- Email: [email protected]
Hydrodynamics and local mass transfer characteristics of gas-liquid ejectors
The Chemical Engineering Jvurrud, 53 (1993) 67-73
67
Hydrodynamics and local mass transfer characteristics of gas-liquid ejectors P.H.M.R. Cramers Department of Chemical Engineering, University of Groningen, NL-9747 AG Groninga (Netherlands)
L. smit Department of Chemical Engineering, DSM Research, PO Box 18, NL-6160 MD Geleen (iVetherlan&]
G.M. Leuteritz Buss AG. Pmtteln 1, CH-4133 Base1 (Switzerland)
L.L. van Dierendonck and A.A.C.M. Beenackers Depart-
of Chemical En.&mring,
University of Gnmingen, NL9747 AG Gmnhgen (Netherlunds~
(Received December 24, 1992; in final form May 13, 1993)
The hydrodynamics and mass transfer characteristics of a straight tube ejector have been investigated. From the experiments it can be concluded that two different hydrodynamic zones exist in the ejector. In the first zone, the “mixing shock” region, extremely high kLa values are obtained. In the remaining part of the ejector volume a fine and homogeneous bubble flow appears in which the mass transfer rate is lower. These observations indicate that for a proper design of gas-liquid ejectors the ejector should be considered as a system of two units in series, requiring separate modelling. Further, it has been shown that the presence of a swirl device in the upstream section of the nozzle has a significant effect on the hydrodynamics and mass transfer performance of ejectors.
1. Introduction In many processes which require gas-liquid contactors, such as petroleum refining, hydrogenation, fermentation and waste water treatment, the overall production rate is frequently limited by gas-liquid interphase mass transfer. High shear rates induced by an appropriate absorber geometry, such as ejectors or other types of high intensity gas-liquid mixer [ 1, 2 1, can enhance mass transfer by generating very small gas bubbles. Recently, jet loop reactors have been recommended for processes where gas-liquid mass transfer is the rate-controlling step of the process. The mass transfer performance of jet loop reactors has been studied by Cramers et al. (31 and Dirix and Van de Wiele [ 41. They demonstrated that the mass transfer characteristics of the ejector and reaction vessel of jet loop reactors are completely different. This indicates that for a proper design and scale-up of these reactors the ejector and reaction vessel should be considered as two units in
0923-0467/93/$6.00
series, requiring separate modelling. Further, it was demonstrated that the benefits of the ejector are not restricted to a large rate of mass transfer in it but also to the generation of smaller bubbles. For non-coalescing media these small bubbles are injected into the reaction vessel and contribute to large specific contact areas in the vessel too. A systematic and detailed investigation of the mass transfer characteristics of ejectors has not been reported yet. Most investigations have been concerned with the gas suction rates [5, 6 1. Much less attention has been paid to their mass transfer performance. The interpretation of the maastransfer data of ejectors is usually based on the assumption that they behave as a single unit. To our knowledge there are only three papers concerned with the mass transfer characteristics of ejectors [3, 4, 71. The proposed correlations which describe the masstransfer characteristics of the ejectors used are summarized in Table 1. Table 1 shows that the volumetric mass transfer rate of all the ejectors used increases with the power 0 1993 - Elsevier Sequoia. All rights reserved
P.H.M.R.
68 TABLE 1. Mass (literature)
transfer
correlations
Crawwrs for
et al. / Hydrod~numics
ejector
systems
Correlation
Ejector
a = 19500(~r&“~4~G( 1 - co)‘.4
Downflow ejector (bubble flow)
k,a = 0.7206(~~)~~**(~~~~) 0492 a = 9 18(4°~74(~r,,)o~37’2 d, = 0.00652(~o)0~281(~D,8)- 0 372
Downflow
k,a = 0.0054(q,~)“‘6B(~G)(dN/dD)o~B6
Downflow ejector (bubble flow) Downtlow ejector (jet flow)
k,a=
0.00085(~DIS)o~66(dN/d~o~6s
free
system
ejector
jet
/ Q==
-
i
I
> :ePgtn
Fig. 1. Principle
of an ejector
and its pressure profile.
