8th International PHOENICS User Conference - 8IPUC Luxembourg, 17-21 May, 2000 THREE-DIMENSIONAL HYDRODYNAMIC MODEL COUPLED WITH DEPTH AVERAGED TWO-DIMENSIONAL.

8th International PHOENICS User Conference - 8IPUCLuxembourg, 17-21 May, 2000

THREE-DIMENSIONAL HYDRODYNAMIC MODEL COUPLED

WITH DEPTH AVERAGED TWO-DIMENSIONAL MODEL :

CASE OF THE MEDJERDA-CAP-BON WATER INTAKE.

Zouhaier HAFSIA (1) et Khlifa MAALEL (2)

Ecole Nationale d’Ingénieurs de Tunis. Laboratoire d’Hydraulique.B.P. 37 - Le Belvédère, 1002, Tunis, Tunisie.

E-mail : (1) [email protected] (2) [email protected]

1

8IPUCENIT - LMHE

National Tunisian Engineering School (ENIT)

Geographic location of the Laroussia dam and its waterworks

B. L

AR

OU

SSIA

Bizerte

Sidi Salem D.

TebourbaTunis

Nabeul

Sejnane D.

Siliana D.

Belli

Tunisia

LibyaAlgeria

Cap

-Bon

Sidi El

Barrek D.

Joumine D.

Med

jerd

a

Algeria

Medjerda

M e d i t e r r a n e a n s e a

Gulf ofTunis

2

8IPUC

Great Channel

MedjerdaCap-BonChannel

Fondek

Jedid

Bejaoua

JoumineMedjerdaChannel

ENIT - LMHE

3

8IPUC

Plane view of the three water intakes of the Laroussia dam

Nomenclature

MCB : Medjerda-Cap-Bon water intake GC : Great-Channel intake C : Hydroelectrical power intake

Crest Level (m NGT)

34.84 34.70

32.00/31.50

GC

16 m3/s13 m3/sMCB

36

3632

28

28

3250 m3/s

C

87°68°

Medjerda Stream

Laroussia dam

ENIT - LMHE

4

8IPUC

Muds deposits in front of the MCB water intake

Deposition zones in front of the MCB and along its junction with the GC intake

GCMCB Muds

deposited

22/09/95

In 1989, volume of depositis was estimated to : 15 700 m3.

In 1989, The volume of deposits was estimated to 484 000 m3 along the

MCB channel and to 674 500 m3 along the GC.

28/10/98

Upstream view of the Laroussia dam on the Medjerda

Laroussia D. (1956)

C1956

Concave bank in front of the MCB intake

GC1974

MCB1985

22/09/95

ENIT - LMHE

5

8IPUC

• Identification of the essential causes of the muds deposits in front of the MCB water intake.

• Proposition of solutions to reduce the sedimentation along the MCB channel.

Objectives

Hydraulic Model with fixed bed

Coupled hydrodynamic model (3-D/2-DH )

ENIT - LMHE

Similitude Ratios Values Gm/GP

Horizontal scale 1/100

Vertical scale 1/25

Velocity 1/5

Time 1/20

Discharge 1/12500

Distortion 4/1

Relative roughness 64/1

6

8IPUC

Similitude ratios of the hydraulic model of the Laroussia dam

2/1rr hU

Re ’=1400

r

r

L

h

rr

rr

r FLg

U,1

rer

rr RLU

,1

ENIT - LMHE

7

8IPUC

Experimental Channel in Hydraulic Laboratary (E.N.I.T.)

12180

b) longitudinal view

1322080001750 1650

8750 2603

a) plane viewUpstream Downstream

2000

800

2336

900

900

4300

600

700

900

730

1050

1825

 Distances are mesured in mm 

ENIT - LMHE

8

8IPUC

Depth avareged hydrodynamic model

(2-DH)

• Identify the currents structure in the MCB convergent

• Explain the islet of muds deposits formation in front of the MCB intake

• To impose more realistic boundary conditions along the MCB intake crest

• Comparaison criteria between the diffrents studied modifications

Objectives of hydrodynamic models

Coupled three dimensional hydrodynamic model

(3-D/2-DH)

