Analitcka Studija Dinamike i Stabinosti Sigurnosnog Ventila

7/29/2019 Analitcka Studija Dinamike i Stabinosti Sigurnosnog Ventila

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Nucle ar Engineer ing and Des ign 72 (1982) 197-204 197N o r th - H o l l a n d P u b l is h in g C o m p a n y

A N A N A L Y T I C A L S T U D Y O F T H E D Y N A M I C S A N D S T A B I L I T Y O F A S P R I N G L O A D E DS A F E T Y V A L V EA v t a r S I N G H ,E P R L P a l o A l t o , C a l if o r n ia , U S AReceived Apr i l 1982

Spr ing loaded se l f -ac tua t ing safe ty va lves a re employed as par t o f the overpressure pro tec t ion systems in va r ious indus t r ia lapp l ica t ions . In o rder to des ign and pred ic t the i r per forman ce i t i s necessary to s tudy the dy namic behav ior o f the va lve over arange of f lu id and sys tem condi t ions . A one-d imensiona l model has been deve loped to s tudy the e f fec ts o f d i f fe ren t va lvepara mete rs such as the spring -ma ss characteristics, geom etry of interna l parts, adjus tme nt ring settings, bellows etc. whichinf luence the dynamic behavior and s tab i l i ty o f the va lve . Analy t ica l resu l ts fo r s team f low condi t ions a re p resen ted todemon st ra te the re la t ive e f fec ts o f these parameters o n the va lve opening t ime, m aximum l i f t, b lowdown (ups t ream pressured i f fe ren t ia l be tween the va lve opening and c los ing) and any osc i l la t ions of the va lve stem. I f the va lve is no t p rop er lybackpressure compensa ted , i t may be come uns tab le as the s tagna t ion pressure a t the va lve in le t decreases . Lower ing of theguide ad jus tment r ing pos i t ion or ra is ing the nozz le ad jus tment r ing genera l ly resu l ts in improved s tab il ity , shor te r va lveopening t ime, h igher l i f t and longer b lowdown. The e f fec t o f dam ping on the va lve stab i l i ty i s a lso demonst ra ted . T he m odelcan be used to eva lua te the des ign of sa fe ty va lves and da mping dev ices to e l imina te uns tab le va lve dynamic behavior .

1 . I n t r o d u c t i o n

H i g h p r e s s u r e v e s s e l s i n v a r i o u s i n d u s t r i e s a r e p r o -t e c t e d a g a i n s t o v e r - p r e s s u r e b y s e l f - a c t u a t i n g s p r i n g -l o a d e d s a f e ty v a l v es . T h e y o p e n w h e n t h e u p s t r e a mp i p e l i n e o r v e s s e l p r e s s u r e e x c e e d s a c e r t a i n a l l o w a b l ev a l u e , t h u s r e l e a s i n g t h e f l u i d t o m a i n t a i n t h e s y s t e mp r e s s u r e b e l o w a c e r t a in d e s i g n v a l u e . I n o r d e r t o p r o p -e r l y d e si g n t h e o v e r p r e s s u r e p r o t e c t i o n s y s t e m f o r v a r i -o u s t r a n s i e n t s, i t i s n e c e s s a r y t o u n d e r s t a n d t h e d y n a m i cb e h a v i o r o f t h e s e s a f e t y v a l v e s . F o r e x a m p l e , a s l o w l yo p e n i n g v a l v e , m a y n o t r e l ea s e a s u f f i c ie n t q u a n t i t y o ff l u i d t o c o n t r o l t h e r i s e i n s y s t e m p r e s s u r e a n d m a i n t a i ni t u n d e r t h e d e s i g n v a l u e . O n t h e o t h e r h a n d , q u i c ko p e n i n g o r c y c l in g m a y c a u s e s u b s t a n ti a l d y n a m i c l o a d -i n g s o n t h e d i s c h a r g e p i p i n g . A p r o l o n g e d o r o s c i l l a t o r yd y n a m i c b e h a v i o r c a n i n f li c t d a m a g e t o t h e v a l v e it s el f .

T o d a t e , n o t m u c h w o r k h a s b e e n d o n e t o a n a l y z et h e d y n a m i c b e h a v i o r o f a s a f e ty v a l v e a n d i t s i n t e r ac -t i o n w i t h t h e p r o t e c t e d s y s t e m . I n m o s t c a s e s i t i sa s s u m e d t h a t t h e s e v a l v es o p e n w i t h i n a c e r ta i n o p e n i n gt i m e w h e n t h e u p s t r e a m p r e s s u r e e x c e e d s a c e r t a in v a l u ec a l l e d t h e S e t P r e s s u r e . W h e n t h e v a l v e i s f u l l y o p e n , i ti s e x p e c t e d t o a l l o w a d e s i r e d f l o w r a te a n d w h e n t h ep r e s s u r e u p s t r e a m o f t h e v a l v e d e c r e a s e s b y a d e s i g n e d

v a l u e c a l le d t h e B l o w d o w n t h e v a l v e i s a s s u m e d t oc lo s e .

