C "O 6 & C c) C) @ | |||
Fig. 2.3.3.1 | |||
wO C .c L mN-w a vN M C C 'C y C *- C n -OmCm L C c ~m | wO C .c L mN-w a vN M C C 'C y C *- C n -OmCm L C c ~m | ||
~ | ~ | ||
C* C Gl mN Lao DC L | C* C Gl mN Lao DC L 3*; | ||
3*; | |||
cy y, am OwGJL mL)2 o*< | cy y, am OwGJL mL)2 o*< | ||
\ e- "L5-c; c; 2 c; e a o | \ e- "L5-c; c; 2 c; e a o | ||
| Line 485: | Line 282: | ||
\ -wo-O- O - a' - - | \ -wo-O- O - a' - - | ||
~w \ d | ~w \ d | ||
@ma \ > | @ma \ > | ||
C-m - | C-m - | ||
| Line 501: | Line 297: | ||
E | E | ||
\ l o | \ l o | ||
C3 | C3 o | ||
o | |||
: n. s. - m => % | : n. s. - m => % | ||
o \ , - | o \ , - | ||
| Line 513: | Line 307: | ||
y *a { : i g a 1 v r- cm. | y *a { : i g a 1 v r- cm. | ||
N 1 .: - | N 1 .: - | ||
co 1 | co 1 | ||
~ s N i. - | ~ s N i. - | ||
Cn . | Cn . | ||
- N u | - N u o | ||
o ' | |||
3 W 11 m l-- *g - | 3 W 11 m l-- *g - | ||
IE | IE | ||
.'Il | .'Il | ||
./ .I e | |||
./ .I | |||
e | |||
~", ,/ | ~", ,/ | ||
/ _ ,,, ., - | / _ ,,, ., - | ||
-:.:~ '~ ~ ' | -:.:~ '~ ~ ' | ||
c, . o | c, . o | ||
- . m a ce wi | - . m a ce wi ca >, m o :. | ||
ca >, m o :. | |||
= ~ w a w | = ~ w a w | ||
,_a | ,_a | ||
| Line 549: | Line 328: | ||
: 3. '3Hn1YH3dN31 . | : 3. '3Hn1YH3dN31 . | ||
I i i i - | I i i i - | ||
i , , i o c2 o c3 o o o C2 C3 C9 C2 o o gwy N .o o C3 CL | i , , i o c2 o c3 o o o C2 C3 C9 C2 o o gwy N .o o C3 CL P"'" | ||
N N N N == | N N N N == | ||
SISd '3HASS3Hd '3*H I i i e i e i , , , , | SISd '3HASS3Hd '3*H I i i e i e i , , , , | ||
o cm es cm em c3 o o c c3 c3 O G3 C43 ai CD 4D ag- N N a .= r. .N .o. | o cm es cm em c3 o o c c3 c3 O G3 C43 ai CD 4D ag- N N a .= r. .N .o. | ||
(S3H3N!) 13A31 H3ZlHASS3Hd Dbg | (S3H3N!) 13A31 H3ZlHASS3Hd Dbg | ||
\99 | \99 | ||
e 2.3.3.2 Davis Besse 9/15/79 Trip Figure 2.3.3.2 shows the RC pressure during this trip. | |||
e | |||
2.3.3.2 Davis Besse 9/15/79 Trip Figure 2.3.3.2 shows the RC pressure during this trip. | |||
Since RC minimum pressure was 1848 psig no steam production was possible per discussion in Section 2.2. | Since RC minimum pressure was 1848 psig no steam production was possible per discussion in Section 2.2. | ||
% e e | % e e | ||
TECO 9/15n9 TRIP 21.840 - | |||
TECO 9/15n9 TRIP | |||
21.840 - | |||
21.420 - | 21.420 - | ||
m[ 21.000 - | m[ 21.000 - | ||
E 1 | E 1 | ||
| Line 584: | Line 346: | ||
S E | S E | ||
g 20.160 - | g 20.160 - | ||
5 O | 5 O | ||
a: | a: | ||
a-19.740 - L.- | a-19.740 - L.- | ||
M l, | M l, 19.320 - | ||
2 t' | |||
19.320 - | |||
2 | |||
- 18.900 - | - 18.900 - | ||
-O [ | -O [ | ||
& 6 C ' ' ' ' ' ' ' | & 6 C ' ' ' ' ' ' ' | ||
18.480 O | 18.480 O | ||
o 49.410 49.815 50.220 50.625 51.030 51.435 51.840 52.245 52.650 0 2 | o 49.410 49.815 50.220 50.625 51.030 51.435 51.840 52.245 52.650 0 2 Time (seconds) (110 ) | ||
Time (seconds) (110 ) | |||
2.3.3.3 Daivs Besse 9/26/79 Trio At 20:56:33 hours on September 26, 1979, a high turbine throttle pressure limit alarm was received. The throttle pressure limiter is used to protect against an excessive decrease of steam pressure when steam generation of the NSS falls below the steam demand of the turbine. It acts directly to close the high pressure turbine control valves in an effort to maintain steam header pressure. Rapid closure of the control valves caused a mismatch between heat generation and heat removal with ? | 2.3.3.3 Daivs Besse 9/26/79 Trio At 20:56:33 hours on September 26, 1979, a high turbine throttle pressure limit alarm was received. The throttle pressure limiter is used to protect against an excessive decrease of steam pressure when steam generation of the NSS falls below the steam demand of the turbine. It acts directly to close the high pressure turbine control valves in an effort to maintain steam header pressure. Rapid closure of the control valves caused a mismatch between heat generation and heat removal with ? | ||
resultant increase in Reactor Coolant System (RCS) temperature and pressure. Seven seconds later (at 20:56:40) the reactor tripped on RCS high pressure and was followed by a turoine trip. | resultant increase in Reactor Coolant System (RCS) temperature and pressure. Seven seconds later (at 20:56:40) the reactor tripped on RCS high pressure and was followed by a turoine trip. | ||
RCS temperature and pressure then dropped and the Integrated Control System (ICS) reduced the feedwater flow abruptly. | RCS temperature and pressure then dropped and the Integrated Control System (ICS) reduced the feedwater flow abruptly. | ||
Reactor Coolant System Tave decreased to 548.5 F approximately 57 seconds after the trip. The pressurizer level indication dropped off scale at 21:57:21 and remained below tne indication range for approximately 21 seconds. | Reactor Coolant System Tave decreased to 548.5 F approximately 57 seconds after the trip. The pressurizer level indication dropped off scale at 21:57:21 and remained below tne indication range for approximately 21 seconds. | ||
The initial conditions prior to the trip are listed below. | The initial conditions prior to the trip are listed below. | ||
Reactor Power: s 100% Rated Power R. C. Temperature (Tave): 5824 | Reactor Power: s 100% Rated Power R. C. Temperature (Tave): 5824 R. C. S. Flow: .4 pumps operating Pressurizer Level: 200 inches The pertinent data during the transient for this analysis is shown on figure 2.3.3.3. The data analysis is as follows. | ||
R. C. S. Flow: .4 pumps operating Pressurizer Level: 200 inches The pertinent data during the transient for this analysis is shown on figure 2.3.3.3. The data analysis is as follows. | |||
qh | qh | ||
Davis Besse 9/26/79 Reactor Trip Time (0) Initial Conditions T = | |||
Davis Besse 9/26/79 | |||
Reactor Trip Time (0) Initial Conditions T = | |||
hot T = 559% P = 2215 psia cold tap Therefore p) = 46.18 p = | hot T = 559% P = 2215 psia cold tap Therefore p) = 46.18 p = | ||
44.59 2 | 44.59 2 | ||
p3= 42.67 p = 44.56 p5" | p3= 42.67 p = 44.56 p5" | ||
* Time (1) = 50 sec T = 552 = 548 p = 1700 psia T | |||
Time (1) = 50 sec T = 552 = 548 p = 1700 psia T | |||
hot cold tap Therefore p' = 46.62 1 ~ - | hot cold tap Therefore p' = 46.62 1 ~ - | ||
p/ = 46.53 2 - | p/ = 46.53 2 - | ||
3 p - 46.22 3 | 3 p - 46.22 3 | ||
| Line 638: | Line 380: | ||
The indicated pressurizer level was 0 inches (level 5). The estimated pressurizer level temperature compensation error (per Attachment 1) is 15" inches (level 3). | The indicated pressurizer level was 0 inches (level 5). The estimated pressurizer level temperature compensation error (per Attachment 1) is 15" inches (level 3). | ||
The initial mass of steam in the pressurizer is 648 'ft x 6.21 lb/ft or 3 3 4030 lb. The final mass of steam is s1234 ft x '4.23 lb/ft or 5219 lb. This additicnal 1190 lb ( 5219 - 4030) of steam will come from s 9" of water. (level 2) | The initial mass of steam in the pressurizer is 648 'ft x 6.21 lb/ft or 3 3 4030 lb. The final mass of steam is s1234 ft x '4.23 lb/ft or 5219 lb. This additicnal 1190 lb ( 5219 - 4030) of steam will come from s 9" of water. (level 2) | ||
Therefore, level 1 - level 2 - level 3 = level 4 = 26.4 9 = 2:4". Level 4 is slightly greater than level 5; therefore, the probability of stear, pockets is iou. | |||
A 4 second hot and cold icg RTD response time delay is incorporated, llotc: 1.'here possible, data used in these analyses is based on computer print out. | |||
The graphs are representations of this data. | The graphs are representations of this data. | ||
. I Fig. 2.3.3.3 I | |||
. I | |||
Fig. 2.3.3.3 I | |||
e 1 | e 1 | ||
1 4 | 1 4 | ||
| Line 654: | Line 390: | ||
5 | 5 | ||
' O G. x ~ | ' O G. x ~ | ||
H . ~ N | H . ~ N uJ s a i R 5 m 3 o j =. | ||
uJ | |||
s a i R 5 m 3 o j =. | |||
Y : | Y : | ||
t | t | ||
^ | ^ | ||
| Line 671: | Line 399: | ||
= _ | = _ | ||
E | E | ||
^^ | ^^ | ||
O 7 - | O 7 - | ||
d e f f f f f i | d e f f f f f i c | ||
c | |||
p k | p k | ||
C | C e | ||
c o | |||
e | h o | ||
(d es) 1 3b I t t I t t 1 1 o S b $ o o o o R N - | |||
c | |||
o | |||
h : : C 2 (alsd) SS3Hd '3'8 f f f f f f I k | h : : C 2 (alsd) SS3Hd '3'8 f f f f f f I k | ||
~ | ~ | ||
o | o | ||
~ | ~ | ||
h h h | |||
* NI) 13A31 'SS3Hd gg3 | |||
h | |||
h h | |||
NI) 13A31 'SS3Hd gg3 | |||
2.3.3.4 Oconee 1 10/8/79 Trip On October 8, 1979, Oconee 1 was operating at 100% FP with on line Reactor Protection Tests in progress. At 13:27:35, Oconee 1 experienced a reactor trip attributed to RPS activation of pressure / temperature channels A, C, and D. | 2.3.3.4 Oconee 1 10/8/79 Trip On October 8, 1979, Oconee 1 was operating at 100% FP with on line Reactor Protection Tests in progress. At 13:27:35, Oconee 1 experienced a reactor trip attributed to RPS activation of pressure / temperature channels A, C, and D. | ||
