Role of Free Surface in Liquid Mixing in Shallow Gas-Liquid Process Vessels
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normal"> EN-US">Several gas-liquid reactors/process equipment involve liquid phase
mixing due to mechanical stirring or gas-induced stirring, for example
gas-liquid bubble columns, mechanically agitated stirred vessels, BOF (Basic
Oxygen Furnace) and ladle used in primary and secondary steel refining,
respectively, etc. In case of tall gas-liquid bubble columns (height to
diameter ratio H/D > font-family:Symbol;color:black;mso-ansi-language:EN-US">~5),
flow is inherently unsteady and the effect of top free surface on dynamics and
therefore on liquid mixing may not be significant. The process vessels having
H/D color:black;mso-ansi-language:EN-US">~ 14.0pt;color:black;mso-ansi-language:EN-US"> 1 or lesser, are generally
referred shallow vessels/columns. In case of mechanically agitated vessels (H/D
mso-ansi-language:EN-US">~ color:black;mso-ansi-language:EN-US">1), flow is mostly dominated by the
agitator/impeller and may not be inherently dynamic as seen in case of bubble
columns. However, in case of shallow vessels with gas-induced stirring (H/D
< 1), where flow is inherently unsteady like in bubble columns, the
free surface at the top is likely to influence the dynamics of bubble plume(s)
and therefore the liquid mixing in such shallow vessels. For example, in BOF
vessel used in primary steel refining process, metal bath height to diameter
ratio is less than one and an inert gas is injected through bottom tuyeres to
provide efficient mixing and homogeneity in the metal bath that increases the
overall process kinetics as well as reduces levels of impurities. Since the liquid
phase mixing in the shallow vessels (BOF vessel) is governed by the dynamics of
gas-liquid flow, there is a need to develop computational models capable of
predicting the dynamics of such gas-liquid flow accurately and verify their
predictive abilities using measurements. The objective of the present work is
to simulate the gas-liquid mixing in a shallow BOF vessel to understand the
effect of free surface on velocity distribution, dynamics and eventually on
liquid phase mixing and verify the predictions using the measured mixing time.
6.75pt;mso-table-bspace:8.0pt;margin-bottom:5.75pt;mso-table-anchor-vertical:
paragraph;mso-table-anchor-horizontal:column;mso-table-left:left;mso-padding-alt:
0cm 0cm 0cm 0cm">
text-align:center;line-height:normal;mso-element:frame;mso-element-frame-hspace:
9.0pt;mso-element-wrap:around;mso-element-anchor-vertical:paragraph;
mso-element-anchor-horizontal:column;mso-height-rule:exactly">
justify;line-height:normal;mso-element:frame;mso-element-frame-hspace:9.0pt;
mso-element-wrap:around;mso-element-anchor-vertical:paragraph;mso-element-anchor-horizontal:
column;mso-height-rule:exactly"> font-family:"Calibri","sans-serif";mso-ansi-language:EN-US'>Figure. 1. BOF
vessel set-up at IIT Delhi (a) complete set-up (b) BOF vessel (c)
conductivity probe
normal">In
the present study, the cold flow experiments were performed at mass flow rate
of 1.30 ×10-3 kg/s in 6:1 scaled-down BOF vessel (shown in Figure 1(a))
filled with demineralized water corresponding to H/D~0.44. Compressed
air was injected through eight equiangular bottom tuyeres placed at the PCD
(pitch to circle diameter) of 0.59. The mixing time measurements were performed
by instantaneous addition of a tracer solution and monitoring the tracer
concentration at multiple locations in the vessel. For this purpose, ?in-house?
developed miniaturized conductivity probes (Figure 1(c)) and a multichannel
online conductivity measurement system (Figure 1(a)) was used. Further details
of the conductivity probe data processing and mixing time definitions will be
provided in the full length manuscript. normal">Three-dimensional
transient Euler-Lagrange (EL) simulations of dispersed gas-liquid flow in a 6:1
scaled-down BOF vessel were carried out with water as the continuous and air as
the dispersed phase. Gas bubbles were injected through eight equiangular
tuyeres placed at PCD of 0.59. Simulations were performed for mono-dispersed (dB
= 5 mm) gas-liquid flow at mass flow rate of 1.30 ×10-3 kg/s.
