Korean J. Chem. Eng.

, 26(4), 1144-1154 (2009)

DOI: 10.1007/s11814-009-0190-y
RAPID COMMUNICATION

CFD simulation of coal-water slurry flowing in horizontal pipelines

Liangyong Chen, Yufeng Duan†, Wenhao Pu, and Changsui Zhao

School of Energy and Environment, Southeast University, Nanjing 210096, China

(Received 29 July 2008 • accepted 5 January 2009)

Abstract−An Eulerian multiphase approach based on kinetic theory of granular flow was used to simulate flow of
coal-water slurries (CWS) in horizontal pipelines. The RNG k-ε turbulent model was incorporated in the governing
equation to model turbulent two-phase flow with strong particle-particle interactions. In this model, the coal particles
with bimodal distribution were considered as two solid-phase components, and the moment exchange between solid
and liquid as well as that between solid and solid were accounted for. The model was firstly validated with pressure
gradient and concentration profile data from the open literature, and then validated with pressure gradient data of the
authors’ experiments. The effects of influx velocity, total influx concentration and grain composition were numeri-
cally investigated, and the results have displayed some important slurry flow characteristics, such as constituent particle
concentration distribution and velocity distribution as well as pressure gradients, which are very difficult to display in
the experiments. The results suggest that both gravity difference between large and small particles and strong particle-
particle interaction had significant effects on concentration distribution as well as velocity distribution.
Key words: Coal-water Slurry, High Concentration, Multi-fluid Model, Kinetic Theory of Granular Flow

INTRODUCTION success. More recently, a numerical model based on space-time av-

eraged multi-phase momentum conservation equations was devel-
The transportation of highly concentrated coal-water slurries in oped by Assar [5], in which concentrations are obtained by solving
pipelines is popular in numerous industrial applications ranging from governing equations derived from convective diffusion equation.
coal combustion to gasification or liquefaction processes [1]. The Those approaches though successful, have a draw back that it needs
most important technical parameters for designing a pipeline slurry many experimental coefficients or empirical equations to enclose
transportation system are usually evaluated by empirical correlations the governing equation. Recently, many researchers used a mixture
or determined by experiments in a laboratory. However, flow behav- model, a simplified form of the Eulerian approach, to predict con-
iors of CWSs are very complex and the experimental investigations centration and velocity distributions as well as pressure drop of slurry
are difficult and expensive. The empirical correlations are usually flow [6-8]. Its computation is relatively inexpensive and it is straight-
developed based on limited data and their applicability is limited forward to introduce a turbulence model into the mixture model
[2]. To develop a CFD model to predict those technical parameters [8]. However, the mixture model does not account for effects of
such as pressure drop, velocity distribution, concentration distribu- particle-particle interaction which extensively occur at high solid
tion and others becomes the endeavor of the researchers. loading, so it is reasonably accurate for slurries with moderate volu-
With development of numerical technique and modeling of mul- metric concentrations.
tiphase turbulent flow, numerical simulations of dense solid-liquid In recent years, the Eulerian multiphase approach incorporated
flow by Eulerian multiphase approach are becoming increasingly with kinetic theory of granular flow was applied to simulate super
attractive [3]. The Eulerian model provides the most rational frame- dense solid-liquid flow. In kinetic theory, solid phase behavior is
work for describing such concentrated solid-liquid slurry flow. It analogous to the behavior of gas, and thus a granular temperature
accounts for liquid, particle and boundary interaction effects. In the is defined to delineate solid phase fluctuations and transport prop-
Eulerian approach one is only required to give physical properties erties. Because kinetic theory accounts for collisional and frictional
of liquid carrier and solids phase as well as operating conditions. characteristics of solid phase, it makes super dense solid-fluid flow
The numerical investigations with this model have displayed some tractable within the framework of Eulerian multiphase model. Many
important slurry flow characteristics, such as concentration distri- researchers use this framework to simulate solid-liquid flow behav-
butions, slurry density, slip velocity magnitude, velocity distribu- ior in a fluidized bed [9-13]. It is intended to predict accurate flow
tions, and slurry mean skin friction coefficient distributions, that is and other characteristics of liquid fluidized beds. A few studies [2,
very difficult to display in the experiments. A CFD model within 14,15] use kinetic theory to predict flow behavior of dense slurry
the framework of the Eulerian approach developed by Hsu [4] for flow in pipelines. Although there have been enormous research ef-
flow of dense slurries through horizontal pipelines achieved great forts on two-phase slurry flow, there appear to be no numerical in-
vestigations on studies of super dense slurries such as CWSs. The
†
To whom correspondence should be addressed. total volume concentration of slurries investigated in the present
E-mail: yfduan@seu.edu.cn work is much higher than those reported in the literature and the
‡
This work was presented at the 7th Korea-China Workshop on Clean average volume concentration is up to more than 50%. Thus, it is
Energy Technology held at Taiyuan, China, July 25-28, 2008. necessary to consider both large-scale fluctuations due to mixture
1144
 CFD simulation of coal-water slurry flowing in horizontal pipelines 1145

turbulence and small-scale fluctuations due to particle-particle col- turbulence viscosity.