per unit mass supplied to the ejector (ais) and with the gas holdup (E&. Given the variety of ejector configurations and mixing-tube-to-nozzle diameter ratios (d,/d,) used, it is not surprising that the constants and exponents of the proposed correlations vary considerably, since the local hydrodynamics inside the ejector were not considered, i.e. it was assumed that the ejector can be modelled as a single unit. In reality an ejector consists of two different hydrodynamical zones with distinct properties, as shown schematically in Fig. 1. This figure shows the hydrodynamics and the change in pressure across the ejector. It is seen that a zone exists where the high velocity jet discharges into the mixing region, which is accompanied by a sudden pressure build-up (“mixing shock”). After this mixing zone both phases flow homogeneously through the remaining part of the ejector. It is expected that this difference in hydrodynamics of these two zones will cause different local mass transfer characteristics (such as k,u). However, to our knowledge there are no literature data which confirm the above statements. This contribution presents an experimental study
of gas-liquid
ejectors
on the local mass transfer characteristics of both zones in a straight tube ejector, with and without a swirl device in the upstream section of the nozzle. A theoretical model has been developed which in this paper will be discussed qualitatively only. Some predictions will be presented, but an extensive derivation will be published elsewhere [8].
2. Experimental
set-up and procedures
A scheme of the straight tube ejector used in the present investigation is shown in Fig. 2. The nozzle diameter used was 11.9 mm and the ejector length and diameter were 700 mm and 29 mm respectively. As a model system the desorption of oxygen from water was used. The liquid (tap water) was saturated with air in a large supply tank and than fed to the ejector. In order to desorb the oxygen from the liquid, nitrogen gas was introduced to the gas suction chamber of the ejector. After passing through the ejector, the tap water was drained. During the experiments the dissolved oxygen concentration was measured continuously at four different positions along the length of the ejector, as shown in Fig. 2. The effects of several parameters on the local mass transfer rates were investigated. The liquid supply ranged from 1.8 to 2.2 dm3 s-‘, while the gas-liquid flow ratio was varied between 0.3 and 1.6. Further, the influence of a swirl device on the volumetric mass transfer coefficient was investigated. Therefore all the experiments were performed with and without a swirl device in the upstream section of the nozzle.
_-__-P
2
:
T,
; C,,
Fig. 2. Schematic diagram of the straight tube ejector.
P.H.M.R. Cramers et aL / Hydrodynamics
of gas-liquid
ejectors
69
The measured decrease in the dissolved oxygen concentration in the liquid phase of the ejector can be described by a first-order differential equation and a mass balance, when the following assumptions are made: (i) the liquid and the gas phase move in concurrent plug flow through the ejector, (ii) the gas volumetric flow rate is considered to be constant, (iii) pure nitrogen is supplied and (iv) the gas-side mass transfer resistance is negligible. QLdCL= k&C,* - CL) dV
(I)
QdG, IN- CJ = QGC, = QGHeCz
(2)
The Henry coefficient for oxygen based on molar concentrations is approximately 27 at room temperature. Therefore it is justified to assume that QL/QcHe4 1 under all experimental conditions. The concentration of the oxygen in the liquid phase can then be represented by
CL -=C L,w
QL +
Q&e
exp( - kLcmd
where ~~=(v~/&J(l +QG/QLHe). With the aid of eqn. (3) it is possible to determine the local kLa values of the mixing and bubble flow zones, since the dissolved oxygen concentrations were measured along the length of the ejector.
3. Experimental
results
with
without
swrl
6.~~1
3. Effect of swirl device in the nozzle on the ejector hydrodynamics (maximum gas suction rates). Fig.
and discussion 0
3.1. Hydrodynamics in the ejector In the literature [5] it is mentioned that a swirl device results in an increase in the maximum rate of gas suction. From the present experiments it is concluded that the hydrodynamics in the ejector is also affected by the swirl. The effect of the swirl device on the hydrodynamicsis shown schematically in Fig. 3. This figure shows the difference between the liquid jet observed with and without the swirl device in the nozzle. In the absence of the swirl device a longer, slowly widening jet existed before the dispersion was created in the ejector. With the swirl device the liquid jet disintegrated quickly, either in the gas suction chamber or in the early part of the ejector. The early disintegration of the jet is thought to be due to the centrifugal force imposed on the liquid jet by the tangential velocity component created by the swirl device. Further, it was observed that without the swirl device the attachment position of the liquid jet on the mixing tube depends on the gas suction rate, whereas with the swirl device this effect is much less pronounced, as illustrated in Fig. 4.
