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KSCE Journal of Civil Engineering (0000) 00(0):1-10

Copyright ⓒ2016 Korean Society of Civil Engineers

DOI 10.1007/s12205-016-1257-z

−1−

pISSN 1226-7988, eISSN 1976-3808

www.springer.com/12205

Water Engineering

Investigation of Flow Over Spillway Modeling and Comparison

between Experimental Data and CFD Analysis

Serife Yurdagul Kumcu*

Received May 14, 2014/Revised 1st: August 13, 2015, 2nd: January 26, 2016/Accepted April 24, 2016/Published Online June 24, 2016

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Abstract

As a part of design process for hydro-electric generating stations, hydraulic engineers typically conduct some form of model

testing. The desired outcome from the testing can vary considerably depending on the specific situation, but often characteristics such

as velocity patterns, discharge rating curves, water surface profiles, and pressures at various locations are measured. Due to recent

advances in computational power and numerical techniques, it is now also possible to obtain much of this information through

numerical modeling. In this paper, hydraulic characteristics of Kavsak Dam and Hydroelectric Power Plant (HEPP), which are under

construction and built for producing energy in Turkey, were investigated experimentally by physical model studies. The 1/50-scaled

physical model was used in conducting experiments. Flow depth, discharge and pressure data were recorded for different flow

conditions. Serious modification was made on the original project with the experimental study. In order to evaluate the capability of

the computational fluid dynamics on modeling spillway flow a comparative study was made by using results obtained from physical

modeling and Computational Fluid Dynamics (CFD) simulation. A commercially available CFD program, which solves the

Reynolds-averaged Navier-Stokes (RANS) equations, was used to model the numerical model setup by defining cells where the flow

is partially or completely restricted in the computational space. Discharge rating curves, velocity patterns and pressures were used to

compare the results of the physical model and the numerical model. It was shown that there is reasonably good agreement between

the physical and numerical models in flow characteristics.

Keywords: dam structures, spilllway modeling, CFD anaysis, numerical model, physical model

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1. Introduction

Hydraulic design of a spillway and a stilling basin has been

one of the most studied subjects in hydraulic engineering.

Properly designed approach flow conditions, spillways and

stilling basins will be able to pass flood flows efficiently and

safely to downstream of dams. Physical scale modeling has been

used in the design and investigation of hydraulic structures for

over 100 years. A hydraulic model is still a precision device for

the experimental investigation of flow over a spillway structure,

which can give reliable information only if it is designed correctly

(Willey et al., 2012).

With increasing computer processing capacity, numerical

simulations for hydrodynamic processes become attractive,

including flow over spillways. A comparison of these numerical

results with experimental or prototype data is still required for

calibration and validation. Computational Fluid Dynamics (CFD) is

a branch of numerical modeling that has been developed for

solving problems involving fluid flow. This includes applications

involving fluid-solid interaction, such as the flow of water in a

river or over and around hydraulics structures. There is therefore

considerable interest on the part of hydraulic engineers into the

applicability of CFD to model fluid flow. The majority of available

literature on applying CFD to spillway modeling came from studies

using Flow-3D, which solves the Reynolds-averaged Navier-

Stokes (RANS) equations (Ho et al., 2003; Savage et al., 2001;

Kim, 2010; Chanel, 2008). To track the free water surface (air/

water interface) as it moves in time and space, the program

implements a sophisticated algorithm called the Volume-of-Fluid

(VOF) method. The VOF method tracks the amount of fluid in

each computational cell. Cells range from completely empty to

completely full and the volume changes as flow moves in or out

from neighboring cells. Flow-3D also uses a Fractional Area/

Volume Obstacle Representation (FAVOR) method to define

obstacles (Hirt and Sicilian, 1985). This method allows Flow-3D to

use fully structured computational grids that are much easier to

generate than the deformed grids used by most other CFD

programs. Teklemariam et al. (2001) prepared a report outlining the

use of Flow-3D and it discusses how Flow-3D was successful in

matching the physical model test results for discharge as well as

flow patterns and velocities in modeling (Flow-3D User’s manual,

2012). The report also introduced the ability of Flow-3D to provide

discharge measurements that were very close to empirical

estimates. Teklemariam et al. (2008) discuss the great potential for

TECHNICAL NOTE

*Assistant Professor, Civil Engineering Dept., Necmettin Erbakan University, Konya, Turkey (Corresponding Author, E-mail: yurdagulkumcu@gmail.com)

Serife Yurdagul Kumcu

−2−KSCE Journal of Civil Engineering

the use of CFD for the assessment of a design, as well as screening

and optimizing of hydraulic structures and cofferdam layouts. They

conclude that CFD has been successful in optimizing the final

conceptual configuration for the hydraulics design of the project,

but recommend that physical modeling still be used as a final

confirmation.

