- Email: [email protected]
THE FLOODING TRANSITION WITH GASSED RUSHTON TURBINES
Symposium Series No. 89
THE FLOODING TRANSITION WITH GASSED RUSHTON TURBINES
M.M.C.G. Warmoeskerken and John M. Smith *
ABSTRACT The flooding t r a n s i t i o n of a Rushton turbine operating i n a g a s - l i q u i d system has been i n v e s t i g a t e d . A clear d e f i n i t i o n for the phenomenon has been given. A r e l a t i o n has been derived from a t h e o r e t i c a l analysis and has been confirmed by experiments i n various vessels up to 1.2 m diameter. The r e s u l t s p r e d i c t gas flow rates f o r the O c c u r r e n c e o f f l o o d i n g t h a t are higher than those found i n l i t e r a t u r e . T h i s has p r o v i s i o n a l y been e x p l a i n e d i n t e r m s o f t h e gas s p a r g e r g e o m e t r i e s used. INTRODUCTION Flooding is one of the characteristic features of stirred tank equipment used to disperse qases in liquids. At high gas loadings the impeller no longer pumps the gas and liquid mixture adequately and the gas rises axially as a bubble stream to the liquid surface. This phenomenon forms an important limitation to the gas handling capacity of a given system both with respect to obtaining effective dispersion and distribution of gas throughout the liquid, and in terms of mass transfer performance (Pollard [9 ] ) . Bimbi net [ 1 ] was one of the first to study this phenomenon. At high gas rates he observed a change in the bulk flow which he called flooding. Since Bimbi net several authors have paid attention to flooding. However there has been little consistency in the definition of the observed effects. Moreover the relations that are presented in the literature are nearly all empirical and based on dimensional analysis. In this paper the authors present a clear definition of flooding,followed by a theoretical approach of the phenomenon. The theoretical equation could be validated by experiments. DEFINITION OF FLOODING The term flooding has often been used in the literature to describe the unsatisfactory operation of an agitator in a gas-liquid system. The term loading has also frequently been used as representing the normal operating state of the system. In the literature several accounts can be found that allow prediction of the transitions between loaded and flooded conditions. However in fact there is significant confusion as to the nomenclature, and indeed not all authors distinguish adequately between the alternative states. The result is that correlations often appear to given conflicting predictions and the results of the various authors are difficult to reconcile.
* Laboratory for Physical Technology, Delft University of Technology, Delft, The Netherlands. 59
Symposium Series No. 89
It seems to the present authors that the situation is considerably clarified if a well defined distinction is drawn between the local conditions determining the flow in the immediate vicinity of the impeller and the changes in the large scale circulation in the tank as a whole. On this basis it is possible to make a preliminary classification into three distinct flow regimes associated with the increasing efficiency of the pumping action as the relative buoyancy forces are steadily reduced. The three stages o c c u r r i n g at p a r t i c u l a r s.tirrer s p e e d s a n d g a s flow r a t e s are as f o l l o w s . I
Impeller flooding. In this regime there is an axial flush of gas through the impeller plane up to the free liquid surface, fig. la. II Impeller loading without gas recirculation. The s tirrer now acts as a pump. However the radial outflow from the imDeller is followed by a buoyancy driven circumferential gas bubble swarm rising to the surface. Although the gas is successfully dispersed by the impeller it is poorly distributed throughout the vessel, fig. lb. III Impeller loading with gas recirculation. In this regime the system is thoroughly aerated, with air distributed throughout the mixing vessel. There is consequently gas recirculation in both upper and lower loops, fig. lc.