Swirl Q(L)=2.2
0
C
-160
I/S
.
NO swtrl O(L)=2.2 l/S
A
SVWI Q(L)= 1.a
I/S
.
No swrl O(L)= 1.a
I/S
-200
0.6
0.4
0.6
1.2
1.6
2.0
Fig. 4. Effect of swirl device on the mixing zone location in the ejector.
This figure shows the mixing zone location in the straight tube ejector as a function of the gas-liquid flow ratio. From these observations it is concluded that by using a swirl device, more gas can be entrained (maximum entrainment rate), whereas the mixing zone position in the ejector becomes almost fixed at a constant location in the ejector. 3.2. Mass ‘transfer in the dgkrent sections of #e ejector The intluence of the gas-liquid flow ratio on the local volumetric mass transfer coefficients of both
P.H.M.R.
70
Cramers
et al. / Hydrodynamics
the mixing and bubble flow zones is shown in Figs. 5(a) and 5(b) for two different liquid flow rates. The data were obtained with a swirl device in the nozzle. Both figures show that the local k,a values of the mixing zone are higher than those of the bubble flow zone. Further, both the mixing and bubble flow zones seem to have a maximum in k,a at gas-liquid flow ratios of approximately 0.8 and 1.4 respectively. The curves shown are the values predicted by the theoretical model, as will be discussed qualitatively in the next section. From the experimental results it is seen that very high kLa values are created in both sections of the ejector. Since the major amount of energy is dissipated locally in the mixing zone section, it is obvious that the kLa values of the mixing zone initially are signifkantly higher than those of the bubble flow zone. In Fig. 6 the effective contribution of the mixing zone section, (VMz/Vm)(kLa)MZ, to the overall k,a value of the ejector, (kLu)EJ, is shown. 12 Q, 10
.
-
d,
=
1.8
=
15.6
I/S
of gas-liquid ejectors
8
J
0 0.0
0.5
1.5
2.0
2.5
3.0
QJQ, Fig. 6. Effective contribution of the mixing zone section to the overall kLa value of the straight tube ejector. This figure shows that the effective mixing zone contribution is approximately 40% or more. From these observations it is concluded that for a proper design and modelling of ejectors both the mixing zone and the two-phase flow zone should be modelled as two different units in series. The overall k,a value of the ejector is then given by
mm
&a a>m =
1
13
V MZ vM,
+
vB,
(haahz +
vM;;;B, &a ahmz (4)
ov 0.0
I 0.4
0.8
1.2
1.6
2.0
QJQ,
(4 12 [
I
indicating that the volume ratios of both zones significantly influence the overall characteristics of ejectors. In the sparse literature a variety of ejector geometries have been used, which means that the volume ratio of both zones may vary significantly. Since only the overall k,a values of the ejectors are reported, it is now not surprising that the constants of the proposed kLa correlations do not agree, since the mixing and two-phase flow zone volumetric mass transfer coefficients were lumped together.
4. Modelling
Q, d,
@I
= =
2.2 16.2
I/s mm
QJQ,
Fig. 5. Influence of gas-liquid flow ratio on the volumetric mass transfer coefficient in the mixing (0) and two-phase flow (0) zones: (a) Q,_= 1.8 1 s-‘; (b) C&,=2.2 1 s-’ (swirl device in the upstream section of the nozzle).
Until now, only the influence of the jet velocity and the volume ratios of the mixing and bubble flow zones has been considered. Another point of discussion is the local kLa value of the mixing zone and which parameters influence it. The local kLa value of the mixing zone is a function of (kL ~7,)~~=flocal
af(p,Y
energy dissipation rate) VMZ)
(5)
in which PJ and V,, are the jet power and mixing zone volume respectively.
