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Chemical Engineering Science 62 (2007) 3839 3848www.elsevier.com/locate/ces

Hollow self-inducing impellers: Flow visualization and CFD simulation

B.N. Murthy, N.A. Deshmukh, A.W. Patwardhan, J.B. Joshi

Department of Chemical Engineering, Institute of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India

Received 20 August 2006; received in revised form 20 February 2007; accepted 23 March 2007

Available online 13 April 2007

Abstract

The experimental fluid dynamics (EFD) as well as computational fluid dynamics (CFD) studies were performed for hollow self-inducing

agitator system. The system is described in detail elsewhere [Deshmukh, N.A., Patil, S.S., Joshi, J.B., 2006. Gas induction characteristics

of hollow self-inducing impeller. Transactions of the Institution of Chemical Engineers 84(A2), 124132]. The low pressure regions on the

impeller blade were determined by single phase CFD simulations. These results were validated with the experimentally measured power number

(NP). Then with the help of single phase CFD results, the orifices were drilled on the impeller blade in low pressure regions. Gas induction

rate (QG), power consumption (P ) and overall fractional gas hold-up (G) were measured experimentally. The comparison of gas induction

rates for both the hole locations has been presented. The two phase CFD simulations yielded satisfactory predictions and proved to be most

promising for the design of efficient gas-inducing system.

2007 Elsevier Ltd. All rights reserved.

Keywords: Hollow self-inducing impeller; Gas induction rate; Pitched blade turbines; CFD

1. Introduction

Gas-inducing impellers are advantageous in situations where

internal recycle of unreacted gas is desirable. This condition

arises in a number of industrially important reactions such as

hydrogenation, alkylation, ethoxylation, ammonolysis, oxida-

tion with pure oxygen, hydrochlorination, etc. In these cases

the use of a gas-inducing impeller may be more beneficial than

a recycle gas compressor for the reasons of safety, economy

and reliability. There are many types of gas-inducing impellers

reported in the literature, such as statorrotor type and hollow

impeller type. The present work is concerned with the hol-

low impellers and is in continuation with the earlier work ofDeshmukh et al. (2006).

When the impeller speed is zero, the level of liquid in hol-

low pipe and in the vessel is the same (in Deshmukh et al.,

2006, Fig. 1). As the impeller speed increases, at any point on

the impeller, pressure reduction occurs due to an increase in

the kinetic head according to Bernoullis equation. At critical

Corresponding author. Tel.: +91 22 24145616; fax: +91 22 2414 5614.

E-mail address: [email protected] (J.B. Joshi).

0009-2509/$- see front matter 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2007.03.043

impeller speed (NCG), the reduction in pressure at the outlet

of orifice on each impeller blade is sufficient to overcome the

static head of liquid and the gas is just induced. This mecha-

nism is explained in detail elsewhere (Deshmukh et al., 2006).

The determination of gas induction rate (QG) is an important

step in designing the hollow impeller system. The gas induction

rate depends on the pressure driving force (local pressure at

the orificehead space pressure) generated due to impeller ro-

tation. From the above discussion it is clear that the local pres-

sure at the orifice is an important parameter that determines the

rate of gas induction. Once the gas starts to induce into the liq-

uid the local pressure field itself is altered. This occurs mainly

due to the gasliquid interactions in the impeller zone. Henceit was thought that it was desirable to estimate the pressure

field in the gasliquid dispersion in the impeller region using

computational fluid dynamics (CFD) simulation. This could

reduce the burden of experimentation considerably. Earlier the

attempts were made by various authors (Martin, 1972; Joshi

and Sharma, 1977; Joshi, 1980; Baczkiewicz and Michalski,

1988; Rielly et al., 1992; Forrester and Rielly, 1994; Rigby

et al., 1994; Mundale and Joshi, 1995) to increase gas induction

rate by (i) putting holes at low pressure region, (ii) minimizing

the pressure drop associated with gas flow and (iii) maximizing
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3840 B.N. Murthy et al. / Chemical Engineering Science 62 (2007) 38393848

Fig. 1. Experimental set-up with impeller having holes on lower edge of each impeller blade.

the pressure differential by changing shape and/or design of the

impeller. In the present work, for the first time, CFD supporthas been employed to identify the location of low pressure

region in order to achieve maximum gas induction rate under

identical operating conditions. For gas-induction, Raidoo et al.