Control Rod Drive Breakers CB 3 and 4 were tripped for the test. An additional breaker for Group 5 was opened which caused Group 5 to drop. This resulted in a P/T Trip. | Control Rod Drive Breakers CB 3 and 4 were tripped for the test. An additional breaker for Group 5 was opened which caused Group 5 to drop. This resulted in a P/T Trip. | ||
| Line 709: | Line 419: | ||
Reactor Power , 100.% | Reactor Power , 100.% | ||
RCS TAVE 579 F Pressurizer level 221 inches The pertinent data during the transient for this analysis are shown on figure 2.3.3.4. The data analysis is as follows. | RCS TAVE 579 F Pressurizer level 221 inches The pertinent data during the transient for this analysis are shown on figure 2.3.3.4. The data analysis is as follows. | ||
1950 | 1950 | ||
Oconee I 10/8/79 Control Rod Drop Trip Time (0) Initial Conditions T = 602 7 T = 558 p = 2150 psia hot cold tap 3 | |||
Oconee I 10/8/79 | |||
Control Rod Drop Trip Time (0) Initial Conditions T = 602 7 T = 558 p = 2150 psia hot cold tap 3 | |||
Therefore p) - 46.26 lb/ft 3 | Therefore p) - 46.26 lb/ft 3 | ||
p = 44.75 lb/ft 2 | p = 44.75 lb/ft 2 | ||
| Line 724: | Line 427: | ||
4 | 4 | ||
= | = | ||
44.70 lb/ft p5" | 44.70 lb/ft p5" | ||
* Time (1) = 60 seconds 553 =1750 psia T = | |||
Time (1) = 60 seconds 553 =1750 psia | |||
T = | |||
T = 550 p hot cold tap Therefore p' = 46.55 lb/ft 3 1 . | T = 550 p hot cold tap Therefore p' = 46.55 lb/ft 3 1 . | ||
p I' = 46.47 lb/ft 2 | p I' = 46.47 lb/ft 2 | ||
| Line 739: | Line 439: | ||
The initial mass of stesm in the pressurizer is 709 3ft x 5.97 lb/ft or 4236 lb. The final mass of steam is 1283 ft3 x 4.4 lb/ft or 5652 lb. This additional 1416 lb (5652 - 4236) of steam will come from s 10' of water (level 2). | The initial mass of stesm in the pressurizer is 709 3ft x 5.97 lb/ft or 4236 lb. The final mass of steam is 1283 ft3 x 4.4 lb/ft or 5652 lb. This additional 1416 lb (5652 - 4236) of steam will come from s 10' of water (level 2). | ||
Therefore, level 1 - level 2 - level 3 = level 4 = 5G-15-10 31". Level 4 is equal to level 5; therefore, the probability of steam pockets is low. | Therefore, level 1 - level 2 - level 3 = level 4 = 5G-15-10 31". Level 4 is equal to level 5; therefore, the probability of steam pockets is low. | ||
A 4 second hot anc cold leg RTD response time delay is incorporated. | |||
Note: 1.'here possible, data used in these analyses is based on computer print out. | Note: 1.'here possible, data used in these analyses is based on computer print out. | ||
The graphs are representations of this data. | The graphs are representations of this data. | ||
gCg Q O | gCg Q O | ||
Fig. 2.3.3.4 | |||
! S 1 | ! S 1 | ||
'l | 'l | ||
& I E .o . . | & I E .o . . | ||
R d T !. . | R d T !. . | ||
m $ w w / S | |||
= | = | ||
r- E E /- | r- E E /- | ||
| Line 762: | Line 458: | ||
= | = | ||
E | E | ||
/ i | / i | ||
~ | ~ | ||
w u | w u | ||
N o | N o | ||
N f, ,E w w ' = //' | N f, ,E w w ' = //' | ||
g w - = | g w - = | ||
#s' / W 5 | #s' / W 5 | ||
O # | O # | ||
/* % | /* % | ||
=s N c2 | =s N c2 | ||
| Line 784: | Line 472: | ||
1 I I I f f I II 1 o | 1 I I I f f I II 1 o | ||
E S S S 3 q | E S S S 3 q | ||
- = | - = | ||
e e 2 : | e e 2 : | ||
| Line 793: | Line 480: | ||
I I I I I I I f I I S | I I I I I I I f I I S | ||
~ | ~ | ||
S | S S | ||
3 S $ | |||
S | |||
3 | |||
S $ | |||
(S3H3NI) 13A31 H32IHOSS3Hd | (S3H3NI) 13A31 H32IHOSS3Hd | ||
2.3.3.5 Oconee II 1/4/74 Trio Figure 2.3.3.6 she',s the pertinent transient results of this trip. | 2.3.3.5 Oconee II 1/4/74 Trio Figure 2.3.3.6 she',s the pertinent transient results of this trip. | ||
During this transient the minimum Tap pressure attained was s 1900 psig. Therefore, a 1940 psia upper vessel pressure would require a 631 F temperature to produce net steam. This temperature was never attained at any position or time during this transient. While it is given that operator action (or plant responses) could have been better, the steam production possibility did not exist. Furthermore, a review of the sequence of events of this trip indicate that the severe level and pressure changes at the beginning and later in the transient were primarily cue to a temporary loss of 10.5 power. | During this transient the minimum Tap pressure attained was s 1900 psig. Therefore, a 1940 psia upper vessel pressure would require a 631 F temperature to produce net steam. This temperature was never attained at any position or time during this transient. While it is given that operator action (or plant responses) could have been better, the steam production possibility did not exist. Furthermore, a review of the sequence of events of this trip indicate that the severe level and pressure changes at the beginning and later in the transient were primarily cue to a temporary loss of 10.5 power. | ||
Fig. 2.3.3.5 N, ,1 | |||
Fig. 2.3.3.5 | |||
N, ,1 | |||
\' / | \' / | ||
I | I | ||
> a g I 1 - o | > a g I 1 - o | ||
\- . | \- . | ||
/ | / | ||
N 5 I | N 5 I u | ||
z | |||
'N. 5 | 'N. 5 | ||
=> | => | ||
= | = | ||
s | s n | ||
n | |||
~ ' | ~ ' | ||
= l m - | = l m - | ||
| Line 843: | Line 507: | ||
- (. / | - (. / | ||
E | E | ||
= | = | ||
5 e | 5 e | ||
z E\ | z E\ | ||
= | = | ||
m | m l . . | ||
l . . | |||
= == | = == | ||
? | ? | ||
t m | t m | ||
: / ;;; | : / ;;; | ||
w f 3 | w f 3 | ||
/ | / | ||
v c:. | v c:. | ||
| Line 867: | Line 524: | ||
== | == | ||
c:3 o .h. | c:3 o .h. | ||
\'N | \'N | ||
- l. | - l. | ||
2 - - | 2 - - | ||
o | o a | ||
a | |||
=I e j o" | =I e j o" | ||
I | I | ||
., \. | ., \. | ||
| Line 887: | Line 535: | ||
o.- o | o.- o | ||
#s#- | #s#- | ||
1 | 1 | ||
.s . - | .s . - | ||
| Line 894: | Line 541: | ||
p | p | ||
/ . | / . | ||
s | s | ||
/ | / | ||
| Line 901: | Line 547: | ||
1 r' $E 8 N . s~ ' % .N | 1 r' $E 8 N . s~ ' % .N | ||
-w | -w | ||
<5 | <5 W -T; I un , | ||
W -T; I un , | |||
[. | [. | ||
l i I. | l i I. | ||
| Line 917: | Line 561: | ||
5 | 5 | ||
~ | ~ | ||
5 a'. E $ $ | |||
5 | |||
a'. E $ $ | |||
(S3HONI) 13A31 H3Zl80SS38d | (S3HONI) 13A31 H3Zl80SS38d | ||
3.0 Conclusion During any B&W reactor trip where a primary system break does not occur or the pressurizer does not empty and HPI is operable - net steam production in the primary system is highly improbable and generation of a volume of steam required to block natural circulation is virtually impossible. | 3.0 Conclusion During any B&W reactor trip where a primary system break does not occur or the pressurizer does not empty and HPI is operable - net steam production in the primary system is highly improbable and generation of a volume of steam required to block natural circulation is virtually impossible. | ||
4.0 References | 4.0 References | ||
: 1. 11/15/79 phone conversation between Cf:W and NRC, Suoject: | : 1. 11/15/79 phone conversation between Cf:W and NRC, Suoject: | ||
Potential Voiding in-the RCS During-Anticipated Transients | Potential Voiding in-the RCS During-Anticipated Transients | ||
ATTACHMENT 1 Pressurizer Level Error The pressurizer level indication is based on the pounds of mass the pressure taps measure and then distributed to varying amounts of water and steam at the saturation conditions at the pressurizer pressure. Since pressure is not measured in the pressurizer (only temperature) pressure is assumed from the temperature measurement being at T sat | ATTACHMENT 1 Pressurizer Level Error The pressurizer level indication is based on the pounds of mass the pressure taps measure and then distributed to varying amounts of water and steam at the saturation conditions at the pressurizer pressure. Since pressure is not measured in the pressurizer (only temperature) pressure is assumed from the temperature measurement being at T sat | ||
* During fast depressurizations the RTD in the pressurizer does not respond efficiently, especially in cases where the RTD is exposed to steam enviroment. The heat transfer time constant can vary from 30 to 180 seconds. Since most depressurization after trips occur in 30 to 50 seconds the RTD will not respond effectively at the low level point. | * During fast depressurizations the RTD in the pressurizer does not respond efficiently, especially in cases where the RTD is exposed to steam enviroment. The heat transfer time constant can vary from 30 to 180 seconds. Since most depressurization after trips occur in 30 to 50 seconds the RTD will not respond effectively at the low level point. | ||
| Line 947: | Line 574: | ||