User-defined functions were implemented in the solver to record the time
evolution of local liquid velocities and tracer mass fraction in the vessel.
Further to see the effect of presence of free surface, transient Euler-Lagrange
(EL) + Volume-of-Fluid (VOF) simulations were performed at the same conditions
as mentioned above. The VOF method is used to capture the dynamic movement of
the free surface. In order to understand the effect of free surface on dynamics
of gas-liquid flows and liquid mixing, simulations were performed by assuming
the top surface as a wall (with no slip or slip boundary condition) or
simulating the free gas-liquid interface. normal">
normal">
justify;line-height:normal"> color:black;mso-ansi-language:EN-US">Figure.2. Instantaneous (a)
bubble positions (colored by bubble velocity magnitude), (b)
liquid velocity distribution (vector plot), (c) liquid velocity
distribution (contour plot) and (d) liquid velocity distribution (contour
plot) at top surface at t=10 s for (i) no-slip (ii) free-slip and (iii) free
surface boundary condition at top wall (mass flow rate = 1.3x10-3
kg/s).
simulated instantaneous snapshots of bubble positions (colored
by bubble velocity magnitude) and liquid velocity distribution in case of (i)
no-slip (zero liquid velocity at top wall) , (ii) free
slip (zero shear at the top wall) and (iii) free surface with free board region
at mass flow rate of 1.29 font-family:Symbol;mso-ansi-language:EN-US">´10-3 kg/s, are
shown in Figure 2. The bubble plumes simulated using the EL approach were found
to oscillate more with a strong re-circulatory liquid flow in comparison with
that simulated using the EL+VOF approach as shown in Figure 2(i) (b), (c) and
(ii) (b), (c). While in the case of EL+VOF simulation, the free surface deforms
and plume causes sloshing at the free interface (Figure 2(iii)a) without
significant plume oscillations. This less re-circulatory flow is shown in
Figure 2(iii) (b) and (c). The detailed description of computational model and
boundary conditions and their effect on liquid velocity distribution will be
described in the full length manuscript. For quantitative analysis of the
meandering motion of bubble plumes, the time-histories of liquid velocity
components at different spatial locations were recorded (see Figures 3 (a), (b)
& (c)). In simulations performed using the EL approach, liquid velocity
components were seen to fluctuate chaotically and that their magnitudes are
also higher than that seen for the EL+VOF simulation, indicating a dynamic and
strong recirculating flow. normal">
normal">
normal">Figure 3. Comparison of liquid velocity
fluctuation time series of (a) Vx, (b) Vy and (c) Vz
components predicted using the EL and EL + VOF approaches (mass flow rate
1.3X10-3 kg/s). The locations of points P1, P2 and P3 are shown in
Figure 2 (i) (c).
margin-right:6.75pt;mso-table-bspace:8.0pt;margin-bottom:5.75pt;mso-table-anchor-vertical:
paragraph;mso-table-anchor-horizontal:column;mso-table-left:left;mso-padding-alt:
0cm 0cm 0cm 0cm">
normal;mso-element:frame;mso-element-frame-hspace:9.0pt;mso-element-wrap:
around;mso-element-anchor-vertical:paragraph;mso-element-anchor-horizontal:
column;mso-height-rule:exactly"> mso-no-proof:yes">
normal;mso-element:frame;mso-element-frame-hspace:9.0pt;mso-element-wrap:
around;mso-element-anchor-vertical:paragraph;mso-element-anchor-horizontal:
column;mso-height-rule:exactly"> color:black;mso-ansi-language:EN-US">Figure 4. Snapshots of simulated tracer
mass fraction distribution at (a) t=0 s, (b) t=2 s, (c) t=6 s and (d) t=30 s
using (i) EL approach and (ii) EL+VOF approach (mass flow rate = 1.30x10-3
kg/s).
