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CFD based Investigations on Solid Suspension in Liquid–Solid and
Gas-Liquid-Solid Agitated Contactors
R.Panneerselvam, S. Savithri∗∗∗∗, G.D. Surender
Process Engineering & Environmental Technology Division,
National Institute for Interdisciplinary Science and Technology (CSIR),
(Formerly Regional Research Laboratory),
Thiruvananthapuram – 695 019.
ABSTRACT
In this work, Multiphase CFD simulation based on Eulerian-Eulerian approach is used to predict the
critical impeller speed for solid suspension in liquid-solid and gas–liquid-solid mechanically agitated
reactor. Experiments are conducted in baffled cylindrical tank of internal diameter of 250 mm and two
type of impeller employed are six-bladed Rushton turbine diameter of 100 mm and four-bladed 45°
pitched blade turbine of 125 mm with impeller clearance of 62.5 mm. A multiple frame of reference is
used to model the impeller and tank region and a standard k-ε model is used to predict the effect of
turbulence. The model predictions are compared with experimental data. The CFD model has been
further extended to study volumetric impeller power for complete solid suspension and gas dispersion
Keywords: agitated contactor, multiphase flow, CFD, solid suspension, critical impeller speed
1. INTRODUCTION
Mechanically agitated reactor involving gas-solid-liquid flows are widely used in the chemical
industries, for mineral processing, wastewater treatment and biochemical processes. It is essential to
know the solid suspension and gas dispersion in three phase reactor for the determination of mass
and heat transfer as well as over all reaction rates of stirred reactors and consequently, which leads to
accurate design and scale up of stirred reactors. In solid suspension, basically three main suspension
states are observed in a stirred tank namely; complete suspension, homogeneous suspension and
incomplete suspension. A suspension is considered to be complete if no particle remain at rest on the
bottom of the tank for more than 1 or 2 sec. One of the main criteria which is often used to investigate
the solid suspension is the critical impeller speed (Njs) at which solids are just suspended. Zwietering
* Corresponding author: [email protected]
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[1] is who proposed a correlation for minimum impeller speed for complete suspension. The three-
phase stirred reactor involves the simultaneous solid suspension and gas dispersion and critical
impeller speed (Njsg) for solid suspension in the presence of gas medium is main parameter to
characteristic hydrodynamics of gas-liquid-solid stirred reactor. This parameter is mainly affected by
the physical properties of the slurry, as well as the operating and geometrical parameters of the
system. Chapman et al. [2] explained that the influence of particle properties and concentrations on the
just suspended condition in gassed systems are similar to but slightly weaker than in the ungassed
case. Rewatkar et al. [3] studied on the just suspended condition in three phase system in flat bottom
stirred tanks and mentioned the critical impeller speed for solid suspension is higher in the presence of
gas than in its absence.
In recent years, computational fluid dynamics (CFD) has emerged as a powerful tool for the
study of fluid dynamics of multiphase reactors. CFD based simulation have been used to model the
liquid-solid flows in stirred tank (Montante et al.,[5], Michile et al., [6], Khopkar et al. [7]) gas-liquid
flows in stirred tanks (Lane et al., [ 8], Khopkar et al [9]) by employing Eulerian-Eulerian approach.
Last few decades different numerical approaches have been proposed to predict the flow pattern of
complex unsteady liquid-solid and gas-liquid flows in mixing tank namely: black-box method, Inner-
Outer approach, multiple frame of reference (MFR), sliding grid approach and snapshot method.
Among them, Multiple frame reference method is simple and steady state approach used in present
method.
In this work, Multiphase CFD simulation based on Eulerian-Eulerian approach is used to
predict the critical impeller speed for solid suspension in liquid-solid and gas–liquid-solid mechanically
agitated reactor. A multiple frame of reference is used to model the impeller and tank region. The
model predictions are compared with experimental data. The CFD model has been further extended to
study impeller power for different type of impeller for complete solid suspension and gas dispersion .
