Instabilities Due to Turbulence through Inlet Jet in Plunging Jet Bubble Column
normal">Instabilities
due to Turbulence through Inlet Jet in Plunging Jet Bubble Column normal"> normal">Ifsana Karima,
Swapnil Ghatagea, Mayur Satheb,
Jyeshtharaj Joshic and Geoffrey Evansa* normal"> font-weight:normal'>a "Times","serif"'>Discipline of
Chemical Engineering, University of Newcastle, Australia normal"> font-weight:normal'>b Department of Chemical
Engineering, Louisiana State University, USA normal"> font-weight:normal'>c "Times","serif"'>Homi Bhabha National Institute, Mumbai, India normal">(*Corresponding Author?s E-mail: Geoffrey.Evans@newcastle.edu.au) normal">
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: inter-ideograph;text-indent:14.45pt;line-height:normal">
               .                                                                                Â
(1) inter-ideograph;text-indent:14.45pt;line-height:normal">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. inter-ideograph;text-indent:14.45pt;line-height:normal">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 (ϵGC) 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). inter-ideograph;text-indent:14.45pt;line-height:normal">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. inter-ideograph;text-indent:14.45pt;line-height:normal">The stability criterion proposed by Joshi
et al. (2001) has been modified to consider the turbulence through incoming
liquid jet. K3 relates the gas phase
fluctuation velocity in two-phase flow, v?, with liquid phase
fluctuation velocity at inlet, u?, as: inter-ideograph;text-indent:14.45pt;line-height:normal">
                                                                                                           Â
                   (2) inter-ideograph;text-indent:14.45pt;line-height:normal">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 K3 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 f1 represents the difference between left and right
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 (ϵGC, low) "Times","serif"'>. However, it
can be seen that transition from heterogeneous regime back to homogeneity was
predicted at point Q corresponding higher gas hold-up (ϵGC, high). The length of occurrence of
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 K3has been tuned such that each of estimated transition gas hold-up (ϵGC, low and ϵGC, high) matches with the experimental gas
hold-up. So, two values of K3 were obtained corresponding to
points P and Q. The estimated values of K3obtained
for the entire range of gas hold-up is plotted in Fig. 3. At lower values of
gas hold-up, the values of K3 showed steady decrease with
increase in gas hold-up. At higher values of dispersed phase hold-up, predicted
values of K3at both lower and higher transition hold-up
(ϵGC, low and ϵGC, high) were observed to be equal, approaching
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 ϵGC, low and ϵGC, high. inter-ideograph;text-indent:14.45pt;line-height:normal">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 K3 predicted were decreasing as we move down the column. It
was observed that CFD predicts values of K3comparable
with predictions of linear stability analysis. text-justify:inter-ideograph;line-height:normal"> text-justify:inter-ideograph;line-height:normal"> text-justify:inter-ideograph;line-height:normal">References 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>Joshi, J.B., Deshpande, N.S., Dinkar, M.,
Phanikumar, D.V., Hydrodynamic stability of multiphase reactors, Adv. Chem.
Eng., 26, 1-130 (2001). 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>Shaikh, A., Al-Dahhan, M.H., A review on flow
regime transition in bubble columns, Int. J. Chem. Reactor Eng., 5,
1-70 (2007). 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>Evans, G.M., A study of plunging jet column, Ph. D.
thesis, University of Newcastle, Australia (1990). 3.6pt;margin-left:13.5pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-13.5pt;line-height:normal"> "Times","serif";color:black'>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). 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>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).
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> left:0px;margin-left:264px;margin-top:93px;width:144px;height:45px">
left:0px;margin-left:255px;margin-top:251px;width:144px;height:45px">
left:0px;margin-left:170px;margin-top:108px;width:137px;height:69px">
0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'>Fig. 2. Stability plot for experimental data of Evans (1990) 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> left:0px;margin-left:137px;margin-top:132px;width:164px;height:285px">
margin-top:523px;width:191px;height:36px">
0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'>Fig. 3. Variation of K3 with gas hold-up
due to Turbulence through Inlet Jet in Plunging Jet Bubble Column normal"> normal">Ifsana Karima,
Swapnil Ghatagea, Mayur Satheb,
Jyeshtharaj Joshic and Geoffrey Evansa* normal"> font-weight:normal'>a "Times","serif"'>Discipline of
Chemical Engineering, University of Newcastle, Australia normal"> font-weight:normal'>b Department of Chemical
Engineering, Louisiana State University, USA normal"> font-weight:normal'>c "Times","serif"'>Homi Bhabha National Institute, Mumbai, India normal">(*Corresponding Author?s E-mail: Geoffrey.Evans@newcastle.edu.au) normal">
Keywords: Turbulence; Instability; Plunging jet.