lision. In addition, the solid phase of CWSs usually exhibits bimo- 2. Interphase Momentum Exchange
dal distribution. It is more rational to consider the solid phase as two The model for exchange coefficient βfi is formulated as Eq. (5)
components according to two peaks of particle size distribution and [18]:
the moment exchange between different solid phases needs to be
included. At present, only few studies [16,17] have reported experi- ⎧
⎪ 150 αsi αf µf ρfαsi
mental results on double-solid-phases slurry flow. Our numerical re- ------------------------ +1.75--------- - usi − uf if αf ≤ 0.8
⎪ αfd2si dsi
sults show more important flow characteristics than these reported. βfi = ⎨ (5)
⎪ 3 αsiρf usi − uf −2.65
We extended the limited earlier work on application of Eulerian -CD ---------------------------- αf
⎪ -- if αf > 0.8
multiphase approach with kinetic theory of granular flow to predict ⎩4 dsi

flow behaviors of CWSs in horizontal pipelines. The RNG k-ε tur-

bulent model was incorporated in the governing equation to model According to Syamlal [19], drag fore between two different solid
solid-liquid two phase turbulent flow with strong particle-particle phases is given by:
interaction in a wide range of Reynolds number. In simulations, the π π2
3 (1+ eij )⎛ --- + Cfr, ij -----⎞ αsiρsiαsi ρsi (dsi + dsj ) g0, ij
2
coal particles with bimodal distribution were subdivided into two ⎝2 8⎠
particle components and drag forces between solid and liquid, solid βij = ----------------------------------------------------------------------------------------------------
- usi − usj (6)
2π(ρsidsi + ρsjdsj)
3 3

and solid were taken into account. The model was validated with
pressure drop data from our experiments as well as pressure gradi- Where eij is restitution coefficient between ith and jth solid phase. dsi
ent and concentration profile data from the open literature. The ef- and dsj are the diameter of particles of ith and jth solid phase, respec-
fects of influx velocity, total influx concentration and grain compo- tively. Cfr, ij is the friction coefficient taken as 0.15 in the present work.
sition on constituent particles concentration and velocity distribu- 3. Constitutive Equation of Solid Phase
tion were investigated. The constitutive equations of solid phases are based on kinetic
theory for granular flow. Analogous to thermodynamic temperature
MATHEMATICAL MODELS in a gas, granular temperature for solid phase can be defined as [20]:

1. Governing Equations 1
Θs = --- 〈 c2〉 (7)
In Eulerian multiphase approaches, the macroscopic balance equa- 3
tions of mass, momentum conservation are solved for each phase.
hereis 〈 c2〉 the mean square of fluctuation velocity of particles, c=
The continuity and momentum equations for liquid and solid phase
us− 〈 us〉.
can be written as:
The transport equation for granular temperature based on con-
∂ servation of particles fluctuating energy is given by [21]:
---- (αfρf) + ∇ ⋅ (αfρfuf ) = 0 (1a)
∂t
3 ∂
--- ----( ρsiαsiΘsi) + ∇ ⋅ (ρsiαsiusiΘsi) = (− Psi I + τsi ): ∇usi
∂ 2 ∂t
---- (αsiρsi ) + ∇ ⋅ (αsiρsi usi ) = 0 (1b)
∂t
+ ∇ ⋅ (KΘsi∇Θsi ) − γΘsi + φfsi + Dfsi (8)
∂
---- (αfρf uf) + ∇ ⋅ (αf ρfufuf ) = − αf∇P + ∇ ⋅ τf
∂t The first term on the right-hand side of this equation represents
2
rates of production of pseudo-thermal energy by shear; the second
+ ∑ βfi (usi − uf ) + αfρf g (2a)
i=1
represents diffusive transport of pseudo-thermal energy. γΘ si repre-
sents dissipation of pseudo-thermal energy through inelastic colli-
∂-
--- (αsiρsi usi) + ∇ ⋅ (αsiρsiusiusi) = − αsi∇P − ∇Psi + ∇ ⋅ τsi sions, φfsi denotes exchange of fluctuating energy between fluid and
∂t
ith component of solid phase, Dfsi is granular energy dissipation rate,
+ βfi(uf − usi ) + βji (usj − usi ) + αsi ρsig (2b)
2
KΘ si is granular conductivity. They are defined as [18]:
∑ αsi + αf =1 (3)
150 ρsi dsi Θsiπ 2
i=1
- 1+ 6
KΘsi = --------------------------------- --- αsig0, ii(1+ eii )
384(1+ eii)g0, ii 5
where αf, ρf and uf are volume fraction, density and velocity of liquid
phase, respectively; αsi, ρsi and usi are volume fraction, density and Θ
+ 2α2siρsidsig0, ii (1+ eii) -----si- (9)
velocity of ith component of solid phase, respectively; ∇P and ∇Psi π
are pressure shared by all phase and collisional solid stress that re-
4
present additional stress in solid phase due to particle collisions. βfi γΘsi = 3(1− e2ii)g0, iiρsiα2siΘsi⎛⎝ ----- Θsi /π − ∇usi⎞⎠ (10)
dsi
and βji are moment exchange coefficients of liquid-solid and solid-
solid flow; ∇·τf and ∇·τsi are viscous stress tensors of liquid and φfsi=− 3βfiΘsi (11)
solid phase. For liquid phase:
dsiρsi ⎛ 18µf ⎞ 2
Dsi = ---------------- uf − usi
2
2 - ----------
2 - (12)
τf = αf µf, eff[ ∇uf + (∇uf ) ] − --- αf µf, eff(∇ ⋅ uf)I 4 πΘ ⎝ dsiρsi⎠
T
(4)
3 si

