Cite this article
Research Article
Zhang X, Yu R and Chen J (2018)
A CFD simulation of CLSM filling with piping on Herschel–Bulkley rheological model.
Emerging Materials Research, https://doi.org/10.1680/jemmr.17.00065
Paper 1700065
Received 09/10/2017; Accepted 01/03/2018
Keywords: material properties/
modelling
ICE Publishing: All rights reserved
Emerging Materials Research
A CFD simulation of CLSM filling with piping
on Herschel–Bulkley rheological model
Xuesong Zhang MS
Rangang Yu PhD
Lecturer, College of Pipeline and Civil Engineering, China University of
Petroleum, Qingdao, China (corresponding author: snowpiner@upc.edu.cn)
(Orcid:0000-0001-7875-6236)
Professor, College of Pipeline and Civil Engineering, China University of
Petroleum, Qingdao, China
Jinping Chen MS
Lecturer, College of Pipeline and Civil Engineering, China University of
Petroleum, Qingdao, China
In order to study and predict the flowing behaviour of controlled low-strength material (CLSM) slurry filling with
piping transportation, a three-dimensional computational fluid dynamics simulation is carried out based on the
Herschel–Bulkley (H-B) rheological model. The simulation is validated by L-pipe flow experiments of CLSM on the
flow time and flow pattern. The analysis results show that it is reliable to use the H-B model to simulate the flow of
the CLSM slurry. On this basis, simulations are performed to predict the dynamic characteristics of CLSM slurry filling
with piping transportation and analyse the velocity distribution and pressure variation in pipeline. The simulation
results are consistent with the basic law of power flow, which proves the rationality and effectiveness of the
method. The study on the filling characteristics of CLSM slurry pipeline lays a theoretical foundation for the
realisation of low-cost, safe and efficient filling of abandoned pipelines.
Notation
F
K
n
p
R1
R2
G0
g_
P
rg
t
tf
1.
generalised source of the conservation equation
consistency coefficient
rheological index
static pressure
inner diameter of the BTRHEOM rheometer
outer diameter of the BTRHEOM rheometer
initial torque
shearing rate
second invariant of the rate of strain tensor
gravity
shear stress
yield shear stress
Introduction
Pipeline abandonment is an increasingly relevant issue as the pipeline
network ages. The pipelines will be abandoned when existing oil
fields are not worthy of sustainable development or existing pipeline
life expires. Pipeline abandonment in-place is generally the preferred
option based on the technical condition and environmental
sustainability of the pipeline.1,2 Internationally, the general practice in
abandonment in place of oil and gas pipelines is to take the physical
isolation and sealing after clearing the medium in the pipeline or
filing the pipeline with harmless material in areas easily affected by
land subsidence or are heavily loaded.3 As described by ACI
Committee 229, controlled low-strength material (CLSM) refers to ‘a
self-compacting, cementitious material used primarily as a backfill in
lieu of compacted fill’.4 CLSMs are cementitious fluid-like materials
that flow freely under their own weight and are self-compacting,
often used in backfill, pavement bases, structural bases and utility
embedment, void-fill, trenching and repair-fill applications. CLSM
for filling abandoned pipeline is made of fly ash as the main raw
material, adding a small amount of cement and using admixture
technology.5 By means of local elevation difference, the segmental
filling of abandoned pipeline is carried out, and the CLSM slurry can
be self-compacting with gravity or pumping. The CLSM has the
properties of high fluidity, low strength, self-levelling and selfcompacting, which can meet the requirements of different
constructions or mechanics when the relevant performance is
adjusted reasonably.6–8 The experiment is supplemented with
analytical calculation, which is the main method to study the
properties of the filling materials, such as rheological properties, flow
properties and the local resistance characteristics. However, the
limitation of its complexity makes it hard to carry out experimental
research on all kinds of working conditions, and the computational
workload is huge and complex. Computational fluid dynamics (CFD)
is used to solve the governing equations of hydrodynamics by
numerical calculation, which method shows great potential for
developing into a powerful tool for the prediction of CLSM filling,
as an important supplement to the experiment.