normal">ABSTRACT
inter-ideograph;text-indent:14.45pt;line-height:normal">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: inter-ideograph;text-indent:14.45pt;line-height:normal">
               .                                                                                 (1) inter-ideograph;text-indent:14.45pt;line-height:normal">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. inter-ideograph;text-indent:14.45pt;line-height:normal">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 (ϵGC) 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). inter-ideograph;text-indent:14.45pt;line-height:normal">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. inter-ideograph;text-indent:14.45pt;line-height:normal">The stability criterion proposed by Joshi
et al. (2001) has been modified to consider the turbulence through incoming
liquid jet. K3 relates the gas phase
fluctuation velocity in two-phase flow, v?, with liquid phase
fluctuation velocity at inlet, u?, as: inter-ideograph;text-indent:14.45pt;line-height:normal">
                                                                                                                               (2) inter-ideograph;text-indent:14.45pt;line-height:normal">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 K3 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 f1 represents the difference between left and right
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 (ϵGC, low) "Times","serif"'>. However, it
can be seen that transition from heterogeneous regime back to homogeneity was
predicted at point Q corresponding higher gas hold-up (ϵGC, high). The length of occurrence of
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 K3has been tuned such that each of estimated transition gas hold-up (ϵGC, low and ϵGC, high) matches with the experimental gas
hold-up. So, two values of K3 were obtained corresponding to
points P and Q. The estimated values of K3obtained
for the entire range of gas hold-up is plotted in Fig. 3. At lower values of
gas hold-up, the values of K3 showed steady decrease with
increase in gas hold-up. At higher values of dispersed phase hold-up, predicted
values of K3at both lower and higher transition hold-up
(ϵGC, low and ϵGC, high) were observed to be equal, approaching
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 ϵGC, low and ϵGC, high. inter-ideograph;text-indent:14.45pt;line-height:normal">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 K3 predicted were decreasing as we move down the column. It
was observed that CFD predicts values of K3comparable
with predictions of linear stability analysis. text-justify:inter-ideograph;line-height:normal"> text-justify:inter-ideograph;line-height:normal"> text-justify:inter-ideograph;line-height:normal">References 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>Joshi, J.B., Deshpande, N.S., Dinkar, M.,
Phanikumar, D.V., Hydrodynamic stability of multiphase reactors, Adv. Chem.
Eng., 26, 1-130 (2001). 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>Shaikh, A., Al-Dahhan, M.H., A review on flow
regime transition in bubble columns, Int. J. Chem. Reactor Eng., 5,
1-70 (2007). 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>Evans, G.M., A study of plunging jet column, Ph. D.
thesis, University of Newcastle, Australia (1990). 3.6pt;margin-left:13.5pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-13.5pt;line-height:normal"> "Times","serif";color:black'>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). 3.6pt;margin-left:14.2pt;text-align:justify;text-justify:inter-ideograph;
text-indent:-14.2pt;line-height:normal"> "Times","serif";color:black'>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).
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Fig. 1. Bubble diameter as a
function of gas hold-up
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> left:0px;margin-left:264px;margin-top:93px;width:144px;height:45px">
left:0px;margin-left:255px;margin-top:251px;width:144px;height:45px">
left:0px;margin-left:170px;margin-top:108px;width:137px;height:69px">
0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'>Fig. 2. Stability plot for experimental data of Evans (1990) 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> left:0px;margin-left:137px;margin-top:132px;width:164px;height:285px">
margin-top:523px;width:191px;height:36px">
0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'> 0cm;margin-bottom:3.6pt;margin-left:14.2pt;text-align:center;text-indent:-14.2pt;
line-height:normal"> color:black'>Fig. 3. Variation of K3 with gas hold-up