increasing power output from francis
TRANSCRIPT
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December 2009
Torbjørn Kristian Nielsen, EPT
Master of Science in Product Design and ManufacturingSubmission date:
Supervisor:
Norwegian University of Science and Technology
Department of Energy and Process Engineering
Increasing power output from FrancisturbinesEffektøkning i vannkraftverk med Francis turbiner
Bente Taraldsten Brunes
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Problem DescriptionThe main objective is to investigate potential increase in power output from the existing turbines at
Ruacana Hydropower station. This is restricted by only consider a runner replacement. The
technical aspect of a rehabilitation project is investigated.
Preliminary study of achievements in refurbishment projects and distribution of turbine types.
Analyze all hydraulic conditions. This entails surge oscillation and water hammer investigations
for both the existing hydraulic conditions and with the aim of increasing volume flow. In addtion to
a review of the state of the waterway.
Use traditional turbine theory to investigate potential increase in power output.
Assignment given: 28. September 2009
Supervisor: Torbjørn Kristian Nielsen, EPT
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P r e f a c e
T h e p r e s e n t e d w o r k h a s b e e n c o m p l e t e d o n t h e b e h a l f o f N a m P o w e r a n d
M u l t i c o n s u l t . I n c o l l a b o r a t i o n w i t h t h e D e p a r t m e n t o f E n e r g y a n d P r o c e s s
E n g i n e e r i n g a t t h e N o r w e g i a n U n i v e r s i t y o f S c i e n c e a n d T e c h n o l o g y ( N T N U )
f a l l 2 0 0 9 . T h e o b j e c t i v e h a s b e e n t o i n v e s t i g a t e t h e p o s s i b i l i t y o f i n c r e a s i n g
p o w e r o u t p u t o f a n e x i s i t i n g t u r b i n e s t r u c t u r e b y o n l y c o n s i d e r r u n n e r
r e p l a c e m e n t . R u a c a n a H y d r o P o w e r P l a n t i n N a m i b i a h a s b e e n u s e d a s
a b a s i s f o r t h e s t u d y .
I w o u l d l i k e t o e s c p e c i a l l y t h a n k N a m P o w e r f o r a n e d u c a t i o n a l t r i p t o
N a m i b i a i n o r d e r t o s u r v e y t h e p l a n t a n d g a i n v i t a l i n f o r m a t i o n . I n a d d i t i o n
w o u l d I l i k e t o t h a n k M u l t i c o n s u l t t h e i r s u p p o r t . M y s u p e r v i s o r P r o f e s s o r
T o r b j ø r n K r i s t i a n N i e l s e n h a v e a l s o c o n t r i b u t e d t o t h e n a l r e s u l t s w i t h
h i s g u i d a n c e . A t l a s t b u t n o t l e a s t , I w o u l d l i k e t o t h a n k a l l t h e s t u d e n t s
a t t h e H y d r o P o w e r L a b o r a t o r y f o r t h e i r c o n t r i b u t e t o a n a m a z i n g w o r k
e n v i r o n m e n t .
B e n t e T a r a l d s t e n B r u n e s
N o r w a y , T r o n d h e i m , D e c e m b e r 2 1 , 2 0 0 9
i
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A b s t r a c t
T h e m a i n o b j e c t i v e i n t h i s t h e s i s w a s t o i n v e s t i g a t e a p o t e n t i a l i n c r e a s e
o f p o w e r o u t p u t f r o m t h e e x i s t i n g t u r b i n e s a t R u a c a n a H y d r o p o w e r S t a t i o n .
T h i s w a s r e s t r i c t e d t o o n l y c o n s i d e r a r u n n e r r e p l a c e m e n t , a n d o n l y t e c h n i c a l
a s p e c t s o f a r e h a b i l i t a t i o n p r o j e c t h a s b e e n e v a l u a t e d . T h i s i n v o l v e d a n
i n v e s t i g a t i o n o f h y d r a u l i c c o n d t i o n s , l i m i t e d t o s u r g e o s c i l l i a t i o n a n d w a t e r
h a m m e r c a l c u l a t i o n s . T h e r e s u l t s w a s t h e r e a f t e r u s e d i n a c a l c u l a t i o n m o d e l
t o e s t i m a t e p o t e n t i a l i n c r e a s e i n p o w e r o u t p u t . V i t a l i n f o r m a t i o n a b o u t t h e
p l a n t a n d t h e c o n d i t i o n o f t h e w a t e r w a y w a s o b t a i n e d f r o m a s t u d y t r i p t o
R u a c a n a .
A n i n c r e a s e i n p o w e r o u t p u t i n a t u r b i n e c a n b e o b t a i n e d b y i n c r e a s i n g
t h e v o l u m e o w a n d / o r e c i e n c y . T h e r s t c r i t e r i a c a n b e a c h i e v e d t h r o u g h
e x p a n d i n g t h e o u t l e t d i a m e t e r o f t h e r u n n e r , a n d / o r a l t e r i n g t h e o w a n g l e s .
T h e r e f o r e h a s t h e h y d r a u l i c c o n d i t i o n s a l s o b e e n a n a l y s e d w i t h t h e a i m o f
i n c r e a s i n g v o l u m e o w . I t w a s f o u n d t h a t i t c a n b e i n c r e a s e d t o a m a x i m u m
n o m i n a l v o l u m e o w o f o n e u n i t t o
85m3
/s. I t w a s l i m i t e d b y t h e m a x i m u m
u p s u r g e i n t h e S u r g e H e a d b a y w i t h t h e i n t a k e l e v e l a t h i g h e s t o o d l e v e l .
T h e r e s t r i c t i o n s a r e a l t e r e d f o r t h e m i n i m u m w a t e r l e v e l s i n t h e i n t a k e a n d
m a x i m u m l e v e l s i n t h e t a i l r a c e w h e n o p e r a t i n g 1 t o 4 u n i t s . T h e a d v a n c e s i n
F r a n c i s r u n n e r d e s i g n o v e r t h e l a s t d e a c a d e s m a k e s a n i n c r e a s e i n e c i e n c y
f e a s i b l e .
F i n a l l y a c a l c u l a t i o n m e t h o d f o r e s t i m a t i n g a p o t e n t i a l i n c r e a s e i n p o w e r
o u t p u t w a s d e v e l o p e d . T h i s w a s b a s e d o n t r a d i t i o n a l t u r b i n e t h e o r y , a n d
t h e a i m w a s t o n d t h e m a x i m u m i n c r e a s e s t a r t i n g f r o m t h e e x i s t i n g d e g r e e
o f s u b m e r g e n c e . I n a d d i t i o n w e r e t h e r e s u l t s c o m p a r e d t o v a l u e s o b t a i n e d
f r o m a c a l c u l a t i o n m e t h o d d e v e l o p e d b y S i n t e f [ 2 1 ] .
F r o m a p r e l i m i n a r y s t u d y o f a c h i e v e m e n t s i n r e f u r b i s h m e n t p r o j e c t s w a s
i t f o u n d t h a t o n a v e r a g e h a s a n i n c r e a s e o f 1 8 % b e e n o b t a i n e d . T h e m e t h o d
d e v e l o p e d i n t h i s t h e s i s c o n c l u d e d t h a t a n i n c r e a s e o f 1 0 1 4 % i n n o m i n a l
p o w e r o u t p u t i s p o s s b l e . A s s u m i n g a t u r b i n e e c i e n c y o f 0 . 9 3 a n d o n l y
r e p l a c i n g t h e r u n n e r . S i n t e f ' s m e t h o d e s t i m a t e d a m a x i m u m v a l u e o f 1 5 %
f o r t h e s a m e c o n d i t i o n s . I t i s a l s o f o u n d t h a t t h e o u t l e t d i a m e t e r a t R u a c a n a
c a n b e i n c r e a s e d b y 6 0 m m . T h e a d d i t i o n a l i n c r e a s e i n p o w e r o u t p u t i s o n l y
e s t i m a t e d t o b e 1 % f r o m t h e m e t h o d d e v e l o p e d i n t h i s t h e s i s . T h e S i n t e f
m e t h o d e s t i m a t e s a d d i t i o n a l 3 % i n c r e a s e f o r t h e s a m e s c e n a r i o .
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S a m m e n d r a g
H o v e d m å l e t m e d d e n n e m a s t e r o p p g a v e n v a r å u n d e r s ø k e m u l i g h e t e n f o r å ø k e
e e k t u t t a k f r a t u r b i n e n e v e d R u a c a n a k r a f t s t a s j o n . D e t t e b l e b e g r e n s e t a v
k u n å v u r d e r e b y t t e a v l ø p e h j u l . K u n t e k n i s k e v u r d e r i n g e r h a r b l i t t g j o r t ,
o g d i s s e b e s t o d a v å u n d e r s ø k e s v i n g n i n g e r o g t r y k k s t ø t . I n f o r m a s j o n f r a
d e t t e b l e v i d e r e b r u k t i e n b e r e g n i n g s m o d e l l f o r å e s t i m e r e m u l i g ø k n i n g i
e e k t u t t a k . D e n n e b l e b a s e r t p å t r a d i s j o n e l l t u r b i n t e o r i o g t o k u t g a n g s p u n k t
i d y k k i n g e n a v t u r b i n e n e p å R u a c a n a . D e t t e h a r o g s å b l i t t b e r e g n e t v e d
b r u k a v e n l i k n e n d e m e t o d e u t v i k l e t a v S i n t e f [ 2 1 ] . V e r d i f u l l i n f o r m a s j o n o m
k r a f t v e r k e t o g t i l s t a n d e n t i l v a n n v e i e n b l e s a m l e t i n n u n d e r e n s t u d i e t u r t i l
R u a c a n a .
E n ø k n i n g a v e e k t u t t a k e t i e n t u r b i n k a n g j ø r e s v e d å ø k e v o l u m s t r ø m -
m e n o g / e l l e r v i r k n i n g s g r a d e n . D e n f ø r s t e m u l i g h e t e n k a n g j e n n o m f ø r e s v e d å
u t v i d e u t l ø p s d i a m e t e r e n p å l ø p e h j u l e t o g / e l l e r v e d å f o r a n d r e s t r ø m n i n g s v i n -
k l e n e . U t v i k l i n g e n a v n y e d e s i g n m e t o d e r f o r F r a n c i s l ø p e h j u l d e s e n e r e å r e n e
h a r f ø r t t i l e n ø k n i n g i v i r k n i n g s g r a d e n .
F o r m å l e t m e d d e t t e h a r v æ r t å s t a d f e s t e h v o r m y e v o l u m s t r ø m m e n i
v a n n v e i e n k u n n e ø k e s u t e n a t d e t g å r u t o v e r s i k k e r h e t e n i k r a f t v e r k e t .
U n d e r s ø k e l s e n e v i s t e a t d e n n o m i n e l l e v o l u m s t r ø m m e n p e r t u r b i n k a n ø k e s
t i l 8 5 m3/s
. D e t t e b l e b e g r e n s e t a v d e t s t ø r s t e o p p s v i n g e t i s v i n g e s j a k t e n
o p p s t r ø m s m e d h ø y e s t v a n n s t a n d i i n n t a k e t . L a v e s t r e g u l e r t v a n n s t a n d i
i n n t a k e t b e g r e n s e r h v o r m a n g e t u r b i n e r s o m k a n k j ø r e , o g n å r v o l u m s t r ø m -
m e n ø k e s m å d e n n e ø k e s . D e t t e g j e l d e r o g s å f o r d e n h ø y e s t e v a n n s t a n d e n i
u t f a l l e t o g d e m a k s i m a l e g r e n s e n e m å s e n k e s .
R e s u l t a t e t a v f o r s t u d i e n a v r e h a b i l i t e r i n g s p r o s j e k t e r v i s t e a t o p p n å d d
ø k n i n g i e e k t u t t a k v a r p å 1 8 % . M e t o d e n s o m b l e u t v i k l e t i o p p g a v e n
k o n k l u d e r e r m e d a t e n ø k n i n g i n o m i n e l t e e k t u t t a k f o r e n t u r b i n m e l l o m p å
1 0 t i l 1 4 % e r s a n n s y n l i g . D e t t e f o r u t s e t t e r a t v i r k n i n g s g r a d e n t i l t u r b i n e n
e r 0 . 9 3 o g l ø p e h j u l e t b y t t e s u t t i l e n m e d h ø y e r e s l u k e e v n e . D e n m a k s i m a l e
ø k n i n g e n g i t t a v b e r e g n i n g e n t i l S i n t e f b l e 1 5 % m e d d e s a m m e b e t i n g e l s e n e .
I t e g n i n g e n e a v t u r b i n e n e b l e d e t f u n n e t a t u t l ø p s d i a m e t e r e n k a n ø k e s m e d
6 0 m m . E t t i l l e g g s u t t a k b e r e g n e t a v m e t o d e n u t v i k l e t h e r b l e k u n 1 % .
S i n t e f s i n m e t o d e e s t i m e r t e e n e k s t r a ø k n i n g p å 2 % .
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C o n t e n t s
P r e f a c e i
A b s t r a c t i i i
S a m m e n d r a g v
C o n t e n t s v i i
L i s t o f F i g u r e s x i
L i s t o f T a b l e s x i i i
N o m e n c l a t u r e x v
1 I n t r o d u c t i o n 1
2 T h e o r y 3
2 . 1 S y s t e m D y n a m i c s . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 . 1 . 1 W a t e r h a m m e r . . . . . . . . . . . . . . . . . . . . . . 4
2 . 1 . 2 S u r g e O s c i l l a t i o n i n S u r g e T a n k s . . . . . . . . . . . . 6
2 . 2 T h e F r a n c i s T u r b i n e . . . . . . . . . . . . . . . . . . . . . . . 7
2 . 2 . 1 S u b m e r g e n c e . . . . . . . . . . . . . . . . . . . . . . . 8
2 . 2 . 2 C a l c u l a t i o n o f N P S H . . . . . . . . . . . . . . . . . . . 8
2 . 2 . 3 C l a s s i c d e s i g n o f a F r a n c i s R u n n e r . . . . . . . . . . . 9
3 P r e l i m i n a r y S t u d i e s 1 1
3 . 1 R e f u r b i s h m e n t o f E x i s t i n g H P P . . . . . . . . . . . . . . . . . 1 1
3 . 1 . 1 D i s t r i b u t i o n o f t u r b i n e s i n t h e w o r l d . . . . . . . . . . 1 2
3 . 1 . 2 A c h i e v e m e n t s . . . . . . . . . . . . . . . . . . . . . . . 1 2
3 . 1 . 3 S i n t e f r e p o r t : P o t e n t i a l i n c r e a s e o f p o w e r o u t p u t . . . 1 3
3 . 2 R u n n e r D e s i g n . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4
4 R e v i e w o f H y d r a u l i c C o n d i t i o n s 1 7
4 . 1 C o m p o n e n t s u p s t r e a m t u r b i n e . . . . . . . . . . . . . . . . . . 1 8
4 . 2 T u r b i n e U n i t s 1 - 3 . . . . . . . . . . . . . . . . . . . . . . . . . 2 0
4 . 2 . 1 O t h e r e v a l u a t e d f a c t o r s . . . . . . . . . . . . . . . . . 2 2
4 . 3 C o m p o n e n t s d o w n s t r e a m t u r b i n e . . . . . . . . . . . . . . . . 2 3
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5 C a l c u l a t i o n M e t h o d s 2 5
5 . 1 G e n e r a l a s s u m p t i o n s . . . . . . . . . . . . . . . . . . . . . . . 2 5
5 . 2 P r e s s u r e c a l c u l a t i o n m o d e l . . . . . . . . . . . . . . . . . . . . 2 5
5 . 2 . 1 N u m e r i c a l e q u a t i o n s w a t e r h a m m e r . . . . . . . . . . . 2 5
5 . 2 . 2 B o u n d a r y c o n d i t i o n s . . . . . . . . . . . . . . . . . . . 2 7
5 . 2 . 3 C a l c u l a t i o n p r o c e d u r e . . . . . . . . . . . . . . . . . . 2 7
5 . 2 . 4 V e r i c a t i o n o f W a t e r h a m m e r M o d e l . . . . . . . . . . 2 7
5 . 3 S u r g e O s c i l l a t i o n m o d e l . . . . . . . . . . . . . . . . . . . . . 2 8
5 . 3 . 1 S y s t e m o f e q u a t i o n s : S u r g e O s c i l l a t i o n . . . . . . . . . 2 9
5 . 3 . 2 W o r s t c a s e s c e n a r i o s . . . . . . . . . . . . . . . . . . . 3 0
5 . 3 . 3 V e r i c a t i o n o f S u r g e O s c i l l a t i o n M o d e l . . . . . . . . . 3 0
5 . 4 I n c r e a s e p o w e r o u t p u t . . . . . . . . . . . . . . . . . . . . . . 3 0
6 R e s u l t s 3 3
6 . 1 A n a l y s i s : E x i s t i n g H y d r a u l i c C o n d i t i o n s . . . . . . . . . . . . 3 3
6 . 1 . 1 O s c i l l a t i o n i n S u r g e H e a d b a y . . . . . . . . . . . . . . 3 3
6 . 1 . 2 O s c i l l a t i o n i n S u r g e C h a m b e r . . . . . . . . . . . . . . 3 4
6 . 1 . 3 P r e s s u r e i n f r o n t o f t u r b i n e . . . . . . . . . . . . . . . 3 4
6 . 2 A n a l y s i s : I n c r e a s i n g V o l u m e F l o w . . . . . . . . . . . . . . . . 3 5
6 . 2 . 1 O s c i l l a t i o n i n S u r g e H e a d b a y . . . . . . . . . . . . . . 3 5
6 . 2 . 2 O s c i l l a t i o n i n S u r g e C h a m b e r . . . . . . . . . . . . . . 3 6
6 . 2 . 3 P r e s s u r e i n f r o n t o f t u r b i n e . . . . . . . . . . . . . . . 3 6
6 . 3 A n a l y s i s : I n c r e a s i n g P o w e r O u t p u t . . . . . . . . . . . . . . . 3 8
7 D i s c u s s i o n 4 1
7 . 1 H y d r a u l i c c o n s i d e r a t i o n s . . . . . . . . . . . . . . . . . . . . . 4 1
7 . 2 P o w e r o u t p u t . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2
8 C o n c l u s i o n 4 3
9 F u r t h e r W o r k 4 5
B i b l i o g r a p h y 4 7
A p p e n d i c e s
A R u a c a n a H y d r o P o w e r P l a n t I
A . 1 H i s t o r y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I I
B M a t l a b P r o g r a m s I I I
B . 1 W a t e r h a m m e r P r o g r a m . . . . . . . . . . . . . . . . . . . . . I I I
B . 2 S u r g e O s c i l l i a t i o n P r o g r a m . . . . . . . . . . . . . . . . . . . V I
B . 3 R e d u c t i o n i n h e a d p r o g r a m . . . . . . . . . . . . . . . . . . . I X
C S u p p l e m e n t R e s u l t s X I
C . 1 V e r i c a t i o n o f S i m u l a t i o n M o d e l s . . . . . . . . . . . . . . . . X I
C . 2 S u p p l e m e n t e x i s t i n g h y d r a u l i c c o n d i t i o n s . . . . . . . . . . . . X I
C . 2 . 1 S u r g e o s c i l l a t i o n i n S u r g e H e a d b a y . . . . . . . . . . . X I
C . 2 . 2 S u r g e C h a m b e r R e s u l t s . . . . . . . . . . . . . . . . . X I I I
C . 3 A n a l y s i s : I n c r e a s i n g V o l u m e F l o w e x t e n t i o n . . . . . . . . . . X V
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D E x c e l C a l c u l a t i o n s X X I
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L i s t o f F i g u r e s
2 . 1 P r e s s u r e a t v a l v e w i t h i n s t a n t a n e o u s c l o s i n g t i m e f o r i d e a l
c o n d i t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 . 2 x - t d i a g r a m f o r s o l v i n g s i n g l e - p i p e p r o b l e m s [ 2 9 ] . . . . . . . 6
2 . 3 C o m p o n e n t s o f a F r a n c i s T u r b i n e . . . . . . . . . . . . . . . . 8
2 . 4 S e v e r e c a v i t a t i o n e r o s i o n o n a r u n n e r . . . . . . . . . . . . . . 8
2 . 5 V e l o c i t y d i a g r a m [ 7 ] . . . . . . . . . . . . . . . . . . . . . . . 1 0
2 . 6 M a i n d i m e n s i o n o f a F r a n c i s R u n n e r , a x i a l v i e w . . . . . . . 1 0
3 . 1 T u r b i n e d i s t r i b u t i o n l a r g e r t h a n 5 0 M W a c r o s s t h e w o r l d . . 1 2
3 . 2 V i s u a l c o m p a r i s o n o f r u n n e r s a t K i a m b e r e [ 2 3 ] . . . . . . . . 1 5
4 . 1 L a y o u t o f R u a c a n a . . . . . . . . . . . . . . . . . . . . . . . . 1 7
4 . 2 S u r g e H e a d b a y b a s e a r e a ( n o t t o s c a l e ) . . . . . . . . . . . . . 1 9
4 . 3 S u r g e H e a d b a y w a l l s ( n o t t o s c a l e ) . . . . . . . . . . . . . . . 1 9
4 . 4 C a v i t a t i o n o n t h e h u b . . . . . . . . . . . . . . . . . . . . . . 2 1
4 . 5 C a v i t a t i o n o n t h e t r a i l i n g e d g e a n d t h e o u t e r r i n g . . . . . . . 2 1
4 . 6 C a v i a t i o n o n t h e t r a i l i n g e d g e n e a r t h e h u b . . . . . . . . . . 2 1
4 . 7 E x i t i n g t u r b i n e s r u n n e r b l a d e s [ 2 ] . . . . . . . . . . . . . . . . 2 2
4 . 8 S u r g e C h a m b e r d i m e n s i o n s [ 2 ] . . . . . . . . . . . . . . . . . . 2 4
5 . 1 I l l u s t r a t i o n o f w a t e r w a y f o r w a t e r h a m m e r c a l c u l a t i o n s . . . . 2 6
5 . 2 V e r i c a t i o n W a t e r H a m m e r p r o g r a m . . . . . . . . . . . . . . 2 8
5 . 3 I l l u s t r a t i o n o f w a t e r w a y u s e d i n s u r g e o s c i l l a t i o n c a l c u l a t i o n s 2 8
5 . 4 V e r i c a t i o n S u r g e H e a d b a y l o a d r e j e c t i o n . . . . . . . . . . . 3 1
5 . 5 V e r i c a t i o n S u r g e C h a m b e r l o a d r e j e c t i o n . . . . . . . . . . . 3 1
6 . 1 P r e s s u r e i n f r o n t o f t u r b i n e , Z max = 909.3
m a s l a n d Qunit =
71m3/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4
6 . 2 S u r g e o s c i l l a t i o n S H , H 0 = 904.5
m a s l Qn,station = 340m3/s
. 3 5
6 . 3 S u r g e o s c i l l a t i o n i n S C , H 0 = 897.8
m a s l a n d Qn,station =
340m3/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6
6 . 4 S u r g e o s c i l l a t i o n i n S C , Qn,station = 340m3/s
, H u = 767.6
m a s l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7
6 . 5 P r e s s u r e i n f r o n t o f t u r b i n e , Z max = 909.7
m a s l Qunit = 85m3/s
3 7
6 . 6 P e r c e n t i l e i n c r e a s e i n p o w e r o u t p u t a s a f u n c t i o n o f v o l u m e
o w a n d r e d u c t i o n i n n e t h e a d . F o r 1 t u r b i n e w h e n 4 a r e i n
o p e r a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9
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A . 1 R u a c a n a F a l l s . . . . . . . . . . . . . . . . . . . . . . . . . . . I
C . 1 V e r i c a t i o n S u r g e H e a d b a y r e l o a d . . . . . . . . . . . . . . . . X I
C . 2 V e r i c a t i o n S u r g e C h a m b e r r e l o a d . . . . . . . . . . . . . . . X I I
C . 3 S u r g e o s c i l l i a t i o n a t h i g h e s t o o d l e v e l 4 u n i t s . . . . . . . . . X I I
C . 4 S u r g e o s c i l l i a t i o n S H , H 0 = 895.2
m a s l a n d Qunit = 71m3/s
. X I I I
C . 5 S u r g e o s c i l l i a t i o n i n S H , H 0 = 896.4
m a s l a n d Q = 142m3/s
. X I I I
C . 6 S u r g e O s c i l l i a t i o n i n S H , H 0 = 897
m a s l a n d Q = 213m3/s
. X I V
C . 7 S u r g e o s c i l l i a t i o n i n S H , H 0 = 897.4
m a s l a n d Q = 284m3/s
. X I V
C . 8 S u r g e o s c i l l a t i o n i n S C , H u = 768
a n d Q = 284m3/s
. . . . . X V
C . 9 S u r g e o s c i l l a t i o n i n S C , H u = 768.3
m a s l a n d Q = 213m3/s
. X V
C . 1 0 S u r g e o s c i l l a t i o n i n S C , H u = 768.7masl
a n d Q = 142m3/s
. X V I
C . 1 1 S u r g e o s c i l l a t i o n i n S C , H u = 769.2masl
a n d Q = 71m3/s
. . X V I
C . 1 2 S u r g e o s c i l l a t i o n i n S H , H 0 = 897.5
m a s l a n d Q = 255m3/s
. X V I
C . 1 3 S u r g e o s c i l l i a t i o n i n S H , H 0 = 897
m a s l Q = 142m3/s
. . . . X V I I
C . 1 4 S u r g e o s c i l l i a t i o n i n S H , H 0 = 906
m a s l Q = 71m3/s
. . . . . X V I I
C . 1 5 S u r g e o s c i l l i a t i o n i n S C H u = 767.9
m a s l a n d Q = 255m3/s
. X V I I I
C . 1 6 S u r g e o s c i l l i a t i o n i n S C
H u = 768.2m a s l a n d
Q = 170m3/s. X V I I I
C . 1 7 S u r g e o s c i l l i a t i o n i n S C , H u = 769.2
m a s l a n d Q = 85m3/s
. X I X
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L i s t o f T a b l e s
3 . 1 R e f u r b i s h e d H P P w i t h F r a n c i s t u r b i n e s [ 2 8 ] , [ 1 9 ] , [ 3 1 ] , [ 2 0 ] ,
[ 2 3 ] , [ 1 4 ] , [ 8 ] . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3
4 . 1 I n t a k e w a t e r l e v e l s . . . . . . . . . . . . . . . . . . . . . . . . 1 8
4 . 2 P r e s s u r e t u n n e l d a t a . . . . . . . . . . . . . . . . . . . . . . . 1 8
4 . 3 S u r g e H e a d b a y l e v e l s . . . . . . . . . . . . . . . . . . . . . . . 1 8
4 . 4 P e n s t o c k d a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0
4 . 5 T u r b i n e u n i t d a t a . . . . . . . . . . . . . . . . . . . . . . . . . 2 0
4 . 6 T a i l w a t e r l e v e l s a n d v o l u m e o w . . . . . . . . . . . . . . . . 2 3
5 . 1 V e r i c a t i o n : I d e a l a n d a c t u a l v a l u e s o f w a t e r h a m m e r . . . . 2 7
6 . 1 R e s u l t s : a n a l y s i s o f e x i s t i n g c o n d i t i o n s i n S u r g e H e a d b a y 4
u n i t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3
6 . 2 R e s u l t s : A n a l y i s o f e x i s t i n g c o n d i t i o n s a t M R W L l e v e l s . . . . 3 3
6 . 3 R e s u l t s : A n a l y s i s o f e x i s t i n g c o n d i t i o n s i n S u r g e C h a m b e r . . 3 4
6 . 4 M R W L l e v e l s f o r i n c r e a s e d v o l u m e o w . . . . . . . . . . . . . 3 5
6 . 5 M a x i m u m l e v e l s i n t a i l r a c e w i t h i n c r e a s e d v o l u m e o w . . . . 3 6
6 . 6 M a x i m u m p e r c e n t i l e i n c r e a s e i n n o m i n a l p o w e r o u t p u t f o r o n e
u n i t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 8
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N o m e n c l a t u r e
S y m b o l D e s c r i p t i o n U n i t
aS p e e d o f s o u n d / A c o u s t i c s p e e d
[m/s]a
S u b m e r g e n c e f a c t o r
bS u b m e r g e n c e f a c t o r
AC r o s s - s e c t i o n a l a r e a
m2
BH e i g h o f r u n n e r
[m]B
P i p e l i n e c h a r a c t e r i s t i c i m p e d a n c e
cH e a d l o s s c o e c i e n t
cm A b s o l u t e m e r i d i n a l v e l o c i t y [m/s]
cu A b s o l u t e t a n g e n t i a l v e l o c i t y [m/s]
DD i a m e t e r r u n n e r / p i p e
[m]g
G r a v i t y c o n s t a n t
m/s2
H
H e a d
[m]H
P i e z o m e t e r p r e s s u r e [mW C ]
H 0W a t e r l e v e l a t i n t a k e
[masl]H u W a t e r l e v e l t a i l r a c e
[masl]H s S u c t i o n h e a d
mh
H y d r a u l i c p r e s s u r e [mW C ]
hb B a r o m e t r i c p r e s s u r e m
hva V a p o u r p r e s s u r e m
hf T o t a l h e a d l o s s i n w a t e r w a y m
K B u l k m o d u l u s
[kg/ms2]L
L e n g t h o f p i p e / n e a r e s t f r e e w a t e r s u r f a c e [m]
nR o t a t i o n a l s p e e d
[rpm]N PSH
N e t P o s i t i v e S u c t i o n H e a d m
P P o w e r o u p u t
[W ]Q
V o l u m e o w
m3/s
R
P i p e l i n e r e s i s t a n c e c o e c i e n t
tT i m e
[s]T
P e r i o d s
T R R e e c t i o n t i m e s
T L C l o s i n g t i m e s
uP e r i p h e r a l v e l o c i t y
[m/s]v
V e l o c i t y [m/s]
wR e l a t i v e v e l o c i t y
[m/s]z
E l e v a t i o n m
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G r e e k S y m b o l s
S y m b o l D e s c r i p t i o n U n i t
β O u t l e t a n g l e r u n n e r
[rad]ω
A n g u l a r v e l o c i t y [rad/s]
ΩS p e e d n u m b e r
ηE c i e n c y
ρD e n s i t y o f w a t e r
kg/m3
λ
F r i c t i o n f a c t o r
S u b s c r i p t s a n d S u p e r s c r i p t s
S y m b o l D e s c r i p t i o n
* B E P J e g n
1 I n l e t o f r u n n e r / C o n d u i t 1
2 O u t l e t o f r u n n e r / C o n d u i t 2
3 C o n d u i t 3
A P r e c e e d i n g v a l u e , p r e v i o u s t i m e s t e p
B S u c c e e d i n g v a l u e , p r e v i o u s t i m e s t e p
e N e t h e a d
m i n m a x i m u m d o w n s u r g e
m a x m a x i m u m u p s u r g e
m M e r i d i a n
n N o m i n a l v a l u e s
n e w N e w v o l u m e o w / h e a d
P C u r r e n t t i m e s t e p
s t a t i o n T o t a l v o l u m e o w s t a t i o n
u n i t V o l u m e o w o f o n e u n i t
A b b r e v i a t i o n s
S y m b o l D e s c r i p t i o n U n i t
m a s l M e t r e s a b o v e s e a l e v e l
H P P H y d r o P o w e r P l a n t
S W A W E K S o u t h W e s t A f r i c a n W a t e r a n d E l e c t r i c i t y C o r p o r a t i o n
B E P B e s t E c i e n c y P o i n t
H R W L H i g h e s t - r e g u l a t e d w a t e r l e v e l [ m a s l ]
H F L H i g h e s t o o d l e v e l [ m a s l ]
N R W L N o r m a l d r a w - d o w n l e v e l [ m a s l ]
M R W L M i n i m u m d r a w - d o w n l e v e l [ m a s l ]
O P O p e r a t i n g p l a t f o r m S u r g e H e a d b a y
G S G e n e r a l s e c t i o n S u r g e H e a d b a y
S H S u r g e H e a d b a y
S C S u r g e C h a m b e r
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C h a p t e r 1
I n t r o d u c t i o n
T o d a y t h e e n e r g y s i t u a t i o n i n N a m i b i a i s s t r a i n e d , a n d i t i s m a i n l y d u e t o t h e
f a c t t h a t t h e c o u n t r y i s o n l y a b l e t o p r o d u c e a b o u t h a l f o f i t s c o n s u m p t i o n .
