2008/1 PAGES 1 – 7 RECEIVED 19. 7. 2007 ACCEPTED 12. 12. 2007
J. KRIŠ, GHAWI A. HADI
Jozef Kriš
Research field: water resources, water supplies, water
treatment plant
Slovak University of Technology, Faculty of
Civil Engineering, Department of Sanitary and
Environmental Engineering Radlinského 11, 813 68
Bratislava Slovak Republic
[email protected]
CFD INVESTIGATION OF
PARTICLE DEPOSITION
AND RESUSPENSION
IN A DRINKING WATER
DISTRIBUTION SYSTEM
Ghawi A. Hadi
Research field: drinking water supply, numerical
modeling.
Slovak University of Technology,
Faculty of Civil Engineering, Department of Sanitary
and Environmental Engineering, Radlinského 11,
813 68 Bratislava, Slovak Republic,
[email protected]
ABSTRACT
KEY WORDS
Water distribution system models have become widely accepted within the water utility
industry as a mechanism for simulating hydraulic and water quality behavior in water
distribution system networks. In this paper the effect of particle size, temperature, and
the velocity of fluid on the deposition and resuspension in water distribution systems of
Holič in Slovakia is examined. A comprehensive computational fluid dynamics (CFD)
investigation was carried out for particle deposition and suspension in a drinking water
distribution system. A satisfactory concordance was established with the experimental
data as validation. This was a steady and unsteady state multiphase mixture problem,
which helped to understand the deposition and suspension characteristics for different
particle sizes and densities. The 3D numerical multiphase mixture model solves
continuity and momentum equations for the mixture and volume fraction equations for
the secondary phases. The governing equations were also solved for the turbulence
parameters of the particulate phases. The comparison of model predicted results with
the experimental data shows good agreement. The deposition of heavier particles at
the bottom of the pipe is greater at a low velocity rather than a high velocity, but light
particles remain suspended in the fluid across the pipes circumference.
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INTRODUCTION
Drinking water in Slovakia meets very high standards; the average
citizen relies on the impeccable quality of the tap water. Drinking
water distribution networks are expected to transport only dissolved
matter rather than a few visible particles. However, it is almost
impossible to make the drinking water free from suspended solid
particles. The ability to determine the origins of these particles
varies between different water supply systems, with possible
sources coming from catchments, treatment processes, biofilm
growth within the water supply pipes, and corrosion products.
Computational Fluid Dynamics (CFD),
pipe distribution systém,
mixture model,
particle deposition
resuspension
This paper will discuss the distribution of sediments in the drinking
water distribution system in Holič in Slovakia. The main interest is
the behavior (deposition and resuspension) of the particles coming
from the Holič treatment plant.
Sediment settling in drinking water networks is not wanted as
it can lead to deteriorating water quality and so called brownwater complaints by customers. In Figure 1, the mass balance of
a drinking water network can be seen, showing the incoming-and
outgoing load and the different processes inside the pipe.
The incoming load consists of water containing suspended solids
particles, color etc., inside the pipe processes such as biofilm
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formation and soughing, corrosion, the formation and coagulation
of particles, and deposition and resuspension; theses processes
affect the outgoing load. Corrosion, resuspension and biofilm
soughing can lead to an increase in sediment, whereas a decrease in
sediment can occur when sediment becomes trapped inside biofilm,
is deposited or suspended by formation and coagulation. Many
researches have attempted to understand the possible deterioration
of water quality once it enters a distribution system (Anderson
and Russell 1970; Laurinat, et al., 1985, David, et al., 1987, and
Thomson, 2003).
An improvement in our understanding of the complex hydrodynamic
behavior of suspended and/or deposited particles involved in these
distribution pipe networks requires mathematical and physical
models. Computational Fluid Dynamics (CFD), along with an
analytical turbulent model is one of the most popular mathematical
techniques, as it has the ability to predict the behavior of complex
flows for such multiphase flow applications. A CFD investigation
was carried out to predict the hydrodynamic behavior of turbid
particles flowing through a pipe network.