Figures A3 and A4 show what typical errors can be expected as a function of indicated level and system pressure. Inese curves can be used to correct the indicated level if system pressure (i.e. Tsat) and pressurizer RTD temperature are known. The difference between RTD temperature and calculated T (Based on Psat) will give the level error. | Figures A3 and A4 show what typical errors can be expected as a function of indicated level and system pressure. Inese curves can be used to correct the indicated level if system pressure (i.e. Tsat) and pressurizer RTD temperature are known. The difference between RTD temperature and calculated T (Based on Psat) will give the level error. | ||
sat In a typical trip @ Oconee 1/1/77 the system pressure went from 2150 to s 1800 psig in 27 seconds. The alams printer monitored a 643 pressurizer temperature at 1800 psig instead of the expected 621 F. At the indicated level of 70" the real level was s 78" (per figure A-3). | sat In a typical trip @ Oconee 1/1/77 the system pressure went from 2150 to s 1800 psig in 27 seconds. The alams printer monitored a 643 pressurizer temperature at 1800 psig instead of the expected 621 F. At the indicated level of 70" the real level was s 78" (per figure A-3). | ||
,.e rigure n-1 f* A | ,.e rigure n-1 f* A | ||
_ = -.- -.___-___7__ . - _ . _ . _ . - . _ | _ = -.- -.___-___7__ . - _ . _ . _ . - . _ | ||
_ _ = _ - | _ _ = _ - | ||
: CZ1-' . _ _ _ _ _ . _ . _ __ '-*=I'' - _ . 22 - | : CZ1-' . _ _ _ _ _ . _ . _ __ '-*=I'' - _ . 22 - | ||
* - - - ~ | * - - - ~ | ||
t--__:.____..._-!---- | t--__:.____..._-!---- | ||
r_ . _ _ . _ _ _ . _ *-_ _-- _ . .__.- -. . | r_ . _ _ . _ _ _ . _ *-_ _-- _ . .__.- -. . | ||
g | g 7'~._;-* | ||
7'~._;-* | |||
p; ;,__~~C , *- -- - - 7 Z ".---_- . ._ . .__ ._.-_.-_"E!.2-'- | p; ;,__~~C , *- -- - - 7 Z ".---_- . ._ . .__ ._.-_.-_"E!.2-'- | ||
h 3-_-..3_..__._-_..-- _ . . . _ - . | |||
h | |||
3-_-..3_..__._-_..-- _ . . . _ | |||
.. : ~=:- -^ ___: _ . ._: | .. : ~=:- -^ ___: _ . ._: | ||
*~ | *~ | ||
- . _ - ' ~ - . _ . _ . ^^* ._.-- L | - . _ - ' ~ - . _ . _ . ^^* ._.-- L | ||
,7__ _ . | ,7__ _ . | ||
_4 I---***'"-- __. ___._. . . .. | _4 I---***'"-- __. ___._. . . .. | ||
.. _.. ---_q | .. _.. ---_q | ||
_ , , , . - . . . + | _ , , , . - . . . + | ||
LZ'._..___. \_'**---*-~~-~~--*----*---* + | LZ'._..___. \_'**---*-~~-~~--*----*---* + | ||
| Line 993: | Line 598: | ||
--- - ; , _ n - - % | --- - ; , _ n - - % | ||
:=r- p. : W | :=r- p. : W | ||
, 1 | , 1 | ||
=. . _ _ . _ . _ . | =. . _ _ . _ . _ . | ||
:- == . D .- = - ---~~t + | :- == . D .- = - ---~~t + | ||
Nq::$n: | Nq::$n: | ||
t - M = = ;+-- _1. ,. _ _ . _ . _.:-= n= | t - M = = ;+-- _1. ,. _ _ . _ . _.:-= n= | ||
...,,g , | ...,,g , | ||
r_ = y -* -L_y -- g + | r_ = y -* -L_y -- g + | ||
+- | +- | ||
_2 = . _ | _2 = . _ | ||
* -t -- q __ :- t | * -t -- q __ :- t I'.r__ | ||
.. % r. .A = __ .__. _ ____._ ,4 ._lkt.g .o ___q w-_ | |||
I'.r__ | |||
.. % r. .A = __ .__. _ ____._ ,4 ._lkt.g .o ___q | |||
w-_ | |||
-m _ ~- | -m _ ~- | ||
;_- ;._- g . . - . - _ . - - | ;_- ;._- g . . - . - _ . - - | ||
. .. ,3 . 4 _ . - . - . - - . - - . - | . .. ,3 . 4 _ . - . - . - - . - - . - | ||
| Line 1,029: | Line 615: | ||
@ = -.-*_ d M W _ ( ,[ ~ | @ = -.-*_ d M W _ ( ,[ ~ | ||
_ ~ 1. /_ . _ . . . . *= . | _ ~ 1. /_ . _ . . . . *= . | ||
o . gA.,.,,,..y, | o . gA.,.,,,..y, g1, g ._ _ _ . _ . | ||
g1, g ._ _ _ . | |||
._ y | ._ y | ||
. _. -__- _. ..D, | . _. -__- _. ..D, | ||
'T N_._ . | 'T N_._ . | ||
_:- . .. J-~1L k | _:- . .. J-~1L k | ||
- t- --O: h*- *;- 1 _.1t ;;/,N -- | - t- --O: h*- *;- 1 _.1t ;;/,N -- | ||
| Line 1,049: | Line 628: | ||
:- . 7_ _ _up, + - | :- . 7_ _ _up, + - | ||
------=_..___.. . _. _ g | ------=_..___.. . _. _ g | ||
==_-- | ==_-- | ||
: = = :=_ __-. - - -_.- ._, | : = = :=_ __-. - - -_.- ._, | ||
. ;-~:.= q%.;.y\. _. | . ;-~:.= q%.;.y\. _. | ||
-~ | -~ | ||
=~ = .== .- . .Q | =~ = .== .- . .Q | ||
{ ZZZ -*-- 7__. _ -*-- . *\L *=:'- :- - " - - - - - | { ZZZ -*-- 7__. _ -*-- . *\L *=:'- :- - " - - - - - | ||
____J-- | ____J-- | ||
~ - - | ~ - - | ||
~in' *h ath :-t | ~in' *h ath :-t | ||
;- n . _ --- _ f'*g;- | ;- n . _ --- _ f'*g;- | ||
y | y | ||
. . = 2-j n = ;_ _ _ ::- - :_ - ----------_. | . . = 2-j n = ;_ _ _ ::- - :_ - ----------_. | ||
Mp_ _ ._ | Mp_ _ ._ | ||
. _ _ . _ . . . _ _ . _ ._ = p - ,- .g n | |||
. _ _ . _ . . . _ _ . _ ._ = p - ,- .g | |||
n | |||
.- g y - | .- g y - | ||
y .-- - .- e _ c gQ | y .-- - .- e _ c gQ | ||
-g _-.__.;_---_-_..._..,.-,,j,_ | -g _-.__.;_---_-_..._..,.-,,j,_ | ||
l _x_r,,- = . | l _x_r,,- = . | ||
tch.4 _ .__ _. | tch.4 _ .__ _. | ||
. r. _ q pr. g__h. | . r. _ q pr. g__h. | ||
_+ - - - + | _+ - - - + | ||
_ _e | _ _e q1 . \ _ _. .__ _ | ||
q1 . \ _ _. .__ | |||
_ | |||
._.._..,=__=....._.,e-*=.- .._=. | ._.._..,=__=....._.,e-*=.- .._=. | ||
g_._..___._.,.__y. | g_._..___._.,.__y. | ||
_N.,_.__- | _N.,_.__- | ||
4 ,, . _ _ .__ | 4 ,, . _ _ .__ | ||
'=* 2 " | '=* 2 " | ||
L--*; | L--*; | ||
mart : \ }h - | mart : \ }h - | ||
} ~ - * -~~ "_; d _ . ._. T. r ., , =_ _ . '"-* , . . _ . _ . - | } ~ - * -~~ "_; d _ . ._. T. r ., , =_ _ . '"-* , . . _ . _ . - | ||
_ _ _ . . . __ ___ _ . 7- rnx= u_ -- --- --. C : | _ _ _ . . . __ ___ _ . 7- rnx= u_ -- --- --. C : | ||
| Line 1,119: | Line 665: | ||
,._, ti:\-?;:---" ._ + | ,._, ti:\-?;:---" ._ + | ||
------==x e - _ _ _ _ . _ . _ . -. _ . _ . , . _ - r, _p 9 | ------==x e - _ _ _ _ . _ . _ . -. _ . _ . , . _ - r, _p 9 | ||
=N | =N i.si Q=iEBEk._ ._ _-?'"_._._* __n---R W .__.. *__.. '= r==_.==- | ||
i.si | |||
Q=iEBEk._ ._ _-?'"_._._* __n---R W .__.. *__.. '= r==_.==- | |||
m=r L_ L_ . .- __ ._,.y/ ..__ Jfq | m=r L_ L_ . .- __ ._,.y/ ..__ Jfq | ||
= pr - | = pr - | ||
| Line 1,133: | Line 674: | ||
* A. | * A. | ||
-; g._ . _ | -; g._ . _ | ||
y t _L -x d f =r= ._ | y t _L -x d f =r= ._ | ||
______,___.___t_.. _ _. _ --__ . t___.1. w _ | ______,___.___t_.. _ _. _ --__ . t___.1. w _ | ||
_ n = tr?: = .sv.G;2._... . | _ n = tr?: = .sv.G;2._... . | ||
-3.______._______. = .r n--- | -3.______._______. = .r n--- | ||
_24 | _24 | ||
._.____ mr = r A = _t- :oa p g23 e _,= g__. . _ _ _ - _ . . . | ._.____ mr = r A = _t- :oa p g23 e _,= g__. . _ _ _ - _ . . . | ||
| Line 1,147: | Line 684: | ||
Q .__ _r *Fn. _ _. 4 - *@ _ __ ._ . : -" p.L._._( | Q .__ _r *Fn. _ _. 4 - *@ _ __ ._ . : -" p.L._._( | ||
,, m A _t .. | ,, m A _t .. | ||
__ = = . =u .- | __ = = . =u .- | ||
p | p | ||
| Line 1,153: | Line 689: | ||
.= L d_ :--- $'=r=m1Vt tr bg=*-. . _ . . _ _ _ _ _ _ | .= L d_ :--- $'=r=m1Vt tr bg=*-. . _ . . _ _ _ _ _ _ | ||
_ '- =c -- | _ '- =c -- | ||
.:M=__:.y:\c.3n= d -- =: .r_r-- _ ._.u= = == =r-r - -.___ | .:M=__:.y:\c.3n= d -- =: .r_r-- _ ._.u= = == =r-r - -.___ | ||
g i==_ o._ p._ | g i==_ o._ p._ | ||
. 9c ___ | . 9c ___ | ||
: g. . _ . _ . - . _ , - . _ . . . | : g. . _ . _ . - . _ , - . _ . . . | ||
3._ .. =n _ __. swx=b.---- -- - | 3._ .. =n _ __. swx=b.---- -- - | ||
c dr . .. - - - | c dr . .. - - - | ||
| Line 1,168: | Line 699: | ||
_ _ : =- -* | _ _ : =- -* | ||
_:- .__ = | _:- .__ = | ||
ggt:=. Y, =n x == --- - - | ggt:=. Y, =n x == --- - - | ||
- ;l., . | - ;l., . | ||
| Line 1,174: | Line 704: | ||
....1-g < =__.=__._ =___:._=__ =_ .4 _.. - | ....1-g < =__.=__._ =___:._=__ =_ .4 _.. - | ||
3 ---C: _.; $ _- _ . _ q _ . _ | 3 ---C: _.; $ _- _ . _ q _ . _ | ||
g - - - _ _.gm ----N,g:s _ T __ | g - - - _ _.gm ----N,g:s _ T __ | ||
_ _ _ . . . = :==y;:S= : h.pN w= .N-t=r - + | _ _ _ . . . = :==y;:S= : h.pN w= .N-t=r - + | ||
=: _ .=- -- - | =: _ .=- -- - | ||
M =_=n : .@ = _;;r | M =_=n : .@ = _;;r | ||
:=:_.72 a 3 ==::--.=L _ _.-- _: 1 ::(L. -- - -- | :=:_.72 a 3 ==::--.=L _ _.-- _: 1 ::(L. -- - -- | ||
:: L . r_ - | :: L . r_ - | ||
.= . - - | .= . - - | ||
, = = . - - - | , = = . - - - | ||
q-c.: w% si. p _:==. .- | q-c.: w% si. p _:==. .- | ||
= : ,.3: u .__ _ g ===.u .. = g x = c = _2 = :== - : --- == ====::===r,nu = | = : ,.3: u .__ _ g ===.u .. = g x = c = _2 = :== - : --- == ====::===r,nu = | ||
c =_= | c =_= | ||
~4 | ~4 | ||
:=:- -W= ==5,=n . : ,,,. .a d :cc:-- - :n== -: .;.,_ _ _.:=: n2 : . ._. _== :- | :=:- -W= ==5,=n . : ,,,. .a d :cc:-- - :n== -: .;.,_ _ _.:=: n2 : . ._. _== :- | ||
-4 =v h'_= Kq \gc._=_ : --- __ | -4 =v h'_= Kq \gc._=_ : --- __ | ||
- :== . =: .=+=.-- - | - :== . =: .=+=.-- - | ||
: 2.: - n : | : 2.: - n : | ||
r . . . _w: n = >:'M z o ;r=t:2ca. : ; =. :- | r . . . _w: n = >:'M z o ;r=t:2ca. : ; =. :- | ||
t=.=:= ,g .1 = ::rn:= ...u==l:;===m:x: = =. . .1:___:n-*_ | t=.=:= ,g .1 = ::rn:= ...u==l:;===m:x: = =. . .1:___:n-*_ | ||
. . = = . == = w\. n.s:_= ; 2 =: .- %w\ o = . . _ _ | . . = = . == = w\. n.s:_= ; 2 =: .- %w\ o = . . _ _ | ||