where µf, eff =µf +µt, f ; µf and µt, f are liquid molecular viscosity and Psi is given by [22]:
Korean J. Chem. Eng.(Vol. 26, No. 4)
1146 L. Chen et al.
2
d3
Psi = ρsi αsiΘsi + ∑ 2 ----3ji-( 1+ eij)ρsi Θsi g0, ijαsiαsj (13)
j=1 dsi

where g0, ii and g0, ij are radial distribution functions and the follow-
ing expressions are adopted [23]:
1/3 1
⎛2 ⎞ 2
α
g0, ii = 1− ⎜ ∑ αsi /αs, max⎟ + 0.5dsi∑ -----sk- (14)
⎝ i=1 ⎠ k=1 d sk

dsig0, ii + dsjg0, jj
g0, ij = ------------------------------
- (15)
dsi + dsj

where αs, max is the maximum packing fraction of the mixture.

The solid phase is dealt with a Newtonian fluid behavior and τsi
is given by: Fig. 1. Schematic diagram of experimental setup.
2
τsi = αsiµsi [∇usi + (∇usi )T ] + αsi⎛⎝λsi − --- µsi⎞⎠ (∇ ⋅ usi )I (16)
3 3 αs
qwi = ------πρsig0, ii ϕ ----------- Θ u ⋅u
6 αs, max si siw siw
where µsi and λsi are shear and bulk solid viscosity. They are defined
as [18,22]: 3 αs 3/2
− ------ πρsi g0, ii( 1− e2siw) ----------- Θ (21)
4 αs, max si
4 Θ 1/2
µsi = --- αsi ρsidsi g0, ii( 1+ eii)⎛⎝ -----si-⎞⎠
5 π Where usiw is particle slip velocity parallel to the wall, ϕ is the spec-
ularity coefficient representing the fraction of total momentum trans-
10 ρsi dsi Θsi π 2
- 1+ 4
+ ----------------------------------- --- αsig0, ii (1+ eii ) (17) ferred to the wall when particle collides with it, qwi is flux of granular
96 αsi (1+ eii )g0, ii 5
temperature toward the wall, and esiw is restitution coefficient of par-
4 Θ 1/2 ticle-wall collision.
λsi = --- αsi ρsidsi g0, ii( 1+ eii)⎛⎝-----si-⎞⎠ (18)
3 π
EXPERIMENTS AND NUMERICAL COMPUTATION
4. Turbulence Model
The homogeneous approach was employed where both phases 1. Experiments
are assumed to share the same values for k and ε. The RNG k-ε The numerical simulations were mainly based on our experimen-
turbulent mixture model is used in this study, which allows the mod- tal investigations on resistance properties of CWSs flowing in a set
el to better handle low Reynolds number and near wall flows than of horizontal pipes. Experiments were performed on a pilot scale
the standard k-ε turbulent model. slurry transport apparatus (at the School of Energy and Environment,
∂ Southeast University of China). A schematic diagram of experimen-
---- (ρmk) + ∇ ⋅ (ρm umk ) = ∇ ⋅ (akµm, eff∇k ) + µm, t S2 − ρmε (19a) tal set-up is shown in Fig. 1. It consists of a storage/preparation part,
∂t
∂- a test loop, measuring devices and a data acquisition system. The
--- (ρmε) + ∇ ⋅ (ρm um ε) = ∇ ⋅ (aεµm, eff ∇ε ) tested coal-water slurries were prepared and stored in the slurry tank.
∂t
A stirring device was mounted on the top of the slurry tank. During
ε ε2
+ C1ε ---µm, t S − C2ερm ---- − Eε
2
(19b) testing, the slurries were under stirring to prevent settling of solid
k k
particles and the slurry tank was well covered to prevent water loss.
where ak and aε are the inverse effective Prandtl number for k and The driving force for pumping test slurries was provided by a screw
ε, respectively. In high Reynolds number limit, ak=aε≈1.393. C1ε pump with a rated flow rate of 16 m3/h, driven by a YCT motor.
and C2ε are equal to 1.42 and 1.68. S is modulus of the mean rate- The flow properties of test slurries were characterized by steel pipes
of-strain tensor. Eε is given by Eε=(Cµρη3(1− η/η0))/(1+ζη3) ε 2/k, with various inner diameters (25 mm, 32 mm, 40 mm and 50 mm).
η=S·k/ε, η0≈4.38, ζ =0.012, Cµ=0.085. ρm and um are mean den- For each diameter, the test section was 2.2 m long and a sufficient
sity and mean velocity of the mixture. entrance before the test section was used to eliminate entrance ef-
5. Boundary Conditions fects. The flow rate Q and the pressure drop ∆P were measured by
The fluid and solid particles’ velocity distribution at the inlet was an electro-magnetic flow meter and electric differential-pressure
treated as uniform and the solid particles evenly distributed. The manometer, respectively. Both signals were converted from analog
continuous phase was assumed to obey a no slip boundary condi- to digital by an A/D converter and then recorded in a computer da-
tion at the wall and the standard wall functions were specified. Partial tabase for later retrieval and analysis. The slurry temperature was
slip boundary conditions for particle-wall interaction proposed by controlled by a heat exchanger incorporated in the end of the test
Johnson and Jackson were applied [24]. loop. At each test, the slurry temperature was maintained at the re-
quired level with deviation less than 1, and the signals of the slurry
3 αs temperature were recorded on-line during testing.
τsw = ------πρsig0, ii ϕ ----------- Θu (20)
6 αs, max si siw The effects of influx velocity, slurry temperature, pipe diameter
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 CFD simulation of coal-water slurry flowing in horizontal pipelines 1147

