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**Unformatted text preview: **Chem. Eng. Comm. 189: 1640—1652, 2002 Copyright iii: 2002 Taylor 81 Francis 6
0098~6445I02 $1100 + .00 oct: 10.1080/00936440290123606 Taylor & Francis Yayloi aFranm Croup INTERSTAGE BACKMIXING IN OSCILLATORY FLOW
IN A BAFFLED COLUMN MOHD SOBRI TAKRIFF
ZUHHINA MASYITHAH Department of Chemical and Process Engineering.
Universiti Kebangsaan Malaysia, Bangi,
Selangor Darul Ehsan, Malaysia An investigation on oscillatory ﬂow in a bafﬂed column was carried out to
determine the effects of various operating parameters on interstage back-
mixing. Among parameters studied in this Work were liquid ﬂow rate, liquid
viscosity. oscillation frequency and oscillation amplitude. The results of this
study indicated [hat the interstage backmiin'ng had a maximum value under
nonﬁow condition but decreased with liquid ﬂow rate. LDWer backrnixing rate
was observed in liquids with higher viscosity. Oscillation frequency and am-
plitude are the dominating factors that increase backmix-ing as these factors
increase. Keywords: Backmixing; Bafﬂed column; Oscillatory ﬂow; Mixing INTRODUCTION Mixing in laminar ﬂow in a straight tube is controlled by molecular
diffusion, which is a very slow mechanism. Under this condition, transfer
processes are usually characterized by steep temperature gradients and by
large concentration gradients within ﬂuid. Enhancement of mixing in a
straight tube is. being actively studied. A technique commonly used to
enhance mixing is to operate the equipment in the turbulent regime.
A high ﬂow rate is required to achieve turbulent ﬂow, but it results in Received 8 November 2000; in final form 18 June 200]. Address correspondence to Mohd Sobri Takril‘f, Department of Chemical and Process
Engineering, Universiti Kebangsaan Malaysia, 43600 Bangi, S'elangor Dani] Eh-san,
Malaysia. E—mail: sobriéiiengukmmy 1640 INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1641 reduction of residence time in the ﬂow system, which is counter—
productive to many process objectives. Oscillatory ﬂow in bafﬂed columns has been reported in numerous
publications as very promising to enhance mixing in a straight and
smooth tube or column (Hewgiil et al., 1993; Mackley, 1987, 1991).
Oscillatory ﬂow mixing can be achieved if there is a fully reversing ﬂow
around bafﬂe plates. which may be produced either by oscillating the
fluid or bafﬂe plates (Mackley, 1991). Oscillatory ﬂow in a bafﬂed tube
can be characterized by the oscillatory Reynolds number Rea, which
describes the intensity of oscillation applied to the system: ”15“?” (1) I4 The second group that is USed to characterize oscillatory ﬂow is the
Strouhal number S, where S, represent a ratio of oriﬁce diameter to
oscillation amplitude: Rea = _ D
# 471x” S, (2) Efﬁcient mixing can be achieved in Oscillatory ﬂow in a bafﬂed tube when
R6,, is greater than 150 (Roberts, 1991). Brunold et a1. (1989) showed that
baffle spacing of the order of 1.5 tube diameter and constriction of ratio
about 60% is optimal to achieve good mixing in oscillatory condition.
The interaction between the sharp edge of the bafﬂe plates and the
oscillating ﬂuids is responsible for the improvement in the mixing and
transport properties. Flow of liquid around bafﬂe plates in one direction
produces vortices behind the plates. These vortices take whatever is near
the column’s wall with them. Upon reversing the ﬂow direction the
vortices are pushed into the center of the column while new vortices are
formed at the same time, and the cycle is repeated. This provides an
effective way of moving ﬂuids from the walls to the center of the conduit.
Formation and disruption of vortices due to the interaction of ﬂuid and
bafﬂes enhance mixing in the space between the two bafﬂes.