ENIT - LMHE

9

8IPUC

Mathematical formulation of 3-D Hydrodynamic model

)(

)(

333231

232221

131211

)(

)(

)(

)()()()(

c

b

a

SJqqqJ

qqqJ

qqqJ

WVU

zyxyxyzxzxxzyzyJ )()()(

PPPx

PS xxxu

; PPP

y

PS yyyv

et PPP

w

PS zzzw

= t +

22211 )()( yxyxzxzxzyzyq 222

22 )()()( yxyxzxzxzyzyq

22233 )()()( yxyxzxzxzyzyq

))((

))(())((2112

yxyxyxyx

zxzxzxzxzyzyzyzyqq

))((

))(())((3223

yxyxyxyx

zxzxzxzxzyzyzyzyqq

))((

))(())((3113

yxyxyxyx

zxzxzxzxzyzyzyzyqq

ENIT - LMHE

10

8IPUC

PHOENICS : Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series

),()(

)()()(

2212

1211

SJqqJ

H

qqJ

HVHUH

bxxxu PHPHPHx

S

)()()( byyyv PHPHPHy

PS

)()()(

2

22

CH

vuugbx

2

22

CH

vuvgby

6/1RKC 16/190

25.8

d

gK

Mathematical formulation of 2-DH Hydrodynamic model

ENIT - LMHE

11

8IPUC

Covariante Derivatives Ordinary Derivatives

pjkkj

pnbjj

pnbnb aaUgaaUaUU )).( ().() ().(~

111

nc

ncncLLHHSSNNWWEEpP baaaaaaaa

Covariante formulation in the PHOENICS code

Traitement of the pressure-velocity coupling :

SIMPLEST Algorithm (SIMPLE ShorTened)

ENIT - LMHE

12

8IPUC

Multiblocks grid in 2-DH

CCM : Collocated Covariant Method

NX x NY = 118x20 = 2360min = 38.5 °

’

Angle of non orthogonality of BFC gridBlock 1

Blocages

Block 2

Multiblocks grid in 2-DH of the Laroussia dam and MCB intake

ENIT - LMHE

Three dimensional grid of Laroussia dam reservoir

(I=20)

13

8IPUC

3-D Grid

Staggered Covariante Formulation

NX x NY x NZ = 76x20x10=15200 min= 37.3°

Free surface

blocagesWall

Inlet

P3

P2P1

MCB

BGE

Outlet

P4 profile grid on the protype P4 profile grid on the model

ENIT - LMHE

14

8IPUC

2-DH grid Vérification. Case of the MCB intake openning :

Uin = 4.3 mm/s

(m2/s)

Streamlines and equipotential field

Direct Method

ENIT - LMHE

15

8IPUC

2-DH Hydrodynamic model

Visualized bottom currents

Qder = 1,3 l/s

Simulated currents : D = 3.6 10-2 m2/s

Uin = 4.3 mm/s

ENIT - LMHE

16

8IPUC

D = 3.6 10-2 m2/s (on hydraulic model)

V (m/s)

Uin = 4.3 mm/s

Comparaison of the currents structures on hydraulic model

scale and prototype scale

V (m/s)

D = 71.74 m2/s (on prototype scale)

Uin = 5 * 4.3 mm/s

Vsim = 0.015 m/s Vmes = 0.019 m/s

ENIT - LMHE

17

8IPUC

Principles of modifications

* Deposits in front of the MCB intake are inevitable

* Reduce the bottom currents ascention

* Correction of the MCB intake shape

Différent types of training wall studied on the Laroussia hydraulic model

(1) : Training wall opned by

its two extremities

36

32

(2) : Training wall opned by

downstream extremity

36

32

(3) : Training wall opned by

upstream extremity

36

32

ENIT - LMHE

18

8IPUC

Choice criteria between the diffrent alternatives

Visualised bottom Currents

Qder = 1.3 l/s

Qder = 1.3 l/s

Qder = 1.3 l/s

Simulated Surface currents

Uin = 4.3 mm/s

t = 5 10-5 m2/s

Secondary currents structure in vicinity of the Laroussia dam

0.005

0.005

0.005

ENIT - LMHE

2

8IPUC

19

With Approach channel

Bottom Currents

Qder = 1,3 l/s

Qder = 1,3 l/s

ENIT - LMHE

20

8IPUC

With Approach channel

Surface Currents

Qder = 1,3 l/s

ENIT - LMHE

21

8IPUC

Comparaison of secondary currents structures upstream of the MCB intake (before and after

approach channel)

0.005 m/s 0.005 m/s

Uin = 21.5 mm/s; t = 2.5 10-2 m2/s

Uin = 4.3 mm/s; t = 5 10-5 m2/s

Before modification

0.005 m/s

After modification

0.005 m/s

ENIT - LMHE

22

8IPUC

Another coupled model: Centrifugal pump predimensioning

H. Azouz et R. Zgolli

Common boundary

Volute beak

Blade

to treat the interactions between rotor flow (rotational) and volute flow :

Iterative procedure was needed in MB-FGE

ENIT - LMHE

23

8IPUC

Another couled model: Centrifugal pump predimensioning

H. Azouz et R. Zgolli

(Pa)

Volute beak

(Pa)

ENIT - LMHE

24

8IPUC

Conclusion

Depth Averaged two dimensional hydrodynamic model is sufficient to

reproduce the visualised currents structure in the MCB convergent.

The currents structure in the convergent are not influenced by the

dispersion coefficient.

Constant turbulence viscosity model is adopted for the 3-D

Hydrodynamic model to overcome the diffuculty of application of the

standard k- Model in severe non orthogonal grid

An approach channel is proposed to reduce the bottom current

ascending toward the MCB intake and allowed the inversion of the

secondary currents.

In the case of centrifugal pump flow, the interactions between rotational

and irrotational flow is treated by iterative coupled 2-D model (H Azouz).

ENIT - LMHE