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

Master’s Thesis Presentation Chalmers University of Technology 2007 –

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**Presentation Schedule**

Introduction and background Method Theory Results Conclusions and future work

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**Vatnsfellsvirkjun hydroelectric scheme from above**

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**The spillway at Vatnsfell – from below**

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**The spillway at Vatnsfell – the crest**

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**The splitter wall and cover from above**

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**The chute cover from below**

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**The spillway and the stilling basin**

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**Layout chute, bottom outlet and stilling basin**

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**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

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**If neither splitter wall nor chute cover...**

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**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

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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

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**Vattenfall’s hydraulic model**

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**Aspects Spillway: Stilling basin:**

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

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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

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**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

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**Computational domain nr. 1**

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**Computational domain nr. 2**

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**Computational domain nr. 3**

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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 cells/grid

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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

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**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

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**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

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Grid nr. 9: different types of mesh; consisting of both hexahedron cells and tetrahedron cells ca cells

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

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**Grid nr. 9: includes a simplified rock rip-rap downstream the basin**

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**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

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**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.

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**Main results! Comparison to the experimental results**

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**Water reservoir head vs**

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

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**Discharge coefficient (C) vs. flow discharge**

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**Water level along the chute sidewalls**

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**Pressure on the chute bottom – location of investigation points**

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**Pressure on the chute bottom point A: 23 % deviation from exp-results**

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**Pressure on the chute bottom point B: 16 % deviation from exp-results**

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**Pressure on the chute bottom point C: 9 % deviation from exp-results**

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**Water surface in the stilling basin**

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**Water surface in the stilling basin**

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**Water surface in the stilling basin**

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**Water level in the left upstream corner of the stilling basin**

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

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**Velocity contours in the spillway and the stilling basin**

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**Velocity vectors in the stilling basin**

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**Pressure on the baffles in the first baffle row**

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

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

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**Static pressure in the stilling basin**

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**Dynamic pressure in the stilling basin**

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**Total pressure in the stilling basin**

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

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**Total pressure on the basin end sill - location of investigation points**

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**Total pressure on the basin end sill**

Location Pressure on upstream face (kPa) Downstream face (kPa) Resultant pressure EXP Results 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

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**Velocity profile above end sill right under the water surface**

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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

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

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Thank you!

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