(1987) and Mundale and Joshi (1995) have shown that the

pitched blade downflow turbine (PBTD) design is superior to

disc turbine as well as other axial flow impellers. Hence in this

case PBTD impeller was selected for further investigations.

In CFD, the flow field is estimated by solution of the trans-

port equations along with suitable turbulence models. Joshi

et al. (1999) initiated the efforts for hollow impeller CFD sim-

ulations. However, full potential of CFD has still remained

unutilized for developing a systematic procedure for optimumdesign of self-inducing impellers. The objective of this paper

is to (i) locate the low pressure region on the impeller blade

in single phase flow through CFD simulations, (ii) validate the

outcome with experimental results and (iii) study the effect of

presence of gas on location and magnitude of low pressure

zone. Also an attempt has been made to calculate the gas in-

duction rate (QG) from local pressure at the orifice, obtained

from two phase CFD simulations.

2. Experimental setup

The tank geometry employed in this work was a flat-

bottomed cylindrical tank, (T=H=0.50 m) with four equally

spaced baffles (b = T /10) and it is the same as that used for

experimental work by Deshmukh et al. (2006). Six bladed 30,45 and 60 hollow PBTDs with D=T /2 diameter were used.

The impeller is located at a distance of T /3 from the base of

the tank. The shaft and the impeller were hollow. The inter-

nal diameter of shaft was 20 mm. In self-induction mode the

rate of gas induction (QG) was measured by a precalibrated

turbine type anemometer. The impeller speed was measured

by magnetic proximity probe. Power drawn by the impeller

was estimated by measuring the torque exerted by the fluid on

the frictionless torque table. The torque table was restrained

from rotating, and the force was measured by connecting it

to a cantilever type load cell. Multiplication of this force and

radius of the torque table (RT) gives torque acting on the table(M=wgRT). Power drawn by the impeller was calculated by

using the measured value of torque (P= 2N M) (Fig. 1).

3. CFD model

For the estimation of flow pattern and the pressure field,

CFD simulations were performed. In the present case, three-

dimensional simulations have been carried out for the both sin-

gle phase and gasliquid multiphase system. Multiple reference

frame (MRF) model has been used to simulate the interaction

between the rotating impeller and the stationary baffles. In or-

der to reduce computational efforts and to keep accuracy, the

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B.N. Murthy et al. / Chemical Engineering Science 62 (2007) 3839 3848 3841

MRF seems to be highly justifiable (Kerdouss et al., 2006).

In single phase simulations turbulence was modeled using the

standard k model. This model is essentially a high Reynolds

number model and assumes the existence of isotropic turbu-

lence and the spectral equilibrium. Details of the flow govern-

ing equations are discussed elsewhere (Sahu and Joshi, 1995;

Sahu et al., 1998).

3.1. Two phase simulations

Gasliquid flow was modeled using the two-fluid Eulerian

Eulerian approach. This model solves continuity and momen-

tum equations for each phase separately. The coupling of the

equations is achieved through the pressure and interphase ex-

change coefficients.

In FLUENT, the derivation of the conservation equations for

mass and momentum for each phase is done by phase weighted

Favre-averaging (Viollet and Simonin, 1994) the local instan-

taneous balances for each of the phases, and then no addi-tional turbulent dispersion term is introduced into the continuity

equation.

The mass conservation for L phase is written as follows:

j

jt(LL) +.(LL

L) = 0. (1)

The momentum conservation equation for the phase L after

averaging is written as follows:

j

jt(LL L) +.(LL L L)

=Lp +.L + (+ t,L ). L + LL

g

+R GL +

F D +

F L, (2)

where L is the Lth phase stressstrain tensor

L = LL( L +

TL) + L(L

23L).

LI. (3)

Here L and L are the shear and bulk viscosity of phase

L,

F L represents the Coriolis and centrifugal forces ap-plied in the rotating reference frame, R GL is an interaction

force between phases, and p is the pressure shared by all

phases.

In the present work the standard k model for single phase

flows has been extended for two phase flow with extra terms that

include interphase turbulent momentum transfer (Elgobashi and

Abou-arab, 1983) to take into account the effects of turbulence.