The rheological properties of cement-based slurrry are both
viscous and elastic–plastic.9 Presently, the Bingham fluid model
or the Herschel–Bulkley (H-B) fluid model is often used to
describe the rheological behaviour of cement paste.10,11 The
Bingham model enables to describe the yield stress, plastic
viscosity and proper thixotropy of slurry properly, while the H-B
model can also describe the rheological index, critical shear rate,
shear thinning, shear thickening and other rheological behaviours
properly.12 The test results of monitoring the rheological
parameters of fly ash cement pastes showed that the rheological
behaviour of fresh cement paste mixed with fly ash or not follows
the Bingham model, and the thixotropy of cement pastes with fly
ash follows shear thinning behaviour.13 Xie and his colleagues
tested the influence of the amount of fly ash on the rheological
behaviour of cement paste and used H-B rheological model to fit
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1
Emerging Materials Research
A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
the experimental data, which showed that there is an inflection
point in the rheological curve, in the left and right sides of which
are shear thinning stage and shear thickening stage, respectively.14
Critical shear rate is rather low, resulting in shear thinning. Using
the H-B rheological model to simulate the rheological behaviour
of the shear thickening is more practical than using the Bingham
fluid model.15 In this paper, the numerical simulation of CLSM
slurry flow on the H-B fluid model is performed by using
interface tracking algorithm based on the finite volume method in
the CFD method. The rationality of CLSM flow simulation is
discussed through the comparison between L-pipe test and
numerical calculation. Then using CFD, the pipe flow dynamic
characteristics of CLSM slurry are analysed by numerical
simulation in different velocities under the stable flow state in the
bending tube. The analysis focuses on the flow behaviour of the
slurry, the pipeline pressure drop and the preliminary probe into
the complex secondary flow in bend, conducive to determining
the parameters of the filling system and guide the engineering
practice by using numerical simulation method.
denaturation test data – that is, tf, n and K are calculated by the
three sets of test data.
2.
H-B is a three-parameter rheological model,17 shown as Equation 1.
The apparent viscosity m in the H-B model is given by
Equation 2.
m ¼ kPn−1 þ t0 P−1
where P ¼ ð2Eij Eji Þ1=2 represents the second invariant of the rate
of strain tensor Eij ¼ ð1=2Þ½ð∂ui =∂xj Þ þ ð∂uj =∂xi Þ.
The estimation of rheological parameters of the H-B model is
essentially a non-linear optimisation problem. The three
parameters of the H-B model, describing the fresh cement fly ash
paste, are obtained by the iterative calculation of the convective
2
n
tmin ¼ tf þ Kgmin
tx ¼ tf þ Kgxn
3.
That is
1
ðt
− tf Þ
K max
1
n
¼ ðtmin − tf Þ
gmin
K
1
gxn ¼ ðtx − tf Þ
K
n
gmax
¼
4.
In Equation 4, multiply the front two formulas after they are
divided by the third formula respectively – that is
t ¼ tf þ K g_ n
where t is shear stress, tf is the yield shear stress, K is the
consistency coefficient, g_ is the shearing rate and n is the
rheological index. For n < 1, it describes pseudoplastic behaviour
(shear thinning), while for n > 1, the behaviour is dilatant
behaviour (shear thickening), and for n = 1, the H-B model
reduces to the Bingham model.
2.
n
tmax ¼ tf þ Kgmax
Calculation principle
2.1 Rheological model of CLSM
The H-B model describes the power-law fluid with dynamic shear
stress, which reflects both the plastic and the pseudoplastic
characteristics of the fluid, and contains two kinds of rheological
models – that is, the Bingham fluid and power-law fluid. It also
has the advantages of a wide range of adaptation and high
computing precision.16
1.
In order to avoid negative yield stress during fitting of the
rheological curve, it is necessary to determine the yield stress tf
of the slurry by rheometer test firstly. And then the other two
parameters are solved by variable transformation into linear model
and linear least square method. Supposing shearing stresses tmax,
tmin and tx, which were measured at shearing rates of gmax, gmin
and g, respectively, and putting them into Equation 1, Equation 3
can be achieved.
5.
gmax gmin
gx2
n
¼
ðtmax − tf Þðtmin − tf Þ
ðtx − tf Þ2
Let
6.
gx ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
gmax gmin
Substitute Equation 6 into Equation 5, which is
tf ¼
7.
tmax tmin − tx2
ðtmax þ tmin Þ2 − 2tx
For example, tf is calculated by Equation 8 with data measured
by a parallel plate rheometer (BTRHEOM rheometer).