Between the situations I and III a further distinction-can be made between characteristic conditions. For example in one situation there may only be gas recirculating in the upper part of the vessel. This was suggested by Nienow et al.[8 ] as the major form of recirculation. If the ratio of tank and impeller diameters are considered, other intermediate situations are possible as drawn in figure 2. Fig. 2a represents the condition at small T/D-ratio. In this case the vertical flows near the tank wall are rapid enough to carry qas downwards below the impeller plane. Recirculation of this gas in the lower region is then inevitable. There need not be gas-recirculation in the uooer region of the tank at the same time. In figure 2b the comparable situation with a large T/D-ratio is drawn. In that case the high axial velocities concentrated on the relatively small impeller rate can capture and recirculate gas above the stirrer. In this study only the transitions from impeller loading to impeller flooding and vi ce-versa have been considered. These are represented by figures la and lb. THEORETICAL CONTEMPLATION Impeller flooding can be described as a condition i n which gas from the sparger rises v e r t i c a l l y upwards through the s t i r r e r r e g i o n , inducinn l i q u i d bulk c i r c u l a t i o n i n the same d i r e c t i o n , as indicated i n f i q u r e la by the dotted l i n e s . On the other hand loadinq may be considered as a s i t u a t i o n where the r a d i a l l i q u i d v e l o c i t y is s u f f i c i e n t l y large to r a d i a l l y remove gas bubbles away from the s t i r r e r ( f i g . l b ) . Westerterp et al. [12] proposed a c r i t e r i o n t h a t was based on f i g . 2b. They defined a minimum s t i r r e r speed f o r gas dispersion by comparing the discharge v e l o c i t y of the l i q u i d w i t h the r i s e v e l o c i t y of the i n d i v i d u a l gas bubbles. This resulted i n a r e l a t i o n which is independent of the gas flow r a t e . However from l i t e r a t u r e and also from t h i s study, i t is clear that the gas flow rate is a s i g n i f i c a n t variable w i t h respect to the flooding t r a n s i t i o n . The t e n d e n c y o f r i s i n g b u b b l e s t o i n d u c e a v e r t i c a l l i q u i d f l o w coirpetes w i t h t h e r a d i a l pumping a c t i o n o f t h e i m p e l l e r . I t i s p o s s i b l e f o r this» 60
Symposium Series No. 89
vertical flow to dominate even when the radial velocity components exceed the corresponding free rise velocity of the bubbles. It seems evident to the present authors that the balance between these vertical and radial velocities must be considered. The pumping action of the impeller is commonly expressed in terms of Q p = C p ND 3
(1)
where Cp is a proportionality constant dependent on the system. The potential axial liquid flow introduced by the buoyancy effects of the bubbles can be estimated if the conditions in the vicinity of a flooded impeller are considered to have similarities to those near an unconstrained bubble column. For such bubble columns Goossens [5] and Smith et al. [Il] have presented a relation derived from the hydrodynamic balance equations, describing the liquid volume rate brought to the surface,Q«w, by the action of a rising bubble column Q
AX — S Q g .g.H b
= C
b
(2)
b
where C. = constant b
Q H g
3 = gas flow rate (m /s) = height of the bubble column (m) 2 = gravitational constant (m/s )
At the flooding transition in a stirred tank the magnitudes of the radial and axial liquid flows can be expected to be the same order:
% ~-
(3)
With equations (1) and (2) this results in: Q g .g.H 5 - N 3 D 9
(4)
Assuming that the height of the bubble column in a vessel with a floodedimpeller is proportional to the stirrer diameter and rearranging the variables of equation 4 gives:
(5)
V*r
This result means that the flooding transition should be described by a linear relation between the gas flow number Fl and the impeller Froude number Fr. A similar relation has been derived by Biesecker[2] who considered the power balance between the bubble flow and the s tirrer. It must be noted here that the equations are developed for a constant T/D-ratio. The influence of this ratio is present in the pumping rate constant of equation 1. However no reliable relations are available concerning the influence of T/D on the pumping capacity of an impeller in gas-liquid systems. On the other hand it seems from literature that the influence of T/D on the flooding transition is considerable. 61