The present model is the most general multiphase turbulence

model which solves a set ofkand transport equations for each

phase. This turbulence model is the appropriate choice when

the turbulence transfer among the phases plays a dominant role.

The turbulent viscosity (t,L ) was computed at each point in

the flow via the solution of the following governing equations

for the k and :

j

jt(LLkL) +.(LLkL

L)

=.

L

+

t,L

k

kL

+ (LGk,L LLL)

+ KGL(CGLkG CLGkL) KGL( G

L)

.t,G

GGLG + KGL(

G L).

t,L

LGLL, (4)

j

jt(LLL) +.(LLL

L)

=.

L

+

t,L

k

L

+L

kL

(C1LGk,L C2LLL) + C3

KGL(CGLkG CLGkL) KGL( G L)

.t,G

GGLG +KGL(

G L)

.t,L

LGLL

.

(5)

The turbulent viscosity is then related to kand by the expres-

sion

t,L = LCk2LL

. (6)

The terms CGL and CLG can be approximated as

CGL = 2, CLG = 2

GL

1+ GL

, (7)

where GL is defined as the ratio between the Lagrangian in-

tegral time scale and the characteristic particle relaxation time

(FLUENT 6.2, 2005). Gk,L is the production of turbulent ki-

netic energy and L is the turbulent kinetic energy dissipation

rate. Standard and default values of all model parameters were

used. The k model constants C, C1, C2, and k were

set as 0.09, 1.44, 1.92, 1.3 and 1.0, respectively (Launder and

Spalding, 1972).

3.2. Interfacial momentum exchange

Eq. (2) needs to be closed with appropriate expressions for

the interphase forces. The most important interphase force is

the turbulent drag force acting on the bubble resulting from the

mean relative velocity between the two phases and an additional

contribution resulting from turbulent fluctuation in the volume

fractions due to averaging of the momentum equation. In the

present simulations, the drag force was modeled through Morsi

and Alexander model (FLUENT 6.2, 2005). Following are the

details:

f=

CD Re

24 ,
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where

CD = a1 +a2

Re+

a3

Re3, (8)

Re =L|

L G|db

L,

a1, a2, a3 =

0, 24, 0, 0 < R e < 0.1,3.690, 22.73, 0.0903, 0.1 < R e < 1,1.222, 29.26,3.89, 1 < R e < 10,0.617, 46.50,116.67, 10 < R e < 100,0.364, 98.33,2778, 100 < R e < 1000,0.357, 148.62,47, 500, 1000 < R e < 5000,0.46,490.546, 578, 700, 5000 < R e < 10, 000,0.52,1662.5, 5, 416, 700, Re10, 000.

Turbulent fluctuations in the volume fraction have been

modeled using the dispersion force term:

F D = KGL

t,G

GLGG

t,L

GLLL

, (9)

where t,G and t,L are diffusivities, and GL is a dispersionPrandtl number. Here the diffusivities t,G and t,L are com-

puted from the transport equations and the default value for

GL is 0.75.

Other forces such as lift and added mass force have not been

included in the present simulation because of the low velocity

gradients in the bulk region (Aubin et al., 2004; Montante et al.,

2006). They have carried out detailed PIV measurements for the

gasliquid flows generated by axial flow impeller (PBTD45)

and radial flow impeller (Rushton turbine) in baffled stirred

vessel, respectively, and it has been observed that the liquid

velocity profiles tend to be more or less flat in the bulk region.

However, in the impeller region, velocity and pressure gradientsare appreciable. Khopkar et al. (2005) have shown that, in the

impeller region, the drag force dominates the bubbles motion.

In their work, an order of magnitude analysis indicated that

the magnitude of the lift force and added mass force are much

smaller than the interphase drag force. Further work on these

aspects is in progress.

3.3. Computational geometry, grid and method of solution

In the present study, entire geometry has been consid-

ered for the simulations. For all the simulations, the bound-

ary of the rotating domain was positioned at r=

0.16 and0.10 mz0.24 m. Tetrahedral elements were used for mesh-

ing the geometry and a good quality of mesh was ensured

throughout the computational domain using the GAMBIT

mesh generation tool.