8.
tf ¼
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3
G
2p R32 − R31 0
Emerging Materials Research
A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
where R1 is the inner diameter of the instrument, R2 is the outer
diameter of the instrument and G0 is the initial torque.
of the phases, or representative of a mixture of the phases,
depending on the volume fraction values.19 In other words, if the
slurry volume fraction in the cell is denoted as as, then the
following three conditions are possible.
Subtract the first formula of Equation 4 from the second and then
transform – that is
9.
K¼
tmax − tmin
n − gn
gmax
min
Equation 10 can be achieved by the transformation of Equation 4.
10.
n
gmax
½1 − ðgx =gmax Þn tmax − tx
¼
gxn ½1 − ðgmin =gx Þn tx − tmin
Substitute Equation 6 into Equation 10 and then take the
logarithm – that is
11.
n¼
lgðtmax − tx Þ=ðtx − tmin Þ
lgðgmax =gx Þ
2.2 Governing equation and the solution
The CLSM slurry can be regarded as an incompressible viscous
fluid. It can be described by Navier-Stokes equation. In
simulating, heat exchange is not considered. Continuity equation
12 and momentum equation 13 are as follows.17
12.
13.
∂p
þ ∇ r!
v ¼ Sm
∂t
∂ r!
v
!
þ ∇ r!
v!
v ¼ − ∇p þ ∇ t þ r!
g þ F
∂t
where p is the static pressure, r is the density, t is the time, Sm is
!
the generalised source phase, t is the stress tensor and r!
g and F
are the gravitational body force and external body forces,
respectively.
In this paper, two-phase (i.e. air and CLSM slurry) numerical
simulations are performed. The volume of fluid (VOF) model can
model two or more immiscible fluids by solving a single set of
momentum equations and tracking the volume fraction of each of
the fluids throughout the domain. For each phase added to the
model, a variable is introduced: the volume fraction of the phase
in the computational cell. In each control volume, the volume
fractions of all phases sum to unity.18 The VOF model is available
only with the pressure-based solver and does not allow for void
regions where no fluid of any type is present. Thus, variables and
properties in any given cell are either purely representative of one
■ as = 0: the cell is empty (of the slurry).
■ as = 1: the cell is full (of the slurry).
■ 0 < as < 1: the cell contains the interface between the slurry
and one or more other fluids.
The tracking of the interface(s) between the phases is
accomplished by the solution of a continuity equation for the
volume fraction of one (or more) of the phases. For the slurry
phase, this equation has the following form.
"
#
n
X
1 ∂
!
ða r Þ þ ∇ as rs v s ¼ Sas þ
ðm_ as − m_ ss Þ
rs ∂t s s
p¼1
14.
where m_ as is the mass transfer from phase slurry to phase air, m_ ss
is the opposite, rs is the density of the slurry, and Sas is the
source term.
3.
L-pipe test numerical simulation and
analyses
3.1 L-pipe test
An experimental setup to study the CLSM slurry flow through
pipes was prepared to monitor the velocity of slurry flowing
under the influence of gravity.
3.1.1 Properties and proportions of the materials
The CLSM used to fill the abandoned pipeline is mainly made of
fly ash mixed with a small amount of cement by the advantage of
admixture technology. The fineness of pulverised coal ash is
0·045 mm, which screened to be 27·5%, and its density is
2300 kg/m3. The cement type is PO 32·5, whose measured value of
28 d compressive strength is 37·1 MPa and density is 3100 kg/m3.
Two kinds of admixtures for water reduction are used – that is,
polycarboxylic high-performance water-reducing agent DW-1 and
DWB01 – and the concentrations are both 10%. The thickener is
carboxymethyl cellulose (CMC). The proportion and the physical
parameter of the CLSM are mentioned in Table 1.
3.1.2 Testing equipment
Figure 1 displays the schematic arrangement of the L-pipe setup.
The L-pipe is composed of a horizontal and a vertical transparent
glass tube of 20 mm inner diameter both. An inverted cone is
connected to the 500 mm long vertical pipe, which is used as a
funnel to collect the material prior to conducting the experiment.
A 90° elbow connects the vertical pipe to the 1000 m long
horizontal pipe. A valve is set at the junction of pipe elbow and
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A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
Emerging Materials Research
Table 1. Mix proportion of slurry in this test
Cement: %
W/B
CMC: %
DW-I: %
DWB01: %
15%
0·30
0·02
0·2
0·2
Fluidity: mm
Compressive strength: MPa
0h
0·5 h
1h
2h
4h
8h
R7
R14
R28
288
270
245
225
225
220
0·41
1·06
1·80
Slurry volume fraction 0: s
1·00
500
0·75
0·50
Support
1000
Support
20
0·25
Valve
0
(a)
(b)
Figure 1. The dimension of L-pipe Setup (a) and the 3D modelling of L-pipe (b)
vertical pipe. Two adjustable support seats are set below the
horizontal section.
