CFD modeling of pilot-scale pump-mixer: Single-phase head
and power characteristics
K.K. Singh b,∗ , S.M. Mahajani b , K.T. Shenoy c , A.W. Patwardhan a , S.K. Ghosh c
a Mumbai University Institute of Chemical Technology, Matunga, Mumbai 400019, India
b Department of Chemical Engineering, Indian Institute of Technology, Powai, Mumbai 400074, India
c Chemical Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India
Abstract
The present work involves single-phase computational fluid dynamics (CFD) simulations of continuous flow pump-mixer employing topshrouded Rushton turbines with trapezoidal blades. Baffle—impeller interaction has been modeled using sliding mesh and multiple reference
frame approaches. Standard k– model has been used for turbulence modeling. Several CFD runs representing different combinations of
geometric and process parameters have been carried out. Results of CFD simulations have been used to find out two macroscopic performance
parameters of pump-mixer—power consumption and head generated by the impeller. The simulation results have been compared with the
experimental data obtained on a pilot-scale setup. Good agreement between CFD predictions and experimental results is observed. In most
cases, sliding mesh approach is found to perform better than multiple reference frame approach. Details from CFD simulations have been used
to have an insight into the pumping action of the impeller.
Keywords: CFD; Sliding mesh; Multiple reference frame; Pump-mixer; Power; Head
1. Introduction
Due to their inherent advantages like simplicity and flexibility of operations, high stage efficiency, etc., mixer-settlers
are widely used for solvent extraction which is an important
unit operation. It is often required to operate several stages of
mixer-settlers giving rise to counter or co-current flow effects
between the contacting phases. At times, recycling of part of
extract or raffinate within the same stage is required to maintain a desirable extract to raffinate phase ratio in the mixer.
This requires inter-stage or intra-stage pumping of the process
fluids. Pumping action of the impeller in a mixer can be harnessed to bring about such inter-stage or intra-stage pumping
thereby reducing the turbo-machinery in the plant and associated preventive and breakdown maintenance. A mixer designed
to serve this dual purpose of mixing and pumping is called a
pump-mixer (Coplan et al., 1954). Though the pump-mixers
are essentially used for producing dispersions of a liquid phase
in another immiscible liquid phase, single-phase characteristics
are equally important as, with the present status of computing
hardware, a practical way of solving population balance in agitated vessels calls for pseudo-single-phase modeling to get the
parameters that eventually control drop breakage and coalescence and hence dictate the drop size distributions (Alopaeus
et al., 1999; Maggioris et al., 2000; Alexopoulos et al., 2002;
Alopaeus et al., 2002). The two important design or performance parameters of a pump-mixer are its power consumption
and head generation both of which are affected by several
parameters which can be classified either as geometric or process parameters. While the important geometric parameters are
type of impeller, number and width of blades in the impeller,
size of the impeller relative to the tank size and location of
the impeller in the tank, the important process parameters are
the flow rate and impeller speed. Several studies that attempt
to investigate effect of these parameters have been reported
in literature. However, most of these studies have been done
on batch vessels and consequently do not address the issue of
1309
effects of these parameters on pumping head generated by the
impeller.
Impeller off-bottom clearance is an important geometric parameter and its effect on flow patterns and power consumption
in batch stirred tanks has been a subject of several experimental
and computational investigations (Nienow, 1968; Conti et al.,
1981; Ibrahim and Nienow, 1995; Armenante and Nagamire,
1998; Montante et al., 1999, 2001a,b). The most important finding of these studies is that below a certain value of clearance
even a radial flow impeller behaves like an axial flow impeller.
This transition is accompanied by a step reduction in power
consumption. A recent study reports the similar observation for
continuous flow pump-mixer (Singh et al., 2004). Studies on the
effect of clearance on head characteristics of pump-mixer are
relatively few (Rao and Baird, 1984; Singh et al., 2003, 2004).
These studies show that for pump-mixers having an orifice at
the bottom plate as an inlet, head generated by the impeller
increases on reducing the clearance.
A few studies investigate the effect of number of impeller
blades on power consumption in batch stirred vessels and show
the power consumption to go up with increasing number of
blades (Bates et al., 1963; Nienow et al., 1995). This could
be explained in terms of the increase in total drag acting on
impeller with increase in number of blades. A study on head
generated by a top shrouded Rushton turbine employed in continuous flow pump-mixer shows head characteristic exhibiting
a maximum with increasing number of blades (Singh et al.,
2003).
Effect of impeller blade width on power consumption in
batch stirred tanks has been reported either as effect of blade
width to tank diameter ratio (Bates et al., 1963) or as effect
of impeller disk thickness to impeller diameter ratio (Bujalski
et al., 1987; Rutherford et al., 1996; Chapple et al., 2002).
Effect of blade width on power consumption in continuous
flow pump-mixer has also been reported (Singh et al., 2003).
Owing to increase in total blade area and hence drag acting
on it, power consumption has been shown to increase with
increasing impeller width to diameter ratio. No study reports
on effect of blade width on head generated by the impeller in
a continuous flow mixer.