I n o r d e r t o d e s i g n a n d e v a l u a t e t h e p e r f o r m a n c ec h a r a c t e r i s t i c s o f a s a f e t y v a l v e i t is n e c e s s a r y t o u n d e r -s t a n d i ts d y n a m i c b e h a v i o r u n d e r d i f f e r e n t f lu i d a n dt h e r m o d y n a m i c c o n d i t i o n s . T h e o b j e c t i v e o f th i s s tu d yi s t o d e v e l o p a c o u p l e d t h e r m a l - h y d r a u l i c a n d s p r i n gm a s s s y s t e m s m o d e l t o b e u t i l i z e d a s p a r t o f t h e o v e r a l ls y s t e m i n t e r a c t i v e m o d e l .

M o s t o f t h e e x i s t i n g t h e o re t i c a l w o r k r e l a t e d t o v a l v e si n v o l v e s a n a l y s i s o f s t e a d y s t a t e m a s s f l o w r a t e , [ 1 - 3 ]v e n t p i p e s i z i n g [ 4] a n d t r a n s i e n t d i s c h a r g e p i p e l o a d s[ 5 ] . F o w l e r e t a l . [ 6 ] a t t e m p t e d t o s i m u l a t e t h e s a f e t yv a l v e d y n a m i c s c o n s i d e r i n g o n l y t h e m a s s - s p r i n g e f f e c to n p r e s s u r e s u r g e s i n a h e a t e x c h a n g e r . F u n k [ 7 ] c o n -s i d e r e d t h e i n t e r a c t i o n b e t w e e n t h e i n l e t p i p e f l u i dd y n a m i c s a n d t h e s p r i n g m a s s s y s t e m o f a p o p p e t v a l v et o a n a l y z e t h e v a l v e d y n a m i c s t a b i l i t y . R a y [ 8] fo r -m u l a t e d a n o n - l i n e a r s e m i - e m p i r i c a l m o d e l o f a s af e t yv a l v e a n d d y n a m i c e q u a t i o n s w e r e d e r i v e d f r o m f u n d a -m e n t a l p r i n c i p l e s o f r i g id b o d y m o t i o n a n d f l u id d y -n a m i c s . T h e a n a l y t i c a l m o d e l d e v e l o p e d i n t h e p r e s e n ts t u d y i s b a s e d o n a s i m i l a r a p p r o a c h w h e r e t h e e m -p i r i c i s m h a s b e e n m i n i m i z e d b y r e p r e s e n t i n g t h e f l u i dd y n a m i c f o r c e a c t i n g o n t h e v a l v e d is c i n t h e f o r m o f a n

0 0 2 9 - 5 4 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 1 98 2 N o r t h - H o l l a n d


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198 A. S ingh / A spring loaded safe(v valvee x p l i c i t a n a l y t i c a l e x p r e s s i o n . E f f e c t s o f p r e s s u r e d i s t r i -b u t i o n i n t h e h u d d l i n g c h a m b e r ( v o l u m e t r i c r e g i o n b e -t w e e n t h e v a l v e d i s c a n d s e a t ) a n d t h e b a c k p r e s s u r e i nt h e b o d y b o w l o n t h e s te m d y n a m i c s h a v e a l so b e e ni n c l u d e d a n d s h o w n t o b e q u i t e s i g n i f i c a n t.

2 . T h e o r yT h e c r o s s s e c t i o n o f a t y p i c a l s a f e t y v a l v e i s s h o w n i n

f ig . 1 . F u n c t i o n a l i n t e r n a l c o m p o n e n t s i n c l u d e a n o z z l e,s e a t , d i s c , p i s t o n r o d , s p r i n g , b e l l o w s a n d a d j u s t i n gr i n g s . T h e b e l l o w s a r e d e s i g n e d t o p e r f o r m t w o f u n c -t i o n s - f i r s t l y t o i s o l a t e t h e b a c k o f t h e d i s c f r o m t h eb a c k p r e s s u r e e x i s t i n g i n t h e b o d y b o w l a n d s e c o n d l y t op r e v e n t l e a k a g e o f f l u i d t o t h e a t m o s p h e r e . I t s h o u l d b en o t e d t h a t t h e b e l l o w s d o n o t c o v e r t h e e n t i r e a r e a a tt h e b a c k o f t h e d i s c , h e n c e a p a r t o f t h i s a r e a l o c a t e da r o u n d t h e o u t e r p e r i p h e r y o f t h e d i s c m a y b e e x p o s e dt o t h e b a c k p r e s s u r e , a s s h o w n i n t h e s i m p l i f i e d s k e t c h o ff ig . 2 . A d j u s t m e n t r i n g s c a n b e m o v e d u p o r d o w nv e r t i c a l ly a n d a r e u s e d t o a d j u s t o p e n i n g a n d c l o s i n gc h a r a c t e r i s t i c s , l i f t a n d b l o w d o w n s e t t i n g s .

G o v e r n i n g e q u a t i o n s f o r o n e - d i m e n s i o n a l fl u id a n dv a l v e st e m m o t i o n h a v e b e e n d e r i v e d f o r t h e c o n t r o lv o l u m e s h o w n b y d o t t e d l i n e s in f i g. 2 . F i g . 3 s h o w s t h e

Be l l ows -

G u i d e r i n g -

Be l l ows

S e a t ~ I. . . . . . . I - < . . . . . .