■ Inlet: At the inlet, constant inlet velocity u = uinlet. Inlet is set
as the pressure inlet whose relative pressure is zero.
■ Outlet: At the outlet, the zero gauge pressure p = poutlet is
The L-pipe, as shown in Figure 1(a), drained after being wetted
with clean water, is placed on a stable test platform with the valve
closed.20 Fill the vertical part of this device with CLSM slurry,
then open the valve after standing for 2–3 min. Upon opening the
valve, the CLSM slurry flows down the pipe under the effect of
its own weight. Record the time when the CLSM flows through
each marked points until the slurry remains stagnant. Eleven
points are marked from the junction of the elbow and the
horizontal pipe with each interval of 100 mm.
specified. The outlet velocity is unknown a priori but needs to
be iterated from the neighbouring computational cells. To get
a better rate of convergence in backflow, the outlet is set as
the pressure outlet.
■ Wall: At the wall, no slip condition is set u = 0.
τ
Bingham (n = 1)
3.2 Rheological parameter measurement
The H-B model is adopted to describe the rheological
characteristics of the non-Newtonian fluid (Figure 2). Tests on
rheological properties of the CLSM are done in the lab to
determine the shear stress of the slurry in each shear rate (the
angular velocity of the rotational viscosimeter). Mathematical
fitting is used to determine the value of each rheological
parameter.
The H-B rheological model parameters in this experiment are
shown in Table 2.
3.3 Modelling and numerical simulation
The three-dimensional (3D) simulation on the L-pipe is used to do
the performance test of CLSM, which adopts VOF multiphase
flow model and pressure-based transient implicit separate solver.
The two phases is air and the CLSM paste characterised by H-B
rheological model, respectively. The following boundary
conditions are prescribed in the developed model.
4
n>1
0<n<1
τ0
.
γ
.
γ0
Figure 2. Rheological characteristic curve of H-B fluid
Table 2. Rheological parameters of the CLSM slurry
Parameters
Value
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Yield stress
s0: Pa
Consistency
coefficient K: Pa sn
Rheological
index n
6
0·012
1·8
Emerging Materials Research
A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
The choice of numerical discretization and pressure–velocity
coupling algorithms is important for accurately predicting flow
behaviour. Here two-order upstream scheme is used for numerical
discretisation, and Simple coupling mode is adopted to implement
the coupling of pressure and speed.21,22
results are shown in Figure 3. The flow patterns of each moment
are basically the same as reality and show the characteristics of
the adhesion of the wall clearly in the vertical pipe. Comparing
the simulation results with the experimental results, it can be seen
that the time and the distance of flow matches each other on the
whole. Closer inspection reveals that the simulation flow time is
slightly shorter than the corresponding test result before the
flowing distance of 300 mm, while a little longer after that.
During the numerical simulation, the valve is opened instantly in
the initial state, while the process of valve opening needs a short
time in actual operation. Even though the time is very short, for
the slurry with low viscosity, the difference between two kinds of
results appears – that is, this is the reason for the former
dissimilarity. When the horizontal flow distance is more than
300 mm, the flow velocity of the slurry becomes obviously slow.
At this time, the velocity is still not 0 in the numerical calculation,
while it is almost motionless by naked eye observation – that is,
the time of experiment record is slightly earlier than that of
numerical calculation.
The volume–fraction display method of VOF model is used to
determine the flow state at some moment. Because the tube is
axisymmetric, half of the circle tube is chosen as the half of the
calculation area. The model consists of 8950 units, most of which
are about 3·5 mm long. The 3D CFD calculation model is shown
in Figure 1(b), where the number 0 represents the air and number
1 represents the CLSM.