Effect of impeller diameter to tank diameter ratio on power
number for batch vessels has also been reported extensively
(Rushton et al., 1950; Bates et al., 1963; Bujalski et al., 1987;
Ibrahim and Nienow, 1995; Chapple et al., 2002). Two studies
report on the effect of impeller diameter to tank diameter ratio
on the power number for a pump-mixer (Singh et al., 2003,
2004). These two studies discuss also the effect of impeller
diameter to tank diameter ratio on the head developed by the
impeller.
Effect of impeller speed on power consumption has been
the most conventional study in batch mixing. These studies
have been done for different impellers and results have been
presented as power number—Reynolds number curves which
can be used for design of the impeller (Rushton et al., 1950;
Bujalski et al., 1987; Ibrahim and Nienow, 1995; Vasconcelos
et al., 2000; Chapple et al., 2002; Shekhar and Jayanti, 2002).
Similar studies on effect of impeller speed on power con-
sumption have been done for pump-mixers (Singh et al., 2003,
2004). Effect of impeller speed on head generated by the impeller has also been reported (Harel et al., 1983; Singh et al.,
2003, 2004).
The effect of flow rate on power consumption in pumpmixers has been investigated and found to be insignificant
(Singh et al., 2003, 2004). Like in a centrifugal pump,
head—flow characteristics are very important for the design of
the pump-mixer. However, only a few studies report on the effect of flow rate on head generated by the impeller (Harel et al.,
1983; Singh et al., 2003, 2004). These studies show, as is true
in case of centrifugal pumps, head to decrease with increasing
flow rate.
There exist several commercial designs of pump-mixer like
IMI design, Krebs design, Denevr design, Kemira design, DavyPowergas design and General Mills design (In Lo et al., 1983;
Godfrey and Slater, 1994). However, in the open literature, only
the qualitative aspects of these designs have been discussed.
Most of the studies cited above are based on experimental investigations and empirical modeling as a large number of
variables and their complex interplay render mathematical description and its solution very difficult. However, advances in
powerful numerical simulation tools like computational fluid
dynamics (CFD) coupled with improvement in computing hardware have enabled us to gradually move from empirical to
knowledge-based design. Going by the literature published in
the recent past, CFD has been extensively used to model mechanically agitated vessels (Aubin et al., 2004; Yeoh et al.,
2004; Montante et al., 2005; Li et al., 2005). However, most of
these studies are focused on batch operations and CFD studies on continuous mixers, especially on head characteristics of
pumping impellers, are difficult to come across. To the best of
the knowledge of the authors, the present work seems to be the
first published CFD study on pump-mixers.
2. CFD modeling of mechanically agitated baffled tanks
CFD modeling of mechanically agitated baffled tanks poses
a unique problem of modeling of interaction between static
baffles and rotating impeller. Over the years dedicated efforts have been made to overcome this problem, as a result of which different techniques have evolved and been
validated.
The earliest attempts at numerical simulations of flow field
in mechanically agitated vessels employed an approach called
impeller boundary condition approach (Harvey and Greaves,
1982; Middleton et al., 1986; Pericleous and Patel, 1987;
Ranade et al., 1989; Ranade and Joshi, 1990; Kresta and
Woods, 1991; Fokema et al., 1994; Armenante et al., 1994).
In this approach, impeller was not physically modeled and
was represented either in terms of boundary conditions at the
surface of the volume swept by it or in terms of source terms
distributed throughout its volume. Values of boundary conditions or source terms were obtained from experimental data or
by simple flow models in impeller region. Experimental data
being a prerequisite, this modeling approach could not be used
as a design tool.
1310
This constraint of impeller boundary condition approach
shifted research focus on developing generic modeling procedures that did not need any recourse to empirical or experimental data as boundary conditions. Consequently, several
general approaches have been reported in literature on explicit
simulation of whole flow field in agitated tanks. The three
main generalized approaches are multiple reference frame
(MRF) approach (Luo et al., 1994; Bujalski et al., 2002), computational snapshot approach (Ranade et al., 1996, 2001) and
sliding mesh (SM) approach (Perng and Murthy, 1993; Murthy
et al., 1994; Tabor et al., 1996; Lee et al., 1996; Daskopoulos
and Harris, 1996). While the first two approaches involve steady
state computations and produce time averaged flow field, the
third approach involves transient computations to produce time
accurate flow field. These approaches have a common feature
in the sense that computational domain representing mixer is
divided into two non-overlapping regions—one surrounding
the impeller and the other representing the rest of the vessel.
In MRF approach, in the first step the simulation of flow
field is done for inner domain surrounding the impeller in a
reference frame rotating with the impeller. The resulting flow
field on the interface separating the inner and outer regions
serves as boundary conditions for simulation of flow field in
the outer domain in laboratory frame of reference. This results
in the improved boundary conditions to be applied for second
round of simulation of flow field in inner domain. The procedure is repeated till suitable numerical convergence criterion is
achieved. The procedure involves steady state approximation
of essential periodic flow and correction for the relative motion and azimuthal averaging are required before using flow
field at the interface as boundary condition for solution of flow
field in the other domain. A variant of MRF approach is the
inner–outer approach in which the inner and outer regions are
partially overlapping (Brucato et al., 1998).