As regards to the particularly mesh quality, we have been

restricted to use tetra mesh element due to complex geom-

etry. However, in this study a very high quality of mesh

(skewness < 0.7) has been ensured throughout the computa-

tional domain. The number of grid elements in all the three

directions in both the impeller and outer zone were systemati-

cally increased. When refining the mesh, care was taken to put

most additional mesh element in the regions of high gradient

around the blades and discharge region. The effect of grid

Fig. 2. (The grid independence study) Pressure contours for both the single

and two phase simulations at an impeller speed of 7 rps.

independence has been shown in Figs. 2A and B. It can be

seen that the predicted pressure distribution is practically the

same for grid elements of 550,000667,800. Further, for these

two numbers of grids, the values of power number and flow

number were also found to be constant.

Simulations were carried out for the PBTD impeller of 60 blade angle for various combinations of speeds of agitation

(4.17, 5, 6 and 7rps). Each impeller blade had six holes of 3 mm

diameter through which gas is induced into the system. The

tank walls, the impeller surfaces and baffles have been treated

as no-slip boundary condition with standard wall functions. The

gas flow rate at the hole is initially specified as pressure outlet

boundary condition and gas flow rate has been calculated and

which was subsequently used for the two phase simulations

and a detailed discussion has been given in Section 4.2.2. The

bubble size distribution in the stirred tank reactor depends on

many design parameters. Unfortunately, available experimental

data of bubble size distribution in the present case is not avail-able. Hence, the mean bubble size of 3 mm has been used for

all the simulations. At a liquid surface, a small gas zone was

added at the free surface of water, a method that has been re-

ported to dampen instabilities (FLUENT 6.2, 2005) and only

gas is allowed to escape using pressure outlet boundary con-

dition which means top surface being exposed to atmospheric

pressure. All terms of the governing equations are discretized

using the second-order upwind differencing and the first-order

implicit scheme for the time integration. The SIMPLE algo-

rithm has been employed for the pressurevelocity coupling.

The convergence criterion (sum of normalized residuals) was

set at 5104 for all the equations. Unsteady simulations have

been performed for the flow time of 8 s with a time step size of
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0.001 s. Every time step took around 25 internal iterations to get

converged. All the simulations have been carried on AMD64

dual processors with clock speed of 2.4 GH and 2 GB memory.

Total simulation time for each was around 120 h. All the simu-

lations were conducted using the commercially available CFD

software FLUENT 6.2.

4. Results and discussions

4.1. Single phase flows

In this section validation of power number and mean quali-

tative flow pattern has been presented. Further, validated sim-

ulations have been used for the identification of low pressure

region.

4.1.1. Validation for NPThe power consumption P is calculated as the product of

torque on the impeller blades and the angular velocity. This is

then used for the estimation of power number and it can be

expressed as follows:

NP =2NM

N3D5, (10)

where torque (M) exerted on all blades was computed from

the total momentum vector which is computed by summing

the cross products of the pressure and viscous force vectors for

each facet on the impeller with the moment vector.

The power number (NP) calculated by Eq. (10) for single

phase simulations was found to be NP = 5.2. This compares

well with the experimental value of NP = 5.1.

4.1.2. Flow field

The stirred tank of given geometry was simulated for both

single and gasliquid multiphase flows for different impeller

rotational speeds (4.17, 5, 6 and 7 rps). Fig. 3 shows the vector

flow field at the impeller rotational speed of 7 rps. It can be

seen that this impeller pumps the liquid in the outward direction

through the vertical periphery of the impeller, which is contrary

to the flow patterns generated by the axial flow impeller with

blade angels in the range 3060. Patwardhan and Joshi (1999)

and Aubin et al. (2004) have studied flow pattern generated by

PBTD45 with D/ T ratio 0.5. For this purpose, they have found

two circulation cells, one is primary. A small secondary cell wasalso observed below the impeller. Therefore, for PBTD60 also

one can expect two clear circulation loops which are shown in

Fig. 3. A primary circulation loop exists just below the impeller

plane and extends up to almost 23 of the vessel. In the upper

part of the tank, the liquid velocities are low and circulation is

poor (Fig. 2).