The time of the front end of the CLSM flow reaching the
calibration distance is recorded. The results of test and numerical
calculation are as shown in Table 3. The 3D CFD calculation
Table 3. Flow time comparison of CLSM
Time of arrival: s
Calibration distance: mm
100
200
300
360
Test
results
Numerical
calculation results
1·2
1·8
2·7
4·8
1·1
1·7
2·7
4·9
Three-dimensional L-pipes based on the Bingham rheological
model simulation are adopted for comparison. The error between
the simulated flow time results and the test results is larger
than the H-B model (the average difference is 10%), which shows
that the H-B model can better characterise CLSM rheological
properties than the Bingham. Moreover, the H-B model can be
used to solve the problem of negative yield stress in the
Slurry volume fraction 1·1: s
1·00
Slurry volume fraction 1·7: s
1·00
0·75
0·75
0·50
0·50
0·25
0·25
0
0
(b)
(a)
Slurry volume fraction 2·7: s
1·00
Slurry volume fraction 4·9: s
1·00
0·75
0·75
0·50
0·50
0·25
0·25
0
0
(c)
(d)
Figure 3. Flow time and the flow state of CLSM: the time of flowing to 100 mm (a), the time of flowing to 200 mm (b), the time of
flowing to 300 mm (c) and the time of flowing to 360 mm (d)
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Emerging Materials Research
A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
regression analysis of rheological parameters to obtain more
stability and reliability in flow simulation.
0·755 m/s (i.e. flow rate = 159 m3/h), respectively, and the
direction is perpendicular to the inlet; (b) The wall boundary
condition is that there was no relative slipping on pipe’s surface;
(c) At the pressure exportation, the pressure value is equal to the
imports and the atmospheric pressure; and (d ) define the
gravitational acceleration as 9·81 m/s2 and the temperature as
normal temperature = 300 K, which is only used for energy
calculation.
Based on the above, it can thus be concluded that the CLSM flow
simulation based on H-B model can predict the time and pattern of
slurry well. The analyses of the rheological parameters can provide
the proportion design of CLSM and the construction with foundation.
4.
CLSM pipeline transportation simulation
Filling pipe with CLSM has problems such as pipe burst, pipe
blocking and pipe wearing fast. To ensure the safety and
continuous operation of the slurry pipeline, the numerical
simulation of pipe transportation is analysed to provide reliable
data and allow the study of the dynamic characteristics and pipe
flow problems of CLSM slurry. Simulations are carried out for
CLSM slurry transportation in a typical oil pipeline with two
different inlet velocity. The H-B model of the CLSM rheological
parameters are shown in Table 2.
In the process of numerical calculation, the convergence
monitoring objects mainly include the velocity, pressure,
turbulence kinetic energy and energy dissipation rate. During the
initial phase, the oscillation appears, but its subsequent
convergence monitoring tends to be converged, which ensures the
reliability of the simulated results. In the pipe, the CLSM slurry’s
flow characteristics are different under various working
conditions. In this paper, the laminar flow of the CLSM slurry is
simulated at different inlet velocities.
4.1 Model establishment
The dimension and geometrical model of the pipeline is shown in
Figure 4. The vertical section is 2000 mm long while the
horizontal part is 3000 mm long, and the two sections are
connected by a right-angled elbow of the same internal diameter
of 273 mm. The model contains more than 32 200 units, and most
of the elements have a length of about 15–18 mm.
4.2 Simulations of the pressure drop
As shown in Figure 5, the pressure field in the pipe is gradually
diminishing. The pressure drop is listed in Table 4. Comparing
two flow pressure distributions at different inlet velocity, it can be
obtained that the pressure drop generally changes obliquely in
general, obviously more quickly at the elbow and then become
stable after about 0·6 m horizontal flow. Specifically, the pressure
loss increases with the increase of flow velocity, and when the
flow velocities v = 0·380 m/s and v = 0·755 m/s at the bend, the
pressure drop is, respectively, 1·39 times and 1·66 times as fast as
that while being at the stability.
To facilitate the modelling and calculation, some assumptions are
made as follows: (a) the CLSM slurry is a pure viscous nonNewtonian fluid that is independent of time and its rheological
model is an H-B model, (b) the slurry is a homogeneous fluid and
(c) heat exchange is not considered.
