Thesis Tidal Power

7/27/2019 Thesis Tidal Power

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a

Ab Ac B

a/bh

Cd Cd Cd,eff CP CT f

F r

U/

gh

g

h

hd ho kt Kc U/LL, L1, L2 n

p

P

Pa Pd Pf Pt P+Pd)t

u= (u, v)T

U

2, 4, 4

T

x,b, y,b

( )

ai A


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b

PW T

X

z

( )b,t b t ( )1,2,3,4,5

u

u, v, w x,y,z

Tf

xx, xy, yy

t

b

c=

gh

F(U,Q)G(U,Q)

F, G, Rx, Ry, i,k,p

hm lv, lh M

n

Q=( u

x, u

y, v

x, v

y)T

Rx(U) Ry(U)

S(U)

U= (u,uh,vh)T Uh, Qh

e ,e B,E G SA M

{k} {lk,}

{k}

( )

( )b ( )

( )L,R


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a2

A

c L

0 A

1

c dxFGC Ft Pmax Q

Qmax, QX,max X= 1, 2, 30, 1 0, 1 0, 1

V, I,L,C, R ()e ( )1,2,3,4 ( )0

b

hc he

j

j=

1l

L

m1, m2 S

xb

0, 1 0, 1 0, 10,

1

0, 1

0,

1

T =0+1)

s b

V, I,L,C, R ( )0


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K

Qc Qf Q

f,0

ul

U0 x0

x,y

(a, b)

E(Y) HI HV

J, Js L1, L2 q, m

S

T

x= (x, y)

Y= (h,uh,vh)T = (1, 2) q qs wq, wqs


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2


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Impounded Area, A

Barrage

Adjoining Ocean or Sea

t1 t2 t3 t4

Ab

21gAba

2

= a

(t)

a

g

t

Ab


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|u.n|3

dAC AC

u n A


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P o w e r

D i s s i p a t e d

T o t a l R e s i s t a n c e t o F l o w

( n a t u r a l a n d d u e t o t i d a l d e v i c e s )

A

B

C

D

E x t r a c t e d P o w e r

T o t a l P o w e r D i s s i p a t e d


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16/27


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F r= u/

gh,

u


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h

g

2/3

1/3


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A

u

T

2 4 2

ai = 1

2,

p

X


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u2 = 2u

41 2

At4 = ( 2/ 4)A

ub4 = u

ut4 = 4uu1 = u

3

AT

X

ub4 = u

At1 = 2A

p+1

2u2 =p2t+

1

222u

2,

p3t

+1

22

2u2 =p+

1

22

4u2.

t

p= p2t p3t=12

u2

1 24

.

T

A=

1

2u2

1 24

.

X T =u2A2(4 1) .


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X

T

A=u22(1 4) .

2 =1 +4

2 ,

2

4

P =T 2u=1

2u3A2

1 24

=

1

2u3A

(1 +4)

2

1 24

.

CT CP

T = 1

2u2A

1 24

=

1

2u2ACT,

P = 1

2u3A

(1 +4)

2

1 24

=

1

2u3ACP.

4 4 = 1/3 2 = 2/3 CT = 8/9

CP = 16/27

X


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41 2

ub 4

At 1

At 4

ub 4

ut 4

u1 = u

3

AT Mixing

5

u5

A/B

X

A/B

B 1

u = ub4

X

X= 0


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4= 1/3

u2AB24+u2A (1 B2) =uAu5,

u5=u1 B (1 24)2

.

B = 0

u5 u

PW

PW =1

2u3A2

24+

1

2u3A

1B

21

2u

A

Bu25,

PW =1

2u3A2(1 4)2

1 B (1 +4)

2

.

= P

P+PW=

(1 +4)

(1 +4) + (1 4) (1 B2) .

4 = 1/3

PW =P /2 2/3 B = 0

4 = 2 = 1


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41 2

ub 4

At 1

At 4

ub 4

ut 4

u1 = u

3

AT Mixing

5

u 5 = u

A/B

X

4

u4b= u (1 B2)

(1 B2/4) =4u,

4>1


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p p4

p p4=12

u2

24 1

=

1

2u2

(1 B2)2

(1

B2/4)

2 1

.

p2t p3t =p p4+12

u2

1 24

,

p2t p3t =1

2u2 (1 B2)

2

(1 B2/4)2 2

4 .

T

A=

1

2u2

(1 B2)2

(1 B2/4)2 24

.

pA/B p4A/B T =u2A2(4 1) + u2A/B (1 B2)

(1 B2)(1 B2/4) 1

.

p

p4 =

T B

A

+u22

4

B (1 4)2

(1 B2/4),

24(22 1 4) +B2

224+2 342

= 0.

B

2 4


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B = 0

2 = (1 +4)/2

B 1

2 1 4 1 B

2 = (1 +4)

(1 +B) +

(1 B)2 +B (1 1/4)2.

2

P =

1

2 Au3

2 (1 B2)2

(1 B2/4)2 2

4 .

B

4 = 1/3

Pmax=1

2Au3

16

27

1

1 B2

.

CP =1627 1

1 B2 ,

B

1 + 2B

CP = P

12

u3A+uAp=

CP1 +BCT

,


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X

B > 0

X

(p p4) A

1/B 24

X=u2A (1/B 2)

(1 B2)

(1 B2/4) 1

,

p

p4

X=1

2u2A

24

(1 4) (4 1) .

4

B >0

B = 0

4 = 1 X = 0

p4 p5 = u2 2B (1 4)2

4(1 B2/4) .

PW =1

2u3A2

24+

1

2u3A (1/B 2) 24 (A/B)

1

2u3 u (p4 p5)

.

PW =

1

2 u

3

A2(1 4)21 + B2(1 B2)24(1 B2/4)2 .

B = 0


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B >0

(p p5) uAC=T u. 2uT

= PP+PW

=2.

2 = 1 B

4

4 = 1/3 2 = 2/[3 (1 +B)]

= 23 (1 +B)

.

p= gz

z

h + a

a h h gh/2 + ga + O(a2/h) ga

a.