Table 1. Parameters of test slurries and operating conditions residual was set at 10−3. A computational domain L≥200D was used
Mean Test pipe to ensure fully developed flow results could be obtained for all pipes.
Solid density Total influx Slurry Owing to symmetry, it would be possible to model only a half of
particle diameter
/(g/cm )
3
concentration/% temperature the pipe. Tests were done to study the effects of mesh size on sim-
size/µm /mm
ulation results, and the investigations revealed that 8×16×800 cells
30.0 32 20
showed mesh-independent results. The values of restitution coeffi-
41.7 25, 32, 40, 50 20
1.465 134.5 cient and packing limit of solid particles have significant effects on
49.5 25, 32, 40, 50 20, 52 simulation results and must be selected with great care. In our in-
53.8 32 20, 52 vestigations, all coefficients of restitution among particles and between
particle and solid boundary were set at 0.7-0.95. The packing limits
for coarse and fine particles were all estimated as 0.65.

RESULTS AND DISCUSSIONS

1. Comparison of Numerical and Experimental Results

The present CFD model was firstly validated with experimental
data from reference [15]. Kaushal’s experiments were conducted
in 54.9 mm diameter horizontal pipe, and the pressure drop and con-
centration profiles were measured. The slurries had been prepared
by mixing 125 µm and 440 µm spherical glass beads with water.
The spherical glass beads have a mean density of 2,470 kg/m3 and
the volume ratio of the fine to coarse particles was 50 : 50 in the
prepared slurries. Fig. 3 depicts the comparison of pressure gradients
along the axis obtained from our CFD model with those of Kaushal’s
experiments. The numerical pressure gradients basically agree well
with the experimental results at all velocities. Only at velocity (V=
1 m/s) lower than the corresponding critical deposition velocity of
Fig. 2. Particle size distribution of coal particles. slurry flow do the data points appear to have an error of more than
20%. Fig. 4(a)-(d) show the comparisons between the model pre-
dicted and measured total volume concentration profiles along the
and total influx concentration on pressure drop were investigated. vertical diameter at various influx velocities. Both the numerical
The operating conditions and the parameters of the test slurries are and experimental data show that the total volume concentrations
listed in Table 1. Effects of influx volume fraction were investigated increase from top to bottom of the pipe when influx velocity is lower
at four different level ranged from 30% to 53.8%. Effects of tem- than 5 m/s. At an influx velocity of 5 m/s, the values of total volume
perature were investigated at 20 oC and 52 oC for 49.5% and 53.8% concentration are almost the same at all heights. It is obvious that
CWSs. The test slurries were self prepared by mixing coal powder the experimental data lie around the lines of the numerical results
with tap water in slurry tank. During testing, slurries were under
stirring to keep homogeneous at the entrance of test pipe. For each
test, new prepared slurries were used. Measurement was repeated
two or three times for more accuracy. Coal particles contained in
slurries have an average diameter 134.5 µm and the particle size
distributions are shown in Fig. 2. In numerical simulation, the solid
phase was regard as a binary mixture of 65 µm and 345 µm pulver-
ized coal according to two peaks as shown in Fig. 2, and the volume
ratio of the small to the large particles was taken as 3 : 1.
2. Numerical Methods
In numerical investigations, the flows were considered as steady
three-dimensional flow and the effects of viscous heating were neg-
ligible. The second-order upwind scheme was selected as the dis-
cretization scheme in all governing equations and the phase-cou-
pled SIMPLE iterative algorithm was used to resolve the coupling
between velocity and pressure. To avoid divergence, under-relax-
ation technique was applied. The under-relaxation factor for pres-
sure was 0.2-0.3, for momentum was 0.5-0.7, for granular tempera- Fig. 3. Comparisons of numerical pressure gradients with those
ture was 0.1-0.2, and these for turbulence kinetic energy and its dis- of Kaushal’s experiments for slurries of the mixture of 125
passion rate were 0.7-0.8. The convergence criteria were set at 10−4 µm and 440 µm particle sizes at 40% total influx concen-
for all equations except for the granular temperature equation which tration.
Korean J. Chem. Eng.(Vol. 26, No. 4)
1148 L. Chen et al.

