cfd modelling of dam spillway aerator

51 Pages·2015·1.55 MB·English

Master Thesis
TVVR 15/5014
CFD MODELLING OF DAM
SPILLWAY AERATOR
_______________________________________________
Raphaºl Damiron

Division of Water Resources Engineering
Department of Building and Environmental Technology
Lund University
CFD MODELLING OF DAM
SPILLWAY AERATOR
By:
Raphaºl Damiron
Master Thesis
Division of Water Resources Engineering
Department of Building & Environmental Technology
Lund University
Box 118
221 00 Lund, Sweden
Water Resources Engineering
TVVR-15/5014
ISSN 1101-9824
Lund 2015
www.tvrl.lth.se
Master Thesis
Division of Water Resources Engineering
Department of Building & Environmental Technology
Lund University
English title: CFD modelling of dam spillway aerator
Author(s): Raphaºl Damiron
Supervisor: Magnus Larson
James Yang
Examiner: Rolf Larsson
Language English
Year: 2015
Keywords: <spillway; aerator; CFD;VOF; 3D flow>
i
LUND UNIVERSITY
Abstract
Lunds Tekniska H¨ogskola
Department of Building and Environmental Technology
Master of Science Thesis
CFD MODELLING OF DAM SPILLWAY AERATOR
by Rapha¨el DAMIRON
Thepurposesofthismasterthesisarethesimulationoftheaeratorairflowdrivenbythe
spillway water flow in the Bergeforsen dam and the behavior of the flow in the stilling
basin. Aerators are employed to supply air at critical locations in the flow where low
pressure and cavitation may occur in order to protect the structure. The simulations
were carried out, first in 2D and then in 3D, with the software FLUENT/GAMBIT
describing the spillway and the stilling basin. Results were mainly concentrate on the
interfacebetweenphases,airentrainmentbutalsovelocityandpressureoftheflow. Lim-
ited data from laboratory experiments were available; however, their usefulness might
be limited due to scale effects occurring in such two-phase flow problems.
Acknowledgements
This work was carried out during my time as a student at the Faculty of Engineering,
Lund University. I would like to thank all persons who supported me in Lund and
contributed to the achievement of this master thesis, in particular:
Thank you to Prof. Magnus Larson for introducing and supervising this project,
for his interest and contribution using his practical experience.
Many thanks to Prof. James Yang from Vattenfall who initiated the project and
assist me with the help of his Phd. student: Penghua Teng.
I am grateful to Ali Al Sam from the Division of Fluid Mechanics who took on
his time to help me with the simulation.
ii
Contents
Abstract i
Acknowledgements ii
1 Introduction 1
1.1 Project description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature review 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Cavitation on spillways . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Method to reduce cavitation damage . . . . . . . . . . . . . . . . . . . . . 6
2.3.1 Effect of air content . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Air entrainment on spillways . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4.1 Self-aerated flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4.2 Artificial aeration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2.1 Types of aerators . . . . . . . . . . . . . . . . . . . . . . 10
2.4.2.2 Aerator submergence . . . . . . . . . . . . . . . . . . . . 14
3 Theory 15
3.1 Governing equations for CFD . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Turbulence Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 VOF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Bergeforsen dam 20
4.1 Site description and adaptations . . . . . . . . . . . . . . . . . . . . . . . 20
5 Numerical model and setup 23
5.1 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Computational domain and grid . . . . . . . . . . . . . . . . . . . . . . . 23
5.2.1 2D-cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2.1.1 2D-case without aerator . . . . . . . . . . . . . . . . . . . 24
5.2.1.2 2D-case with aerator. . . . . . . . . . . . . . . . . . . . . 25
iii
iv
5.2.2 3D-cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6 Results and discussion 29
6.1 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.1.1 Necessity of an aerator . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.1.2 Water surface profile . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.1.3 Velocity and flow circulation . . . . . . . . . . . . . . . . . . . . . 32
6.1.4 Pressure at the bottom . . . . . . . . . . . . . . . . . . . . . . . . 33
6.1.5 Air entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.2 Discussion and accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.2.1 Verification of the model . . . . . . . . . . . . . . . . . . . . . . . . 37
6.2.2 Uncertainty and error in CFD simulations . . . . . . . . . . . . . . 38
7 Conclusion 40
Bibliography 41
Symbols, Constants v
Symbols
a Local speed of sound
C Mean air concentration of developed aeration
a
d Depth of flow at the beginning of the ramp
0
e Total energy
o
k Turbulent Kinetic Energy (TKE) per unit mass
m˙ Mass transfer from phase q to phase p
qp
m˙ Mass transfer from phase p to phase q
pq
M Turbulent Mach number
t
n;n+1 Time step
p pressure intensity
p Local pressure
0
p Vapor pressure of water
v
P Production of turbulent kinetic energy due to
k
the mean velocity gradients
P Production of turbulence kinetic energy due to
b
buoyancy
q Unit discharge of air
a
q Unit discharge of water
w
S User-defined source terms of k
k
S User-defined source terms of ǫ
ǫ
∗
S Traceless viscous strain-rate tensor component
ij
S User-defined mass source for each phase
αq
t Time
t Ramp height
r
t Offset/duct height
s
u Velocity magnitude
i
′
u Fluctuating component of velocity magnitude
i
U ,u¯ Average flow velocity
i i
V Volume flux through a face based on normal ve-
f
locity
V Volume of cell
X Horizontal distance from end of ramp to jet
i
impact location
X Horizontal distance from end of ramp to
n
centerline of jet at impact location
Symbols, Constants vi
Y Elevation at impact point
i
Y Elevation of centerline of jet at impact point
n
Y Contribution of the fluctuating dilatation to ǫ
M
α Ramp angle
α Volume fraction of a fluid in a cell
q
β Air entrainment coefficient
β Coefficient of thermal expansion
Buoyancy
δ Kronecker delta
ij
ǫ Turbulence dissipation rate per unit mass
σ Cavitation number (index)
θ Spillway slope
µ Dynamic viscosity
µ Eddy/Turbulent viscosity
t
ρ Density
τ Viscous stress tensor component
ij
Constants
k - ǫ Model Constants C = 1.44
1ǫ
C = 1.90
2
C = 0.33
3ǫ
−
Turbulent Prandtl numbers σ = 1.00
k
σ = 1.20
ǫ
Abbreviations
CFD Computational Fluid Dynamics
RANS Reynolds-Averaged Navier-Stokes
VOF Volume Of Fluid