4.1.3. Pressure field

Figs. 4AD show the contours of static pressure on impeller

blades for various speeds of operation for single phase flow. As

shown in Fig. 4 it was observed that for all the impeller speeds,

the low pressure region is formed at the upper edge of the rear

face of the blade and not at the lower edge of the blade. It has

Fig. 3. Axial velocity (m s1

) flow field for liquid phase in the mid-planebetween two baffles.

been found that the static pressure decreases with an increase

in the impeller speed which should lead to an increase in the

gas induction rate. It also becomes clear that the pressure at the

lower face of the impeller is higher than that at rear face.

4.2. Two phase flows

It is envisaged from the single phase simulations that the

gas induction rate can be enhanced if holes are placed in the

low pressure zone (rear face of the blade near the upper edge).Therefore, the impeller design was altered by drilling holes in

the low pressure region which is shown in Fig. 5. In order to

assess the gas-induction performance, power number and gas

induction rate were measured experimentally and compared

against previous impeller design with bottom holes. Further,

CFD simulations have been performed for the same system

(i) to see the change in the magnitude of low pressure in the

presence of gas, (ii) verify that whether the low pressure region

remains at the same location even in the presence of gas and

(iii) to develop a predictive procedure for the gas-induction rate

using the values of local pressure.

4.2.1. Validation for NPIn case of two phase simulations the experimentally mea-

sured and predicted values of gassed power numbers are given

in Table 1. It is evident that, in the case of two phase flows, CFD

simulations tend to underpredict the measured power number,

and it may be due to complex hydrodynamics at higher gas

hold-up values in the given system.

4.2.2. Two phase flow field

In the case of gas induction, the liquid velocity vectors show

that the same qualitative flow pattern as in case of single phase

flow remains but, the magnitude is relatively less which is

shown in Fig. 6. This is attributed to the formation of a gas

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Fig. 4. Contour plots of static pressure (Pascal) on impeller blade for PBTD 60 (A: N= 4rps, B: N= 5rps, C: N= 6rps, D: N= 7 rps).

Fig. 5. Modified impeller geometry.

Table 1Experimental and simulated values of power number and gas hold-up for two

phase simulations

Impeller speed (s1) Power number (NP G)

Experimental Simulated

4.17 4.1 3.3

5 4.0 3.2

6 3.67 2.8

7 3.4 2.5

cavity behind the impeller which effectively reduces the power

given to the liquid. The flat, inclined blade of the PBT leads

to the formation of a low pressure trailing vortex at the rear of

the blade.

4.2.3. Gas induction rate

The single phase CFD simulations have revealed that

the low pressure zone is at the upper edge of rear face of the

impeller blade (new location) and not at the lower face of theblade. Hence the hole of similar diameter and spacing as those

at lower edge were drilled at new locations and experiments

were performed. The rate of gas-induction was measured for

three impeller blade angles (viz. 30, 45 and 60) and various

speed of operation and it has been compared against impeller

design where holes are on the bottom edge. The experimental

results have been shown in Fig. 7. It can be seen that the gas

induction rate for the new location is 100200% higher than

that when the holes were drilled on the bottom edge. Thus, the

identification of low pressure regions by CFD has enabled a

substantial improvement in the performance of gas-inducing

impeller.Further, an attempt has been made to predict the gas induc-

tion rate using CFD simulations to minimize cumbersome and

expensive experimentation. The present work adopted an itera-

tive method for calculating the gas induction rate. This method

involves carrying out the CFD simulations for the two indepen-

dent geometries i.e., single phase simulations for hollow shaft

and impeller and two phase simulations for the stirred tank.

The following procedure was adopted:

(i) The pressure drop in the gas pathway for a given gas flow

rate was estimated as follows:

(a) Pressure loss (PG), due to induced gas flow in the

gas phase involves frictional pressure loss along the gas

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Fig. 6. Axial velocity (m s1

) vectors for liquid in presence of gas in themid-plane between two baffles.