Fig. 4. Comparisons of numerical concentration profiles along vertical diameter with those of Kaushal’s experiments for slurries of the
mixture of 125 µm and 440 µm particle sizes at 40% total influx concentration (S-Simulation; M-Measurement).

with perfect agreement, and the accuracy of the predictions is slightly

dependent on the influx velocities. Fig. 4(a)-(d) also give the calcu-
lated constituent particles concentrations along the vertical diame-
ters. The concentrations of larger particles along the vertical diameters
vary considerably at low influx velocities, and the fine particles are
distributed more uniformly at all height for various influx veloci-
ties. Those numerical data reasonably agree with Kaushal’s results,
although he did not give the detailed constituent particle concentra-
tion distributions for all influx velocities investigated. It can be con-
cluded from the above discussion that the present CFD model can
be used with confidence in predicting flow properties of slurries
with solid particle having a bimodal distribution.
The numerical results from the CFD model were also checked
and validated with the mean pressure gradient of our experiments
over a wide range of operating conditions. Comparisons of experi-
mental pressure drops with numerical data for 49.5% CWSs in dif-
ferent pipes and those for 49.5% and 53.8% CWSs at temperature
of 20 oC and 50 oC are shown by Fig. 5(a) and (b) respectively. The
discrete points and the corresponding solid curves represent experi-
mental data and numerical results, respectively. Clearly, all numeri-
cal results are in good agreement with experimental data. The mean
fraction deviations between the numerical and experiment results
are less than 20%, which is much lower than the predictive error of
25-50% with empirical correlations for pressure drops.
In Fig. 5(b) the experimental data shows that the fluidity of 53.8%
CWSs at temperature of 20 oC and 50 oC greatly decreases when
compared with that of lower concentrations. The biggest discrep-
ancies between the numerical results and experiment data take place
in the low range of influx velocities. When volume concentration
of solid particles approximates to its maximum packing fraction,
the flow regime of slurries becomes under control of solid motion
and these effects of properties of solid particles such as solid shape
come into play. However, non-spherical effects of coal particles are
not under consideration in the CFD model in which the solid par-
ticles are considered as spherical ones with the same diameters. Thus, Fig. 5. Comparisons of numerical and experimental pressure gra-
numerical results from the CFD model result in under-prediction dients for CWSs.
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 CFD simulation of coal-water slurry flowing in horizontal pipelines 1149

compared with the experimental data. It should be pointed out that

the discrepancies between the two would be greatly decreased at
high influx velocities. For slurries with concentrations lower than
50%, the numerical results also lead to a little underestimation of
pressure gradients in the low range of influx velocities. At low flow
velocities, the amount of solid particles at the low part of the pipe
increases due to gravitational effects. Similar to super dense slur-
ries, the effects of shape of solid particles cause more energy losses
in suspensions than the predictive results. However, the relative de-
viation between the simulation and experimental results did not ex-
ceed 10% because additional pressure losses are only confined to
the area of bottom of the pipe.
2. Concentration and Velocity Distributions in Vertical Plane
The volume concentration distribution of components and veloc-
ity distribution are mainly affected by influx velocity and total influx

Fig. 7. Volume concentration distributions of components and ve-

locity distribution in vertical plane at influx velocity of 0.5
m/s for 49.5% CWSs.