: h. C n ni=:._ ; M .-. . _r. :. x_ b. _. . i. . 2 . T ' E_ _ .='_~__:i. '_~-3. . _ d. _2 | : h. C n ni=:._ ; M .-. . _r. :. x_ b. _. . i. . 2 . T ' E_ _ .='_~__:i. '_~-3. . _ d. _2 | ||
_ . . _ . . . .. _ _ . - ;_ -.. - -- . _ . - _--M. . . _i. r e . N. x .1. si\'~ . | _ . . _ . . . .. _ _ . - ;_ -.. - -- . _ . - _--M. . . _i. r e . N. x .1. si\'~ . | ||
: i. . . . . _. . : ~ '. . . _ . . ' Z :.'L_ . ._. ! (l :" T . * * ' | : i. . . . . _. . : ~ '. . . _ . . ' Z :.'L_ . ._. ! (l :" T . * * ' | ||
| Line 1,212: | Line 730: | ||
l - . _ _l _. _ 4'*J. C . '; : : .1:='m .\ [_\\ . i ._ _. . . | l - . _ _l _. _ 4'*J. C . '; : : .1:='m .\ [_\\ . i ._ _. . . | ||
p.- ;=-i._ . ,- : ==E _i .[- __ +E ==1.1 c= := .! zq_g=g.g='Q$.ig; | p.- ;=-i._ . ,- : ==E _i .[- __ +E ==1.1 c= := .! zq_g=g.g='Q$.ig; | ||
'._._.7. | '._._.7. | ||
~n_ | ~n_ | ||
| Line 1,221: | Line 738: | ||
a' ##. | a' ##. | ||
~'^ ,4l.2'.C.I _ . _ _=_ _ . . _~7_7__ C '" | ~'^ ,4l.2'.C.I _ . _ _=_ _ . . _~7_7__ C '" | ||
.. .. . $ .: ~....~.'l.**l'.$.*_.__4_._____Q.__._.g., | .. .. . $ .: ~....~.'l.**l'.$.*_.__4_._____Q.__._.g., | ||
_ _ .. _m 4_,__. . . | _ _ .. _m 4_,__. . . | ||
: g. __4 . | : g. __4 . | ||
---Q =: '4, -- . 4 =- =. -Q'' . ._ ._ Q;- - t-- 4 :=; | ---Q =: '4, -- . 4 =- =. -Q'' . ._ ._ Q;- - t-- 4 :=; | ||
:-- ;;;; =:_ m .f .: _: n -0 = =o rn-e _. :_6 ___._.A3 w _ ._ .wrn_1,. | :-- ;;;; =:_ m .f .: _: n -0 = =o rn-e _. :_6 ___._.A3 w _ ._ .wrn_1,. | ||
---ee - r -a | ---ee - r -a | ||
--+- 3 =--:f_ == _: . | --+- 3 =--:f_ == _: . | ||
(aA.am=,.Q q g 9 mM4qy wm p 1950 101 | (aA.am=,.Q q g 9 mM4qy wm p 1950 101 | ||
Figure m.2 | Figure m.2 | ||
- --- - --- - -- - - ~ ~ - - ~ - - - -- - - - | - --- - --- - -- - - ~ ~ - - ~ - - - -- - - - | ||
*'t-..;;=-!=__..~+._=.___*.__..__._.__.w___.__._.._._.__.__.'~--~--.__:*..____..______=---- | *'t-..;;=-!=__..~+._=.___*.__..__._.__.w___.__._.._._.__.__.'~--~--.__:*..____..______=---- | ||
. ._. . .L_ _1, | . ._. . .L_ _1, | ||
= = = = _ = = _ = - ._ | = = = = _ = = _ = - ._ | ||
= = = . = | = = = . = | ||
:_ - .: r- 1 rc- - ;____._ _ _. | :_ - .: r- 1 rc- - ;____._ _ _. | ||
*___=.__.__.* --+ - --~ - n r n == = = - r = ._ - . | *___=.__.__.* --+ - --~ - n r n == = = - r = ._ - . | ||
m . | m . | ||
| Line 1,259: | Line 760: | ||
:~ =_=Z=--.~.--."=*_-----~--!ZE=L | :~ =_=Z=--.~.--."=*_-----~--!ZE=L | ||
= = - - . = = _- | = = - - . = = _- | ||
h | h | ||
.- I~~... ~. C "~.~.!~. L~~!---~* !-~~ | .- I~~... ~. C "~.~.!~. L~~!---~* !-~~ | ||
~ | ~ | ||
__.~12 ^*'~-~~~^~!~.~.~~_~^--'.'''*_.. | __.~12 ^*'~-~~~^~!~.~.~~_~^--'.'''*_.. | ||
= ,/' ..z--rL____-~.-----__ _ : = z _*- - n. __ - = = _ _ _ _ _ .___.-_==: . . | = ,/' ..z--rL____-~.-----__ _ : = z _*- - n. __ - = = _ _ _ _ _ .___.-_==: . . | ||
. \ | . \ | ||
. . g((- . __ . _ -_ _;-]*_..___.__._._.__. | |||
. . g | |||
- : --' -'- - -{ =C = -~ Q C = =T Z ; -_ ._ " -- . . _ . ..- | - : --' -'- - -{ =C = -~ Q C = =T Z ; -_ ._ " -- . . _ . ..- | ||
. _ _ = . _ _ . | . _ _ = . _ _ . | ||
= __.===:= ..- - | = __.===:= ..- - | ||
l __. ..- . ..: n\71 \ u\ -s \ \\ =rnanx=:=_____._ _ ___._- _ - - - + - - _._ _ __;L__._ = = _. K 7 ----*--*-~*'-----*~_.-.-* *--- - : _. ____~..__ | l __. ..- . ..: n\71 \ u\ -s \ \\ =rnanx=:=_____._ _ ___._- _ - - - + - - _._ _ __;L__._ = = _. K 7 ----*--*-~*'-----*~_.-.-* *--- - : _. ____~..__ | ||
* M T- | * M T- | ||
_ _ ..-..{ ii_ _:'.a. _ \ ?[N\ _ . . _ _ _ _ _ . _ . - . ' . " _~ | _ _ ..-..{ ii_ _:'.a. _ \ ?[N\ _ . . _ _ _ _ _ . _ . - . ' . " _~ | ||
i : ---.= .. _2\ | i : ---.= .. _2\ | ||
'v.~=. s.'. &. , ' ?. =. . __~_~. .__ __. ._ :- | 'v.~=. s.'. &. , ' ?. =. . __~_~. .__ __. ._ :- | ||
: ~~__.__._______=--_i.=___=__J.__.:._=_-.. | : ~~__.__._______=--_i.=___=__J.__.:._=_-.. | ||
E | E | ||
_ = = = = . _ = . = . _ = _ . . _ = _ . ._: | _ = = = = . _ = . = . _ = _ . . _ = _ . ._: | ||
= =1 | = =1 | ||
._c_. n.g __:. | ._c_. n.g __:. | ||
y w__. 4n.j.= = _w. ._ _=.=. . . _ . - | y w__. 4n.j.= = _w. ._ _=.=. . . _ . - | ||
- ~ ~ - - | - ~ ~ - - | ||
V U_T.-m iu .:'._.M,)T...\$,\ - _E- i.- | V U_T.-m iu .:'._.M,)T...\$,\ - _E- i.- | ||
~22=____~~"-= . . _ . - | ~22=____~~"-= . . _ . - | ||
. 4 _- _ _. | . 4 _- _ _. | ||
.n b | .n b | ||
-g.g m | -g.g m | ||
p.-.o~ M.- .__ | p.-.o~ M.- .__ | ||
e = & -- . . q#m = | e = & -- . . q#m = | ||
=-- _s4=-____.___. = _ - | =-- _s4=-____.___. = _ - | ||
M_ - | M_ - | ||
| Line 1,324: | Line 794: | ||
:1 - no. n =.. | :1 - no. n =.. | ||
tr:n n - . ..xt br .-.kh=__=_. _ r | tr:n n - . ..xt br .-.kh=__=_. _ r | ||
_r--------~ = _ - - r nx_= _.3 ' | _r--------~ = _ - - r nx_= _.3 ' | ||
d e ---- --- - - - - - | d e ---- --- - - - - - | ||
| Line 1,331: | Line 800: | ||
* : r :T4 nr | * : r :T4 nr | ||
.. __ __ z. .__ . _ . 4 -\in\ : 4% r r 4%g\r | .. __ __ z. .__ . _ . 4 -\in\ : 4% r r 4%g\r | ||
.__. r :----" - . . | .__. r :----" - . . | ||
. - . r_.__In = = ._ __ 1- = J | . - . r_.__In = = ._ __ 1- = J | ||
| Line 1,337: | Line 805: | ||
+ ---~ - nn _ n = r r- ". | + ---~ - nn _ n = r r- ". | ||
* rz r = n. = ._ . . _. | * rz r = n. = ._ . . _. | ||
y __ ;,_ . g_._ _ _. _ _ _ _ _ . _ _ . _ . _ .- _ | y __ ;,_ . g_._ _ _. _ _ _ _ _ . _ _ . _ . _ .- _ | ||
4s | 4s | ||
' ==. c : = _ _ _ | ' ==. c : = _ _ _ | ||
n- - | n- - | ||
. == : ._ . =. :_ = - - | . == : ._ . =. :_ = - - | ||
.= nh. . -- _=__. : = = 1 __ =-\r..g ._ = +. . :\.w=:\ _= ~t ~K \ A:._ | .= nh. . -- _=__. : = = 1 __ =-\r..g ._ = +. . :\.w=:\ _= ~t ~K \ A:._ | ||
g - u- _-_.- ._. --- - - - - - - - | g - u- _-_.- ._. --- - - - - - - - | ||
_2_ = = _;; - | _2_ = = _;; - | ||
r- n Q = g =.. - ..._pt-- | r- n Q = g =.. - ..._pt-- | ||
.p. \t_. - | .p. \t_. - | ||
__.__._:____. ._ _ ..___: - - :_- r . | __.__._:____. ._ _ ..___: - - :_- r . | ||
g | g | ||
_9- _ _. _ _ .__ _ | _9- _ _. _ _ .__ _ | ||
r . V=( . == 1 c =-& 1._ a. ..._.. 1 ,%._ _. _ | r . V=( . == 1 c =-& 1._ a. ..._.. 1 ,%._ _. _ | ||
. . _ . . :- -- 1: - | . . _ . . :- -- 1: - | ||
;==_ ..a= :=- ~= _.. $ ==== A= _:m_g===-Lgw_. ._ | ;==_ ..a= :=- ~= _.. $ ==== A= _:m_g===-Lgw_. ._ | ||
-------,-_:--,=_=x... | -------,-_:--,=_=x... | ||
_=--. - | _=--. - | ||
=-- = = = . -- | =-- = = = . -- | ||
. _;_ w 3 _. . | . _;_ w 3 _. . | ||
e ., | e ., | ||
. . _ _ .1-_h- - - - - - - - -- | . . _ _ .1-_h- - - - - - - - -- | ||
% h | % h | ||
_j_;=:Qu(=t'4t4p:s: % --- n--=---- - .- : -- - -- __n.__.;=------- - -- . ._ | _j_;=:Qu(=t'4t4p:s: % --- n--=---- - .- : -- - -- __n.__.;=------- - -- . ._ | ||
t: Lax: __ ___ g =2. _ =- - | t: Lax: __ ___ g =2. _ =- - | ||
1.Lr:=r = = =%g = ==_ : .- -- | 1.Lr:=r = = =%g = ==_ : .- -- | ||
= = = = . = | = = = = . = | ||
== ; n - n\- ===\=\====_m\;s t 1\=- : _- ._ _ _ _ _: _ __ n --- :- : : - - r_. - | == ; n - n\- ===\=\====_m\;s t 1\=- : _- ._ _ _ _ _: _ __ n --- :- : : - - r_. - | ||
w: | w: | ||
r2-rm ..=z == ==r y==4: um_w_._.4=.=g --- 5 _tex=tntt. . w --- :===.=n:-- =- . | r2-rm ..=z == ==r y==4: um_w_._.4=.=g --- 5 _tex=tntt. . w --- :===.=n:-- =- . | ||
| Line 1,392: | Line 843: | ||
;- .:rn :-Q.t; rn1bg==22: ==i: | ;- .:rn :-Q.t; rn1bg==22: ==i: | ||
t= =- r- t-\r=h=\ \--\ -t:% .tX r _ ---+- -- - -- - - - - - - - - | t= =- r- t-\r=h=\ \--\ -t:% .tX r _ ---+- -- - -- - - - - - - - - | ||
_9 0 t == = = :_ | _9 0 t == = = :_ | ||
, ----- nt__.V v +-- q;t a- ._: r - - - ; _. __ = - | , ----- nt__.V v +-- q;t a- ._: r - - - ; _. __ = - | ||
-3r. | -3r. | ||
-~ --- | -~ --- | ||
t ==u ==_ .Q.===. rq . G_.= : Q =__ | t ==u ==_ .Q.===. rq . G_.= : Q =__ | ||
. _. - _ \. n; -------_:---=2. | . _. - _ \. n; -------_:---=2. | ||
- m,a | - m,a | ||
. g | . g | ||
| Line 1,409: | Line 854: | ||
7 J, _ . __ . . g=_ = m -Wr__.: . ._._-- .._.p_....g_=__:__-_-____.__.__ | 7 J, _ . __ . . g=_ = m -Wr__.: . ._._-- .._.p_....g_=__:__-_-____.__.__ | ||
g_ ..__t=_t.,- .g | g_ ..__t=_t.,- .g | ||
_. _ ._._ . :1__.__. . | _. _ ._._ . :1__.__. . | ||
r - - | r - - | ||
S. | S. | ||
-' ' -- - b C*d . 1._. . . . M _ g -~=!7 -- ~~-" "--* *h~g\ T T A : S.. :--,2- --_**_2:(ri_--.Y._1____ ~ | -' ' -- - b C*d . 1._. . . . M _ g -~=!7 -- ~~-" "--* *h~g\ T T A : S.. :--,2- --_**_2:(ri_--.Y._1____ ~ | ||
e ... _. . _ __ ___-:---- nn;. C * ,_ _ . . _ . - - -- ;_ . _ | e ... _. . _ __ ___-:---- nn;. C * ,_ _ . . _ . - - -- ;_ . _ | ||
V | V | ||
: =x 1.g= nr . __:- _- r_ - | : =x 1.g= nr . __:- _- r_ - | ||
--Q | --Q tt ==rg: =a.g :--==D. g = ~ 4'4 =- ---~ =W.g==:.t x tb\ =- : := =:==== =x __r 1. - | ||
tt ==rg: =a.g :--==D. g = ~ 4'4 =- ---~ =W.g==:.t x tb\ =- : := =:==== =x __r 1. - | |||
.._ _x: = ==+ = s _- ; s= v .y v = r== : ==.. :== r- . | .._ _x: = ==+ = s _- ; s= v .y v = r== : ==.. :== r- . | ||
o | o | ||
*: .m | *: .m | ||
| Line 1,432: | Line 868: | ||
: = _. =.==$ - - v, . . - - ~ t------ - | : = _. =.==$ - - v, . . - - ~ t------ - | ||