T h e o n e h y d r o p o w e r p l a n t i s R u a c a n a w h i c h p r o d u c e s 9 7 . 8 % o f t o t a l e l e c t r i c
p o w e r p r o d u c t i o n . T h e p l a n t c o n s i s t s o f t h r e e m e d i u m h e a d F r a n c i s t u r b i n e s
w h i c h w e r e c o m m i s s i o n e d i n 1 9 7 8 . T h i s p l a n t s e r v e s a s a b a s i s f o r t h i s t h e s i s .
T h e c o u n t r y i s d e p e n d e n t o n i m p o r t i n g e n e r g y f r o m t h e S o u t h e r n A f r i c a n
P o w e r P o o l ( S A P P ) . T h i s s y s t e m m a i n l y c o n s t i t u t e s o f l a r g e c o a l p l a n t s , a n d
t h e a c c e s s i b i l i t y t o p e a k p o w e r i s l o w .
T h e a d v a n c e m e n t s i n t u r b i n e t e c h n o l o g y h a v e b e e n r e m a r k a b l e o v e r t h e
l a s t 2 0 y e a r s , e s p e c i a l l y w i t h i n t h e d e s i g n o f F r a n c i s t u r b i n e s e l d . I t i s
p r o v e n t o i n c r e a s e e c i e n c y a n d i m p r o v e c a v i t a t i o n b e h a v i o u r . T h e r e s u l t i s
a t a n g i b l e i m p r o v e m e n t p o t e n t i a l i n e c i e n c y a n d p o w e r o u t p u t f o r e x i s t i n g
t u r b i n e s .
T h i s t h e s i s c o n s i d e r s t h e t e c h n i c a l a s p e c t s o f a r e h a b i l i t a t i o n p r o j e c t . T h e
m a i n o b j e c t i v e i s t o i n v e s t i g a t e t h e p o s s i b i l i t y o f i n c r e a s i n g t h e p o w e r o u t p u t
f r o m t h e e x i s t i n g t u r b i n e s b y r e p l a c i n g t h e r u n n e r s . T h i s c a n b e a c h i e v e d
e i t h e r b y i n c r e a s i n g t h e v o l u m e o w a n d / o r e c i e n c y . T h e r s t c r i t e r i a c a n
b e a c h i e v e d t h r o u g h e x p a n d i n g t h e o u t l e t d i a m e t e r a n d / o r a l t e r i n g t h e o w
a n g l e s .
T h i s t h e s i s w i l l a p p r o a c h t h e p r o b l e m b y i n v e s t i g a t i n g t h e e x i s t i n g
h y d r a u l i c c o n d i t i o n s f o r s u r g e o s c i l l i a t i o n a n d w a t e r h a m m e r . T h e s e l e c t e d
m e t h o d t o s o l v e t h e p r o b l e m i s t o d e v e l o p M a t l a b p r o g r a m s . T h e o b j e c t i v e
i s t o i d e n t i f y t h e m a x i m u m i n c r e a s e i n v o l u m e o w t h a t d o n o t c o m p r o m i s e
t h e h y d r a u l i c d e s i g n c o n d i t i o n s i n t h e w a t e r w a y . T h e r e s u l t s a r e t h e n u s e d
a s r e s t r i c t i o n s i n t h e d e v e l o p i n g o f a c a l c u l a t i o n m o d e l f o r i n v e s t i g a t i o n o f
p o t e n t i a l p o w e r o u t p u t .
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1
2
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C h a p t e r 2
T h e o r y
T h e p r e s e n t e d t h e o r y i s s e l e c t e d o n t h e b a s i s o f r e l e v a n c e f o r t h e s t u d y . I t
s t a r t s w i t h s y s t e m d y n a m i c s t h e o r y , a n d e n d s w i t h a s y n o p s i s o f t h e g e n e r a l
t u r b i n e t h e o r y w i t h a n e m p h a s i s o n r u n n e r d e s i g n .
2 . 1 S y s t e m D y n a m i c s
T h e u n s t e a d y o w i n p i p e l i n e s i s k n o w n a s s u r g e , a n d o c c u r s d u e t o t h e
i n e r t i a o f t h e w a t e r m a s s e s w h e n c h a n g i n g t h e o p e r a t i n g l o a d . A n y c h a n g e
i n t h e v o l u m e o w c h a n g e s t h e p r e s s u r e i n f r o n t o f t h e t u r b i n e d u e t o a n
a c c e l e r a t i o n o r a d e c e l e r a t i o n o f t h e w a t e r m a s s e s . T h e g o v e r n i n g e q u a t i o n s
a r e d e s c r i b e d b y t h e c o n t i n u i t y e q u a t i o n ( 2 . 1 ) a n d t h e e q u a t i o n o f m o t i o n
( 2 . 2 ) f o r a u i d e l e m e n t [ 3 7 ] .
∂H
∂t+
a2
g
∂v
∂x= 0
( 2 . 1 )
g∂H
∂x+
∂v
∂t+ λ
v |v|2D
( 2 . 2 )
H - P i e z o m e t e r p r e s s u r e , h + z [ m W C ]
h- H y d r a u l i c p r e s s u r e [ m W C ]
z- E l e v a t i o n [
m]
a- S p e e d o f s o u n d [
m/s]
v - V e l o c i t y [ m/s]
t- T i m e [ s ]
λ- F r i c t i o n f a c t o r
g- G r a v i t y c o n s t a n t
m/s2]
D- D i a m e t e r o f p i p e [
m]
I n a w a t e r w a y a r e t h e h e a d l o s s e s d u e t o f r i c t i o n a n d s h e a r s t r e s s e s
b e t w e e n t h e w a t e r a n d t h e t u n n e l w a l l s . W h e n i n c r e a s i n g t h e v o l u m e o w
w i l l t h e l o s s e s i n c r e a s e , a n d c o n s e q u e n t l y r e d u c e s t h e a v a i l a b l e h e a d f o r t h e
t u r b i n e . I t a l s o m a k e s i t n e c e a s s a r y t o i n v e s t i g a t e i f a n e x i s t i n g p o w e r p l a n t
c a n h a n d l e t h e p r e s s u r e c h a n g e . T h i s i s u s u a l l y d o n e b y i n v e s t i g a t i o n t h e
s u r g e o s c i l l a t i o n a n d w a t e r h a m m e r e e c t s . T h e s e a r e t r e a t e d s e p a r a t e l y ,
3
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2 S y s t e m D y n a m i c s
b e c a u s e t h e p e r i o d o f w a t e r h a m m e r e e c t s i n p e n s t o c k a r e o f m u c h s h o r t e r
p e r i o d t h a n s u r g e t a n k u c t u a t i o n s [ 3 7 ] .
2 . 1 . 1 W a t e r h a m m e r
T h e v o l u m e o w i n a p i p e l i n e c a n b e v i e w e d a s a s p r i n g - m a s s s y s t e m . T h e
s p r i n g r e p r e s e n t s t h e e l a s t i c i t y o r t h e c o m p r e s s i b i l i t y o f t h e w a t e r
K , a l s o
c a l l e d t h e b u l k m o d u l u s . I f a f o r c e i s i n d u c e d o n t h e s p r i n g , i t i s c o m p r e s s e d
a n d r e p r e s e n t s t h e p o t e n t i a l e n e r g y i n t h e s y s t e m . T h e e l a s t i c i t y a n d i n e r t i a
o f w a t e r a r e t h e c a u s e s o f w a t e r h a m m e r e e c t s w h i c h i s d e n e d a s t h e
r e t a r d a t i o n p r e s s u r e , a n d p r o p a g a t e s f r o m t h e t u r b i n e t o t h e n e a r e s t f r e e
w a t e r s u r f a c e u p s t r e a m w i t h t h e s p e e d o f s o u n d a
. F o r a v e r y t h i c k - w a l l e d
p i p e i s a
t h e a c o u s t i c s p e e d o f a s m a l l d i s t u r b a n c e i n a n i n n i t e u i d u s e d ,
d e n e d i n e q u a t i o n ( 2 . 3 ) [ 3 7 ] , a n d i t s v a l u e i s a p p r o x i m a t e l y 1200m/s
.
a ≈ K
ρ( 2 . 3 )
K - B u l k m o d u l u s [kg/ms2]
ρ- D e n s i t y o f w a t e r
kg/m3
A t u r b i n e i s m o d e l l e d a s a v a l v e , a n d t h e p r o g r e s s o f t h e p r e s s u r e i n f r o n t
c a n b e e a s i e s t d e s c r i b e d w h e n i m a g i n i n g a o w f r o m a r e s e r v o i r t h r o u g h a
s i n g l e p i p e t o a v a l v e . F o r i d e a l c o n d i t i o n s i s t h i s i l l u s t r a t e d i n g u r e 2 . 1 .
T h e s t a t i o n a r y p r e s s u r e l i n e i s g i v e n b y t h e e l e v a t i o n i n t h e r e s e r v o i r a t
t = 0. T h e p r e s s u r e i n f r o n t o f t h e t u r b i n e i s a c o m b i n a t i o n o f t h e e l e v a t i o n
p r e s s u r e i n t h e r e s e r v o i r a n d t h e d y n a m i c p r e s s u r e o f t h e w a t e r h a m m e r .
A t t = 0 i s t h e v e l o c i t y v = v0 i n t h e e n t i r e p i p e i n d i r e c t i o n o f t h e
v a l v e . W h e n t h e v a l v e c l o s e s t h e w a t e r m a s s e s a r e s l o w e d d o w n t o v0 = 0
.
U p s t r e a m t h e w a t e r i s " u n a w a r e " o f t h e c h a n g e r e s u l t i n g i n a g a g e p r e s s u r e
a t t h e v a l v e . W h e n t h e p r e s s u r e w a v e h a s r e a c h e d t h e r e s e r v o i r i s t h e v e l o c i t y
o f t h e w a t e r m a s s e s z e r o i n t h e e n t i r e p i p e l e n g t h . T h e w a t e r o w s i n t o t h e
r e s e r v o i r w i t h a v e l o c i t y o f v = −v0 d u e t o t h e g a g e p r e s s u r e . U n t i l t h e
p r e s s u r e d i e r e n c e d i s a p p e a r s a n d v = −v0 i n t h e p i p e . T h i s i s i l l u s t r a t e d
b y t h e d e s c e n d i n g l i n e i n t h e g u r e , a n d r e s u l t s i n a n e g a t i v e p r e s s u r e a t t h e
v a l v e . T h e n e g a t i v e p r e s s u r e w a v e w i l l p r o p a g a t e i n t h e p i p e t o t h e r e s e r v o i r ,
a n d a t t h e t i m e w h e n t h e p r e s s u r e e q u a l i z e d i s d e n o t e d b y t h e a s c e n d i n g l i n e
i n t h e g u r e . T h e n t h e p r o c e s s s t a r t s a g a i n .
T h e p r e s s u r e w a v e d e p e n d s o n t h e r a t i o b e t w e e n t h e l e n g t h t o t h e n e a r e s t
f r e e w a t e r s u r f a c e u p s t r e a m a n d t h e c r o s s - s e c t i o n a l a r e a o f t h e p i p e ( L / A )
[ 2 9 ] . T h e r e b y d e n i n g t h e p e r i o d o f t h e w a v e T
i n e q u a t i o n ( 2 . 4 ) .
T =4L
a( 2 . 4 )
L - L e n g t h t o t h e n e a r e s t f r e e w a t e r s u r f a c e [ m
]
T h e r e e c t i o n t i m e T R i n e q u a t i o n ( 2 . 5 ) i s d e n e d a s t h e t i m e t h e p r e s s u r e
w a v e u s e s t o r e t u r n t o t h e t u r b i n e . T h e c l o s i n g t i m e o f t h e t u r b i n e T L s h o u l d
b e s l o w e r t h a n T R i n o r d e r t o a v o i d t h e h i g h e s t o b t a i n a b l e p r e s s u r e d e n e d
b y J o u k o w s k y i n e q u a t i o n 2 . 6 . I n w o r s t c a s e d o e s t h e e l a s t i c i t y o f w a t e r
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2 T h e o r y
F i g u r e 2 . 1 : P r e s s u r e a t v a l v e w i t h i n s t a n t a n e o u s c l o s i n g t i m e f o r i d e a l
c o n d i t i o n s
d o u b l e t h e p r e s s u r e i n f r o n t o f t h e t u r b i n e c o m p a r e d i n e l a s t i c c a l c u l a t i o n s
[ 2 9 ] .
T R =2L
a( 2 . 5 )
h =
a∆v
g( 2 . 6 )
T h e l a r g e s t m a g n i t u d e o f c h a n g e i n v o l u m e o w p e r u n i t o f t i m e o c c u r s
d u r i n g l o a d r e j e c t i o n , a n d t h e r e f o r e y i e l d s t h e d e s i g n c o n d i t i o n i n r e g a r d
t o t h e d y n a m i c p r e s s u r e [ 2 9 ] . I t i s i m p o r t a n t t o s o l v e e q u a t i o n s ( 2 . 1 ) a n d
( 2 . 2 ) t o n d t h e d e s i g n c o n d i t i o n s o f t h e p i p e s a n d v a l v e s w h e n b u i l d i n g a
n e w h y d r o p o w e r p l a n t . O r t o c h e c k i f a n i n c r e a s e d v o l u m e o w d o e s n o t
c o m p r o m i s e t h e d e s i g n i n a n e x i s t i n g p l a n t .
M e t h o d o f C h a r a c t e r i s t i c s
T h e m e t h o d o f c h a r a c t e r i s t i c s i s a n u m e r i c a l m e t h o d f o r s o l v i n g h y p e r b o l i c
d i e r e n t i a l e q u a t i o n s i n t h e x t - p l a n e . I t t r a n s f o r m s t h e p a r t i a l d i e r e n t i a l
e q u a t i o n s ( P D E ) ( 2 . 1 ) a n d ( 2 . 2 ) i n t o o r d i n a r y d i e r e n t i a l e q u a t i o n s ( O D E )
[ 3 7 ] . T h e y a r e c o m b i n e d u s i n g a n u n k n o w n m u l t i p l i e r a n d t h e r e s u l t i s
t h e e q u a t i o n s s y s t e m g i v e n b y ( 2 . 7 ) a n d ( 2 . 8 ) . C +
d e n e s t h e p r e s s u r e w a v e
w h e n i t p r o p a g a t e s w i t h t h e o w a n d C −
w h e n t h e p r e s s u r e w a v e p r o p a g a t e s
a g a i n s t t h e o w .
C + :
ga
dH dt + dv
dt + λv|v|2D = 0
dxdt = +a
( 2 . 7 )
C − : − ga
dH dt + dv
dt + λv|v|2D = 0
dxdt = −a( 2 . 8 )
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2 S y s t e m D y n a m i c s
F i g u r e 2 . 2 : x - t d i a g r a m f o r s o l v i n g s i n g l e - p i p e p r o b l e m s [ 2 9 ]
I t i s c o n v e n i e n t t o v i s u a l i z e t h e s o l u t i o n b y g u r e 2 . 2 a s i t d e v e l o p s o n
t h e x t p l a n e [ 3 7 ] . W h e r e
dxdt = ±a
r e l a t e s t h e c h a n g e i n p o s i t i o n o f a w a v e
t o t h e c h a n g e i n t i m e b y t h e a c o u s t i c s p e e d a
. T h i s r e l a t i o n s h i p w i l l p l o t
t h e
+as t r a i g h t l i n e b e t w e e n A a n d P i n w h i c h t h e r s t e q u a t i o n i n ( 2 . 7 ) i s
v a l i d . B e t w e e n p o i n t s B a n d P i s t h e −a
l i n e p l o t a n d t h e r s t e q u a t i o n i n
( 2 . 8 ) i s v a l i d . T h e s e l i n e s a r e k n o w n a s t h e c h a r a c t e r i s t i c s l i n e s .
I n o r d e r t o t r a n s f o r m t h e e q u a t i o n s e t i n t o n i t e d i e r e n c e e q u a t i o n s ,
a r e e q u a t i o n s ( 2 . 7 ) a n d ( 2 . 8 ) a p p r o x i m a t e d b y u s i n g t h e t r a p e z o i d a l r u l e .
T h e l i n e a r f o r m o f t h e e q u a t i o n s a r e m a i n t a i n e d , a n d i t i s a s a t i s f a c t o r y
a p p r o x i m a t i o n f o r m o s t p r o b l e m s . A s o l u t i o n i s o b t a i n e d b y r s t c a l c u l a t i n g
t h e v a l u e s f o r H
a n d Q
a t t = 0
. T h e c a l c u l a t i o n o f t h e v a l u e s f o r t h e
n e x t t i m e s t e p u s e s t h e v a l u e s a t t h e p r e v i o u s a n d s o o n . T h e r e s u l t i n g
e q u a t i o n s y s t e m c a n b e f o u n d i n s e c t i o n 5 . 2 a l o n g w i t h d e n i t i o n o f b o u n d a r y
c o n d i t i o n s .
2 . 1 . 2 S u r g e O s c i l l a t i o n i n S u r g e T a n k s
I n m e d i u m t o h i g h p r e s s u r e p l a n t s i t m a y b e n e c e s s a r y t o c o n s t r u c t a s u r g e
c h a m b e r b e t w e e n t h e i n t a k e a n d t h e t u r b i n e . T h i s d e c r e a s e s t h e p r e s s u r e i n
f r o n t o f t h e t u r b i n e , a n d i m p r o v e s t h e r e g u l a t i o n o f t h e s y s t e m [ 2 9 ] . D u e t o
t h e p r e s e n c e o f a s u r g e c h a m b e r t h e m o m e n t u m o f w a t e r i s n o t d e s t r o y e d
q u i c k l y , b u t t h e w a t e r o w s i n t o t h e c h a m b e r r e s u l t i n g i n a n o s c i l l a t i n g w a t e r
l e v e l . T h e s e w i l l e v e n t u a l l y d i e o u t o v e r t i m e d u e t o f r i c t i o n l o s s e s i n t h e
t u n n e l s , l o s s e s a t t h e i n l e t a n d i n t h e s u r g e c h a m b e r i t s e l f [ 1 6 ] .
O n t h e c o n t r a r y t o t h e w a t e r h a m m e r t h e o s c i l l a t i o n i n a s u r g e t a n k i s
s l o w , a n d t h e e l a s t i c e e c t o f w a t e r h a s l i t t l e s i g n i c a n c e . I t i s t h e r e f o r e
p o s s i b l e t o a s s u m e t h a t w a t e r a n d p i p e s a r e r i g i d , w h i c h i m p l i e s t h a t t h e
c o m p r e s s i b i l i t y a n d t h e r e b y t h e s p e e d o f s o u n d i n e q u a t i o n ( 2 . 1 ) i s i n n i t e .
R e a r r a n g i n g e q u a t i o n ( 2 . 1 0 ) a n d a l l o w i n g a
→ ∞i n e q u a t i o n ( 2 . 9 ) , t h e
r e l a t i o n s h i p i n e q u a t i o n ( 2 . 1 0 ) i s o b t a i n e d .
6
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2 T h e o r y
∂v
∂x= − g
a2∂H
∂t( 2 . 9 )
∂v
∂x = 0 ( 2 . 1 0 )
g∂H
∂x− ∂v
∂v+ λ
v |v|2D
= 0( 2 . 1 1 )
I n t r o d u c i n g Q = vA
a n d
∂H ∂x = H 2−H 1
L i s t h e r e l a t i o n s h i p ( 2 . 1 2 ) o b t a i n e d :
L
gA
dQ
dt= H 1 − H 2 − cQ |Q|
( 2 . 1 2 )
W h e r e :
c = λL
2gA2D( 2 . 1 3 )
S u r g e c h a m b e r s u p s t r e a m o f t h e t u r b i n e a r e d i m e n s i o n e d i n a m a n n e r t o
a v o i d b o t h o o d i n g f o r s t a r t - u p l o a d a n d a i r s u c t i o n i n t o p e n s t o c k f o r l o a d
r e j e c t i o n . T h e s e s h o u l d b e s e t f o r w o r s t c a s e s c e n a r i o s , i . e . w h e n a f u l l l o a d
r e j e c t i o n i s f o l l o w e d b y a f u l l s t a r t u p l o a d a t t h e t i m e t h e s h a f t l e v e l i s i n
b a l a n c e w i t h t h e s t a t i o n a r y p r e s s u r e l i n e [ 2 9 ] . A s u r g e c h a m b e r d o w n s t r e a m
d a m p s s t r o n g o s c i l l a t i o n s a n d t o p r e v e n t s o o d i n g .
2 . 2 T h e F r a n c i s T u r b i n e
A F r a n c i s t u r b i n e i s a r a d i a l r e a c t i o n t u r b i n e a n d i s a l s o c a l l e d a f u l l t u r b i n e
b e c a u s e t h e w a t e r c o m p l e t e l y l l s t h e p a s s a g e s . T h e d i e r e n t c o m p o n e n t s o f
t h e t u r b i n e a r e i l l u s t r a t e d i n g u r e 2 . 3 .
T h e s p i r a l c a s i n g i s d e s i g n e d w i t h a d e c r e a s i n g c r o s s s e c t i o n a l a r e a
a l o n g t h e c i r c u m f e r e n c e i n o r d e r t o k e e p t h e u i d v e l o c i t y ' s m a g n i t u d e
c o n s t a n t b e f o r e e n t e r i n g t h e s t a y v a n e s .
T h e s t a y v a n e s / g u i d e v a n e s i m p a r t a t a n g e n t i a l v e l o c i t y o n t o t h e o w
w h i c h c r e a t e s a n a n g u l a r m o m e n t u m i n t h e w a t e r b e f o r e i t e n t e r s t h e r u n n e r .
T h e o b j e c t i v e i s t o o b t a i n a h i g h l y u n i f o r m o w p a t t e r n w i t h i n c r e a s i n g
r o t a t i o n [ 7 ] . T h i s i s o n e o f t h e m a i n f e a t u r e s t h a t d i e r e n t i a t e a F r a n c i s
f r o m o t h e r t u r b i n e t y p e s , o n l y a p a r t o f t h e t o t a l s p e c i c e n e r g y a t t h e i n l e t
o f t h e t u r b i n e i s c o n v e r t e d t o k i n e t i c e n e r g y b e f o r e t h e r u n n e r i s r e a c h e d .