This paper provides experimental studies performed on Kav ak

Dam and analyses the stability of spillway design by using

FLOW-3D model. It compares the hydraulic model tests with

FLOW-3D simulation results and gives information on how

accurately a commercially available Computational Fluid Dynamic

(CFD) model can predict the spillway discharge capacity and

pressure distribution along the spillway bottom surface.

2. Physical Model

A 1/50-scaled undistorted physical model of the Kavsak Dam

spillway and stilling basin was built and tested at the Hydraulic

Model Laboratory of State Hydraulic Works of Turkey (DSI).

The model was constructed of plexiglas and was fabricated to

conform to the distinctive shape of an ogee crest. The spillway

has 45.8 m in width and 57 m long with a bottom slope of 125%.

The length of the stilling basin is about 90 m. During model tests,

flow velocities were measured with an ultrasonic flow meter.

Pressures on the spillway were measured using a piezometers

s

ç

Table 1. Upstream and Downstream Operating Conditions of the

Kavsak Dam

Run Upstream reservoir

elevation (m)

Downstream tailwater

elevation (m)

1 306.55 168.00

2 311.35 174.50

3 314.00 178.90

4 316.50 182.55

Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at the

Approach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approach

in the Laboratory

Investigation of Flow Over Spillway Modeling and Comparison between Experimental Data and CFD Analysis

Vol. 00, No. 0 / 000 0000 −3−

board reading provided the average pressure reading at each

pressure tap location. Both the upstream reservoir lake level and

downstream tailwater elevations were measured using piezometers.

A control valve was used to set the flow in the physical model.

The model was operated at four different upstream reservoir

elevations as given in Table 1. The 3rd and 4th runs in Table 1

belong to corresponding Q1000 and Q10000 discharge values of the

project. The downstream tailwater elevations was adjusted by

another control gate located far downstream of the model

(Kumcu, 2010).

3. Approach Flow Conditions

In order to obtain uniform flow conditions and decreasing the

energy losses through the approach, velocity must be less than 5

m/s ( entürk, 1994). As the flow velocities are high and flow is

vortex flow, the streamlines are separated in front of the gate

piers and the flow is not uniform. In order to obtain uniform flow

conditions some modifications were made in the reservoir

topography. The piers were extended into the dam reservoir and

their shapes were changed to pass the flow safely. As the piers

behave as a console they are also extended longitudinally in

vertical direction up to mixing with the dam body (290 m above

the talweg) for stability issues. Flow measurement sections and

modifications which were done after experimental investigations

are given in Fig. 1. Flow velocity measurements belonging to

original project and experimentally modificated project are given

in Fig. 2. It is clear from the Fig. 2 that, approach flow velocities

are decreasing after doing modifications. In the theoretical study

of the project, the discharge capacity of the spillway was

computed considering that all gates would be completely open

for all reservoir water levels. Discharge rating curve varies withS

ç

Fig. 2. Flow Velocity Measurements at the Approach Belonging to Theoretical Project Design and the Design which is Observed after the

Experimental Modifications

Serife Yurdagul Kumcu

−4−KSCE Journal of Civil Engineering

the water level over the crest. As the spillway rating curve is an

important parameter to show the consistency and accuracy of the

model application to prototype, the spillway rating curves obtained

from the theoretical and experimental studies are compared with

each other. According to Savage and Johnson (2001) the theoretical

flow discharge through a spillway can be expressed by:

(1)

where Q denotes the flow discharge, C discharge coefficient, L

the spillway crest length or width and H upstream head measured

from the crest to the unaffected upstream water stage. The

discharge coefficient, C is not constant. It is influenced by a

variety of factors including the depth of approach, relation of the

actual crest shape to the ideal nappe shape, upstream face slope,

downstream apron interference, and downstream submergence

(Design of small dams, 1977). Each of the conditions has ranges

and design curves that describe the effect of the parameters

mentioned. The theoretical flow discharges were calculated for

various water depths to obtain the rating curve over the spillway

by using Eq. (2). Experimental measurements were also gained

by using gauging of water depths for a given discharge. Comparison

of theoretical discharge measurements with experimental study

is shown in Fig. 3. It was seen in Fig. 3 that, although both values

are very close to each other, when the discharge capacity is

higher than Q= 3000 m3/s. For a given discharge, the flow can

pass over the spillway with lower flow depths than the

theoretical calculations, so it is in the safe side.

4. Pressure and Velocity Measurements on Spill-

way

Cavitation depends on the pressure and speed of flow, which is

shown by the Cavitation number. Office of the United States

claims an paper under the title “Cavitation on spillways and

chutes” (1990), presented the Cavitation Number as follows:

(2)

where; σ is the dimensionless cavitation number; P is the

absolute pressure (N/m2); Pu is the vapor pressure of the fluid (N/

m2); r is the flow density (kg/m3) and U is mean flow velocity

(m/s). If the flow pressure drops below the vapor pressure the

water begins to vaporize, just like if it was boiling (Wagner,

1967). As the bubbles can't escape they will implode. The

pressures fluctuations associated with bubble collapse produce

noise and vibrations and, eventually can lead to the structure

failure (Vischer and Hager, 1997). Cavitation can cause damage

in a very short time (Falvey, 1990). The cavitation number at

which cavitation starts is here referred as the critical cavitation

number (Kokpinar and Gogus, 2002). According to Erfanian-

Azmoudeh and Kamanbedast (1990) the critical cavitation

number is σ = 0.25, and cavitation will occur if σ< 0.25.

In order to investigate the flow characteristics and to calculate

the cavitation numbers; flow depths, the pressures and flow rates

were measured at Km: 22.5, 30.5 and 43.0 (Spillway crest is

Km: 0 + 000.00) for the reservoir discharge capacities of Q = 500

m3/s, 1000 m3/s, 2500 m3/s, 3856 m3/s and 5053 m3/s considering

that for spillway gates are fully open. Flow depths were measured

directly, and pressures were measured by using manometers. The

details of the experimental study and the calculations are given in

the report of Hydraulic Model Studies of Kavsak Dam and HPP

(Kumcu, 2010).

In the original design case, when the flow discharge is 3856

m3/s and 5053 m3/s, some negative pressures were attended

along the spillway and cavitation numbers are calculated. These

results indicate that the velocities were very high and the

pressure variations strongly affect the flow in this area. Flow

characteristics which were observed at these points presented in

Table 2. It is clearly seen that, cavitation numbers are under the

critical cavitation number, σ= 0.25 at Km: 0+043.00 for

Q = 3856 m3/s and 5053 m3/s. Therefore the cavitation risk is

real. Protection of the surface from cavitation erosion is usually

QCLH

3

2

---

=

σPPv–

1

2

---ρU2

---------------

=

Fig. 3. Rating Curves of Theoretical Project Design and the Design

which is Observed after the Experimental Modifications

Table 2. Flow Characteristics Along the Spillway from the Physical

Model

Cross-section

No

Distance from

Spillway crest

(Km)

Q

(m3/s)

U ave

(m/s)

Cavitation

Number

1 0+022.50 500 20.67 0.413

2 0+030.50 500 15.04 0.923

3 0+043.00 500 15.47 0.870

1 0+022.50 1000 18.21 0.544

2 0+030.50 1000 18.38 0.632

3 0+043.00 1000 20.51 0.509

1 0+022.50 2500 19.14 0.493

2 0+030.50 2500 20.40 0.549

3 0+043.00 2500 26.26 0.329

1 0+022.50 3856 20.30 0.429

2 0+030.50 3856 20.17 0.583

3 0+043.00 3856 27.78 0.218

1 0+022.50 5053 20.33 0.415

2 0+030.50 5053 21.72 0.517

3 0+043.00 5053 29.20 0.212

Investigation of Flow Over Spillway Modeling and Comparison between Experimental Data and CFD Analysis

Vol. 00, No. 0 / 000 0000 −5−

achieved by introducing air next to the flow structure surface.

