Computational Modeling of Flow

over a Spillway

In Vatnsfellsstífla Dam in Iceland

Master’s Thesis Presentation

Chalmers University of Technology

2007 – 02 - 02

Presentation Schedule

• Introduction and background

• Method

• Theory

• Results

• Conclusions and future work

Vatnsfellsvirkjun hydroelectric scheme

from above

The spillway at Vatnsfell – from below

The spillway at Vatnsfell – the crest

The splitter wall and cover from above

The chute cover from below

The spillway and the stilling basin

Layout

chute, bottom outlet and stilling basin

The spillway – characteristics

• Function: cope with accidental flooding

• Height above stilling basin bottom: 27.5 m

• Lenght of spillway crest: 50 m

• Equipped with a splitter wall and cover to

prevent overtopping of the chute sidewalls

• The velocity of the water is above 20 m/s

(=72 km/hour!) where it flows into the

stilling basin

If neither splitter wall nor chute cover...

The stilling basin – characteristics

• Function: Decrease flow velocity in order to

decrease risk for erosion in the river wally

downstream the basin

• Equipped with 28 energy dissipating baffles

(height from 1.5 to 2.0 m)

• Length ca. 33 m and the width increasing from

22 m in the upstream part to 33 m in the

downstream part, depth ca. 7 m

• Downstream the stilling basin is a 35 m long

rock rip-rap made of rocks with diameter of

0.4 – 1.2 m

Background and goals

• In 1999 Vattenfall in Sweden did hydraulic

experiments for the spillway with a 1:30 model

• In the experiments flow was investigated over

the spillway, through the bottom outlet and in the

stilling basin

• Goals of the present study:

– investigate flow over the spillway and in the stilling

basin with computational methods (CFD)

– compare CFD-results with experimental results

Vattenfall’s hydraulic model

Aspects • Spillway:

– water head in the reservoir vs. the discharge capacity of the spillway

– Water level along the chute sidewalls

– Pressure acting on the chute bottom

• Stilling basin:

– Water level

– Pressure acting on the baffles and the end sill

– Flow velocity out of the basin

Method 1. Identify the computational domain to be modeled

(according to the goals!)

2. Draw the computational domain in 3D in Autodesk

INVENTOR

3. Import the geometry into the mesh making software

GAMBIT and divide the computational domain into

computational cells of different size in GAMBIT

4. Import the mesh into the CFD-solver FLUENT, set up

the numerical model, compute and monitor the solution

5. Postprocessing with FLUENT and MATLAB; examine the results and consider revisions to the model

The computational domain

• Three different domains:

– One for head vs. flow discharge

– One for water level and pressure in the

spillway chute

– One for water level, pressure and flow velocity

in the stilling basin

• Why different domains?

– to spare computational power and get more

precise results

Computational domain nr. 1

Computational domain nr. 2

Computational domain nr. 3

Grids nr. 1 – 7 as seen from above

- one grid for each of the seven different cases with flow

discharge of 50 – 350 m3/s, ca. 653 000 cells/grid

Cut through grids nr. 1 and 7 in the

downstream end of the reservoir by the

spillway crest – different water levels

• Grid to the left: designed for flow discharge of 50 m3/s

• Grid to the right: designed for flow discharge of 350 m3/s

Grid nr. 8: finer in the chute than

grids nr. 1 – 7, ca. 1393 000 cells

• The mesh in the spillway bottom

– To the left: mesh 7 which is NOT specifically designed to

investigate pressure and water level in the spillway chute

– To the right: mesh 8 which is specifically designed to investigate

pressure and water level in the spillway chute

Mesh nr. 8: finer in the chute than meshes

nr. 1 - 7

• The grid perpendicular to the splitter wall

– To the left: mesh 7 which is NOT specifically designed to

investigate pressure and water level in the spillway chute

– To the right: mesh 8 which is specifically designed to investigate

pressure and water level in the spillway chute

Grid nr. 9:

different types of mesh; consisting of both

hexahedron cells and tetrahedron cells

ca. 498 000 cells

Grid nr. 9 includes the stilling basin though coarse in view of the size of the

computational domain

Grid nr. 9: includes a simplified rock

rip-rap downstream the basin

Setting up the numerical model

• Define

– Material properties (air, water, concrete)

– Boundary conditions (inlet, outlet, walls,

air pressure,...)