concentration of solid phases. Fig. 6 and Fig. 7 show volume con-

centration distribution of components and velocity distribution in
vertical plane at influx velocity of 0.2 m/s and 0.5 m/s for 49.5%
CWSs, respectively. Here, the mean velocity of the mixture is selected
to present slurry velocity because the slip velocity between solid
and liquid phase is so small to be negligible. It is observed that coarse
particle concentration varies considerably along the vertical height
due to gravitational force, while 65 µm particles are slightly more
uniformly distributed. The slurry velocities near the wall drop down
sharply due to strong viscous shear stress. The velocity profiles be-
come distorted from a circular shape due to the nonuniform distri-
bution of solid phases in the cross-sectional area of the pipe. It also
Fig. 6. Volume concentration distributions of components and ve- shows that increasing influx velocity leads to increase of unifor-
locity distribution in vertical plane at influx velocity of 0.2 mity of solid phase distribution, and the shape of constant velocity
m/s for 49.5% CWSs. contour curve becomes less distorted from a circular shape.
Korean J. Chem. Eng.(Vol. 26, No. 4)
1150 L. Chen et al.

Fig. 8. Volume concentration distribution along the vertical diameter.

3. Concentration Profile phase [3].

Fig. 8(a)-(d) depicts the calculated constituent particle concen- Fig. 8(a) shows that there are large gradients of total volume con-
trations and total volume concentrations along the vertical diame- centration on the top and bottom of pipelines for 30% slurries with
ters in the fully developed region for slurries at various influx ve- V=0.2 m/s, and the degree of uniformity of solid distribution along
locities and total influx concentrations, by volume concentration the vertical diameter increases with increase in influx velocity. This
vs. r/R, with r being the distance from the pipe center and R being is expected because with increase in influx velocity there will be
the pipe radius. From Fig. 8(a)-(c), it is observed that the total vol- an increase in turbulent energy, which is a main responsibility for
ume concentration distribution of solid phases shows large gradi- keeping solid suspended. For a given influx velocity, increasing con-
ent along the vertical diameter because of gravitational effects in centration enhances uniformity of solid distribution due to enhanced
the low range of influx velocities, which indicates that the flow of interference effects between solid particles. Fig. 8(d) shows that 53.8%
slurries belongs to heterogeneous regime. It is also observed that slurries keeps almost homogeneous flow even at very low influx
the distributions of total volume concentration at various influx veloc- velocity, which suggests that the interaction and interference effects
ities are similar to each other for the same slurries. In the central between solid particles become the controlling factor of slurry flow.
part of the pipeline, the total volume concentration is slightly higher From Fig. 8(a)-(d), it is observed that for a given influx velocity,
than the total influx concentrations and is almost kept constant when the central region with zero total volume concentration gradient ex-
influx velocity is increased. On the top of the pipeline, the total vol- pands with increasing total influx concentration. Simultaneously, the
ume concentration is lower than its total influx concentration and de- region with lower concentration on the top of the pipeline is con-
creases gradually with increasing r/R. However, in the low part of tracted, while the region with higher concentration in the low part
the pipeline, the same tendency has been observed but the gradient of pipeline remains almost unchanged, which occupies 1/4 height
of total volume concentration is higher than that on the top of the in the vertical diameter. Another surprising finding is that increas-
pipeline. This suggested that for our slurries with solid phase having ing influx velocity enhances the uniformity of solid distribution, while
bimodal distribution, the total volume concentration profile along the sizes of three regions keep almost invariant.
the vertical diameter is similar to that of slurries with single solid It is clear in Fig. 8(a)-(c) that the concentrations of 345 µm par-
July, 2009
 CFD simulation of coal-water slurry flowing in horizontal pipelines 1151

Fig. 9. Axial velocity distribution along the vertical diameter.

ticles along vertical diameters vary considerably due to gravitational concentrations and constituent particle concentrations in the hori-
force at low influx velocity and they show a similar distribution with zontal diameter remain uniform irrespective of influx velocity and
those of total volume concentration. However, 65 µm particles are total influx concentration. This conclusion is consistent with the
distributed more uniformly at all heights expect for in the low part experimental results from literature [16].
of pipelines. This distribution pattern is similar to those of dense 4. Velocity Profile
slurries with double species having different particle size or density The addition of solid particles to turbulent liquid flow will mod-
showed by experiments [16] as well as by CFD simulation [25]. ify velocity distribution of the flow. Fig. 9(a)-(d) depict the calcu-
The volume ratio of coarse to fine particles in low parts of pipelines lated dimensionless axial velocity profiles along the vertical diameters
shows significant deviation from influx value at low influx velocity. in fully developed region for slurries at different influx velocities.
The more coarse particles accumulate in the low part of the pipe- Here the dimensionless velocities are calculated in terms of ratio of
line, the more fine particles are piled out of the same region. This mean velocity of the mixture to influx velocity, um/V. From Fig. 9(a)-
suggests that the solid distribution is not only affected by gravita- (b), one can observe that the axial velocity profiles are obviously
tional effects but also by strong particle-particle interactions between asymmetric along the vertical diameter in flow of 30% slurries and
fine and coarse particles. With increase of influx velocity and total 41.7% slurries when influx velocity is lower than 0.5 m/s. The veloc-
influx concentration, inhomogeneity of the constituent particle con- ity profiles in lower part of the pipe centerline would be lower than
centration profile is gradually reduced. When total influx concentra- those in the upper part. This is expected because the solid concen-
tion is beyond 50%, the flow almost becomes homogeneous regime trations in the lower part of the pipelines are much higher than those
with constituent particles being distributed uniformly at all influx in the upper part based on the effects of gravity, and more dissipated
velocities investigated. energy will be consumed to drive particles for water in the lower
As expected, the calculated results suggest that the total volume part, which results in a lower velocity in this area. With increase of
Korean J. Chem. Eng.(Vol. 26, No. 4)
1152 L. Chen et al.