Aeration devices are designed to introduce artificially air within

the flow upstream of the first location where cavitation damage

might occur. Aerators are designed to deflect high velocity flow

away from the chute surface. The water taking off from the

deflector behaves as a free jet with a large amount of interfacial

aeration. This is made by means of aeration devices located on

the bottom and sometimes on the sidewalls of the structure

(Chanson, 2002). If the gate piers are not going on longitudinally

along the spillway and the spillway is steep and short, aeration

slot located at the downstream end of the gate piers is used for

aeration (Chanson, 2005). In this design tip of the gate piers also

increases. In order to prevent cavitation, aerators were fixed at

the downstream end of the gate piers. In order to increase the

amount of air introduced by aerators the deflectors were placed

in front of the aerators (Demiröz, 1986). The plan view of

experimental arrangement of aerators and the damps is shown in

the Fig. 4.

It can be clearly seen from Fig. 5 that, aerators and deflector

are working very efficient, and face of the spillway has been

aerated enough by aerators.

5. Numerical Simulation

After serious modification are made on the original project, a

comparative study was made for flow over a spillway structure

using results obtained from 1/50 scaled physical modeling with

full scaled (prototyped) Computational Fluid Dynamics (CFD)

simulation. The commercially-available CFD package FLOW-

3D Version 10.0 was used in the simulation of the flow field. The

CFD package applies finite-volume method to solve the RANS

equations.

One of the main characteristics of turbulent flow is fluctuating

velocity fields. These fluctuations cause mixing of transported

quantities like momentum, energy and species concentration and

thereby also fluctuations in the transported quantities. Because of

the small scales and high frequencies of the fluctuations they are

too computationally expensive to simulate directly in practical

engineering situations. Instead, the instantaneous governing

equations are time-averaged to remove the small scales and the

result is a set of less expensive equations containing additional

Fig. 4. Plan View and Section View of the Aerator and Damp

Fig. 5. Aerators and Damps: (a) Shape of the Aerators and Deflectors (Chanson, 2005), (b) Application of the Aerators and Deflectors in

the Experimental Study

Serife Yurdagul Kumcu

−6−KSCE Journal of Civil Engineering

unknown variables. These unknown (turbulence) variables are

determined in terms of modeled variables in turbulence models.

This process of time-averaging is called Reynolds averaging.

When this is done the solution variables in the instantaneous

Navier-Stokes equations are decomposed into the mean (time-

averaged) and fluctuation components (Reynolds decomposition,

Margeirsson, 2007). For the velocity components:

(3)

where and are the mean and fluctuating velocity components

respectively. Scalar variables are decomposed in a similar way.

When expressions of this form for the flow variables are substituted

into the instantaneous continuity and momentum equations and a

time (ensemble) average is taken the Reynolds-averaged Navier-

Stokes (RANS) equations are yielded. They can be written as;

(4)

(5)

Here the overbar on the mean velocity has been dropped. The

velocities and other solution variables now represent time-

averaged values instead of instantaneous values. The additional

terms that have appeared are called Reynolds stresses

and must be modeled in order to close Eq. (5). Because

turbulence is the main cause of entrainment, a turbulence-

transport model must be used in connection with the air-

entrainment model and the traditional k-epsilon (ε) turbulence

model be employed in the present study. It is one of the two-

equation models which are considered the simplest of the so

called complete models of turbulence. Ever since it was proposed

in 1972 its popularity in industrial flow simulations has been

explained by its robustness, economy and reasonable accuracy

for a wide range of turbulent flows. The details of the k-ε model

can be found in Kim (2007). Free surfaces are modeled with the

Volume of Fluid (VOF) technique, which was first reported in

Nichols and Hirt (1975), and more completely in Hirt and

Nichols (1981). Trademarked as TruVOF, this technique is one of

the defining features of the program and provides three important

functions for free surface flow: location and orientation of free

surfaces within computational cells, tracking of free surface

motion through cells, and a boundary condition applied at the

free surface interface.