Symposium Series No. 89
EXPERIMENTAL TECHNIQUE The experiments have been performed in mixing tanks of standard geometry, using tank diameters of 0.44, 0.64 and 1.20 m filled to a denth H equal to the tank diameter T. In all cases the T/D rato for the 6-blade Rushton turbines was 2.5. The vessels were fitted with the usual four 0.1 T width baffles, fig. 3. The clearance between the stirrer Diane and the vessel bottom was in all cases equal to the stirrer diameter. All measurements were made in the air-water system, with air supplied from a ring sparger mounted below the stirrer. The transition between impeller loading and flooding can be detected in different ways. The most simple technique is visual observation of the bulk flow. However, this method is subjective and limited to transparent vessels. Mikulcova et al .[7] detected the presence of bubbles in the radial outflow with a conductivety probe. In this study the technique of Roustan [101 has been applied. This method is based on qualitative determination of the liquid radial outflow vector near the impeller by a micro propeller. This propeller produces a signal that is proportional to its rotational speed. The propeller was placed near the stirrer to produce an optimal signal. Fig. 4 shows an example of the measured signals. When there is no gas, Qg = 0, then the signal from the propeller increases linearly with the stirrer speed N. At a constant gas flow rate with an increasing stirrer speed the signal stays on a lower level as long as the impeller is flooded. As the impeller begins to pump radially, the propeller signal starts to increase rapidly. The stirrer speed and gas flow rate at which this transition occurs correspond unambiguously to the flooding transition. Experimentswith both increasing and decreasing stirrer speeds showed that hysteresis is negligible. This was also reported by Dickey [4] , though other authors, for example Roustan [ 10], do not agree. EXPERIMENTAL RESULTS- AND DISCUSSION Figure 5 shows the results of about seventy independent determinations of the transition for the three vessels. In this figure the gas flow rate and stirrer speed at flooding transition are expressed in terms of the gas flow number Fl and Froude number Fr, in accordance with equation 5. From this it was clear that the experimental results are in close agreement with the proposed theoretical relation. The proportionality constant has been found to be 1.2. So the relation describing the flooding transition becomes : Fl = 1.2 Fr
(6)
A s i m i l a r r e l a t i o n has been found by Zwietering [ 1 3 ] , Biesecker [ 2 ] and Mickulcovâ et a l . [ 7 ] . However t h e i r p r o p o r t i o n a l i t y constants are smaller than found i n t h i s study as shown i n f i g u r e 6. I t i s possible t h a t the difference i n the constant of p r o p o r t i o n a l i t y l i e s i n the f a c t that our experiments were a l l made using a r i n g sparger, while the three other authors employed pipe spargers.
From the results of Roustan [ 10] it is clear that the dimensions and location of the qas sparger have a significant influence on the flood ing t r a n s i t i o n . Whilst the measuring techniques used here and t h a t of Roustan were the same,the r e s u l t s d i f f e r completely from each other as shown in 62
Symposium Series No. 89
Figure 7. The only apparent reason for this is the fact that Roustan dis tributed the gas into his vessel through a perforated bottom. Figure 7 also compares the results of other authors with this study. The various correlations have been presented in terms of the stirrer speed and maximum gas flow rate for the 0.44 m vessel. The results of Nienowet al.[8 lare more or less separated from the other data. This is a result of his use of somewhat different definition for flooding.
Nienow's curve related flooding to the d i s t r i b u t i o n of gas throughout the mixing vessel as a whole, f i g . lc w h i l s t the lower curves due to Dickey [ 4 ] , Bruxelmane [ 3 ] , Judat [ 6 ] and ourselves r e s t r i c t consideration of the flooding phenomenon to the immediate v i c i n i t y of the impeller, f i g la and lb.