In the computational snapshot approach, the solution of flow
field is obtained for a particular relative position of blades
and baffles. If necessary, simulations are carried out at different relative positions to obtain ensemble-averaged results. Like
MRF, in this approach also, the solution domain is divided into
two regions. In the inner region surrounding the impeller, time
derivative terms are approximated in terms of spatial derivatives. In the outer region, time derivative terms are usually quite
small in magnitude in comparison with the other terms in the
governing equations and are neglected.
Contrary to these two approaches, SM approach involves
transient computations to produce time accurate flow field. The
flow equations in the inner domain are written in laboratory reference frame while it is the grid in this domain that is allowed
to rotate. However, the rotation of the grid results in acceleration terms which are completely equivalent to the body forces
arising in non-inertial frames. The grid in the outer domain is
stationary. The two regions are implicitly coupled at the interface via a SM algorithm which takes into account the relative
motion between the two regions and performs required interpolation. Advances in computing hardware have, for all practical
purpose, overcome the time inefficiencies associated with transient simulations and consequently SM technique has emerged
as the most widely used and validated approach to model
flow in agitated tanks (Yeoh et al., 2004; Aubin et al., 2004;
Montante et al., 2005; Li et al., 2005). In fact, research on agitated vessels seems to be shifting focus from impeller–baffle
interaction modeling to application of more advanced turbulence models within the framework of SM approach.
In the present study, both MRF and SM approaches have
been used to carry out CFD simulations of continuous flow
pump-mixers.
3. Experimental
Fig. 1 gives the schematic diagram of the experimental setup.
The experimental setup had a cylindrical tank of 700 mm diameter and 700 mm height of the liquid overflow level. The
tank had four baffles (not shown in the figure), each of 650 mm
height, having width equal to 10% of tank diameter. At the bottom plate of the tank was a suction orifice with diameter equal
to 41 of the tank diameter. The suction orifice provided connectivity between the tank and a cubical chamber called suction
box (200 mm side-length), which in turn was connected with
two feed tanks. A small flange (not shown in the figure) was
provided at the suction orifice to have the provision to mount
a draft tube. Under steady state operation at a given flow rate,
rotation of impeller in the tank caused suction of liquid from
feed tank into the mixing tank. The liquid came under the influence of impeller in the mixing tank and eventually overflowed
back to the settler. From the settler it overflowed to two storage
tanks (not shown in figure) and from there it was again pumped
back to feed tanks. Thus the system operated in a closed loop
steady state. The flow rates were maintained at the desired values using valves and orifice meters located downstream of the
pumps.
Several single-phase steady state closed loop experiments
were conducted using water. For each run, for a given flow rate,
levels in the feed tanks were measured both for still impeller
and for impeller rotating at the desired speed. The difference
in the two levels was recorded as the head developed by the
impeller. Power consumed by the impeller was measured by
means of voltmeter and ammeter in the DC power supply line
to motor after suitably deducting the losses in the armature and
power consumed by the impeller in the dry runs.
Five different top shrouded impellers with trapezoidal blades
were used in the study. Fig. 2 shows the schematic drawing
of such an impeller. Table 1 gives geometric details of the impellers along with the experimental conditions in which each
of them has been used. For all the impellers, disk thickness
was 6 mm, blade thickness was 5 mm, hub outer diameter was
40 mm and hub height was 40 mm. Hub inner diameter was
20 mm to accommodate a shaft of 20 mm diameter. Impeller
off-bottom clearance was defined as distance between mixer
bottom and bottom of the disk. Note that for all the impellers
blade length was 25% of the impeller diameter. Two different values of clearance (0.5T and 0.3T ) and five different values of flow rates (0, 2, 4, 6 and 8 m3 /h) were used in the
experiments.
1311
+
D.C. SUPPLY
BEARING
HOUSING
A
V
DC MOTOR
TOP
BAFFLE
TO
SETTLER
ORIFICE
METER
HEAD
ORIFICE
METER
MIXER
SUCTION
ORIFICE
FEED TANK
FEED TANK
SUCTION
BOX
FROM
SETTLER
FROM
SETTLER
Fig. 1. Schematic of experimental setup.