T h e g u i d e v a n e s c a n a l s o b e u s e d t o r e g u l a t e t h e o w r a t e .
I n t h e r u n n e r t h e e n e r g y t r a n s f e r o c c u r s d u e t o a n i m p u l s e a c t i o n
b e t w e e n t h e w a t e r a n d t h e b l a d e s . A b o u t 5 0 % o f t h e t r a n s f e r i s d u e t o a
p r e s s u r e d r o p b e t w e e n t h e i n l e t a n d t h e o u t l e t . T h e o w l e a v e s t h e r u n n e r
w i t h a r e d u c e d a n g u l a r m o m e n t u m a n d a d e c r e a s e d p r e s s u r e .
T h e d r a f t t u b e c o n n e c t s t h e o u t l e t o f t h e r u n n e r t o t h e t a i l r a c e . I t s
p r i m a r y f u n c t i o n i s t o r e d u c e t h e v e l o c i t y o f t h e d i s c h a r g e d w a t e r i n o r d e r t o
m i n i m i s e t h e l o s s o f k i n e t i c e n e r g y . T h e d e s i g n o f t h e d r a f t t u b e a n d d e g r e e
o f s u b m e r g e n c e i s a n i m p o r t a n t d e s i g n f a c t o r t o a v o i d c a v i t a t i o n [ 7 ] .
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2 T h e F r a n c i s T u r b i n e
F i g u r e 2 . 3 : C o m p o n e n t s o f a F r a n c i s T u r b i n e
2 . 2 . 1 S u b m e r g e n c e
" C a v i t a t i o n f o r m i n a o w i n g l i q u i d i n a n a r e a w h e r e t h e l o c a l p r e s s u r e
a p p r o a c h e s v a p o u r p r e s s u r e : e n t r a i n e d a n d d i s s o l v e d g a s f o r m b u b b l e s w h i c h
g r o w a n d t h e n c o l l a p s e " [ 3 4 ] . T h i s i s a n u n s t a b l e p r o c e s s w h i c h g i v e s r i s e
t o o w i n s t a b i l i t y a n d r e s u l t s i n n o i s e , v i b r a t i o n a n d s u r f a c e d a m a g e . T h e
l a t t e r i s a l s o k n o w n a s c a v i t a t i o n e r o s i o n a n d c a n s o m e t i m e s a l t e r t h e o w
a r e a i n a r u n n e r s i g n i c a n t l y , a s o n e c a n o b s e r v e i n p i c t u r e 2 . 4 . T h i s u s u a l l y
o c c u r s i n t h e d i s c h a r g e a r e a w h e r e t h e p r e s s u r e i s l o w . T h e c o m m o n l y u s e d
m e t h o d t o c a l c u l a t e c a v i t a t i o n i s b y u s i n g t h e t e r m " N e t P o s i t i v e S u c t i o n
H e a d ( N P S H ) " .
F i g u r e 2 . 4 : S e v e r e c a v i t a t i o n e r o s i o n o n a r u n n e r
2 . 2 . 2 C a l c u l a t i o n o f N P S H
I t i s n o r m a l t o d i s t i n g u i s h b e t w e e n N PSH T a n d
N P H S A w h i c h i s r e s p e c -
t i v e l y d e t e r m i n e d b y t u r b i n e c h a r a c t e r i s t i c s i n e q u a t i o n ( 2 . 1 4 ) a n d p l a n t d a t a
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2 T h e o r y
i n e q u a t i o n ( 2 . 1 5 ) [ 2 1 ] .
N PSH T = ac2m2
2g+ b
u222g
( 2 . 1 4 )
a - S u b m e r g e n c e c o e c i e n t
b- S u b m e r g e n c e c o e c i e n t
cm - A b s o l u t e m e r i d i n a l v e l o c i t y a t n o m i n a l l o a d [m/s]
u- P e r i p h e r a l v e l o c i t y [
m/s]
T h e e q u a t i o n f o r N PSH T y i e l d s a v a l u e f o r t h e v e l o c i t y e n e r g y i n t h e
a r e a o f d i s c h a r g e . N PSH A t u r b i n e i s d e s c r i b e d b y e q u a t i o n ( 2 . 1 5 ) . T h e
c o n s t a n t s a
a n d b
a r e d e t e r m i n e d e m p i r i c a l l y , a n d d e p e n d s o n t h e s p e e d
n u m b e r
∗Ωa t B E P :
∗Ω < 0.55 → a = 1.12a n d
b = 0.055∗Ω > 0.55
→a = 1.12
a n d b = 0.1∗Ω
N PSH A = −H s + hb − hva ( 2 . 1 5 )
T h e s u c t i o n h e a d H s i s n e g a t i v e w h e n t h e t u r b i n e i s s u b m e r g e d a n d c a n
b e u s e d t o i n c r e a s e t h e p r e s s u r e e n e r g y . T h e b a r o m e t r i c p r e s s u r e hb = 0.13m
a t s e a l e v e l d e c r e a s e s b y 0.12m
f o r e a c h 100m
a b o v e . T h e v a p o u r p r e s s u r e
hva i s a p p r o x i m a t e d t o b e
0.3a t
25C . T h e c r i t e r i a f o r a v o i d i n g c a v i t a t i o n
i s g i v e n i n e q u a t i o n ( 2 . 1 6 ) [ 7 ] .
N PSH T < NPSH A ( 2 . 1 6 )
2 . 2 . 3 C l a s s i c d e s i g n o f a F r a n c i s R u n n e r
T h e r e a r e a n u m b e r o f m e t h o d s t o d e s i g n a F r a n c i s r u n n e r . T h e f o l l o w i n g i s
a b r i e f p r e s e n t a t i o n o f H . B r e k k e ' s m e t h o d d e s c r i b e d i n " P u m p s & T u r b i n e s "
[ 7 ] .
T h e d e s i g n p r o c e d u r e s t a r t s b y d e t e r m i n i n g n o m i n a l h e a d H n a n d v o l u m e
o w a t b e s t e c i e n c y p o i n t ( B E P ) d e n o t e d b y
∗Q. I t i s c o n v e n i e n t t o s t a r t
b y d e s i g n i n g t h e o u t l e t . A p e r i p h e r a l v e l o c i t y u2 a n d m e r i d i a n v e l o c i t y
cm2 i s s e l e c t e d b a s e d o n e q u a t i o n ( 2 . 1 4 ) . T h e v a l u e o f u2 l i e s b e t w e e n 3 5
a n d 4 3 m/s
, w h e r e t h e h i g h e s t v a l u e i n d i c a t e s h i g h h e a d . T h e c o r r e l a t i o n
b e t w e e n t h e s e v e l o c i t i e s c a n b e s e e n i n g u r e 2 . 5 , t h e s o l i d l i n e s r e p r e s e n t
t h e v e l o c i t y d i a g r a m s a t B E P a n d t h e d o t t e d l i n e s r e p r e s e n t s o w p a s t B E P .
I t i s i m p o r t a n t t o n o t i c e t h a t t h e o u t l e t a n g l e β 2 d o e s n o t c h a n g e f o r t h e
d i e r e n t o w s a n d t h e a b s o l u t e t a n g e n t i a l v e l o c i t y
∗cu2 = 0a n d
α2 = 90a t
B E P . T h e o u t l e t a n g l e c a n t h e r e f o r e b e d e t e r m i n e d b y e q u a t i o n ( 2 . 1 7 ) .
β 2 = tan−1
∗cm2
u2
( 2 . 1 7 )
T h e o u t l e t d i a m e t e r i s f o u n d f r o m t h e r e l a t i o n s h i p g i v e n b y e q u a t i o n
( 2 . 1 8 ) . I t i s t h e n u s e d t o n d t h e r o t a t i o n a l s p e e d o f t h e r u n n e r i n e q u a t i o n
( 2 . 1 9 ) . T h e r o t a t i o n a l s p e e d m u s t b e c o r r e c t e d t o o b t a i n s y n c h r o n o u s s p e e d
i n o r d e r t o c o n n e c t t h e g e n e r a t o r t o t h e g r i d . A c c o r d i n g l y c o r r e c t t h e o u t l e t
d i a m e t e r a n d t h e o t h e r p r e c e d i n g v a l u e s . F i n a l s t e p i s t o s e l e c t a p o i n t a l o n g
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2 T h e F r a n c i s T u r b i n e
F i g u r e 2 . 5 : V e l o c i t y d i a g r a m [ 7 ]
t h e h u b w h e r e t h e b l a d e s a r e n i s h e d a n d d e t e r m i n e t h e b l a d e a n g l e s f r o m
t h e a s s u m p t i o n o f p e r p e n d i c u l a r o u t l e t .
W h e n d e s i g n i n g t h e i n l e t i t i s i m p o r t a n t t o b e a r i n m i n d t h a t t h e i n l e t
a n g l e d e p e n d s o n t h e v o l u m e o w , a s s e e n i n g u r e 2 . 5 . F o r m e d i u m a n d l o w
p r e s s u r e t u r b i n e s i s cm1 n o t c o n s t a n t o v e r t h e i n l e t d u e t o l a r g e d i e r e n c e s
b e t w e e n t h e h u b a n d r i n g . B e c a u s e t h e o w s t a r t s t o c u r v e i n f r o n t o f t h e
r u n n e r .
∗cm2 =4∗Q
πD22
( 2 . 1 8 )
u2 =πD2n
60( 2 . 1 9 )
F i g u r e 2 . 6 : M a i n d i m e n s i o n o f a F r a n c i s R u n n e r , a x i a l v i e w
1 0
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C h a p t e r 3
P r e l i m i n a r y S t u d i e s
T h e r s t p r e l i m i n a r y s t u d y f o c u s e s o n m o t i v a t i o n f o r r e f u r b i s h m e n t p r o j e c t s
f o r h y d r o p o w e r p l a n t s . I t a l s o p r e s e n t s a p e r c e n t i l e d i s t r i b u t i o n o f t u r b i n e
t y p e s i n t h e w o r l d . T h i s i s f o l l o w e d b y a c h i e v e d i n c r e a s e i n p o w e r o u t p u t a n d
e c i e n c y f o r k n o w n p l a n t s . T h e s e c o n d s t u d y p r e s e n t s n e w a d v a n c e m e n t s
c o n c e r n i n g F r a n c i s r u n n e r d e s i g n .
3 . 1 R e f u r b i s h m e n t o f E x i s t i n g H P P
M o r e t h a n 5 0 % o f o l d p o w e r p l a n t s h a s o p e r a t i o n a l p r o b l e m s s u c h a s
c a v i t a t i o n e r o s i o n a n d v i b r a t i o n o f t h e s t r u c t u r e [ 1 7 ] . T h e p a r a m o u n t
o b j e c t i v e s o f a r e h a b i l i t a t i o n p r o j e c t a r e t o m a x i m i s e o u t p u t , e c i e n c y a n d
t h e r e b y t h e a n n u a l e n e r g y p r o d u c t i o n . A n a d v a n t a g e o u s e e c t i s r e d u c e d
o p e r a t i n g a n d m a i n t e n a n c e c o s t s , w h i c h i n t h e e n d e x t e n d s t h e p l a n t s
o p e r a t i n g l i f e .
A r e h a b i l i t a t i o n p r o j e c t i s o f t e n m o t i v a t e d b y t h e n e c e s s i t y t o r e p l a c e
k e y c o m p o n e n t s t h a t a r e a t t h e e n d o f t h e i r l i f e t i m e . O r a r e q u i r e m e n t t o
a d a p t t h e h y d r a u l i c c h a r a c t e r i s t i c s o f a t u r b i n e t o n e w o p e r a t i n g c o n d i t i o n s .
N o w a d a y s t h i s i s o f t e n t h e c a s e s i n c e m a n y e n e r g y m a r k e t s i n t h e w o r l d a r e
d e r e g u l a t e d . T h e m a j o r i t y o f p l a n t s i n t h e w e s t e r n w o r l d w e r e b u i l t b e f o r e
d e r e g u l a t i o n , a n d a r e n o w o p e r a t e d i n o r d e r t o m e e t t h e e n e r g y d e m a n d s
k n o w n a s h y d r o p e a k i n g . T h i s i m p l i e s f r e q u e n t o p e r a t i o n o u t s i d e t h e b e s t
e c i e n c y p o i n t ( B E P ) . T h i s e n t a i l s d e c r e a s e d e c i e n c y a n d i n s o m e c a s e s
i n c r e a s e d w e a r a n d t e a r o n t h e p l a n t s . A s i d e e e c t o f t h e h y d r o p e a k i n g i s
t h a t i t a l s o c a u s e s s t r o n g v a r i a t i o n s i n t h e r i v e r o w , w h i c h i n t u r n a e c t s t h e
e c o l o g i c a l e n v i r o n m e n t . T h i s i n t r o d u c e s t h e d e m a n d f o r r e g u l a t i o n s c h e m e s
w i t h t h e s m a l l e s t a m o u n t o f i m p a c t o n t h e s u r r o u n d i n g e n v i r o n m e n t . W o r k
h a s s t a r t e d t o m a p t h e e e c t o f h y d r o p e a k i n g i n N o r w a y [ 9 ] . I n A f r i c a i t
i s n o t a n u n f a m i l i a r p r o b l e m . W h e r e t h e w a t e r o w v a r i e s s t r o n g l y w i t h t h e
s e a s o n s a n d t h e d e m a n d f o r w a t e r f o r d o m e s t i c a n d i r r i g a t i o n p u r p o s e s i s
h i g h [ 1 ] .
A n y r e h a b i l i t a t i o n p r o j e c t h a s t o b e e c o n o m i c a l l y j u s t i e d . N o t o n l y
m u s t t h e c o s t o f t h e p r o j e c t b e c o n s i d e r e d , b u t a l s o t h e c o s t o f d o w n t i m e .
O f t e n d o e s t h i s a s p e c t d e t e r m i n e t h e r e h a b i l i t a t i o n s c e n a r i o . I t h a s b e e n
c o m m o n p r a c t i c e t o l i m i t t h e r e h a b i l i t a t i o n f o r s m a l l t o m e d i u m t u r b i n e s
1 1
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3 R e f u r b i s h m e n t o f E x i s t i n g H P P
t o o n l y c o n s i d e r a r e p l a c e m e n t o f t h e r u n n e r . W h i l s t f o r l a r g e u n i t s a n
o p t i m i s a t i o n o f t h e e n t i r e h y d r o l o g i c a l p r o l e i s v i a b l e [ 1 7 ] , [ 3 2 ] .
3 . 1 . 1 D i s t r i b u t i o n o f t u r b i n e s i n t h e w o r l d
A n i n i t i a l s u r v e y o f t h e d i s t r i b u t i o n o f t u r b i n e u n i t s r a t i n g o v e r 5 0 M W
a c r o s s t h e w o r l d i s p r e s e n t e d i n g u r e 3 . 1 [ 1 0 ] [ 1 1 ] . T h e F r a n c i s t u r b i n e h a s
t h e h i g h e s t p e r c e n t i l e d i s t r i b u t i o n o n e a c h c o n t i n e n t , c l o s e l y f o l l o w e d b y t h e
P e l t o n t u r b i n e . A f r i c a h a s t h e h i g h e s t n u m b e r o f p u m p e d s t o r a g e s c h e m e s ,
a n d t o n o s u r p r i s e f e w K a p l a n t u r b i n e s a r e p r e s e n t e d .
F i g u r e 3 . 1 : T u r b i n e d i s t r i b u t i o n l a r g e r t h a n 5 0 M W a c r o s s t h e w o r l d
3 . 1 . 2 A c h i e v e m e n t s
T h e r e h a s b e e n a s i g n i c a n t i n c r e a s e i n r e f u r b i s h m e n t p r o j e c t s t h e l a s t
d e c a d e s . S o m e o f t h e s e a r e n i s h e d , b u t o n l y a f e w h a v e p u b l i s h e d t h e i r
a c c o m p l i s h e d r e s u l t s w i t h a d e q u a t e i n f o r m a t i o n .
B e s i d e s a l l t h e c h a l l e n g e s o f r e h a b i l i t a t i o n p r o j e c t s , d o e s s o m e c l a i m
t h a t a n e w d e s i g n e d r u n n e r i n s t a l l e d i n s i d e e x i s t i n g t u r b i n e s t r u c t u r e s c a n
i m p r o v e p o w e r o u t p u t b y 1 0 t o 3 0 p e r c e n t a g e p o i n t s [ 3 3 ] , [ 1 7 ] , [ 3 6 ] . O n
t h e o t h e r h a n d d o e s A n d r i t z H y d r o p o s t a m o r e c o n s e r v a t i v e s t a t e m e n t ,
t h e p o w e r o u t p u t c a n b e i n c r e a s e b y 1 0 t o 1 5 % w h e n m o d e r n i z i n g a n d
r e f u r b i s h i n g e x i s t i n g t u r b i n e s a n d g e n e r a t o r s [ 1 9 ] .
A n e x a m p l e o f a n e a r l y n i s h e d r e f u r b i s h m e n t p r o j e c t i s t h e s i x F r a n c i s
t u r b i n e s a t t h e A k o s o m b o p l a n t i n A f r i c a . I n t h e b e g i n n i n g i t w a s c l a i m e d
t h a t t h e f o l l o w i n g r e s u l t s c o u l d b e a c h i e v e d [ 1 9 ] :
1 2
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3 P r e l i m i n a r y S t u d i e s
C a v i t a t i o n - f r e e p e r f o r m a n c e w i t h i n t h e f u l l o p e r a t i n g r a n g e
I n c r e a s e o f a n n u a l e n e r g y p r o d u c t i o n b y 2 0 %
I n c r e a s e o f a v e r a g e m a x i m u m o u t p u t b y 1 8 %
I n c r e a s e o f p e a k e c i e n c y b y 5 %
I n c r e a s e o f f u l l l o a d e c i e n c y b y 5 %
U n i t 1 i s n o w c o m m i s s i o n e d a n d e l d t e s t s s h o w t h a t t h e g u a r a n t e e d
i n c r e a s e i n e c i e n c y o f 5 % h a s b e e n r e a c h e d [ 1 4 ] . T h e r e f u r b i s h m e n t o f
B a d u O z z a n a p o w e r p l a n t ( T a l o r o I I ) i n I t a l y i s n i s h e d . T h e t w o F r a n c i s
t u r b i n e s b u i l t i n 1 9 6 0 n e v e r m e t t h e i r w a r r a n t e d p e r f o r m a n c e s a l t h o u g h
s e v e r a l m o d i c a t i o n s w e r e p e r f o r m e d . A l l m a i n c o m p o n e n t s o f t h e t u r b i n e
w e r e r e p l a c e d a n d s i t e t e s t c o n r m e d a n i m p r o v e m e n t o f 4 % i n e c i e n c y a n d
n e a r l y 1 5 % i n c r e a s e i n p o w e r o u t p u t [ 1 9 ] . S t a t k r a f t h a s s t a r t e d t h e w o r k o f
r e h a b i l i t a t i n g a l a r g e p a r t o f t h e i r h y d r o p o w e r p l a n t s i n N o r w a y . A b o u t 2 1
u n i t s h a v e b e e n r e f u r b i s h e d , a n d o n a v e r a g e t h e y h a v e a c h i e v e d a n i n c r e a s e
i n e c i e n c y o f 2 . 3 % [ 3 5 ] .
T a b l e 3 . 1 p r e s e n t s a n o v e r v i e w o f r e f u r b i s h e d p o w e r p l a n t s w i t h F r a n c i s
t u r b i n e s . T h e a v e r a g e d i n c r e a s e i n p o w e r o u t p u t i s 1 8 % . A d d i t i o n a l
i n f o r m a t i o n a b o u t t h e p l a n t s c a n b e f o u n d i n A p p e n d i x D , w h i c h a l s o
i n c l u d e s r e f u r b i s h e d P e l t o n a n d K a p l a n t u r b i n e . I n c l u d i n g t h e s e t h e t o t a l
a v e r a g e i n c r e a s e i n p o w e r o u t p u t i s 2 0 % .
O u t p u t [ M W ]
P l a n t O l d N e w I n c r e a s e [ % ]
L a V i l l i t a 7 6 8 2 8
G u r i I I 6 1 0 7 1 5 1 7
K i a m b e r e 7 2 8 4 1 7
P a n t a b a n g a n 5 1 . 6 6 0 . 4 1 7
A m b u k l a o 2 5 3 5 4 0
T a l o r o I I 1 3 . 6 1 5 . 6 1 5
H a r s p r å n g e t 1 1 7 1 4 0 2 0
K i l f o r s e n 1 0 0 1 2 0 2 0
B a j i n a B a s t a 9 5 . 4 1 0 8 1 3
N e d r e V i n s t r a 5 0 6 5 3 0
M e q u i n e n z a 8 0 . 9 1 0 2 2 6
S å h e i m 5 4 6 0 1 1
S o n g a 1 2 0 1 3 6 1 3
A v e r a g e i n c r e a s e i n p o w e r o u t p u t 1 8
T a b l e 3 . 1 : R e f u r b i s h e d H P P w i t h F r a n c i s t u r b i n e s [ 2 8 ] , [ 1 9 ] , [ 3 1 ] , [ 2 0 ] , [ 2 3 ] ,
[ 1 4 ] , [ 8 ]
3 . 1 . 3 S i n t e f r e p o r t : P o t e n t i a l i n c r e a s e o f p o w e r o u t p u t
T h e r e p o r t " C a l c u l a t i o n o f p o t e n t i a l i n c r e a s e o f p o w e r o u t p u t i n N o r w e g i a n
h y d r o p o w e r p l a n t s " [ 2 1 ] p r e s e n t s a m e t h o d i n w h i c h a p o t e n t i a l i n c r e a s e i n
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3 R u n n e r D e s i g n
p o w e r o u t p u t c a n b e e s t i m a t e d . T h e m a i n i d e a i s t o i n c r e a s e t h e v o l u m e o w
t h r o u g h t h e r u n n e r w i t h o u t a d d i n g t o t h e c a v i t a t i o n r i s k . T h e d i m e n s i o n s o f
t h e r u n n e r i s i n c r e a s e d , b u t l i m i t e d t o t i n s i d e a n e x i s t i n g t u r b i n e w i t h o u t
m a j o r a l t e r a t i o n s . I t i s m a d e l a r g e r b y i n c r e a s i n g t h e o u t l e t d i a m e t e r
D2 a n d
i s l i m i t e d b y t h e c a s t - i n d i a m e t e r o f t h e d r a f t t u b e . F o r a F r a n c i s t u r b i n e i t i s
n o t p o s s i b l e t o i n c r e a s e D2 s i g n i c a n t l y w i t h o u t l a r g e a l t e r a t i o n s u p s t r e a m
t h e r u n n e r . T h i s r e l a t e s e s p e c i a l l y t o l o w p r e s s u r e t u r b i n e s , b e c a u s e i t a e c t s
t h e s t a y a n d g u i d e v a n e s i n a d d i t i o n t o t h e d r a f t t u b e . T h e o b j e c t i v e i s t o
e n s u r e t h a t i t i s o n l y n e c e s s a r y t o r e p l a c e t h e l o w e r c o v e r a n d t h e u p p e r p a r t
o f t h e d r a f t t u b e a l o n g w i t h t h e r u n n e r .
T h e n e w D2 i s e i t h e r e q u a l t o t h e c a s t - i n d i a m e t e r o r c a l c u l a t e d u s i n g
e q u a t i o n ( 3 . 1 ) b y S i e r v o a n d L e v a [ 1 3 ] . T h e s m a l l e s t d i a m e t e r i s s e l e c t e d a n d
t h e e x i s t i n g e c i e n c y o f t h e t u r b i n e i n q u e s t i o n i s u s e d . T h e r e s u l t s d o n o t
t a k e i n t o a c c o u n t a l i k e l y i n c r e a s e i n e c i e n c y d u t o a n e w a n d i m p r o v e d
r u n n e r . T h e r e d u c t i o n i n a v a i l a b l e h e a d d u e t o i n c r e a s e d h e a d l o s s e s f o r
i n c r e a s e d v o l u m e o w i s n o t a c c o u n t e d f o r i n t h e r e s u l t s . I t i s i n c l u d e d a t a
l a t e r s t a g e .
D2,new =
1.10 +
(0.80 − Ω)
6
D2 ( 3 . 1 )
3 . 2 R u n n e r D e s i g n
O v e r t h e l a s t d e c a d e s t h e r e h a s b e e n m a d e g r e a t h e a d w a y i n r u n n e r d e s i g n
o f t h e F r a n c i s t u r b i n e . T h e n e w d e s i g n p h i l o s o p h y d i e r s f r o m t h e o l d w i t h
a n i n c r e a s e d c u r v a t u r e o f t h e b l a d e a l o n g w i t h a c u r v e d s h a p e o f t h e t r a i l i n g
e d g e s [ 1 7 ] . T h e r e v o l u t i o n w i t h i n c o m p u t e r c a p a c i t y h a s m a d e i t p o s s i b l e t o
g o f r o m g r a p h i c a l l y b a s e d d e s i g n t o a v i r t u a l m e t h o d w i t h t h e a i d o f t o o l s
s u c h a s c o m p u t a t i o n a l u i d d y n a m i c s ( C F D ) . T h i s a l s o m a k e s i t p o s s i b l e
t o n u m e r i c a l l y a n a l y z e t h e p e r f o r m a n c e o f a r u n n e r b e f o r e b u i l d i n g i t . T h e
r e s u l t s a r e p r o v e n t o b e i n f a i r l y g o o d a g r e e m e n t w i t h m e a s u r e d d a t a [ 3 0 ] .
T h e d e s i g n m e t h o d u s i n g C F D u s u a l l y s t a r t s o u t w i t h a n i n i t i a l g u e s s o f t h e
r u n n e r g e o m e t r y b a s e d o n t r a d i t i o n a l 1 D o r 2 D p o t e n t i a l o w t h e o r y s u c h
a s E u l e r . I t i s s u b s e q u e n t l y f o l l o w e d b y a n o p t i m i z a t i o n p r o c e s s w h e r e t h e
d e s i g n i s a d j u s t e d i n o r d e r t o o b t a i n t h e d e s i r e d c h a r a c t e r i s t i c s [ 3 3 ] . T h e
t r a d i t i o n a l t h e o r y r e p r e s e n t s t h e d i r e c t d e s i g n m e t h o d w h e r e t h e o w e l d
i s d e t e r m i n e d b y a g i v e n b l a d e s h a p e . I n r e c e n t y e a r s , t h e r e h a s b e e n a n
i n c r e a s e d i n t e r e s t i n u s i n g a n i n v e r s e d e s i g n m e t h o d f o r t h e i n i t i a l g u e s s .
T h e d e s i r e d c h a r a c t e r i s t i c s o f t h e o w e l d a r e u s e d t o d e t e r m i n e a s u i t a b l e
b l a d e g e o m e t r y [ 4 ] .
A n o t h e r m a j o r a d v a n c e i s t h e i n t r o d u c t i o n o f p r e s s u r e b a l a n c e d b l a d e s
w i t h s k e w e d o u t l e t s n a m e d t h e " X - b l a d e " . I t h a s m a d e i t p o s s i b l e t o s t a b i l i z e
d y n a m i c b e h a v i o u r a n d i m p r o v e e c i e n c y d u r i n g o - d e s i g n p o i n t [ 6 ] . X -
b l a d e h a s b e e n s u c c e s s f u l l y i n s t a l l e d a t K i a m b e r e H P P i n K e n y a a n d t h e
d i e r e n c e b e t w e e n t h e o l d a n d t h e n e w r u n n e r i s s e e n i n g u r e 3 . 2 . T h e
r e s u l t o f t h e p r o j e c t i s c a v i t a t i o n f r e e o p e r a t i o n a n d a n i n c r e a s e i n p o w e r
o u t p u t o f 1 7 % [ 2 3 ] . S i t e t e s t s a r e s c h e d u l e d t o c o m m e n c e s p r i n g 2 0 1 0 .
