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Study on Flow Properties of Coal-Water Paste in Pipes.

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Dev. Chem. Eng. Mineral Process., 8(3/4),pp.323-332,2#0.
Study on Flow Properties of Coal-Water
Paste in Pipes
L. Meng*, M. Zhang and L. Shen
Thennoenergy Engineering Research Institute, Southeast University,
Nanjing 2 10096, l? R. CHINA
In this paper the similitude criterion known as generalized Reynolds number
f ('1
is proposed to characterize the flow state of
coal-water paste in pipes, on the assumption of coal-water paste as a non-Newtonian
fluid and for slip jlow phenomenon in pipes. It can be used to describe the no-slip
jlow of non-Newtonian and Newtonian fluidsbehaving as steady-state laminarflow in
pipes. A convenient new method of determining the resistance properries of coalwater paste is suggested.
Keywords: coal-waterpaste (CWP); slip flow; generalized Reynolds number (Re, ).
With the development of Pressurized Fluidized Bed Combustion (PFBC), a new
feedstock technique of pumping coal-water paste (CWP) with high solids
concentrations into a pressurized fluidized bed has become the focus of power energy
researchers in many countries. Coal-water paste often has non-Newtonian fluid
properties, therefore wall slip flow and negative wall slip flow exist in pipes, and it is
difficult to determine the resistance properties in pipes by theoretical methods (e.g.
Wardell, 1995).
* Authorfor correspondence (email:
L. Meng, M. Utang and L Shen
Our objective was to find a convenient new method to determine the resistance
properties of CWP and to calculate its flowing resistant loss in pipes. Experimental
and theoretical studies were conducted on the flow characteristics in the slip layer of
CWP. On the assumption that CWP is a two-phase non-Newtonian fluid, the
similitude criterion of generalized Reynolds number (Red is proposed, which can
characterize the flowing state of CWP in pipes.
Resistance Properties of CWP in Pipes
One of the problems for pressurized fluidized bed combustion is the stable feeding of
coal. There are two types of feeding methods, wet and dry. The wet feeding method
has many advantages, e.g. it eliminates the need for coal dryers, promotes the
reliability of its apparatus, and attains a uniform temperature profile in the bed.
Information on wet coal feeding is of great importance for PFBC, however little
research has been done on wet coal feeding, especially for resistance properties of the
flow of coal-water paste and the slip flow in pipes. As a result, this aspect is not well
understood. Thus, it is necessary to provide a new method of determining the
resistance properties of CWP for pumping calculations.
Derivation of the Generalized Reynolds Number, Re,
To derive the general Reynolds number Ree, the following assumptions are made.
The coal-water paste of high solids concentration flows as a steady-state
laminar flow in pipes, and its rheological model can be expressed by the
Herschel-Bulkleyequation (Zhang and Kong, 1990).
T=Z, + Ky"
There is a positive slip flow of C W P near the pipe wall, and the slip
velocity in the slip layer Us> 0.
The CWP in the slip layer at the pipe wall has a low solid concentration,
and the slip layer is very thin.
The CWP flows in the slip layer as a laminar flow and the shear stress in the
slip layer is constant, i.e. Z = 2,, as shown in Figure 1.
Flow Properties of Coal-Water Paste in Pipes
Figure I . Schematic diagram of CWP flowing in pipes.