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2. EXPERIMENT
The schematic diagram of experimental setup is shown in figure 1. Experiments were conducted in
baffled cylindrical tank of internal diameter of 250 mm and which is transparent to light so that the
suspension of solids can easily visible. The bottom of tank was considered as elliptical. The two type of
impeller employed were six-bladed Rushton turbine diameter of 100 mm and four-bladed 45° pitched
blade turbine of 125 mm with impeller off bottom clearance of 62.5 mm. The liquid was tap water and
the solid was ilmenite particle of 210-250 micron diameter with density of 4200 kg /m3. Air was
admitted to the reactor using pipe sparger and placed at a clearance of 2.5 cm from the center of the
impeller. Solid loading used as in the range of 10-40 % by mass. Agitation was carried out using a
variable speed DC motor and the speed of agitation was noted using a tachometer. Power
consumptions were computed measured values of current and voltages. The critical impeller speed for
solid suspension was predicted by both visually using the Zwietering criteria [1] that the solids remain
at the tank bottom for not more than 2 seconds and a typical plot of NRe versus NP
3. CFD MODELLING
3.1. Governing Equations
Hydrodynamic Model equations used gas-liquid-solid flows are given below
Continuity Equations for k= (g, l, s)
Momentum Equations
Gas phase (dispersed fluid phase)
Liquid phase (continuous phase)
( ) ( ) 0u..ερ..ρε.t
kkkkk =∇+∂
∂ r
( ) ( ) ( )( )( ) lsD,lgD,llTllleff,lllllllll FF.g.ερuuµε.P.εuu..ερ.u..ερ.t
+++∇+∇∇+∇−=∇+∂
∂ rrrrr
( ) ( ) ( )( )( ) gsD,lgD,ggTgggeff,ggggggggg FF.g.ερuuµε.P.εuu..ερ.u..ερ.t
+−+∇+∇∇+∇−=∇+∂
∂ rrrrr
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( ) sss εεGP ∇=∇
( ) ( )( )sms0s εεcexpGεG −=
lµ
lT ,µ
tstg µ,µ
Solid phase (Dispersed solid phase)
Where P is pressure, µeff is the effective viscosity. The second term of solid phase momentum
equation shows additional solids pressure due to solid collision and last term (FD) of above momentum
equation represents the interphase drag force between phases.
Constitutive Equations for turbulence and inter phase momentum
For liquid phase effective viscosity is calculated as
where is the liquid viscosity, is the liquid phase turbulence viscosity or shear induced eddy
viscosity, which is calculated based on the k-ε model as
where the values of ε and k come directly from the differential transport equations for the turbulence
kinetic energy and turbulence dissipation rate.
represents the gas and solid phase induced turbulence viscosity respectively and is given by
the equation proposed by Sato et al., (1981) as
Solid pressure model
where G (εs) is the elasticity modulus and it is given as
as proposed Bouillard et al. (1989)
where G0 is the reference elasticity modulus, c is the compaction modulus and Ism is the maximum
packing parameter
The momentum transfer due to drag is
( ) ( ) ( )( )( ) gsD,lsD,ssTsseff,sssssssssss FF.g.ερuuµε.PP.εuu..ερ.u..ερ.t
−−+∇+∇∇+∇−∇−=∇+∂
∂ rrrrr
tstglT,lleff, µµµµµ +++=
e
kρcµ
2
lµTl =
lgsssµptg uudερcµrr
−=
lssssµpts uudερcµrr
−=
( )lslsp
sl,,D
uuuud
ερ
4
3CF
rrrr−−=
lsDls
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3
p
D0
D0D
λ
dK
C
CC
=
−
( )
0.15Re1Re
24 C
0.687
P0 +=D
Drag models for liquid –solid
Brucato et al.,(1998) proposed that the increase in drag coefficient may be related to the ratio of
particle size, dp to the Kolmogorov length scale λ as
Where CD is the drag coefficient in turbulent liquid and CD0 is the drag coefficient in stagnant liquid and
given as
Momentum transfer between gas and liquid
Drag models for gas-liquid
3
p6
D0
D0D
λ
d105.6
C
CC
×=
− −
The drag coefficient exerted by gas phase on the liquid phase is obtained by the modified Brocade
drag model (khopkar et al., 2006), which is given as
3.2. Numerical Simulation
ANSYS CFX-11 software code was used for simulating the hydrodynamics of gas-liquid-solid
flows Figure 2 depicts typical numerical mesh used for simulation. A k-epsilon model was used to
predict the effect of turbulence. A multiple reference frame (MFR) approach was used to simulate the
impeller rotation in a fully baffled reactor. No-slip boundary conditions are applied on the tank walls and
shaft. The free surface of suspension can be interpreted as a slip wall because it is described by zero
( )lglgb
g
llg,lg,Duuuu
d
ερ
4
3CF
rrrr−−=
D
( )
++=
4E
E
3
8,0.15Re1
Re
24MaxC
o
o0.687
b
D0 b
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gradients of velocity and all other variables and zero shear stress. In case of three phase simulation,
the free surface of tank is considered as the degassing boundary condition.