y _ . _ _ . ---\. 3: \n\. - --------. . -._____ - | y _ . _ _ . ---\. 3: \n\. - --------. . -._____ - | ||
=, . _ . | =, . _ . | ||
. . __n- .-... | . . __n- .-... | ||
._.~a... | ._.~a... | ||
. ,g.q. - | . ,g.q. - | ||
p p a--.$:- .n_C. | p p a--.$:- .n_C. | ||
.m _. ,,-._ . . . . | .m _. ,,-._ . . . . | ||
.._._...__.____n__g_...._.s..._. | .._._...__.____n__g_...._.s..._. | ||
g\rny- :._.___:=...=._-=..---.-.- | g\rny- :._.___:=...=._-=..---.-.- | ||
g sM %=r==z s =- ===w - | g sM %=r==z s =- ===w - | ||
:=1uJmg-r-- | :=1uJmg-r-- | ||
: V 2==w. | : V 2==w. | ||
n = - MQ3==-::=r_ | n = - MQ3==-::=r_ | ||
| Line 1,458: | Line 883: | ||
=n =- r=;r;mwe~.. _ . =. .=_x =,\ =.\. .v = | =n =- r=;r;mwe~.. _ . =. .=_x =,\ =.\. .v = | ||
=. - d h=. v: | =. - d h=. v: | ||
=== r- :_2_ =_ :- -- - | === r- :_2_ =_ :- -- - | ||
=== = | === = | ||
g-- | g-- | ||
9 y : = 4: | 9 y : = 4: | ||
r=- y _;"_cP a =___._ -~ : ot_. nn -- ---- :=_ _=.r --- g21 2 | r=- y _;"_cP a =___._ -~ : ot_. nn -- ---- :=_ _=.r --- g21 2 | ||
| Line 1,470: | Line 892: | ||
.__ u = :_ | .__ u = :_ | ||
n---- -- - - ... _ e | n---- -- - - ... _ e | ||
- :--- . | - :--- . | ||
* r - . . 2. . | * r - . . 2. . | ||
| Line 1,476: | Line 897: | ||
- ._ . _._. m - ._= =_. _= _ ._ ._ = .:_.= __ . ,\_nN: =2_ xb= % : . | - ._ . _._. m - ._= =_. _= _ ._ ._ = .:_.= __ . ,\_nN: =2_ xb= % : . | ||
= .= = ===-.;.2=====. : | = .= = ===-.;.2=====. : | ||
7____ .. _ e._,;__.....x...g......._ | 7____ .. _ e._,;__.....x...g......._ | ||
,---. n ;. . . . _ = . . ?g . . a '- -- | ,---. n ;. . . . _ = . . ?g . . a '- -- | ||
=..--_...=_ _. = = . . _. 1 r._. 4 :&c:=t ra. ._1. : . ._ =. | =..--_...=_ _. = = . . _. 1 r._. 4 :&c:=t ra. ._1. : . ._ =. | ||
==. . . | ==. . . | ||
=- " | =- " | ||
_,--- ~ggi id=Q [=-J : - $-pj~].j Q--- 9= - . | _,--- ~ggi id=Q [=-J : - $-pj~].j Q--- 9= - . | ||
-5 E: i ;r; | -5 E: i ;r; b | ||
i \ M1 @h Q.f- r . ._ . . | |||
1. | 1. | ||
, -: j. , _ | , -: j. , _ | ||
,=:sy s=s=====v= - e.74=g= swww= r- - ;= , | ,=:sy s=s=====v= - e.74=g= swww= r- - ;= , | ||
k _._.. ..s T: __. j r | k _._.. ..s T: __. j r | ||
.=. | .=. | ||
_..2:_..=.,a | _..2:_..=.,a | ||
: 1: : | : 1: : | ||
,.-.r=c=.w m _.v.o_._,o._----.__._ | ,.-.r=c=.w m _.v.o_._,o._----.__._ | ||
_- g ;-- no _ _. _.g: - ~ | _- g ;-- no _ _. _.g: - ~ | ||
..= _ .. | ..= _ .. | ||
_ _. . y . s - .2 | _ _. . y . s - .2 4_. - -. | ||
4_. - -. | |||
4..4:..=_i- y = w .9 rs -. ._ | 4..4:..=_i- y = w .9 rs -. ._ | ||
g a. _=_qm.= m, - g, _r_.: .m 4-: r,_j. r. | g a. _=_qm.= m, - g, _r_.: .m 4-: r,_j. r. | ||
syg.>p~.2 n a ~a-w mw.e 1950 10, | syg.>p~.2 n a ~a-w mw.e 1950 10, | ||
. s.- | . s.- | ||
Figure A-3 | Figure A-3 | ||
'---2 | '---2 | ||
-------.-----:--}-- | -------.-----:--}-- | ||
-----~..._._..------.-*--- | -----~..._._..------.-*--- | ||
. _ . _ _ ._ =. - ~ - - | . _ . _ _ ._ =. - ~ - - | ||
__ ~ --_ = 7 T~~__...__.__. | __ ~ --_ = 7 T~~__...__.__. | ||
| Line 1,546: | Line 930: | ||
~~ ~ | ~~ ~ | ||
* = ~ ~ ~ ~ ' = ~ ~ ~ ~ ~ . :-T~~ | * = ~ ~ ~ ~ ' = ~ ~ ~ ~ ~ . :-T~~ | ||
%~ | %~ | ||
.i- .__ .y" - - ' .-_ - . . _ _-.__ | .i- .__ .y" - - ' .-_ - . . _ _-.__ | ||
-t= -- __.._._ | -t= -- __.._._ | ||
.__ _ . _ . _ _ . _ _ _ _ . - . = _ = _ _ . - _ _ - _ . _ _ . - - _ _ . _ _q_+ | .__ _ . _ . _ _ . _ _ _ _ . - . = _ = _ _ . - _ _ - _ . _ _ . - - _ _ . _ _q_+ | ||
4 | 4 | ||
._=.___ | ._=.___ | ||
= ' =;' -- E " C I C '. " ' Z ~~ # | = ' =;' -- E " C I C '. " ' Z ~~ # | ||
'_. T --- > | '_. T --- > | ||
=__ ~=_. - _. .= "'i;. E_ F.r2 . =_= { H_ 1_.=___._.-._'~._'___.-._--'_.2C-- | =__ ~=_. - _. .= "'i;. E_ F.r2 . =_= { H_ 1_.=___._.-._'~._'___.-._--'_.2C-- | ||
~- =_ E1_. =_a_ _ - _ | ~- =_ E1_. =_a_ _ - _ | ||
o w.. _ ___..._-=__. ,=. a., m)_ e. =-=.==_a_=._=._..=n.--- . | o w.. _ ___..._-=__. ,=. a., m)_ e. =-=.==_a_=._=._..=n.--- . | ||
':_?- | ':_?- | ||
'^ | '^ | ||
*} '''~~~--^T.~~ .--y_;.~_.-._ _____ y | *} '''~~~--^T.~~ .--y_;.~_.-._ _____ y | ||
'.'~_~_-''--'-*~ | '.'~_~_-''--'-*~ | ||
M-._ | M-._ | ||
====___=-____ __ __--_~ ___ v | ====___=-____ __ __--_~ ___ v n _= | ||
n _= | |||
-- -. n _-__l- _ _ . - . . _ ., . . _ _ - _ _ . . _ . _ . . . _ _ _ - - _ - _ - - - - . - - | -- -. n _-__l- _ _ . - . . _ ., . . _ _ - _ _ . . _ . _ . . . _ _ _ - - _ - _ - - - - . - - | ||
== | == | ||
i = .=. ,==m=g wm=-a . | i = .=. ,==m=g wm=-a . | ||
====s _. __ - 16 | ====s _. __ - 16 | ||
= = == = =w ==- | = = == = =w ==- | ||
-.=m.__=_.._.____==._-== | -.=m.__=_.._.____==._-== | ||
=u=_ | =u=_ | ||
Ti | Ti | ||
===--.- | ===--.- | ||
,_1 . -- m ss %- ' " " | ,_1 . -- m ss %- ' " " | ||
-- % '_ a _._g-__.-_.__--_..-___.__:. . - _ - _ . - . . . - - . - . _ - _ . . . - . - - _ . . - _ _ . . | -- % '_ a _._g-__.-_.__--_..-___.__:. . - _ - _ . - . . . - - . - . _ - _ . . . - . - - _ . . - _ _ . . | ||
_-=__..-__.a=~.-a_ =_%~_------ -- - - - - - -- | _-=__..-__.a=~.-a_ =_%~_------ -- - - - - - -- | ||
=^ - ~ ~ | =^ - ~ ~ | ||
___ . _. ._y _ ,_. _, s... | ___ . _. ._y _ ,_. _, s... | ||
_. -_ =L | _. -_ =L | ||
'' W ~ - ~ _ " ' - ' - ~ ~ ' ' ' - ~ ~ ~ ~ -.r --%r._ _r-~_ ~ ~ - - - | '' W ~ - ~ _ " ' - ' - ~ ~ ' ' ' - ~ ~ ~ ~ -.r --%r._ _r-~_ ~ ~ - - - | ||
Q | Q | ||
~~~ . | ~~~ . | ||
E;$C_ _.-A _ l _ _. . | E;$C_ _.-A _ l _ _. . | ||
'cr- _ .E=- | 'cr- _ .E=- | ||
~ ' ' ' | ~ ' ' ' | ||
==? 3- -q A-- \=.g,4 _== :p == ;= == . .. ,._. -- - | ==? 3- -q A-- \=.g,4 _== :p == ;= == . .. ,._. -- - | ||
| Line 1,621: | Line 973: | ||
- . . _ _ _-_.-..._s_y__ , | - . . _ _ _-_.-..._s_y__ , | ||
g _ . _y ,. | g _ . _y ,. | ||
. . . _ . _ ._._ V._W s . . _ . . . . _ . _ _ --- ;_ ; _ . . _ . _ _ . _ _ . . _ _ . ._ _ . _ . -%3-- | . . . _ . _ ._._ V._W s . . _ . . . . _ . _ _ --- ;_ ; _ . . _ . _ _ . _ _ . . _ _ . ._ _ . _ . -%3-- | ||
________-_h o $ -~-~; | |||
________-_h | |||
o $ -~-~; | |||
_ _ _ _ -__ c __ \_.._..-..____.---.N.--__..___-.-.___- | _ _ _ _ -__ c __ \_.._..-..____.---.N.--__..___-.-.___- | ||
,e g. | ,e g. | ||
__ e . < _._ _.______-__''_ _ _~ _ q-._ ;. | __ e . < _._ _.______-__''_ _ _~ _ q-._ ;. | ||
s | s | ||
. __m_ "1____. | . __m_ "1____. | ||
M.._._._.-. | M.._._._.-. | ||
, ._____.._ \ 4..-___--. | , ._____.._ \ 4..-___--. | ||
w | w m. | ||
m. | |||
a .-.=. - _ | a .-.=. - _ | ||
os= | os= | ||
u._== v= x-. _-..=_-.r-- _+w | u._== v= x-. _-..=_-.r-- _+w | ||
= . _ _ _ . . _ _ . _ _ _ - - __-____-...- =_ s =. . | = . _ _ _ . . _ _ . _ _ _ - - __-____-...- =_ s =. . | ||
=m | =m | ||
, _ . . . _ . _ - _ . . x _ r _-. | , _ . . . _ . _ - _ . . x _ r _-. | ||
m _. - - - . . | m _. - - - . . | ||
^ -- | ^ -- | ||
| Line 1,669: | Line 997: | ||
. = Q5 .5 | . = Q5 .5 | ||
= .s =C=- a == - w | = .s =C=- a == - w | ||
=t.mch -e r== _ =. . _ _ __ _r=_r; ZG - =E | =t.mch -e r== _ =. . _ _ __ _r=_r; ZG - =E | ||
\ | \ | ||
EM~ - * =_ _'~.Z _ | EM~ - * =_ _'~.Z _ | ||
: 1. . l_ .-A~Y% : _.- . . _ __ _. _ . - _ _ . . __ _ _ _ , . | : 1. . l_ .-A~Y% : _.- . . _ __ _. _ . - _ _ . . __ _ _ _ , . | ||
___y FMG2. . | ___y FMG2. . | ||
___________..t 9 n | ___________..t 9 n | ||
_=___m pa_=m ___s-1_1- -N.__.._.__..______ | _=___m pa_=m ___s-1_1- -N.__.._.__..______ | ||
r= ,4_. _. _ _ . . _ | r= ,4_. _. _ _ . . _ | ||
5_4 _.g ==_ :- --- - _= g ===r n:_=y_ p -- - - - - - - - - | 5_4 _.g ==_ :- --- - _= g ===r n:_=y_ p -- - - - - - - - - | ||
= - - - | = - - - | ||
__q_ =; | __q_ =; | ||
= =_; | = =_; | ||
(~ w .__ m _- c w_.m_=._ -_ - | (~ w .__ m _- c w_.m_=._ -_ - | ||
r== -- -- | r== -- -- | ||
,-._w _ _ _._ _ | ,-._w _ _ _._ _ | ||
= r. .=_-. - % =; | = r. .=_-. - % =; | ||
- a =.m, g --z ._ . .._ _ = | - a =.m, g --z ._ . .._ _ = | ||
=- | =- | ||
-_4_ _ | -_4_ _ | ||
\ _1_A __ _ _ | \ _1_A __ _ _ | ||
. _ _ _ - .__= | . _ _ _ - .__= | ||
= == .3c, : | = == .3c, : | ||
@N __ _ . -. 3 E~Yt-zm= N=S $x--~ - - - - - - - | @N __ _ . -. 3 E~Yt-zm= N=S $x--~ - - - - - - - | ||
?= = | ?= = | ||
g g=.w u | g g=.w u | ||
=" _- +- . 4 .4.=_- | =" _- +- . 4 .4.=_- | ||
-- c aqm: % g: . A | -- c aqm: % g: . A | ||
:)== -: Q ._- - 1.-.t- s _ __ | :)== -: Q ._- - 1.-.t- s _ __ | ||
S _~~~~.. - | S _~~~~.. - | ||
_ k . .Y . . _YY Y--' ~ | _ k . .Y . . _YY Y--' ~ | ||
| Line 1,725: | Line 1,030: | ||
.C, n - =. | .C, n - =. | ||
g . _. p. . g yy_ _ c. ._:.._._w | g . _. p. . g yy_ _ c. ._:.._._w | ||
: 9. _y_ . ..m.m . __g =_ _ g m__-- _ =. . ._ _ ._ | : 9. _y_ . ..m.m . __g =_ _ g m__-- _ =. . ._ _ ._ | ||
s 2 | s 2 | ||
M F- q b' :~~ -' '. ._-. -_- g.,m_ rt, _: 2 D 1-_ _- t) i .. . _- =. .k=-.o W S_~~ N. .'s~iE. ~c' _~ ~._--*_ _-- _-- - - "--_ = :' =. l , fs ' ~ ~ " | M F- q b' :~~ -' '. ._-. -_- g.,m_ rt, _: 2 D 1-_ _- t) i .. . _- =. .k=-.o W S_~~ N. .'s~iE. ~c' _~ ~._--*_ _-- _-- - - "--_ = :' =. l , fs ' ~ ~ " | ||