,\ I \ \

\ \ \ \\ I I \ '

tFlow

/ , ~ - ~ S p r i n g

D i s cf Gu i dead ;us tmen tr ing

~ " " " ~ N OZz ead j us tmen tr ing

Fig. 2. Schematic diagram of valve components .

f o r c e s a c t i n g o n t h e c o n t r o l v o l u m e i n t h e v e r t i c a ld i r e c t i o n ; F D r e p r e s e n t i n g t h e r e a c t i o n f o r c e e x e r t e df r o m t h e v a l v e d i s c o n t o t h e f l u i d . P s d e n o t e s a v e r a g ep r e s s u r e d i s t r i b u t i o n o v e r t h e s e a t a r e a A s a n d i s a p -p r o x i m a t e d b y t h e c r i t i c a l p r e s s u r e P c b a s e d o n t h ea s s u m p t i o n t h a t d u r i n g t h e o p e n i n g a n d c l o s i n g o f t h ev a l v e, c h o k i n g o c c u r s a t t h e i n n e r r a d i u s o f t h e s e a t.

A p p l y i n g t h e m o m e n t u m e q u a t i o n , in t h e x d i re c -t i o n , t o t h e c o n t r o l v o l u m e o f f i g . 3 t h e f o l l o w i n g c a n b ed e r i v e d :

V s , ~ e - - ~ L J . Ldisc -~ Fsprmg

M IT F D

Va l v e s t em Id i s p l ac emen t ( x )~F~

m [ )

t t t t t t P ,Fig. 1. Cross section of a typic al safety valve. Fig. 3. Forc e dis trib utio n in the valve.


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A. Singh / A spring loaded safety valve 199

P I A t + P s A s - F D = ~ f f f~ .v P Vx d v+ (~ PVxV:, d A

c.s.

where the first term on the right hand side representsthe rate of change of momentum inside the controlvolume. Because of the small geometric distance insidethe valve and the time scales involved during the valvemotion, this term is negligible; however, it has beenapproximat ed by assuming negligible pressure and den-sity gradients inside the valve. The second term denotesthe rate of momentum effhix from the control surface.

Expanding and simplifying the above equation, thefollowing can be obta ined for the force exerted by thefluid on the disc for frictionless compressible flow:F D = P i A i + P s A s + A t p i V ~ - - p l A l

( .dV, v d x ) m ~ V e c o s O ( L + x ) - d - f + l d t + , (1)gc

where the last term in the above equation approximatesthe x component of the exit flux from the valve.

the is calculated by assuming that ideal gas chokeflow occurs at the mi nimu m flow area, which is definedas follows:A * = 2 ~ rR l x f o r O < x ~ R ~ / 2 R i , ( 2 )A* = rrR~ for x ~ R2N / 2R1 ,and,

m o = C oA *e o T ~ i I ( 3 )where for steam k = 1.3. F represents the exit velocity,which is approximated by the average fluid velocitybetween the seat and disc. Fluid properties inside thevalve are calculated by applying the ideal compressiblegas flow equations. Choked mass flow rate through thevalve is corrected by applying a discharge coefficient(assumed to be 0.9). 0 represents the effective angle atwhich the fluid discharges as it comes out of the flowarea between the guide and nozzle adjustment rings. 0can be altered by moving the two adjustment rings upor down.

The equation of motion for the valve disc may bewritten as follows considering the forces acting on thedisc as shown in fig. 3:MD :i + c~ = F D - - ksp~i ,s ( x + Xo ) - - V aA B - M Dg . (4)Here the second term on the right hand side represents

the spring force, the third denotes the force due tobackpressure and the last term is the weight of the discand other moving parts inside the valve. The valvestroke x is assumed to be zero when it is closed and themaximum valve lift Xmax is limited by a mechanicalstop. At either limit the stem velocity must be zero, i.e.d x / d t = O , i f x : O o r x = X m ~ X.

3 . A p p l i c a t i o n s a n d r e s u l t sA typical safety valve install ation may consist of a

high pressure vessel (to be protected against over-pres-surization) connected to the safety valve through acertain piping configuration upstream of the valve.Downstream of the valve there may also be a connec-tion to some piping in order to discharge the effluent ata certain location. The set point pressure at which thevalve opens is designed to be higher than the normaloperating pressure in the vessel by a certain designmargin. In a typical safety valve operation transient, thefollowing sequence of events may occur. Pressure in thevessel may start to rise at a certain rate depending uponthe rate of increase in total energy caused by somenormal or abnormal system conditions. As the pressureupstream of the safety valve reaches the set point pres-sure, the valve starts to open at some finite rate. As thevalve opening proceeds, the discharge flow rate throughthe valve increases which may cause the vessel pressureto drop after it has reached some peak value. The designof the valve opening time and discharge capacity areexpected to be such that a maximum or peak pressurereached in the vessel is below the allowable designpressure of the vessel. As the vessel depressurizes, some-times it is also required that the valve be designed toclose to limit the pressure drop to a certain design valuecalled at Blowdown. On the downstream side, as thevalve opens, the pressure in the valve body bowl andany connected piping increases with time resulting insome dynamic structural loading.