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p p4=4B (3 B)9 (1 B)2 u

2,

p5 p4= 8B9 (1 B) u

2,

CT = 8 (1 +B)

9 (1 B)2 .

B

CD CT/2

(p p4)/gh 1

F r2 = u2

gh


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Mixing

41 2 5

ub 4

h5

At 1

At 4

ub 4

u5ut 4

h

h1

= h

u1

= u

3

AT

X

h

b

u


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h A

b

ur ne rea(a) (b)

AA

b

A AA

h+u2

2g=h4+

u2242g

,

h+u2

2g =h2t+

u2222g

,

h3t+u222

2g =h4+

u2242g

.

h2t h3t = u2

2g

24 24

,


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T

gBbh=

u2

2g

24 24

.

1

2gb

h2 h24 T =u2bhB2(4 1) +u2hb (1 B2) (4 1) .

T

12gb h2 h24 Bbh u22 24 24= u2bhB2(4 1) +u2hb (1 B2) (4 1) .

h4 = Bh24

+h(1 B2)

4,

2= 4Bh

(h (1 4) +4(h h4))(4 4) ,

2=2 (4+4) (4 1)3 (B24 B44)1

4 + (24 1) (44)1 .

4 B

2 4

4 F r

h4 2


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0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

4

Cp,

CP

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

Cp,

4

CP

4

F r= 0.1

B = 0.1

B = 0.2

B = 0.3

B = 0.4

B = 0.2

F r= 0.01

F r= 0.1

F r = 0.2

F r = 0.3

F r2

2 44+ 24F r

234

2 2B+F r2 24 44+ 24F r2 4 4+F r2

2 + 44 2B24 2

= 0.

4

F r

B

4

T

P = 2uT

T =1

2u2Bbh

24 24

=

1

2u2BbhCT,

P =1

2u3Bbh2

24 24

=

1

2u3BbhCP.

4


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4 = 1/3,

2

4

B 0

4 1

(4 1)3 B

2 = (1 +4)/2,

F r = 0

(1 B) 24 (24 2) 4+

24 B24 1

= 0,

4= 1 B21

B2/4

,

B

F r


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E4= u2

2g+h=

2

4 u2

2g +h4.

dE4/dh4= 0

h4

h4

d

d (h4/h)

24

= 2F r2

.

4

B 0

B 1

1

2gb

h2 (h h)2 T =bhu uhh h u

.


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0 0.2 0.4 0.6 0.8 115

10

5

0

5

10

4

4

Unphysical solutions

Real part of complex 4

Supercritical Bypass flow

Subcritical Bypass flow

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Fr

B

4=0.01

0.99

0.8

0.50.2

Physically inadmissible

Physically admissible

F r = 0.14

B = 0.64

F r = 0.3

B = 0.2

4 4

1

2

h

h

33

2

h

h

2+

1 F r2 + CTBF r

2

2

h

h CTBF r

2

2 = 0.

h/h 0, 1

h

PW =1

2u3Bbh2

24+

1

2u3bh (1 B2) 24

1

2u3bh

h

h h2

+hbu (h4 h5) g.

P+PW =gubhh

1 F r2 1 h/(2h)

(1 h/h)2

.

gubhh


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= P

P+PW=

P

gubhh

1 F r2 1 h/2h

(1 h/h)21

.

F r 0

2

F r2

P= (2u) T

= 2uTgubhh

,

u

uT =gubhh h2 hh F r2 hhh h =gubhh,

F r2

h/h

h/h 0 F r 0

2

CTBF r

2/2

=2(1 h/(2h)) F r2 (1 h/h)1

1 F r2 (1 h/(2h))(1 h/h)2 .

F r2 (1 h/h)1

1

2

1 12

h

h

.


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1 1

2h/h

,

2

2

B

2


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0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

2

=(1h/(2h))1

B

h/h=0.01

0.02

0.05

0.1

0.010.020.05

2 B F r = 0.05 F r = 0.15

2

2 B

2 B


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4 = 1/3

F r = 0)

F r < 0.1

B = 0.05

B = 0.4

4

4

4 = 1/2 4 = 1/6) 4

u2h

4= 1/3


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0 0.1 0.2 0.3 0.40

5

10

15

20

25

Fr

CT


B=0.7

0.6

0.5

0.4

0.30.2

0.10.05

0 0.1 0.2 0.3 0.40

5

10

15

Fr

CT

B=0.4

B=0.05

Physicallyinadmissable

0 0.1 0.2 0.3 0.40

2

4

6

8

10

Fr

CP

Physically inadmissable

B=0.7

0.6

0.5

0.40.3

0.2

0.10.05

0 0.1 0.2 0.3 0.40

1

2

3

4

5

Fr

CP

B=0.4

B=0.05

Physicallyinadmissable

CT CP

CT

F r

4 = 1/3

CT F r 4 = 1/2 4 = 1/3 4 = 1/6

CP F r 4 = 1/3 CP F r 4 = 1/2

4 = 1/3 4= 1/6


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0 0.2 0.4 0.6 0.8 1

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

B

Fr=0.3

0.20.05 00.1


0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

B

h/h


Fr=0.3 0.1

0.2

0.05

4= 1/3,

4= 1/3,

F r= 0

4

B 0.45 F r 0.2


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0 0.1 0.2 0.3 0.40

0.02

0.04

0.06

0.08

0.1

Fr

h/h

0.5

0.40.4

0.4

0.3

0.2

0.6

0.05

0.1

B=0.7

0 0.1 0.2 0.3 0.40

0.02

0.04

0.06

0.08

0.1

0.12

Fr

h/h

B=0.60.4

0.2

0.1

h/h

4 = 1/3 4 = 1/2 4 = 1/6

h/h


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102

2

2 < 1/2

2


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ux

+v

y +

wz

= 0,

ut

+uux

+vuy

+wuz

= X1

p

x+

2ux2

+2u

y 2 +

2uz2

,

v

t

+uv

x

+vv

y

+wv

z

= Y

1

p

x

+

2v

x2 +

2v

y 2 +

2v

z2 ,

wt

+uwx

+vwy

+wwz

=Z1

p

x+

2wx2

+2w

y 2 +

2wz2

,

u= (u, v, w)T

x= (x,y,z)T p

,

X, Y,

Z

u, u

u = u+ u

.