R u n n e r r e p l a c e m e n t s a r e a g r e a t h y d r a u l i c d e s i g n c h a l l e n g e b e c a u s e o f
t h e g e o m e t r i c a l c o n s t r a i n t s o f t h e e x i s t i n g m a c h i n e s [ 3 6 ] . A n i n c r e a s e i n
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3 P r e l i m i n a r y S t u d i e s
( a ) O l d r u n n e r
( b ) N e w X - b l a d e r u n n e r
F i g u r e 3 . 2 : V i s u a l c o m p a r i s o n o f r u n n e r s a t K i a m b e r e [ 2 3 ]
p o w e r o u t p u t c a n b e o b t a i n e d b y i n c r e a s i n g e c i e n c y a n d / o r i n c r e a s i n g t h e
o w r a t e [ 3 2 ] , [ 1 7 ] , [ 2 1 ] , [ 1 9 ] . I m p r o v e m e n t o f c a v i t a t i o n b e h a v i o u r c a n b e
o b t a i n e d b y i n c r e a s i n g t h e r u n n e r o u t l e t d i a m e t e r a n d d e c r e a s e t h e o u t l e t
a n g l e . " A f u l l y p r e s s u r e b a l a n c e d b l a d e m u s t h a v e i n c r e a s e d a n g l e s n e a r
t h e i n l e t i n o r d e r t o o b t a i n a n i n c r e a s e d p r e s s u r e t o w a r d s t h e b a n d " [ 6 ] .
T h i s p h e n o m e n o n i s e a s i e s t e x p l a i n e d r e f e r r i n g t o e q u a t i o n 5 . 2 5 . A l a r g e
d i a m e t e r r e d u c e s t h e b l a d e o u t l e t a n g l e β 2 w i c h i n t u r n r e d u c e s t h e r e q u i r e d
s u b m e r g e n c e . I n a m e d i u m h e a d t u r b i n e i t i s n o r m a l t h a t t h e v a l u e o f β 2
i s i n t h e r a n g e f r o m 13
t o 18
. F o r t h e b l a d e i n l e t a n g l e β 1 i s a n o r m a l
v a l u e i n t h e r a n g e 50
t o 70
. T h e s e a n g l e s h a v e s i g n i c a n t i n u e n c e o n t h e
m e r i d i a n c r o s s s e c t i o n o f t h e c r o w n a n d t h e s h r o u d [ 5 ] .
A n o t h e r g e o m e t r i c p a r a m e t e r t h a t i n u e n c e s t h e c a v i t a t i o n c h a r a c t e r i s -
t i c s i s t h e b l a d e c u r v a t u r e . I n a s u c c e s s f u l d e s i g n e d r u n n e r t h e c a v i t a t i o n
b u b b l e c o l l a p s e s i n t h e w a t e r d o w n s t r e a m t h e b l a d e s . T h i s i s a c h i e v e d b y
i n c r e a s i n g t h e c u r v a t u r e o f t h e b l a d e l e t t i n g t h e c o n v e x s u c t i o n s i d e h a v e
i n c r e a s e d v e l o c i t i e s . E s p e c i a l l y i f t h i s i s d o n e t o w a r d s t h e b l a d e o u t l e t t h e
s e p a r a t i o n a n d c a v i t a t i o n i s m o v e d d o w n s t r e a m [ 5 ] .
T h e b l a d e o u t l e t g e o m e t r y a l s o a e c t s t h e p r e s s u r e o s c i l l a t i o n i n t h e d r a f t
t u b e . A s k e w e d o u t l e t ( i . e . n o t r a d i a l ) i s p r o v e n t o h a v e a s t a b i l i z i n g e e c t .
T h i s m a y b e d u e t o t h e f a c t t h a t t h e b l a d e o u t l e t s a r e l o c a t e d a t a s m a l l e r
d i a m e t e r f r o m t h e c r o w n , a n d a m o r e h a r m o n i c p r e s s u r e s u r g e a t p a r t l o a d
i s o b s e r v e d . L o w p r e s s u r e r e g i o n s a t t h e s h r o u d i n t h e i n l e t m a y b e d u e t o
i t s c u r v a t u r e a n d c a n b e c o m p e n s a t e d f o r b y c h a n g i n g t h e b l a d e l e a n a n g l e
[ 5 ] .
1 5
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3 R u n n e r D e s i g n
1 6
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C h a p t e r 4
R e v i e w o f H y d r a u l i c
C o n d i t i o n s
T h i s r e v i e w o f t h e c o n d i t i o n o f t h e w a t e r w a y a t R u a c a n a i s b a s e d o n
d a t a s u b m i t t e d b y N a m P o w e r , i n a d d i t i o n t o t h e t e n d e r d o c u m e n t s f o r t h e
c o n s t r u c t i o n o f t h e n e w 4th
U n i t . A r e v i e w o f t h e a v a i l a b l e m a c h i n e d r a w i n g s
[ 2 ] i s p e r f o r m e d i n o r d e r t o d e t e r m i n e t h e a s - b u i l t d a t a . I n f o r m a t i o n a b o u t
t h e c o n d i t i o n s o f t h e w a t e r w a y w a s a l s o o b t a i n e d t h r o u g h i n t e r v i e w s w i t h
A . E s p a g [ 1 5 ] a n d E . K l e i n h a n s e n [ 2 4 ] . T h e c o m p o n e n t s t h a t h a v e n o t
e x p e r i e n c e d a n y p a r t i c u l a r p r o b l e m s a r e n o t d e s c r i b e d i n d e t a i l . T h e g e n e r a l
l a y o u t o f R u a c a n a c a n b e s e e n i n g u r e 4 . 1 , a n d t h e f o l l o w i n g p r e s e n t s t h e
c o m p o n e n t s o f t h e p o w e r p l a n t s t a r t i n g a t t h e t o p . B a c k g r o u n d i n f o r m a t i o n
a b o u t R u a c a n a c a n b e f o u n d i n a p p e n d i x A .
F i g u r e 4 . 1 : L a y o u t o f R u a c a n a
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4 C o m p o n e n t s u p s t r e a m t u r b i n e
4 . 1 C o m p o n e n t s u p s t r e a m t u r b i n e
D i v e r s i o n W e i r a n d P r e s s u r e T u n n e l
T h e p l a n t i s a r u n - o f - r i v e r p o w e r p l a n t w i t h a n i n t a k e i n t h e s h a p e o f a
d i v e r s i o n w e i r . T a b l e 4 . 1 p r e s e n t s t h e h e a d w a t e r l e v e l s w h i c h v a r i e s s t r o n g l y
w i t h t h e s e a s o n s a n d d e t e r m i n e s t h e r e g u l a t i o n o f t h e p l a n t . A t m i n i m u m
d r a w - d o w n l e v e l t h e o p e r a t i o n o f t h e p o w e r p l a n t i s r e s t r i c t e d t o o n e u n i t d u e
t o s u r g e p r o b l e m . T h e d i v e r s i o n w e i r h a s b e e n d r a i n e d a n d i n s p e c t e d o n c e
a n d n o m a j o r f a u l t s w e r e f o u n d . T h e w a t e r i s t h e n d i v e r t e d i n t o t h e p r e s s u r e
t u n n e l , w h i c h h a s o n l y e x p e r i e n c e d a l e a k a g e p r o b l e m d u e t o m a i n t e n a n c e
e r r o r . I t s d a t a i s p r e s e n t e d i n t a b l e 4 . 2 .
L e v e l , [ m a s l ] S i g n i c a n c e
9 0 4 . 5 H i g h e s t o o d l e v e l
9 0 2 . 7 H i g h e s t r e g u l a t e d w a t e r l e v e l ( H R W L )
9 0 1 . 0 N o r m a l d r a w - d o w n l e v e l ( N R W L )
8 9 5 . 2 M i n i m u m d r a w - d o w n l e v e l ( M R W L )
T a b l e 4 . 1 : I n t a k e w a t e r l e v e l s
C o m p o n e n t L e n g t h [ m ] D i a m e t e r [ m ]
P i p e 1 1 2 1 5 8 . 3
P i p e 2 2 8 5 7 . 4
T o t a l 1 5 0 0
H e a d l o s s c o e c i e n t , c 5.2 · 10−5
T a b l e 4 . 2 : P r e s s u r e t u n n e l d a t a
T h e S u r g e H e a d b a y
T h e d i m e n s i o n s o f t h e S u r g e H e a d b a y a r e f o u n d i n d r a w i n g " N o . 3 2 H 3 9 e ,
S u r g e H e a d b a y , p e n s t o c k i n t a k e w a l l s " [ 2 ] . T h e b a s e a r e a a t l e v e l 8 8 2 . 5
m a s l i s i l l u s t r a t e d i n g u r e 4 . 2 a n d t h e w a l l s i n g u r e 4 . 3 . T h e w a l l s a r e
d i v i d e d i n t o a g e n e r a l s e c t i o n ( G S ) a n d a n o p e r a t i n g p l a t f o r m ( O P ) . T h e
O P s e c t i o n p r o t r u d e s i n t o t h e c r o s s - s e c t i o n a l a r e a u p t o a l e v e l o f 9 0 7 m a s l .
I n t h e S u r g e H e a d b a y h a v e t h e r e n o t b e e n f o u n d a n y m a j o r f a u l t s d u r i n g
i n s p e c t i o n s . T h e i n d i c a t e d l e v e l s i n g u r e 4 . 3 a r e i d e n t i e d i n t a b l e 4 . 3 . F o r
t h e a i r s u c t i o n l e v e l a s a f e t y f a c t o r i s i n c l u d e d .
L e v e l , [ m a s l ]
9 0 9 . 7 T o p l e v e l
9 0 7 T o p l e v e l f o r O p e r a t i n g P l a t f o r m
9 0 5 A i r i n t a k e f o r P e n s t o c k
8 9 1 . 5 C a l c u l a t e d a i r s u c t i o n l e v e l
8 8 2 . 5 B o t t o m l e v e l o f S u r g e H e a d b a y
T a b l e 4 . 3 : S u r g e H e a d b a y l e v e l s
1 8
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4 R e v i e w o f H y d r a u l i c C o n d i t i o n s
F i g u r e 4 . 2 : S u r g e H e a d b a y b a s e a r e a ( n o t t o s c a l e )
F i g u r e 4 . 3 : S u r g e H e a d b a y w a l l s ( n o t t o s c a l e )
P e n s t o c k
A f t e r t h e S u r g e H e a d b a y t h e w a t e r w a y d i v i d e s i n t o f o u r p e n s t o c k s t h a t a r e
a l l i d e n t i c a l , a n d t h e d a t a i s p r e s e n t e d i n t a b l e 4 . 4 . T h e y a r e r e g u l a r l y
i n s p e c t e d b u t n o s i g n i c a n t p r o b l e m o t h e r t h a n s o m e p a i n t p e e l i n g i s f o u n d .
1 9
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4 T u r b i n e U n i t s 1 - 3
C o m p o n e n t D i a m e t e r L e n g t h
V e r t i c a l : 3 . 6 m 1 2 0 m
H o r i z o n t a l : 3 . 6 m 5 5 m
H e a d l o s s c o e c i e n t , c 6.5 · 10−4
T a b l e 4 . 4 : P e n s t o c k d a t a
4 . 2 T u r b i n e U n i t s 1 - 3
A t t h e p r e s e n t t h r e e t u r b i n e s a r e i n s t a l l e d , a n d t h e p r o c e s s o f i n s t a l l i n g t h e
f o u r t h u n i t h a s s t a r t e d . T h e p l a n t w a s c o m i s i o n e d i n 1 9 7 8 a n d t h e e x i s t i n g
t u r b i n e u n i t d a t a a r e p r e s e n t e d i n t a b l e 4 . 5 .
M a n u f a c t u r e r V ö e s t A l p i n e
N u m b e r o f U n i t s 3
N o m i n a l O u t p u t p r . t u r b i n e ,
P n 82 MWN o m i n a l d i s c h a r g e ,
Qn 68 m3/s
N o m i n a l h e a d , H n 134.0 m
R o t a t i o n a l s p e e d , n 230.8 rpm
D i r e c t i o n o f r o t a t i o n C o u n t e r c l o c k w i s e
I n l e t d i a m e t e r , D1 3734 mm
O u t l e t d i a m e t e r , D2 2940 mm
I n l e t h e i g h t , B0 650 mm
N u m b e r o f b l a d e s , z 13
I n t e r n a l h e a d l o s s t o d r a f t t u b e e x i t ,
ct 0.4·
10−4
T a b l e 4 . 5 : T u r b i n e u n i t d a t a
C a v i t a t i o n p r o b l e m s
T h e h u b e x p e r i e n c e s c a v i t a t i o n e r o s i o n i n t h e a r e a a s s e e n i n p i c t u r e 4 . 4 . I t
i s n o t a d v a n t a g e o u s t h a t i t i s m a d e o f c a s t i r o n . T h e p r o b l e m h a s n o t b e e n
c o n s i d e r e d t o b e s e r i o u s e n o u g h t o r e p a i r .
T h e r u n n e r e x p e r i e n c e s c a v i t a t i o n i n t h e d i s c h a r g e a r e a a l o n g t h e e n t i r e
t r a i l i n g e d g e w h i c h c a n b e o b s e r v e d i n p i c t u r e s 4 . 5 a n d 4 . 6 . T h e s e a r e a s a r e
i n s p e c t e d a n d m e a s u r e d e a c h y e a r a n d a r e a t t h e p r e s e n t n o t c o n s i d e r e d t o
y i e l d a n y s i g n i c a n t p r o b l e m s . T h e c a v i t a t i o n a e c t s t h e r e g u l a t i o n o f t h e
t u r b i n e a n d f o r c e d a i r a d m i s s i o n i n t h e d r a f t t u b e i s u s e d i n t h e r a n g e o f 3 5
4 0 M W a n d 7 0 8 0 M W . T h e t u r b i n e s a r e n o r m a l l y o p e r a t e d a t 8 0 M W a n d
c a n r u n u p t o 8 3 M W d u r i n g e m e r g e n c i e s , b u t t h e n i t i s n o t p o s s i b l e t o a v o i d
c a v i t a t i o n b y u s i n g f o r c e d a i r a d m i s s i o n . T h e c a u s e o f t h e c a v i t a t i o n i s n o t
e a s i l y d e t e r m i n e d , b u t i t i s p o s s i b l e t o r u l e o u t t h e N PSH A o f t h e s y s t e m .
D u r i n g t h e c o n s t r u c t i o n o f t h e p o w e r s t a t i o n , t h e " n o r m a l " h i g h t a i l w a t e r
l e v e l w a s a s s e s s e d t o b e 7 6 4 . 7 m a s l f o r a t o t a l v o l u m e o w o f 2 2 5 m3/s
.
T h i s y i e l d s a s u b m e r g e n c e o f H s = 8.5m
, a n d a t o t a l N PSH A = 17.5m
a c c o r d i n g t o e q u a t i o n ( 2 . 1 5 ) . T h e t a i l w a t e r l e v e l v a r i e s w i t h t h e v o l u m e
o w a n d i t h a s b e e n d e e m e d s u c i e n t t o s u b t r a c t 1 5 % f r o m N PSH A f o r
f u t u r e c a l c u l a t i o n s . T h e n o m i n a l v o l u m e o w u s e d i n c a l c u l a t i o n s t o d a y i s
2 8 4 m3/s f o r f o u r u n i t s .
2 0
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4 R e v i e w o f H y d r a u l i c C o n d i t i o n s
F i g u r e 4 . 4 : C a v i t a t i o n o n t h e h u b
F i g u r e 4 . 5 : C a v i t a t i o n o n t h e t r a i l i n g e d g e a n d t h e o u t e r r i n g
F i g u r e 4 . 6 : C a v i a t i o n o n t h e t r a i l i n g e d g e n e a r t h e h u b
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4 T u r b i n e U n i t s 1 - 3
T h i s d e g r e e o f s u b m e r g e n c e s h o u l d b e s u c i e n t , a n d t h e r e f o r e i t i s
p r o b a b l e t h a t t h e c a v i t a t i o n p r o b l e m i s d u e t o t h e d e s i g n o f t h e r u n n e r s .
U n f o r t u n a t e l y t h e r e d o e s n o t e x i s t s u c i e n t i n f o r m a t i o n a b o u t t h e e x i s t i n g
r u n n e r d e s i g n i n o r d e r t o e s t a b l i s h a d e t a i l e d p i c t u r e . T h e m a i n d i m e n s i o n s
a r e p r e s e n t e d i n t a b l e 4 . 5 , a n d g u r e 4 . 7 p r e s e n t s a n e x t r a c t o f t h e o n l y
a v a i l a b l e m a c h i n e d r a w i n g o f t h e r u n n e r b l a d e s " M B 9 0 4 8 1 1 0 9 A , R u n n e r "
[ 2 ] . F r o m d i s c u s s i o n s w i t h O l e G u n n a r D a l h a u g i t h a s b e e n p o i n t e d o u t t h a t
t h e 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 i n l e t m a y c a u s e t h e c a v i t a t i o n p r o b l e m i n
t h e o u t l e t [ 1 2 ] . I t i s t h e r e f o r e p r o b a b l e t h a t w i t h a n e w d e s i g n o f t h e r u n n e r
t h e c a v i t a t i o n p r o b l e m s m a y v a n i s h .
4 . 2 . 1 O t h e r e v a l u a t e d f a c t o r s
A r e p l a c e m e n t o f t h e s t a y r i n g / w i c k e t g a t e i s o u t o f t h e q u e s t i o n . T h e s t a y
r i n g i s q u i t e t h i c k , b e c a u s e i t s u p p o r t s t h e t h r u s t b e a r i n g . I n t h e b e g i n n i n g
w e r e t h e r m a n y p r o b l e m s w i t h t h e t h r u s t b e a r i n g , a n d t h e t u r b i n e c o u l d n o t
o p e r a t e o v e r 7 0 M W . I t w a s r e p l a c e d a n d t h e p r o b l e m s d i s a p p e a r e d . T h e
g u i d e v a n e s a n d t h e d r a f t t u b e a r e a l s o r e g u l a r l y i n s p e c t e d b u t t h e r e h a v e
n o t b e e n a n y n o t a b l e p r o b l e m s . I n t h e s p i r a l c a s i n g t h e a l l o w a b l e p r e s s u r e
i s 1 7 8 m W C [ 2 5 ] . T h e n e w u n i t i n c o m p a r i s o n t o t h e e x i s t i n g t u r b i n e s h a s
a s m a l l e r o u t l e t d i a m e t e r a n d c o n s e q u e n t l y a h i g h e r r o t a t i o n a l s p e e d . I n
o r d e r t o b e a b l e t o c o m p a r e t h e u n i t s a t R u a c a n a t o s i m i l a r i n s t a l l a t i o n s
h a s i t b e e n v e r y d i c u l t t o o b t a i n a d e q u a t e i n f o r m a t i o n . F o r t h e t u r b i n e s
i s n12
≈59
a t R u a c a n a . A c o m p a r i s o n w i t h t h e p o w e r p l a n t s p r e s e n t e d i n
3 . 1 i t i s f o u n d t h a t t h e p o w e r p l a n t s w i t h s i m i l a r v a l u e s h a v e o b t a i n e d a n
a v e r a g e i n c r e a s e i n o u t p u t o f 1 9 % .
F i g u r e 4 . 7 : E x i t i n g t u r b i n e s r u n n e r b l a d e s [ 2 ]
2 2
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4 R e v i e w o f H y d r a u l i c C o n d i t i o n s
4 . 3 C o m p o n e n t s d o w n s t r e a m t u r b i n e
S u r g e C h a m b e r a n d T a i l r a c e
T h e d i s c h a r g e f r o m t h e f o u r t u r b i n e s a r e j o i n e d i n t h e S u r g e C h a m b e r , b e f o r e
i t i s l e a d o u t i n t o t h e o p e n t h r o u g h t h e t a i l r a c e . T h e s h a p e a n d m e a s u r e d
c r o s s - s e c t i o n a l a r e a i s p r e s e n t e d i n g u r e 4 . 8 , w h i c h i s t a k e n f r o m d r a w i n g
" 0 - 4 2 / 3 7 5 r e v . 5 S u r g e C h a m b e r G e n e r a l A r r a n g e m e n t " [ 2 ] . T h e A c c e s s
G a l l e r y l e a d s d o w n t o t h e m a i n s t a t i o n h a l l , a n d t h e r e f o r e t h e u p s u r g e l e v e l
i s o f p a r t i c u l a r i n t e r e s t f o r t h e s a f e t y o f t h e p l a n t . T h i s i s d e n o t e d i n t h e
g u r e a s " p e r m i s s i b l e o o d w a t e r l e v e l " a t 7 7 5 m a s l . D u r i n g i n s p e c t i o n s
n e i t h e r t h e S u r g e C h a m b e r n o r t h e T a i l r a c e h a s b e e n s u b j e c t e d t o a n y
n o t a b l e m a i n t e n a n c e p r o b l e m s .
T h e t a i l w a t e r l e v e l r e s u l t s f r o m a c o m b i n a t i o n o f h e a d l o s s i n t h e t a i l r a c e
t u n n e l a n d t h e r i s e i n w a t e r l e v e l i n t h e r i v e r o u t s i d e t h e t u n n e l e x i t . T h e
w a t e r l e v e l i n t h e r i v e r i s d i c u l t t o d e t e r m i n e b e c a u s e i t d e p e n d s o n
t h e a v e r a g e o w i n t h e r i v e r o v e r a p e r i o d o f t i m e . T a b l e 4 . 6 p r e s e n t s
t h e i d e n t i e d t a i l w a t e r l e v e l s c o r r e s p o n d i n g t o t h e v o l u m e o w i n t h e
s t a t i o n . T h e l a s t e n t r y i s f a i r l y r e p r e s e n t a t i v e f o r c o n d i t i o n s a t n o r m a l h i g h
w a t e r l e v e l i n t h e r i v e r . D r a w i n g a s t r a i g h t l i n e b e t w e e n t h e t w o m i d d l e
m e a s u r e m e n t s a n i n c l i n e o f a p p r o x i m a t e l y 0.003
i s o b t a i n e d . T h i s y i e l d s a n
a c c e p t a b l e r e l a t i o n s h i p f o r t h e w a t e r r i s e i n t h e t u n n e l : ∆h = 0.003Qstation .
T h e h i g h e s t o o d l e v e l i n t h e t a i l w a t e r i s 7 6 9 . 2 m a s l .
W a t e r l e v e l , [ m a s l ] V o l u m e o w ,
[m3/s]
7 6 1 . 0 0 M e a s u r e d l e v e l a f t e r s t o p f o r
1 2 h o u r s
7 6 2 . 6 6 8 M e a s u r e d l e v e l , o n e u n i t i n
o p e r a t i o n
7 6 2 . 8 1 3 6 M e a s u r e d l e v e l , t w o u n i t s i n
o p e r a t i o n
7 6 4 . 5 2 2 5 A s s e s s e d l e v e l d u r i n g c o n -
s t r u c t i o n
T a b l e 4 . 6 : T a i l w a t e r l e v e l s a n d v o l u m e o w
2 3
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4 C o m p o n e n t s d o w n s t r e a m t u r b i n e
F i g u r e 4 . 8 : S u r g e C h a m b e r d i m e n s i o n s [ 2 ]
2 4
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C h a p t e r 5
C a l c u l a t i o n M e t h o d s
T h i s s e c t i o n p r e s e n t s t h e c a l c u l a t i o n m e t h o d s f o r w a t e r h a m m e r a n d s u r g e
o s c i l l a t i o n . F i n a l l y , a c a l c u l a t i o n m o d e l f o r i n v e s t i g a t i n g p o s s i b l e i n c r e a s e i n
p o w e r o u t p u t i s p r e s e n t e d .
5 . 1 G e n e r a l a s s u m p t i o n s
T h e c r o s s - s e c t i o n a l a r e a i n t h e S u r g e H e a d b a y i s c a l c u l a t e d b a s e d o n g u r e s
4 . 2 a n d 4 . 3 . A t a b l e i s g e n e r a t e d w h i c h c o n t a i n s t h e a r e a f r o m t h e b a s e t o
t h e t o p w i t h a n i n c r e m e n t o f 0.1m
i n t h e M a t l a b . T h e c r o s s - s e c t i o n a l a r e a
o f t h e S u r g e C h a m b e r i s f o u n d i n g u r e 4 . 8 . F o r t h e c a l c u l a t i o n s a t t i m e
n + 1i t i s a s s u m e d s u c i e n t t o u s e t h e a r e a c o r r e s p o n d i n g t o t h e s u r g e l e v e l
a t t i m e
n.
5 . 2 P r e s s u r e c a l c u l a t i o n m o d e l
A M a t l a b p r o g r a m i s d e v e l o p e d t o c a l c u l a t e t h e p r e s s u r e a t R u a c a n a , a n d i t
i s p r e s e n t e d i n a p p e n d i x B . 1 . T h e f o l l o w i n g p r e s e n t s t h e s y s t e m o f e q u a t i o n s
b a s e d o n t h e e x i s t i n g c o n d i t i o n s a t R u a c a n a w h i c h i s s i m p l i e d a c c o r d i n g t o
g u r e 5 . 1 . I t i s t h e f r e e s u r f a c e o f t h e S u r g e H e a d b a y t h a t a e c t s t h e p r e s s u r e
w a v e . I t c a n i n p a r t b e r e g a r d e d a s a n e x t e n s i o n o f t h e t h e o r y p r e s e n t e d i n
s e c t i o n 2 . 1 . 1 . A l l o f t h e f o u r p e n s t o c k s a r e i d e n t i c a l w h i c h m e a n s t h a t t h e
w a t e r h a m m e r i s t h e s a m e f o r e a c h t u r b i n e s i n c e t h e y a r e a l l o p e n e d a n d
c l o s e d i n t h e s a m e m a n n e r [ 3 ] .
5 . 2 . 1 N u m e r i c a l e q u a t i o n s w a t e r h a m m e r
T h e r e s u l t i n g n u m e r i c a l e q u a t i o n s y s t e m f r o m a p p l y i n g t h e t r a p e z o i d a l r u l e
o n e q u a t i o n s ( 2 . 7 ) a n d ( 2 . 8 ) i s g i v e n b y e q u a t i o n s ( 5 . 1 ) a n d ( 5 . 2 ) . W h e r e
t h e s u b s c r i p t P
d e n o t e s t h e v a l u e a t t h e c u r r e n t t i m e s t e p , A
r e f e r s t o t h e
p r e c e d i n g v a l u e a t x − dx
a n d B
t o t h e s u c c e e d i n g v a l u e a t x + dx
.
