1

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: sivakumarsavi@gmail.com

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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

4

( ) 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

5

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