gas-induced liquid phase mixing simulations were performed for H/D~0.44 by adding a
passive tracer and simulating its transport in the continuous phase (water)
using the EL and EL+VOF approaches. Typical snapshots of tracer mass fraction
distributions are shown in Figure 4. In case of EL simulations, owing to the
dynamic re-circulatory flow, the tracer was transported quickly. Within the
first 10 s (Figures 4 (i) (a), (b), (c)), it spreads all over the domain except
some corner regions of the vessel and get completely mixed at 30 s (Figure 4
(i) (d)). In case of EL+VOF simulation (Figure 4 (ii) (a), (b), (c), (d)), it
takes more time for complete mixing than that predicted by the EL approach. In
order to analyze the mixing time difference in both cases, time histories of
tracer mass fraction were recorded at eight different points by implementing
user-defined functions and the (mixing) time required for the tracer mass
fractions to reach within ±5% of the final (equilibrium) tracer concentration
was calculated. It was found that average mixing time predicted using the
EL+VOF approach was about font-family:Symbol;mso-ansi-language:EN-US">~10 % more than predicted using
the EL approach at the flow rate of 1.3x10-3 kg/s. The mixing time
predicted using the EL+VOF approach showed a good agreement (see Table 1) with
the experimentally measured mixing times in comparison to EL simulation in
terms of local as well as average mixing time. The detailed analysis and
comparison of the experimental and simulated mixing time will be presented in
the full length manuscript. normal">
normal"> color:black;mso-ansi-language:EN-US'>Table 1. Comparison of predicted (using
EL and EL+VOF approaches) and measurements at mass flow rate of 1.3x10-3
kg/s color:black;mso-ansi-language:EN-US'>.
text-align:center;line-height:normal"> mso-ansi-language:EN-US">Case
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">H/D ratio
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">Mixing time (s)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">Mixing time (s)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">Mixing time (s)
padding:0cm 5.4pt 0cm 5.4pt;height:20.6pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">Experiment
padding:0cm 5.4pt 0cm 5.4pt;height:20.6pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">EL approach
padding:0cm 5.4pt 0cm 5.4pt;height:20.6pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">EL+VOF approach
text-align:center;line-height:normal"> mso-ansi-language:EN-US">(i)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
normal">0.88
(symmetric gas injection)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">--
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">65
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">68
text-align:center;line-height:normal"> mso-ansi-language:EN-US">(ii)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
normal">0.44
(symmetric gas injection)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">44
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">36
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">40
text-align:center;line-height:normal"> mso-ansi-language:EN-US">(iii)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
normal">0.22
(symmetric gas injection)
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">--
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">14.5
padding:0cm 5.4pt 0cm 5.4pt;height:20.15pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">21.5
text-align:center;line-height:normal"> mso-ansi-language:EN-US">(iv)
padding:0cm 5.4pt 0cm 5.4pt;height:30.3pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">0.44 (asymmetric gas injection, at mass flow rate of 2.6x10-3 kg/s)
padding:0cm 5.4pt 0cm 5.4pt;height:30.3pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">--
padding:0cm 5.4pt 0cm 5.4pt;height:30.3pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">25
padding:0cm 5.4pt 0cm 5.4pt;height:30.3pt">
text-align:center;line-height:normal"> mso-ansi-language:EN-US">38
were performed for BOF vessels with H/D = 0.22 and 0.88 to see the effect of
free surface on mixing at different H/D ratio (see Table 1). The predicted
mixing time in case of free surface flow simulation (EL+VOF approach) was ~30% higher for H/D
= 0.22 (case iii) and was ~ 5% higher for H/D = 0.88 (case i) than that
predicted using the EL approach without the free surface. Further simulations
were also performed by increasing the gas flow rate and introducing it from one
half of the vessel (through 4 tuyeres instead of 8 tuyeres) and as a result the
sloshing of free surface was found to increase, leading to increase in mixing
time in case of free surface simulation by ~34% (case iv). A
detailed comparison of effects H/D ratio, surface tension and differential flow
scheme on the dynamics of free surface, re-circulatory flow and consequently on
mixing time will be reported in the full length manuscript. The experimentally
verified computational models will be useful to simulate mixing in shallow
vessels and to optimize their performance in terms of improved mixing and
subsequently improved product quality.