C + : H P = H A − B (QP − QA) − RQP |QA|( 5 . 1 )
C − : H P = H B + B (QP − QA) + RQP |QB| ( 5 . 2 )
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5 P r e s s u r e c a l c u l a t i o n m o d e l
F i g u r e 5 . 1 : I l l u s t r a t i o n o f w a t e r w a y f o r w a t e r h a m m e r c a l c u l a t i o n s
B i s k n o w n a s t h e p i p e l i n e c h a r a c t e r i s t i c i m p e d a n c e , a n d i s g i v e n b y
e q u a t i o n ( 5 . 3 ) . R i s t h e p i p e l i n e r e s i s t a n c e c o e c i e n t o v e r t h e s t r e t c h ∆x
a n d
i t i s h e r e d e n e d a s i n e q u a t i o n ( 5 . 4 ) d u e t o t h e k n o w n h e a d l o s s c o e c i e n t
g i v e n i n 4 .
B =a
gA( 5 . 3 )
R = c( 5 . 4 )
F u r t h e r d i s c r e t i s a t i o n o f e q u a t i o n s ( 5 . 1 ) a n d ( 5 . 2 ) a r e d o n e b y s e p a r a t i n g
t h e s e i n t o e q u a t i o n s f o r H a n d Q i n ( 5 . 5 ) a n d ( 5 . 6 ) . A s o l u t i o n c a n b e
o b t a i n e d f o r e a c h i n t e r i o r p o i n t P a t (x)
i n w h i c h t h e v a l u e s C A ,
C B a n d QR
a r e k n o w n a n d d e n e d b y e q u a t i o n s ( 5 . 7 ) ( 5 . 9 ) .
H (x, n) =1
B(C A − BQR) +
1
BC B ( 5 . 5 )
Q(x, n) = 1B (H (x, n) − C B) + Q(x + dx,n − 1) ( 5 . 6 )
C A = H (x − dx,n − 1) − RQ(x − dx,n − 1) |Q(x − dx,n − 1)|( 5 . 7 )
C B = H (x + dx,n − 1) + RQ(x + dx,n − 1) |Q(x + dx,n − 1)|( 5 . 8 )
QR = Q(x + dx,n − 1) − Q(x + dx,n − 1)( 5 . 9 )
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5 C a l c u l a t i o n M e t h o d s
5 . 2 . 2 B o u n d a r y c o n d i t i o n s
A t H (x0, n)
t h e p i e z o m e t e r p r e s s u r e i s d e n e d b y t h e s u r g e o s c i l l a t i o n i n t h e
S u r g e H e a d b a y a s i n e q u a t i o n ( 5 . 1 0 ) . T h e v o l u m e o w i s c a l c u l a t e d f r o m
e q u a t i o n ( 5 . 6 ) .
H (x0, n) = Z (n − 1) + dtQ(x − dx,n − 1) − Q(x + dx,n − 1)
As1(n − 1)( 5 . 1 0 )
I n t h i s s y s t e m t h e t u r b i n e i s s e t t o b e h a v e a s a v a l v e , a n d t h e v o l u m e
o w t h r o u g h t h e t u r b i n e i s d e n e d b y e q u a t i o n ( 5 . 1 1 ) . T h e v a l v e e l e v a t i o n
i s u s e d a s t h e r e f e r e n c e d a t u m w h e r e t h e o w d i s c h a r g e s t o t h e a t m o s p h e r e .
T h e p r e s s u r e i s c a l c u l a t e d a c c o r d i n g t o e q u a t i o n ( 5 . 1 3 ) .
Q(L, n) = −0.5BC V + 0.5
(BC V )2 + 4C V C P ( 5 . 1 1 )
C V =(κQn)2
H n( 5 . 1 2 )
H (x, n) =
Q(x, t)
κQn
2H n ( 5 . 1 3 )
5 . 2 . 3 C a l c u l a t i o n p r o c e d u r e
T h e c a l c u l a t i o n p r o c e d u r e i s [ 2 9 ] , [ 3 7 ] :
1 . T h e c o n d u i t i s d i v i d e d i n t o p a r t i t i o n s d e t e r m i n e d b y t h e r e l a t i o n s h i p
∆x = a∆t. I n o r d e r t o o b t a i n b o u n d a r y c o n d i t i o n s a t t h e e n d s L∆xm u s t b e a p o s i t i v e i n t e g e r .
2 . I n i t i a l v a l u e s a t t = 0
f o r Q a n d H a r e c a l c u l a t e d a t e a c h i n t e r i o r p o i n t
a n d s t o r e d .
3 . T h e e q u a t i o n s y s t e m d e s c r i b e d i n 5 . 2 . 1 a n d 5 . 2 . 2 i s s o l v e d t h e r e a f t e r
f o r t i m e s t e p s d e t e r m i n e d b y d t .
5 . 2 . 4 V e r i c a t i o n o f W a t e r h a m m e r M o d e l
A n a l y t i c N u m e r i c D e v i a t i o n
T L 0 s 0 . 0 0 4 2 s 0 . 0 0 4 2 s
T R 0 . 3 4 s 0 . 3 3 s 0 . 1 s
p 0 . 6 s 0 . 6 s 0 s
∆h8 5 5 . 9 m W C 8 5 5 . 8 m W C 0 . 1 m W C
T a b l e 5 . 1 : V e r i c a t i o n : I d e a l a n d a c t u a l v a l u e s o f w a t e r h a m m e r
T h e w a t e r h a m m e r p r o g r a m i s v e r i e d b y c a l c u l a t i n g t h e o w e l d
w i t h o u t l o s s e s , a n d t h e r e s u l t s a r e s h o w n i n g u r e 5 . 2 . I n t h e g u r e t h e
c l o s i n g t i m e o f t h e v a l v e i s T L = dt = 0.0042s
, a n d i t i s s h o r t e r t h a n t h e
r e e c t i o n t i m e o f a p r e s s u r e w a v e T R c a l c u l a t e d b y e q u a t i o n ( 2 . 5 ) . T h e
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5 S u r g e O s c i l l a t i o n m o d e l
F i g u r e 5 . 2 : V e r i c a t i o n W a t e r H a m m e r p r o g r a m
p r e s s u r e i n t h e S u r g e H e a d b a y i s s e t t o b e c o n s t a n t . I n t a b l e 5 . 1 a r e t h e
i d e a l a n a l y t i c v a l u e s a c c o r d i n g t o t h e t h e o r y i n 2 . 1 . 1 p r e s e n t e d a l o n g w i t h
t h e v a l u e s f o u n d i n t h e g r a p h . T h i s r e p r e s e n t s t h e n u m e r i c a l e r r o r i n t h e
M a t l a b p r o g r a m .
5 . 3 S u r g e O s c i l l a t i o n m o d e l
T h e d e v e l o p e d M a t l a b p r o g r a m w h i c h i n v e s t i g a t e s t h e s u r g e o s c i l l a t i o n s
l e v e l s i n b o t h s u r g e t a n k s b y u s i n g a n E u l e r c o d e i s f o u n d i n a p p e n d i x B . 2 .
F i g u r e 5 . 3 r e p r e s e n t s t h e s i m p l i e d w a t e r w a y s y s t e m a t R u a c a n a u s e d i n
t h e s u r g e o s c i l l a t i o n c a l c u l a t i o n s . H e r e i s t h e p r e s s u r e t u n n e l a s s u m e d t o
c o n s i s t o f o n e t u n n e l . A w e i g h t e d c r o s s - s e c t i o n a l a r e a o f 5 1 . 9 9 m2
i s u s e d .
I n a d d i t i o n , t h e f o u r p e n s t o c k s a r e a s s u m e d t o b e o n e .
F i g u r e 5 . 3 : I l l u s t r a t i o n o f w a t e r w a y u s e d i n s u r g e o s c i l l a t i o n c a l c u l a t i o n s
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5 C a l c u l a t i o n M e t h o d s
5 . 3 . 1 S y s t e m o f e q u a t i o n s : S u r g e O s c i l l a t i o n
E q u a t i o n s 5 . 1 4 t o 5 . 2 1 a r e l i n e a r p a r t i a l d i e r e n t i a l e q u a t i o n s u s e d t o s o l v e
s u r g e o s c i l l a t i o n i n t h e t w o s u r g e t a n k s i l l u s t r a t e d i n g u r e 5 . 3 [ 1 6 ] [ 2 9 ] . A
s o l u t i o n c a n b e o b t a i n e d b y u s i n g a n E u l e r c o d e i n M a t l a b . A s a b a s i s f o r
t h e e q u a t i o n s i s i t i m p o r t a n t t o n o t e t h e f o l l o w i n g a s s u m p t i o n s :
1 . T h e e l a s t i c e e c t o f t h e w a t e r i s n e g l e c t e d b e c a u s e t h e s e t y p e s o f
o s c i l l a t i o n s a r e s l o w a n d t h e r e f o r e t h e c h a n g e v o l u m e o w i s s l o w .
2 . T h e m a s s e s o f t h e s h a f t s a r e n e g l e c t e d . T h e r e f o r e i s t h e p r e s s u r e i n
i n t e r s e c t i o n 1 e q u a l t o t h e w a t e r l e v e l i n s u r g e t a n k 1 , a n d t h e p r e s s u r e
i n i n t e r s e c t i o n 2 e q u a l t o t h e w a t e r l e v e l i n s u r g e t a n k 2 .
3 . C o m p r e s s i b i l i t y e e c t s a r e n o t s i g n i c a n t .
dQ1
dt=
gA1
L1
(H 0 − z1 − c1Q1 |Q1|) ( 5 . 1 4 )
dQ2
dt=
gA2
L2
z1 − z2 − H n
Q2
κQn
− c2Q2 |Q2|
( 5 . 1 5 )
dQ3
dt=
gA3
L2
(z2 − H u − c3Q3 |Q3|) ( 5 . 1 6 )
W h e r e t h e g e n e r a l e q u a t i o n f o r h e a d l o s s c o e c i e n t c
i s g i v e n i n e q u a t i o n
( 5 . 1 7 )
c =f L
2gA2D( 5 . 1 7 )
F o r t h e w a t e r w a y s y s t e m a t R u a c a n a a r e m e a s u r e d v a l u e s u s e d . T h e
c o n t i n u i t y e q u a t i o n s ( 5 . 1 8 ) a n d ( 5 . 1 9 ) d e s c r i b e t h e r e l a t i o n b e t w e e n t h e s u r g e
s h a f t s a n d t u n n e l s . R e s p e c t i v e l y i n i n t e r s e c t i o n s 1 a n d 2 i n g u r e 5 . 3 .
Qs1 = Q1 − Q2 ( 5 . 1 8 )
Qs2 = Q2 − Q3 ( 5 . 1 9 )
T h e w a t e r l e v e l i n t h e s u r g e t a n k s a r e g i v e n b y e q u a t i o n s ( 5 . 2 0 ) a n d
( 5 . 2 1 ) . T h e s e e q u a t i o n s a r e s o l v e d w i t h a n E u l e r c o d e i n M a t l a b , a n d t h e
p r o g r a m i s p r e s e n t e d i n a p p e n d i x B . 2 .
dz1dt
=1
As1Qs1 ( 5 . 2 0 )
dz2
dt=
1
As2
Qs2 ( 5 . 2 1 )
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5 I n c r e a s e p o w e r o u t p u t
5 . 3 . 2 W o r s t c a s e s c e n a r i o s
T h e w a t e r o w o f t h e K u n e n e r i v e r i s h i g h l y d e p e n d e n t o n t h e s e a s o n a n d
o o d c o n d i t i o n s , a n d m u s t b e t a k e n i n t o a c c o u n t w h e n d e t e r m i n i n g t h e w o r s t
c a s e s c e n a r i o s .
T h e o b j e c t i v e s o f t h e s i m u l a t i o n s o f t h e S u r g e H e a d b a y a r e :
E n s u r e t h a t t h e w a t e r d o e s n o t r i s e o v e r t h e t o p o f t h e S u r g e H e a d b a y
a t a l e v e l o f 909.7 masl
.
A v o i d s u c t i o n o f a i r i n t o t h e p e n s t o c k . T h i s h a p p e n s i f t h e w a t e r
r e c e d e s t h e l e v e l o f 895.1 masl
.
A l l s i m u l a t i o n s o f s u r g e o s c i l l a t i o n s t a r t s b y r e j e c t i n g f r o m n o m i n a l
v o l u m e o w Qn d o w n t o z e r o . I n o r d e r t o n d t h e m a x i m u m u p - a n d
d o w n s u r g e i s t h i s f o l l o w e d b y r e l o a d i n g o f o n e t u r b i n e a n d a s u b s e q u e n t
r e j e c t i o n a t t h e w o r s t p o s s i b l e t i m e . L a t e r t h i s i s r e f e r r e d t o a s a r e l o a d / r e j e c t
s e q u e n c e . F o r 4 u n i t s i n o p e r a t i o n a t e x i s t i n g c o n d i t i o n s i s t h e n o m i n a l
v o l u m e o w Qn = 284m3/s
, a n d 1 u n i t Qn1 = 71m3/s
. T h e v a l v e i s c l o s e d
u s i n g a n a d m i s s i o n s d e g r e e w h i c h i s d e n e d a s κQn . T h i s e n t a i l s t h a t f o r
o n e t u r b i n e w h e n 4 u n i t s a r e i n o p e r a t i o n i s t h e r e l o a d / r e j e c t s e q u e n c e r u n
u p t o 0 . 2 5 , f o r o n e t u r b i n e w h e n 3 u n i t s a r e i n o p e r a t i o n 0 . 3 3 a n d s o o n . T h e
f a s t e s t o p e r a t i o n t i m e f o r r e l o a d / r e j e c t s e q u e n c e o f o n e u n i t i s a t m i n i m u m
3 minutes. T h e t a i l w a t e r l e v e l i s c a l c u l a t e d a c c o r d i n g t o
H u = 0.03Q0 +764
m a s l .
T h e o b j e c t i v e f o r t h e s i m u l a t i o n s o f t h e S u r g e C h a m b e r i s t o e n s u r e t h a t
t h e w a t e r d o e s n o t e x c e e d t h e m a x i m u m p e r m i s s i b l e w a t e r l e v e l o f 7 7 5 m a s l .
O n l y t h e u p s u r g e i s c r i t i c a l t o t h e s t a t i o n . B e c a u s e a d o w n s u r g e w i l l o n l y
l e a d t o a t r a n s i t i o n b e t w e e n s u b m e r g e d a n d f r e e w a t e r s u r f a c e c o n d i t i o n s
i n t h e t a i l r a c e t u n n e l . T h e w o r s t c a s e s c e n a r i o i s w h e n t h e l e v e l i n t h e
t a i l r a c e i s a t o o d l e v e l o f 7 6 9 . 2 m a s l . R e l o a d / r e j e c t s e q u e n c e s s h o u l d a l s o
b e e v a l u a t e d .
5 . 3 . 3 V e r i c a t i o n o f S u r g e O s c i l l a t i o n M o d e l
T h e s u r g e p r o g r a m i s v e r i e d b y c a l c u l a t i n g t h e o w e l d w i t h o u t l o s s e s
a n d u s i n g a n i n n i t e c o n s t a n t c r o s s - s e c t i o n a l a r e a o f 2 8 , 5 5 0 m2
i n t h e S u r g e
H e a d b a y a n d 4 3 6 , 8 8 0 m2
i n t h e S u r g e C h a m b e r . T h e r e s u l t f o r l o a d r e j e c t i o n
i n t h e S u r g e H e a d b a y i s s h o w n i n g u r e 5 . 4 a n d g u r e 5 . 5 . T h e r e s u l t s o f
r e l o a d f o r b o t h c h a m b e r s c a n b e f o u n d i n a p p e n d i x C . 1 . T h e c a l c u l a t i o n s
s h o w t h a t t h e o s c i l l a t i o n l e v e l s e x c e e d s a l l l i m i t s b e c a u s e t h e s y s t e m i s n o t
d a m p e d b y h e a d l o s s e s . T h i s i s a l s o t h e c a s e w h e n l o o k i n g a t t h e c u r v e s
f o r r e l o a d i n t h e S u r g e H e a d b a y i n g u r e C . 1 a n d i n t h e S u r g e C h a m b e r i n
g u r e C . 2 . T h e g u r e s a r e n u m e r i c a l s t a b l e w h e n u s i n g dt = 0.1
, a n d t h e
m a x i m u m a n d m i n i m u m v a l u e s d i e r s i n s i g n i c a n t l y . T h e o s c i l l a t i o n i n t h e
S u r g e H e a d b a y i s s l o w e r t h a n i n t h e S u r g e C h a m b e r .
5 . 4 I n c r e a s e p o w e r o u t p u t
A c a l c u l a t i o n m o d e l f o r i n v e s t i g a t i n g a p o t e n t i a l i n c r e a s e i n p o w e r o u t p u t o f
t h e e x i s t i n g t u r b i n e s i s p r e s e n t e d h e r e . T h e p a r a m e t e r s n , D1 , D2 N PSH A
3 0
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5 C a l c u l a t i o n M e t h o d s
F i g u r e 5 . 4 : V e r i c a t i o n S u r g e H e a d b a y l o a d r e j e c t i o n
F i g u r e 5 . 5 : V e r i c a t i o n S u r g e C h a m b e r l o a d r e j e c t i o n
a n d H n a r e k n o w n . T h e c a l c u l a t i o n m o d e l s t a r t s b y u s i n g t h e c a v i t a t i o n
l i m i t a s a d e s i g n c r i t e r i a , a n d a s a f e t y f a c t o r o f 1 5 % i s s u b t r a c t e d y i e l d i n g
t h e r e l a t i o n s h i p ( 5 . 2 2 ) .
N PSH T ≤ N PSH A(1 − 0.15)( 5 . 2 2 )
E q u a t i o n ( 2 . 1 4 ) f o r c a l c u l a t i n g N PSH T i s r e a r r a n g e d i n o r d e r t o n d
β 2d i r e c t l y i n e q u a t i o n ( 5 . 2 5 ) . T h i s c o r r e l a t i o n i s f o u n d b y u s i n g t h e r e d u c e d
v a l u e o f u2 ( 5 . 2 3 ) a n d t h e r e l a t i o n s h i p i n ( 5 . 2 4 ) .
u2 =u2√
2gH n( 5 . 2 3 )
A t n o m i n a l l o a d d o e s t h e a b s o l u t e m e r i d i a n v e l o c i t y i n c r e a s e , w h i l e t h e
o u t l e t a n g l e β 2 r e m a i n s t h e s a m e . E q u a t i o n ( 5 . 2 4 ) y i e l d s t h e c o r r e l a t i o n
b e t w e e n o w a t f u l l l o a d a n d b e s t e c i e n c y p o i n t . T h e v a l u e o f t h e a d m i s s i o n
c o e c i e n t κ
i s a s s u m e d t o b e 1 . 1 5 f o r a m e d i u m h e a d F r a n c i s t u r b i n e .
κ =
cm2
∗cm2 =
Qn
∗Q( 5 . 2 4 )
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5 I n c r e a s e p o w e r o u t p u t
A s e l e c t i o n o f f a v o u r a b l e o u t l e t a n g l e s a r e f o u n d f o r a r a n g e o f N PSH T
s t a r t i n g f r o m ( 5 . 2 2 ) a n d d e c r e a s e w i t h a n i n c r e m e n t o f 0.1m
. A n i t e r a t i v e
p r o c e d u r e i s u s e d t o n d β 2 f r o m e q u a t i o n ( 5 . 2 5 ) w h e r e t h e v a l u e o f
bd e p e n d s
o n t h e s p e e d n u m b e r g i v e n b y e q u a t i o n ( 5 . 2 6 ) . O u t l e t a n g l e s t h a t a r e l a r g e r
t h a n
20
, o r s m a l l e r t h a n
13
a r e d i s c a r d e d .
β 2 = tan−1
1
aκ2
N PSH T
H nu22− b
( 5 . 2 5 )
∗Ω = u3/22
πtan(β 2)
( 5 . 2 6 )
I n o r d e r t o v e r i f y t h a t t h e g u r e s a r e c a l c u l a t e d a t B E P t h e v a l u e s o f
∗cm2 a n d
∗cu2 a r e c a l c u l a t e d a c c o r d i n g t o e q u a t i o n s ( 5 . 2 7 ) a n d ( 5 . 2 8 ) . W h e r e
∗cu2 = 0a t B E P .
∗cm2 = u2tan(β 2)( 5 . 2 7 )
∗cu2 = u2 −∗cm2
tan(β 2)= 0
( 5 . 2 8 )
T h e v o l u m e o w
∗Qi s c a l c u l a t e d u s i n g e q u a t i o n ( 5 . 2 9 ) . A n i n c r e a s e i n
t h e v o l u m e o w c o m p a r e d t o t h e e x i s t i n g i s e x p e c t e d .
∗Q =
∗Ω(2gH n)3/4
ω
2
( 5 . 2 9 )
N PSH T i s r e c a l c u l a t e d a c c o r d i n g t o ( 2 . 1 4 ) t o e n s u r e t h a t t h e c a v i t a t i o n
c r i t e r i a i s f u l l l e d a t n o m i n a l l o a d . T h e r e a f t e r , t h e p o w e r o u t p u t i s c a l c u l a t e d
a c c o r d i n g t o t h e p o w e r e q u a t i o n ( 5 . 3 2 ) f o r h y d r a u l i c e c i e n c y i n t h e r a n g e
f r o m 0 . 9 2 t o 0 . 9 6 . H new i s t h e r e d u c t i o n i n n e t h e a d
H e , w h i c h i s a c c o u n t e d
f o r b y r s t c a l c u l a t i n g t h e h e a d l o s s e s i n t h e w a t e r w a y a c c o r d i n g t o
e q u a t i o n 5 . 3 0 a n d t h e n e w h e a d i s c a l c u l a t e d a c c o r d i n g t o e q u a t i o n 5 . 3 1 .
A m a t l a b p r o g r a m i s d e v e l o p e d i n o r d e r t o p r e s e n t t h e c o r r e l a t i o n b e t w e e n
t h e r e d u c t i o n i n n e t h e a d a n d t h e p o w e r o u t p u t . T h e p r o g r a m i s p r e s e n t e d
i n a p p e n d i x B . 3 .
hf = c1Q2station + c2Q2
unit + ctQ2unit;
( 5 . 3 0 )
H new = H 0 − hf
Q2new
Q2unit
( 5 . 3 1 )
hf - T o t a l h e a d l o s s f r o m i n t a k e t o e x i t o f d r a f t t u b e [ m
]
Qstation - T o t a l v o l u m e o w i n t h e s t a t i o n [ m3/s
]
Qunit - V o l u m e o w o n e u n i t [ m3/s
]
Qnew - N e w v o l u m e o w f o r o n e u n i t [ m3/s
]
P n = ηρgQunitH new ( 5 . 3 2 )
A n i n v e s t i g a t i o n o f d r a w i n g " M B 9 - 0 4 3 . 1 1 0 9 A ; R u n n e r " h a s l e a d t o t h e
c o n c l u s i o n t h a t i t i s p o s s i b l e t o i n c r e a s e t h e o u t l e t d i a m e t e r b y m a x i m u m 6 0
m m . T h i s c o m p r i s e s a c h a n g e o f l o w e r c o v e r a n d d r a f t t u b e c o n e .
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C h a p t e r 6
R e s u l t s
T h e o b j e c t i v e o f t h e s i m u l a t i o n o f t h e d y n a m i c r e s p o n s e i n t h e w a t e r w a y i s
t o n d o u t i f t h e s y s t e m c a n h a n d l e a n i n c r e a s e i n v o l u m e o w . T h e r e s u l t
i s t h e n u s e d i n t h e i n v e s t i g a t i o n o f p o t e n t i a l i n c r e a s e i n p o w e r o u t p u t .
6 . 1 A n a l y s i s : E x i s t i n g H y d r a u l i c C o n d i t i o n s
T h e f u l l a n a l y s i s o f t h e e x i s t i n g h y d r a u l i c c o n d i t i o n s i s d e s c r i b e d i n a p p e n d i x
C . 2 , a n d a s u m m a r y i s p r e s e n t e d i n t h e f o l l o w i n g . O n l y w o r s t c a s e s c e n a r i o s
a r e c o n s i d e r e d .
6 . 1 . 1 O s c i l l a t i o n i n S u r g e H e a d b a y
T a b l e 6 . 1 p r e s e n t s t h e m a x i m u m u p - a n d d o w n s u r g e i n t h e S u r g e H e a d b a y
w i t h 4 u n i t s i n o p e r a t i o n . A l l s u r g e l e v e l s w a s w i t h i n t h e l i m i t s . T h e
m a x i m u m u p s u r g e Z max w a s 9 0 9 . 3 m a s l a t h i g h e s t o o d l e v e l ( H F L ) i n
t h e i n t a k e i l l u s t r a t e d i n g u r e C . 3 . I n t a b l e 6 . 2 t h e m i n i m u m l e v e l s i n t h e
i n t a k e f o r o p e r a t i o n o f 1 t o 4 u n i t s p r e s e n t e d .
F o r t h e m i n i m u m d r a w - d o w n w a t e r l e v e l ( M R W L ) o f 8 9 5 . 2 m a s l i n
t h e i n t a k e w a s i t f o u n d t h a t o n l y o n e u n i t c a n b e o p e r a t e d . I n a l l t h e s e
s i m u l a t i o n s t h e u p s u r g e i n t h e S u r g e C h a m b e r d i d n o t e x c e e d t h e l i m i t o f
7 7 5 m a s l , n o r d i d t h e d o w n s u r g e g o b e l o w 7 6 4 . 7 m a s l .
S c e n a r i o Z max , [ m a s l ]
Z min , [ m a s l ] F i g u r e
H F L 9 0 9 . 3 8 9 8 . 8 C . 3
T a b l e 6 . 1 : R e s u l t s : a n a l y s i s o f e x i s t i n g c o n d i t i o n s i n S u r g e H e a d b a y 4 u n i t s
N o o f u n i t s H 0 , [ m a s l ] F i g u r e
1 8 9 5 . 2 C . 4
2 8 9 6 . 4 C . 5
3 8 9 7 C . 6
4 8 9 7 . 4 C . 7
T a b l e 6 . 2 : R e s u l t s : A n a l y i s o f e x i s t i n g c o n d i t i o n s a t M R W L l e v e l s
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6 A n a l y s i s : E x i s t i n g H y d r a u l i c C o n d i t i o n s
6 . 1 . 2 O s c i l l a t i o n i n S u r g e C h a m b e r
F o r 1 t o 4 u n i t s i n o p e r a t i o n t h e m a x i m u m l e v e l s i n t h e t a i l r a c e a r e p r e s e n t e d
i n t a b l e 6 . 3 . T h e s i m u l a t i o n s c l e a r l y s h o w e d t h a t r e l o a d / r e j e c t s e q u e n c e s
m u s t b e c a r r i e d o u t c a r e f u l l y i n o r d e r t o a v o i d e x c e s s i v e s u r g e s . A l l o t h e r
t a i l r a c e l e v e l s i n t a b l e 4 . 6 l e a d t o s u r g e s t h a t a r e w e l l w i t h i n t h e l i m i t s o f
t h e c h a m b e r . I n t h e g r a p h s a r e t h e u p s u r g e s s u d d e n b e c a u s e t h e o s c i l l a t i o n
a l t e r s b e t w e e n a f r e e - w a t e r s u r f a c e w i t h a l a r g e a r e a i n t h e t u n n e l . W h e n
t h e w a t e r l e v e l r i s e a b o v e t h e t a i l r a c e t u n n e l r o o f d e n o t e d b y t h e t u r q u o i s e
d o t t e t l i n e , a s u d d e n a r e a c o n t r a c t i o n o c c u r s . T h e g r a p h s p r e s e n t s w o r s t
c a s e s c e n a r i o s w i t h a h i g h w a t e r l e v e l i n t h e t a i l r a c e , w h i c h i s n o t n o r m a l l y
t h e c a s e .