Simulations prediction of the velocity field under
different speed conditions
The plug flow is developed for the CLSM slurry as shown in
Figure 6. Because of the influence of the pipe and boundary
4.3
The setting of the boundary conditions are as follows: (a) The
inlet velocity is taken as 0·380 m/s (i.e. flow rate = 80 m3/h) and
2000
Inlet
73
R2
1
Outlet
Y
273
2
3
4
600
5
6
600
600
7
200
Z
3000
(a)
(b)
Figure 4. Dimension of the pipeline (a) and geometrical shape and mesh generation of the pipeline (b)
6
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A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
Emerging Materials Research
1600
1400
Pressure: Pa
1200
1000
v = 0·380 m/s
v = 0·755 m/s
800
600
400
200
0
0
1
2
3
4
5
6
Length: m
Figure 5. Chart of pressure change along the pipe axis (from inlet to outlet)
Table 4. Pressure drop per unit length
Inlet velocity: m/s
0·380
0·755
Pressure value: Pa
Pressure drop per unit length: Pa/m
Inlet
1-1
3-3
4-4
Outlet
The whole
Vertical section
Bend parts
When stable
800·66
1547·97
496·71
934·52
387·40
702·86
294·15
519·84
0
0
141·89
274·32
151·98
306·73
170·02
360·34
122·56
216·60
conditions, the flow of the slurry near the inlet, the bend and a
certain part after the bend behave obviously unstably and is not
real laminar flow. It is noted that velocity acceleration at the high
inlet velocity is higher than that at low inlet velocity. After a
certain horizontal distance, the laminar flow core appears.
Comparing these two kinds of velocity conditions, the velocity of
the flow core when v = 0·755 m/s is greater than that when v =
0·380 m/s, while the flow rate decreases.
At the elbow, the generation of centrifugal forces and flow
separation results in non-uniform velocity distributions: a highvelocity profile is generated at the bottom of the pipe, and a back
flow region is developed at the top of the pipe near the elbow,
particularly at the high inlet velocity. This is mirrored by
reduction in centrifugal force at low inlet velocity. As the flow
enters the bending section, significant radial pressure gradients
appear caused by the presence of centrifugal force due to
curvature in the flow core region. However, the axial velocity and
the centrifugal force approach zero in the proximity of the inner
and outer walls of the elbow. Secondary flow is developed along
the outer wall to balance the momentum transport as can be seen
in Figure 6.
When the average flow velocities are v = 0·380 m/s and v =
0·755 m/s, the flow reaches the basic stability at 700 mm and
1700 mm away from the lower section of the elbow, respectively.
As a result, the greater the velocity, the longer the distance
required for steady flow.
After steady flow, the distribution patterns of section 6-6 shows
the following: (a) In general, the velocity varies more rapidly
when closer to the pipe edge at the two flow rates. (b) At v =
0·380 m/s and v = 0·755 m/s, the change becomes smoother at
distances of about 60 and 45 mm from the centre of the pipeline,
respectively. Comparison of the two conditions: when the inlet
velocities are v = 0·380 m/s and v = 0·755 m/s, the flow core
velocities are about 0·552 and 1·095 m/s, and the radius of flow
cores are about 50 and 40 mm, respectively, namely, the velocity
of flow core increases with the average flow velocity increasing,
while the radius of flow core is on the contrary. The distribution
pattern of the velocity of the cross-section is similar to a
trapezoid, which conforms to the state of laminar flow
distribution.
The velocity distribution of section 7-7 in the Y direction is
shown in Figure 7(a). Under the condition of different
slurry flow velocities, Y axial velocity clouds’ form is similar to
(a) the region where Y axial velocity is equal to 0 is
distributed near the pipe wall and Y = 0 (the Z axis); (b) when
the average flow velocities are v = 0·380 m/s and v = 0·755 m/s,
the maximum velocities in the Y axis are, respectively, 2·29 ×
10−6 m/s and 3·06 × 10−6 m/s; (c) the maximised speed
appeared when it is near point y = ±90 mm; (d) the speed in
the Y direction is distributed symmetrically with the Z axis;
(e) on the chord, which is parallel to Z axis, the velocity
distribution is symmetrical based on the Y axis. The maximum
value is in the middle and the value reduced gradually in the
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A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
Emerging Materials Research
0·55
0·50
0·45
0·40
0·35
0·30
0·25
0·20
0·15
0·10
0·05
0
[m/s]
Z
1-1
X
Y
Y
X
Y
2-2
Z
Z
Y
X
Z
3-3
Y
Y
X
4-4
5-5
Z
X
Z
6-6
X
Y
Z
X
(a)
1·10
1·00
0·90
0·80
0·70
0·60
0·50
0·40
0·30
0·20
0·10
0
[m/s]
Z
1-1
X
Y
Y
2-2
X
Y
Z
3-3
Z
Y
X
Z
Y
Y
Z
X
4-4
Z
X
5-5
X
6-6
Y
Z
X
(b)
Figure 6. Velocity profile for CLSM slurry in the pipeline: v = 0·380 m/s (a) and v = 0·755 m/s (b)
opposite direction until it becomes 0; and ( f ) the magnitude of Y
axial velocity is smallest, so the maximum speed is 3–4
magnitudes lower than that of the slurry flow rate, and the
quantity is also small. It can be seen that the trend of flow of the
slurry to the centre of the section in the horizontal pipeline is
very weak. Thus, in the horizontal pipeline, the slurry is in a
stable laminar condition. The fluid’s velocity distribution in the
Z direction is similar to that in the Y direction as shown in
Figure 7(b).