The numerical simulations of the discrete governing equations were achieved by element based on the
finite volume method. Pressure Velocity coupling was achieved by the Rhie Chow algorithm. The
governing equations were solved using the advanced coupled multi grid solver technology of CFX-11.
The second order equivalent to high-resolution discretization scheme of momentum, volume fraction of
phases, turbulent kinetic theory and turbulence dissipation rate equations was chosen in sense of
accuracy and stability concerned. The simulations were carried out till the system reached the pseudo
steady state. The convergence criteria for all the numerical simulation is based on monitoring the mass
flow residual and the value of 1.0e-04 is set as converged value.
4. RESULT AND DISCUSSION
4.1. Critical Impeller Speed
4.1.1 Solid-liquid flows
Since the incorporation of Zwietering criteria to predict critical speed for suspension in the CFD
simulation is difficult, the quality of solid suspension quantified by using standard deviation of solid
concentration. This standard deviation was initially proposed by Bohnet and Niesmak and was
successfully employed for liquid- solid suspension by various authors. It was defined as
………………… (1)
Where n is the number of sampling locations used for measuring the solid holdup. The increase in the
homogenization (better suspension quality) is manifested as the reduction of the standard deviation
value. The range of standard deviation is broadly divided into three ranges based on the quality of
suspension. For uniform suspension σ 0.8 .
The solid-liquid flow filed inside the stirred vessel is simulated at critical impeller speed of 6.67 rps in
the case of Rushton turbine impeller and 7.5 rps in the case of 4 bladed pitched blade turbine with
downward pumping, which is obtained from experiment for a particle size equal to 250 µm and solid
2n
1i
i 1Cavg
C
n
1σ ∑
=
−=
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loading of 30 by wt%. Figure 3 and 4 shows solid volume fraction and solid velocity profiles predicted
from CFD simulation at midbaffle plane. In case of Rushton turbine impeller, the two circulation loops
above and below the impeller and the radial jet of solids in the impeller stream can be clearly seen in
the figures 3. In case of axial turbine impeller of pitched blade, a single circulation loop can be clearly
shown in figure 4
4.1.2. Gas –liquid-Solid flows
For gas-liquid-solid flows, CFD simulations are carried out at critical impeller speed of 8.33 rps, in the
case of Rushton turbine impeller and 10 rps in the case of 4 bladed pitched blade turbine with
downward pumping, which is obtained from experiment for a particle size of 250 µm with solid loading
of 30 by wt % at the gas sparging rate of 1e-04 m3/s. Figure 5 and 6 shows solid volume fraction, gas
volume fraction and solid velocity profiles predicted from CFD simulation at midbaffle plane. The CFD
predicted flow pattern of solid motion in three phase agitated reactor is consistent with literature work.
The standard deviation was calculated using the values of the solid volume fraction stored at
all computational cells. The variation of the standard deviation values with respect to the impeller
rotational speed is shown in Table 1. It can be seen that the value of standard deviation (σ< 0.8)
calculated from solid volume fraction predicted CFD simulation shows the just suspended condition.
4.2. Power consumption
The power consumption is calculated as the product of torque on the impeller blades and the angular
velocity and it can be expressed as follows
P=2πNT ……………….. (2)
Where torque (T) exerted on all blades was computed from the total momentum vector, which is
computed by summing the cross products of the pressure and viscous forces vectors for each facet on
the impeller with the moment vector.
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5. CONCLUSIONS
The two-fluid model along with the standard k-ε model of turbulence was developed to study solid
suspension in liquid-solid flows and gas-liquid-solid stirred tank reactor. The predicted results were
compared with the experimental data. The model was also used to estimate the critical impeller speed
required for a just off bottom suspension. The CFD model was further extended to study the volumetric
impeller power for solid suspension in liquid-solid and gas-liquid-solid stirred tank.
