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Turbulent Flow Simulations Through Tarbela Dam Tunnels Considering the
Effect of Sediment Particles
Conference Paper · July 2010
DOI: 10.1115/ESDA2010-24201
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Muhammad Abid
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COMSATS Institute of Informaton Technology, Wah Catt, Pakistan
Kyungpook National University
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Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis
ESDA2010
July 12-14, 2010, Istanbul, Turkey
ESDA2010-24201
TURBULENT FLOW SIMULATIONS THROUGH TARBELA
DAM TUNNELS CONSIDERING THE EFFECT OF SEDIMENT
PARTICLES
Muhammad Abid
Faculty of Mechanical Engineering
GIK Institute of Engineering Sciences & Technology,
Topi 23640, NWFP, Pakistan
Tel:92-938-271858, Fax:92-938-271889,
abid@giki.edu.pk
ABSTRACT
The sediments inflow in the Tarbela reservoir is resulting in
reduction in water storage capacity and damage to the tunnels
carrying water to the power generating units and ultimately to
the plant equipment. The turbulent flow in tunnel-2 of the
Tarbela Dam Project (TDP) is analyzed for the sediment
particles tracking in ANSYS CFX. The particles flow in the
tunnel is considered random and striking the tunnel walls at
different impact angles. Langrangian particles tracking
approach is used for the particles deposition, which is a oneway coupling phenomena as the carrier phase is unaffected by
the sediment particles because of particle mass loadings less
than 0.2 and unaltered flow field. Reynolds Stress Model
(RSM) is used for turbulent modeling as it takes care of
anisotropic effects near the tunnel walls and is used in flows
with strong curvature, swirling flows, flows with strong
acceleration/retardation.
Keywords: Tunnels, Turbulent flow, Sediment particles,
Turbulent modeling, Tarbela Dam
NOMENCLATURE
CD
dp
E
FD
g
k
m
n
p
drag coefficient
particle diameter
erosion rate density
drag force
gravitational acceleration
erosion model constant
particle mass
erosion model constant
fluid pressure
Adnan Aslam Noon
Faculty of Mechanical Engineering
GIK Institute of Engineering Sciences & Technology,
Topi, NWFP, Pakistan
Tel:92-938-271858, Fax:92-938-271889,
maangiki@yahoo.com
Rep
p
f
Uc
Up
U
β
γ
ρf
ρp
τp
μ
ν
particle Reynolds number
particulate phase volume fraction
fluid phase volume fraction
fluid velocity
particle velocity
particle relative velocity
particle mass loadings
particle impact angle
fluid density
particle density
particle response time
fluid dynamic viscosity
fluid kinematic viscosity
INTRODUCTION
Tarbela Dam Project comprises of six tunnels, three of which
are used for power generation and three for irrigation purposes.
Tunnel number 2 is analyzed which is used for power
generation. The maximum (in summer) and minimum (in
winter) pool levels are 1550 ft and 1300 ft respectively. This
tunnel is about half a mile long 858.7 m (2820 ft). The gross
head is 444 ft. Intake portion is at an elevation of (1225 ft)
above the sea level. The straight portion is placed at an
elevation of (1112 ft). The diameter of water at inlet and outlet
portion is 10.96 m (36 ft) and 4.87 m (16 ft) respectively. The
average pressure difference between two levels i.e. ΔP is 950
kPa. The water is discharging at an average flow rate of 978.63
m3/s. The construction material is concrete with steel liner
placed inside the concrete. The tunnel water is divided into six
branch pipes which end at the turbine inlet section.
This paper presents a computational fluid dynamics (CFD)
based erosion prediction model and its application to water flow
1
Copyright © 2010 by ASME
in the tunnel at different critical locations of the tunnel
geometry specifically at the main bend, straight portion and
branch pipes. This comprehensive procedure consists of three
major components: flow simulation, particle tracking, and
erosion calculation. The effect of the particle rebound model on
the particle trajectories as well as erosion pattern in the main
bend, straight portion and branch pipes is also investigated.
PARTICLE
SELECTION
TRANSPORT
MODEL
During the analysis, considering wide particle size distribution,
built-in erosion models in CFX were integrated with the
Lagrangian particle tracking routines, and one-way coupled
Eulerian-Lagrangian model was selected [1] for the current
study.
The choice of one-way or full coupling for sediment particles
depends on the mass loading i.e. β and is defined as the ratio of
the particulate mass per unit volume flow [2] to the fluid mass
per unit volume flow and is expressed as;
β=
rp ρ p
(1)
rf ρ f
If is less than 0.2, one-way coupling is used. Therefore oneway coupling of sand particles is used to visualize and analyze
the particles once they enter the tunnel. One-way coupling
simply predicts the particle paths during post-processing based
on the flow field, but without affecting the flow field. In
addition it is assumed that the particles do not interact with each
other. As sediment particles concentration calculated is almost
1.0% [3], so β = 0.0255 is considered.