The transient fluid and thermodynamic conditionsupstream and downstream of the valve will not onlydepend upon the valve performance characteristics butwill also be a strong function of the upstream anddownstream system configurations. The model de-scribed in this study does no t inclu de the analysis of theupstream system and its interaction with the valve. Inorder to study the effect of different upstream pressureconditions expected to occur during a typical valveoperation transient, a time varying pressure boundary


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20 0 A. Singh / A spring loaded safe(y valve

8 = 3 0c = O O

2 6 0 0 k s p ,, ~ g = 2 2 3 3 1 0 5 I b / f iA B = 0 0

2 5 0 0

~ 2400

23OO

2 2 o o I i , ~ i [ J J i ~ I i i ~ ~ I i ~ i i i i0 1 2 3 4

T i m e (s )F i g . 4 . P res cr i b ed s ta g n a t i o n p res s u re t i m e h i s to ry a t th e v a l v ein let .

c o n d i t i o n h a s b e e n p r e s c r i b e d a t t h e v a l v e i n l e t a ss h o w n i n f i g . 4 . T h e u p s t r e a m r e s e rv o i r p r e s s u r e i s a s -s u m e d t o r i s e a t a c o n s t a n t r a t e o f 3 0 0 p s i / s s t a r t i n gf r o m t h e s e t p o i n t v a l u e o f 2 5 0 0 p s i a . A f t e r a p e a k v a l u eo f 2 6 0 0 p s i a i s r e a c h e d , t h e u p s t r e a m p r e s s u r e i s p r e -s c r i b e d t o d r o p a t a c o n s t a n t r a t e o f 1 0 0 p s i / s u n t i l t h ev a l v e c l o se s . U p s t r e a m s t a g n a t i o n t e m p e r a t u r e is a l s op r e s c r i b e d a s r e m a n i n i n g c o n s t a n t a t 6 5 0 F .

B a c k p r e s s u r e d o w n s t r e a m o f t h e v a l v e i s a p p r o x i -m a t e d b y a s s u m i n g t h e d o w n s t r e a m p i p i n g s y s t e m t o b ea l u m p e d c a p a c i to r v o l u m e w h i c h i s f ed b y t h e v a l v ed i s c h a r g e f l o w a t o n e e n d a n d a s s u m e d t o b e o p e n t ot h e a t o m s p h e r e a t t h e o t h e r e n d ( c h o k e f l o w i s a s s u m e dt o e x i s t a t t h e o p e n e n d ) . F o r t h e c a l c u l a t i o n s p r e s e n t e d

i n t h is s tu d y t h e d o w n s t r e a m p i p e i s a s s u m e d t o b e o f6 " i n s i d e d i a m e t e r a n d 1 2 f t l o n g .

T h e v a l v e d e s i g n a n d r a n g e o f p a r a m e t e r s c o n s i d e r e di n t h i s s t u d y a r e t y p i c a l o f a s a f e t y v a l v e u s e d f o r h i g hp r e s s u r e a p p l i c a t i o n . S i n c e t h e o b j e c t i v e o f t h i s s t u d y i st o d e m o n s t r a t e t h e a n a l y t i c a l c a p a b i l i t i e s o f t h e p r o -p o s e d m o d e l , t h e n u m e r i c a l r e s u l t s p r e s e n t e d h e r e ar et y p i c a l o n l y o f t h e s e l e c t e d v a l v e t y p e a n d d e s i g n a n dp r e s c r ib e d b o u n d a r y c o n d i t i o n s. H o w e v e r , t h e m o d e lc a n b e u s e d t o e v a l u a t e t h e d e s i g n a n d s t a b i l it y o f o t h e re x i s t i n g v a l v e s o r f o r d e s i g n i n g a n e w v a l v e .

T h e c a l c u l a t e d v a l v e s t e m p o s i t i o n a s a f u n c t i o n o ft i m e i s s h o w n i n f i g . 5 f o r t h e f o l l o w i n g v a l u e s o fv a r i o u s p a r a m e t e r s :

m a s s o f t h e m o v i n g p a r t s , m = 1 1 0 p o u n d s ;s p r i n g c o n s t a n t , k s p r i n g z 2.233 105 p o u n d s / f o o t :e f f e c t i v e a r e a f o r b a c k p r e s s u r e , A B = 0 . 0 :d a m p i n g c o e f f i c i e n t , C = 0 ;m a x i m u m l if t = 0 . 0 4 4 f e e t ;d i s c h a r g e a n g l e , 0 = 3 0 d e g r e e s ;e f f e c t i v e s e a t a r e a , A S = 2 0 % o f t h e a r e a ~ 'R ~ .

T h e v a l v e o p e n s t o a s t a b le f u l l li f t in 9 0 m s a n d s t a y sf u l l o p e n a g a i n s t t h e m a x i m u m l i f t s t o p s u n t i l t h eu p s t r e a m s t a g n a t i o n p r e s s u r e d r o p s t o a b o u t 2 5 2 0 p s i a ,a t wh ich t im e the f lu id force F D act ing on the d i sc fa l l sb e l o w t h e d o w n w a r d f o r c e a n d t h e v a l v e s t a r t s t o c lo s e .T h e f l u i d f o r c e F D o n t h e d i s c i s s h o w n i n f ig . 6 a . B e f o r et h e v a l v e o p e n s , F o i s e q u a l t o t h e v a l v e u p s t r e a mpressure m ult ip l ied by the d i sc area ~rR 2 expose d to thein le t pressure . As the va lve beg ins to open , f lu id f lowst h r o u g h t h e o p e n i n g b e t w e e n t h e d i s c a n d se a t , h e n c e a na d d i t i o n a l a r e a A s g e t s e x p o s e d t o t h e i n l e t p r e s s u r egiv ing r i se to an increase in upstream force [es t imted byt h e t e r m P~A~ n e q . ( 1 ) ]. T h i s r e s u l t s i n a f a s t e r o p e n i n g

0 0 5

e = 3 0c = 0 0

0 0 4 k s D r, n g = 2 2 3 3 X 1 0 5 I b / f tA 8 = 0 0

~ =0 0 3

~5Eo~ 0 0 2

O 0 1

0 O 01 2 3 4

T i m e (s )F i g . 5 . V a l v e s t e m p o s i t i o n a s a f u n c t i o n o f t i m e .