P.H.M.R. Cramers et al. / Hydrodynamics
The local energy dissipation rate of the mixing zone region can be found by considering what happens to the entrained’ gas. Therefore a scheme of the mixing zone is given in Fig. 7. Where the high velocity jet discharges into the mixing zone, the resulting submerged jet will expand to occupy the entire cross-sectional area of the tube [9, lo]. In our opinion the effective volume of the mixing zone equals the conical volume of the submerged two-phase jet as shown in Fig. 7. Once the submerged jet occupies the entire cross-sectional area of the tube, the mixing zone is completed. Assuming that the energy is dissipated uniformly throughout the mixing zone (submerged jet region), the specific energy dissipation rate is given by EDIS=
-
flJ
(6)
PMvMZ
PJ= ; PL(v,)3(dJ>2
(7)
VM= ; (dd2L,
(8)
ejectors
cf gas-liquid
71
No theoretical model is available in the open literature that predicts the mixing zone length. Therefore a model has been developed in our laboratories. It predicts this length as a function of the operating and geometrical parameters of the ejector. In this paper we will show some predictions; an extensive derivation of the model will be published elsewhere [ 8 1. That our model predicts the experimental data very well is seen from Figs. 5(a) and 5(b). Further, it is concluded from our model that the ratio dJ/ dM,where dJis the actual jet diameter at the plunging point, has a significant effect on the mixing zone length (and hence on V& and consequently on cn,s (eqns. (6) and (8)). The influence of the d,/d, ratio on the mixing zone length (&Z>, the local energy dissipation rate (ED& and the mass transfer characteristics (kL and a) is shown in Figs. 8(a) and 8cb). These figures show that d,/d, has a signillcant effect on the local energy dissipation rate within the mixing zone and consequently on the local kL and a values within this zone. Further, it is seen 8
1.0
K is the fraction of the jet power (PJ) which is effectively dissipated for “mixing” of both phases in the mixing zone, pi is the two-phase mixture density @M = p~(1 - co)) and I;Mzis the mixing zone length.
0.6
0.0
0.2
0.4
0.6
0.6
1.0
d, 1%
04 20000
0.0°4
I
16000 A 7 <
LIZ
12000
3
$
8ooo
V two
ph+e
flow
zq3e 0.0
> pressure
f
> 4
Fig. 7. Schematic representation of the mixing zone: expansion of the submerged jet.
0)
0.2
0.4
“,
0.6
0.0
1 .o
/=L
Fig. 8. Influence of d,/d, at the point of impact on the local mixing zone characteristics (calculations: &/QL= m s-‘, dM= 29 mm).
1,
U, = 16.8
P.H.M.R.
72
Crammers et al. / Hpdrodpamics
that there exists an optimum value at a d.,/dM ratio of approximately 0.4. Prom these model calculations it can be concluded that the actual d,/d, ratio at the plunging point is of crucial importance for the local kL a values of the mixing zone and consequently for the overall mass transfer characteristics of ejectors. An interesting illustration of this effect is presented by some experiments with and without a swirl device in the upstream section of the nozzle. The effect of the swirl device on the local (k,a),, values is illustrated in Pig. 9. This figure shows that the ejector configuration without the swirl device in the nozzle creates k,a values which are approximately twice as high, although the dNdM ratio and initial jet power are constant. The physical explanation for the observed phenomenon is in fact very simple. F’igure 3 showed that the swirl device forces the jet to disintegrate much faster than in the absence of the swirl device. Thus with a swirl device in the nozzle the actual jet diameter at the point of impact is wider. The dN/dM ratio used in the experiments was 0.41. Thus, when a swirl device is used, the d,/d, ratio is larger than without a swirl device, resulting in a decrease in the local (kLa)MZ value (see Fig. 8(b)). The main conclusion that can be drawn from the theoretical and experimental observations is that the ratio of the actual jet and mixing tube diameters is of crucial importance for the local volumetric mass transfer coefficient of the mixing zone, since it determines the mixing zone length and hence its local volumetric mass transfer coefficient in this region. This indicates that the mass transfer performance of ejectors should not be related directly to ejector dimensions such as dN/dM as is done in all the existing literature.