Application of oscillatory ﬂow in a bafﬂed column produces a certain
amount of baekmixing, which is a disadvantage in a continuous system
when plug flow is desired. A brief literature review indicated that no work
has been carried out to investigate this phenomena in oscillatOry flow in a
bafﬂed column. The only related work was by Howes and Mackley
(1990), in which they observed that backmixing occurs .in oscillatory ﬂow
in bafﬂed column. However, the effects of operating parameters and the
magnitude of backmixing were not quantiﬁed. The objectives of this
work are to quantify the magnitude of backmixing and to investigate the 1642 M. S. TAKRIFF AND 2. MASYITHAH effects of operating parameters on the backmixing. rate in Oscillatory ﬂow-
in a bafﬂed column. MATERIALS AND METHODS A schematic of the experimental apparatus is shown in Figure 1. The
experiments were carried out in a two—stage bafﬂed column. The height of
the column was 282 mm and the diameter was 94 mm. The column made
of Perspex, was mounted on a stainless piston sleeve. A pneumatically
driven piston mounted at the bottom of the column was used to oscillate
the liquid. The range of experimental variables used in this study is
presented in Table I. At constant oscillation frequency and amplitude and liquid ﬂow rate,
60mL of 30wt% KCl solution was injected into the exit stage of the
liquid phase. Twelve samples were taken from each stage at periodic
intervals, The KCl concentration in each sample was determined using an electric-a1 conductivity apparatus. Kmil &.\\_\‘\WI mm
an—Cz) .®—> @———> “I‘—£\\ll :1
_a
,4
.’ ‘4 -Hﬂl—L\\'IKJ ...||::I a]
_s._ I!
e ‘m.‘\\<_\\:\.‘..\ ". !
L §i§ Figure 1. Schematic of the experimental apparatus. (1) top plate, (2) water inlet, (3) perspex
column, (disampling ports, (5) bafﬂe plate, (6) injectioujsampﬁng parts, ('7) water outlet,
(8) pistc‘m, (9) piston bar, (10) Frame. INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1643 Table 1 Range of Experimental Variables Variable Range of value
Liquid ﬂow rate 0.0—1.2 L/min
Liquid viscosity 0,001—0.0l kg/m.s
Oscillation frequency 0.5—1.0 Hz
Oscillation amplitude 7.5—l 5 mm The Ideal Stage with Backmixing (ISB) model (X11, 1994) was
employed in this investigation to determine the magnitude of back—
mixing“. The ISB model represents backmi-xing using ﬁnite difference
with the assumption that backtnixing ﬂow occurs between adjacent
stages in addition to the net forward ﬂow of liquid. For single-phase
ﬂow in absence of chemical reaction, the. mass balance for each com-
ponent in j—stagc is given by: dC}: _ , - .
V'(E) = (Ff+ Fb)C}-_1 “ (FfthJ + FhJ+IlCl + Fb.j+1C.r‘+I (3)
where V is the stage volume, Ff and F}, are forward flow and backmixing
ﬂow rates, respectively, and C is concentration. Application of this
equation to each individual stage in the. apparatus used for this study
gives the following equations. For the ﬁrst stage: dCl V1? = Fpro + Fsz -'(Ff.1 + Falcz. (4)
For the second stage:
dC .
V27: = (Fla + F001 — (Fﬁz + F052” (5) Equations (4) and (5) describe the transient behavior of both stages.
Solving these equations for a value of F3, gives the concentrations C1 and
C2 with time. The interstage backrnixing rate for a given run was deter-
mined by selection of Ft, which provided the best match of the experi—
mental result With predicted transient concentration proﬁles. RESULTS AND DISCUSSION
Data Reduction The data obtained from the experiments was analyzed with the ISB
model. Differential Equations (4) and (.5) were solved using MatLabﬁ’ to
obtain the concentration proﬁle for each stage with time. An estimated 1644 M. S. TAKHIFF AND 2. MASYITHAH 1 r 1 ' W.i; . 7 r _]
| Water {1.001 kglm.s l o Stage1
0-9i Do 3 cm, f 0.33 Hz. to 7.5 mm. :1 Stage 2
Vf 0 cmls, Vb 5.29 cmls . -:- 133 Mgelu CUCO 0.2 _. L 2e 40 so 30 1'00 ' 1'20
Time(5) Figure 2. Temporal proﬁles of tracer concentration for both stages for zero ﬁow. value of the backmixing flow rate F}, was chosen until a good match
between the experimental concentrations and the concentrations gener—
ated from the [SB model was obtained. Stage 1 is the inlet stage and stage
2 is the outlet stage; the KC! solution was always injected into stage 2
throughout the experiments. Figures 2 and 3 present a typical match of the experimental con-
centration proﬁles and the concentration proﬁles generated from the ISB
model for runs without ﬂow and with forward ﬂow, respectively. These
ﬁgures show that 1813 model successfully predicted the transient behavior
of the column and can be used to determine the magnitude of interstage
backmixing in oscillatory ﬂew in a bafﬂed column. The assumption of
perfect mixing in each stage was reasonable. These ﬁgures show that
uniform concentration was achieved in both stages after a short period of
time. The average difference between the experimental concentrations
and the concentration proﬁles. generated from the ISB model was less
than 10% over the range of the experimental data. Zero Flow Experiment Backrnixing experiments under zero ﬂow condition were carried out to
establish a basis for comparison with experiments with forward ﬂow. The
data collected are plotted against oscillatory Reynolds number Reo in INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1645 ‘T _ Water 0.001 kg!m.s 0 Stage‘!