For the above assumptions, the shear stress in the slip layer can be derived as:
z=p,u,/s =z,
When there is a negative slip flow of C W P near the pipe wall, the slip velocity in the
slip layer is Usc 0. The shear stress in the negative slip layer can also be expressed
by (Hanand Jiang, 1990; Antonini et al., 1984):
z = -psusI s = z,
(2b 1
For convenience, both Equations (2a) and (2b)can be expressed as:
z, = p y, = pu, I 6
(3 1
At the position r = R- 6 shown in Figure 1, by combining Equations (1) and (3):
z = p[(r, -z,)/K]'"
For a viscous fluid flowing in pipes, the friction loss factor
A = 82, / ( p V 2 )
2 can be given by:
Substituting Equation (3) into Equation (5), then:
A = 64M /Re
Re = pVDIp
M = y, /(8V I D)
L Meng, M.Zhang and L Shen
Re./M is h o w as the generalized Reynolds number, Re,, that is:
Re, = Re/M
Substituting Equation (9) into Equation (6):
A = 64/Re,
For determining the specific form of Re, in Equation (9), using Equation (1):
Y=-- dUc - [(.-.,)/K]””
Thus, the volumetric flow rate of no slip Q c in a pipe is as follows:
Substituting Equation (11) into Equation (12), and integrating:
3n + 1
(2n + 1)(3n+ 1) (2n + 1)(3n+ l)(n + 1)
- (2n + 1)(3n+ l)(n+ 1)1 ”(7,
where a = 2, / Z, = rb/ R , is the ratio of the radius in the plug flow region to the
pipe radius:
+l)(n +1) (2n+1)en+1)(n+1)
f ( a )=3n +1 (2n +I)@
+1) - (2.n +
Because 4Qc/ ( M 3 =
) 8Vc /D,y,=[(Z, --Z,)/K]””, Equation (13) can be
rewritten as:
8V, 1D = Y , f ( 4
Flow Properties of Coal-Water Paste in Pipes
Assuming that additional slip flow rate is induced by slip flow, Qs=X R2Us,the actual
flow rate Q in pipes is equal to the flow rate of no-slip Qe and Qs,
that is:
Q = Q c +Q,
( 16a)
v =vc+us
Substituting Equations (15) and (16b) into Equation (8):
M = ( l - U s 1V)l f ( a )
Substituting Equation (4)into Equation (7):
Re =-pvD [(z, - z, ) / K3l'"
Substituting Equations (17) and (18) into Equation (9), the generalized Reynolds
number, Re,, of coal- water paste can be obtained:
Discussion of Generalized Reynolds Number, Re,
Effect of slipjlow on Re,
To determine the generalized Reynolds number given in Equation (19), the slip
velocity (Us)in the slip layer is defined as follows (Antonini et al., 1984; Jastrzebski,
U s= P,z, I R
( 20 )
Q, =RRpczw
where the slip correction coefficient
is a function only of the wall shear stress 2,,
and has no relation to the radius of the tube R. When CWP flows through two
L. Meng, M. Zhang and L Shen
different size diameter pipes, in which wall sheer stress 2, is in the common range,
the slip correction coefficient can be written as follows (Meng and Zhang, 1995):
SubstitutingEquations (13) and (21) into (16a):
- z , ) / k ] " " f ( a )+ R RP,r,
can be experimentally determined from Equation (22). The value of 2,
for the specific coal-water paste can be obtained from Equation (23) corresponding to
the experimental flow rate, Q. Therefore, Re, and h can be calculated from Equations
(19) and (lo),respectively.
and Usare positive when there is a positive slip flow of CWP in a pipe, that is b, >O
From the above discussion on slip flow, and using Equation (19), the values of
and U,>O. Under the same conditions, the positive slip flow makes the generalized
Reynolds number larger than no slip flow. As shown in Equation (lo), the slip flow
reduces the friction loss factor h, and the flowability of CWP increases. However, the
values of
p, and Usare negative when there is a negative slip flow of CWP in a pipe,
that is p,cO and U, <O.
Also, under the same conditions, the negative slip flow
reduces the generalized Reynolds number than for no-slip flow, the friction loss factor
h increases, and the flowability of CWP reduced.
The commonness of Re,
Under the condition of low concentration, coal-water paste often behaves as a
Bingham fluid, that is n=l, 7, = 2, , K = 7,so Equation (19) can be simplified as:
- pVD(1 - a )
f (a>
- q(1- us/V)
- pVD(1- 4a 13 + a413)
N1- usl V >
Flow Properties of Coal-Water Paste in Pipes
If no slip flow occurs, that is Us=O,
v =vc,then Equation (24) can be further
simplified as:
Re; = Reb/(l+ -)' b
= Reb/(l+ -)Hzb
6 Re,
where Re, = pm/q and
= pZbD2/ q 2 are called the Bingham-Reynolds
number and Bingham-Hertz number, respectively. Re," is often called the generalized
Reynolds number of a Bingham fluid under the condition of no-slip flow, which is a
special form of Equation (19).
For no slip flow of a power-law fluid, it can be shown that Equation (19) can
also be simplified in the same way:
pV2-"Dn(-)n 4n
= pV2-"Dn
where K'=K[(3n+1)/4nIn. Equation (26) is simply the Reynolds number for a powerlaw fluid under the no-slip flow conditions (see Lyczkowski et al., 1992). For
Newtonian fluid flow in pipes, Equation (19) can be simplified to Equation (7),which
is the normal form of Reynolds number.