2 7 , 5 0 0

8 = 3 02 5 , 0 0 0 - - c = 0 0

kspr ,ng = 2 2 3 3 1 0 5 1 b / f tA e = 0 0

g--> 200 00 --go 1 7 , 5 0 0 - -

15,000 --

0 1 2 3 4T i m e (s }

F i g . 6 a . U p w a r d f l u id f o r c e a c t i n g o n v a l v e d i s c a n d s t e m .


5/8

A. Singh / A spring loaded safety valve 2012000

15OO8 = 3 0 'c = O 0

k s p r, n g = 2 2 3 3 X 1 0 5 I b / f tA B = 0 0A s = 0 2 X n R 2

tat5,~ 10o0 -

~ 500 --

0 --

- I I I I I I I I I I [ I I I I I I I I I [ I1 2 3 4

T i m e ( s )

F i g . 6b . N e t u p w a r d f o r c e a c ti n g o n t h e v a l v e d i s c a n d stem asa function of time.

or pop ping action of the valve. The net upward force onthe disc is shown in fig. 6b. As the valve openingincreases, the mass flow rate through the valve alsoincreases as shown in fig. 7, giving further rise to thedisc force due to increased momentum flux. As theupstream stagnation pressure decreases, the mass flowrate a nd F o decrease and the valve starts to close due tothe unbalanced compressive spring force. As the valvecloses, the mass flow rate decreases resulting in a rapiddecrease in the momentum component of the disc forceF o. Finally, the valve fully closes at a lower stag nationpressure than the set point (about 10% below the open-ing pressure) due to an increased area exposed to theupstream pressure during the open position versus the

fully closed position. The results described above will beconsidered as the base case valve performance. In thefollowing calculations, sensitivity results are presentedto show the effect on valve opening, closing characteris-tics and stability, by varyi ng some of the valve parame-ters listed above. Prescribed inlet pressure and tempera-ture conditions are kept unchanged.

4 . E f f e c t o f b a c k p r e s s u r e

When the valve is fully closed the backpressure inthe body bowl is approximately equal to the atmo-spheric pressure. As the valve opens, the backpressurebuilds up as the flow increases. If the valve is not fullybackpressure c ompensated, some area A B at the back ofthe disc is exposed to the pressure downstream of thedisc in the valve body bowl. This causes a downwardforce PBAa on the disc opposing the flu id force F D andreinforcing the compressive spring force tending theclose the valve.

Fig. 8 shows the calculated valve stem displacementtime hi story for an effective backpressure area A n equalto 0.10 of the disc area (erRS) exposed to the inletpressure when the valve is fully closed. Due to a de-crease in the net upward force on the disc, the valvebecomes slightly unstable during opening until the inletstagna tion pressure rises to a sufficiently high value(approximately 70 psia above the set point) when thevalve can be kept in stable fully open position. As theupstream pressure decreases, the valve starts to closeearlier and starts oscillating during closing due to feed-back between the forces acting on the upward anddownward direction on the disc which excites the spring

15 0

0 = 3 0 c = 0 0

k $ 0 rl n g = 2 2 3 3 X 1 0 5 I b / f lA 8 = 0 0

~ 1 0 0 - - s =

EI~ 50 --

0 --i i I i i 1 1 I i i I i i I ~ I i i i i I I

0 1 2 3 4T i m e { s )

F i g . 7 . S t e am m a s s f lo w r a t e t h r o u g h t h e v a l v e a s a f u n c t i o n o ftime.

k s w i n g = 2 2 3 3 X 1 0 5 1 b i l lA B = 0 1 X ~R 2

A A s = 0 2 ~R 2~ 0.03

002 i0.01

0.00 1 2 3 4T im e (s )

F ig . 8 . E f f ec t o f bac k p res s ure on v a l v e s t em mot ion .


6/8

20 2 A. Singh / A spring loaded safety valve

1 0 0 0=~52o=o o

- 1 0 0 0

0 = 3 0c = O 0

k = g o q ' ~ w l n~b / f l

I l l l ~ l l l l ~ l l l l l J l f l ~ l i0 1 2 3 4

T i m e ( s )

Fig . 9 . Ne t upwa rd forc e on the va lve d i sc unde r the inf lue nc eof ba c k pre s sure .