0.9L Do 3 cm, f 0.833 Hz, to 1.5 mm, a Stage 2 Vi 1.18 cmls, Vb 4.55 cmls _ {33 Model
0.8, —-- _ CHCO 20 " 4o 60' 30 1-00 1'20
Time{s) Figure 3. Temporal proﬁles of tracer concentration for both stages with forward ﬂow. .—h
M D... 3 cm. vf o llmin, 621<Ren<8858, o.5<s,_<1.5 .Water. 0.001 kglms
‘CMC. 0.006 karma .1.
on .Q Backmlxing Velocity, Vb (arms)
a: 0 2000 4000 6000 8000 10000
Oscillatory Reynolds Number, Rea Figure 4. Lulerstage backmixing under zero ﬂow. 1646 M. S. TAKHIFF AND 2. MASYITHAH Da 3 cm, Wt) limin, 621<Re°<4429, 0.5<St<1.5 .Watet, 0.001 kgfms
‘CMC, 0.006 kglme Backmlxlng Valoclty,_ Vh(cm1‘s) 0 0.2 0.4 0.6 0.8 ‘l Oscillation Velocity, fo (emis) Figure 5. Effect of liquid viscosity on backmixing rate. Figure 4. This ﬁgure shows that backmixing increases linearly with
oscillatory Reynolds number. The effect of liquid viscosity on back-
mixing was also investigated in this part of the study. The range of liquid
viscosity used in this study was 0.001 kg/m.s to 0.01 kg/ 111.5. Figure 5
plots the backmixing velocity versus oscillatory Reynolds number for
liquids at different viscosity to illustrate the effects of viscosity on
bac'kmixing rate. This ﬁgure shows that interstage backmixing is lower in
liquids with higher viscosity. In Figure 6 backmixing velocity is plotted against the oscillation
velocity or the product of the oscillation amplitude and oscillation fre»
quency. This ﬁgure shows that backrnixing increased linearly with oscil—
lation velocity. As the liquid oscillates back and forth, a certain amount
of the liquid ba'ckmixes into the previous stage. At a constant frequency,
a longer oscillation amplitude displaced the liquid to a further distance,
and liquid at the interstag‘e opening is pushed further into the previous
stage, resulting in a greater level of backmixing. While at a constant
amplitude, eddies with greater intensity are generated from the interac-
tion of the liquid and the edge of the bafﬂe plates for a higher value of the
oscillation frequency. As a result a greater amount of liquid at the
interstage opening will be pushed into the previous stage and backmixing
increases. Figure 6 suggests that the combination of the oscillation
amplitude and frequency is the dominating factor that controls back-
mixing rate. INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1647 12 no 3 cm, vf 0 "min. 2214<Reo<3858. o.5<s,<o.99 _\.
D . Water, 0.001 kg!m'.s
O Backmixlng Velocity, Vbtcmfsj
c: 0 0.3 0.6 0.9 1.2 1.5 1.3
Oscillation Velocity, x°*f (cmls) Figure 6. Effect of oscillation amplitude and frequency on backmixing. Experiment with Forward Flow The effects of liquid ﬂow rate on ba‘ckmixing are presented in Figure 7.
This ﬁgure shows that maximum backmixing occurred under nonﬂow
conditions. The backmixing gradually decreasod with an increase in the
liquid ﬂow rate. A similar observation was made by Xu (1994) in his
backmixing study in an agitated—compartmented column. Forward ﬂow
of liquid from one stage to the next resists the tendency of the liquid from
a stage to backmix into a previous one. As the flow rate increases, the
resistance increases, resulting in a lower backmixing rate. Backmixing Correlation The results of this study show that backmixing rate is affected by col-
umn geometry, liquid physical properties, and operating variables.
Backmixing increases with increasing oscillation frequency and oscilla—
tion amplitude and decreases with increasing forward ﬂow rate and
liquid viscosity. Data collected in this work are correlated with
these parameters. Backmixing under zero ﬂow condition is correlated based on the
approach used by Lelli et al. (1976) and Magelli et a1. (1986). They
correlated the volumetric backmixing ﬂow rate, viscosity, and impeller 1848 M. S. TAKRIFF AND Z. MASYITHAH Water 0.001 kglm.s, Do 4 cm.