It is therefore concluded that the introduction of a precise definition for flooding such as that suggested here is meaningful. From figure 7 it is obvious that equation 6 predicts the largest gas flow rate before flooding occurs. Further study is necessary to determine whether the sparger geometry is indeed responsible for these deviations. CONCLUSIONS
A precise definition of flooding in a stirred gas liquid dispersion is indispensable for describing this phenomenon quantitatively. For the impeller flooding transition a linear relation between Fl and Fr could be derived by comparison of the radial liquid flow due to the pumoing action of the stirrer and the axial flow induced by a bubble column. Experiments have shown that this relation can be described as Fl = 1.2 Fr The values of the gas flow number at flooding transition from this study are higher than others reported in the literature. SYMBOLS USED
DP Fl Fr g H N T
QAX
Qg Qn
constant in equation 2 constant in equation 1 stirrer diameter ^ gas flow number (= Q/ND ) Froude number (= N^D/g) gravitational constant height of the bubble column stirrer speed vessel diameter Axial liquid flow Gas flow rate impeller pumping capacity
m / s 2) «·> m3/s) m3/s) m3 /s)
63
Symposium Series No. 89
LITERATURE CITED Bimbinet, J.J., M.S. Thesis, Purdue University, Lafayette, USA 1959. Biesecker, B.O., VDI-Forschungsheft 554, (1972). Bruxelmane, M.Z.A., Proc. Int. Symp. on Mixing, Mons, (1978), paper XC-1. Dickey, D.S., 72nd Annual Meeting Am. Inst. Chem. Engrs., San Francisco, (1979), paper 116 d. 5. Goossens, L.H.J., PhD-Thesis Delft Unviversity of Technology, (1979). 6. Judat, H., Fortschritte der Verfahrenstechnik, (1977), 141. 7. Mikulcovâ, E., Kudrna, V. and Vlcek, J., Scientific papers of the Inst. of Chem. Techn., Prague, Kl, (1967, 167. (in Czech). 8. Nienow, A.W., Wisdom, D.J. and Middleton, J.C., Proc. 2nd European Conf. on Mixing, Cambridge, (1977), paper Fl. 9. Pollard, J., Proc. Int. Symp. on Mixing, Mons, (1978), paper C-4. 10. Roustan, M. and Bruxelmane, M.Z.A., CHISA, Prague, (1981), paner B 3.3. 11. Smith, J.M. and Goossens, L.H.J. Proc. 4th Euron. Conf. on Mixing, Leeuwenhorst, The Netherlands, (1982), paper C2. 12. Westerterp, K.R. , van Dierendonck, L.L. and De Kraa, J.A., Chem. Eng. Sci., 18, (1963), 157. 13. ZwieterTng, Th.N., De Ingenieur, 7i5, (1963), Ch 60. (in Dutch). 1. 2. 3. 4.
64
Symposium Series No. 89
__ / /
1 1 1
1 1
\
\ 1—1
\
1 ι—ι
1
/ (a)
(b)
(c)
F i g . 1. Floodinn and loadinq regimes.
(a)
(b)
F i g . 2. Loadinn regimes f o r d i f f e r e n t T / D - r a t i o s .
motor data processing
ffi
torque meter
Γ
B-U-S
F i g . 3. Experimental set-un.
65
Symposium Series No. 89
06
" T -
.__ —»
> - "<=
/ / /
0
T :0 4 4 m
3 o Qg= O m / s
A
-
3
Δ Qg= 6 24 10" m /s
S- /
0.4
o
Uo
/
--1
K f
lΓ/
0.2 L
/
/
/
/
Δ
o
Δ/
Flooding transition
o /
/ Δ
\
/ /
/
_Δ
'
_L 1
■
F i g . 4. Determination of the flooding t r a n s i t i o n from the micro-proneller signal.
NO^'
»
5 · » o T : AAm Δ T s 6«m ♦ T=12 m
*Λ
♦
.
^
F " m a x « ' 2 F r m in
-<*?)
*
F i g . 5. Experimental r e s u l t s . 66
i
Symposium Series No. 89
riq.