influx velocity, the degree of asymmetry of the velocity profile de- variance of total volume concentration and constituent particle con-
creases. For slurries with single solid phase, the degree of asym- centration. The axial velocity distribution along the vertical diame-
metry of axis velocity along the vertical diameter is a measurement ter is much different from that along the horizontal one, though the
of the uniformity of solid particle concentration distribution in the asymmetry of velocity profile along the vertical diameter is reduced
vertical plane [5]. However, for slurries with solid phase having bi- by the difference in local volume ratio of coarse to fine particles
modal distribution, the asymmetry of the axis velocity along the between the lower and upper parts of pipelines. The velocity and
vertical diameter is also affected by the local volume ratio of coarse its gradient along the horizontal diameter are much higher than those
to fine particles. From Fig. 8(a)-(b) and Fig. 9(a)-(b), it is clear that along the vertical diameter in a short region near the pipe wall, while
there are fairly high gradients of total volume concentration in the in the region near the centerline, the velocity along the horizontal
lower and upper parts of pipelines for 30% and 41.7% slurries at diameter is higher and distributed more uniformly. This makes the
influx velocities of 1.0 m/s and 0.5 m/s, respectively. However, the constant velocity contour curve in vertical plane become oblate, as
velocity profiles along vertical diameters become almost symmetric. shown by Fig. 7(d). For slurries with single solid phase, the velocity
This is mainly due to the fact that the difference in volume ratio of profiles along the vertical and horizontal diameters are symmetric
coarse to fine particles between the lower and upper parts of pipe- and exactly the same in a homogeneous flow regime. Discrepan-
lines reduces the asymmetry of the velocity profile along the verti- cies between the two profiles would appear for nonuniform distri-
cal diameter which arises from nonuniformity of the total volume bution of volume concentration in slurry flow. However, for our
concentration distribution in slurries. For 49.5% slurries and 53.8% slurries with solid phase having bimodal distribution, the discrep-
slurries, the velocity profiles along vertical diameters are symmetric ancies between the two profiles are the synthesis results of nonuni-
even at the lowest influx velocity studied. form distribution of total volume concentration and the differences
For comparison, the velocity profile of single phase turbulent in local volume ratio of coarse to fine particles between the lower
flow is also given by one-seventh power law u/V=60/49(1−(r/R))1/7 and upper parts of pipelines.
in Fig. 9(a)-(d). Single phase turbulent flow is characterized for its 5. Effects of Grain Composition
high velocity gradient very near the pipe wall and an approximately It is very difficult to investigate the effects of grain composition
uniform flow velocity across the rest of the pipe. The velocity pro- on flow behaviors of CWSs by experiments on our pilot scale trans-
files of 30% slurries in fully developed suspended flow show less port apparatus, but it is easy to obtain them in numerical investiga-
velocity gradient near the pipe wall and more velocity gradient in tion. Numerical investigations of effects of grain composition were
the region near the centerline than single phase turbulent flow. As carried out by comparing numerical results of our double-solid-phase
the solid concentration is increased, the velocity and its gradients in- method with those of single-solid-phase method in the same frame-
crease more near the centerline as a result of further reduced turbu- work of Eulerian multiphase approach. In the single-solid-phase
lence intensity. As mentioned above, the flow of 53.8% slurries be- method, the coal particles with bimodal distribution are considered
comes under control of the solid motion, and the velocity gradient as single solid phase, which has the same mean particle diameter
disappears in the region near the centerline. as solid phases in our double-solid-phase methods. Fig. 11 shows
Fig. 10 shows the comparison of axial velocity distribution along the comparison of experimental pressure gradients with numerical
vertical diameter with that along horizontal diameter for 49.5% coal- results obtained by single/double-solid-phase methods for 41.7%
water slurry at influx velocity of 0.5 m/s. Clearly, the axial velocity slurries. The numerical pressure gradients by double-solid-phase
profile along the horizontal diameter is symmetric as a result of in- methods are in good agreement with the experimental data. How-

