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Seismic Behaviour of a PWR Reactor Core: Fluid Structure Interaction Effects (K558)

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g t t a i } Љ i l ˆ a Š ut g tui q Ša ^k l  ’ ž Ÿˆ a y e a a l c ce a a ˆ l i £ l tp uŠŠg ^ l e ea q e a t a ] ^u] y ^ _ a ¥ e t ^ ¦ g ] ˆ § q e a ˆ l i u] g ] ^

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} a ^k a a ] g t ta i } Šua t k u^ _ } l ^_ u] a e ^ ug Š g ] ˆ ˆ ut t uq g ^ uw a a ª a p ^t ˆ  a ^ l ^ _ a ™  uˆ  \i q g p ^ t } a ^k a a ] ^ _ a g t t a i } Šua t g e a

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Ž _ a p l ea l c g  ‚ „ e a g p ^ l e p l ] tut^ t l c w a e ^ up g Š c a Š g tt a i } Šua t g e e g ] y a ˆ u] g t Ä  g e a q u^ p _ g ee g ‰ Ÿ Å Æ Ç g t t a i ›

} Šua t u] g È É É Ê ‚ a e a g p ^ l e £  Ž _ a c a Š g t ta i } Šua t g ea ^ g ŠŠ g ] ˆ ™ a  u} Ša t ^ e p ^  e a t ‡ e a t ^ e g u] a ˆ l ] Љ g ^ ^ _ a ue a ] ˆ t

} ‰ ^ _ a  q q a e g ] ˆ Šl k a e p l e a q Šg ^ a t  Ž _ a ‰ p l i q e ut a c a Š e l ˆ t p l ] ^ g u] u] y ^ _ a ¥ t tuŠa i g ^a e ug Ї g ] ˆ y  uˆ a ^ _ ui } Ša t ‡

g e e g ] y a ˆ u] g tÄ  g e a g e e g ‰ ‡ a w a ] Љ tq g p a ˆ } ‰ y e uˆ t  Ž _ a p l ea Šg ^ a e g Š ˆ ut q Šg p a i a ] ^ t  ] ˆ a e t a ut i up Šl g ˆ t q e l ˆ  p a

g t t a i } Љ Šg ^a e g Š ˆ a cl e i g ^ul ] t ‡ g ] ˆ ui q g p ^ t } a ^ k a a ] g t t a i } Šua t l e k u^ _ ^ _ a p l ea } g Ì a t g ^ ^ _ a y euˆ Šl p g ^ ul ] t 

Ž _ a i l ˆ a Šu] y l c ^ _ a  ‚ „ p l e a ta ut i up } a _ g w ul  e p l i q e ut a t ^ _ a i l ˆ a Šu] y l c ^_ a g t ta i } Šua t ‡ g ] ˆ ^_ a i l ˆ a Šu] y

l c ^_ a l w a e g ŠŠ } a _ g w ul  e l c ^ _ a p l e a ‡ k u^ _ ^ _ a u] ^ a e g p ^ ul ] t } a ^ k a a ] g t t a i } Šua t Ÿž uy  e a Å £ 

Guide thimbles

Fuel rods and

Grid

Fuel assemblies

Lateral

structure

Seismic motion

at the top and the bottom)

Assembly models (embedded

Í ¿Î Ï ¾ »

­ ³

Í Ï » Ð Ñ ¼ ¼ » Ò Ó ÐÔ Õ ¾ » Ñ ½ Á Â ¾ ½ Â ¾ » Ö Á Â À Ø ¿ » Ù Ú Õ Ñ Ã Û ¾ Â Ù Ò Â Û » Ð

Transactions of the 17

th

International Conference on

Structural Mechanics in Reactor Technology (

SMiRT 17)

Prague, Czech Republic, August 17 –22, 2003

(2)

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ž ž ž + ]«  › ^ C K ! + & 8$& 5   ( 8 $& 5 & ? 8! = ! & 4 & ( 5 . / $/ + $4 & . ( / / 4 8 & $ 5 & 8 8 $& 5 /

 £ ¤¥ «  " $ % '

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+ 8 $j ]. $ E & 5 / & ^ A = $8 ! 8 ! ( C K ! . ( 4 . . + P $5 E £ ¤¥ 4 & / P & 5 . / 8& 8 ! / 8 ( 4 8 ( . + P $5 E & ?