% w ~~ q z. :% - - - ---- Q l _.- L. _.- O ' ~ - - n "D ;z Jbyy'a="'"'\ --- - - - - - - | % w ~~ q z. :% - - - ---- Q l _.- L. _.- O ' ~ - - n "D ;z Jbyy'a="'"'\ --- - - - - - - | ||
.Q = :_=:-~ - ~ ~ ~ | .Q = :_=:-~ - ~ ~ ~ | ||
Ce - ' 2 0** a'r- | Ce - ' 2 0** a'r- | ||
'.=. _ EM . 9 _ 2 -..y__ ~M_--_--__________-__-.>___. | '.=. _ EM . 9 _ 2 -..y__ ~M_--_--__________-__-.>___. | ||
C4Q . _1- ~ ~1- _ ___ - e . . _ . - t _=_c g . _ _ . . . .g--_..;_ .. | C4Q . _1- ~ ~1- _ ___ - e . . _ . - t _=_c g . _ _ . . . .g--_..;_ .. | ||
~- :_ -.-6r .z= s _ | ~- :_ -.-6r .z= s _ | ||
= | = | ||
"e . | "e . | ||
" ~ ' | " ~ ' | ||
i t_.,.__ \=nr_= \ -- 4,__ | i t_.,.__ \=nr_= \ -- 4,__ | ||
._ ---=1== __ | ._ ---=1== __ | ||
__g g - N -._- _ =__=i. = . _ . _-_,=_ ._ - - __=_c_=, _= _= r._\r.r _= - . _ _- \=:r.___h_..=._- =___=__ = rr _r o g C==2 | |||
__g g - N -._- _ =__=i. = . _ . _-_,=_ ._ - - __=_c_=, _= _= r._\r.r _= - . _ _- \=:r.___h_..=._- =___=__ = rr _r o | |||
g C==2 | |||
-._.:E 55___. =-a.____, -TA__ g,__u - $-- _ _ ,__._{RE __ =1__ ; ___. | -._.:E 55___. =-a.____, -TA__ g,__u - $-- _ _ ,__._{RE __ =1__ ; ___. | ||
_ ; ? 4 --i == | _ ; ? 4 --i == | ||
w_=.-..=_.._u._=..=_..___ | w_=.-..=_.._u._=..=_..___ | ||
___g__.____ _ -_, ==\ _ _ _ - - _ _ _ _= _=- == | ___g__.____ _ -_, ==\ _ _ _ - - _ _ _ _= _=- == | ||
_ .E.== - | _ .E.== - | ||
= cau.= r ==_g== w= , | = cau.= r ==_g== w= , | ||
.-- ='#. M 5 ~ 5 NT=_I5 "-i"---5'N. _ _-N1.i'~~~-~Y-'-3EE5- i' _ n - J _i5 | .-- ='#. M 5 ~ 5 NT=_I5 "-i"---5'N. _ _-N1.i'~~~-~Y-'-3EE5- i' _ n - J _i5 | ||
: =. == _ g 7.= ;_= - - - - | : =. == _ g 7.= ;_= - - - - | ||
4.==. _=\ ; ; g =:3=_._g __ . n - 7 =- | 4.==. _=\ ; ; g =:3=_._g __ . n - 7 =- | ||
- . . _ - _ . . . _ . = = .._==;_,= | - . . _ - _ . . . _ . = = .._==;_,= | ||
= =. = - . _ _ . ___ -7 _.,_ -,,, _ - , + - _ __ _ - + _ | = =. = - . _ _ . ___ -7 _.,_ -,,, _ - , + - _ __ _ - + _ | ||
--....n._ . _ . - - | --....n._ . _ . - - | ||
_ -. _ _ _ . _.___.--..g-.__.__.,__.__.., .._._._g | _ -. _ _ _ . _.___.--..g-.__.__.,__.__.., .._._._g | ||
-_ = = . = . - | -_ = = . = . - | ||
.__ ,= -.. | .__ ,= -.. | ||
= | = | ||
==m. . _ _ _ .m. =E _ m_ m == | ==m. . _ _ _ .m. =E _ m_ m == | ||
- h .W?- ~ -51_ E=3E:M ? ^";~;~~- - E l-~~$l | - h .W?- ~ -51_ E=3E:M ? ^";~;~~- - E l-~~$l | ||
~ | ~ | ||
~ | ~ | ||
c _ _ m =x.. | c _ _ m =x.. | ||
~"^^~T~ | ~"^^~T~ | ||
= | = | ||
: s. _ E ., | : s. _ E ., | ||
= | = | ||
"l- .d $_ __ - 55 | "l- .d $_ __ - 55 | ||
*Q r -s. ''. =E--;i: E_ . ~. _~=2 W, ,-_ _ x-O= 9. m. | *Q r -s. ''. =E--;i: E_ . ~. _~=2 W, ,-_ _ x-O= 9. m. | ||
'_E_E_*.. . _==__A, .---,._ 7 n._w.__,__. L t ^ -~.a" ^_. ' ' - . _ _ . | '_E_E_*.. . _==__A, .---,._ 7 n._w.__,__. L t ^ -~.a" ^_. ' ' - . _ _ . | ||
: s. w m.m. _m. _. + __ _ | : s. w m.m. _m. _. + __ _ | ||
-___._=. | -___._=. | ||
, = = | , = = | ||
= :wmm=mm==n =~-- . . . _ - | = :wmm=mm==n =~-- . . . _ - | ||
=_ =a_=. -- | =_ =a_=. -- | ||
1950 iM | 1950 iM | ||
O | O | ||
, e # | , e # | ||
s Figure A-4 e | |||
Figure A-4 | |||
e | |||
: "-- 1*- _. '!-- .7*J | : "-- 1*- _. '!-- .7*J | ||
~. * ;.I._ - | ~. * ;.I._ - | ||
= ~y=- ~~ i = =:== : E =.=^ _~~- ~.% _: . - | = ~y=- ~~ i = =:== : E =.=^ _~~- ~.% _: . - | ||
^ | ^ | ||
C ^ ^R= . . | C ^ ^R= . . | ||
_. _ ~&~ _2-~ q = -. -_ ._ _ | _. _ ~&~ _2-~ q = -. -_ ._ _ | ||
.T_^.'= 9 | .T_^.'= 9 | ||
._ _ . . N | ._ _ . . N | ||
- . , _ . .* -e._ _= | - . , _ . .* -e._ _= | ||
_ . _ . . _ -_ e__.g._wo.-a - - - .*.-=.e_'e.-_a- - = | _ . _ . . _ -_ e__.g._wo.-a - - - .*.-=.e_'e.-_a- - = | ||
.__ . L -_-.u n h =. ' f =__ i-j =3.=.a.=_:- - _ ; i _ - .. ._ . .i_:___ :} | .__ . L -_-.u n h =. ' f =__ i-j =3.=.a.=_:- - _ ; i _ - .. ._ . .i_:___ :} | ||
_ :.g[ ._.____ _ | _ :.g[ ._.____ _ | ||
= = - - - = | = = - - - = | ||
- ' : ' . . ' T r - -** --'_' -~~- .L '. : -- _:n--* | - ' : ' . . ' T r - -** --'_' -~~- .L '. : -- _:n--* | ||
| Line 1,862: | Line 1,103: | ||
* _ : - -~2 :: ---_- 7 _ | * _ : - -~2 :: ---_- 7 _ | ||
Eb .3. 5; *- --* --- ~~~_Y. 5-~ ._ ['_._~ i-_ _[ ; __, b -- k g | Eb .3. 5; *- --* --- ~~~_Y. 5-~ ._ ['_._~ i-_ _[ ; __, b -- k g | ||
_ _ . _ _ _ _ _ ___.)- _ _ _ _ _ . ._ . . - - ^ '~ | _ _ . _ _ _ _ _ ___.)- _ _ _ _ _ . ._ . . - - ^ '~ | ||
*----~----*--:'_.______._.._. | *----~----*--:'_.______._.._. | ||
.___._-M-H . 5$ | |||
.___._-M- | |||
H . 5$ | |||
~ ^ | ~ ^ | ||
Gi^E::= - i =55:E EE E '==33 5 " ^f E~ = i= '-~--#=b-~E *i: ^=~-$ f ~~~ =D 2 - f F - - - F '- 3 -~~r r : ' ___ - ,,= . _ | Gi^E::= - i =55:E EE E '==33 5 " ^f E~ = i= '-~--#=b-~E *i: ^=~-$ f ~~~ =D 2 - f F - - - F '- 3 -~~r r : ' ___ - ,,= . _ | ||
| Line 1,886: | Line 1,111: | ||
-._=_____ y_ _ _g | -._=_____ y_ _ _g | ||
_- . - _ _ . _ _ _ ..__.L_____._-__.- _ . . - | _- . - _ _ . _ _ _ ..__.L_____._-__.- _ . . - | ||
.i..i..._.g,, | .i..i..._.g,, | ||
l-._'..---*---_----.= ..- . } | l-._'..---*---_----.= ..- . } | ||
| Line 1,893: | Line 1,116: | ||
~*----____.:,..*_--Q-- | ~*----____.:,..*_--Q-- | ||
g_ | g_ | ||
_ . _^ . . | _ . _^ . . | ||
I | I | ||
,,--------"-----------]--._:.._. -. . % -5 | ,,--------"-----------]--._:.._. -. . % -5 y..---__w... _ _ _ ..L- | ||
y..---__w... _ _ _ ..L- | |||
. . _ .- ~ n: _;._ g -_. . _ _ - . | . . _ .- ~ n: _;._ g -_. . _ _ - . | ||
- - = :. ; -==.---;..---~_---' | - - = :. ; -==.---;..---~_---' | ||
[ :=';;r =="- Ef - .T_f]E i=:==f :=. --- | [ :=';;r =="- Ef - .T_f]E i=:==f :=. --- | ||
-- 1*_ , __ g___;. | -- 1*_ , __ g___;. | ||
f = % ==i o -- . _ _ - | f = % ==i o -- . _ _ - | ||
=rr --~ z____ _ . _ _ _ _ _ _ _ _ - . _ - - | =rr --~ z____ _ . _ _ _ _ _ _ _ _ - . _ - - | ||
p- u t-- ._.y__ _ _ _ . . _ _ ..=1 r=2 -rd. :: -. n --- --~. r::=r-- r . _r | p- u t-- ._.y__ _ _ _ . . _ _ ..=1 r=2 -rd. :: -. n --- --~. r::=r-- r . _r It) m p._. __-._..--%.__.._ | ||
It) m p._. __-._..--%.__.._ | |||
.. D ---2 | .. D ---2 | ||
--~_.- - - - - - *--- | --~_.- - - - - - *--- | ||
w t-~.___ _ = n' ..,.= | w t-~.___ _ = n' ..,.= | ||
g _ . =__.__--_law = . __ _ _ _- _=__= _=._==_w__.__=_.- --_-=_g_ _ . _ _ n_ g z_. | g _ . =__.__--_law = . __ _ _ _- _=__= _=._==_w__.__=_.- --_-=_g_ _ . _ _ n_ g z_. | ||
~_ _y__._ | ~_ _y__._ | ||
~--'_.__T---:- _ _ | ~--'_.__T---:- _ _ | ||
_ _ _ . _..M.'.--* | _ _ _ . _..M.'.--* | ||
tr_. _ MF_j ! i | tr_. _ MF_j ! i | ||
__ y.s., | __ y.s., | ||
_v v_ .m | _v v_ .m | ||
_ _ h | _ _ h | ||
= _ _ _ _ ___ - . | = _ _ _ _ ___ - . | ||
p_ E_=. _== ==%_ = %= ,.W____. __ ___- ___- _9 = ~R u m._ .;_._1+ | p_ E_=. _== ==%_ = %= ,.W____. __ ___- ___- _9 = ~R u m._ .;_._1+ | ||
w p__ __ .- . . =u yn | w p__ __ .- . . =u yn | ||
=_:=.=:---------____:- | =_:=.=:---------____:- | ||
. _ _ __ rn 3.,s 4 E 2~-f # | |||
. _ _ __ rn | |||
3.,s 4 E 2~-f # | |||
E'- . __ ._.J - N _._.__.__. | E'- . __ ._.J - N _._.__.__. | ||
,.__.___._r_ . | ,.__.___._r_ . | ||
~~=- | ~~=- | ||
.4 F - | .4 F - | ||
| Line 1,976: | Line 1,150: | ||
= | = | ||
T :_-- | T :_-- | ||
_._q.=----- | _._q.=----- | ||
3 _._ - | 3 _._ - | ||
y__ - a a -r=._=_ | y__ - a a -r=._=_ | ||
- - _. -M4..____.___._.__.. | - - _. -M4..____.___._.__.. | ||
b :- -=Eh-5 N | b :- -=Eh-5 N | ||
--] f 3,_ p- | --] f 3,_ p- | ||
.q - . | .q - . | ||
j E==_ y g=Ei $_ _ _._ ._- =:- - - 1 M_._ _=- | j E==_ y g=Ei $_ _ _._ ._- =:- - - 1 M_._ _=- | ||
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b_.__- __ n , | b_.__- __ n , | ||
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Latest revision as of 00:07, 28 February 2020
| ML19260D869 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 01/31/1980 |
| From: | BABCOCK & WILCOX CO. |
| To: | |
| Shared Package | |
| ML19260D868 | List: |
| References | |
| TAC-45218, NUDOCS 8002120531 | |
| Download: ML19260D869 (32) | |
Text
{{#Wiki_filter:' I Docket No. 50-346 h f%- License No. NPF-3 Serial No. 588 February 7, 1980 POTENTIAL REACTOR SYSTEM VOIDING DURING ANTICIPATED TRANSIENTS PREPARED BY BABC0CK & WILC0X NUCLEAR POWER GENERATION DIVISIO.? LYNCHBURG, VIRGINIA JANUARY, 1980 8002120 5%l
CONTENTS 1.0 Problem Introduction and Summary 1.1 Introduction 1.2 Summary 2.0 Analysis, Assumptions and Event Descriptions 2.1 Analysis of Steam in the Upper Vessel Plenum 2.1.1 Stagnant " Hot" Water 2.1.2 Residual Heat Stored in Metal 2.1.3 Conclusion 2.2 Analysis of Steam in the Candy Cane 2.2.1 Pressurizer Outsurge Water Mixing in Hot Leg Flow 2.2.2 Residual Heat Stored in Metal 2.2.3 Conclusion 2.3 Event Description for Mass / Volume Balance 2.3.1 Description of Analysis 2.3.2 Derivation of Equations Used 2.3.3 Mass / Volume Analysis 2.3.3.1 Davis Besse 9/18/79 Trip 2.3.3.2 Davis Besse 10/15/79 Trip 2.3.3.3 Davis Besse 9/26/79 Trip 2.3.3.4 Oconee I 10/8/79 Trip 2.3.3.5 Oconee II 1/4/74 Trip 3.0 Conclusion 4.0 References h