24 I l
Swrl O(i)= 1.E l/S
of gas-liquid
ejectors
6. Conclusions The experiments have shown that it is essential to consider the mixing and bubble flow zones in ejectors as a system of two separate units in series, each requiring separate modelling. Further, the phenomena occurring in ejectors should be related to the actual jet diameter at the impact position (d,l d,) instead of the ejector configuration (dN/dM). Prom the experimental results it is concluded that the use of a swirl device has several advantageous results, i.e. stabilization of the mixing zone position and improvement in the maximum gas suction rates. However, it was also shown that for a given gas-liquid flow ratio the ejector with a swirl device in the upstream section of the nozzle creates lower k,a values in the mixing zone (approximately 50%), which is disadvantageous for creating maximal mass transfer. Acknowledgments The authors are gratefully indebted to DSM Research (Geleen, Netherlands) and Buss AG. (Pratteln, Switzerland) for their financial and technical support of this research programme. The experimental work of the present investigation was carried out using the facilities of the Process Engineering Division of the BHR Group Limited (Cranfield, UK). References 1 M.Z. Zhu, J. Harmon and A. Green, Chem. Eng. Sci., 47 (1992) 2847-2852. 2 C.L. Briens, L.X. Huynh, J.F. Farge, A. Catros, J.R. Berbard and M.A. Bergougnou, Chem. Eng. Sci., 47 (1992) 3549-3556. 3 P.H.M.R. Cramers, A.A.C.M. Beenackers and L.L. van Dierendonck, Chem. Eng. Sci., 47 (1992) 3557-2564. 4 C.A.M.C. Dirix and K. Van de Wiele, Chent. Eng. Sci., 45 (1990) 2333-2340. 5 H.J. Henzler, VT Verfahrenstechnik, 15 (1981) 738-749. 6 H. Jekat and T. Pilhofer, VT [email protected], II (1981) 572-577. 7 X. Changfeng, L. Remie and D. Game, Chem. React. Eng. Technol., 7 (1991) 143-149. 8 P.H.M.R. Cramers, Ph.D. Thesis, to be published. 9 G.M. Evans, Ph.D. Thesis, Department of Chemical Engineering, University of New Castle, NSW, 1990. 10 S. Ogawa, M. Kobayashi, S. Tone and T. Otake, J. C&m. Eng. Jpn., 15 (1982) 469-474.
01 0.0
0.4
0.8
1.2
1.6
2.0
Appendix
A: Nomenclature
Q&t
9. Influence of swirl device on the local k,a mixing zone.
Fig.
value in the
U
volumetric gas-liquid area (m’ mW3)
specific
interfacial
P.H.M.R.
CG CL
cm G 6 dPrl dN He
kL (kLa),m (kL a)m
Cramers
et al. / Hydrodynamics
oxygen concentration in gas phase (km01 mP3) oxygen concentration in liquid phase (km01 rnm3) oxygen concentration in liquid phase at inlet (km01 m-“) oxygen concentration in liquid at G-L interface (km01 rnd3) jet diameter at moment of impact (m) mixing tube diameter (m) nozzle diameter (m) Henry number, C,*/Co physical mass transfer coefficient (m s-‘) local volumetric mass transfer coefficient in BFZ (s-l) overall volumetric mass transfer coefficient of ejector (s-l)
(kLu)MZ
2 PJ
QG QL
UJ V VBE2 VE.l VMZ
of gas-liquid
ejectors
local volumetric mass transfer coefficient in MZ (s-l) mixing zone length (m) pressure differential (N rne2) jet power (W) volumetric gas flow rate (m3 s-l) volumetric liquid flow rate (m3 s- ‘) jet velocity (m s-r) volume (m”) two-phase flow volume (m’) ejector volume (m”) mixing zone volume (m3)
Greek letters energy dissipation rate (W kg- ‘) EDIS EC
PL
PM TEJ
73
gas
fraction,
QG/&G+ QJ
liquid density (kg m- 3, two-phase mixture density (kg rnm3) residence time (s)
67
Hydrodynamics and local mass transfer characteristics of gas-liquid ejectors P.H.M.R. Cramers Department of Chemical Engineering, University of Groningen, NL-9747 AG Groninga (Netherlands)
L. smit Department of Chemical Engineering, DSM Research, PO Box 18, NL-6160 MD Geleen (iVetherlan&]