If k– model (Launder and Spalding, 1974) is used to model
turbulence, the following two equations need to be solved along
with the above equations:
t
j
{k} + div{Uk} = div
∇k + 2t Eij × Eij − , (3)
jt
k
t
j
∇ + C1 2t Eij × Eij
{} + div{U} = div
jt
k
2
− C2 ,
(4)
k
IMPELLER DIAMETER (D)
HUB
DISK
BLADE
WIDTH
(B)
BLADE
BLADE LENGTH (L)
Fig. 2. Schematic of impeller.
where,
Table 1
Details of impellers and experimental conditions
S. D
B/D L/D n C/T
no. (mm)
1
2
3
4
5
280
350
350
350
420
0.20
0.20
0.20
0.157
0.20
0.25
0.25
0.25
0.25
0.25
6
6
8
6
6
0.3,
0.3,
0.3,
0.3,
0.3,
0.5
0.5
0.5
0.5
0.5
Q
(m3 /h)
0,
0,
0,
0,
0,
2,
2,
2,
2,
2,
4,
4,
4,
4,
4,
6,
6,
6,
6,
6,
1
Eij =
2
N (rpm)
8
8
8
8
8
158.5, 174.25, 204.75
136.5, 150, 164, 177.5
136.5, 150, 164
136.5, 150, 164, 177.5
113.75, 121, 125, 136.5
CFD simulations involve solution of discretized equations—
continuity equation for incompressible flow and time averaged
Navier–Stokes equations:
div{U} = 0,
(1)
j
{U} + div{UU} = − ∇p + div{∇U}
jt
+ div{−u u } + F.
(2)
.
(5)
Solution of Eqs. (3) and (4) give spatial variation of k
and which in turn can be used to find out spatial variation of turbulent viscosity or eddy viscosity t using the
Prandtl–Kolmogorov relation:
t = C
4. CFD simulations
jUj
jUi
+
jxj
jxi
k2
.
(6)
Once t is known, expression of turbulent stresses appearing
in Eq. (2) can be given as
−ui uj = 2t Eij − 23 kij .
(7)
The standard values of different constants appearing in Eqs.
(3), (4) and (6) are C = 0.09, k = 1.00, = 1.30, C1 = 1.44
and C2 = 1.92.
Commercial CFD software FLUENT was used to carry out
the simulations. Before starting the final CFD simulations,
several exploratory simulations were carried out using MRF
1312
Table 2
Results of grid independence tests
Outlet
Test no.
No. of
cells
Power
from MRF
(W)
Power
from SM
(W)
Computation
time for
MRF (h)
Computation
time for
SM (h)
1
2
3
133,694
225,236
392,787
213
217
218
243
238
236
1.4
5.2
12.4
16
25
66
Baffle
Shaft
Disk
0.6
Blade
Test - 1
Test - 2
Test - 3
Vz (m/s)
0.4
Draft tube
flange
0.2
0
Suction box
-0.2
Inlet
-0.4
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
z/H
Fig. 4. Computational domain.
Fig. 3. Axial velocity profile along a vertical line close to impeller blade.
approach to finalize the geometry and to conduct grid independence tests. To check whether grid independence depends on the
simulation technique, three of the grid independence tests were
repeated with SM simulations. Unstructured tetrahedral grids
were used to discretize the domain. All the grid independence
tests were carried out for a particular geometric and process
conditions. The monitored variable was power consumption by
the impeller. Results of three of these tests are given in Table 2.
As can be seen, on increasing the grid density by a factor of 3,
while power consumption estimate changes marginally, computational time increases enormously. As will be discussed later,
the power values reported in Table 2 have been obtained from
pressure field adjacent to the impeller blades. This shows that
pressure field near the impeller blades does not change much
on increasing the grid density. Fig. 3 shows the axial velocity
profile along a vertical line close to impeller blade tip. It can be
seen, the profile is also not much affected by the grid density.
It can be concluded, therefore, that even for the coarsest grid
in Table 2, the results are fairly grid independent. The drastic
increase in computational time with increasing grid density being a great concern, especially for transient SM simulations, the
grids similar to the coarsest of the three grids were used in the
subsequent final simulations. This corresponded to grid size of
0.015 m in inner volume surrounding the impeller and suction
box and 0.025 m in the remaining volume. Further exploratory
simulations were done to finalize the geometry to be used in
the final simulations. To start with, the simplest possible representation of actual geometry of the tank was used. However,
based on the comparison of the results with experimental data,
the fine details of the physical model like suction box and draft
tube flange were incorporated in the computational geometry.
The tank geometry, which was used in the final simulations, is
shown in Fig. 4.
A total of 27 final CFD runs were carried out representing
different combinations of geometric variables like impeller diameter, off-bottom clearance, blade width, blade number and
process variables like flow rate and impeller speed. Each of
these runs had its experimental counterpart for validation purpose. MRF and SM approaches were used to take into account
impeller–baffle interaction. The interface separating the inner
volume surrounding the impeller and outer volume surrounding the baffles was located midway between the impeller tip
and baffle tip. Second order upwind scheme was used for descretization of momentum and turbulence equations. SIMPLE
algorithm was used for pressure–velocity coupling. Symmetry
of geometry was exploited to cut down on computation time by
simulating only half of the tank volume after defining periodic
boundary conditions. For each simulation, power consumption
by impeller was computed both by calculating torque acting
on the impeller blades as recommended in a previous study
(Shekhar and Jayanti, 2002) and by evaluating volume integral
of turbulence energy dissipation rate. In the results that follow,
values of power reported are based on torque computations as
the power values computed form turbulence energy dissipation
rates were found to be significantly smaller than the experimental values. This discrepancy in satisfaction of energy balance is discussed later. For each simulation run, a steady state
initial run was carried out for static impeller and difference between outlet pressure and inlet pressure was recorded. Head
was computed by subtracting this difference from difference of
outlet and inlet pressures obtained from a converged solution
for rotating impeller. Solution was deemed to converge when
residuals for all the equations fell below 10−4 . A typical SM
simulation was carried out for 1000 time steps with time step
size of 0.01 s and 20 iterations per time step. Fig. 5 shows the
inlet and outlet pressure as a function of number of impeller
1313
rotation for a 136.5 rpm case. It can be seen that about 10 impeller rotations are sufficient to reach the steady state.