MATERIALS AND METHODS
The CFD model uses the characteristics of sediment as input; this
means that velocities at which the sediment suspends, resuspends
and/or settles have to be determined. This was performed by
obtaining samples of particulates from the water distribution systems
of Holič in Slovakia and of Melbourne, Adelaide, Sidney and
Brisbane in Australia. The samples in Australia were analyzed using
a pipe test-loop and a water tunnel at CMIT (CSIRO Manufacturing
& Infrastructure Technology) (Grainger, et al., 2003). The rig
consisted of a test pipe with a diameter of 100 mm; a schematic
drawing of the test pipe and boundary conditions are shown in
Figure 2 and Table 1 respectively. The test rig was used to model
the validation and determine the flow velocity of the water when
the sediment starts to settle and the sediment velocity with which
the sediment settles.
GOVERNING EQUATION
The multiphase mixture model of Fluent 6.2 (Fluent Inc., 2005)
used in this study solves the continuity and momentum equations
for the mixture. The volume fraction equations are solved for the
secondary phases. The model also solves the well-known algebraic
expressions for the relative velocities for the secondary phases
(Fluent Inc., 2006).
Table 1 Physical and hydraulic characteristics of the system used
for CFD simulation.
Fig. 1 Mass balance of a pipe in a drinking water network.
Pipe loop length (m)
41.0
Pipe length in Holič (m)
1200
Diameter of the pipe D (m)
0.1
Total volume of water (m3)
0.322
No. of phases
VF of each secondary phase
Particle density (kgm-3)
Particle sizes (μm)
Average water velocities (ms-1)
6
342 ppm
1640
1 – 100
0.05-0.50
Continuity Equation for the Mixture
The term “mixture” can be defined by the combination of all the
primary and secondary phases. The continuity equation for the
mixture is
Fig. 2 Schematic drawing of pipe a test loop (Grainger, et al.,
2003).
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(1)
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Where
is the mass-averaged velocity of the mixture, which is:
Where
is the secondary-phase particle’s acceleration and τqp is
the particulate relaxation time. Following Manninen, et al., 1996 τqp
is of the form:
(2)
(10)
And ρm is the mixture density:
(3)
αk is the volume fraction of phase k.
Where dp is the diameter of the particles of the secondary phases
p, and the drag function fdrag is taken from Schiller and Naumann,
1935:
(11)
Momentum Equation for the Mixture
The momentum equation for the mixture can be obtained by totaling
the individual momentum equations for all the phases. It can be
expressed as:
And the acceleration
is of the form
(12)
(4)
Where n is the number of phases,
viscosity of the mixture:
is the body force, and μm is the
The simplest algebraic slip formulation is the so-called drift flux
model, in which the acceleration of the particle is given by gravity
and/or a centrifugal force, and the particulate relaxation time is
modified to take into account the presence of other particles.
Volume Fraction Equation for the Secondary Phases
(5)
From the continuity equation for the secondary phase p, the volume
fraction equation for the secondary phase p can be obtained:
(6)
(13)
is the drift velocity for the secondary phase k:
Relative (Slip) Velocity and the Drift Velocity
The relative velocity (also referred to as the ”slip” velocity) is
defined as the velocity of the secondary phase (p) relative to the
velocity of the primary phase (q):
Turbulence Viscosity (The Spalart-Allmaras Model)
Instead of μm (equation 5) the turbulent viscosity, μt, is computed
from
(7)
(14)
The drift velocity and the relative velocity (
the following expression:
) are connected by
Where the viscous damping function, fv1, is given by
(8)
(15)
The basic assumption of the algebraic slip mixture model is that
in order to prescribe an algebraic relation for the relative velocity,
a local equilibrium between the phases should be reached over short
spatial length scales. The form of the relative velocity is given by
Where Cv1 = 7.1 and
(16)
(9)
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VALIDATION OF MODEL
In this paper the results have been validated with the experimental
result conducted by Grainger, et al., 2003. At CSIRO Grainger, et
al., 2003, demonstrated an experiment for particle distribution and
deposition in a test loop. In order to compare the experiment results
(Grainger, et al., 2003), we have used the same geometric and
boundary conditions. Figure 3 represents the cumulative particle
volume fraction as a function of the heights across the pipe at
a certain location in the loop for both the experiment and the CFD
results.
Nevertheless, the trend is similar, but the experimental results
show a marginally lower volume fraction. This is because of the
shortcomings of the measuring instruments that were used in the
experiment.
Figure 4 shows the change in the settling velocity of particles with
a given particle size and density in water with a fixed density for
different temperatures (and changing dynamic viscosities).