8

6

4

2

0RATEOFGASINDUCTION>Q0x104(m

3/s)

4 5 6 7 8 9 10

IMPELLER SPEED, N (rps)

Fig. 7. Comparison of rate of gas induction (m3 s1), (: PBTD 30 (lower

edge), : PBTD 45 (lower edge), : PBTD 60 (lower edge), : PBTD 30

(new location), : PBTD 45 (new location), : PBTD 60 (new location).

pathway through the shaft, blade and pressure drop across

the gas orifice on the blade surface. For this purpose, the

following equation was used:

PG =CG1

2

QG

A0

2. (11)

For the estimation of CG a separate set of experiments

was performed in which the measured quantity of gas

(by turbine anemometry, QG) was introduced at the inlet

(Fig. 1) and the pressure drop was measured. In the ab-

sence of liquid in the vessel the pressure drop was de-

noted by PG. A data set of about 10 measurements of

10

8

6

4

2

0

RATEGASINDUCTIO

N.Q0x10-3(m

3/s)

3 4 5 6 7 8

IMPELLER SPEED, N (rps)

Fig. 8. Comparison of experimental and predicted values of rate of gas

induction (m3 s1), experimental, CFD predictions.

PG, QG enables the estimation of CG in Eq. (11) and

was found to be 3 1005.

(ii) In the presence of liquid, the pressure drop (P ) consists

of the following components:

P= PG + PL + PH, (12)

where PH is the hydrostatic head of liquid above the

orifice and PL is the pressure drop required for creating

gasliquid interface (at the orifice outlet) and for imparting

energy to the liquid phase. PL was correlated by the

following equation:

PL = CLQAG

H

SA0

B(2N r)C . (13)

The values of CL, A , B, and C were estimated from the

data set ofP versus QG and were found to be 0.093,

0.12, 0.29, and 1.89, respectively.

The pressure drop in the gas path and at the orifice outlet

(PT) is given by

PT = PG + PL. (14)

(iii) The pressure driving force is the pressure difference be-

tween the gas inlet (Pi , point A in Fig. 1) and the pressureat the outlet of the orifice (P). The value of P was es-

timated by CFD using the following stepwise procedure:

(a) For a given hole location, P was obtained from CFD

solution assuming that the gas phase is absent and the

impeller moves only in liquid. The (Pi P) becomes

the pressure driving force, PT.

(b) For PT obtained in step (a) the gas flow rate was esti-

mated using Eqs. (11)(14).

(c) For the gas flow rate and the hole location in step (b), the

two phase CFD simulation gives improved value of P

and hence PT.

(d) The steps (b) and (c) were repeated till the driving and

the resistive forces become equal.

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Fig. 9. Contour plots of static pressure (Pascal) of mixture on impeller blade for PBTD 60 (A: N=4 rps, QG=0.001m3 s1, B: N=5 rps, QG=0.003m

3 s1,

C: N= 6 rps, QG = 0.0055 m3 s1, D: N= 7 rps, QG = 0.008m

3 s1).

Fig. 10. Contours of gas volume fraction ( N=250rpm, QG=0.001m3 s1)

in the mid-plane between two baffles.

The predicted gas flow rate has been compared with the ex-

perimental value of gas induction rate for PBTD60 impeller

for all operating speeds in Fig. 8. For further details of the above

expressions, reader may refer Deshmukh et al. (2006). In the

present work, the pressure driving force has been estimated us-

ing CFD. The comparison is excellent at low speeds (250 and

300 rpm). At higher speeds (above 5 rps) the present iterative

technique based on CFD slightly underpredicts the gas induc-

tion rate. Overall the comparison is fairly good considering the

complexity of two phase flow field in the vicinity of impeller.

Fig. 11. Contours of gas volume fraction ( N=250rpm, QG=0.001m3 s1)

in the horizontal impeller center plane.

4.2.4. Pressure field

After the commencement of gas induction, pressure field gets

modified which is depicted in the form of pressure contours in

Fig. 9 AD. It can be seen that the low pressure region was

still located near the top edge of the each impeller blade. This

result is very important because the location of holes can be

estimated by only single phase simulations and the complex and

expensive two phase simulations need not be performed in a

majority of the cases. The present modification of placing holes

near the top edge of the impeller rear face enabled enhancement

in the induction rate.