ACKNOWLEDGEMENT
R.Panneerselvam gratefully acknowledges the financial support for this work by Council scientific and
Industrial Research (CSIR), Government of India.
6. REFERENCES
[1] T.N. Zwietering, Suspending of solid particles in liquid agitators, Chem. Eng. Sci. 8 (1958) 244–253.
[2] M.Bohnet, G.Niesmak, Distribution of solids in stirred suspension, Ger. Chem. Eng. 3 (1980) 57-65.
[3] C.M. Chapman, A.W. Nienow, M. Cooke, J.C. Middleton, Particle–gas–liquid mixing in stirred
vessels, part III: three phase mixing. Chem. Eng. Res. Des. 60, (1983) 167–181.
[4]. V.B. Rewatkar, K.S.M.S. Raghava Rao, J.B. Joshi, Critical impeller speed for solid suspension in
mechanical agitated three-phase reactors. 1. Experimental part. Ind. Eng. Chem. Res. 30
(1991)1770–1784
[3] A. Brucato, F. Grisafi, G.Montante, Particle drag coefficients in turbulent fluids, Chem. Eng. Sci. 53
(18) (1998) 3295-3314
[5] G.Montante, G.Micale, F. Magelli, A. Brucato, Experiments and CFD prediction of solid particle
distribution in a reactor agitated with four pitched blade turbines. Trans. Inst. Chem. Eng., Part A
79 (2001) 1005-1010.
[6] G. Micale, F. Girsafi, L. Rizzuti, A. Brucato, CFD simulation of particle suspension height in stirred
vessels. Chem. Eng. Res. Des. 82 (2004) 1204-
[7] A.R.Khopkar, V.V Ranade, Computational Fluid Dynamics Simulation of the Solid Suspension in a
stirred slurry reactor, Ind. Eng. Chem. Res. 45 (2006) 4416-4428
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[8] G.L.Lanea, M.P. Schwarza, G.M. Evans, Numerical modelling of gas–liquid flow in stirred tanks,
Chem. Eng. Sci. 60 (2005) 2203–2214.
[9]. A.R. Khopkar, G.R. Kasat, A.B. Pandit, V.V Ranade, CFD simulation of mixing in tall gas–liquid
stirred vessel: role of local flow patterns. Chem. Eng. Sci. 61(2006) 2921–2929.
List of figures
Figure i: A schematic diagram of the experimental setup.
Figure ii: Typical numerical mesh used for present simulation
Figure iii: Simulated solid holdup distribution and solid velocity profiles at the midbaffle plane for dp=
250 micron and impeller speed N = 6.67 rps
Figure iv: Simulated solid holdup distribution and solid velocity profiles at the midbaffle plane for dp=
250 micron and impeller speed N = 7.5 rps
Figure v: Simulated solid holdup distribution, gas volume fraction and solid velocity profiles at the
midbaffle plane for Rushton turbine impeller with particle diameter of 250 micron and
impeller speed of 8.33 rps at the gas flow rate of 1e-04 m3/s
Figure vi: Simulated solid holdup distribution, gas volume fraction and solid velocity profiles at the
midbaffle plane for Pitched blade turbine with particle diameter of 250 micron and impeller
speed N = 10.0 rps at the gas flow rate of 1e-04 m3/s
List of Tables
Table i shows the standard deviation values with critical impeller speed
Table ii Experimental and predicted values of power consumption at critical impeller speed
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Figure i
(a) Rushton Turbine (b) Pitched Blade turbine
Figure ii
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Figure iii
Figure iv
Figure v
Figure vi
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Type of
impeller
Critical impeller
speed (rps)
Standard
deviation
σ
Liquid –solid flow
Rushton 6.67 0.8
Pitched blade 7.5 0.78
Gas - Liquid –solid flow
Rushton 8.33 0.726
Pitched blade 10.0 0.84
Table i
Type of
impeller
Power consumption
Experimental
(W)
CFD
(W)
Liquid –solid flow
Rushton 15.79 15.82
Pitched blade 16.63
Gas - Liquid -solid flow
Rushton 20.67 26.62
Pitched blade 31.0
Table ii