8 ! /8 ( 4 8( C

K ! & 5 2 $5 8 4 8 $& 5 / 8= 5 8 ! & / 4 $ 8& / $+ P 4 8 / A = $8! ( & ?  *7 p ž 9 + ?& 8! $+ P 4 8 / 8 $… †

5 // C K ! $/ ( $/ 8 ` 5 ? & + P $& ( / 8= & † + / / + 2 + & . / 8 ( . $ / C K !   ( 8 $& 5 / 4 & / P & 5 . $5 E 8& 8! $/

+ & . 4 5 /& . ( / $5 E + & . / $/ A $5 5 ( + $4 4 & . A = $8 ! j 8 5 ?& 4 / ?& 8 ! $+ P 4 8 / = ! 5 8 ! 2

& 4 4 ( C Y & p ¨ ­ / / + 2 4 & A 8 ! + & . / $/ & $& ( / 2 4 & + P $/ /  p 7 + & . / = ! $4 ! ! 8 ! / + ?   ( 5 4 2

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4 & / P & 5 . $5 E 8& & 5 ?( & . ]Y $E (  ^ C K ! / / ( 8/ ! / 5 ( / . 8 & ( $8 P $& ( / & 5 & = + & . kp n C

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  ( 8 $& 5 / 8 & . /4 $ $8/ ! $& ( J L

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(3)

" $ % & $ & * % & % $ 0 & 2 5 78 " $ % &

2$ & = 2$ 0 % @ A & 7 0 $ % @ A & & = 2$ 0 % A E 22 " $ % & $ %

H $ 22 & J K $ L $ 2 $ % J " H L $ % $ 2 E L O J K $ L 2 L J A & % L & 2 E L @ A & @ O %

= A 0 & $ K V $ 2L X Y 7 & $ E % $ 2 J $ & & & 0 $ J 0 $ Z $ 2A [ & $ E % $ 2 0 7

& $ E % $ 2 J & = 2$ & 0 $ J 0 $ Z $ 2A [ & $ E % $ 2 0 7

Liquid

Solid

Darcy acceleration

L

S

T

Total

boundary

through the

] ^_ ` b c

d f

g ic j c l m n b o q c ii r ` ^u n q q c ic b n m ^w l x w b b w u j w m ^w l r n l u w b ` ^u j w m ^w l

@ A & 0 0 % & A $ 0 H 2 0 0 % " O 22 H = H 2 20 % $

% Z |

= % $ = = 2 & H L @ A & " $ % & $ ~ % $ A % % & L % $ 0  A $ %

7 % 0 E % € & & L % $ 0  A $ % @ A & " $ ~ % E % $ A % 0 0 % $ 0 H 2 " $ %

H & & A & 0 & L % $ 0  A $ % @ A & $ % & 0 Z = % $ = = 2 & % $ 0 H 2 #

$ 8 *

+

$ * ‚

ƒ = $ $ 0 * & * % & $ #

[ [

[ [ [ 3

[ 3 $ 5 3 " „ E A 7 … % O L $ " O

Z = % " 8 % $

+

-" $  A $ % = @ A & 7

; L 2 % E  A $ % ‚ % $ & 0 $ % = % |

% E " = H 2 H $ % @ A & $ 2 |

$ % L $ 0 H 2L 0 0 % 7 ƒ „ |

E A ‚ = % 0 A & % A 0 $ 2 0 A 2$ % 7

‰ $ 8 ‹ Œ „ % ‰ 2 0 % = % & %

$ 0 H 2L 7 ƒ @ A & 0 0 % % O 2 & |

0 % & $ 2 0 % $ L 0 0 % $ 0 |

H 2 7 = %  A % 2L " = H 2 " O ‚ 8 ? 2 0 % $ L

$ 2 A 2$ % Ž $ % &  0 0 % " H $ % $ J @ A &

0 $ Z J " $ L # 7

(4)

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1 1 4 4 1 4

6 7 # ) - & ; < - - # & B - ) " # $ - &

1 1 4 4 $

/ 1 4

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F 1H 4

I K( M O Q Q OR T U OW X Y * X [ U Q

\ & - ^ - $ & $ &) - " # $

_ & & - $ < < )& - )b

) - c 6 & # < & 1 < -

" 4 $ ) $ - ) & # - # & &

& - & # - # & $ c h - )

i \ k & - & & < $ < $ # ' - b

" c m & - &) & $ < b

& - $ & $ $ - &

o o c c k ^ $ # & & < $ $

$ ) & " # $ " & # < ^ c 6

$ _ B - & & & 7 # & )

" # $ & _ _ - ^ 1s - - < tv w4 c 6 ^ - $

$ < & # x y + 1{ - & - $ t| w / 1

2

# _ $ tx w4 c

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‚ X ƒT U OW X 5  O „ T … „ Q † ƒO„ W X ƒ† [ OU OX Q

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Œ Ž Y  Œ ‚ Y ’ Œ M Y Ž

6 & $ # - ) $ _ B - 7 # 1H 4 < _ - & $ - # _ 7 # c

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M O Q Q OR T U OW X X * X [ U Q

m & < & $ _ & $ $ & _ _ - ^ ) " # $ $ )

