# Instabilities Due to Turbulence through Inlet Jet in Plunging Jet Bubble Column

**Instabilities
due to Turbulence through Inlet Jet in Plunging Jet Bubble Column**

** **

**Ifsana Karim ^{a},
Swapnil Ghatage**

^{a}**, Mayur Sathe**

Jyeshtharaj Joshi

^{b},Jyeshtharaj Joshi

^{c}and Geoffrey Evans^{a*}** ^{a }**Discipline of

Chemical Engineering, University of Newcastle, Australia

^{b }**Department of Chemical
Engineering, Louisiana State University, USA**

** ^{c }**Homi Bhabha National Institute, Mumbai, India

(^{*}Corresponding Author?s E-mail: **Geoffrey.Evans@newcastle.edu.au****)**

**Keywords:** Turbulence; Instability; Plunging jet.

**ABSTRACT**

The multiphase reactors such as bubble

columns, stirred tanks, fluidized beds, etc. are central to any chemical

process. Bubble columns are favoured over other multiphase equipment due to

various advantages resulting in higher efficiency. Bubble columns can operate

in one of two characteristic regimes i.e. homogeneous and heterogeneous. The

turbulent conditions give rise to instabilities causing regime transition in

bubble column. The knowledge of instabilities and regime transition is of utmost

importance in order to optimize the efficiency. The heterogeneity is associated

with higher turbulence and generally provides better heat, mass and momentum

transfer rates. Conversely, it can be detrimental to efficiency of some

processes such as flotation. Joshi et al. (2001) have developed one dimensional

stability criterion based on linear stability approach. The criterion can be

used to estimate the gas hold-up at which regime transition occurs from

homogeneous to heterogeneous in bubble columns. The regime transition will occur

when:

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(1)

Equations to estimate parameters *A*, *B*,

*C*, *G*, *F* and *Z* involved in Eq. (1) are functions of

operating parameters, dispersion coefficients of phases, bubble diameter,

bubble terminal velocity and can be found in Joshi et al. (2001). They have

also discussed stability

plots to show the stable and unstable operation of bubble column.

The so far published literature on linear

stability mainly focuses on equipment wherein turbulence through a single phase

is significant (Shaikh

and Al-Dahhan,

2007). However, in many applications the turbulence through all phases can be

comparable and have to be quantified for accurately determining the transition

conditions. As a case study, Evans (1990) have analysed regime transition in

plunging jet column. Author applied well known drift flux analysis [Wallis,

1962] and discussed transition on the basis of change in bubble diameter. Author?s

results for air-water system in a column of 44 mm diameter are used for present

study. The liquid jet of constant velocity of 11.5 m/s is entering from a

central nozzle of diameter 4.8 mm. Superficial gas velocity was varied and the

bubble diameter was estimated from measured gas hold-up. The variation of

estimated bubble diameter with variation in measured gas hold-up is plotted in

Fig. 1. It can be seen that the drift flux analysis indicated linear increase

in bubble diameter at gas hold-up higher than 0.38 showing transition gas

holdup (*ϵ _{GC}*) of 38%. However, the lower values of bubble

diameter (less than 3 mm) even at higher superficial gas velocities make it

difficult to comment on regime transition. Computational fluid dynamics (CFD)

can also provide detailed insights into the turbulence, particularly, with respect

to instabilities and transition (Monahan and Fox, 2007).

The present study focuses on relating the

turbulence in various phases in plunging jet bubble column. The bubble size has

been estimated using the drift flux analysis. Also, CFD simulations have been

carried out to provide more insights into the turbulence present in system.

The stability criterion proposed by Joshi

et al. (2001) has been modified to consider the turbulence through incoming

liquid jet. *K _{3}* relates the gas phase

fluctuation velocity in two-phase flow,

*v?*, with liquid phase

fluctuation velocity at inlet,

*u?*, as:

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Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (2)

In systems such as bottom-sparged bubble

columns which are operated in a batch-wise mode there is no liquid inflow to

the system so there is no contribution to the liquid fluctuating velocity.