G.M. Leuteritz Buss AG. Pmtteln 1, CH-4133 Base1 (Switzerland)
L.L. van Dierendonck and A.A.C.M. Beenackers Depart-
of Chemical En.&mring,
University of Gnmingen, NL9747 AG Gmnhgen (Netherlunds~
(Received December 24, 1992; in final form May 13, 1993)
The hydrodynamics and mass transfer characteristics of a straight tube ejector have been investigated. From the experiments it can be concluded that two different hydrodynamic zones exist in the ejector. In the first zone, the “mixing shock” region, extremely high kLa values are obtained. In the remaining part of the ejector volume a fine and homogeneous bubble flow appears in which the mass transfer rate is lower. These observations indicate that for a proper design of gas-liquid ejectors the ejector should be considered as a system of two units in series, requiring separate modelling. Further, it has been shown that the presence of a swirl device in the upstream section of the nozzle has a significant effect on the hydrodynamics and mass transfer performance of ejectors.
1. Introduction In many processes which require gas-liquid contactors, such as petroleum refining, hydrogenation, fermentation and waste water treatment, the overall production rate is frequently limited by gas-liquid interphase mass transfer. High shear rates induced by an appropriate absorber geometry, such as ejectors or other types of high intensity gas-liquid mixer [ 1, 2 1, can enhance mass transfer by generating very small gas bubbles. Recently, jet loop reactors have been recommended for processes where gas-liquid mass transfer is the rate-controlling step of the process. The mass transfer performance of jet loop reactors has been studied by Cramers et al. (31 and Dirix and Van de Wiele [ 41. They demonstrated that the mass transfer characteristics of the ejector and reaction vessel of jet loop reactors are completely different. This indicates that for a proper design and scale-up of these reactors the ejector and reaction vessel should be considered as two units in
0923-0467/93/$6.00
series, requiring separate modelling. Further, it was demonstrated that the benefits of the ejector are not restricted to a large rate of mass transfer in it but also to the generation of smaller bubbles. For non-coalescing media these small bubbles are injected into the reaction vessel and contribute to large specific contact areas in the vessel too. A systematic and detailed investigation of the mass transfer characteristics of ejectors has not been reported yet. Most investigations have been concerned with the gas suction rates [5, 6 1. Much less attention has been paid to their mass transfer performance. The interpretation of the maastransfer data of ejectors is usually based on the assumption that they behave as a single unit. To our knowledge there are only three papers concerned with the mass transfer characteristics of ejectors [3, 4, 71. The proposed correlations which describe the masstransfer characteristics of the ejectors used are summarized in Table 1. Table 1 shows that the volumetric mass transfer rate of all the ejectors used increases with the power 0 1993 - Elsevier Sequoia. All rights reserved
P.H.M.R.
68 TABLE 1. Mass (literature)
transfer
correlations
Crawwrs for
et al. / Hydrod~numics
ejector
systems
Correlation
Ejector
a = 19500(~r&“~4~G( 1 - co)‘.4
Downflow ejector (bubble flow)
k,a = 0.7206(~~)~~**(~~~~) 0492 a = 9 18(4°~74(~r,,)o~37’2 d, = 0.00652(~o)0~281(~D,8)- 0 372
Downflow
k,a = 0.0054(q,~)“‘6B(~G)(dN/dD)o~B6
Downflow ejector (bubble flow) Downtlow ejector (jet flow)
k,a=
0.00085(~DIS)o~66(dN/d~o~6s
free
system
ejector
jet
/ Q==
-
i
I
> :ePgtn
Fig. 1. Principle
of an ejector
and its pressure profile.