N o o f u n i t s H u , [ m a s l ] F i g u r e
4 7 6 8 C . 8
3 7 6 8 . 3 C . 9
2 7 6 8 . 7 C . 1 0
1 7 6 9 . 2 C . 1 1
T a b l e 6 . 3 : R e s u l t s : A n a l y s i s o f e x i s t i n g c o n d i t i o n s i n S u r g e C h a m b e r
6 . 1 . 3 P r e s s u r e i n f r o n t o f t u r b i n e
T h e p r e s s u r e i n f r o n t o f t h e t u r b i n e i s d e t e r m i n e d b y t h e h i g h e s t w a t e r l e v e l
i n t h e S u r g e H e a d b a y a n d w i t h t h e v o l u m e o w o f o n e t u r b i n e 7 1 m3/s
. T h e
r e s u l t i s s h o w n i n g u r e 6 . 1 , a n d t h e m a x i m u m w a t e r p r e s s u r e i n f r o n t o f
o n e t u r b i n e i s 1 7 2 . 4 m W C . T h e p r e s s u r e r i s e i s g o v e r n e d b y t h e e l e v a t i o n i n
t h e S u r g e H e a d b a y u n t i l t h e v a l v e c l o s e s . T h e r e a f t e r d o e s t h e o s c i l l a t i o n o f
t h e w a t e r h a m m e r g o v e r n t h e p r e s s u r e w i t h a p e r i o d o f 0 . 6 6
s.
F i g u r e 6 . 1 : P r e s s u r e i n f r o n t o f t u r b i n e , Z max = 909.3
m a s l a n d Qunit =
71m3/s
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6 R e s u l t s
6 . 2 A n a l y s i s : I n c r e a s i n g V o l u m e F l o w
T h e a n a l y s i s a i m s t o n d t h e m a x i m u m i n c r e a s e i n v o l u m e o w , w h i c h d o e s
n o t c o m p r o m i s e t h e s a f e t y o f t h e p l a n t . O n l y t h e w o r s t c a s e s c e n a r i o s a r e
e v a l u a t e d .
6 . 2 . 1 O s c i l l a t i o n i n S u r g e H e a d b a y
I t i s f o u n d t h a t a n i n c r e a s e i n n o m i n a l v o l u m e o w o f t h e s t a t i o n t o 340m3/s
i s p o s s i b l e . T h e u p s u r g e i n t h e S u r g e H e a d b a y r e a c h e s a l e v e l o f 9 0 9 . 7 m a s l ,
a n d a r e l o a d / r e j e c t s e q u e n c e d o e s n o t l e a d t o a h i g h e r l e v e l a s c a n b e s e e n
i n g u r e 6 . 2 .
F i g u r e 6 . 2 : S u r g e o s c i l l a t i o n S H , H 0 = 904.5
m a s l Qn,station = 340m3/s
T h e m i n i m u m d r a w - d o w n l e v e l m u s t b e i n c r e a s e d f o r t h e n e w v o l u m e
o w . F o r o p e r a t i o n o f 1 4 u n i t s a r e t h e y p r e s e n t e d i n t a b l e 6 . 4 . T h e r e s u l t
o f 4 u n i t s i n o p e r a t i o n i s i l l u s t r a t e d i n g u r e 6 . 3 , a l l o t h e r g u r e s c a n b e
f o u n d i n a p p e n d i x C . 3 .
N o . o f u n i t s M R W L [ m a s l ] I n c r e a s e , [ m ] F i g u r e
1 8 9 6 0 . 8 C . 1 4
2 8 9 7 0 . 6 C . 1 3
3 8 9 7 . 5 0 . 5 C . 1 2
4 8 9 7 . 8 0 . 4 6 . 3
T a b l e 6 . 4 : M R W L l e v e l s f o r i n c r e a s e d v o l u m e o w
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6 A n a l y s i s : I n c r e a s i n g V o l u m e F l o w
F i g u r e 6 . 3 : S u r g e o s c i l l a t i o n i n S C , H 0 = 897.8
m a s l a n d Qn,station =
340m3/s
6 . 2 . 2 O s c i l l a t i o n i n S u r g e C h a m b e r
N o o f u n i t s H u [ m a s l ] D e c r e a s e [ m ] F i g u r e
4 7 6 7 . 6 0 . 4 6 . 4
3 7 6 7 . 9 0 . 4 C . 1 5
2 7 6 8 . 2 0 . 5 C . 1 6
1 7 6 9 . 2 0 C . 1 7
T a b l e 6 . 5 : M a x i m u m l e v e l s i n t a i l r a c e w i t h i n c r e a s e d v o l u m e o w
T h e i n c r e a s e d v o l u m e o f 85m3/s
f o r o n e u n i t a l s o i n u e n c e s t h e m a x i m u m
l e v e l i n t h e t a i l r a c e . T h e i d e n t i e d l e v e l s a r e p r e s e n t e d i n t a b l e 6 . 5 . F i g u r e
6 . 4 i l l u s t r a t e s t h e r e s u l t f o r 4 u n i t s i n o p e r a t i o n , a l l o t h e r g u r e s c a n b e
f o u n d i n a p p e n d i x C . 3 . T h e o s c i l l a t i o n h a s c h a r a c t e r i s t i c p e a k s d u e t o a
s u d d e n a r e a c o n t r a c t i o n w h e n t h e w a t e r r i s e s a b o v e t h e t u n n e l r o o f .
6 . 2 . 3 P r e s s u r e i n f r o n t o f t u r b i n e
T h e r e s u l t o f p r e s s u r e c a l c u l a t i o n s w i t h a n i n c r e a s e d o w r a t e o f 8 5
m3
/sf o r
o n e u n i t w i t h H 0 = 909.7
m a s l i s s h o w n i n g u r e 6 . 5 . T h e c l o s i n g t i m e i s 7
s e c o n d s a n d t h e m a x i m u m p r e s s u r e i s 1 7 7 m W C .
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6 R e s u l t s
F i g u r e 6 . 4 : S u r g e o s c i l l a t i o n i n S C , Qn,station = 340m3/s
, H u = 767.6
m a s l
F i g u r e 6 . 5 : P r e s s u r e i n f r o n t o f t u r b i n e , Z max = 909.7
m a s l Qunit = 85m3/s
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6 A n a l y s i s : I n c r e a s i n g P o w e r O u t p u t
6 . 3 A n a l y s i s : I n c r e a s i n g P o w e r O u t p u t
I t i s c o n c l u d e d f r o m t h e a n a l y s i s o f i n c r e a s i n g p o w e r o u t p u t t h a t a n i n c r e a s e
o f n o m i n a l v o l u m e o w f o r o n e u n i t i s p o s s i b l e u p t o Qn,unit = 85m3/s
. T h e
c a l c u l a t i o n m e t h o d d e v e l o p e d i n t h i s t h e s i s i s p r e s e n t e d i n s e c t i o n 5 . 4 . T a b l e
6 . 6 p r e s e n t s t h e m a x i m u m p e r c e n t i l e i n c r e a s e i n n o m i n a l p o w e r o u t p u t f o r
o n e t u r b i n e , w h i c h i s c o m p a r e d t o t h e e x i s t i n g P n = 82
M W . D i a 0 0 r e f e r s t o
t h e e x i s t i n g o u t l e t d i a m e t e r , D i a 0 6 t o a n i n c r e a s e d d i a m e t e r o f 6 0 m m w h e n
t h e m e t h o d p r e s e n t e d i n s e c t i o n 5 . 4 i s u s e d . T h e S i n t e f m e t h o d p r e s e n t e d i n
s e c t i o n 3 . 1 . 3 i s a l t e r e d b y s t a r t i n g w i t h a s s u m i n g a p o w e r o u t p u t t h a t y i e l d s
a v o l u m e o w o f 8 5 m3/s
, w h i c h i s w i t h i n t h e c a v i a t i o n l i m i t . I n t h e t a b l e
S i n t e f 0 0 r e f e r s t o t h e e x i s t i n g d i a m e t e r a n d S i n t e f 0 3 t o t h e i n c r e a s e d . T h e
c a v i a t i o n l i m i t i n t h e s e c a s e s i s n o t e x c e e d e d . A l l c a l c u l a t e d v a l u e s c a n b e
f o u n d i n a p p e n d i x D . I t i s c a l c u l a t e d f o r a r a n g e o f t u r b i n e e c i e n c i e s f r o m
0 . 9 3 t o 0 . 9 5 a t n o m i n a l l o a d . N o n e o f t h e v o l u m e o w s e x c e e d s t h e l i m i t o f
8 5
m3
/s, a n d t h e o u t l e t a n g l e s a r e w i t h i n n o r m a l r a n g e . T h e d i e r e n c e s i n
p r e s e n t e d n e t h e a d a r e d u e t o d i e r e n t c a l c u l a t e d v o l u m e o w s .
E c i e n c y
D i a 0 0 D i a 0 6 S i n t e f 0 0 S i n t e f 0 6
H e [ m ] % H e [ m ] %
H e [ m ] % H e [ m ] %
0 . 9 3 1 2 3 . 3 1 4 1 2 2 1 5 1 2 1 . 9 1 3 1 2 1 . 9 1 6
0 . 9 4 1 2 3 . 3 1 5 1 2 2 1 6 1 2 1 . 9 1 4 1 2 1 . 9 1 7
0 . 9 5 1 2 3 . 3 1 6 1 2 2 1 7 1 2 1 . 9 1 5 1 2 1 . 9 1 8
T a b l e 6 . 6 : M a x i m u m p e r c e n t i l e i n c r e a s e i n n o m i n a l p o w e r o u t p u t f o r o n e
u n i t
T h e r e d u c t i o n i n h e a d d u e t o i n c r e a s e d v o l u m e o w i s a c c o u n t e d f o r a n d
i l l u s t r a t e d b y t h e b l u e l i n e i n g u r e 6 . 6 . T h e g u r e p r e s e n t s t h e r e s u l t o f
o n e t u r b i n e w h e n f o u r u n i t s a r e i n o p e r a t i o n . T h e p i n k , g r e e n a n d r e d l i n e
r e p r e s e n t i n c r e a s e i n p o w e r o u t p u t a s a f u n c t i o n o f v o l u m e o w a n d n e t
h e a d f o r t h e u s e d t u r b i n e e c e n c i e s . T h e d o t t e d b l a c k l i n e r e p r e s e n t s t h e
m a x i m u m a l l o w a b l e v o l u m e o w 8 5 m3/s
. T h e c i r c l e s a r e t h e c a l c u l a t e d
v a l u e s f o r D i a 0 0 . F o r a t u r b i n e e c i e n c y o f 0 . 9 3 d o e s t h e p o w e r o u t p u t
a l m o s t c o i n c i d e w i t h t h e r e d u c e d h e a d l i n e .
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F i g u r e 6 . 6 : P e r c e n t i l e i n c r e a s e i n p o w e r o u t p u t a s a f u n c t i o n o f v o l u m e o w a n d r e d u c t i o n i n n e t h e a d . F o r
3
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6 A n a l y s i s : I n c r e a s i n g P o w e r O u t p u t
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C h a p t e r 7
D i s c u s s i o n
I n o r d e r t o p r e p a r e a n a l c o n c l u s i o n i s t h e p u r p o s e o f t h i s c h a p t e r t o e v a l u a t e
t h e r e s u l t s p r e s e n t e d i n 6 .
7 . 1 H y d r a u l i c c o n s i d e r a t i o n s
T h e r e s u l t s s h o w t h a t t h e d e s i g n o f t h e S u r g e H e a d b a y e e c t i v e l y d a m p s
d o w n t h e o s c i l l i a t i o n . I n t h e i n v e s t i g a t i o n o f t h e e x i s t i n g h y d r a u l i c c o n d i t i o n s
d i d r s t u p s u r g e y i e l d s t h e m a x i m u m l e v e l o f 9 0 9 . 3 m a s l . A d d i t i o n a l
r e l o a d / r e j e c t s e q u e n s e d i d n o t r i s e a b o v e t h i s l e v e l , a n d t h e r e f o r e d o e s t h e
s e q u e n c e o n l y c o n s i s t o f o n e t u r b i n e o n e t i m e . T h e s u r g e r i s e s a b o v e t h e
p l a t f o r m l e v e l , b u t t h i s i s n o t c o n s i d e r e d t o b e a p r o b l e m a s l o n g a s t h e r e
a r e n o t s t o r e d a n y e q u i p m e n t t h a t m a y b e d e s t r o y e d t h e r e . T h e a r e a c r o s s -
s e c t i o n a l a r e a i n t h e S u r g e C h a m b e r i s m e a s u r e d , a n d i t i s p r o b a b l y l a r g e r .
T h e s u d d e n u p s u r g e s m a y t h e r e f o r e b e a s s e v e r e a s t h e y s e e m . T h e s u d d e n
u p s u r g e i s d u e t o a t r a n s i t i o n b e t w e e n f r e e w a t e r s u r f a c e c o n d i t i o n s i n t h e
t u n n e l t o t h e s m a l l e r c r o s s - s e c t i o n a l a r e a . I n t h e M a t l a b p r o g r a m a n E u l e r
c o d e w h i c h i s u s e d w h i c h i s n o t t h e m o s t a c c u r a t e n u m e r i c a l m e t h o d . T h i s
p r o g r a m i s b a s e d o n a s i m p l i e d w a t e r w a y s y s t e m , a n d a l l v a r i a b l e s a r e n o t
a c c o u n t e d f o r . D u e t o a l l r e a s o n s m e n t i o n e d a b o v e i t i s h i g h l y p r o b a b l e t h a t
t h e o s c i l l a t i o n s i n t h e c h a m b e r s a r e o v e r e s t i m a t e d . I t i s a s s u m e d t h a t t h i s
a l s o a p p l i e s t o t h e w a t e r h a m m e r c a l c u l a t i o n s .
I t i s c l e a r f r o m t h e a n a l y i s o f e x i s t i n g h y d r a u l i c c o n d i t i o n s t h a t t h e
h i g h e s t r e g u l a t e d w a t e r l e v e l i m p o s e s t h e l a r g e s t c o n s t r a i n t o n i n c r e a s i n g
v o l u m e o w . A l l o t h e r c r i t i c a l l e v e l s i m p o s e a c o n s t r a i n t o n t h e r e g u l a t i o n
o f t h e p l a n t . T h e m i n i m u m d r a w - d o w n l e v e l d e p e n d s o n t h e n u m b e r o f
t u r b i n e s i n o p e r a t i o n , a n d a l a r g e r v o l u m e o w i n c r e a s e s t h e l e v e l s . O n t h e
c o n t r a r y t o t h e m a x i u m t a i l r a c e l e v e l s , w h i c h d e c r e a s e s . T h e u s e d h e a d l o s s
c o e c i e n t s a r e o b t a i n e d f r o m s i t e t e s t s a t R u a c a n a . F o r t h e s u r g e c a l c u l a t i o n
c o u l d i t h a v e b e e n o f i n t e r e s t t o i n c l u d e t h e g o v e r n o r e q u a t i o n s . T h e p r e s s u r e
i n f r o n t o f t h e t u r b i n e s i s n o t o f c o n c e r n f o r i n c r e a s e d v o l u m e o w . I f i t h a d
b e e n a p r o b l e m c o u l d t h e c l o s i n g t i m e o f t h e t u r b i n e b e i n c r e a s e d , a n d t h e
p r e s s u r e i s r e d u c e d .
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7 P o w e r o u t p u t
7 . 2 P o w e r o u t p u t
T h e s u b m e r g e n c e o f t h e s y s t e m i s n o t a r e s t r i c t i v e f a c t o r a n d t h e r e f o r e i t
y i e l d s a c l e a r i m p r o v e m e n t p o t e n t i a l . T h e a v a i l a b l e i n f o r m a t i o n a b o u t t h e
d e s i g n o f t h e e x i s t i n g r u n n e r s i s n o t s u c i e n t t o e s t a b l i s h a c o m p l e t e p i c t u r e .
I t i s u n f o r t u n a t e l y i m p o s s i b l e t o e s t a b l i s h c h a r a c t e r i s t i c s a s o w a n g l e s e c t .
A n e w r u n n e r i s l i k e l y t o a v o i d t h e c a v i t a t i o n p r o b l e m b y i n c r e a s i n g t h e
i n l e t a n g l e s a n d a l t e r t h e b l a d e l e a n a n g l e . L a r g e c h a n g e s i n i n l e t a n d o u t l e t
a n g l e s c a n b e c o m p e n s a t e d f o r b y r e p l a c i n g t h e g u i d e v a n e s .
I t i s c a l c u l a t e d f o r a r a n g e o f t u r b i n e e c i e n c i e s f r o m 0 . 9 3 t o 0 . 9 5 a t
n o m i n a l l o a d , b e c a u s e w i t h o u t f u r t h e r a n a y l s i s o f a p o t e n t i a l n e w r u n n e r
d e s i g n i t i s i m p o s s i b l e t o d e t e r m i n e a n a c c u r a t e v a l u e . T h e e c i e n c y o f a
n e w r u n n e r i m p l e m e n t e d i n t o a n e x i s t i n g t u r b i n e s t r u c t u r e i s l o w e r t h a n f o r
a n e w t u r b i n e . I t h a s b e e n c o n s i d e r e d f e a s i b l e t o u s e a t u r b i n e e c i e n c y o f
0 . 9 3 . I n f o r m a t i o n a b o u t t h e e c i e n c y o f o t h e r c o m p o n e n t s o f t h e t u r b i n e
a r e n o t k n o w n , a n d a r e t h e r e f o r e n o t i n c l u d e d .
T h e c a l c u l a t i o n m e t h o d d e v e l o p e d i n t h i s t h e s i s n d s t h e p o t e n t i a l
i n c r e a s e i n v o l u m e o w f r o m t h e s u b m e r g e n c e o f t h e s y s t e m , a n d t h e r e a f t e r
e s t i m a t e s t h e n o m i n a l p o w e r o u t p u t . T h i s i s t h e m a i n d i e r e n c e f r o m t h e
S i n t e f m e t h o d , w e r e i n c r e a s e i n n o m i n a l p o w e r o u t p u t i s a s s u m e d a t t h e
b e g i n n i n g . T h e o v e r a l l r e s u l t i n t h e S i n t e f m e t h o d c l a i m s a n i n c r e a s e i n
p o w e r o u t p u t o f 2 0 % w h e n t h e r e d u c t i o n i n h e a d i s n o t a c c o u n t e d f o r .
T h e e s t i m a t e d v a l u e s o f p o t e n t i a l n o m i n a l p o w e r o u t p u t d i e r s f o r t h e
t w o m e t h o d s . I n t h e c a s e o f k e e p i n g t h e e x i s t i n g d i a m e t e r d o e s t h e m e t h o d
f r o m t h i s t h e s i s p r e d i c t a n i n c r e a s e o f 1 4 % w i t h a n t u r b i n e e c i e n c y o f 0 . 9 3 .
T h e S i n t e f m e t h o d e s t i m a t e s a n i n c r e a s e o f 1 6 % . T h e s e c a l c u l a t i o n s h a v e
n o t i n c l u d e d a l l v a r i a b l e s a n d a s s u m e s a n e w r u n n e r d e s i g n w i t h a n i n c r e a s e d
v o l u m e o w c a p a c i t y . A n e w n o m i n a l v o l u m e o w o f 8 5 m3/s
i s 2 5 %
l a r g e r t h a n t h e e x i s t i n g . T h e p e r c e n t i l e i n c r e a s e i s v e r y l a r g e a n d p r o b a b l y
u n o b t a i n a b l e . A n i n c r e a s e i n v o l u m e o w o f 1 6 % i s m o r e c o n s e r v a t i v e a n d
y i e l d s a n o m i n a l p o w e r o u t p u t i n c r e a s e o f 1 0 % , w i t h a t u r b i n e e c i e n c y o f
0 . 9 3 a n d t h e n e t h e a d i s 1 2 6 m
. T h e n e w u n i t u n d e r i n s t a l l a t i o n i s d e s i g n e d
f o r a h e a d r a n g e d e t e r m i n e d b y t h e e x i s t i n g c o n d i t i o n s . A l a r g e i n c r e a s e
i n v o l u m e o w c o u l d a l s o a e c t t h e d e s i g n c o n d i t i o n s f o r t h i s t u r b i n e , a n d
p r o b a b l y l e a d t o a d i e r e n t h e a d r a n g e .
B o t h c a l c u l a t i o n s a r e i n a g r e e m e n t t h a t i t i s m o r e t o g a i n b y i n c r e a s i n g
t h e d i a m e t e r . I n t h i s c a s e m u s t t h e u p p e r p a r t o f t h e d r a f t t u b e c o n e a n d
l o w e r c o v e r b e r e p l a c e d i n a d d i t i o n t o t h e r u n n e r . T h e i n c r e a s e i n d i a m e t e r i s
n o t l a r g e a n d t h e r e f o r e i t i s n o t n e c e s s a r y t o r e p l a c e w i c k e t g a t e s a n d s p i r a l
c a s i n g . F o r t h e S i n t e f m e t h o d i s t h e p e r c e n t i l e i n c r e a s e i n p o w e r o u t p u t 1 8 %
a n d t h e m e t h o d d e v e l o p e d h e r e p r e d i c t s 1 5 % . T h e q u e s t i o n a b o u t e c o n o m i c
v i a b i l i t y a r i s e s i n c e t h e i n c r e a s e i s s m a l l . B o t h e s t i m a t e s a r e p r o b a b l y t o
h i g h .
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C h a p t e r 8
C o n c l u s i o n
T h i s t h e s i s a i m s t o e s t i m a t e a p o t e n t i a l i n c r e a s e i n n o m i n a l p o w e r o u t p u t
a t R u a c a n a b y o n l y r e p l a c i n g t h e r u n n e r . T h e e x i s t i n g t u r b i n e s h a v e b e e n
r e v i e w e d t o t h e e x t e n t i t i s p o s s i b l e , a n d i t i s c o n c l u d e d t h a t t h e r e e x i s t s a n
i m p r o v e m e n t p o t e n t i a l .
T h e p o w e r o u t p u t c a n b e i m p r o v e d e i t h e r b y i n c r e a s i n g t h e v o l u m e o w
a n d / o r e n h a n c i n g e c i e n c y . T h e e x i s t i n g h y d r a u l i c c o n d i t i o n s h a v e b e e n
e v a l u a t e d , a n d a n i n v e s t i g a t i o n c o n c l u d e d t h a t a m a x i m a l i n c r e a s e i n t h e
n o m i n a l v o l u m e o w t o Qn,unit = 85m3/s
i s p o s s i b l e . I t i s f o u n d t h a t t h i s
i s w i t h i n t h e r e s t r i c t i o n s o f s u r g e o s c i l l a t i o n a n d p r e s s u r e i n f r o n t o f t h e
t u r b i n e s . T h e m i n i m u m - d r a w d o w n l e v e l i n t h e S u r g e H e a d b a y m u s t b e
i n c r e a s e d a n d d e p e n d s o n t h e n u m b e r o f t u r b i n e s i n o p e r a t i o n . T h i s a l s o
y i e l d s f o r t h e h i g h e s t l e v e l i n t h e t a i l r a c e w h i c h h a s t o b e d e c r e a s e d . A n
i n c r e a s e i n e c i e n c y c a n b e e x p e c t e d w i t h a n e w r u n n e r .
I t i s c o n c l u d e d t h a t i t c a n b e p o s s i b l e t o i n c r e a s e t h e n o m i n a l p o w e r
o u t p u t f r o m 1 0 1 4 % . A s s u m i n g a t u r b i n e e c i e n c y o f 0 . 9 3 a n d a r e p l a c i n g
t h e r u n n e r w i t h h i g h e r v o l u m e o w c a p a c i t y .
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8
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C h a p t e r 9
F u r t h e r W o r k
T h e o b j e c t i v e o f t h i s t h e s i s w a s t o i n v e s t i g a t e t h e p o s s i b i l i t y o f i n c r e a s i n g
p o w e r o u p u t . A l l a s p e c t s o f a r e h a b i l i t a t i o n p r o j e c t h a v e n o t b e e n e v a l u a t e d .
S o m e e x a m p l e s o f a d d i t i o n a l i n q u i r e s a r e p r e s e n t e d h e r e .
F u r t h e r d e s i g n o f a F r a n c i s t u r b i n e t h a t c a n b e a p p r o p r i a t e f o r a l l e x i s t i n g
c o n s t r a i n t s i s n e c e s s a r y . I t s h o u l d b e f o l l o w e d b y a n o p t i m i z a t i o n p r o c e s s
u s i n g c o m p u t a t i o n a l u i d d y n a m i c s . O t h e r p a r t s o f t h e t u r b i n e c o u l d b e
i n v e s t i g a t e d i n m o r e d e p t . R e v i e w t h e g u i d e v a n e s a n d w i c k e t g a t e c o n d i t i o n s
f o r i n c r e a s e d v o l u m e o w . A n e w d e s i g n o f t h e r u n n e r m a y l e a d t o a l t e r e d
i n l e t a n g l e s t h a t a r e n o t i n c o r r e s p o n d a n c e t o t h e g u i d e v a n e s . F u r t h e r
i n s p e c t i o n o f t h e o w c o n d i t i o n s o f t h e e x i s t i n g g u i d e v a n e s i s n e c e s s a r y .
H e r e , o n l y t h e t e c h n i c a l a s p e c t s h a s b e e n e v a l u a t e d a s m e n t i o n e d
e a r l i e r . A n a n c i a l a n a l y s i s c a n b e p e r f o r m e d , b e c a u s e t h e r e a l i z a t i o n o f
a r e h a b i l i t a t i o n p r o c j e c t s i s h i g h l y d e p e n d e n t o n t h e e c o n o m i c v i a b i l i t y .
T h e c a l c u l a t i o n m e t h o d d e v e l o p e d i n t h e t h e s i s i s n o t v e r e d a n d s h o u l d
b e v e r i e d .
O t h e r h y d r o l a u l i c a s p e c t s c a n b e e v a l u a t e d , s u c h a s t h e r i v e r o w . I s
i t e n o u g h w a t e r t h r o u g h o u t t h e y e a r t h a t i t i s f a v o u r a b l e t o i n c r e a s e t h e
v o l u m e o w ? A r e v i e w o f t h e r e g u l a t i o n s c h e m e a t R u a c a n a c a n a l s o b e
p e r f o r m e d .
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B i b l i o g r a p h y
[ 1 ] 2 1 s t A f r i c a n H y d r o S y m p o s i u m . P r o c e e d i n g s . N a m i b i a , 2 0 0 9 .
[ 2 ] V ö e s t A l p i n e . M e c h a n i c a l d r a w i n g s . R e c i e v e d f r o m N a m P o w e r , 1 9 7 3 .
[ 3 ] G . V . A r o n o v i c h , N . A . K a r t v e l i s h v i l i , a n d Y a . K L y u b i m t s e v . W a t e r
H a m m e r a n d S u r g e T a n k s . K e t e r P r e s s , 1 9 7 0 .
[ 4 ] J . E . B o r g e s . A t h r e e - d i m e n s i o n a l i n v e r s e m e t h o d f o r t u r b o m a c h i n e r y :
P a r t 1 - t h e o r y . J o u r n a l o f T u r b o m a c h i n e r y , 1 1 2 , 1 9 9 0 .