Converged solution of a SM simulation is essentially periodic with value of any flow variable at a particular point in
solution domain being dependent on the relative location of
impeller blades and baffles. If experimentally observed value
of a flow variable at a particular point is used for validation of
CFD simulations, the time averaging of the flow field resulting
from CFD simulations is essential. However, in the present
Pressure (N/m2)
101600
study, the validation is based on head and power. Head is computed from face average values of pressure at inlet and outlet. This averaging irons out the periodicity of pressure field
at inlet and outlet faces. Power consumption is computed from
difference in pressure on upstream and downstream side of
the blades. Though the pressure values on either side of the
blade will depend on the relative location of blade and baffle, the difference is likely to remain unaffected. Considering
this, the need for time averaging of SM simulation results was
not felt.
5. Results
101200
5.1. Effect of off-bottom clearance
100800
100400
Inlet
Outlet
100000
99600
0
5
10
15
20
Number of Impeller Rotations
25
Fig. 5. Effect of number of impeller rotations on inlet and outlet pressure in
a sliding mesh simulation.
800
700
Power (W)
600
500
Figs. 6 and 7 show power consumption and head generated
by the impeller as a function of impeller speed with impeller
off-bottom clearance as a parameter. As expected, power consumption as well as head generated by the impeller increase
with increasing impeller speed. Experimental data in Fig. 6
show that power consumption goes up on increasing the clearance. Similar trend is predicted by both the CFD modeling
approaches. However, while SM approach gives predictions
close to the experimental values the MRF approach gives larger
discrepancies.
EXP C/T = 0.3
EXP C/T = 0.5
CFD (SM) C/T = 0.3
CFD (SM) C/T = 0.5
CFD (MRF) C/T = 0.3
CFD (MRF) C/T = 0.5
400
300
200
100
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 6. Effect of off-bottom clearance on power (Q = 2 m3 /h, n = 6, B = 0.2D, D = 0.5T ).
16
14
EXP C/T = 0.3
EXP C/T = 0.5
CFD (SM) C/T = 0.3
Head (cm)
CFD (SM) C/T = 0.5
12
CFD (MRF) C/T = 0.3
CFD (MRF) C/T = 0.5
10
8
6
4
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 7. Effect of off-bottom clearance on head (Q = 2 m3 /h, n = 6, B = 0.2D, D = 0.5T ).
1314
600
Power (W)
500
400
EXP B/D = 0.157
EXP B/D = 0.2
CFD (SM) B/D = 0.157
CFD (SM) B/D = 0.2
CFD (MRF) B/D = 0.157
CFD (MRF) B/D = 0.2
300
200
100
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 8. Effect of impeller blade width on power (Q = 2 m3 /h, n = 6, C = 0.3T , D = 0.5T ).
16
Head (cm)
14
12
EXP B/D = 0.157
EXP B/D = 0.2
CFD (SM) B/D = 0.157
CFD (SM) B/D = 0.2
CFD (MRF) B/D = 0.157
CFD (MRF) B/D = 0.2
10
8
6
4
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 9. Effect of impeller blade width on head (Q = 2 m3 /h, n = 6, C = 0.3T , D = 0.5T ).
Fig. 7 shows that the head generated by the impeller is less
for a larger clearance. This suggests that pumping capacity of
impeller is directly linked to its proximity to the suction orifice.
Fig. 7 shows that for C/T = 0.3, while both the approaches
are good for lower impeller speeds, for higher impeller speeds
SM performs better. For C/T = 0.5, SM approach tends to
overestimate the head while predictions of MRF approach are
in good agreement with experimental observations.
5.2. Effect of blade width
Figs. 8 and 9 give power consumption and head generated
by the impeller as a function of impeller speed with blade
width to impeller diameter ratio as a parameter. Experimental
data show that power consumption increases with increasing
speed and blade width to impeller diameter ratio. Similar trend
is predicted by both the CFD modeling approaches. Again,
predictions of SM approach are better than MRF approach and
compare very well with the experimental values. Fig. 9 shows
that head increases with increasing blade width. Results from
both the modeling approaches show the same trend. However,
while at lower impeller speed prediction from both the approaches are comparable, at higher impeller speeds, predictions
form SM approach are distinctly better.
5.3. Effect of flow rate
Figs. 10 and 11 give power consumption and head generated
by the impeller as a function of impeller speed for two different flow rates (Q = 2, 8 m3 /h). Experimental data and both the
CFD modeling approaches show that power consumption by the
impeller is hardly affected by flow rate. However, as has been
seen in previous two cases, predictions of power consumption
from SM approach are very close to experimental values. MRF
approach again tends to under-predict the power consumption.