Tf

u = 1

Tf

t+Tft

udt, u

= 1

Tf

t+Tft

u

dt= 0.

Tf


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ux

+v

y +

wz

= 0,

x

ut

+uux

+vuy

+wuz

= X1

p

x+

1

x

ux

uu

+

1

y

uy

uv

+1

z

uz

uw

uu

u

v

u

w

uu=t

ux

+u

x

, uv=t

uy

+v

x

, uw=t

uz

+w

x

,

t

ut

+uux

+vuy

+wuz

= X1

p

x+

x

t

ux

+u

x

+

y tuy +vx + ztuz +wx ,

X= 2f v, Y =

2f u, , Z=

g,

g

f


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z

x

(x,y,t)

h(x,y)

y

u*(x,y,-h,t)=0

1

P

z g= 0.

P =Pa+g ( z) ,

Pa z=

ho

udz+

y

ho

vdz u(x , y, , t) x

u(x,y, ho, t) hox

v(x , y, , t)

y v(x,y, ho, t)ho

y +w(x , y, , t) w(x,y, ho, t) = 0.

z = (x,y,t)

z =ho(x, y)


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u(x,y, ho, t) = 0,

t+u(x , y, , t)

x+ v(x , y, , t)

y =w(x , y, , t).

t+

uh

x +

vh

y = 0,

h= ho+

u= 1

h

ho

udz, v=1

h

ho

vdz.

u

x

ho

ut

+u2

x +

uvy

+uw

z

dz=

ho

f vdz 1

ho

P

xdz+

ho

x

2t

ux

+

y

t

uy

+v

x

+

z

t

uz

dz.

uh

t +

xxu2h

x +

xyuvh

y =f vh 1

ho

P

xdz+

x

ho

2tux

dz 2t ux

x 2t u

x

ho

hox

+

y

ho

t

uy

+ v

x

dz t

uy

+v

x

y+

t

uy

+ v

x hohoy

+t

uz

t

uzho

,


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xx xy

xx= 1

hu2

ho

u2dz, xy = 1

huv

ho

uvdz.

y

yy = 1

hv2

ho

v2dz.

u v

xx, xy yy

ho

tux

dz=Thu

x,

T

u/y, v/x v/y. T

z= (x,y,t)

W.

z =ho(x, y)

x,b

b,x

=t

uz

ho

+ 2tux

ho

hox

+t

uy

+v

x

ho

hoy

.


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b,x

=t

uz

ho

.

b,y

y

t+

uh

x +

vh

y = 0,

uh

t +

u2h

x +

uvh

y =f vh gh

x

b,x

+

x

2Th

u

x

+

y

Th

u

y+

v

x

,

vh

t +

uvh

x +

v2h

y = f uh gh

y

b,y

+

x

Th

uy

+v

x

+

y

2Th

v

y

.

(b,x, b,y)T =t

uz

ho

,

vz

ho

T=Cdu|u|,

u = (u, v)T Cd

fDW C n

Cd= fDW8

= gC2

= gn2

h1/3.


63/253

u(z) =uf

(z/zo) , uf=

|b|

1/2,

= 0.4

zo

Cd =

1 +

(zo/h)

2.

zo

zos zof

zof=2r

r,

r r

zof

t+

uh

x +

uh

y = 0,

uh

t +

u2h

x +

uvh

y = f vh gh

x+

b,x

,

vh

t +

uvh

x +

v 2h

y = f uh gh

y+

b,y

,


64/253

t +ho

u

x +ho

v

y = 0,

u

t +g

x = b,x

ho+f v,

v

t+g

y = b,y

ho f u.


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67/253

t u r b i n e s

t u r b i n e s

t u r b i n e s

(a) Strait between two oceans (b) Bay or estuary

(d) Headland(c) Strait between an island and a

semi-infinite landmass.

(i)

(ii)

(i)

(ii)

t u r b i n e s

t u r b i n e s

t u r b i n e s

L

L

L

L

L2

L1

L

L1 L2

0

5

10

15

20

25

(a) (b) (c) (d)

(a)/(b)

(a)/(b)

(a)/(c)

(a)/(c)

(a)/(d)

(a)/(d)(c)/(d)

(c)/(d)


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n+ 1

n

n= 15

n < 5


72/253

U

t +

F(U,Q)

x +

G(U,Q)

y =S(U),

QRx(U)x

Ry(U)y

= 0,

U = (h,uh,vh)T Q =

( ux

, uy

, vx

, vy

)T

F(U,Q) =

uhu2h+gh2/2 2hT uxuvh hT

vx

+ uy

, G(U,Q) =

vh

uvh hT

vx

+ uy

v2h+gh2/2 2hT vy

,


73/253

Rx(U) =

uhh

0

vhh

0

, Ry(U) =

0

uhh

0

vhh

, S(U) =

0

gh zx

x,b

+f vh

gh zy

y,b f uh

,

/t = h/t

gh= (gh2/2) ghz z= ho

T = 0

F(U) =

uho

ghoh

0

, G(U) =

vho

0

ghoh

,

ho(x, y)

U= (h,uho, vho)

T

n = 1

T = 0

(x, y)

Ne e(x, y)

i

e

U

t +

F(U,Q)

x +

G(U,Q)

y S(U)

ide= 0,


74/253

e

QRx(U,Q)

x Ry(U,Q)

y

ide= 0.