6. Comparison of equation 6 with l i t e r a t u r e .
Q G (10- 3 m 3 /s)
0'
'
1
'
1
'
1
'
L
0 2 4 6 8 Fig. 7. Comparison of the results with other literature data. 67
THE FLOODING TRANSITION WITH GASSED RUSHTON TURBINES
M.M.C.G. Warmoeskerken and John M. Smith *
ABSTRACT The flooding t r a n s i t i o n of a Rushton turbine operating i n a g a s - l i q u i d system has been i n v e s t i g a t e d . A clear d e f i n i t i o n for the phenomenon has been given. A r e l a t i o n has been derived from a t h e o r e t i c a l analysis and has been confirmed by experiments i n various vessels up to 1.2 m diameter. The r e s u l t s p r e d i c t gas flow rates f o r the O c c u r r e n c e o f f l o o d i n g t h a t are higher than those found i n l i t e r a t u r e . T h i s has p r o v i s i o n a l y been e x p l a i n e d i n t e r m s o f t h e gas s p a r g e r g e o m e t r i e s used. INTRODUCTION Flooding is one of the characteristic features of stirred tank equipment used to disperse qases in liquids. At high gas loadings the impeller no longer pumps the gas and liquid mixture adequately and the gas rises axially as a bubble stream to the liquid surface. This phenomenon forms an important limitation to the gas handling capacity of a given system both with respect to obtaining effective dispersion and distribution of gas throughout the liquid, and in terms of mass transfer performance (Pollard [9 ] ) . Bimbi net [ 1 ] was one of the first to study this phenomenon. At high gas rates he observed a change in the bulk flow which he called flooding. Since Bimbi net several authors have paid attention to flooding. However there has been little consistency in the definition of the observed effects. Moreover the relations that are presented in the literature are nearly all empirical and based on dimensional analysis. In this paper the authors present a clear definition of flooding,followed by a theoretical approach of the phenomenon. The theoretical equation could be validated by experiments. DEFINITION OF FLOODING The term flooding has often been used in the literature to describe the unsatisfactory operation of an agitator in a gas-liquid system. The term loading has also frequently been used as representing the normal operating state of the system. In the literature several accounts can be found that allow prediction of the transitions between loaded and flooded conditions. However in fact there is significant confusion as to the nomenclature, and indeed not all authors distinguish adequately between the alternative states. The result is that correlations often appear to given conflicting predictions and the results of the various authors are difficult to reconcile.
* Laboratory for Physical Technology, Delft University of Technology, Delft, The Netherlands. 59
Symposium Series No. 89
It seems to the present authors that the situation is considerably clarified if a well defined distinction is drawn between the local conditions determining the flow in the immediate vicinity of the impeller and the changes in the large scale circulation in the tank as a whole. On this basis it is possible to make a preliminary classification into three distinct flow regimes associated with the increasing efficiency of the pumping action as the relative buoyancy forces are steadily reduced. The three stages o c c u r r i n g at p a r t i c u l a r s.tirrer s p e e d s a n d g a s flow r a t e s are as f o l l o w s . I
Impeller flooding. In this regime there is an axial flush of gas through the impeller plane up to the free liquid surface, fig. la. II Impeller loading without gas recirculation. The s tirrer now acts as a pump. However the radial outflow from the imDeller is followed by a buoyancy driven circumferential gas bubble swarm rising to the surface. Although the gas is successfully dispersed by the impeller it is poorly distributed throughout the vessel, fig. lb. III Impeller loading with gas recirculation. In this regime the system is thoroughly aerated, with air distributed throughout the mixing vessel. There is consequently gas recirculation in both upper and lower loops, fig. lc.