Experimental data in Fig. 11 show that head generated by the
impeller decreases with increasing flow rate. While SM approach predicts the similar trend, MRF approach predicts the
opposite trend.
5.4. Effect of number of blades
Figs. 12 and 13 give power consumption and head generated
by the impeller as a function of impeller speed for two different numbers of blades in the impeller (n = 6, 8). Experimental
data suggest that power consumption goes up with increasing
number of blades. Both the modeling approaches predict the
similar trend. While SM predictions are very close to experimental values, MRF predictions are on the lower side.
1315
600
Power (W)
500
EXP Q = 2
EXP Q = 8
CFD (SM) Q = 2
CFD (SM) Q = 8
CFD (MRF) Q = 2
CFD (MRF) Q = 8
400
300
200
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 10. Effect of flow rate on power (B = 0.2D, n = 6, C = 0.3T , D = 0.5T ).
16
Head (cm)
14
12
EXP Q = 2
EXP Q = 8
CFD (SM) Q = 2
CFD (SM) Q = 8
CFD (MRF) Q = 2
CFD (MRF) Q = 8
10
8
6
4
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 11. Effect of flow rate on head (B = 0.2D, n = 6, C = 0.3T , D = 0.5T ).
Power (W)
600
500
EXP n = 6
EXP n = 8
CFD (SM) n = 6
CFD (SM) n = 8
CFD (MRF) n = 6
CFD (MRF) n = 8
400
300
200
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 12. Effect of number of blades on power (Q = 2 m3 /h, C = 0.3T , B = 0.2D, D = 0.5T ).
Experimental data suggest that head generated by the impeller increases with increase in number of impeller blades.
Both the modeling approaches predict the similar trend. For
both n = 6, 8, predictions of head by MRF approach are on the
lower side. For n = 6, predictions are of SM approach are very
close to the experimental values. For n = 8, predictions of SM
approach are also on the lower side, however, its predictions
are better than the multiple reference approach.
5.5. Effect of impeller diameter
Figs. 14 and 15 give power consumption and head generated
by the impeller as a function of impeller speed for three different impeller diameters (D/T = 0.4, 0.5, 0.6). Experimental
data show that the power consumption increases on increasing
impeller diameter. Both the modeling approaches predict similar trend. While SM predictions for power are again close to
1316
20
EXP n = 6
EXP n = 8
CFD (SM) n = 6
CFD (SM) n = 8
CFD (MRF) n = 6
CFD (MRF) n = 8
Head (cm)
18
16
14
12
10
8
130
140
150
160
Impeller Speed (rpm)
170
180
Fig. 13. Effect of number of blades on head (Q = 2 m3 /h, C = 0.3T , B = 0.2D, D = 0.5T ).
EXP D/T = 0.4
CFD (SM) D/T = 0.4
CFD (MRF) D/T = 0.4
EXP D/T = 0.5
CFD (SM) D/T = 0.5
EXP D/T = 0.6
CFD (SM) D/T = 0.6
CFD (MRF) D/T = 0.5
CFD (MRF) D/T = 0.6
600
Power (W)
500
400
300
200
100
0
100
120
140
160
Impeller Speed (rpm)
180
200
Fig. 14. Effect of impeller diameter on power (Q = 2 m3 /h, n = 6, B = 0.2D, C = 0.3T ).
EXP D/T = 0.4
CFD (SM) D/T = 0.4
CFD (MRF) D/T = 0.4
EXP D/T= 0.5
CFD (SM) D/T = 0.5
CFD (MRF) D/T = 0.5
EXP D/T = 0.6
CFD (SM) D/T = 0.6
CFD (MRF) D/T = 0.6
21
Head (cm)
18
15
12
9
6
3
100
120
140
160
Impeller Speed (rpm)
180
200
Fig. 15. Effect of impeller diameter on head (Q = 2 m3 /h, n = 6, B = 0.2D, D = 0.5T ).
the experimental values, especially for medium and large size
impeller, estimates from MRF approach are once again on the
lower side.
Experimental data suggest that head generated by the impeller increases with increasing impeller diameter. Both SM
and MRF approaches predict the similar trend. For medium size
impeller, SM performs better than MRF approach, especially
at higher impeller speeds. For smaller impeller, while both the
approaches tend to predict head on the higher side, MRF performs better than SM approach. For larger impeller, while both
1317
800
EXP
CFD (SM)
CFD (MRF)
700
600
P (W)
500
400
300
200
100
0
0
3
6
9
12
15
Run No.
18
21
24
27
Fig. 16. Comparison of power predicted by CFD simulations with experimental values.
25
EXP
CFD (SM)
CFD (MRF)
H (cm)
20
15
10
5
0
0
3
6
9
12
15
Run No.
18
21
24
27
Fig. 17. Comparison of head predicted by CFD simulations with experimental values.
the approaches tend to predict head on the lower side, MRF
performs better than SM approach.