Uh

i

U(x, y) Uh(x, y) =Mk

Uk(x, y)k(x, y) =Mk

Uk(x, y)k(x, y),

Q(x, y) Qh(x, y) =Mk

Qk(x, y)k(x, y) =Mk

Qk(x, y)k(x, y),

{Uk} {Qk}

{Uk} {Qk} {k} {k}

n

M

M= 1

2(n+ 1)(n+ 2)

t

e

M

k

Uklk

ide

e

ix

F (Uh,Qh) +i

yG (Uh,Qh)

de+

e

(F (Uh,Qh) nx+ G (Uh,Qh) ny) ide=

e

S (Uh) ide

{ak} (a1, . . . , aM)T ,k

M


75/253

e

M

k

Qklk

ide+

e

ix

Rx(Uh) + i

yRy(Uh)

de

e

(Rx(Uh) nx+ Ry(Uh) ny) ide= 0,

n= (nx, ny)T

e e

e

n = 0

FGRx Ry

t

e

M

k

Uklk

ide

e

ix

F (Uh,Qh) +i

yG (Uh,Qh)

de+

e

F (Uh,Qh) nx+G (Uh,Qh) nyide= e

S (Uh) ide,

e

M

k

Qklk

ide+

e

ix

Rx(Uh) + i

yRy(Uh)

de

e

Rx(Uh) nx+Ry(Uh) nyide= 0.

{Uk} {Qk}

i = lk

M


76/253

d

dt{Uk} = M1 [B+ E S] , {Qk} = M1 [A G] ,

M

M(i,k)=

e

lilkde, i, k M,

B(i) = Bx(i)+ By(i) =

e

lixF (Uh,Qh)

de+

e

liyG (Uh,Qh)

de,

E(i) =

e

S (Uh) lide,

S(i) =

e

li

F(Uh,Qh)nx+ G(Uh,Qh)ny

de,

A(i) =

e

Rx(Uh) nx+Ry(Uh) ny lide, G(i) = Gx(i)+ Gy(i)=

e

lixRx(Uh)

de+

e

liyRy(Uh)

de.

iM. {Uk} {Qk}

d

dt{Uk} =LU(Uh,Qh), {Qk} = LQ(Uh).

{U(p)k } {U(p+1)k } t


77/253

U

(1)k

=U

(p)k

+ tLU(U

(p)h ,Q

(p)h ),

U(2)k

=

3

4{Upk} +

1

4

U

(1)k

+

1

4tLU(U

(1)h ,Q

(1)h ),

U

p+1k

=

1

3{Upk} +

2

3

U

(2)k

+

2

3tLU(U

(2)h ,Q

(2)h ),

{Q(i)k} =LQ(U(i)h ) t

t=

hm

0.5n2(

u2 +v2 +

gh)

hm

n= 1

n2

n

n

2n+ 1


78/253

Cd

CT ot = Cd+kt,

kt

P

P = kt

Cd+ktPt,

Pt CT ot.


79/253

kt

lv


80/253

Top ViewLine

Discontinuity y

x

u

u=uv=v

y

z

lv

lhLine

Discontinuity

y

x

Top V ew

v=v

u=u

u

y

z

lv

Side View

z

xu5u

h5h

lv

u

u

v,


81/253

lv

b

lv

lv

lv lh

lv


82/253

A

B

A

hL uL hR uR

A

F(hL, u

L, v

L) B F(h

R, u

R, v

R)

hL u

L h

R u

R


83/253

Line Discontinuity

Element, A

Element, B

x

y

hL

,uL

,vL

hR

,uR

,vR

x

t

hL

uL

vL

*

*

* hR

uR

vR

* * *

hL

uL

vL

hR

uR

vR

I+ = uL+ 2cL= uL+ 2c

L,

I = uR 2cR=uR 2cR,

(cL)2uL= (c

R)

2uR,

c(L,R) =

gh(L,R)

1

2

h

h

33

2

h

h

2+

1 F r2 + CTBF r

2

2

h

h CTBF r

2

2 = 0,

B

F r

h

h


84/253

|hR hL| CT

4

h/h = p (F r, B , 4)

g(z) =z

1 p(F r, B , 4),

z=cL, F r= (I

+ 2z) /z, B =Ag/z2; uL>0,

z=cR, F r= (I + 2z) /z, B =Ag/z2; uL 0,

I+ 2g(z)

z2

z2g(z)2

[I+ I 2 (g(z) +z)] , z=cR; uL


85/253

=ktu |u| , u

g(z) =z

1 p(F r, B , 4), =

2|x|Lf

3+ 3|x|Lf

2, |x| < Lf

1 , |x| Lf,

x

Lf

= 1/40


86/253

2000

Cd= 5 103

4

Cd = 5 104


87/253

Turbine fence

Upstream

Boundary

Downstream

Boundary

0 0.05 0.1 0.15 0.2 0.25 0.30

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Fr

h/h

B=0.6

4

=1/3

B=0.2

4

=1/3

B=0.4

4

=1/3

0 0.05 0.1 0.150

0.005

0.01

0.015

Fr

h/h


88/253

0 2000 4000 6000 8000 10000

0

1000

2000

3000

4000

0 2000 4000 6000 8000 10000

0

1000

2000

3000

4000

B = 0.6

4 = 1/3

Cd= 5 4 h= 10

10000

4= 1/3

= 1/40

n= 5

n.

n


89/253

B = 0.25

Cd= 1105

B = 0.5, 0.6

t = 80000

104


90/253

0 0.2 0.4 0.6 0.8 10

0.005

0.01

0.015

0.02

0.025

0.03

Position Along Fence

h/h

Intended Depth Change

Simulated Depth Change

1 2 3 4 5

6.75

6.8

6.85

6.9

x 104

n

P(W)

1 2 3 4 5

302.6

302.8

303

303.2

303.4

303.6

303.8

304

304.2

n

Q(

m3/s)

n

n

200 250 300 3505

5.1

5.2

5.3

5.4

5.5

5.6x 10

4

Q [m3/s]

P[W]

B=0.5

B=0.7

B=0.6

Cd = 1

105.


91/253


92/253

O p e n B o u n d a r y

O p e n B o u n d a r y

Ub= (hb, ubhb, vbhb)T.

h(s, t)

s s(b) s

ti,

hb= h(s(b), ti) ub=uin+ 2

ghin ghb .