List of Figures 2.2.1 Column Whldment Flow Paths 2.2.2 Upper Plenum Flow Paths 2.3.1 RC Volume Breakdown 2.3.3.1 TECO 9/18/79 Trip 2.3.3.2 TECO 10/15/79 Trip 2.3.3.3 TECO 9/26/79 Trip 2.3.3.4 Oconee 1 10/8/79 Trip 2.3.3.5 Oconee II 1/4/74 Trip A-1 Pressurizer level 52. corrected pressure tap measurements (320" pressurizer) A-2 Pressurizer level vs. corrected pressure tap measurements (400" pressurizer) A-3 Error in level indication vs. indicated level (400" pressurizer) A-4 Error in level indication vs. indicated level (320" pressurizer) AttacNnents Pressurizer Level Error
l.0 PROBLEM INTRODUCTION AND
SUMMARY
1.1 Introduction The NRC has expressed concern that steam pockets can and do fom in B&W primary systems during some reactor trip 5 and furthermore, this steam could collect in the candy cane and potentially hinder natural circulation after loss of offsite power. The source ci this steam is postulated to be from stored heat 11: metal, stagnant pockets of " hot" water, or pressurizer outsurge water (350 F); ,ny or all causing flashing during low pressure periods afe.c a trip. The purpose of this report is to show that the formation of a steam pocket in the primary system during most reactor trips is highly improbable and that the production of a volume of steam required to hinder natural circolation is virtually impossible. 1.2 Summary Based on review of several past B&W reactor trips along with several assumptions and calculations discussed in Section 2, the following statements can be made: (1) Minimum RC pressure after trips occurs about the same time as the minimum coolant temperature (as expected) and not because of a primary system " Steam Pocket" restricting a further pressure decrease. These minimum temperatures errelate with secondary side steam pressures. (2) With the most conservative assumptions steam pockets are virtually impossible during transients where minimum measured pressure is greater than 1740 psig. Specific concern per reference 1 \3
(3) Using more realistic assumptions regarding potential steam production, it is unlikely that any net steam production can occur at measured pressures greater than 1500 psig. 2.0 Analysis, Assumotions and Event Descriotions 2.1 Analysis of Steam in the Vocer Vessel Plenum 2.1.1 Stacnant " Hot" Water Typically, the hottest bundle in a 2772 MWT core is a 1.5 relative peaked bundle. This localized power could conservatively result in localized stagnant water temperatures of s 620*F in the upper control rod guide (column weldment). For this situation to occur, at least 53 in of flow area in the column weldment (see flow path 2 on figure 2.1.1) would have to be blocked. If this blockage could occur, then the following statement can be made: Any B&W reactor trio resulting in minimum RC tao pre.ssures less than 1740 psig (the tap pressure 1.s s 40 psid lower than core plenum pressure) voiding may occur. Since this blockage is highly unlikely, a somewhat more realistic hot spot assumption would be localized maximum temperatures of 610*F (instead of 620') in the upper vessel plenum. This assumption is based on (1) water stagnating (or having an extremely low flow rate) in the upper plenum (per Fig. 2.1.2) and acquiring the steady state enviromental temperature of the 59 column weldment flow temperatures and (2) plugged return holes (per figure 2.1.2, Flow Path 3). This condition would not allow flashing until the pressure decreases to 1660 psia, i.e.,1605 psig at the pressure tap. Typical outlet temperatures were verified from TMI-2 pre March, 1979 100". power outlets thermocouple data.
}
The most realistic assumption is the desian condition of s 5% core flow through the guide tubes into the upper pl enum. Following a reactor trip, the coolant temperature in this region will decrease rapidly to below 600F as core outlet temoerature-eliminating the potentid for " hot" water pockets at arty pressures above HPI injection levels. 2.1.2 Residual Heat Stored in Metal After a trip, the metal in the upper vessel will be conservatively assumed to remain at 610 F until a minimum pressure is reached. The upper plenum coolant temperature at this minimum pressure should be s 550 F (in this region) but 575 F will be conservatively assumed due to hypothetical " slow" mixing. The available stored energy in the metal will be: Stored Energy = Cp x Mass x AT m m Cpm = .11 BTU /lh, F AT = 610 - 575 = 35 F Mass s 5x10' lbm = total mass of metal above the outlet hot leg piping including reactor vessel Stored Energy = 1.925x10 BTU's The amount of water in this region is 1366 ft.
- 3 4 1366 ft.3 x 44.5 lbm/ft = 6.08x10 lb of water Conservatively assuming this energy is instantly released to the water, the water temperature will increase from 575 F to s 601 -
The pressure required for flashing at this temperature is s 1505 psig (at the pressure tap). Therefore, in order to fill this region with This is water density at 575 F, 1600 psia.
**l.925x106BTU's/6.08x1041b = 32 BTV/lb or s 26 F temperature increase.
950 078
steam (to cause spillover into the hot legs) from just residual heat, 20 times more mass of hot metal would be required. (s 10 BTU /lb are needed to reach Tsat and another 533 BTU /lb to vapori7.e the water. This equals 543 BTU required to convert a pound of water to lb a pound of steam). 2.1.3 Conclusion The previous calculations and discussion basically show that it is impossible to produce steam in the upper head above a measured pressure of 1740 psig, highly improbable above 1620 psig, and highly .unlikely above 1500 ps.ig. (Very few . transients have ever gone below 1600 psig .) This statement assumes no primary system breaks. 2.2 Analysis of Steam in the Candy Cane 2.2.1 Pressurizer outsurge water mixing with hot leg flow At the time period of mi'.imum pressure after a trip the hot leg coolant temperature is s 550 F during 4-pump operation and s 5700F durin9 natural circulation. The respective hot leg flow 6 6 rates are s 70x10 and 2.5x10 lb/hr during this period. The pressurizer is outsurging s 650 F water at s 40000 lb/hr into the hot leg. Conservatively assuming only10% of the hot leg flow mixes with the pressurizer outsurge , the resulting maximum fluic temperature in the candy cane will be s 551oF for four pump operation and 5810F for natural circulation. Qh
The saturation pressures for these temperatures is well below 1500 psig. 2.2.2 Residual Heat Stored in Metal The residual heat stored in the hot leg metal is conservatively 5 calculated to be s 1.89x10 BTV's. This calculation is based on (1) hot leg piping temperature remains at s 605 F for 60 seconds after the trip and (2) the residual heat is dumped instantaneously into the hot leg flow volume at the RTD indicated temperature of s 550 F and 1600 psia. Hot leg metal volume = 70.45 ft 3 3 4 Hot leg metal mass = 70.45 ft x 490 lb = 3.45 x 10 lbm ft* The AT driving function will be 605 - 555 or 50 AT. Therefore stored energy released is
.11 BTU x 50 F x 3.45x10 = 1.89x10 BTU's ib*F 4
The volume of water in the hot leg is s 1.97x10 lb . Therefore: 1.89x10 BTU s10 BTV/lb 4 197x10 lb This is equivalent to s 8 F in temperature addition. Therefore, the saturation pressures for 551oF* + 8oF = 559 F and 5810F + 80F = 5896 F are below 1500 psig. Per previous calculation O
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2.2.3 Conclusion Using the conservative as'umptions on residual stored heat and hot leg - pressurizer outsurge mixing, the RC pressure which would allow fla.shing is below 1500 psig. This low pressyre ,. snould not ce reacned during normal transients. 2.3 Evt.nt Description For Mass / Volume Balance 2.3.1 Description of Analysis A mass volume balance on the RC system before and after trips was analysed for five cases. These cases were chosen because of their abnormally low pressuri:or level, low RC pressure, or were referred to in reference 1. The method of analysis was basically: (1) To break the RC system down into 4 different temperature / pressure volumes (per figure 2.3.1)- (2) Calculate the ' shrinkage" of each volume at a lower temperature / pressure condition after a trip and (3) Determine how much water from the pressurizer is required to maintain a solic system conditions. (4) Subtract this volume of water from the initial pressurizer volume to get " level 1". (5) Calculate the amount of water that would have flashed in the pressurizer due to the lower pressure condition. This is " level 2". -
. (6) Fine.lly, calculate the pressurizer level error per attacnment 1. This is " level 3".