– Operating conditions (air pressure, gravity, temperature...)

– Turbulence model (standard k-ε)

– Initial solution (nB: steady flow)

– Convergence criteria

Theory – equations of motion

and the VOF method

• The continuity equation for incompressible flow:

• The momentum equation for incompressible flow:

• VOF method in FLUENT

– assumes that the two phases (air and water) are not

interpenetrating

– denoting αq as the volume fraction of the q-th phase three possibilities

for a given cell can be noted:

– i) : the cell is empty of the q-th phase,

– ii) : the cell is full of the q-th phase,

– iii) : the cell contains the interphase between the q-th phase and one or more phases.

0i iu∂ =

0

1i i j j iD u p uν

ρ= − ∂ + ∂ ∂

0q

α =

1qα =

0 1q

α< <

Main results! Comparison to the experimental results

Water reservoir head vs. flow discharge; Q=CBH3/2

where Q= flow discharge, C= discharge coefficient, B = length of crest, H=head

Discharge coefficient (C) vs. flow discharge

Water level along the chute sidewalls

Pressure on the chute bottom

– location of investigation points

Pressure on the chute bottom

point A: 23 % deviation from exp-results

Pressure on the chute bottom

point B: 16 % deviation from exp-results

Pressure on the chute bottom

point C: 9 % deviation from exp-results

Water surface in the stilling basin

Water surface in the stilling basin

Water surface in the stilling basin

Water level in the left upstream corner

of the stilling basin

Volume fraction of water in the basin

(longitudinal profile) – determines the water level

Velocity contours in the spillway and

the stilling basin

Velocity vectors in the stilling basin

Pressure on the baffles in the first baffle row

Pressure on two baffles in the first row (deviations from experimental results in

parantheses)

Baffle

Pressure on

upstream face

(kPa)

Pressure on downstream

face (kPa)

Resultant pressure

(kPa)

B1CFD_case

9

151 18 133 (53 % dev.)

B1CFD_case

6

155 1 154 (46 % dev.)

B1EXP 272 -14 286

B2CFD_case

9

199 - 2 201 (16 % dev.)

B2CFD_case

6

200 -11 211 (11 % dev.)

B2EXP 233 -5 238

Static pressure in the stilling basin

Dynamic pressure in the stilling basin

Total pressure in the stilling basin

Total pressure on the basin end sill - a view under the water surface in the

downstream end of the basin

Total pressure on the basin end sill

- location of investigation points

Location Pressure on

upstream face

(kPa)

Pressure on

Downstream

face (kPa)

Resultant

pressure

(kPa)

EXP

Results

(kPa)

K 32.4 29.2 3.2 2.5

L 35.9 34.3 1.6 8.7

M 31.3 26.6 4.7 3.7

N 29.3 26.2 3.1 0.3

Total pressure on the basin end sill

Velocity profile above end sill right under the water surface

Main results - summary

• Good agreement is reached between the experiments and CFD calculations for the following aspects:

– head vs. discharge capacity (Q=CBH3/2)

– pressure in the spillway chute

– flow velocity above the basin end sill

• Worse agreement is reached for:

– pressure on baffles in the upstream end of the basin

– water depth along chute sidewalls and in the left upstream corner of the basin

– pressure on the basin end sill

Future work – what might to be

done better or added?

• Calculate the flow through the bottom

outlet

• Better resolve the turbulent boundary

layers close to walls

⇒ finer mesh

⇒ more computational power

⇒ even parallel processing

What more can be done? - e.g. time dependent calculations

Thank you!