Fig. 10. Comparison of axial velocity distribution along vertical Fig. 11. Comparison of experimental pressure gradients with nu-
diameter with that along horizontal diameter (Ct=49.5%, merical results obtained by single/double-solid-phase meth-
V=0.5 m/s, T=20 oC, D=32 mm). ods (Ct =41.7%, T=20 oC, D=32 mm).
July, 2009
 CFD simulation of coal-water slurry flowing in horizontal pipelines 1153

vertical diameter varies considerably at lower influx velocity and

concentration, while the fine particles are distributed more uniformly
in the vertical plane. The solid phases are distributed more uniformly
at higher influx velocity and solid concentration.
(3) The axial velocity profiles along vertical diameter are affected
not only by the total volume concentration distribution but also by
the local volume ratio of fine to coarse particles. The axial velocity
distribution along the vertical diameter usually shows great dis-
crepancies from that along the horizontal diameter.
(4) Coal-water slurries filled with binary solid phase are distrib-
uted more uniformly and exhibit higher fluidity than slurries with
single solid phase.

ACKNOWLEDGMENT

This study was funded by the State Basic Research Development

Program (973 Plan) of China (No. 2004CB217701).
Fig. 12. Numerical concentration profiles along vertical diameter
obtained by single/double-solid-phase methods (Ct=41.7%,
T=20 oC, D=32 mm). NOMENCLATURE

CD : drag coefficient
ever, the single-solid-phase method overestimates the values of pres- Ct : total volume concentration [%]
sure drops, especially at high velocity. This suggests that fluidity of D : test pipe diameter [mm]
slurries filled with both fine and coarse particles is enhanced by fine Dfsi : granular energy dissipation rate [kg/s3m]
particles filling up the interspaces formed by coarse particles. Fig. 12 d : particle diameter [m]
presents numerical (total) volume concentration profiles along the e : restitution coefficient
vertical diameters obtained by single/double-solid-phase methods g : acceleration gravity [m/s2]
for 41.7% slurries. Obviously, the solid phases of slurries filled with g0 : radial distribution function
fine and coarse coal particles are distributed more uniformly than I : unit tensor
those of slurries filled with single solid phase at all influx velocities, KΘ si : granular conductivity
especially on the top of pipelines. It is concluded that the arrange- k : turbulence kinetic energy [m2/s2]
ment of particles in the mixture is improved with the fine particles L : length of pipe [mm]
filling the void spaces between the coarse particles, and the stability P : pressure [kg/m·s2]
of slurries is enhanced by the strong particle-particle interactions R : test pipe radius [mm]
between fine and coarse particles. This also well explains why lower r : radius [m]
energies are consumed in flow of slurries with solid phase having T : slurry temperature [oC]
bimodal distribution. u : velocity vector
u : velocity [m/s]
CONCLUSION V : influx velocity [m/s]

The Eulerian multiphase approach with kinetic theory of granu- Greek Letters
lar flow was applied to predict flow behaviors of coal-water slurries α : volume fraction
in horizontal pipelines. The numerical investigations have displayed β : inter-phase drag coefficient [kg/m3 ·s]
some important slurry flow characteristics, such as constituent par- λ : bulk viscosity [kg/m·s−1]
ticles concentration and velocity distribution as well as pressure gradi- µ : viscosity [kg/m·s−1]
ents. Based on our experimental and numerical investigations, the µt, f : turbulence viscosity of liquid [kg/m·s2]
following conclusions can be made: ρ : density [g/cm3]
(1) The model proposed here captures the main features of solid- ε : dissipation rate of k [m2/s3]
liquid flow of super dense coal-water slurries in horizontal pipe- ϕ : specularity coefficient
lines over a wide range of operating conditions. Numerical predic- τ : viscous stress tensor [kg/m·s−2]
tions for the pressure gradients are in good agreement with the ex- γΘ si : collision dissipation of energy [kg/s3m]
perimental data when total influx concentrations are not more than Θs : granular temperature [m2/s2]
50%. φfsi : transfer rate of kinetic energy [kg/s3m]
(2) The total and constituent particle volume concentration pro-
files along the vertical diameter are affected not only by gravitational Subscripts
force but also by strong particle-particle interactions between fine f : fluid
and coarse particles. The concentration of coarse particles along ij : between ith and jth solid phase
Korean J. Chem. Eng.(Vol. 26, No. 4)
1154 L. Chen et al.

m : mean value of the mixture neering Journal, 132, 159 (2007).

max : maximum 12. S. Roy and M. P. Dudukovic, Industrial and Engineering Chemis-
si, sj : ith or jth component of solid phase try Research, 40, 5440 (2001).
13. Y. Cheng and J. Zhu, Canadian Journal of Chemical Engineering,
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