0 0 5

O = 2 0c = O 0

0 0 4 - - k s p rm ~ = 2 2 3 3 1 0 5 I b / f tA A 8 = O 01= As = 02 X ~rR21

i0 0 3 - -

Em 0 0 2 --

0 0 1 --

o . o o - I I ~ I I I I I J i i0 1 2 3 4

T i m e ( s )Fig . 11 . Ef fe c t of lowe r ing the guide r ing on va lve s t e m m ot ion .

m a s s s y s t e m . F i g . 9 s h o w s t h e t o t a l f o r c e s a c t i n g o n t h ev a l v e d i sc . A s t h e u p s t r e a m p r e s s u r e a p p r o a c h e s 1 0 %b e l o w t h e o p e n i n g p r e s s u r e , v a l v e s t e m o s c i l l a t io n s d e -c r e a s e u n t i l t h e v a l v e d i s c r e s e a t s .

5 . Effect o f adjustment r ing sett ingsA s d i s c u s s e d e a r l i e r , t h e e f f e c t i v e a n g l e o f d i s c h a r g e

O c a n b e v a r i ed b y m o v i n g t h e a d j u s t m e n t r in g s u p o rd o w n . M o v i n g t h e g u i d e a d j u s t m e n t r i n g u p w il l i n -c r e a s e t h e d i s c h a r g e a n g l e 8 , r e s u l t in g i n a r e d u c t i o n i nt h e f l u i d f o r c e o n t h e d i s c F D i n e q . ( 1 ) . F i g . 1 0 s h o w st h e o p e n i n g a n d c l o s i n g c h a r a c t e r i s t i c s o f t h e v a l v e f o r8 - - 4 0 a n d n o b a c k p r e s s u r e e f fe c ts . A s e x p e ct e d , d u et o a n e t d e c r e a s e i n t h e t o t a l u p w a r d f o r c e o n t h e d i s c ,

t h e v a l v e a t t a i n s a s t a b l e fu l l y o p e n p o s i t i o n a n d s t a r tst o c l o se a t a h i g h e r i n l e t s t a g n a t i o n p r e s s u r e t h a n t h eb a s e c a s e ( 8 = 3 0 , f ig . 5 ) . I t s h o u l d b e n o t e d t h a t t h ec o m p l e t e c l o s u r e o f t h e v a l v e st il l o c c u r s a t a b o u t 1 0%( b l o w d o w n ) b e l o w t h e o p e n i n g s t a g n a t i o n i n l et p r es s u r ea n d r e m a i n s u n a f f e c t e d b y t h e c h a n g e i n 8 .

L o w e r i n g o f t h e g u i d e a d j u s t m e n t r i n g w il l d e c r e a s et h e e f f e c t i v e a n g l e o f d i s c h a r g e 8 , r e s u l t i n g i n a n i n -c r e a s e d m o m e n t u m f o r c e o n t h e di s c. H e n c e , a s s h o w ni n f i g. 1 1 , f o r 8 - - 2 0 t h e v a l v e o p e n s a t a f a s t e r r a t er e a c h i n g a s t a b l e f u l l li f t i n 1 5 m s a n d d o e s n o t s t a r t t oc l o s e u n t i l a t a b o u t 1 .9 s w h e n t h e i n l e t s t a g n a t i o np r e s s u re h a s d r o p p e d a p p r o x i m a t e l y 5 0 p s i a b e lo w t h eo p e n i n g o r s e t p o i n t p r e s s u r e . A g a i n , t h e c o m p l e t ec l o s u r e o c c u r s a t t h e s a m e b l o w d o w n , i . e. , 1 0% .

0 05

0 = 4 0c = O 00 0 4 - - k s p r, n g = 2 2 3 3 1 0 5 ~b / ft

A B = O 0= A s = 0 2 X ~ R 125 0 0 3 - -o=

$0 0 2 --

0 0 1 - -

o o o - ~ I I i J1 2 3 4

T i m e ( s )Fig . 10 . Ef fe c t of r a i s ing the guide a d ju s tm e n t r ing or inc re a s -ing the a ngle 0 on va lve s t e m m ot ion .

0 05

00 4

0 0 3

0 02

0 0 1

0 . 0 0

8 = 3 0 c = O 0k s p r i n g = 2 . 2 3 3 X 1 0 5 I b / f i

A 8 = 0 . 0= o l . R ,

I i = J I I J I I I I I"ll k f I I I I = I t0 1 2 3 4

T i m e (s )Fig. 12. Effec t or redu ced effec t ive sea t a rea or lowering of thenoz z le r ing on va lve s t e m m ot ion .


7/8

A. Sing h / A spring loaded safety valveLowering of the nozzle adjustment ring primarily

decreases the effective seat area As, which reduces thetotal upward seat force component acting on the valvedisc. The effect of reducing the effective seat area by50% from the base case is shown in fig. 12. Due to thedecreased upward fluid force F D in eq. (1), the valvebecomes unstable during opening causing it to flutterduring opening and closing. The valve does not achievea stable fully open position and starts to close at a muc hhigher inlet pressure (approximately 2580 psia). Notethat the valve completely closes at about 2375 psiacorrespo nding to a 5% blowdown.

6. Effect of spring stiffnessFor a stiffer spring (ksp,~,8 = 2.5 105 lb /f t) , the

stiffness con stant ksprin$ is higher which causes a biggerdownward spring force for a given deflection or valvestem position. This causes the valve to become lessstable in the absence of any damping as shown in fig.13a. A l s o , as expected, the valve does not remain openin the full position and starts to close at much higherinlet stagnation pressures (2600 psia).