The location of the flow obstacles is evaluated by the program

implementing a cell porosity technique called the fractional area/

volume obstacle representation of FAVOR method (Hirt, 1992).

The free surface was computed using a modified volume-of-fluid

method (Hirt and Nichols, 1981). For each cell, the program

calculates average values for the flow parameters (pressures and

velocities) at discrete times using staggered grid technique

(Versteeg and Malalasekera, 1996). On the Cartesian coordinate

system (x, y, z), governing equations for analysis of incompressible

three dimensional flow are given below by Kim et al. (2010):

(6)

Where, are velocity components in the coordinate

directions , are fractional areas open to flow

in the coordinate directions of , ρ is density and RSOR is a

density source term.

(7a)

(7b)

(7c)

where, VF is a fractional volume open to flow, p is pressure,

are body accelaration in the coordinate direction

, and are viscous accelerations in the coordinate

direction .

The VOF method is based on the assumption that the two

fluids are not interpenetrating. Each phase (fluid) is given a

variable that accounts for how much percentage of each

computational cell is occupied by the phase. This variable is

called a volume fraction of the phase. The volume fractions of all

phases sum up to unity in each computational cell. The fields for

all variables and properties are shared by the phases and represent

volume-averaged values. Variables and properties represent either

only one phase or a mixture of phases in a given cell depending

on the volume fractions of the phases in the cell. If is

equal to 1, the control volume will be full of fluid, and F is equal

to 0, no fluid will exist in a control volume. Furthermore, in the

case of a free water surface, F is shown to have the value

between 0 and 1. Applying function F to Eq. (6) governing

equation becomes:

(8)

FLOW-3D version V10.0 was used to simulate flow over the

Kavsak Dam along with the renormalized group turbulence

model. A rectangular grid was defined in the computation

domain shown in Fig. 6. Total number of grid cells was

approximately 6.24E+06 in which only 4.36E+06 of them were

active. The corresponding uniform mesh size used in meshing

was ∆x = ∆y = ∆z = 0.5 m with rectangular grid system and 40-hr

elapsed computational duration. There were many tests have

been conducted to validate the usefulness of the air-entrainment

model. In each one, after finding the mesh size for each case, the

air entrainment rate coefficient was selected as Cai r = 0.5. Souders

and Hirt (2004) also indicated that, the value of air entrainment

coefficient, Cair, is expected to be less than unity because only a

portion of the raised disturbance volume is occupied by air. Cair =

0.5 assumes on average that air will be trapped over about half

uiuiu′

i

+≡

uiui

′

∂ρ

∂t

------∂

∂xi

------ ∂ui

()+0=

∂

∂t

---- ρui

()

∂

∂xj

------ ρuiuj

()+∂p

∂xi

------

–∂

∂xj

------ u∂ui

∂xj

-------∂uj

∂xi

-------2

3

---δij

∂ul

∂xl

-------–++=

+∂

∂xj

------ ρui′u′j

–()

ρui′u′j

–()

VF

∂ρ

∂t

------∂

∂x

----- uAx

()

∂

∂y

----- vAy

()

∂

∂z

----- wAz

()+++ RSOR

ρ

----------

=

uvw,,()

xyz,,()AxAxAx

,,()

xyz,,()

∂u

∂t

------1

VF

------uAx

∂u

∂x

------vAy

∂u

∂y

------wAz

∂u

∂z

------++

⎝⎠

⎛⎞

+1

ρ

---∂p

∂x

------– Gxfx

++=

∂v

∂t

----- 1

VF

------uAx

∂v

∂x

----- vAy

∂v

∂y

----- wAz

∂v

∂z

-----++

⎝⎠

⎛⎞

+1

ρ

---∂p

∂y

------– GyGyfy

+++=

∂w

∂t

-------1

VF

------uAx

∂w

∂x

-------vAy

∂w

∂y

-------wAz

∂w

∂z

-------++

⎝⎠

⎛⎞

+1

ρ

---∂p

∂z

------– Gzfz

++=

GxGyGz

,,()

xyz,,() fxfyfz

,,()

xyz,,()

Fxyzt,,,()

∂F

∂t

------ 1

VF

------∂

∂x

----- FuAx

()

∂

∂y

----- FvAy

()

∂

∂z

-----FwAz

()+++0=

Investigation of Flow Over Spillway Modeling and Comparison between Experimental Data and CFD Analysis

Vol. 00, No. 0 / 000 0000 −7−

the surface area. Usta E. (2014) selected air entrainment rate

coefficient 0.5 as the value which is suitable for most cases

recommended by Flow 3D User Manuel, 2012.