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Table 2

Experimental and predicted values of overall gas hold-up

Impeller speed (s1) % Gas hold-up (G)

Experimental Predicted

4.17 7.5 8.5

5 13.21 15.14

6 15.1 17.287 24.2 27.3

4.3. Gas hold-up

In addition to gas induction, its dispersion in the liquid

also plays an important role in the performance of the reactor.

Figs. 10 and 11 show (for N= 250 rpm, induced gas flow rate

of 0.001m3 s1) the computed gas volume fraction in a verti-

cal plane containing the impeller and in the horizontal impeller

center plane, respectively. It can be observed from the figures

that the gas induced through the holes follows impeller dis-

charge stream. The flow pattern shows the gas accumulation in

the recirculating flow regions both above and below impeller

center plane. Further, in the low pressure region behind the im-

peller blades gas tends to accumulate by forming the so-called

gas cavities and the gas leaving the orifices was entering the

cavity directly without discrete bubbling or jetting. It is clear

from Fig. 10 that the high gas fractions are encountered in the

near shaft zone, where liquid flows downwards and drags the

gas. Fig. 11 shows the accumulation of gas behind the baffles

due to recirculation of liquid. The total gas hold-up predicted

by the present CFD simulations is shown in Table 2. A satis-

factory agreement can be seen between the simulated overall

gas hold-ups and the experimentally observed values.

5. Conclusions

(1) In the present work, an optimization procedure has been

suggested for the rate of gas induction using CFD.

(2) For the maximization of the gas induction rate, the outlet

holes on the impeller need to be located in the low pres-

sure region. The present investigation gives a systematic

procedure for the identification of low pressure region.

(3) The location of low pressure regions (as estimated from

CFD) was found to be the same using single and two phase

simulations. This important result is useful because the

complex and expensive two phase simulations need notbe performed as the single phase simulations suffice the

objective of optimization.

(4) The CFD predictions were compared with the experimen-

tal values of gassed power number and overall gas hold

up. It has been observed that the gassed power number

was under predicted at all the above mentioned operating

conditions. Whereas, the overall hold-up values have been

over predicted.

(5) CFD simulations for single phase and multiphase flows

have been extended to calculate the gas inductions rate it-

eratively. The predicted gas induction rates were found to

be in excellent agreement with the experimentally mea-

sured values.

Notation

a1, a2, a3 draglaw constants

A empirical constant

A0 cross sectional area of orifice, m2

b baffle width, m

B empirical constantC, C1, C2, C3 turbulence model constants

C empirical constant

CD drag coefficient

CG constant

CL constant

CP pressure coefficient

db bubble diameter, m

D impeller diameter, m

f drag functionF volumetric force, N m3

g acceleration due to gravity, m s2

Gk production of turbulent kinetic energy,m2 s3

H liquid height, m

I unit tensor

k turbulent kinetic energy, m2 s2

K exchange coefficient, kg m3 s1

M torque, N m

N impeller rotation speed, s1

NCG critical impeller speed for onset of gas in-

duction, s1

NP impeller power number

NP G gassed impeller power number

p pressure, N m2

P power consumption,W

Pi pressure at shaft inlet, N m2

P pressure at the outlet of the orifice, N m2

PG pressure loss in gas phase, N m2

PL pressure loss in liquid phase, N m2

PD total pressure driving force generated by

liquid flow, N m2

PT total pressure loss associated with gas

flow, N m2

QG rate of gas induction, m3 s1

r orifice distance from the impeller axis, m

R interphase force, N m3

Re Reynolds number

RT radius of the torque table, m

t time, s

T tank diameter, m

average velocity, m s1

V volume of liquid, m3

w weight of the load cell, kg

z axial coordinate, m

Greek letters

volume fraction

turbulent energy dissipated per unit mass,

m2 s3

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bulk viscosity, kg m1 s1

viscosity, kg m1 s1

density of fluid, kg m3

k turbulent Prandtl number for the turbulent ki-

netic energy

turbulent Prandtl number for the dissipation rate

GL dispersion Prandtl number

stress tensor, kg m1 s2

Subscripts

G gas phase

L liquid phase

t turbulent

Acknowledgment

B.N. Murthy and N.A. Deshmukh gratefully acknowledge

the financial support during this work by Department of Atomic

Energy (DAE), and Board of Research in Nuclear Sciences(BRNS), Government of India, respectively.

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