As stated above, the Reynolds number used in Equation (19) is a universal form
for almost all viscous and plastic fluids, therefore it is referred to as the generalized
Reynolds number. For the steady laminar flow of general viscous and plastic fluids in
pipes, the calculation of friction loss factors is the same as for a Newtonian fluid
given by Equation (lo), provided the Reynolds numbers are calculated from Equation
Experimental results
Experimental measurements were investigated. The diameters of the flow loops are:
@2.0cm and @3.2cm, respectively. The coal-water pastes with different water
contents of 25.48-28.8 wt% were prepared by blending two components of 0-0.4 mm
fine and 0.4-5 mm coarse coal powder at three different ratios. The ratios of coarse
powder to fine one were as follows: 7525, 60:40, 8515. The actual flow rate in the
test loops was measured by an electromagnetic flowmeter, which is calibrated using
L.Meng, M . B a n g and L Shen
water and the actual coal-water paste. The pressure drops (AP)through a section of
pipe of radius R and length L, lying in a horizontal plane, were measured by an
electric differential manometer with the diaphragm apparatus. The actual measured
friction loss factor is given by:
The experimental results show that the relative deviations between the calculated
value of the friction loss factor from Equation (lo), and the measured value are
generally within 5%. Also, the maximum deviation is less than 10%in the range of
Re, = 2 - 1OOO. The experimentalresults are shown in Figure 2.
The generalized Reynolds number is proposed to characterize the two-phase
(solid-liquid) flow of a non-Newtonian fluid, in which the slip flow factor Usis
taken into account. It can also be used to describe the no-slip flow of nonNewtonian and Newtonian fluids behaving as steady-state laminar flow in pipes.
The form of the generalized Reynolds number defined in Equation (19), which is
used to calculate the friction loss factor for the complex non-Newtonian fluid
with slip flow, is similar to that used for a simple Newtonian fluid. In exhibits
satisfactory accuracy in calculation.
Under the same conditions, the positive slip makes the generalized Reynolds
number larger than for no-slip flow. Also, it reduces the friction loss factor h,
and the flowability of C W P increases. However, the negative slip makes the
generalized Reynolds number less than no-slip flow, the friction loss factor h
larger, and the flowability of CWP reduced.
Flow Properties of Coal-Water Paste in Pipes
Figure 2. Frictionfactor-Reynoldr number relationshipfor CWP through straight
PB is the ratio of coarse coal powder tofine coal;
Wt means that the water content in CWP .
PB =75:25, D=32mm, Wk28.796; 0 PB = 7525, D=2Omm, Wt=25.74%
PB = 7525, D=2Omm,Wt==8.8%; PB = 7525, D=32mm, Wt==S.74%
VPB = 60.40, D=20mm,Wt==8.53%; PB = 60:40, DdOmm, Wt==5.48%
PB = 60:40, D=32mm,Wt==8.53%; PB = 85:15, D==Omm,Wt=28.7%
PB = 85:15, D=2Omm,Wt==5.64%; V PB = 85:15, D==Omm,Wt==7.1%
+ PB = 85:15, D=32mm, Wt=28.7%; x PB = 8525, DdOmm,Wt==5.64%
L.Meng, M.Ba n g and L Shen
Parameter in Equation ( 13)
Diameter (m)
Hertz number (dimensionless)
Denseness factor of nonNewtonian fluid (Pas")
J-ength (m)
Parameter in Equation (7)
Flow exponent of nonNewtonian fluid (dimensionless)
Pressure (Pa)
Pressure drop (Pa)
Volumetric flow rate <m3/s)
Volumetric flow rate of slip flow
Reynolds number
Velocity (mls)
Slip velocity (mls)
Average velocity in tube (ds)
Axial co-ordinate (m)
Greek Wers
q Bingham fluid viscous factor
Pc Slip correction coefficient
y Shear rate (s-' )
6 Thickness of slip layer (m)
5 Friction loss factor
p Liquid viscous factor (Pas)
p Density (kg/m3)
z Shear stress (Pa)
b Bingham
c no slip
w wall
y yield
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Rheology, East China Institute of Chemical Technology Press, Shanghai, pp.56-58.
Han, Y.,and Jiang, T. 1990. Study on the effect of wall slip for Sesbania gum flowing through capillary
tubes and porous media, J. Chem. Ind. & Eng. (China),Vo1.38.30-35.
Antonini, G., Fmcois, O., Gislais, P., Touret, A.. and Gitand, P. 1984. 6th International Symposium on
Coal Slurry Combustion and Technology, Orlando, Florida, pp.266-288.
Jashzebski. Z.D.1%7. Ind. Eng. Chem. Fund., 6, pp.445-454.
Kozicki, W.,Pasri, S.N.,and Rao. A.R.K. 1970. Chem. Eng. Sci., 25, p.41.
Meng, L., and Zhang, M. 1995. The measurement of coal-water slurry flow-rate in pipes, Journal Of
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flow, past, water, properties, coal, stud, pipes
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