8

8 c < < & ) & 1 $ ) 7 # & ) & 4 $ # < " # $ " - && $

^ & B - # & _ # ^ $ — $ " # $ & ' c 6 $ ) & -

/ ? 1@ 4 8 1@ $ ^ & ' 4 c 6 ) & ) 7 # _ $ ) & ' - "

$ _ B - - & & $ < _ # ) ? c s & # - # & $ < - $ & $ c

( KI E † W X € … O… ~ X G  T U O† …

6 $ ^ - 7 # ) - & ; - - # & $ $ _ B - )

" # $

1 1 4 4 ? 1@ 48 š L F ›œ  8 $

/ 1 4

F 1P b 4

& 1 1 4 4 ? 8 š L F ›œ  8 $

/ 1 4

(5)

$ ! " * ' 5

6

7 6 7 :

; =>

? @ 6

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7

#

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6C E ' 7

' 6 7 : ; => ? @ 6 " 7

#

; 6C E # 7

+ ' ! !' ) $ / ' ) 6, E' 7 ' 6, E# 7 $ !! # ' !! Q ' ! !' ) $ ! " Q R + ' ! !' ) $

/ ' ) 6C E' 7 ' 6C E # 7 $ !! # ' !! Q ' ! !' ) $ ! " Q R

- V- . XY Z [ \ X] ^ _ ] ` a b

c * / ' ) 6, 7 ' 6C 7 ) ) ) # ! * f # ' * ) R h c " i ) )

f ' ! j k 0 / ) 6 k i C * ) m ' k i C q 7 # Q $ ! " Q ' Q $

! " Q ' ) ) R h * # * ) ) ) f ) ) / v R ' # ) ' , Q $

! " Q ' ) , ' !! / ) ' / ' ! : Rk , z { R Q $ ! " Q ' ) , k 2 , * ) ' f ) : Rk ,

z { / v R h k : 2 * ) ' f " / v , ' !' ) * ' ) ' / v : R0 0 z { 6 ! )

: Ri z { E ' / v 7 R

FREQ

NB MODES

2.15

2.20

2.25

2.30

2.35

2.40

2.45

.00

.50

1.00

1.50

2.00

2.50

3.00

3.50

X1.E2

FREQ

NB MODES

1.00

1.50

2.00

2.50

3.00

3.50

.00

.50

1.00

1.50

2.00

2.50

3.00

3.50

X1.E2

 X‚ ƒ Z a 5 „  Z a 7 ƒ a ^ … † ] 9 \ ‡ a - ˆ : _ ] ` a b ‰ ; Š X\ ‡ … ] ƒ ‹ ŒX^ ‚ ; [ ^ ` ; Š X\ ‡ ] ƒ \ … ] ƒ ‹ ŒX^ ‚ ; … [ b a

h c " ) , E' ' , E# ) ) ' Ž * ) R h  ) ) ' ! $ ) : Rk ,

z { / ) R @ " ! # ' ! * f * ) R h i ) ' ) ) " ! # ' ! * f *

R h " / v ) # ' " " " ' { ' 6 k !! 7 ' ! $

!' f ) !' * ) # $ ' ' )) * # ! ) R ) * ) $ " ! # ' ! * f * ,

' ) # $ ' ) ) * # ! ) # $ $ ' ‘ !' R

MODE 11 FR 2.16164E+00

MODE 187 FR 2.17200E+00

MODE 230 FR 2.36444E+00

 X‚ ƒ Z a A ” [

„

•

‡

(6)

MODE 289 FR 2.43055E+00

MODE 299 FR 2.43579E+00

MODE 314 FR 2.43817E+00

" # ' # + - / 1 24 4 26 8 + 29 / + / => 1 / 6 / A 1 4 2A 8 D2A / 8 = G 8 J K A +- / > 8 4 4 8 A 1 4 + 2Q A / 4 4

> 8 + = 2S / 4 U V K W + - / > K 1 8 D 1 8 > 6 2A Z 1 / 6 / A 1 4 K A + - / \= / ] _ / A ` J K \ + - / ` K A 4 21 / = / 1 > K 1 / U c K = + - / 4 + 8 Z A 8 A + G 8 +/ =