Fig. 16 shows the quality of CFD predictions for impeller
power consumption for all the runs together with ±5% error
bars around the experimental points. It shows that except for
four runs (Run Nos. 6, 25–27), estimates of power consumption obtained by SM CFD simulations are within ±5% of experimental values. Even for these four runs, the deviations are
not very far off. On the other hand, except for two runs (Run
Nos. 9, 24), predictions of MRF approach are outside the ±5%
band. Therefore, as far as the CFD-based prediction of impeller
power is concerned, SM approach is conclusively better than
the MRF approach. It should be noted that the power values
reported here have been obtained from the torque acting on the
impeller which was calculated from the pressure field resulting
from CFD simulations. Power estimates based on volume integral of turbulence dissipation rate were found to be much lower
than the experimental values. This discrepancy is not surprising
considering the k– model, which has been used to model turbulence in the present study, has been developed and validated
for the flows which are much simpler than the flow in an agi-
tated vessel. In the reported literature, the extent to which the
energy balance is satisfied varies from about 11% (Armenante
and Chou, 1996) to 90% (Ranade et al., 1989). Methods to enforce energy balance have been reported either by adjustment in
values of constants of turbulence model or by different prescription for computation of turbulence velocity and length scales
(Sahu et al., 1999). In the present work, with SM simulations,
the power consumption values as obtained from turbulence dissipation rates, were found to range between 52% and 73% of
power consumption values obtained from torque computations.
For MRF approach this figure ranged between 71% and 83%.
Fig. 17 shows the quality of predictions of SM and MRF
approaches for the head generated by the impeller with ±10%
error bars around experimental values. Clearly, CFD-based predictions for head are not as accurate as for power. Still for most
of the cases either of the two or both the modeling approaches
predicts head to be within ±10% of the experimental values.
Except for eight cases (Run Nos. 5–8, 20, 25–27) SM-based
predictions of head are within ±10% band. On the other hand,
except for 11 runs (Run Nos. 13–20, 25–27) the predictions of
MRF approach are within the ±10% error bands. The runs for
1318
which performance of SM is poor correspond to C/T = 0.5
(Run Nos. 5–8) and D/T =0.4 (Run Nos. 25–27), respectively.
However, for these cases MRF approach predicts better results.
6. Discussions
CFD-based results having been validated in the previous section, wealth of information revealed from CFD simulations can
be used to gain an insight into the physics of the pump-mixer.
Fig. 18 gives pressure contours in a vertical central plane of
the mixer as predicted by SM simulation. As can be seen, just
below the impeller eye and blades a zone of low pressure is
created which is responsible for suction caused by the impeller.
Fig. 18. Pressure contours in a vertical central plane predicted by sliding mesh
simulations (Q=2 m3 /h, n=6, C =0.3T , D =0.5T , B =0.2D, N =150 rpm).
Fig. 19 shows pressure profiles along a vertical central line
in the mixer (zero along the vertical line corresponds to the suction orifice). As can be seen, starting from bottom of the suction
box as we approach towards impeller, static pressure gradually
reduces and encounters a minimum at around z = 0.14 which
is just below the impeller blades. As can be seen, increasing
the impeller speed brings down the pressure without changing
the location of the pressure minimum. Therefore, it can be concluded that while it is geometry of the system that fixes the
location of minimum pressure, its value is fixed by impeller
speed. Fig. 20 shows how the velocity changes along the same
vertical central line. As can be seen that velocity increases as
one moves towards the impeller and a velocity maximum is
encountered. The location of this velocity maximum roughly
coincides with that of pressure minimum and, even though the
flow is highly turbulent and dissipative, a qualitative observation of principle of conservation of mechanical energy can be
felt.
Fig. 21 shows the path lines traced by fluid as it traverses
from inlet to impeller. As can be seen, the effects of impeller
rotation are certainly felt in the suction box where the fluid
coming in through inlet churns its way up to the impeller, hits
the disk and then leaves the impeller radially. As is evident
from comparison of twists of path lines and flow cross-sections
in Fig. 21, for identical geometric and process conditions, the
effect of impeller agitation on the incoming fluid and suction
box are more marked in case of SM simulation. In other words,
interaction between impeller and suction box is stronger in case
of SM approach than the MRF approach. Considering a qualitative observation of principle of conservation of mechanical
energy, the larger flow cross-section in case of MRF case would
mean that the pressure in the region below the impeller will be
larger compared to SM approach. This would probably explain
the MRF approach, in most of the cases, predicting lesser head
than the SM approach.
It was seen that for Run Nos. 5–8 (C/T = 0.5, D/T = 0.5,
B/D = 0.20, n = 6) and 25–27 (C/T = 0.3, D/T = 0.4,
B/D = 0.2, n = 6) the deviations of head predicted by SM
simulations were more than 10% from the experimental values.
N = 136.5 rpm
Vertical Distance (m)
0.2
N =150 rpm
N =164 rpm
0.1
N = 177.5 rpm
0
-0.1
-0.2
-1400
-1200
-1000
-800
Static Pressure (Pa)
-600
-400
Fig. 19. Static pressure profile along a vertical central line predicted by sliding mesh simulations (Q = 2 m3 /h, n = 6, C = 0.3T , D = 0.5T , B = 0.2D).
