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Computational Modeling of Flow over a Spillway In Vatnsfellsstífla Dam in Iceland

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### Computational Modeling of Flow over a SpillwayIn 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

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

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

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

- Identify the computational domain to be modeled (according to the goals!)
- Draw the computational domain in 3D in Autodesk INVENTOR
- Import the geometry into the mesh making software GAMBIT and divide the computational domain into computational cells of different size in GAMBIT
- Import the mesh into the CFD-solver FLUENT, set up the numerical model, compute and monitor the solution
- 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

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 cellsca. 498 000 cells

Grid nr. 9 includes the stilling basinthough coarse in view of the size of the computational domain

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.

Water reservoir head vs. flow discharge; Q=CBH3/2where Q= flow discharge, C= discharge coefficient, B = length of crest, H=head

Volume fraction of water in the basin (longitudinal profile) – determines the water level

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

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

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

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