93/253

x

t

h u*

*

hi n

ui n

vi n

hb

ub

vb

I+ I-

x

in

b

I =

u2gh

u(hho)g/ho ho

I+ =uin+ (hin ho)

g/ho

I =ub (hb ho)

g/ho

I

ub= (hb

ho)g/ho

I

ub hb


94/253

I

hb ub = vb = 0

(x,y,t) =exp[(x+L/4)2/(3h)2]

u(x,y, 0) =(x,y,t)

g/ho,

ho= 100 (x, y) [L, 0][0, L/10]

L = 1000

x =L

x = 0

ub = hb = 0.

hm=L/20

E=

B/2B/2

0L/2

1

2g2 +

1

2hu2

dxdy.

L2

E


95/253

5 4 3 2 1 0

x 105

100

100.1

100.2

100.3

100.4

100.5

100.6

x (m)

ho

+(

m)

5 4 3 2 1 0

x 105

100

100.1

100.2

100.3

100.4

100.5

100.6

x (m)

ho

+(

m)

5 4 3 2 1 0

x 105

100

100.1

100.2

100.3

100.4

100.5

100.6

x (m)

ho

+(

m)

5 4 3 2 1 0

x 105

100

100.1

100.2

100.3

100.4

100.5

100.6

x (m)

ho

+(

m)

n= 3

t= 0.44tf, t= 0.53tf, t= 0.61tf, t= 0.70tf.

tf= (L/2)/

gh

102, 105,

108,

n= 1, 2

i = (A/2) (kx+t) k = /

gho ho

=

A1 (k(x+L))e

jt

x 0,

H

(1)0

1 = 1

(kL) + (2ka/)

(kL)

(2ka/e) jka

(kL) ,

2 = 1jka (kL).

a/L = 0.1

ho = A/ho = 2.5 103


96/253

2a

L

y

x

= ( A / 2 ) c o s ( k x + w t )

8 9 10 11 12

1

0.5

0

0.5

1

t/T

2/A

8 9 10 11 120.08

0.06

0.04

0.02

0

0.02

0.04

0.06

0.08

t/T

2/A

(L, 0)

(R, 0),

kL = 0.5.

hb, ub)

R

3L

hb=ho+ A (k(x+L))ejt , ub= jgk A (k(x+L))ejt , vb= 0,

kL = 0.5

(L, 0) (0, R)


97/253

0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6

7

8

9

2||/A

kL

1 2 3 4 56.65

6.7

6.75

6.8

6.85

6.9

2||/A

n

2 3 4 5 60

1

2

3

4

5

6

7

8

R/kL

2||/A

kL=1.4

kL=3

kL=0.8

n

kL = 1.4

ka

1

kL = 1.4

kL = 0.8, 3


98/253


99/253


100/253

g x

=u

t +u

u

x+

Cd |u| uh

,

x u

Cd

U,

L

1

g x

= Uu

t +

U2

Lu

u

x+

U2

hd

Cd |u| uh

,

hd

= 1

Kc=

L

U ,

=Cd =CdL

ho

L

ho

Kc

C

d


101/253

0 10 20 30 400

0.2

0.4

0.6

0.8

1

L (km)

B/L

Ave~0.35

0 10 20 30 400

0.05

0.1

0.15

0.2

0.25

0.3

L (km)

Fr

0 0.5 1 1.5 20

0.5

1

1.5

2

Cd

1/K

c

Cd = 0.001

1/Kc 0.5, C

d 0.5 1/Kc 0.5, C

d 0.5

1/Kc 0.5, C

d 0.5

Q


102/253

0 10 20 30 400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Reduction in velocity (%)

P/

(rawk

ineticflux)

Figure 1.3(a)


103/253

u

t +u

u

x+g

x= FGC,

FGC

Q

cdQ

dt go =

L0

FGCdx 12

|ue| ue,


104/253

c=

L0

A1c dx Ac(x) o(t)

o =a (t) a

ue

g)

Cdu

2/h

Cd

L0

FGCdx=

L0

Cdu2

h dx+

L0

Ftdx=

L0

Cdh

dx+1

|Q| Q,

Ft FGC 1

P =Q

L0

Ftdx= 1|Q| Q2,

ga

t = cdQ

dt + (0+1) |Q| Q, 0=

L0

CdhA2c

dx+1

2

1

(Ac)e

2.


105/253

t= 1t

Q = ga (c)1 Q

0 = 0(c)2(ga)1

1 = 1(c)

2(ga)1

t =

dQ

dt + (0+1) |Q| Q.

0

0

0

1

1 = 0 1 1

Q 0

Pmax,

Pmax = gaQmax,

Qmax

0

0 = 0.22

0 0 0 0)


106/253

0 5 10 15 20 25 300.5

0.55

0.6

0.65

0.7

0.75

0

Q/Qmax

o

o

Pmax= 0.38

1

2 (Ac)e |ue|3

,

1

N

B

4

L0

Ftdx= NCTB

2 u2 =1Q |Q| , CT = (1 B2)

2

(1 B2/4)2 24,


107/253

2= (1 +4)

(1 +B) +

(1 B)2 +B(1 1/4)21

P=Q

L0

Ftdx= NCTB

2 ACu

3,

Pa=P =2P .

4 = 1/3

Pa = 2Pmax= 23(1 +B)gaQmax.