The settling velocity at 0 0C and at 24.5 0C are respectively
1.95*10-4 and 3.90*10-4 m/s; this is the difference in the settling
velocity of 199%. This shows that the effect of the temperature on
settling in laminar conditions is very large. Also the temperatures
that can occur inside networks range from 0 to 22.3 0C (Vreeburg,
et al., 2004). This means that the viscosity of the fluid is affected.
This viscosity directly affects the settling velocity in laminar
flow conditions; a difference of settling speed of 199% between
0 and 24.5 0C is possible. If these temperature differences are not
considered, the settling of the sediment can be totally different.
Particles will resuspend when the flow is turbulent because the
profile of the flow velocity in a pipe is different for a laminar or
Fig. 3: Comparison of the CFD results and experimental data for the
velocity 0.43 m.s-1 at the center of the pipe.
Fig. 4 Dynamic viscosities and settling velocities at different
temperatures (20 μm, 1310 density particle kg/m3) at Holič.
RESULTS AND DISCUSSION
By determining the velocities for the typical sediment found in
Australian networks, the problems with the theory of settling and
resuspension are short cut. This simplification was made in order to
characterize the sediment characteristics and use them in the CFD
model. Deposition is the phenomenon by which particles settle
under the influence of the gravity force. In water, the rate at which
a particle settles is a function of both the grain and fluid properties.
Resuspension is the phenomenon by which particles collected in
drinking water pipes are resuspened due to hydraulic changes.
Resuspension occurs when forces caused by the flow of a fluid are
larger than the forces of the own weight of the particle captured
inside a sediment bed under water.
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Fig. 5 Particle and turbidity (NTU) measurements of the distribution
network at Holič.
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turbulent flow. The velocity in turbulent flows changes little over
the pipe diameter compared to the laminar flow. The turbulence
causes a lateral mixing of the fluid, leading to flows that reach
the pipe wall. As we have seen, water flowing in drinking water
networks is usually turbulent.
The sizes of particles coming from a treatment plant and in
distribution networks usually range from 1 to 100 μm and have
density that is smaller than 2000 kg/m3. Figure 5 shows a picture of
the continued measurement of the turbidity in a distribution network.
A pattern can be seen, thus identifying the extra contribution to the
sediment caused by corrosion. At night when stagnant water occurs,
the cast iron pipes corrode, leading to a deterioration of the water
quality.
A large contribution to the total sediment load originates from the
treatment plant. Elements like Fe, Mn and Al are present in treated
drinking water. These elements are mainly present as oxides: Fe as
Fe(OH)3, Mn as MnO2 and Al as Al(OH)3. This assumption does not
necessarily hold, because Al could also come from the leaching of
asbestos-cement pipes and Fe from corroding cast-iron pipes.
A lot of research has been performed concerning the growth and
origin of biofilm (Boe Hansen, et al., 2003; and Van de Kooji, et al.,
1995). Van de Kooji suggests for instance that iron and manganese
are entrained in the biofilm, leading to a smaller iron and manganese
concentration in the water. Biofilm is a small layer of organic
material that is formed in drinking water pipes. Biofilm grows on
pipe walls; nutrients that are present in the water are converted into
a biomass.
Figure 6 shows the relative concentration plotted as a function of
the different heights of 0.125D-1D from the bottom of the pipe and
time for various particle diameters. The relative concentration is
a dimensionless parameter, which represents the ratio of the local
particle concentration to that of the bottom of the pipe. Particles
Fig. 6 Relative concentration of particles plotted as a function of
different heights and times for various particle diameters at Holič.
of a size of 1-5 μm are evenly distributed throughout the drinking
water distribution system. The concentration of 10 μm size particles
shows a gradual increase towards the bottom. The concentration of
20 μm size particles is localized near the bottom. The larger size
particles 50-100 μm are all localized at the bottom of the pipe.
According to a test carried out (Grainger, et al., 2003) using a test
pipe loop, particles disappeared from the suspension in a wide range
of velocities up to 0.3 m/s or more. The particles resuspended again
from the pipe bottom in a range of 0.15-0.25 m/s; this is also found
on tests that were performed by Lut (2004).
The velocity at which the water flows is u; the velocity at which it
resuspends is called urs and the velocity at which all particles will
suspend is called ud. Figure 7 shows the possible behavior of the
sediment and the corresponding velocities.