Between the situations I and III a further distinction-can be made between characteristic conditions. For example in one situation there may only be gas recirculating in the upper part of the vessel. This was suggested by Nienow et al.[8 ] as the major form of recirculation. If the ratio of tank and impeller diameters are considered, other intermediate situations are possible as drawn in figure 2. Fig. 2a represents the condition at small T/D-ratio. In this case the vertical flows near the tank wall are rapid enough to carry qas downwards below the impeller plane. Recirculation of this gas in the lower region is then inevitable. There need not be gas-recirculation in the uooer region of the tank at the same time. In figure 2b the comparable situation with a large T/D-ratio is drawn. In that case the high axial velocities concentrated on the relatively small impeller rate can capture and recirculate gas above the stirrer. In this study only the transitions from impeller loading to impeller flooding and vi ce-versa have been considered. These are represented by figures la and lb. THEORETICAL CONTEMPLATION Impeller flooding can be described as a condition i n which gas from the sparger rises v e r t i c a l l y upwards through the s t i r r e r r e g i o n , inducinn l i q u i d bulk c i r c u l a t i o n i n the same d i r e c t i o n , as indicated i n f i q u r e la by the dotted l i n e s . On the other hand loadinq may be considered as a s i t u a t i o n where the r a d i a l l i q u i d v e l o c i t y is s u f f i c i e n t l y large to r a d i a l l y remove gas bubbles away from the s t i r r e r ( f i g . l b ) . Westerterp et al. [12] proposed a c r i t e r i o n t h a t was based on f i g . 2b. They defined a minimum s t i r r e r speed f o r gas dispersion by comparing the discharge v e l o c i t y of the l i q u i d w i t h the r i s e v e l o c i t y of the i n d i v i d u a l gas bubbles. This resulted i n a r e l a t i o n which is independent of the gas flow r a t e . However from l i t e r a t u r e and also from t h i s study, i t is clear that the gas flow rate is a s i g n i f i c a n t variable w i t h respect to the flooding t r a n s i t i o n . The t e n d e n c y o f r i s i n g b u b b l e s t o i n d u c e a v e r t i c a l l i q u i d f l o w coirpetes w i t h t h e r a d i a l pumping a c t i o n o f t h e i m p e l l e r . I t i s p o s s i b l e f o r this» 60
Symposium Series No. 89
vertical flow to dominate even when the radial velocity components exceed the corresponding free rise velocity of the bubbles. It seems evident to the present authors that the balance between these vertical and radial velocities must be considered. The pumping action of the impeller is commonly expressed in terms of Q p = C p ND 3
(1)
where Cp is a proportionality constant dependent on the system. The potential axial liquid flow introduced by the buoyancy effects of the bubbles can be estimated if the conditions in the vicinity of a flooded impeller are considered to have similarities to those near an unconstrained bubble column. For such bubble columns Goossens [5] and Smith et al. [Il] have presented a relation derived from the hydrodynamic balance equations, describing the liquid volume rate brought to the surface,Q«w, by the action of a rising bubble column Q
AX — S Q g .g.H b
= C
b
(2)
b
where C. = constant b
Q H g
3 = gas flow rate (m /s) = height of the bubble column (m) 2 = gravitational constant (m/s )
At the flooding transition in a stirred tank the magnitudes of the radial and axial liquid flows can be expected to be the same order:
% ~-
(3)
With equations (1) and (2) this results in: Q g .g.H 5 - N 3 D 9
(4)
Assuming that the height of the bubble column in a vessel with a floodedimpeller is proportional to the stirrer diameter and rearranging the variables of equation 4 gives:
(5)
V*r
This result means that the flooding transition should be described by a linear relation between the gas flow number Fl and the impeller Froude number Fr. A similar relation has been derived by Biesecker[2] who considered the power balance between the bubble flow and the s tirrer. It must be noted here that the equations are developed for a constant T/D-ratio. The influence of this ratio is present in the pumping rate constant of equation 1. However no reliable relations are available concerning the influence of T/D on the pumping capacity of an impeller in gas-liquid systems. On the other hand it seems from literature that the influence of T/D on the flooding transition is considerable. 61