To simulate given flow, it is important that the boundary

conditions accurately represent what is physically occurring.

Because the flow is defined in Cartesian coordinates, there are

six different boundaries on the computational mesh domain. The

boundary conditions on the mesh were set as follows: sidewalls

y- common no slip, non-porous/wall; top z-pressure boundary

with gauge pressure equal to zero (atmospheric); bottom z-no

slip/wall; left x-local stagnation pressure based on upstream total

head H over the spillway crest with a hydrostatic pressure

distribution; and right x-local static pressure based on downstream

tailwater elevation with a hydrostatic pressure distribution. 50 m

upstream and 200 m downstream of the spillway crest were used

as the boundary conditions of left x and right x, respectively.

In running the FLOW-3D CFD software, computation modules

of viscosity and turbulence, gravity, air-entrainment, and density

evaluation were activated for all cases studied. Since there are no

prototype data available for comparison to the CFD solution, the

data from the physical model have been scaled to prototype

dimensions.

6. Discussion and Results

The main purpose of this part of the studies to compare results

from a physical model with that of a CFD model for flow over an

ogee crest spillway and through stilling basin. The flow rates

over the spillway crest and free surface elevations, depth-

averaged velocity distributions, and the pressures acting on the

crest and on the stilling basin are used to compare the differences

between the physical model and the CFD model. The existing

Kavsak Dam physical model data have been used as a baseline

of this comparison (Kumcu, 2010).

Table 2 shows the physical model measured flow rates (QPM)

and the numerically calculated flow rates from the CFD model

(QCFD). The results have been normalized to allow a comparison

in their simplest form in Fig. 4. The 10000 years return period

parameters, (H0)10000 = 16.46 m and Q10000 = 5053 m3/s, from

physical model are used as the basis. In Fig. 7 the static head

above crest, H0, is normalized by the (H0)10000 and shown in the

abscissa. The discharge Q is normalized by Q10000 and shown on

the ordinate. Using the physical model and its discharge as

observed standard, the relative percent difference in discharge is

calculated in Table 3. The relative percent difference at a given

(H0)/(H0)10000 is defined as (QCFD - QPM)/QPM x100 and shows that

the CFD model agrees within 3.2% in average with the physical

model.

The data for Q10000 = 5053 m3/s in the physical model was used

for the comparison of free surface elevation between the physical

model and the CFD model as seen in Fig. 8. Since similar results

Table 3. Comparison of Observed Flow Rate Versus Computed

Flow Rate (prototype scale)

Run QPM

(m3/s)

QCFD

(m3/s)

Percent

difference

1 1000 1034 3.4

2 2500 2415 3.4

3 3856 4001 3.7

4 5053 5170 2.3

Fig. 6. (a) Solid Model, (b) Solid Model with Mesh of the Kavsak

Dam Spillway used in the CFD Simulations (final design)

Fig. 7. Comparison between the Physical Model (PM) and the

Numerical Model (CFD) Predictions for Flow Rates Over

Spillway

Fig. 8. Comparison of Free Surface Elevations between Physical

Model and CFD Model for Q= 5053 m3/s

Serife Yurdagul Kumcu

−8−KSCE Journal of Civil Engineering

were obtained, other simulation plots and comparison with

physical model data will not be given here. In the comparison,

free surface data is plotted in elevation where the crest is at 300

m above the sea level. As seen in the figure, the majority of the

points overlap exceptionally well, while only the hydraulic jump

roller region on the profile seems to exhibit any notable error.

This is due to the difficulties of both CFD modeling and

measurement in physical model in accounting effects of strong

turbulence at the hydraulic jump region and flow aeration with

related consequences on bulking of flow depth.