` 8 4 / \K = / S / > 6 D/ e/ ] _ 8 + 2K A g 8 i W +- 24 1 8 > 6 2A Z 24

j e l m i e eo o i m

i eo

p

o i

s t u t v w s x y t z | } v y  v |  y € t z

V / 24 > 2`  / - 8 9 2K _ = 4 2> _ D8 + 2K A 4 - 8 9 /  / / A 6 / =\K => / 1

G 2+ - + - / G - K D/ ` K =/ > K 1 / DU † - / > 8 2A 6 8 = / > / + / =4 + - 8 +

` 8 A 9 8 = J 8 =/ +- / 4+ = _ ` + _ = 8 D 1 8 > 6 2A Z W + - / ‰ _ 21 1 8 > g

6 2A Z e4/ / Š ‹ UŒ i W + - / 2> 6 8 ` + 4 + 2Q A / 44 W + - / 2> 6 8 ` + 1 8 > g

6 2A Z W +- / Z 8 6  / +G / / A + - / 8 44 / >  D2/ 4 W 8 A 1 + - / 4 / 24 > 2`

> K 9 / > / A + U † - / 8 6 6 D2/ 1 4 K DD2` 2+ 8 +2K A _ 4 / 1 2A + - /  = 4 +

` 8 D` _ D8 + 2K A 4 24 6 = / 4 / A +/ 1 2A + - / c 2Z _ = / ‘ U " 8 D` _ D8 + 2K A 4

8 = / 6 / = \K = > / 1 _ 4 2A Z + - / ` K > 6 _ +/ = ` K 1 / " % V † ‹ ’ e ”' •i U

† - / c 2Z _ = / ' 6 = / 4/ A +4 / S / > 6 D/ 4 K \ + - / / 9 K D_ + 2K A

9 / = 4_ 4 + 2> / K \ +- / 6 K 4 2+ 2K A K \ + - / 8 4 4 / >  D2/ 4 K \ ` / A + = 8 D

= K G U † - / Z 8 6  / +G / / A + - / 8 4 4/ >  D2/ 4 24 Œ > > W 8 A 1 2> g

6 8 ` + 4 K ` ` _ = e+- / 4 + =K A Z / = 2> 6 8 ` + 24 K  + 8 2A / 1  / + G / / A

Œ UŒ – 8 A 1 Œ UŒ — 4 i U

SOLLICITATION (m/s2)

.00

5.00

10.00

15.00

20.00

25.00

−4.00

−3.00

−2.00

−1.00

.00

1.00

2.00

3.00

4.00

* y ' " ''" #

TEMPS (s)

DEPL (m)

.00 .20 .40 .60 .80 1.00 1.20 1.40 1.60 1.80 2.00

−.20

.00

.20

.40

.60

.80

1.00

1.20

1.40

1.60

1.80

X1.E−2

TEMPS (s)

DEPL (m)

.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

−2.00

−1.00

.00

1.00

2.00

3.00

4.00

5.00

6.00

X1.E−3

(7)

) # - : ;= ? @ ) 8 # - # E F G ) # 8 I 8 ) %# ) - # F E

G G G / # @ # = ! = 7 = # ) L 8 # N O P # ) !! # @ O

) - / ! - ! I !! = - # # 8 ) 8 @ W # I ) ) # !7 # !7 -

8 ) - 8 - 7 ! N O P # 8 !@

2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50

−1.20

−1.00

−.80

−.60

−.40

−.20

.00

X1.E4

2.75

2.77

2.79

2.81

2.83

2.85

2.87

2.89

−10.00

−9.00

−8.00

−7.00

−6.00

−5.00

−4.00

−3.00

−2.00

−1.00

.00

X1.E3

\ ]_ ` a b

c e

f g h i j k a i b l

m / ) # ! m # 8 ! ; n o @N ? I q #

) ) # ) # ! I ! 8 # = - #

# 8 / % u ) 7 / # ) # !

; n o @o ? @ w # !# # q ! 7 # % #

# 8 ) # # % ) # @

F G 7 =

/ # ! ) # = @ 7

# % # ! 7 ;8 # L # %

N O P # ) !! # ? 8 # % q ) 7 @

) = 8 %# m / ) # ! m )

= # ! # = # % 7 # % o F # 8 I

= # ! # = # % 7 # % F N @F

€  # 8 I 8 = # ! # = # % 7

# % F N # 8 / % u ) 7 N @F €  @

w m / ) # ! m ) I - # G # %

7 !# / % u ) 7 # 8 I - - # F G

% u ) 7 # 8 @

ENERGIES 330 MODES MODREF MODREF

TIME

ENERGY

.00

.20

.40

.60

.80

1.00

1.20

1.40

1.60

1.80

2.00

.00

.50

1.00

1.50

2.00

2.50

3.00

X1.E2

LOW FREQUENCY ENERGY

HIGH FREQUENCY ENERG

TOTAL ENERGY

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Ž a b Š]f ]‡ h a ˆ a b l ` Šj l

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q r i : ' . m L | /' L W ' ' ) L * )% . 2 | , : ' % : . ) { . % . '

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References

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