4= 1/3

4

CTB/2


108/253


109/253

L W ho Cd A A/ho F r L/U C dL/h


110/253

=(A/2)cos(wt-kx)TurbineFence

L

W

Ri

P2

P3

P1

x

yaa

Section aa

n = 3

4L

P1, P2

P3

4L, 0), (0, 0)

(L/2, 0)

u

y = 0


111/253

( |u|)2 /2g

|u|

.

x

4 = 1/3


112/253

5000 0 5000 10000

6000

4000

2000

0

2000

4000

6000

x (m)

y(m)

0.5 0 0.5 1 1.524.5

25

25.5

26

26.5

27

x/L

+h

o(m)

2 1 0 1 2 3 4

x 104

2

1

0

1

2

x 104

x (m)

y(m)

0.5 0 0.5 1 1.579

79.5

80

80.5

81

81.5

82

x/L

+h

o(m)

1000 0 1000 2000 3000

1500

1000

500

0

500

1000

1500

x (m)

y(m)

0.5 0 0.5 1 1.59.4

9.6

9.8

10

10.2

10.4

x/L

+h

o(m)

u

t/T = 8

y = 0


113/253

105 3/

(4L, 0)

(5L, 0)

P1, P2 P3

P1

P3

P2


114/253

0.4 0.6 0.8 1 1.2 1.4 1.6

x 105

0

0.5

1

1.5

2

2.5

3

3.5x 10

8

Q (m3/s)

AveragePower(W)

Extracted Power

Dissipated Power

Available Power

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.2

0.3

0.4

0.5

0.6

0.7

0.8

B

||(m)

Pt 1

Pt 2

Pt 3

0 0.1 0.2 0.3 0.4 0.5 0.60

10

20

30

40

50

60

70

80

90

B

Phase

Lag

(o)

Pt 1

Pt 2

Pt 3

P1, P2 P3

P1, P2 P3

2/3

P2 P3

P1

Cd

Cd

PGC


115/253

a

Qmax 3/ ) P P /PGC P /Pf P /Pd Cd,eff Q/Qmax a/a0

Pf Pd

a/a0

(4L, 0)

(5L, 0)


116/253

Cd,eff

Fr = 0 4 = 1/3 Fr = 0

Cd,eff = 0.35

Kc C

d

Cd


117/253

3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

P/Pmax

t/T

0 2 4 6 8 1 00

0.2

0.4

0.6

0.8

1

/M2

u()[m/s]

3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

P/Pmax

t/T

0 2 4 6 8 1 00

0.2

0.4

0.6

0.8

1

/M2

u()[m/s]

4 = 1/3


118/253

Cd,eff

Cd,eff=

CTB/2 F r = 0

Cd,eff Fr = 0

B

4

Fr = 0


119/253

102

101

100

101

102

0

0.5

1

1.5

2x 10

8

CTB/2

MaximumAv

eragePower(W)

102

101

100

101

102

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

CTB/2

Fr

4=1/6

4=3/4

4=17/20

4=1/3*

4=1/3

Cd,eff=CTB/2

Cd,eff = CTB/2 Cd,eff F r = 0

B

4

1/3


120/253

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0.2

0.2

0.2

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.

B

4

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

0.1

0.1

0.1

0.

0.1

0.1

0.1

0.1

0.1

0.

0.5

0.5

0.5

0.5

0.5

0.5

0.9

0.9

0.9

0.9

0.9

0.9

0.9

B

4

B = 0.5.

Cd,eff


121/253

0.1

0.1

0.1

0.1

0.2

0.2

0.2

0.2

0.3

0.3

0.3

0.3

0.3

0.3

0.4

0.4

0.4

0.4

0.4

0.4

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.80.9

0.9

0.9

0.9

0.9

0.9

0.9

B

4

0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.1

0.1

0.1

0.

0.2

0.2

0.2

0.2

0.3

0.3

0.3

0.3

0.4

0.4

0.4

0.4

0.5

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.7

0.8

0.8

0.80

.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

B

4

0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 .1

0.

1

0.1

0.

0.

2

0.2

0.2

0.2

0.

3

0.3

0.3

0.3

0.4

0.4

0.4

0.

0.5

0.5

0.5

0.5

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.8

0.8

0.8 0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

B

4

0.2 0.4 0.6 0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8

0

0.2

0.4

0.6

0.8

B

a4

0.1

0.1

0.1

0.1

0.1 0.1

0.1

0.1

.1

.

0.2

0.2

0.2

0.2

0.2

0.2

.

.

0.4

0.4

0.4

0.4

0.4

0.4

.4.

0.6

0.6

0.6

0.6

.

0.8

0.8

0 0.2 0.4 0.6 0.8

0

0.2

0.4

0.6

0.8

B

a4

0.1

0.1

0.1

0.1

0.1

0.1

0.1

0 .1

0.

1

0.2

0.

2

0.2

0.2

0.2

0.20.2

0.2

0.4

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

.

0.8

0.8

0.8

.

0 0.2 0.4 0.6 0.8

0

0.2

0.4

0.6

0.8

B

a4

0.1

0.1

0.1

0.1

0.10.1

0.2

0.2

0.2

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.

0.8

0.8

.0.8

0.8

0.8

0

B >0.95

B > 0.9.


122/253

0.4 0.6 0.8 1 1.2 1.4 1.6

x 105

0

0.5

1

1.5

2x 10

8

Q

AveragePower(W)

Line Sink

Roughness


123/253


124/253

0 2000 4000 6000

3000

2000

1000

0

1000

2000

3000

x (m)

y(m)

3 m/s

0 2000 4000 6000

3000

2000

1000

0

1000

2000

3000

x (m)

y(m)

3 m/s

o20

32

1

0 2000 4000 6000

3000

2000

1000

0

1000

2000

3000

x (m)

y(m)

3 m/s

1

30o

3

2

0 2000 4000 6000

3000

2000

1000

0

1000

2000

3000

x (m)

y(m)

3 m/s

30 m40 m

0 2000 4000 6000

3000

2000

1000

0

1000

2000

3000

x (m)

y(m)

3 m/s

40 m40 m

30 m

2 1 0 1 2

x 104

1.5

1

0.5

0

0.5

1

1.5x 10

4

x (m)

y(m)

90 m

40 m


125/253

6 6.5 7 7.50

1

2

3

4

x 105

t/T

P(W/m)

Point 1

Point 2

Point 3

6 6.5 7 7.50

0.5

1

1.5

2

2.5

x 105

t/T

P(W/m)

Point 1

Point 2

Point 3

a

Q0 3

P

PGC a/a0

hb=ho+(A/2) (tkx)

ub = g/hohb vb = 0 A= 3.5

Cd,eff 9.3 4= 1/3


126/253

8 0 k m

4 0 k m

8 k m

Tidal Strait

1.5 1 0.5 0 0.5 1 1.5

x 105

0

5

10

15

20x 10

4

x (m)

y(m)

21

5 5.5 6 6.5 7 7.5 858

58.5

59

59.5

60

60.5

61

61.5

62

t/T

Pt 1

Pt 2

Cd = 0.0025

15 .