Symposium Series No. 89
EXPERIMENTAL TECHNIQUE The experiments have been performed in mixing tanks of standard geometry, using tank diameters of 0.44, 0.64 and 1.20 m filled to a denth H equal to the tank diameter T. In all cases the T/D rato for the 6-blade Rushton turbines was 2.5. The vessels were fitted with the usual four 0.1 T width baffles, fig. 3. The clearance between the stirrer Diane and the vessel bottom was in all cases equal to the stirrer diameter. All measurements were made in the air-water system, with air supplied from a ring sparger mounted below the stirrer. The transition between impeller loading and flooding can be detected in different ways. The most simple technique is visual observation of the bulk flow. However, this method is subjective and limited to transparent vessels. Mikulcova et al .[7] detected the presence of bubbles in the radial outflow with a conductivety probe. In this study the technique of Roustan [101 has been applied. This method is based on qualitative determination of the liquid radial outflow vector near the impeller by a micro propeller. This propeller produces a signal that is proportional to its rotational speed. The propeller was placed near the stirrer to produce an optimal signal. Fig. 4 shows an example of the measured signals. When there is no gas, Qg = 0, then the signal from the propeller increases linearly with the stirrer speed N. At a constant gas flow rate with an increasing stirrer speed the signal stays on a lower level as long as the impeller is flooded. As the impeller begins to pump radially, the propeller signal starts to increase rapidly. The stirrer speed and gas flow rate at which this transition occurs correspond unambiguously to the flooding transition. Experimentswith both increasing and decreasing stirrer speeds showed that hysteresis is negligible. This was also reported by Dickey [4] , though other authors, for example Roustan [ 10], do not agree. EXPERIMENTAL RESULTS- AND DISCUSSION Figure 5 shows the results of about seventy independent determinations of the transition for the three vessels. In this figure the gas flow rate and stirrer speed at flooding transition are expressed in terms of the gas flow number Fl and Froude number Fr, in accordance with equation 5. From this it was clear that the experimental results are in close agreement with the proposed theoretical relation. The proportionality constant has been found to be 1.2. So the relation describing the flooding transition becomes : Fl = 1.2 Fr
(6)
A s i m i l a r r e l a t i o n has been found by Zwietering [ 1 3 ] , Biesecker [ 2 ] and Mickulcovâ et a l . [ 7 ] . However t h e i r p r o p o r t i o n a l i t y constants are smaller than found i n t h i s study as shown i n f i g u r e 6. I t i s possible t h a t the difference i n the constant of p r o p o r t i o n a l i t y l i e s i n the f a c t that our experiments were a l l made using a r i n g sparger, while the three other authors employed pipe spargers.
From the results of Roustan [ 10] it is clear that the dimensions and location of the qas sparger have a significant influence on the flood ing t r a n s i t i o n . Whilst the measuring techniques used here and t h a t of Roustan were the same,the r e s u l t s d i f f e r completely from each other as shown in 62
Symposium Series No. 89
Figure 7. The only apparent reason for this is the fact that Roustan dis tributed the gas into his vessel through a perforated bottom. Figure 7 also compares the results of other authors with this study. The various correlations have been presented in terms of the stirrer speed and maximum gas flow rate for the 0.44 m vessel. The results of Nienowet al.[8 lare more or less separated from the other data. This is a result of his use of somewhat different definition for flooding.
Nienow's curve related flooding to the d i s t r i b u t i o n of gas throughout the mixing vessel as a whole, f i g . lc w h i l s t the lower curves due to Dickey [ 4 ] , Bruxelmane [ 3 ] , Judat [ 6 ] and ourselves r e s t r i c t consideration of the flooding phenomenon to the immediate v i c i n i t y of the impeller, f i g la and lb.