per unit mass supplied to the ejector (ais) and with the gas holdup (E&. Given the variety of ejector configurations and mixing-tube-to-nozzle diameter ratios (d,/d,) used, it is not surprising that the constants and exponents of the proposed correlations vary considerably, since the local hydrodynamics inside the ejector were not considered, i.e. it was assumed that the ejector can be modelled as a single unit. In reality an ejector consists of two different hydrodynamical zones with distinct properties, as shown schematically in Fig. 1. This figure shows the hydrodynamics and the change in pressure across the ejector. It is seen that a zone exists where the high velocity jet discharges into the mixing region, which is accompanied by a sudden pressure build-up (“mixing shock”). After this mixing zone both phases flow homogeneously through the remaining part of the ejector. It is expected that this difference in hydrodynamics of these two zones will cause different local mass transfer characteristics (such as k,u). However, to our knowledge there are no literature data which confirm the above statements. This contribution presents an experimental study
of gas-liquid
ejectors
on the local mass transfer characteristics of both zones in a straight tube ejector, with and without a swirl device in the upstream section of the nozzle. A theoretical model has been developed which in this paper will be discussed qualitatively only. Some predictions will be presented, but an extensive derivation will be published elsewhere [8].
2. Experimental
set-up and procedures
A scheme of the straight tube ejector used in the present investigation is shown in Fig. 2. The nozzle diameter used was 11.9 mm and the ejector length and diameter were 700 mm and 29 mm respectively. As a model system the desorption of oxygen from water was used. The liquid (tap water) was saturated with air in a large supply tank and than fed to the ejector. In order to desorb the oxygen from the liquid, nitrogen gas was introduced to the gas suction chamber of the ejector. After passing through the ejector, the tap water was drained. During the experiments the dissolved oxygen concentration was measured continuously at four different positions along the length of the ejector, as shown in Fig. 2. The effects of several parameters on the local mass transfer rates were investigated. The liquid supply ranged from 1.8 to 2.2 dm3 s-‘, while the gas-liquid flow ratio was varied between 0.3 and 1.6. Further, the influence of a swirl device on the volumetric mass transfer coefficient was investigated. Therefore all the experiments were performed with and without a swirl device in the upstream section of the nozzle.
_-__-P
2
:
T,
; C,,
Fig. 2. Schematic diagram of the straight tube ejector.
P.H.M.R. Cramers et aL / Hydrodynamics
of gas-liquid
ejectors
69
The measured decrease in the dissolved oxygen concentration in the liquid phase of the ejector can be described by a first-order differential equation and a mass balance, when the following assumptions are made: (i) the liquid and the gas phase move in concurrent plug flow through the ejector, (ii) the gas volumetric flow rate is considered to be constant, (iii) pure nitrogen is supplied and (iv) the gas-side mass transfer resistance is negligible. QLdCL= k&C,* - CL) dV
(I)
QdG, IN- CJ = QGC, = QGHeCz
(2)
The Henry coefficient for oxygen based on molar concentrations is approximately 27 at room temperature. Therefore it is justified to assume that QL/QcHe4 1 under all experimental conditions. The concentration of the oxygen in the liquid phase can then be represented by
CL -=C L,w
QL +
Q&e
exp( - kLcmd
where ~~=(v~/&J(l +QG/QLHe). With the aid of eqn. (3) it is possible to determine the local kLa values of the mixing and bubble flow zones, since the dissolved oxygen concentrations were measured along the length of the ejector.
3. Experimental
results
with
without
swrl
6.~~1
3. Effect of swirl device in the nozzle on the ejector hydrodynamics (maximum gas suction rates). Fig.
and discussion 0
3.1. Hydrodynamics in the ejector In the literature [5] it is mentioned that a swirl device results in an increase in the maximum rate of gas suction. From the present experiments it is concluded that the hydrodynamics in the ejector is also affected by the swirl. The effect of the swirl device on the hydrodynamicsis shown schematically in Fig. 3. This figure shows the difference between the liquid jet observed with and without the swirl device in the nozzle. In the absence of the swirl device a longer, slowly widening jet existed before the dispersion was created in the ejector. With the swirl device the liquid jet disintegrated quickly, either in the gas suction chamber or in the early part of the ejector. The early disintegration of the jet is thought to be due to the centrifugal force imposed on the liquid jet by the tangential velocity component created by the swirl device. Further, it was observed that without the swirl device the attachment position of the liquid jet on the mixing tube depends on the gas suction rate, whereas with the swirl device this effect is much less pronounced, as illustrated in Fig. 4.