105 3/


127/253

ga

(t) =cdQ

dt +0 |Q| Q+1 |Q| Q.


128/253

R1

=

R0

=

V=

ga

(t)

V

Q

I

V = LdIdt

+RI+ C

Idt,

L

C

R

L = c

R0 =

83

0 |Q|

R1 = 83 1 |Q|

R1

R1

R1


129/253

R0

g (1 4) = (c1+c4)dQ1dt

+ (0,1+0,4) |Q1| Q1+g (2 3) ,

g (2 3) = c2 dQ2dt

+0,2 |Q2| Q2+1 |Q2| Q2,

g (2 3) = c3dQ3

dt +0,3 |Q3| Q3,

Q = Q1 +Q2, ci 0,i

1 2 3

0,3 |Q3| c3


130/253

1

2

3

4

Q

1

Q

2

Q

3

c2, c3 c1+c4 0,2, 0,3 0,1+0,4

c2, c3 c1 +c4 0,2, 0,3 0,1 +0,4

4= 1/3

Cd=

)

a

Qmax


131/253

2000 0 2000 4000 6000 8000

4000

3000

2000

1000

0

1000

2000

3000

4000

5 m/s

4 6 8 10 12

x 104

0

5

10

15x 10

7

AveragePower(W)

Flowrate (m3/s)

4 6 8 10 12

x 104

0.7

0.8

0.9

1

1.1

1.2

1.3

(Q3

)max

/(Q3,0

)max

B=0

0.1

0.2

0.7

0.6

0.50.4

0.3

0 5000 10000 15000 20000

4000

2000

0

2000

4000

6000

8000

10000

12000

x (m)

y

(m)

8000 9000 1000011000120002000

1000

0

1000

x (m)

y(m)

5 m/s

5 m/s

Point 2(11250,650)

Point 1(8750,650)

4 6 8 10 12

x 104

0

0.5

1

1.5

2

x 108

Averag

ePower(W)

Flowrate (m3/s)

4 6 8 10 12

x 104

0.5

0.6

0.7

0.8

0.9

1

(Q1)max

/(Q1,0

)max

300 GW GC05

B=0

0.1

0.2

0.4

0.3

0.5

0.6

0.7


132/253

0,20,3

=

(Q3,0)max(Q2,0)max

2.

(Q2,0)max (Q3,0)max

Q1

Q2=Q1

1 +

0,20,3

+ 10,3

1/21,

P=1 |Q2| Q22 = 1 |Q1| Q21

1 +

0,20,3

+ 10,3

1/23.

Pref=gQ2,0(2,0 3,0) =0,2 |Q2,0| Q22,0

P

gQ2(2,0 3,0) = P

2 |Q2,0| Q22,0=

10,3

0,30,2

1 + 0,20,31/21 +

0,20,3

+ 10,3

1/23

.

2 1/0,3

0,2/0,3 2

0,2/0,3 2/33/2

(Q2)max / (Q2,0)max 1/31/2,

0,2/0,3 0 2 (Q2)max / (Q2,0)max 1/3.


133/253

0 1 2 3 4 50

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2

0,2

/0,3

0 1 2 3 4 50.3

0.3375

0.375

0.4125

0.45

0.4875

0.525

0.5625

0.6

(Q2

)max

/(Q2,0

)max

2

Q1

Pmax=2g (2,0 3,0) Q2,0.

2,0 3,0 = a2 (t) (2,0 3,0) Q2,0 a2(Q2,0)max | (t)|3/2

Pmax = 0.562ga2(Q2,0)max .

a2 a2

2 = 1


134/253


135/253

2000 0 2000 4000 6000 8000 1 0000

4000

3000

2000

1000

0

1000

2000

3000

4000

x (m)

y(m)

5 m/s

2 4 6 8 10

x 104

0

0.5625

1.125

1.6875

2.25x 10

8

AveragePower

(W)

Flowrate (m3/s)

2 4 6 8 10

x 104

0.5

0.75

1

1.25

1.5

(Q1

)max

/(Q1,0

)max,

(Q3)m

ax

/(Q3,0

)max

Current Limit

GC05

2000 0 2000 4000 6000 8000 1 0000

4000

3000

2000

1000

0

1000

2000

3000

4000

x (m)

y(m)

5 m/s

2 4 6 8 10

x 104

0

0.5625

1.125

1.6875

2.25x 10

8

AveragePower(W)

Flowrate (m3/s)

2 4 6 8 10

x 104

0.5

0.75

1

1.25

1.5

(Q1

)max

/(Q1,0

)max,

(Q3

)max

/(Q3,0

)max

CurrentLimit

GC05

2000 0 2000 4000 6000 8000 1 0000

4000

3000

2000

1000

0

1000

2000

3000

4000

x (m)

y(m)

5 m/s

4 6 8 10 12

x 104

0

0.625

1.25

1.875

2.5x 10

8

AveragePower(W)

Flowrate (m3/s)

4 6 8 10 12

x 104

0.5

0.75

1

1.25

1.5

(Q

1)m

ax

/(Q1,0

)max,

(Q3

)max

/(Q3,0

)max

CurrentLimit GC05

Cd =

0.0025


136/253


137/253


138/253

g( b) =c dQdt

+ (0+1) |Q| Q, c= L

0

A1c dx,

Q

L

Ac

0 1

= b

b

dbdt = QS0, b= 1S0

Q dt,


139/253

R1

=V=

S0

=a

(t)

ga

(t) =cdQ

dt + (0+1) |Q| Q+ 1

(S0/g)

t0

Q dt.