[ 5 ] H . B r e k k e . H y d r a u l i c d e s i g n s t r a t e g y f o r F r a n c i s t u r b i n e s . H y d r o p o w e r
& D a m s , 1 9 9 6 .
[ 6 ] H . B r e k k e . S t a t e o f t h e a r t i n t u r b i n e d e s i g n . I A H R c o n g r e s s B e i j i n g ,
C o n f e r e n c e P r o c e e d i n g s , 2 0 0 1 .
[ 7 ] H . B r e k k e . P u m p e r o g T u r b i n e r . N T N U , V a n n k r a f t l a b o r a t o r i e t , 2 0 0 3 .
[ 8 ] N . C a r o n a n d F . A r z o l a . P e r f o r m a n c e m e a s u r m e n t s o n r e f u r b i s h e d
t u r b i n e s o f 7 7 0 , 0 0 0 k w a t G u r i h y d r o e l e c t r i c c o m p l e x .
5thI G H E M
I n e t e r n a t i o n a l C o n f e r e n c e , L u c e r e n - S w i t z e r l a n d , 2 0 0 4 .
[ 9 ] C E D R E N . I n t e r n a t i o n a l s e m i n a r o n e n v i r o n m e n t a l e e c t s o f h y d r o p e a k -
i n g . T r o n d h e i m , N o r w a y , M a r c h 2 0 0 9 .
[ 1 0 ] W a t e r P o w e r & D a m C o n s t r u c t i o n . Y e a r b o o k . W i l m i n g t o n M e d i a L t d ,
2 0 0 6 .
[ 1 1 ] W a t e r P o w e r & D a m C o n s t r u c t i o n . Y e a r b o o k . W i l m i n g t o n M e d i a L t d ,
2 0 0 9 .
[ 1 2 ] O . G . D a h l h a u g . P e r s o n a l c o n v e r s a t i o n .
[ 1 3 ] F . d e S i e r v o a n d F . d e L e v a . M o d e r n t r e n d s i n s e l e c t i n g a n d d e s i g n i n g
F r a n c i s t u r b i n e s . W a t e r P o w e r & D a m C o n s t r u c t i o n , p a g e s 2 8 3 5 ,
A u g u s t 1 9 7 6 .
[ 1 4 ] N . D é s y , A D e m e r s , a n d A . N i c h t a w i t z . E x p e r i e n c e w i t h l a r g e F r a n c i s
r e h a b i l i t a t i o n p r o j e c t s . H y d r o p o w e r & D a m s , H y d r o 2 0 0 9 c o n f e r e n c e
L y o n , 2 0 0 9 .
[ 1 5 ] A . E s p a g . P e r s o n a l c o n v e r s a t i o n .
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[ 1 6 ] R . E F e a t h e r s t o n e a n d N a l l u r i C . C i v i l E n g i n e e r s H y d r a u l i c s . B S P
P r o e s i o n a l B o o k s , 1 9 8 8 .
[ 1 7 ] E . G ö d e . P e r f o r m a n c e u p g r a d i n g o f h y d r a u l i c m a c h i n e r y w i t h t h e h e l p o f
C F D . N o t e s o n N u m e r i c a l F l u i d M e c h a n i c s a n d M u l t i d i s i p l i n a r y D e s i g n ,
1 0 0 : 2 9 9 3 1 0 , 2 0 0 9 .
[ 1 8 ] P a u l a H a r d y a n d M a t t h e w D . F i r e s t o n e . L o n e l y P l a n e t : B o t s w a n a &
N a m i b i a . 2 0 0 7 .
[ 1 9 ] A n d r i t z H y d r o . H y d r o n e w s . C u s t o m e r m a g a z i n e , - 2 0 0 9 .
[ 2 0 ] V o i t h H y d r o . H y p o w e r . C o m p a n y b r o c h u r e , 2 0 0 9 .
[ 2 1 ] H . J e r n s l e t t e n a n d H . B r e k k e . B e r e g n i n g a v e e k t ø k n i n s p o t e n s i a l i
n o r s k e k r a f t v e r k . S i n t e f E n e r g i f o r s k n i g , 1 9 9 6 .
[ 2 2 ] A f r i c a n B u s i n e s s J o u r n a l . N a m p o w e r . h t t p : / / w w w . t r a d e r s a f r i c a .
c o m / i n d e x . a s p , F e b r u a r y M a y 2 0 0 2 .
[ 2 3 ] A . K i m a n i a n d S k u n c k e O . U p g r a d i n g o f K i a m b e r e h y d r o e l e c t r i c p l a n t
i n k e n y a . H y d r o p o w e r & D a m s , H y d r o 2 0 0 9 c o n f e r e n c e L y o n , 2 0 0 9 .
[ 2 4 ] E . K l e i n h a n s e n . P e r s o n a l c o n v e r s a t i o n .
[ 2 5 ] G M u l l e r . E x p a n d i n g R u a c a n a p o w e r s t a t i o n . 2 1 s t A f r i c a H y d r o
S y m p o s i u m .
[ 2 6 ] N a m P o w e r . h t t p : / / w w w . n a m p o w e r . c o m . n a / i n d e x . a s p .
[ 2 7 ] N a m P o w e r . R u a c a n a . I n f o r m a t i o n p a m p h l e t , 1 9 7 8 .
[ 2 8 ] A . N i c h t a w i t z a n d C . A n g e r e r . B o x c a n y o n p . s a n d c a b i n e t g o r g e p . s .
t y p i c a l i s s u e s a t u p g r a d i n g o f t u r b i n e s . H y d r o p o w e r & D a m s , H y d r o
2 0 0 9 c o n f e r e n c e L y o n , 2 0 0 9 .
[ 2 9 ] T o r b j ø r n N i e l s e n . D y n a m i s k D i m e n s j o n e r i n g a v V a n n k r a f v e r k . H y d r o
P o w e r L a b o r a t o r y .
[ 3 0 ] H . W . O h a n d E . S . Y o o n . A p p l i c a t i o n o f c o m p u t a t i o n a l u i d d y n a m i c s
t o p r e f o r m a n c e a n a l y s i s o f a F r a n c i s h y d r a u l i c t u r b i n e . P r o c e e d i n g s o f
t h e I n s t i t u t i o n o f M e c h a n i c a l E n g i n e e r s , P a r t A : J o u r n a l o f P o w e r a n d
E n e r g y , 2 0 0 7 .
[ 3 1 ] E . V . R . R a m ó n , J . L . R i b a l t a , C . A . T e l l e r í a , a n d R . T . M a r t í n e z .
L a r g e F r a n c i s u p g r a d e i n S p a i n . s u c c e s s f u l h i s t o r y o f c o l l a b o r a t i o n .
H y d r o p o w e r & D a m s , H y d r o 2 0 0 9 c o n f e r e n c e L y o n , 2 0 0 9 .
[ 3 2 ] M . S a l l a b e r g e r , C h . M i c h a u d , H . B o r n , S t . W i n k l e r , a n d M . P e r o n .
D e s i g n a n d m a n u f a c t u r i n g o f F r a n c i s r u n n e r s f o r r e h a b i l i t a t i o n p r o j e c t s .
h t t p : / / w w w . a n d r i t z . c o m / h y d r o - m e d i a - m e d i a - c e n t e r - f r a n c i s _
r u n n e r s _ e . p d f .
[ 3 3 ] P . S w i d e r s k i a n d J . M a r t i n . H i g h p o w e r F r a n c i s r u n n e r u p g r a d e w i t h
a n e w d e s i g n r u n n e r . N o r c a n H y d r a u l i c T u r b i n e I n c . r e p o r t , 1 9 9 9 .
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[ 3 4 ] R . K . T u r t o n . P r i n c i p l e s o f T u r b o m a c h i n e r y . C h a p m a n & H a l l , 1 9 9 5 .
[ 3 5 ] E . J . W i b o r g . C o r r e s p o n d a n c e .
[ 3 6 ] J . W U , K . S h i m m e i , K . T a n i , K . N i i k u r a , a n d J . S a t o . C F D - b a s e d
d e s i g n o p t i m i z a t i o n f o r h y r d o t u r b i n e s . J o u r n a l o f F l u i d s E n g i n e e r i n g ,
1 2 9 , 2 0 0 7 .
[ 3 7 ] E . B . W y l i e a n d V . L . S t r e e t e r . F l u i d T r a n s i e n t s i n S y s t e m s . P r e n t i c e -
H a l l I n c , 1 9 9 3 .
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A p p e n d i x A
R u a c a n a H y d r o P o w e r P l a n t
N a m i b i a h o l d s t h e o l d e s t d e s e r t i n t h e w o r l d a n d i s t h e d r i e s t c o u n t r y s o u t h
o f S a h a r a . I t b o r d e r s A n g o l a a n d Z a m b i a i n t h e n o r t h , B o t s w a n a i n t h e e a s t
a n d S o u t h A f r i c a i n t h e s o u t h . T h e c o u n t r y i s m o s t l y r e n o w n e d f o r i t ' s s t a r k
a n d a r i d l a n d s c a p e c o n s t i t u t i n g t h e g r e a t d u n e s o f t h e N a m i b D e s e r t , a n d
t h e f a m o u s s c o r c h e d d u n e s o f t h e S k e l e t o n C o a s t . T h i s i s i n s t a r k c o n t r a s t
t o t h e w e l l - w a t e r e d p a r a d i s e o f t h e n o r t h e r n C a p r i v i a n d K a v a n g o r e g i o n s
[ 1 8 ] , w h i c h i s t h e l o c a t i o n o f t h e R u a c a n a f a l l s h o m e t o t h e R u a c a n a H y d r o
P o w e r P l a n t .
F i g u r e A . 1 : R u a c a n a F a l l s
W h e n t h e c o n s t r u c t i o n o f t h e p l a n t s t a r t e d , t h e c o u n t r y w a s k n o w n
a s S o u t h W e s t A f r i c a a n d t h e e l e c t r i c i t y c o m p a n y w a s n a m e d t h e S o u t h
W e s t A f r i c a n W a t e r a n d E l e c t r i c i t y C o r p o r a t i o n ( S W A W E K ) [ 2 6 ] . T h e
c o u n t r y c h a n g e d o c i a l l y i t s n a m e t o N a m i b i a i n 1 9 6 8 , b u t d i d n o t b e c o m e
i n d e p e n d e n t f r o m S o u t h A f r i c a u n t i l 1 9 9 0 . I n 1 9 9 6 t h e c o m p a n y c h a n g e d i t s
n a m e a n d b e c a m e N a m P o w e r [ 2 6 ] .
I
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T h e e n e r g y s i t u a t i o n i n N a m i b i a i s t o d a y s t r a i n e d , a n d t h e c o u n t r y
e x p e r i e n c e s m o r e a n d m o r e s h o r t a g e s o f p o w e r . T h e a v e r a g e n a t i o n a l l o a d
h a s i n c r e a s e d b e y o n d 3 2 0 M W , w h i c h i s h i g h e r t h a n t h e 2 4 0 M W g e n e r a t e d
a t R u c a n a . T h e c o u n t r y h a s j o i n e d t h e S o u t h e r n A f r i c a n P o w e r P o o l ( S A P P )
i n o r d e r t o i m p o r t e n e r g y , w h i c h c o n s t u t e s m a i n l y o f l a r g e c o a l r e d p o w e r
s t a t i o n s . I n o t h e r w o r d s , t h e a c c e s s i b i l i t y t o p e a k p o w e r i s n o t h i g h e n o u g h .
T h e r e a r e m a n y p r o j e c t s t h a t h a s b e e n i n v e s t i g a t e d a n d p l a n n e d , b u t
t h e b u i l d i n g h a s u s u a l l y b e e n s t o p p e d d u e t o p o l i t i c a l r e a s o n s . O n e e x a m p l e
i s t h e 3 6 0 M W E p u p a F a l l s w h i c h a l s o i s c o n n e c t e d t o t h e K u n e n e r i v e r .
P o l i t i c a l d i e r e n c e s w i t h A n g o l a h a s s t o p p e d t h e b u i l d i n g o f t h i s [ 2 6 ] . I n
M a y 2 0 0 6 , N a m P o w e r i n i t i a t e d a n e n e r g y a w a r e n e s s c a m p a i g n .
A . 1 H i s t o r y
T h e c o n s t r u c t i o n o f R u a c a n a e x p e r i e n c e d s o m e p o l i t i c a l d i c u l t i e s b e c a u s e
t h e r i v e r K u n e n e o w s t h r o u g h A n g o l a a n d N a m i b i a . T h e r e f o r e , a n y
d e v e l o p m e n t u t i l i s i n g t h e r e s o u r c e h a s t o b e a g r e e d u p o n b y b o t h c o u n t r i e s '
g o v e r n m e n t s . T h e o r i g i n a l R u a c a n a s c h e m e w a s n e g o t i a t e d w i t h t h e
P o r t u g u e s e A u t h o r i t i e s a n d r e a c h e d i t s c o n c l u s i o n i n 1 9 6 9 [ 2 2 ] , a n d c o n s i s t
o f t h e f o l l o w i n g c o m p o n e n t s i n t h e K u n e n e R i v e r :
A l a r g e s t o r a g e d a m o f 2600
m i l l i o n c u b i c m e t r e s i s s i t u a t e d a b o u t 240 km
u p s t r e a m f r o m R u a c a n a . I t i s d e s i g n e d f o r r e g u l a t i n g t h e o o d w a t e r b y
s t o r i n g t h i s w a t e r d u r i n g t h e r a i n y s e a s o n a n d a u g m e n t t h e o w i n t h e
d r i e r m o n t h s . T h i s r e s u l t s i n a m o r e o r l e s s s t e a d y g e n e r a t i o n o f e l e c t r i c i t y
a t R u a c a n a , a n d a c o n s i d e r a b l e s o u r c e o f f o o d f o r A n g o l a . T h e d a m w a s
c o m p l e t e d a n d c o m m i s s i o n e d i n 1 9 7 5 . A n o t h e r s t o r a g e d a m a t C a l u e q u e a t
a b o u t 65 km a w a y f r o m R u a c a n a i s a l s o u s e d a s a r e g u l a t i o n d a m . I t i n c l u d e s
a p u m p i n g s t a t i o n f o r s u p p l y i n g t h e O w a m b o l a n d w i t h w a t e r d u r i n g t h e d r y
s e a s o n s f o r h u m a n a n d a n i m a l c o n s u m p t i o n .
T o b e a b l e t o s u c i e n t l y d i v e r t t h e w a t e r a c r o s s t h e b o r d e r i n t o t h e
p o w e r s t a t i o n i n S o u t h W e s t A f r i c a i t w a s n e c e s s a r y t o b u i l d a d i v e r s i o n
w e i r 1.5 km
u p s t r e a m o f R u a c a n a . T h i s w a s c o m p l e t e d i n J a n u a r y 1 9 7 8 .
H o w e v e r , t h e A n g o l a n A u t h o r i t i e s w o u l d n o t a l l o w c l o s i n g o f t h e d i v e r s i o n
w e i r ' s s l u i c e g a t e s .
T h e h y d r o p o w e r s t a t i o n i s b u i l t o n N a m i b i a n t e r r i t o r y w i t h a S u r g e
H e a d b a y o n t h e s u r f a c e a n d t h e r e s t o f t h e s t a t i o n l i e s a b o u t 140 m
b e l o w .
I t c o n s i s t s o f f o u r w a t e r w a y s , b u t o n l y t h r e e v e r t i c a l s h a f t F r a n c i s u n i t s w a s
i n s t a l l e d o r i g i n a l l y a n d c o m p l e t e d J a n u a r y 1 9 7 8 . A f o u r t h u n i t i s c u r r e n t l y
u n d e r p r o d u c t i o n [ 2 7 ] . F u r t h e r d e s c r i p t i o n o f t h e w a t e r w a y s , r u n n e r e t c i s
f o u n d i n c h a p t e r 4 . T h e l a s t c o m p o n e n t w a s t h e b u i l d i n g o f a 570 km
l o n g
t r a n s m i s s i o n l i n e t o a d i s t r i b u t i o n s t a t i o n n e a r O m a r u r u .
A l l t h e a b o v e c o m p o n e n t s i n c l u d i n g h o u s i n g f o r p e r s o n n e l a t R u a c a n a
b r o u g h t t h e t o t a l c o s t u p t o 1 6 2 m i l l i o n s o f S o u t h A f r i c a n R a n d s ( Z A R )
w h i c h c o n v e r t s t o a b o u t 1 1 3 m i l l i o n s N o r w e g i a n K r o n e r s ( N O K ) a t t o d a y s
e x c h a n g e r a t e s [ 2 6 ] .
I I
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A p p e n d i x B
M a t l a b P r o g r a m s
I n t h i s a p p e n d i x p r e s e n t s o n l y s o m e p a g e s o f t h e d e v e l o p e d M a t l a b p r o g r a m s
f o r w a t e r h a m m e r a n d s u r g e o s c i l l a t i o n c a l c u l a t i o n s . T h e c o d e f o r g e n e r a t i n g
g r a p h s i s l e f t o u t . T h e e n t i r e p r o g r a m s c a n b e f o u n d i n t h e e l e c t r o n i c
a t t a c h m e n t . T h e p r o g r a m f o r g e n e r a t i n g t h e c r o s s - s e c t i o n a l a r e a i n t h e S u r g e
H e a d b a y c a n b e f o u n d e n t i r e l y i n t h e e l e c t r o n i c a t t a c h m e n t .
B . 1 W a t e r h a m m e r P r o g r a m
clear all
clc
tic
disp('calculating');
%−−−−−−−−−−−−−−−− PARAMETERS −−−−−−−−−−−−−−
Hv = 756.2; % Elevation of turbine, reference
g = 9.781 ; % Gravity [m/s^2]
% Penstock
tunnel.L = 180 ;
tunnel.D = 3.6 ;
tunnel.A = (pi/4)*tunnel.D^2;
tunnel.np = 4;tunnel.c = 0.000615;
%−−−−−−−−−−−−−READING CROSSECTION AREA FOR SURGE HEADBAY MATRIX−−−−−−−−−−
A_surgelevel = dlmread('crossection.xls');
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
L = tunnel.L;
a = 1200;
d x = 5 ;
dt = dx/a;
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x0 = dx;
Q0 = 85;
tmax = 2500;
x = x0;
l = 1 ;y = 1 ;
Qn = Q0;
Z(1) = 909.3; % Maximum surge level in SH.
B = a/(g*tunnel.A);
R = tunnel.c;
Tl= round(7/dt); % Closing time turbine
k = ( 1−1e−7)/Tl;
%−−−−−−−−−−−−−−−−−−−−−−−−−−−
for t = 1:1:tmax
for x = x0:dx:L % Storing inital values at t=0
Q(x,t) = Q0;
H(x,t) = Z(1);
end
end
%%
kappa = 1;
for n = 1:1:tmax
if n <Tlkappa = kappa − k;
else
kappa = 1e−7;
end
K(n,1) = kappa;
for x = x0:dx:L
if n = = 1 %Inital values at t = 1
Q(x,n) = Q0;
if x == x0;
H(x,n) = Z(1);
else
H(x,n) = H(x−dx,n) − R*Q(x−dx,n)*abs(Q(x−dx,n));
end
Hn = H(L,1);
elseif x == x0
z1s = round(Z(n−1)*10)/10 ; %Round off to one decimal
for i = 1:length(A_surgelevel)
l = A_surgelevel(i,1);
if l == z1s
y = i ;
end
end
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As = A_surgelevel(y,2);
Z(n) = Z(n−1) + dt*Q(x,n−1)/As;
H(x,n) = Z(n);
Cb = H(x+dx,n−1) + R*Q(x+dx,n−1)*abs(Q(x+dx,n−1));
Q(x,n) = (1/B)*(H(x,n)−
Cb) + Q(x+dx,n−
1);
elseif x>x0 && x<L
Ca = H(x−dx,n−1) − R*Q(x−dx,n−1)*abs(Q(x−dx,n−1));
Cb = H(x+dx,n−1) + R*Q(x+dx,n−1)*abs(Q(x+dx,n−1));
Qr = Q(x+dx,n−1) − Q(x−dx,n−1);
H(x,n) = 0.5*(Ca + Cb − B*Qr);
Q(x,n) = (1/B)*(H(x,n) − Cb) + Q(x+dx,n−1);
elseif x = = L
Cv = ((kappa*Qn)^2)/Hn;
Ca = H(x−dx,n−1) + B*Q(x−dx,n−1) − ...
R*Q(x−dx,n−1)*abs(Q(x−dx,n−1));
Q(x,n) =−
B*Cv*0.5 + 0.5*sqrt((B*Cv)^2 + 4*Cv*Ca);
H(x,n) = (Q(x,n)/(kappa*Qn))^2*Hn;
end
end
end
%%
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B . 2 S u r g e O s c i l l i a t i o n P r o g r a m
%−−−−−−−−−−−−−−−−−−−−
OSCILLIATION ENTIRE SYSTEM−−−−−−−−−−−−−−−−−−−−−−−−−
clear all
clc
tic
disp('calculating');
%−−−−−−−−−−−−−−−−−−−−−−−− PARAMETERES −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
H_0 = 904.5; % Normal water level in diversion weir
g = 9.781 ; % Gravity [m/s^2]
c_s = 0.00001; % Assumed value
%Pressure tunnel 1.1L_t1 = 1215 ; % Length [m]
D_t1 = 8.3 ; % Diameter [m]
A_t1 = (pi/4)*D_t1^2 ; % Area [m^2]
%Pressure tunnel 1.2
L_t2 = 285 ; % Length [m]
D_t2 = 7.4 ; % Diameter [m]
A_t2 = (pi/4)*D_t2^2 ; % Area [m^2]
%Average pressure tunnel 1
L_1 = L_t1 + L_t2 ; % Length [m]
A_1 = (L_t1*A_t1 + L_t2*A_t2)/(L_t1+L_t2); % Area [m^2]
c_1 = 5.2e−5 ; % Headloss coefficient
% Penstock, tunnel 2
L_2 = 182.1 ;
D_2 = 3.6 ;
A_2 = (pi/4)*D_2^2;
np = 4; % Number of penstocks
c_2 = 6.5e−4;
% Surge Chamber
A2_s = [765 40000; 766 40000; 767 40000; 768 40000; 769 816; 770 802; ...
771 768; 772 850; 773 802; 774 789; 775 782 ];
%Tailrace tunnel roof is at 769, areas below are therefore LARGE....
%Read from drawing
% Tailrace, tunnel 3
L_3 = 675 ;
w_3 = 11; % Width of tunnel
h_3 = 13.9; % Height
A_3 = w_3*h_3 ;
H_u = 769.2; % Water level in Tailrace
c_3 = 0.4e−4;
%−−−−−−−−−−−−READING CROSSECTION AREA FOR SURGE HEADBAY MATRIX−−−−−−−−−−
A_surgelevel = dlmread('crossection.xls');
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%−−−−−−−−−−−−−−−−− INITIAL VALUES AT t=0 s −−−−−−−−−−−−−−−−−−−−−−−−−−−−−
Q0 = 4*71;
Q_1(1,1) = Q0; % Volume flow in pressure tunnel (1)
Q_2(1,1) = Q0; % Volume flow in penstock (2)
Q_3(1,1) = Q0; % Volume flow in tailrace (3)
z1(1,1) = H_0−
c_1*Q0*abs(Q0); % Initial level in Surge Headbayz2(1,1) = Q0*0.003+ 762.4; % Initial level in Surge Chamber
Q_s1(1,1) = 0; % Volume flow into Surge Headbay
Q_s2(1,1) = 0; % Volume flow into Surge Chamber
Hn = 130.2; % Design head
Qn = 284; % Design flow
dt = 0.1; % Time step
tmax = 5000; % Maximum calculation time
kappa(1,1) = 1;
y =1;
l=1;
%−−−−−−−−−−−−−−−−−−−−− Surge Oscilliation −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
%%
n = 3068; %Second interception point with stationary pressure line
o = n + 5;
p = 6659; % Third interception point with stationary pressure line
q = p + 1 8 ;
r = 6368;
s = r + 1 8 ;
u = 6800;
v = u + 1 8 ;
for t = 2: tmax
if t< 70 %Determines the opening degree of the turbine
kappa(t,1)= 1 − t*0.01329;
% elseif t<n% kappa(t,1) = 0.07;
% elseif t≥n & & t < o
% kappa(t,1) = 0.07 + 0.01*(t−n); %Reloading one turbine
% elseif t≥ o & & t < p
% kappa(t,1) = 0.25;
% elseif t≥p & & t < q
% kappa(t,1) = 0.25 − 0.01*(t−p);
% elseif t≥q & & t < r
% kappa(t,1) = 0.07;
% elseif t≥ r & & t < s
% kappa(t,1) = 0.07 + 0.01*(t−r); %Reloading one turbine
% elseif t ≥s & & t < u
% kappa(t,1) = 0.25;
% elseif t≥u & & t < v% kappa(t,1) = 0.25 − 0.01*(t−u);
else
kappa(t,1) = 0.07;
end
z1s = round(z1(t−1,1)*10)/10 ; %Round off to one decimal
% Finds the crossectional area corresponding to the surge level
% in the Surge Headbay
for i = 1:length(A_surgelevel)
x = A_surgelevel(i,1);
if x == z1s
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y = i ;
end
end
% Finds the crossectional area corresponding to the surge level in
% the Surge Chamber
z2s(t−1,1) = round(z2(t−1,1)); %Round off to zero decimal
for j = 1:length(A2_s)
k = A2_s(j,1);
if k == z2s(t−1,1)
l = j ;
end
end
As1 = A_surgelevel(y,2);
As2 = A2_s(l,2);
Q_s1(t−1,1) = Q_1(t−1,1) − Q_2(t−1,1);
Q_s2(t−
1,1) = Q_2(t−
1,1)−
Q_3(t−
1,1);
hf_1(t−1,1) = c_1*Q_1(t−1,1)*abs(Q_1(t−1,1));
hf_s1(t−1,1) = c_s*Q_s1(t−1,1)*abs(Q_s1(t−1,1));
hf_2(t−1,1) = c_2*Q_2(t−1,1)*abs(Q_2(t−1,1));
hf_s2(t−1,1) = c_s*Q_s2(t−1,1)*abs(Q_s2(t−1,1));
hf_3(t−1,1) = c_3*Q_3(t−1,1)*abs(Q_3(t−1,1));
Q_1(t,1) = Q_1(t−1,1) + (g*dt*A_1/L_1)*(H_0 − z1(t−1,1) ...
− (hf_1(t−1,1) + hf_s1(t−1,1)));
Q_2(t,1) = Q_2(t−1,1) + (g*dt*A_2/L_2)*(z1(t−1,1) − z2(t−1,1) ...
− Hn*(Q_2(t−1,1)/(kappa(t−1,1)*Q0))^2 − hf_2(t−1,1));
Q_3(t,1) = Q_3(t−1,1) + (g*dt*A_3/L_3)*(z2(t−1,1) − H_u ...