It is therefore concluded that the introduction of a precise definition for flooding such as that suggested here is meaningful. From figure 7 it is obvious that equation 6 predicts the largest gas flow rate before flooding occurs. Further study is necessary to determine whether the sparger geometry is indeed responsible for these deviations. CONCLUSIONS
A precise definition of flooding in a stirred gas liquid dispersion is indispensable for describing this phenomenon quantitatively. For the impeller flooding transition a linear relation between Fl and Fr could be derived by comparison of the radial liquid flow due to the pumoing action of the stirrer and the axial flow induced by a bubble column. Experiments have shown that this relation can be described as Fl = 1.2 Fr The values of the gas flow number at flooding transition from this study are higher than others reported in the literature. SYMBOLS USED
DP Fl Fr g H N T
QAX
Qg Qn
constant in equation 2 constant in equation 1 stirrer diameter ^ gas flow number (= Q/ND ) Froude number (= N^D/g) gravitational constant height of the bubble column stirrer speed vessel diameter Axial liquid flow Gas flow rate impeller pumping capacity
m / s 2) «·> m3/s) m3/s) m3 /s)
63
Symposium Series No. 89
LITERATURE CITED Bimbinet, J.J., M.S. Thesis, Purdue University, Lafayette, USA 1959. Biesecker, B.O., VDI-Forschungsheft 554, (1972). Bruxelmane, M.Z.A., Proc. Int. Symp. on Mixing, Mons, (1978), paper XC-1. Dickey, D.S., 72nd Annual Meeting Am. Inst. Chem. Engrs., San Francisco, (1979), paper 116 d. 5. Goossens, L.H.J., PhD-Thesis Delft Unviversity of Technology, (1979). 6. Judat, H., Fortschritte der Verfahrenstechnik, (1977), 141. 7. Mikulcovâ, E., Kudrna, V. and Vlcek, J., Scientific papers of the Inst. of Chem. Techn., Prague, Kl, (1967, 167. (in Czech). 8. Nienow, A.W., Wisdom, D.J. and Middleton, J.C., Proc. 2nd European Conf. on Mixing, Cambridge, (1977), paper Fl. 9. Pollard, J., Proc. Int. Symp. on Mixing, Mons, (1978), paper C-4. 10. Roustan, M. and Bruxelmane, M.Z.A., CHISA, Prague, (1981), paner B 3.3. 11. Smith, J.M. and Goossens, L.H.J. Proc. 4th Euron. Conf. on Mixing, Leeuwenhorst, The Netherlands, (1982), paper C2. 12. Westerterp, K.R. , van Dierendonck, L.L. and De Kraa, J.A., Chem. Eng. Sci., 18, (1963), 157. 13. ZwieterTng, Th.N., De Ingenieur, 7i5, (1963), Ch 60. (in Dutch). 1. 2. 3. 4.
64
Symposium Series No. 89
__ / /
1 1 1
1 1
\
\ 1—1
\
1 ι—ι
1
/ (a)
(b)
(c)
F i g . 1. Floodinn and loadinq regimes.
(a)
(b)
F i g . 2. Loadinn regimes f o r d i f f e r e n t T / D - r a t i o s .
motor data processing
ffi
torque meter
Γ
B-U-S
F i g . 3. Experimental set-un.
65
Symposium Series No. 89
06
" T -
.__ —»
> - "<=
/ / /
0
T :0 4 4 m
3 o Qg= O m / s
A
-
3
Δ Qg= 6 24 10" m /s
S- /
0.4
o
Uo
/
--1
K f
lΓ/
0.2 L
/
/
/
/
Δ
o
Δ/
Flooding transition
o /
/ Δ
\
/ /
/
_Δ
'
_L 1
■
F i g . 4. Determination of the flooding t r a n s i t i o n from the micro-proneller signal.
NO^'
»
5 · » o T : AAm Δ T s 6«m ♦ T=12 m
*Λ
♦
.
^
F " m a x « ' 2 F r m in
-<*?)
*
F i g . 5. Experimental r e s u l t s . 66
i
Symposium Series No. 89
riq.
6. Comparison of equation 6 with l i t e r a t u r e .
Q G (10- 3 m 3 /s)
0'
'
1
'
1
'
1
'
L
0 2 4 6 8 Fig. 7. Comparison of the results with other literature data. 67