C = S0

g

L =c

R = (0+1) |Q| ,

1 |Q|


140/253

0,1=0,1(c)

2/(ga) =a, b=a

b, Q= Q

ga/(c)

t= 1t

(t) =

dQ

dt + (0+1) |Q| Q +b,

dbdt

=Q,

= g

2cSo,

0

So

Ac 0

P =1|Q|3) 0

Pmax = gaQmax,

ga

Qmax

a

=ab/a,

0 0 1

0 0


141/253

0 10 20 30 40 500.18

0.2

0.22

0.24

0.26

0.28

0.3

0

=9

=4

=2.5

=1.25

0 10 20 30 40 500.5

0.55

0.6

0.65

0.7

0.75

0.8

0

/

0

=9

=4

=2.5

=1.25

4 = 1/3


142/253

=(A/2)cos(wt-kx)TurbineFence

L

Rai

x

y

W

Rab

n = 3

4L

Rab A Qmax 3 0 0 Cd,eff P PB

o

o

o

o

o

o

A

Qmax 0

ab/a ab

Cd,eff

PB

Cd= 0.0025 Rai=


143/253

2 4 6 8

x 104

0

1

2

3

4

5

x 108

Flowrate (m3/s)

Avera

gePower(W)

0.6

0.5

0.4

B=0

0.8 0.70.75

0.9

0.85

0.3

0 0.2 0.4 0.6 0.80

2

4

ElevationAmplitude(m)

Blockage Ratio

0 0.2 0.4 0.6 0.80

50

100

PhaseLag(Deg)

|b|

|b|

Phase Lag

MaximumPower

|b|

| b|

4= 1/3

0

0

o

1


144/253

101

100

101

102

0

1

2

3

4

5x 10

8

CTB/2

P(W)

Case 64

Case 61

101

100

101

102

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

CTB/2

Fr

Case 61

Case 64

Cd,eff = CTB/2 Cd,eff = CTB/2 Fr = 0 Cd,eff

4 = 1/3

4= 1/3.

Cd,eff)

Cd,eff

4 = 1/3

4 = 1/2

Cd,eff

F r= 0


145/253

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

.

0.1

0.1

0.1

0.1 0.1

0.1

0.1

0.2

0.2

0.2

0.2

0.2

0.2

0.

2

0.2

0.4

0.4

0.4

0.4

0.4

0.

4

0.4

0.6

0.6

0.6

0.6 0.

6

0.8

0

0.8

B

a4

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

0.1

0.1

0.1

0.1

0.

0.2

0.2

0.2

0.4

0.4

0.4

0.6

0.6

0.8

B

a4

Cd,eff

Cd,eff


146/253

1 0 1 2

x 104

1

0.5

0

0.5

1

x 104

x (m)

y(m)

Tidal fence

104

3/ .

= 0.21


147/253

5000 10000 150000

0.5

1

1.5

2

2.5

3

3.5x 10

6

Flowrate (m3/s)

Averag

ePower(W)

Revised Calculation: 2.0E+06 W

Blanchfield et al. (2008): 2.8E+07 W

B=0

0.3

0.4

0.5

0.6

0.70.8

0.9

0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Elevation

Amplitude(m)

Blockage Ratio

0 0.2 0.4 0.6 0.80

2

4

PhaseLag(Deg)

|b|

|b|

Phase Lag

MaximumPower

|b| | b|

4 = 1/3

a

= 0.21


148/253

S(b) =So

1 +

bhe

,

he So

dbdt

=Q (1 +b)

,

= a/he = 0

= 0

T =0 +1)


149/253

S

o

L

A ( x )

x

Top View Side View

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

1/2

(V)

max

T

=0.075

T

=0.15

T

=0.5

= 1

= 0.5

T = 0.075.

t 1/2t

V

Q =dV/dt,

(1/2t) =

d2V

dt2 +1(0+1)

dV

dt

dV

dt +1

(1 + (+ 1)V )

1/(+1) 1

.

(1/2t) =

d2V

dt2 +1(0+1)

dVdt dV dt +V 2(V )2 + 22 (V)3 ,

= 1.

V

1/2

1T

0.5

= 1

T 0.15

T 0.15 0.5 = 1

T,


150/253

7.613 0 9.811.5

1.45 0 8

= 1

= 1 he

ab/a 1.1

1.5S0 = 1

0.5

0 = 10 = 1 = 4 = 0

= 0.5),

= 0.5

= 0.5


151/253

0 0.5 1 1.5 2

1

0.5

0

0.5

1

t/T

Q

0 0.5 1 1.5 20.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

t/T

S/S0

0 = 10 = 1 = 4 = 0

= 0.5

= 0.5

T

T

T

T

T 0

= 4

T


152/253

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

t/T

P

= 2.5, T = 10.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

t/T

P

= 4, T = 10.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

t/T

P

= 9, T = 10.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

t/T

P

= 2.5, T = 50.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

t/T

P

= 4, T = 50.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

t/T

P

= 9, T = 50.

P / (g2a2/ (c))

= 0.5

= 1

= 0

= 0.2

= 0.5

0 5 10 150

0.1

0.2

0.3

0.4

0.5

a2

/a

T=10, =0.5

T=100, =0.5

T=50, =0.5

T=10, =0.2

T=10, =0.05

a2,

a

T .

= 1.


153/253

0

0

Pmax/gaQmax,

= 4 .

.

= 0.22

s =Smax Smin, s,0 >0

= 0

0

0

/0 s/s,0

0


154/253

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0

DimensionlessAveragePower

0.5 1 1.5

0.14

0.15

0.16

=2.5

=4

=9

0 20 40 60 80

0.14

0.16

0.18

0.2

0.22

0.24

0

=0.2

=0.5

=0

0 10 20 30 400.55

0.6

0.65

0.7

0.75

0

S

/S,0

,/

0

=0.5

=0

=0.2

Documents

Thesis Tidal Power