− (hf_3(t−1,1) + hf_s2(t−1,1)));
z1(t,1) = z1(t−1,1) + (dt/As1)*(Q_1(t−1,1) − Q_2(t−1,1));
z2(t,1) = z2(t−1,1) + 10*(dt/As2)*(Q_2(t−1,1) − Q_3(t−1,1));
end
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B . 3 R e d u c t i o n i n h e a d p r o g r a m
%−−−−−−−−−−−−−− Reduction in head program −−−−−−−−−−−−−−−−−−−−−−−−
clear all
clc
H0 = 902.7;
Hv = 764; % Elevation of turbine, reference
Qn = 68;
Pn = 82;
tmax = 1300;
c_1 = 5.2e−5 ; % Headloss coefficient
c_2 = 6.15e−4;
c_s = 0.00001; % Assumed value
eta = 0.94;
rho = 997;
g = 9.781 ; % Gravity [m/s^2]
Q2(1,1) = 68;
Q1(1,1) = Q2(1,1)*4;
hf(1,1) = c_1*Q1(1,1)^2 + c_2*Q2(1,1)^2 + 0.4e−4*Q2(1,1)^2;
k = hf(1)*Q2(1,1)^2/(Qn^2);
Hnew(1,1) = H0 − k ;
Pnew(1,1) = rho*g*Q2(1,1)*(Hnew(1,1)−Hv)*10^(−6);
for t = 2:tmax
Q_s1(t,1) = Q1(t−1,1) − Q2(t−1,1);
hf(t−1,1) = c_1*Q1(t−1,1) 2 + c_2*Q2(t−1,1) 2 + 0.4e−4*Q2(t−1,1)^2;
k = hf(t−1)*Q2(t−1,1)^2/(Qn^2);
Hnew(t,1) = H0 − k ;
Pnew(t,1) = rho*g*Q2(t−1,1)*(Hnew(t−1,1)−Hv)*10^(−6);
Q1(t,1) = Q1(t−1,1)+ 0.1;
Q2(t,1) = Q1(t−1,1)/4 + 0.1;
end
Hnew = Hnew − Hv;
P93 = ((Pnew*0.93/Pn)−1)*100;
P94 = ((Pnew*0.94/Pn)−
1)*100;
P95 = ((Pnew*0.95/Pn)−1)*100;
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A p p e n d i x C
S u p p l e m e n t R e s u l t s
T h i s c h a p t e r i s i n t e n d e d t o b e a s u p p l e m e n t t o t h e p r e s e n t e d r e s u l t s .
T h e r e f o r e , v a l u e s a n d d e s c r i p t i o n o f t h e g r a p h s c a n b e f o u n d i n c h a p t e r
6 .
C . 1 V e r i c a t i o n o f S i m u l a t i o n M o d e l s
F i g u r e s C . 1 a n d C . 2 s h o w s t h e o s c i l l a t i o n f o r i d e a l c o n d i t i o n s w h e n r e l o a d i n g .
F i g u r e C . 1 : V e r i c a t i o n S u r g e H e a d b a y r e l o a d
C . 2 S u p p l e m e n t e x i s t i n g h y d r a u l i c c o n d i t i o n s
O n l y t h e c r i t i c a l w a t e r l e v e l s i n t h e i n t a k e a n d t a i l r a c e i s c o n s i d e r e d i n t h e
a n a l y s i s o f e x s i t i n g h y d r a u l i c c o n d i t i o n s . A d d i t i o n a l r e l o a d / r e j e c t s e q u e n c e s
h a v e b e e n i n v e s t i g a t e d , b u t o n l y t h e s c e n a r i o s t h a t d o e s n o t e x c e e d t h e l i m i t
i s p r e s e n t e d .
C . 2 . 1 S u r g e o s c i l l a t i o n i n S u r g e H e a d b a y
T h e s u r g e o s c i l l a t i o n r e s u l t s a r e p r e s e n t e d i n t h e f o l l o w i n g f o r t h e w o r s t c a s e
s c e n a r i o s . A l l s i m u l a t i o n s i n c l u d e a r e l o a d / r e j e c t s e q u e n c e .
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F i g u r e C . 2 : V e r i c a t i o n S u r g e C h a m b e r r e l o a d
F i g u r e C . 3 : S u r g e o s c i l l i a t i o n a t h i g h e s t o o d l e v e l 4 u n i t s
H i g h e s t o o d l e v e l H F L
T h e h i g h e s t o o d l e v e l i n t h e i n t a k e i s 904.5
m a s l , a n d t h e s u r g e o s c i l l a t i o n
i s s h o w n i n g u r e C . 3 . T h e m a x i m u m u p s u r g e i s 9 0 9 . 3 m a s l a n d m i n u m u m
d o w n s u r g e i s 8 9 9 m a s l . T h e r e s u l t o f t h e S u r g e C h a m b e r i s n o t p r e s e n t e d
h e r e , b u t t h e l o a d s e q u e n c e y i e l d s a m a x i m u m u p s u r g e o f 7 7 4 . 4 m a s l .
M i n i m u m d r a w - d o w n l e v e l M R W L
T h e m i n i m u m d r a w - d o w n l e v e l i n t h e i n t a k e i s 8 9 5 . 2 m a s l , a n d i t i s f o u n d
t h a t o n l y o n e t u r b i n e c a n o p e r a t e a s s h o w n i n g u r e C . 4 .
T h e m i n i m u m l e v e l i n t h e i n t a k e f o r r e j e c t i n g t w o u n i t s i s f o u n d t o b e
8 9 6 . 5 m a s l . T h e m i n i m u m d o w n s u r g e i s 8 9 1 . 6 m a s l , a n d t h e m a x i m u m
u p s u r g e i s 9 0 0 . 9 a s s h o w n i n g u r e C . 5 .
I n g u r e C . 6 t h e l o w e s t l e v e l i n t h e i n t a k e i s 8 9 7 m a s l w h e n o p e r a t i n g
3 u n i t s . T h e m a x i m u m u p s u r g e i s 9 0 1 . 5 m a s l , a n d t h e d o w n s u r g e i s 8 9 1 . 5
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F i g u r e C . 4 : S u r g e o s c i l l i a t i o n S H ,
H 0 = 895.2m a s l a n d
Qunit = 71m3/s
F i g u r e C . 5 : S u r g e o s c i l l i a t i o n i n S H , H 0 = 896.4
m a s l a n d Q = 142m3/s
m a s l . T h e l e v e l i n t h e i n t a k e m u s t b e 8 9 7 . 4 m a s l f o r o p e r a t i n g 4 u n i t s a n d
i t i s s h o w n i n g u r e C . 7 . T h e m a x i m u m d o w n s u r g e i s 8 9 1 . 6 m a s l a n d t h e
u p s u r g e i s 9 0 2 . 7 m a s l .
C . 2 . 2 S u r g e C h a m b e r R e s u l t s
4 u n i t s
T h e r e s u l t o f t h e i n v e s t i g a t i o n o f t h e S u r g e C h a m b e r s h o w s t h a t f o r a f u l l
l o a d r e j e c t i o n f r o m 4 u n i t s i s o n l y p o s s i b l e w i t h a t a i l w a t e r l e v e l o f 7 6 8 m a s l
a s d e m o n s t r a t e d i n g u r e C . 8 . T h e m a x i m u m u p s u r g e i s 7 7 4 . 8 m a s l , a n d i t
s h o w s t h a t a r e l o a d / r e j e c t s e q u e n c e a t a n y o f t h e u p s u r g e s w i l l e x c e e d t h e
m a x i m u m l i m i t i f i t i s r e l o a d e d b e f o r e t h e t h i r d u p s u r g e .
3 u n i t s
T h e h i g h e s t t a i l w a t e r l e v e l i s 7 6 8 . 3 m a s l w h e n o p e r a t i n g 3 u n i t s . A l o a d
r e j e c t i o n s h o w s t h a t t h e r s t u p s u r g e y i e l d s t h e m a x i u m o f 7 7 5 . 1 m a s l .
F i g u r e C . 9 s h o w s t h e p r o g r e s s i o n f o r r e l o a d / r e j e c t i n g a u n i t a t t h e t h i r d
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F i g u r e C . 6 : S u r g e O s c i l l i a t i o n i n S H ,
H 0 = 897m a s l a n d
Q = 213m3/s
F i g u r e C . 7 : S u r g e o s c i l l i a t i o n i n S H , H 0 = 897.4
m a s l a n d Q = 284m3/s
u p s u r g e w h i c h a c h i e v e d a l e v e l o f 7 7 3 . 9 m a s l , w h i c h i s s m a l l e r t h a n t h e r s t
u p s u r g e .
2 u n i t s
F o r 2 u n i t s i n o p e r a t i o n c a n t h e t a i l w a t e r h a v e a l e v e l o f 7 6 8 . 7 m a s l . A l o a d
r e j e c t i o n y i e l d s a m a x i m u m u p s u r g e o f 7 7 5 , a n d i s s h o w n i n g u r e C . 1 0 . A
r e l o a d / r e j e c t s e q u e n c e t h a t s t r i k e s o n e o f t h e u p s u r g e s i s n o t p o s s i b l e u n t i l
a l o n g t i m e h a s p a s s e d .
1 u n i t
F o r t h e h i g h e s t l e v e l o f 7 6 9 . 2 m a s l i n t h e S u r g e C h a m b e r i s i t o n l y p o s s i b l e
t o o p e r a t e w i t h o n e u n i t a s t h e r e s u l t i n g u r e C . 1 1 s h o w s . T h e m a x i m u m
u p s u r g e l e v e l i s 7 7 3 . 2 m a s l , a n d a r e l o a d / r e j e c t s e q u e n c e t h a t s t r i k e s o n e o f
t h e u p s u r g e s a t t h e w o r s t p o s s i b l e t i m e c a n n o t b e p e r f o r m e d u n t i l a l o n g
t i m e h a s p a s s e d .
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F i g u r e C . 8 : S u r g e o s c i l l a t i o n i n S C ,
H u = 768a n d
Q = 284m3/s
F i g u r e C . 9 : S u r g e o s c i l l a t i o n i n S C , H u = 768.3
m a s l a n d Q = 213m3/s
C . 3 A n a l y s i s : I n c r e a s i n g V o l u m e F l o w e x t e n t i o n
T h e r e s u l t s o f t h e a n a l y s i s i s p r e s e n t e d i n d e t a i l i n s e c t i o n 6 . 2 . H e r e a r e o n l y
t h e g r a p h s p r e s e n t e d .
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F i g u r e C . 1 0 : S u r g e o s c i l l a t i o n i n S C , H u = 768.7masl
a n d Q = 142m3/s
F i g u r e C . 1 1 : S u r g e o s c i l l a t i o n i n S C , H u = 769.2masl
a n d Q = 71m3/s
F i g u r e C . 1 2 : S u r g e o s c i l l a t i o n i n S H , H 0 = 897.5
m a s l a n d Q = 255m3/s
X V I
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F i g u r e C . 1 3 : S u r g e o s c i l l i a t i o n i n S H , H 0 = 897
m a s l Q = 142m3/s
F i g u r e C . 1 4 : S u r g e o s c i l l i a t i o n i n S H , H 0 = 906
m a s l Q = 71m3/s
X V I I
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F i g u r e C . 1 5 : S u r g e o s c i l l i a t i o n i n S C H u = 767.9
m a s l a n d Q = 255m3/s
F i g u r e C . 1 6 : S u r g e o s c i l l i a t i o n i n S C H u = 768.2
m a s l a n d Q = 170m3/s
X V I I I
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F i g u r e C . 1 7 : S u r g e o s c i l l i a t i o n i n S C , H u = 769.2
m a s l a n d Q = 85m3/s
X I X
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X X
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A p p e n d i x D
E x c e l C a l c u l a t i o n s
D . 1 D i s t r i b u t i o n o f t u r b i n e t y p e s
D . 2 S u r v e y
D . 3 D i a 0 0
D . 4 D i a 0 3
D . 5 C a l c u l a t i o n o f p o t e n t i a l i n c r e a s e i n p o w e r o u t p u t
( S i n t e f )
X X I
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Appendix D.1: Distribution of turbine types
no Unit
Plant Turbine type units Output [MW] Diameter Head [m] Speed
Asia
Lohair Nagpala Pelton 4 167.5 3350 427 250
Sorang Pelton 2 59.2 1760 673 600
Teesta Urja II Pelton 6 233.75 3020 817 375
Chukha Pelton 4 84 2870 463.2 300
East Toba River Pelton 2 78.5 2210 569.88 450
Yazuihe-Yangang Pelton 2 65.6 1650 631.75 600
Jiniu Pelton 2 123 2890 506.5 300
Varahi II Pelton 2 126.5 2910 460 300
Vishnupraguay Pelton 1 120.4 2880 953.4 428.6
Jinwo Pelton 2 143.6 2630 595 375
Rezonghai Pelton 2 123 2550 560 375
Xi Luo Du Francis 3 784 7655 197 125
GongGuoQiao Francis 4 225 6760 66 93.75
JiangBian Francis 3 110 2100 306.2 333.3JiangPingHe Francis 2 225 4030 178.89 187.5
XiGu Francis 3 83 1560 431.4 500
Nam Ngum 2 Francis 3 209.2 4080 166.6 214.3
Kami-Shiiba Francis 1 47.6 2630 144 300
Siguragura Francis 2 73.2 2110 230.9 333
DaYiangJiang Francis 4 175 2110 331 300
Li Yuan Francis 4 612 8150 106 93.8
Da Gang Shian Francis 4 663 7000 160 125
Ting Zi Kou Francis 4 275 6640 73 100
Jing Ping II Francis 8 610 6500 318.8 166.7
Nuo Zha Du Francis 3 650 7250 215 125
An Khe Francis 2 81.6 2518 377.5 500Ji Shi Xia Francis 3 340 7650 66 85.7
Yewa Francis 4 195.5 4850 91.7 12.8
Si Lin Francis 4 267.85 6810 64 93.75
Xiao Wan Francis 3 700 6600 216 150
Xe Kaman III Francis 2 127.55 1600 515.38 500
Nathpa Jhakri Francis 4 336 2519 487 300
Karebbe Francis 2 66.4 3284 73.6 200
Cheongpeyong Kaplan 1 60 6400 22.3 102.9
Cao Jie Kaplan 4 128.2 9500 20 68.18
Karnafuli Kaplan 1 67.7 5607 32 115.38
Australasia
Benmore Francis 6 93.2 4085 93 166.7Bogong Francis 2 74.6 2050 419.3 600
Dartmouth Francis 1 180 410
Devils Gate Francis 1 60
Gordon River Francis 3 144
Murray-1 Francis 10 95
Tumut - 3 Francis 6 250
Clyde Francis 4 108
Agus II Francis 3 60
Pulangui Francis 3 85
North - America
Noxon Rapids Francis 3 115.8 5500 48.158 100
Folsom Francis 3 66.2 3510 60 163.6Gordon M Shrum Francis 1 310 4870 152.4 150
Eastmain 1 A Francis 3 260 6600 63 100
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Picote II Francis 1 248 6150 66.6 115.4
Abitibi Francis 1 66.41 3520 72.5 150
Revelstoke Francis 1 512 7100 127.1 112.5
Sir Adam Beck Francis 8 55 3030 89 225
Des Joachimes Francis 8 57.5 4470 40 105.9
Jocasse Pump 2 208 7500 92 120
Rocky Mountain Pump 3 370 4200 210 225
Holtwood Kaplan 2 59.2 7150 15.5 85.7Rainbow Kaplan 1 62 5400 35.8 144
South America
Parigo De Souza Pelton 1 65 2700 754 514
El Platanal Pelton 2 110 2190 608.7 450
Hornitos Pelton 1 55.02 1910 561.56 500
Guri II Francis 5 770 8000 136 112.5
Confluencia Francis 2 81.6 1650 334.51 500
Serra Do Facao Francis 2 108.2 3920 78.3 171.4
Mazar Francis 2 80 3000 131.44 257.14
Salto Pilao Francis 2 93 2650 194.9 360
Antuco Francis 2 165 3150 196 250
Rapel Francis 2 77 3500 75.5 187.5Infiernillo Francis 4 205 4735 114.5 163.64
La Villita Francis 2 81.65 5000 46.41 120
Simplicio Francis 3 104 3250 105.3 225
Macagua I Francis 6 83 4900 46 120
Itaipu Francis 20 715 8100 118.4 90.9
El Cajon Francis 4 75 2475 156 300
Jirau Kaplan 10 76.55 7500 15.2 94.7
Santo Antonio Kaplan 13 71.05 7500 13.9 100
Estreito Kaplan 8 138.65 9500 18.94 62.98
Europe
Sedrun Pelton 3 52 2150 588 428.6
Fionnay Pelton 6 70 2650 872 428.6Kaprun Pelton 1 63 2255 868 500
Kjosnesfjorden Pelton 1 84.1 1905 785 600
Uvdal Pelton 2 53.72 1935 571.17 500
Florli Pelton 1 88.3 1874 773.99 600
Zaramagaskaya Pelton 2 171 3350 610 300
Akkoey II Pelton 2 116.78 1940 1220 750
Naturno Pelton 1 61.7 2700 1129 500
Lotru Ciunget Pelton 3 170 3810 788 375
Grosio Pelton 1 107 2970 600 333
Aguayo Pump 1 85 3000 307 500
La Muela II Pump 4 210 3180 494 600
Limberg II Pump 2 240 3910 420 428.57Obrovac Pump 1 151.8 1137 541 600
Dez Dam Francis 8 91.5 2490 164 250
Zakucac Francis 4 150 2500 265 333.33
Uluabat Francis 2 50 1850 292 600
Driva Francis 1 81 2390 540 600
Mequinenza Francis 4 83.5 5000 50 136.5
Orichella Francis 1 75 2200 474 600
Akkoeprue Francis 2 59.3 3150 86.8 214.3
Waldeck II Francis 1 240 3350 325 375
Belesar Francis 3 78 3110 120 214
Bemposta Francis 1 193.5 5900 67.5 115.4
Hacininoglu Francis 2 60.13 2382 140.24 300Harspranget Francis 1 122.6 3725 110 166.8
Kilforsen Francis 1 105.74 3725 100 166.7
Feldsee Francis 1 70.4 1912 524 1000
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Songa Francis 1 127 2304 264 300
Hintermuhr Francis 1 74.85 1870 517.02 1000
Picote II Francis 1 248 6150 66.6 115.4
Castrelo Kaplan 2 56 6800 20 93.75
Ligga Kaplan 3 185 7500 39 107.14
Cachoeira Dourada Kaplan 1 55.45 5540 34.5 128.6
Akkats Kaplan 2 75 5200 42.6 166.7
Uglich Kaplan 1 70 9000 14.5 600Vardinili I Kaplan 1 73.3 4000 59 187.5
Africa
Gilgel Gibe II Pelton 4 105 2580 485 333
Ingula Pump 4 342 4260 441 428.6
Drakensberg Pump 4 250
Afourer Pump 2 176 594
Kiambere Francis 2 84 2700 153.7 300
Beles Francis 4 119.4 1900 320 375
Shiroro Francis 4 155 4460 97 150
Aswan High Dam Francis 2 175 74 100
Merowe Francis 10 125 43
Cahora Bassa Francis 5 415Turkwell Francis 2 57.5 364
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Appendix D.2: Survey
Plant Type of turbine Old New % increase Old New Old New Old New Old New
La Villita Francis x 4, 1973 76 82 8 44 41.8 100 120 5315 5098 80 95
Guri II Francis x 5 610 715 17 130 134 112.5 112.5 6900 6900 68 67
Kiambere Francis x 2 72 84 17 150.5 150.5 300 300 2500 2500 61 61
Pantabangan Francis 51.6 60.4 17 70 75 180 180 3458 3458 74 72
Ambuklao Francis 25 35 40 154.3 154.3 360 400 1700 1700 49 55
Taloro II Francis x 2 13.6 15.64 15 191 191 600 600
Harsprånget Francis 117 140.4 20 105 105 166.7 166.7 3750 3750 61 61
Kilforsen Francis 100 120 20 95 95 166.7 166.7 3750 3750 64 64
Bajina Basta Francis x 4 95.4 108 13 67.5 67.5 136.4 136.4 4250 4250 71 71
Nedre Vinstra Francis x 4 50 65 30 448 448
Mequinenza Francis x 4 80.9 101.934 26 62 47 136.36 136.36 4300 4300 74 86
Såheim Francis x2 54 60 11 255 265
Songa Francis 120 136 13 264 264
Average 18
Hjartdøla Pelton 60.85 66.6 9 555 555
Riddes Pelton 50.3 55.7 11 1005 1005 600 600 2450 2450 46 46
Sernf Pelton 15 19.5 30 223 223 375 375 1560 1560 39 39
Niedernbach Pelton 28.4 36.92 30 1077 1077 750 750 1800 1800 41 41
Aurland I Pel ton 225 280 24
Average 21
Aschach Kaplan 85 98 15 15.9 15.9 68.2 68.2 8400 8600 144 147
Grossraming Kaplan x 2 28 35.5 27 23 23 142.9 136.4
Geithusfoss Kaplan 12.8 15 17 9.5 9.3 4880 4880
Cabinet Gorge Kaplan 24
Average 21
Total average 20
n12Output [MW] H [m] n [rpm] Runner Diameter [mm]
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Appendix D.3: Dia00Assumed Given Rules Calculated
Known data:
Nominal output Pn MW 82
Rotation speed n rpm 230.8
Nominal volume flow Q n m3/s 68
Gravity constant g m2/s 9.78
Density ρ kg/m3
997
Pådragskoeff κ 1.15
Inlet diameter D1 m 3.312
Outlet diameter D2 m 2.94
B0 m 0.65
B1 m 0.649
Angular velocity ω rad/s 24.17
Increase D2 By m 0
New m 2.94
Area outlet A2 m2
6.79
Safety factor 0.15
NPSHA m 16.9
Subtract from NPSH 0 0.1 0.2 1 0.4 0.5
NPSHT m 14.3 14.2 14.1 13.3 13.9 13.8
a 1.12
b 0.060 0.060 0.059 0.058 0.059 0.059
u2 m/s 35.5
u2 0.72β2 rad 0.29 0.29 0.29 0.28 0.29 0.28
deg 16.71 16.63 16.55 15.90 16.39 16.31
*Ω 0.60 0.60 0.59 0.58 0.59 0.59
*cm2 m/s 10.66 10.61 10.56 10.12 10.45 10.40
*cu2 0 0 0 0 0 0
OK OK OK OK OK OK
*Q 72.39 72.03 71.67 68.71
Q n m3/s 83.25 82.83 82.42 79.02
OK OK OK OK
Increase % 22 22 21 16
cm2 m/s 12.26 12.20 12.14 11.64
NPSHTnew m 12.47 12.37 12.28 11.51
OK OK OK OK
Nominal Head Hn m 123.3 123.6 123.9 126
(Retrived from Matlab)
Assumed Efficiency ηH 0.93
Pnew MW 93.08 92.84 92.60 90.29
Pnew - Pold MW 11 11 11 8Increase % 13.51 13 13 10
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Assumed Efficiency ηH 0.94
Pnew MW 94.08 93.84 93.59 91.26
Pnew - Pold MW 12 12 12 9
Increase % 14.73 14 14 11
Assumed Efficiency ηH 0.95
Pnew MW 95.08 94.84 94.59 92.23Pnew - Pold MW 13 13 13 10
Increase % 15.95 16 15 12
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Appendix D.6: Dia06Assumed Given Rules Calculated
Known data:
Nominal output Pn MW 82
Rotation speed n rpm 230.8
Nominal volume flow Q n m3/s 68
Gravity constant g m2/s 9.78
Density ρ kg/m3
997
Pådragskoeff κ 1.15
Inlet diameter D1 m 3.312
Outlet diameter D2 m 2.94
B0 m 0.65
B1 m 0.649
Angular velocity ω rad/s 24.17
Increase D2 By m 0.06
New m 3
Area outlet A2 m2
7.07
Safety factor 0.15
NPSHA m 16.9
Subtract from NPSH 0 0.1 0.2 0.3 0.4 0.5
NPSHT m 14.3 14.2 14.1 14.0 13.9 13.8
a 1.12
b 0.061 0.061 0.061 0.060 0.060 0.060
u2 m/s 36.3u2 0.74
β2 rad 0.28 0.28 0.28 0.28 0.28 0.27
deg 16 16 16 16 16 16
*Ω 0.61 0.61 0.61 0.60 0.60 0.60
*cm2 m/s 10.45 10.40 10.34 10.29 10.23 10.18
*cu2 0 0 0 0 0 0
OK OK OK OK OK OK
*Q 73.86 73.48 73.10 72.72
Q n m3/s 84.94 84.50 84.06 83.63
OK OK OK OK
Increase % 25 24 24 23
cm2 m/s 12.02 11.95 11.89 11.83
NPSHTnew m 12.36 12.26 12.17 12.07
OK OK OK OK
Nominal Head Hn m 122.0 122.4 127.7 123.0
(Retrived from Matlab)
Assumed Efficiency ηH 0.93
Pnew MW 93.97 93.79 97.35 93.27
Pnew - Pold MW 12 12 15 11Increase % 15 14 19 14
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Assumed Efficiency ηH 0.94
Pnew MW 94.98 94.80 98.39 94.28
Pnew - Pold MW 13 13 16 12
Increase % 15.82 16 20 15
Assumed Efficiency ηH 0.95
Pnew MW 95.99 95.81 99.44 95.28Pnew - Pold MW 14 14 17 13
Increase % 17 17 21 16
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Appendix D.7: Calculation of potential increase in power output (Sintef)Assumed Given Rules Calculated
Nominal volume flow Q n m3/s 68
Nominal output Pn MW 82
Nominal Head Hn m 121.9
Rotation speed n rpm 230.8
Gravitation g m2/s 9.78
Outlet diameter D2 m 2.94 3.00
Density ρ kg/m3
997
Hydraulic efficiency ηH 0.95
Sintef00 Sintef06
Assume increase in output % 17.00 17.00
Pincrease MW 95.94 95.94
Q increase m3/s 84.96 84.96
25 25
Calculations:
Pådragskoeff κ 1.15 1.15
Best volume flow *Q m3/s 73.9 73.9
Increase 9 9
Angular velocity ω rad/s 24.2 24.2
Speed number Ω 0.609 0.609
Specific speed ns 1.0 1.0
Outlet area A2 m2
6.8 7.1
Best operating point
Meridian velocity BEP *cm2
m/s 10.9 10.5
Periferal velocity u2 m/s 35.5 36.3
Outlet angle β2 rad 0.3 0.3
deg 17.0 16.1
Nominal load
Meridian velocity cm2 m/s 12.5 12.0
Tangential velocity cu2 m/s 5.3 5.4
a 1.12 1.12
b 0.061 0.061
NPSHT m 12.9 12.4
NPSHA m 14.4 14.4
YES YES
The geometry must be changed in order to allow more water
NPSHT Constant
Case 1:
Draft tube D22 m 2.94 3
New possible diameter D'2 m 2.94 3
Case 2:
w2 and cm2 increases while β2 remains the same
Net Positive Suction Head
Is the cavitation criteria fulfilled?:
Calculation of increased output
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New possible diameter D''2 m 3.328 3.396
The smallest diameter will be chosen
D2new m 2.94 3
Which case scenario? Case 1 Case 1
Checking cavitation cm2new m/s 12.5 12.0
u2new m/s 35.5 36.3
NPSHTnew m 12.9 12.4
Is the cavitation criteria fulfilled?: YES YES
New values
Volume flow Q new m3/s 85.0 87.6
Output Pnew MW 95.9 98.9
reduced head factor εh 1
Output Pnew,f MW 95.9 98.9
Pnew-Pn MW 13.9 16.9
% 15 18