Hence, for these systems *K _{3}* would be equal to zero. In

contrast, it can have significant values in plunging jet columns. The published experimental data

of Evans (1990) is used for present analysis. The stability plot expressed to

show the stable and unstable operation of bubble column is shown in Fig. 2

where

*f*represents the difference between left and right

_{1 }hand sides in Eq. (1).

Initially the

system can be considered as stable i.e. operating in homogeneous regime. The

transition from homogeneous to heterogeneous regime was observed at point P

corresponding to lower transition hold-up (ϵ

_{GC, low}). However, it

can be seen that transition from heterogeneous regime back to homogeneity was

predicted at point Q corresponding higher gas hold-up (

*ϵ*

*). The length of occurrence of*

_{GC, high}instability (the distance between points P and Q) also showed typical behaviour

decreasing continuously with increase in gas hold-up or superficial gas

velocity. While applying linear stability analysis, the value of

*K*

_{3}_{}has been tuned such that each of estimated transition gas hold-up (

*ϵ*

*and*

_{GC, low}*ϵ*

*) matches with the experimental gas*

_{GC, high}hold-up. So, two values of

*K*were obtained corresponding to

_{3}points P and Q. The estimated values of

*K*

_{3}_{}obtained

for the entire range of gas hold-up is plotted in Fig. 3. At lower values of

gas hold-up, the values of

*K*showed steady decrease with

_{3}increase in gas hold-up. At higher values of dispersed phase hold-up, predicted

values of

*K*

_{3}_{}at both lower and higher transition hold-up

(

*ϵ*

*and*

_{GC, low}*ϵ*

*) were observed to be equal, approaching*

_{GC, high}one. It can be attributed to the fact that at higher gas hold-up values (around

56%), bubble and surrounding liquid is fluctuating at similar intensity. Also,

the length of occurrence of instability showed steady decrease as can be viewed

from overlapping of the lines corresponding to

*ϵ*

*and*

_{GC, low}*ϵ*

*.*

_{GC, high}Eulerian-Eulerian CFD simulations have also

been carried out in a system of identical geometric and operating conditions. Standard

*k*-*ε* turbulence model has been

employed to simulate fluid flow in 2D axisymmetric geometry of mixing length of

plunging jet column. The mesh was refined at jet region to provide higher

resolution giving number of volumes of 7050. It should be noted that the simulations

were only limited to mixing zone where substantial variation in turbulence

properties exist. The continuous and discontinuous phase velocity fluctuations

are estimated from turbulent kinetic energy and slip velocity respectively. From the predicted results,

values of turbulent kinetic energy (*k*) and energy dissipation rate (*ε*) were observed to be high in near

jet region. The variation of fluctuating velocities, *k* and *ε* along the column height was

studied. The values

of *K _{3}* predicted were decreasing as we move down the column. It

was observed that CFD predicts values of

*K*

_{3}_{}comparable

with predictions of linear stability analysis.

**References**

Joshi, J.B., Deshpande, N.S., Dinkar, M.,

Phanikumar, D.V., Hydrodynamic stability of multiphase reactors, *Adv. Chem.
Eng.,*

**26**, 1-130 (2001).

Shaikh, A., Al-Dahhan, M.H., A review on flow

regime transition in bubble columns, *Int. J. Chem. Reactor Eng.*, **5**,

1-70 (2007).

Evans, G.M., A study of plunging jet column, Ph. D.

thesis, University of Newcastle, Australia (1990).

Wallis, G.B., A simplified one-dimensional

representation of two-component vertical flow and its application to batch

sedimentation, Symp. on the Interaction between Fluids and Particles, London,

9-16 (1962).

Monahan, S.M., Fox, R.O., Linear stability

analysis of a two-fluid model for air-water bubble columns, *Chem. Engg. Sci.*,

**62**, 3159-3177 (2007).

Fig. 1. Bubble diameter as a

function of gas hold-up

Fig. 2. Stability plot for experimental data of Evans (1990)

Fig. 3. Variation of K_{3 }with gas hold-up