Governing equations of fluid motion
Navier–Stokes equations The governing equations of
flow employed in CFX-11 are discussed in this section. The
continuity and momentum equations are given in Eqs. (2) and
(3), respectively
∂ρ
+ ∇. ( ρU ) = 0
∂t

∂ ρU
( ) + ∇.( ρU ×U )=
p
σ =−
ρ
I+
 T
µ 
[∇U + ∇U ]
ρ
( )
(4)
Generally, a small, rigid spherical particle entrained in turbulent
pipe flow encounters many forces, some of which can be
justifiably neglected in the particle equations of motion in this
study [4]. These neglected terms include pressure (buoyancy)
force, virtual mass force, the Basset force, and Brownian
diffusion. Gravitational settling and the Saffman lift force are
also neglected. Therefore, the governing particle equation of
motion is given as follows:

dU p
= FD (U c − U p )
dt
(5)
The drag force per unit mass and is defined as;
FD =
and
τp =
1
τp
CD
Re p
(6)
24
is the particle response time and is defined as;
ρ p d p2
18µ
(7)
Rep is the particle Reynolds number based on the relative
velocity between the particle and the carrier phase and is
defined as;
Re p =
d p (U − U p )
ν
(8)
Discharge coefficient is implemented in CFX by the Schiller
Naumann correlation. As the Schiller Naumann correlation is
derived for flow past a single spherical particle, it is only valid
in the dilute limit of very small solid phase volume fractions.
EROSION MODELING
(2)
(
)
(3)
B + ∇. − ρ u × u + σ
t
∂

U is the instantaneous velocity vector, U is the mean
velocity component, u is the fluctuating velocity

component due to turbulence (i.e., U= U + u ). ρ u × u is
the Reynolds stress; and the stress tensor, is given by
In the present study, for the water flow conditions considered as
the sand concentration is fairly small so that the effect of
sediment particles on the carrier fluid is assumed negligible.
Thus, one-way coupling method is employed to calculate
sediment particles trajectories in this study [5]. Finnie erosion
model is used which require the less number of model constants
and is easy to implement. One-way coupling assumes that the
presence of solid particles has little effect on the flow field.
Usually, for a given mass of sediment, the trajectories of tens of
thousands of particles that are randomly distributed at the inlet
is determined to obtain statistically representative sediment
2
Copyright © 2010 by ASME
impingements on the wall in order to acquire representative
erosion profiles for the geometry. Impingement information,
such as particle impact speed, impact angle, and impact
locations, are obtained from the particle trajectory calculations.
The impingement information is applied to erosion models to
finally predict the erosion caused by sediment particles within
the entire simulated geometry. The properties of pipe wall
material as well as particle shape can be accounted for to
quantify the erosion.
Governing Equation to predict erosion rate is given below as;
E =k ⋅ V p2 ⋅ f ( γ )
particle tracks in conjunction with a transient flow. Therefore to
develop an instantaneous erosion map at several points in time
the flow field was saved after every 4 sec and particle tracks
were then run on each of these result files as post-processing.
Length 858.70 m
(9)
where,
1
1
f ( γ ) = cos 2 ( γ ) , if tan ( γ ) >
3
3
=
f ( γ ) sin ( 2γ ) − 3sin 2 ( γ ) , if tan ( γ ) <
1
3
In the present study the velocity power n was set to 2.0 and the
constant k was set to 1.0. In the CFX implementation an overall
erosion rate at each point on the surface is then found by
multiplying E by the mass flow carried by the Lagrangian
particle impacting the surface, and then summing over all
particles. This ultimately leads to an erosion rate density
variable with units of kgs-1m-2 which can be displayed in the
post-processor.
(a)
MODELING AND ANALYSIS
Flow simulation of the continuous fluid (carrier fluid) is the first
step of the CFD-based erosion prediction procedure. The
conservation equations (Navier–Stokes equations) for mass,
momentum and fluid turbulence were solved within the
commercial code CFX-11 using a finite volume technique.
Convection terms in the momentum equations were discretised
using a second-order accurate scheme. Detailed modeling [6] of
tunnels is done in Pro-E software [Fig. 1] then model is
imported into ICEM CFX for meshing [7], then mesh is
imported into ANSYS CFX for detailed analysis.
Computational grid of the geometry containing approximately
2855120 tetrahedral elements is used [Fig.2]. Boundary
conditions at the tunnel inlet, outlet and at the wall are
specified. A velocity of 7.57 m/s and a pressure of 578 kPa are
specified at the tunnel inlet. A zero pressure is specified at the
tunnel outlet because it is exposed to the atmosphere. The
particles were assumed to be randomly distributed at the inlet
and the particle velocity distribution was assumed to be
identical to that for the fluid phase. Standard no-slip wall
functions were applied at all solid surfaces for the fluid phase
and the coefficient of restitution for the particles was left at the
default value of 1.0.
(b)
(c)
Fig. 1: Tunnel Model; (a) main view, (b) intake, (c) outlet branches
The transient analysis was run for 20 sec of real time using time
steps of 0.1 sec with convergence achieved in 3-5 iterations per
time step. In CFX-11 it was not possible to use Lagrangian
3
Copyright © 2010 by ASME
periphery where the velocity has it highest value. The pressure
reduces again at the main branch and at the outlet branches.