Fig. 7 Cross section of a pipe illustrating suspension, resuspension
and settling velocity.
There are three situations that can occur, depending on the
mixture velocity vm: (1) vm >urs the flow velocity is more than
the resuspension velocity, so the resuspension of all the sediments
occurs. urs is the critical velocity beyond which the particles are
resuspended; urs is a function of the particle diameter, density
and packing of the sediment, (2) ud<u< urs the particle mass is
transported through the pipe with no settling/resuspension, because
the mixture velocity vm is between the velocity at which the
sediment suspends (urs) and the velocity at which it settles (ud), and
(3) vm <ud all the particles will settle, because the velocity of the
water is so low that all the sediment will suspend.
Now we can test if the distribution of the sediment change a lot if
these parameters (us, ud, urs) are slightly changed.
(1) us is the velocity with which the sediment deposits. If us is
lowered, this will lead to a slower settling of particles and a different
kind of distribution of the sediment over the network, the sediment
will settle further away in the network. If us is raised, this will lead
to a quicker settling of sediment (Table 2).
(2) If the parameter ud is changed, this means that the flow velocity
of the water at which the sediment starts to deposit is changed.
When this velocity is lowered, it will lead to more sediment that
suspends. This would lead to a different kind of distribution of the
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Table 2 Settled and suspended mass compared to the initial
situation
us m/s
Deposited per
meter pipe kg/m
In suspension per meter
pipe kg/m
5.45*10-6
0.08312541
0.00046126
1.06*10-7
0.00286004
0.00056135
1.06*10-5
0.12845790
0.00050561
Table 3 Settled and suspended mass compared to the initial
situation.
ud m/s
Deposited per
meter pipe kg/m
In suspension per meter
pipe kg/m
0.14
0.08012501
0.00047412
0.11
0.06756893
0.00045613
0.26
0.10845790
0.00040561
Table 4 Settled and suspended mass compared to the initial
situation.
urs m/s
Deposited per meter
pipe kg/m
In suspension per meter
pipe kg/m
0.26
0.07801250
0.00043412
0.11
0.906756893
0.05004561
0.51
0.09645790
0.00042356
CFD results have also been validated with the experimental results
(Grainger, et al., 2003). In these numerical simulation six different
flow profiles and particle-load profiles were used to compute
the particles’ deposition and re-entrainment into the systems
and to identify the conditions of the deposition and suspension
mechanisms. The velocity at which particles start to deposit was
found to be at least 0.15 m/s; the velocity at which particles start to
resuspend was found to be 0.25 m/s. These values are used to make
predictions for the whole network of a drinking water distribution
system. A reasonably good concordance between the simulation and
experiment results has been established.
ACKNOWLEDGEMENT
Thanks are due to Ing. Ales Prechazkza for his help in the laboratory
in Holič water treatment plant and to the numerous collaborators
involved in the sampling at the treatment plant.
This study was supported by Grant No. 1/3313/06 and projected
APVT 20-031804 solved at the Department of Sanitary and
Environmental Engineering, Faculty of Civil Engineering, Slovak
University of Technology, Bratislava.
Notation
ρm
u
Average velocity (m.s-1)
αk
Particle volume fraction
q
Primary phase
p
Secondary phase
μm
sediment over the network. If the velocity ud is increased, this will
lead to less material settling (Table 3).
(3) If the velocity at which the sediment resuspends is lowered,
the sediment that was previously suspended will resuspend. This is
because during the day, the flow velocity in the pipes will increase
because of the larger water demand. This flow velocity then exceeds
the resuspension velocity of the sediment (Table 4).
CONCLUSION
The effect of velocities on the deposition of particles has been
investigated numerically. This paper investigated the effect of
particle size, temperature, and the velocity of fluid on deposition and
resuspension in the Holič drinking water distribution system. This
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Mixture density (kg.m-3)
Dynamic mixture viscosity (Pa-s)
τqp
Particulate relaxation time (s)
fdrag
Drag function
dp
Diameter of the particles (μm)
Re
Reynolds number
D
Pipe diameter (m)
Acceleration (m.s-2)
Drift velocity (m.s-1)
Relative velocity (m.s-1)
Mass-averaged velocity (m.s-1)
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