(7) Subtract level 2 and 3 from level 1 to get level 4. If
" level 4" is less than the plant measured level (" level 5")
then a viable explanation would be potential " steam pockets" h
in the RCS. The results of this study show that the :ndicated pressurizer level (level 5) is less than or equal to the calculation of level 4 and therefore a steam pocket occurring in the RCS is highly unlikely. 2.3.2 Serivation of Ecuations Used The equation used for this analysis is: - 1 1 I l V)p) + V P22+V933+YP44+VP55
* + E P +VE
+V 44 55 l '1 22 P 33 Where p = Coolant density at tin 0 p = Coolant den'sity at Time 1 V5 = Volume of water in pressurizer et Time 0 V 5 = Volume of water in pressurizer at Time 1 1
Solving for V 5
~ +
V 5 l(P1-P1 2(P2 - P 2) 3+ v (P3-P 3} + 4(P4~P45 5 1 p 5 For raised loop plants (TECO) V 5 (APl } + ( 2 3}+ (P 4 1 + 3.207 (level)] p 5 1 p 5 9' For lowered loop plants V
= 3800(ao)) + 887(ap 2 ) + 3197 (ap3) + 2774 (ap4) + [A) + 3.207 (level)] p 5 1
P5 Eq.2 h
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l l = Pressurizer Water Volume = A + 3.207 X A + 3.207 X l t ;-- Level (inches) Level (inches) A = 263 (Davis Besse)' A = 134 (Oconee) Pz=Ptap 8 1 = f(P) Tcold) - P =P tap + 50 #2 = f(P 2, Tave) 2 3 = f(P3, Thot) P3=Ptap 4 f(P4, Tave) P4=P tap 0 5 = f(P5, Tsat) p5ptap g 395B
2.3.3.1 Davis Besse 9/18/79 Trio At 12:43 on September 18, 1979, while operating at s 100% power a test was in progress on the main steam turbine Electro Hydraulic Control System (EHC) at Davis Besse 1. While transferring EHC pumps a low pressure signal in the EHC initiated a turbine trip. The Anticipatory Reactor Trip on Turbine Trip tripped the reactor s 0.4 seconds after the turbine trip. The reactor trip caused the RC pressure, RC T average and pressurizer level to decrease rapidly. The pressurizer level indication dropped off scale.some 50 seconds a,fter the reactor trip, remained down scale for some 50 seconds and then slowly increased. The RC pressure reached a minimum of about 1710 psig at 1 minute after reactor trip and recovered. RC T reached a minimum of 546 F following the trip and stabilized at 550 F. The initial conditions prior to the trip are listed below. Reactor Power s 100% Rated Power RC Temperature (T,y,): 582 F R.C.S. Pressure: 2200 psig R.C.S. Flow: 4 pumps operating Pressurizer Level: 202 inches Tests in Progress: EHC Test The pertinent data during the transient is shown on figure 2.3.3.1. The data analysis is as follows. h
- Davis Besse 9/18/79
, Reactor Trip Time (0) Initial Conditions T =
hot T # eold " tap " Therefore p)
=
46.24 p = 44.64 p = 42.57 p = 44.60 4 p5" Time (1) = 42 sec
- w T = 557 T = 550 p = 1740 psia hot cold tap Therefore p' = 46.40 p/ = 46.27 2
3 p'= E 97 3 1, pi = 46.23 4. p# = 41.18 Solving Equation i V ' = 415 ft 5 -- This corresponds to a calculated pressurizer level of 47.5 inches. (level 1) The indicated pressurizer level was 21.6 incher(level 5), The estimated pressurizer level temperature compensation error (per Attachment 1) is laa inches (level 3). The initial mass of steam in tne pressurizer is 650 'ft x 6.21 lb/ft or 3 4037 lb. The final mass of steam is 1214 ft x 4.37 lb/ft or 5304 lb. This additional 1267 lb (5304 - 4037) of steam will come from s 10" of water . (level 2). Therefore, level 1 - level 2 - level 3 = level 4 = 47.5-14-10 = 23.5". Level 4 is slightly great:r than level 5; therefore, the proba,bility of steam pockets is low. A 4 second hot and cold leg RTO response time delay is incorporated. Note: Where possibic, data used in thc:e analyses is based on ccmputer print cut. The graphs arc representati ns of this data. h
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e 2.3.3.2 Davis Besse 9/15/79 Trip Figure 2.3.3.2 shows the RC pressure during this trip. Since RC minimum pressure was 1848 psig no steam production was possible per discussion in Section 2.2.
% e e
TECO 9/15n9 TRIP 21.840 - 21.420 - m[ 21.000 - E 1 { 20.580 - S E g 20.160 - 5 O a: a-19.740 - L.- M l, 19.320 - 2 t'
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2.3.3.3 Daivs Besse 9/26/79 Trio At 20:56:33 hours on September 26, 1979, a high turbine throttle pressure limit alarm was received. The throttle pressure limiter is used to protect against an excessive decrease of steam pressure when steam generation of the NSS falls below the steam demand of the turbine. It acts directly to close the high pressure turbine control valves in an effort to maintain steam header pressure. Rapid closure of the control valves caused a mismatch between heat generation and heat removal with ? resultant increase in Reactor Coolant System (RCS) temperature and pressure. Seven seconds later (at 20:56:40) the reactor tripped on RCS high pressure and was followed by a turoine trip. RCS temperature and pressure then dropped and the Integrated Control System (ICS) reduced the feedwater flow abruptly. Reactor Coolant System Tave decreased to 548.5 F approximately 57 seconds after the trip. The pressurizer level indication dropped off scale at 21:57:21 and remained below tne indication range for approximately 21 seconds. The initial conditions prior to the trip are listed below. Reactor Power: s 100% Rated Power R. C. Temperature (Tave): 5824 R. C. S. Flow: .4 pumps operating Pressurizer Level: 200 inches The pertinent data during the transient for this analysis is shown on figure 2.3.3.3. The data analysis is as follows. qh
Davis Besse 9/26/79 Reactor Trip Time (0) Initial Conditions T = hot T = 559% P = 2215 psia cold tap Therefore p) = 46.18 p = 44.59 2 p3= 42.67 p = 44.56 p5"
- Time (1) = 50 sec T = 552 = 548 p = 1700 psia T
hot cold tap Therefore p' = 46.62 1 ~ - p/ = 46.53 2 - 3 p - 46.22 3 1 pi = 46.35 4. p'.
= 41.00 0
Solving Equation 1 y ' = 243 ft 5 - This corresponds to a calculated pressurizer level of 26.4 inches. (level 1) The indicated pressurizer level was 0 inches (level 5). The estimated pressurizer level temperature compensation error (per Attachment 1) is 15" inches (level 3). The initial mass of steam in the pressurizer is 648 'ft x 6.21 lb/ft or 3 3 4030 lb. The final mass of steam is s1234 ft x '4.23 lb/ft or 5219 lb. This additicnal 1190 lb ( 5219 - 4030) of steam will come from s 9" of water. (level 2) Therefore, level 1 - level 2 - level 3 = level 4 = 26.4 9 = 2:4". Level 4 is slightly greater than level 5; therefore, the probability of stear, pockets is iou. A 4 second hot and cold icg RTD response time delay is incorporated, llotc: 1.'here possible, data used in these analyses is based on computer print out. The graphs are representations of this data.
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2.3.3.4 Oconee 1 10/8/79 Trip On October 8, 1979, Oconee 1 was operating at 100% FP with on line Reactor Protection Tests in progress. At 13:27:35, Oconee 1 experienced a reactor trip attributed to RPS activation of pressure / temperature channels A, C, and D. Control Rod Drive Breakers CB 3 and 4 were tripped for the test. An additional breaker for Group 5 was opened which caused Group 5 to drop. This resulted in a P/T Trip. The initial conditions prior to the trip are listed below. Reactor Power , 100.% RCS TAVE 579 F Pressurizer level 221 inches The pertinent data during the transient for this analysis are shown on figure 2.3.3.4. The data analysis is as follows. 1950
Oconee I 10/8/79 Control Rod Drop Trip Time (0) Initial Conditions T = 602 7 T = 558 p = 2150 psia hot cold tap 3 Therefore p) - 46.26 lb/ft 3 p = 44.75 lb/ft 2 3 p , 42.87 lb/ft p 4
=
44.70 lb/ft p5"
- Time (1) = 60 seconds 553 =1750 psia T =
T = 550 p hot cold tap Therefore p' = 46.55 lb/ft 3 1 . p I' = 46.47 lb/ft 2 3 P'3
= 46.40 lb/ft pI = 46.51 lb/ft 4.
P' = 40.81 lb/ft 3 Solving Equation i V , = 315 ft 5 - This corresponds to a calcalated pressurizer level of 56.2Minches. (level 1) The indicated pressurizer level was 31.0 inches (level 5) The estimated pressurizer level temperature cocpensation error (per Attachment 1) is 15.0 inches (level 3). The initial mass of stesm in the pressurizer is 709 3ft x 5.97 lb/ft or 4236 lb. The final mass of steam is 1283 ft3 x 4.4 lb/ft or 5652 lb. This additional 1416 lb (5652 - 4236) of steam will come from s 10' of water (level 2). Therefore, level 1 - level 2 - level 3 = level 4 = 5G-15-10 31". Level 4 is equal to level 5; therefore, the probability of steam pockets is low. A 4 second hot anc cold leg RTD response time delay is incorporated. Note: 1.'here possible, data used in these analyses is based on computer print out. The graphs are representations of this data. gCg Q O
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2.3.3.5 Oconee II 1/4/74 Trio Figure 2.3.3.6 she',s the pertinent transient results of this trip. During this transient the minimum Tap pressure attained was s 1900 psig. Therefore, a 1940 psia upper vessel pressure would require a 631 F temperature to produce net steam. This temperature was never attained at any position or time during this transient. While it is given that operator action (or plant responses) could have been better, the steam production possibility did not exist. Furthermore, a review of the sequence of events of this trip indicate that the severe level and pressure changes at the beginning and later in the transient were primarily cue to a temporary loss of 10.5 power.
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3.0 Conclusion During any B&W reactor trip where a primary system break does not occur or the pressurizer does not empty and HPI is operable - net steam production in the primary system is highly improbable and generation of a volume of steam required to block natural circulation is virtually impossible. 4.0 References
- 1. 11/15/79 phone conversation between Cf:W and NRC, Suoject:
Potential Voiding in-the RCS During-Anticipated Transients
ATTACHMENT 1 Pressurizer Level Error The pressurizer level indication is based on the pounds of mass the pressure taps measure and then distributed to varying amounts of water and steam at the saturation conditions at the pressurizer pressure. Since pressure is not measured in the pressurizer (only temperature) pressure is assumed from the temperature measurement being at T sat
- During fast depressurizations the RTD in the pressurizer does not respond efficiently, especially in cases where the RTD is exposed to steam enviroment. The heat transfer time constant can vary from 30 to 180 seconds. Since most depressurization after trips occur in 30 to 50 seconds the RTD will not respond effectively at the low level point.
Figures Al and A2 show potential level errors for 400" and 320" pressurizers. Figures A3 and A4 show what typical errors can be expected as a function of indicated level and system pressure. Inese curves can be used to correct the indicated level if system pressure (i.e. Tsat) and pressurizer RTD temperature are known. The difference between RTD temperature and calculated T (Based on Psat) will give the level error. sat In a typical trip @ Oconee 1/1/77 the system pressure went from 2150 to s 1800 psig in 27 seconds. The alams printer monitored a 643 pressurizer temperature at 1800 psig instead of the expected 621 F. At the indicated level of 70" the real level was s 78" (per figure A-3).
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