5.
Conclusions
The pipeline transportation characteristic of CLSM slurry study
has laid the theoretical foundation on the realisation of low-cost,
safe and highly efficient filling of abandoned pipeline.
8
(a) The H-B rheological model pertains to the three-parameter
rheology model, which can reflect the slurry’s rheological
properties greatly. When using the H-B rheological model, it is
necessary to analyse the results of experiments with the
rheological curve characterised by the three-parameter method to
make the regression analysis using the least square method. But
the process is relatively complex, and its practicability remains to
be further improved.
(b) The flow performance simulation of CLSM was carried on the
H-B rheological model by using CFD method. The reliability that
the H-B model can be used to stimulate the shear thickening of
the CLSM slurry flow was demonstrated by comparing the
computation with the test result. Moreover, the result has a
Downloaded by [ La Trobe University] on [03/05/18]. Copyright © ICE Publishing, all rights reserved.
A CFD simulation of CLSM filling with
piping on Herschel–Bulkley rheological
model
Zhang, Yu and Chen
Emerging Materials Research
Velocity v
2·50 × 10−6
Velocity v
3·00 × 10−6
1·94 × 10−6
2·39 × 10−6
1·39 × 10−6
1·78 × 10−6
8·33 × 10−7
1·17 × 10−6
2·78 × 10−7
5·56 × 10−7
−2·78 × 10−7
−5·56 × 10−8
−8·33 × 10−7
−6·67 × 10−7
−1·39 × 10−6
−1·28 × 10−6
−1·94 × 10−6
−1·89 × 10−6
−2·50 × 10−6
[m/s]
−2·50 × 10−6
[m/s]
v = 0·380 m/s
v = 0·755 m/s
(a)
Velocity w
0·00 × 100
Velocity w
0·00 × 100
−5·00 × 10−7
−5·00 × 10−7
−1·00 × 10−6
−1·00 × 10−6
−1·50 × 10−6
−2·00 × 10−6
−1·50 × 10−6
−2·50 × 10−6
−2·00 × 10−6
−2·50 ×
−3·00 × 10−6
10−6
−3·50 × 10−6
[m/s]
[m/s]
v = 0·380 m/s
v = 0·755 m/s
(b)
Figure 7. Distribution of different velocities at the cross-section 7-7: Y direction (a) and Z direction (b)
guiding role in the mix design of CLSM and the prediction of the
CLSM’s liquidity.
(c) Through the numerical simulation research on the flowing of
CLSM slurry in horizontal pipe flow, the pressure and velocity
distribution in the pipeline under different average flow velocities can
be forecasted. The result shows that when the average velocity is
0·380 m/s (flow rate of 80 m3/h), the pipeline’s pressure loss is about
432·49 Pa/m, the flow core’s velocity is 0·552 m/s and its radius is
50 mm; when the average velocity is 0·755 m/s (flow rate of
159 m3/h), the pipe pressure loss is about 975·40 Pa/m, the flow
core’s velocity is 1·095 m/s and its radius is 40 mm. In conclusion,
when the slurry in the pipe is at the laminar condition, with the
average velocity increasing, the pressure loss and flow velocity will
increase, while the flow core’s radius will reduce.
(d ) The velocity characteristics of the fluid particle are obtained
by the study. Cross-section high point in the Y axial velocity
distribution characteristics of constitution: the wall circumference
and Z axis is zero, and other particles with the Z axis into
axisymmetric distribution, speed down above the Z axis, whereas
upwards, have very low value. The velocity distribution of the
upper body of the cross-section is similar to that of the Y axis.
The study shows that the stable flow is consistent with the state of
laminar flow.
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