For a softer spring (ksp,~,g = 2 . 0 105 lb/ ft) , fig.13b, the valve opens to a stable fully open positionfaster (valve open ing time = 14 ms) due to the smallerspring force, and does not start to close until the inletstagnat ion pressure drops to 2420 psia, ab out 3% belowthe opening set pressure. Finally, the valve completelycloses at an inlet pressure of 2250 psia.

k ~ = 2 . 5 0 X 1 0 s I b / f tA B = 0 0= . n 2

0 0 3

0 0 2

0 . 0 1 ~ ' - I

0 0 0 It l l l l l l L t l l l l0 1 ;2 3T i m e ( $ )Fig. 13a. Effect of increasing spring stiffness on the valve stemmotion.

0 . 0 5

203

= 0 = 3 0 *

0 . 0 4 c = 0 . 0k lmt ing = 2.0 X 105 Ib, 'I t&- A B = 0 .0

i =0 O 3

~ 0 0 2>

0.01

0 0 0 _ _2 3 4T i m e ( s )

Fig. 13b. Effect of decreasing spring stiffness on the valve stemmotion.

7 . Effect o f dampingIn the calculations presented above, the friction atthe sliding surfaces of moving parts was assumed to be

negligible. In a real valve, due to a slight asymmetrybetween the surfaces of the moving and fixed parts,some friction force may exist opposing the valve sternmotion. In certain applications where safety valves areobserved to be u nstable causing fluttering or chattering,it may be possible to employ a damper device to thevalve stem to su bdue the valve stem oscillations.

In fig. 8, it was shown that due to a higher backpres-sure, the valve may become unstable and start to oscil-late at lower upstream stag nation pressures. These oscil-lations can be eliminated by providing a damping de-vice to damp the valve stem motion as shown in fig. 14,

0 0 5

0.04 - - = ,0 f b - s / f tk i t) r in g = 2 2 3 3 X 1 0 5 l b / f t

~0 0 3

i~5~ 0 . 0 2 ~

0.01

0 0 0 " 1 I I 1 [ 1 1 I I [ I I [ 1 1 I I ~ 1 " % [ I1 2 3 4T i m e ( s )

Fig. 14. Effect of damping on valve stem motion.


8/8

20 4 , .t . Sm gh / A ,wring loaded safe (v valvew h e r e t h e v a l v e d y n a m i c r e s p o n s e w a s c a l c u l a t e d u n d e rt h e s a m e c o n d i t i o n s a s f o r f i g . 8 , e x c e p t a d a m p i n gc o e f f i c i e n t c = 5 0 0 lb s / f t ( a p p r o x i m a t e l y o n e t h i r d o ft h e c r i t i c a l d a m p i n g ) w a s u s e d i n e q . ( 4 ) .

8 . C o n c l u s i o n s a n d d i sc u s s i o nA o n e - d i m e n s i o n a l v a l v e d y n a m i c m o d e l h a s b ee n

d e v e l o p e d c o n s i d e r i n g t h e e f f e ct s o f v a r i o u s v a l v e de s -i g n p a r a m e t e r s t h a t c a n b e u s e d to s t u d y t h e v a l v ed y n a m i c r e s p o n s e a n d s t a b i l i t y u n d e r d i f f e r e n t u p -s t r e a m a n d d o w n s t r e a m c o n d i t i o n s . S a m p l e c a l c u l a t io n sm a d e f o r s t e a m f l o w t h r o u g h a t y p i ca l h i g h - p r e ss u r ea p p l i c a t i o n s a f e ty v a l v e d e m o n s t r a t e t h e a n a ly t i c a l c a -p a b i l i t i e s o f t h e m o d e l a n d t h e r e l a t i v e e f f e c t s o f d i f f e r -e n t p a r a m e t e r s . V a l v e s ta b i l it y a n d d u r a t i o n o f f ul lo p e n i n g i n g e n e r al c a n b e i n c r e a s e d b y a l o w e r i n g o f t h eg u i d e a d j u s t m e n t r i n g ( s m a l l e r d i s c h a r g e a n g l e 0 ) , as o f t e r s p r i n g o r s m a l l e r b a c k p r e s s u r e e f f e c t s , o n t h eo t h e r h a n d , a s t i f f e r s p r i n g , h i g h e r b a c k p r e s s u r e o r al o w e r i n g o f t h e n o z z l e a d j u s t m e n t r i n g ( l o w e r b l o w -d o w n ) m a y l e a d t o i n s t a b i l i t i e s o r f l u t t e r i n g o f t h e v a l v e .A d a m p i n g d e v i c e a p p l ie d t o t h e v a l v e s t er n m a y h e l p toe l i m i n a t e v a l v e d y n a m i c i n s t a b il i t ie s o r o s c i l l at i o n s.