0.5<S,<0.99, 4429<Rea<8858 Liq. ﬂow rate: .9.Vf 0 cm/s
+Vf 0.4 cmls
+Vf 0.93 cmls Backmixing Velocity, Vh(cmls) 0- 2000 4000 6000 8000 10000
Oscillatory Reynolds Number. Re0 Figure 7. Effect of forward ﬂow rate on interstage backmixing. diameter as a function of impeller Reynolds number. Based on the
observation made in this work, the following relation is hereby proposed: — 0: R6“ (6) This relation takes into account all the parameters that were identiﬁed. to
inﬂuence backmixing as discussed in the previous paragraphs. Ni and
Gough (1997) stated that the bafﬂe geometry is also an important cri-
terion that must be considered in the dimensionless parameters that
characterize oscillatory ﬂow. The variable (D / Do)'1 is added to Equation
(6) to take into account the effect of bafﬂe geometry on backmixing as
follows: F59 D n
”D DC Re" (DH) (7) A backmixing parameter (Nbo) is used to represent the left-hand Side of
Equation (7): Nae = —— (8) lNTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1649 1 000 100 Water 0.001 kglm.s, VF 0 llmin, —
— — 621<Reo<88585t9<DiD¢ <41 0 2000 4000 6000- 8.000 10000 12000
(moot-me... Figure 8. The correlation of- baclcmixing in zero ﬂow. Figure 8 plots N'bu Versus the modiﬁed oscillatory Reynolds number. This
ﬁgure shows that the N50 increases with oscillatory Reynolds number and
the value of n that gives the best ﬁt for all of the data is 0.1. The curve ﬁt
constant fOr the curve shewn in. Figure 8 is given by: N59 2 —57.364 + 0.14m: _ 6 x 10*“);2 (9) 0.1
where x = Reﬂ (1%) The correlation ﬁts the experimental data well and the regression
value (R2) is 0.9484. Comparison between the experimental data and the
values given by Equation (9) give an average error of 7% for the entire
range of this experiment. A similar approach as used by (Xu, 1994) was. employed to correiate
the backrnixing data. under ﬂow condition. He suggested that the ratio of
baekmixing velocity (V3,) to hackmixing velocity at zero forward flow
(V50). is related to the ratio of forward ﬂow velocity (Vf) to V50 as follows: Vf Vb
Woman “0) The (a?) was plotted versus (7%) in Figure 9. This ﬁgure shows that the
(a?) decreases with (1%). The correlation obtained in the column with 1650 M. S. TAKHIFF AND Z. MASYITHAH 1.0 0.8 0.6 . VbNbo 0.4 0.2 4
Water 0.001 kglms 2214<Reo<8853, 2.35<DID.,<3.13 o_o , i _
0.0 0.2 0.4 0.6 0.8 1.0
“Who Figure 9. The correlation of ' backmixing in forward ﬂow. forward ﬂow is given in Figure 9. The data in Figure 9 were ﬁtted with the
following equation: Z1: 1.0—0.5202(ﬁ) 4.015(3) (11)
Van Van The regression value (R2) for the curve .ﬁt was 0.9373, and the average
error of cor-relation was less than 5% for the whole range of experi-
mental data. CONCLUSIONS Backmixing is signiﬁcant in oscillatory ﬂow in a bafﬂed column. The
magnitude of backrnixing'under zero ﬂow and continuous flow conditions
is dominated by amplitude and oscillation frequency. Backmixing was
found to increase linearly with an increase in any of these two variables.
Backmixing rate in oScillatory ﬂow in a bafﬂed tube also depends on the
forward ﬂow rate. The maximum backmixing rate occurs under nonﬁow
condition. Backmixing. gradually decreased with an increase in the liquid
ﬂow rate. Another variable that affects backmixing rate is liquid Visc—
osity. The resalt of this study shows that backmixing decreases with
liquid viscosity. INTERSTAGE BACKMIXING IN OSCILLATORY FLOW 1651 ACKNOWLEDGMENTS This. research has been carried out with ﬁnancial support from the
Ministry of Science, Technology, and Environment of Malaysia through
IRPA grant, 09-02-02-0032, which is gratefully acknowledged. NOTATION Cl KC] concentration at stage I, nunol/L C3 KC] .conCentralion at stage 2, mmol/L 1) column diameter. mm 0., opening diameter, mm f oscillation frequency, Hz Fb volumetric backmixing ﬂow rate, coll/s F} volumetric forward ﬂow rate, ch/s V}, backmixing velocity through the opening, cm/s
V; forward liquid velocity through stage divider opening , cm/s
V, volume of stage I. em3 V2 volume of stage 2, cm3 x,, oscillation amplitude (center to peak). mm xnf oscillation velocity, cm/ 5 u viscosity, [Kg/111.5 ,0 density, kg/rn3 REFERENCES Brunold, C. R., Harms, J. C. B. and Thompson, J. W. (1989). Experimental
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