Figures 9 shows 2D view of depth-averaged velocity contours

obtained from the CFD model for the flow rate of Q = 5053 m3/s.

Since most of the free surface elevation data of physical model

overlaps the CFD model data, the depth-averaged velocity

values of both models also show similarities. The maximum

value of depth-averaged velocity was found as approxiamtely 32

m/sec which creates a potential risk for cavitation damage.

The distiribution of air antrainment rate obtained from the

CFD model data along with the flow over spillway and through

stilling basin for the flow rate of Q = 5053 m3/s was given in

Fig. 9. CFD Solution of 2D Depth-averaged Velocity Distribution

Along the Spillway Structure for Q10000 = 5053 m3/s (velocity

values are in m/s)

Fig. 10. 2D-CFD Solution of Volume Fraction of Entrained Air Con-

tours Along the Spillway Structure for Q10000 = 5053 m3/s

Fig. 11. Comparison of CFD and Physical Model Pressures for: (a) Q = 1000 m3/s, (b) Q = 2500 m3/s, (c) Q = 3856 m3/s, (d) Q = 5053 m3/s

Vol. 00, No. 0 / 000 0000 −9−

Figure 10. According to the Fig. 7, the bottom surface of the

spillway downstrean of the aerator structure, where potentially

under the risk of cavitation damage, is sufficiently aerated. Since

the value of 1-3% of air concentration can be generally accepted

as a critical value for the prevention of cavitation damage, CFD

results promise always more than 10% of air conenration value.

With the horizontal distance starting from the crest axis the

bottom pressure distributions (in Pascal) along the spillway and

stilling basin have been shown on Figs. 8 to provide a comparison

of spillway and stilling basin average pressures for four different

flow rate conditions on the physical model as; Q = 1000 m3/s,

2500 m3/s, 3856 m3/s, and 5053 m3/s. Pressures from the CFD

model compared quite favorably with the scaled physical model

data with the exception of pressure data obtained around baffle

blocks located at the longitudinal distances of 50.5 m and 86 m

from the spillway crest. On prototype scale, the maximum

absolute pressure difference was predicted at the longitudinal

distance of 86 m from the crest as ∆H = 19.2 m for Q10000 = 5053

m3/s. The possible source of error was considered from the

selection of uniform mesh size as ∆x = ∆y = ∆z = 0.5 m

throughout the computation domain. For a finer meshing with

nested mesh blocks (e.g. ∆x = ∆y = ∆z = 0.25 m or finer) better

predictions around baffle blocks could be expected from the

CFD model that will be part of the another subsequent research

study.

The data presented in Fig. 11 demonstrates that CFD modeling

is capable of reasonably predicting pressures on spillways and

stilling basins. The concern of modeling supercritical flow

transitioning to subcritical flow has been still a difficult problem

to solve, however numerical advances are rapidly reducing the

inherent difficulties of this problem (Savage and Johnson, 2006).

7. Conclusions

In this study, 1/50-scaled physical model was conducted in

order to investigate flow conditions and rating curves for full

openings of the radial gates of the spillway and flow over the

spillway for the operating conditions in the Kavsak Dam. A

series of experiments are tested in the State Hydraulic Works

Hydraulic Laboratory. Some modifications were done to obtain

uniform flow conditions and decreasing the energy losses

through the approach. Cavitation risk was tested flow along the

spillway. Aerators and damps are added as there was cavitation

risk. After observing final design for the approach flow

conditions and spillway, an attempt was made to simulate flow

over a spillway structure using commercially available CFD

software. Obtained results from the full-scaled (prototyped) CFD

model was compared to existing physical model data of the

Kavsak Dam and HEPP.

The flow rate results show that the CFD model provided a

reasonable solution. The average relative percent difference

between the CFD model and the physical model was obtained as

3.2%.

The CFD results obtained for free surface elevation and depth-

averaged velocity fit generally the physical model data, whereas

some difficulties observed at the flow transition from supercritical

to subcritical through the hydraulic jump region mainly due to

effects of high turbulence and flow bulking.

Although numerical methods offer a potential to provide

solutions with increasing accuracy, physical model studies are

still considered as the basis from which all other solution

methods used.

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