Erosion rate density profiles at the critical locations are shown
in the Fig. 5 below. Highest value of the erosion rate density is
6.23 e-5 kgs-1m-2. The value of E changes abruptly at the main
branch and at the outlet branches due to the high impactvelocity
and impact angle at these locations.
Results for velocity, pressure and erosion rate density are also
tabulated in Table 1.
(a)
(a)
(b)
(c)
Fig. 2: Tetrahedral Mesh; (a) inlet, (b) branch pipe,
(c) outlet branches
(b)
RESULTS AND DISCUSSION
Velocity profiles for the the critical locations (main bend,
branch pipe and outlet branches) are shown in the Fig. 3 with
sediment particles flowing through the tunnel. Maximum value
of the velocity is 49.76 ms-1 at the inner periphery of the of the
main bend. The velocity decreases after the main bend to 31.70
ms-1 and finally reduces to 18.88 ms-1 when the water flow is
fully developed at 150 m from the vertical section. The velocity
increases again at the branch pipe and at the outlet branches.
Pressure profiles for the the critical locations are shown in the
Fig. 4 with sediment particles flowing through the tunnel.
Maximum value of the pressure is 803 kPa at the fully
developed flow location i.e 150 m from the vertical section. The
minimum pressure is found to be 33 kPa at the main bend inner
(c)
Fig. 3: Results at main bend; (a) velocity, (b) pressure, (c) erosion
rate density
4
Copyright © 2010 by ASME
(a)
(a)
(b)
(b)
(c)
(c)
Fig. 4: Results at branch pipe (a) velocity, (b) pressure, (c) erosion
rate density
Fig. 5: Results at outlet branches; (a) velocity, (b) pressure, (c)
erosion rate density
5
Copyright © 2010 by ASME
Table 1: Velocity, Pressure and Erosion rate density results
Location
Velocity
(V) ms-1
Pressure
(P) kPa
Erosion
rate
density
(E)
10-5 kgs1 -2
m
1
2
3
4
5
6
7
8
48
36
36
36
36
38
35
35
29
791
164
164
164
29
164
29
6.2
4.5
3.1
3.1
4.7
4.9
2.5
4.1
•
•
•
EXPERIMENTAL VALIDATION
The simulation results are validated through the experimental
work [8]. The straight portion of the pipe used in the
experiment is modeled, meshed and analyzed in the way the
tunnel is analyzed. The comparison between the experimental
and simulation results is shown in the Table 2.
REFERENCES
[1]
Table 2: Comparison between experimental and simulation
results
Experimental Simulation
%
Difference
Erosion
rate
0.16
0.1473
7.94
density (E)
-1 -2
g hr m
[2]
[3]
[4]
ACKNOWLEDGEMENT
Authors acknowledge Pak-US project for providing financial
support and TarbelaDam personnel for all technical support.
CONCLUSIONS
•
•
The commercial CFD code CFX-11 is used to investigate
the reasons of highly localized erosion along critical
locations including main bend, branch pipe and outlet
branches. The motion of sediments particles is predicted
using an Eulerian-Lagrangian approach in conjunction with
a Reynolds stress turbulence model (RSM), and an erosion
map is developed using the Finnie erosion model.
The results are shown for eight different locations of
critical importance with sediment particles flowing through
[5]
[6]
[7]
[8]
6
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the tunnel where the velocities and pressures are changing,
causing the erosive damage at these locations.
The erosion rate density is the maximum at the main bend
and branch pipes due to several reasons like the higher
impact velocity and impact angle, the lower pressure and
the production of turbulent eddies.
Numerical simulations as well as experimental erosion tests
are performed. Comparisons show that the CFD-based
erosion prediction procedure is able to reasonably predict
the erosion profile and satisfactorily capture the trend of
erosion with respect to the carrier velocity with an error of
about 8%.
The modeling was able to successfully predict the cause of
the erosion and was subsequently used in the development
of a flow simulation. This resulted in increased confidence
in CFD as a tool in the engineering design process, rather
than only to investigate problems after these are occurred.
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Melbourne, Australia 13-15 December, (2006)
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Consultant Inc. Volume 2, March 1998.
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Shirazi, Application and experimental validation of a
computational fluid dynamics (CFD)-based erosion
prediction model in elbows and plugged tees,
Computers & Fluids 33 (2004). pp. 1251–1272.
Latif Bouhadji, Three Dimensional Numerical
Simulation of Turbulent Flow over Spillways, ASLAQFlow Inc. Sidney, British Columbia, Canada,
1999.
Pro/Engineer. Wildfire Release 4.0 © 2009.
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Release 11.0. © 1996-2006 ANSYS Europe Ltd.
R.J.K Wood and T.F. Jones Investigations of sandwater induced erosive wear of AISI 304L stainless
steel pipes by pilot-scale and laboratory-scale testing.
(2004), pp. 1-35.
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