1319
Vertical Distance (m)
0.2
0.1
0
N = 136.5 rpm
N =150 rpm
-0.1
N =164 rpm
N = 177.5 rpm
-0.2
0
0.1
0.2
0.3
0.4
0.5
Velocity Magnitude (m/s)
0.6
0.7
0.8
Fig. 20. Velocity profile along a vertical central line predicted by sliding mesh simulations (Q = 2 m3 /h, n = 6, C = 0.3T , D = 0.5T , B = 0.2D).
Fig. 21. Path lines from inlet to impeller (Q = 2 m3 /h, n = 6, C = 0.3T ,
D = 0.5T , B = 0.2D, N = 150 rpm): (a) sliding mesh; (b) multiple reference
frame.
These cases correspond to an impeller located away from suction box and a smaller impeller interacting with the suction
box, respectively. Both of these physical conditions suggest
relatively weak interaction between impeller and suction box.
Therefore, prima facie, it appears that even for physical conditions suggesting relatively weak interaction between the
impeller and the suction box, SM approach predicts stronger
interaction. The multiple reference frame approach which predicts weaker interaction between the impeller and the suction
box gives better results for these cases. Therefore, based on the
observations made here, it can be argued that the MRF should
be preferred for predicting the head in those physical situations
which suggest relatively weak interaction between the impeller
and the suction box. However, before being conclusive more
validation is required.
Fig. 22 shows the tangential velocity contours and velocity
vectors in a horizontal plane passing through the impeller as
predicted by SM simulation. Fig. 23 shows the axial velocity
contours and velocity vectors as predicted by SM simulations
Fig. 22. Tangential velocity contours and velocity vectors (colored by tangential velocity) in a horizontal plane through the impeller as predicted by sliding
mesh simulation for anti-clockwise rotation (Q = 2 m3 /h, n = 6, C = 0.3T , D = 0.5T , B = 0.2D, N = 150 rpm): (a) contour plot; (b) vector plot.
1320
Fig. 23. Axial velocity contours and velocity vectors (colored by axial velocity) in a vertical central plane predicted by sliding mesh simulation (Q = 2 m3 /h,
n = 6, C = 0.3T , D = 0.5T , B = 0.2D, N = 150 rpm): (a) contour plot; (b) vector plot.
in a vertical central plane. The velocity vectors and contours
in the horizontal plane are typical of a radial flow impeller.
The vector plot in the vertical plane shows the presence of two
recirculation loops, one below the impeller and one above the
impeller. This is again typical of a radial flow turbine.
It should be noted that the trapezoidal and top shrouded
blades used in this study provide a partially shielded conical
region below the disk where low pressures are encountered.
An impeller having conventional rectangular blades will not
provide such a region and it will be interesting to repeat such
simulations to see if impeller with such blades match the head
generated by the impellers used in this study.
7. Conclusions
From the work presented here, it can be concluded that CFD
simulations can closely predict the single-phase head and power
characteristics of pump-mixer. Based on the information obtained from CFD simulations, an insight has been provided into
the pumping action of the impeller.
While CFD-based predictions of power are very close to the
experimental values, CFD-based head predictions are not that
accurate. Still in majority of cases the head values predicted by
CFD simulations are within ±10% of the experimental values.
Since all the simulations have been done with more or less similar grid size it does not seem logical to attribute discrepancy
in head predictions in certain cases to insufficient grid density. Possibly this discrepancy is due to inadequate turbulence
model.
SM and MRF approaches have been compared. For all the
runs representing different geometric and process conditions,
for prediction of power consumed by the impeller, SM approach
was found to be conclusively better than the MRF approach. For
most cases, for prediction of head, SM approach was found to
give better result, however, in certain configurations that suggest
relatively weak physical interaction between rotating impeller
and suction box, the head predictions of MRF were found to
be better than the SM approach. Therefore, more simulations
and validations are felt necessary to conclusively establish the
superiority of one modeling approach over the other as far as
head predictions are concerned.
Since CFD predictions have been validated for a wide range
of geometric and process parameters, it can be said that CFDbased predictions for a new geometric and process configuration
can be safely relied upon for design purpose.
Notation
B
C
D
F
H
k
L
n
N
impeller blade width, m
impeller off-bottom clearance, m
impeller diameter, m
body force vector, kg m/s2
tank height, m
specific turbulent kinetic energy, m2 /s2
impeller blade length, m
number of blades in impeller, dimensionless
impeller speed, 1/s
1321
p
Q
T
u
U
z
pressure, kg/m/s2
total flow rate, m3 /s
tank diameter, m
fluctuating velocity vector, m/s
mean velocity vector, m/s
distance along vertical axis, m
Greek letters
t
specific turbulence energy dissipation rate, m2 /s3
viscosity, kg/m/s
turbulent viscosity or eddy viscosity, kg/m/s
density, kg/m3
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