V a l v e d y n a m i c p e r f o r m a n c e d e p e n d s s t ro n g ly u p o nt h e u p s t re a m a n d d o w n s t r e a m t h e r m a l - h y d r a u l i c c o n d i-t i o n s , h e n c e f o r a g i v e n s a f e t y v a l v e a p p l i c a t i o n , c o u p l e di n t e r a c t i o n s b e t w e e n t h e v a lv e a n d u p s t r e a m a n d d o w n -s t r e a m s y s t e m m u s t b e c o n s i d e r e d t o e v a l u a t e th e d e si g na d e q u a c y o f t h e o v e r p r e s s u r e p r o t e c t i o n s y s t e m . T h em o d e l p r e s e n t e d h e r e c o u l d b e u s e d i n c o n j u n c t i o n w i t ht h e t r a n s ie n t s i m u l a t i o n o f o t h e r c o m p o n e n t s o f t h es y s t e m s u c h a s t h e v e s s e l , n o z z l e s , u p s t r e a m a n d d o w n -s t r e a m p i p i n g w i t h e l b o w s , b e n d s a n d o t h e r f l o w r e s tr i c -t i on s . F u r t h e r w o r k n e e d s t o b e d o n e t o c a l i b r a te t h em o d e l a g a i n s t t e s t d a t a o n a c t u a l v a l v e s .

A c k n o w l e d g e m e n tT h i s st u d y w a s p e r f o r m e d a s pa r t o f th e E P R I / P W R

S a f e t y a n d R e l i e f V a l v e T e s t P r o g r a m s p o n s o r e d b yE l e c t r ic P o w e r R e s e a r c h I n s t i t u t e a n d p a r t i c i p a t i n gP W R u t il i ti e s. T h e a u t h o r i s t h a n k f u l t o D r J o h n C a r e yo f E P R I f o r i n i t ia t i n g t h is w o r k a n d t o D r A l a n J .B i l a n i n o f C o n t i n u u m D y n a m i c s f o r h e l p f u l d is c u s si o n s .C o m p u t i n g a n d g r a p h i c s h e l p f r o m M r G l e n S n y d e r o fE P R I i s a l s o g r a t e f u l l y a c k n o w l e d g e d .

N o m e n c l a t u r eA ~ s e a t a r e a a t i n n e r r a d i u s R ~ ;

A Bm ~ ;A *CC DF Dgkk s p r i n gLrnM DP iP BRR1R yVjvo

XX oXmaxOt

a r e a o f d is c s u b j e c t e d t o b o d y b o w l b a c k p r e s -s u r e ;s e a t a r e a ;n o z z l e o r o r i f i c e a r e a ;d a m p i n g c o e f f i c i e n t f o r v a lv e st e m m o t i o n ;v a l v e d i s c h a r g e f l o w c o e f f i c i e n t ;u p w a r d f l u id d y n a m i c f o r c e o n v a l v e d i s c:g r a v i t a t i o n a l c o n s t a n t ;i s e n t r o p i c e x p o n e n t :s p r i n g c o n s t a n t ;l e n g t h o f v a l v e n o z z l e ;v a l v e m a s s f l o w r a t e ;m a s s o f v a l v e d i sc a n d m o v i n g p a r t s ;s t a t i c p r e s s u r e a t t h e i n n e r s e a t r a d i u s ;b a c k p r e s s u r e i n t h e b o d y b o w l ;g a s c o n s t a n t ;i n n e r s e a t r a d i u s ;n o z z l e r a d i u s ;u p w a r d f l u i d v e l o c i t y a t t h e i n n e r s e a t r a d i u s :e x i t f l u i d v e l o c i t y a t r i n g s ;v a l v e st e m d i s p l a c e m e n t ;i n i ti a l s p r i n g c o m p r e s s i o n ;m a x i m u m v a lv e st e m d i s p l a c em e n t ;f l u i d d e n s i t y a t t h e i n n e r s e a t r a d i u s .

R e f e r e n c e s[1 ] L . Thompson and O.E . Bux ton , Maximum isen t rop ic f lowof dry saturate d stea m th rough pre ssure relief valves, pre-

sented at the Pressure V essel and P iping Con f. Montrea l.Quebec, Canada (July 1978).

[2] D.W. Sailer , The flow of l iquids and gases through pressurere l ie f va lves , p resen ted a t the Th i rd Na t iona l Congr . onPressure Vessel and Piping, San Francisco, California (June24-29, 1979).

[3] J .W. Sale, Safety valve mass f low rate calcu lations andcor rec t ion fac to rs , p resen ted a t the Th i rd Na t iona l Congr .on Pressure Vessel and Piping, San Francisco, California(June 24-29, 1979).

[4] G.S. Liao , Analysis of pow er plant safety and relief valvevent stacks, AS M E Trans., J . Engrg. Pow er (Octo ber, 1975)pp . 484-494 .

[5] F .J . M oody , A. J . Whee le r and M .G. W ard , The ro le o fva r ious pa ramete rs on sa fe ty and re l ie f va lve p ipe fo rces,presented at the Third National Congr. on Pressure Vesselsand Piping, San Franc isco, California (June 24-29 , 1979).[6] D.W. Fowler , T .R . Herdon and R .C . Wahrmund , A n ana ly -s i s o f po ten t ia l overp ressu re o f a hea t exchanger she l l due

to a rup tu red tube , AS ME P e t ro leum Eng ineer ing Conf .Preprints (September, 1968).[7] J .E. Fun k, P oppe t valve stabili ty , T rans. A MS E, J . BasicEngrg. , paper number 62-WA-160.[8] A shok Ray , D ynam ic mode l l ing and s im ula t ion o f a re l ie fvalve, J . Simula tion (Novem ber, 1978) pp. 167-172.

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