Swirl Q(L)=2.2
0
C
-160
I/S
.
NO swtrl O(L)=2.2 l/S
A
SVWI Q(L)= 1.a
I/S
.
No swrl O(L)= 1.a
I/S
-200
0.6
0.4
0.6
1.2
1.6
2.0
Fig. 4. Effect of swirl device on the mixing zone location in the ejector.
This figure shows the mixing zone location in the straight tube ejector as a function of the gas-liquid flow ratio. From these observations it is concluded that by using a swirl device, more gas can be entrained (maximum entrainment rate), whereas the mixing zone position in the ejector becomes almost fixed at a constant location in the ejector. 3.2. Mass ‘transfer in the dgkrent sections of #e ejector The intluence of the gas-liquid flow ratio on the local volumetric mass transfer coefficients of both
P.H.M.R.
70
Cramers
et al. / Hydrodynamics
the mixing and bubble flow zones is shown in Figs. 5(a) and 5(b) for two different liquid flow rates. The data were obtained with a swirl device in the nozzle. Both figures show that the local k,a values of the mixing zone are higher than those of the bubble flow zone. Further, both the mixing and bubble flow zones seem to have a maximum in k,a at gas-liquid flow ratios of approximately 0.8 and 1.4 respectively. The curves shown are the values predicted by the theoretical model, as will be discussed qualitatively in the next section. From the experimental results it is seen that very high kLa values are created in both sections of the ejector. Since the major amount of energy is dissipated locally in the mixing zone section, it is obvious that the kLa values of the mixing zone initially are signifkantly higher than those of the bubble flow zone. In Fig. 6 the effective contribution of the mixing zone section, (VMz/Vm)(kLa)MZ, to the overall k,a value of the ejector, (kLu)EJ, is shown. 12 Q, 10
.
-
d,
=
1.8
=
15.6
I/S
of gas-liquid ejectors
8
J
0 0.0
0.5
1.5
2.0
2.5
3.0
QJQ, Fig. 6. Effective contribution of the mixing zone section to the overall kLa value of the straight tube ejector. This figure shows that the effective mixing zone contribution is approximately 40% or more. From these observations it is concluded that for a proper design and modelling of ejectors both the mixing zone and the two-phase flow zone should be modelled as two different units in series. The overall k,a value of the ejector is then given by
mm
&a a>m =
1
13
V MZ vM,
+
vB,
(haahz +
vM;;;B, &a ahmz (4)
ov 0.0
I 0.4
0.8
1.2
1.6
2.0
QJQ,
(4 12 [
I
indicating that the volume ratios of both zones significantly influence the overall characteristics of ejectors. In the sparse literature a variety of ejector geometries have been used, which means that the volume ratio of both zones may vary significantly. Since only the overall k,a values of the ejectors are reported, it is now not surprising that the constants of the proposed kLa correlations do not agree, since the mixing and two-phase flow zone volumetric mass transfer coefficients were lumped together.
4. Modelling
Q, d,
@I
= =
2.2 16.2
I/s mm
QJQ,
Fig. 5. Influence of gas-liquid flow ratio on the volumetric mass transfer coefficient in the mixing (0) and two-phase flow (0) zones: (a) Q,_= 1.8 1 s-‘; (b) C&,=2.2 1 s-’ (swirl device in the upstream section of the nozzle).
Until now, only the influence of the jet velocity and the volume ratios of the mixing and bubble flow zones has been considered. Another point of discussion is the local kLa value of the mixing zone and which parameters influence it. The local kLa value of the mixing zone is a function of (kL ~7,)~~=flocal
af(p,Y
energy dissipation rate) VMZ)
(5)
in which PJ and V,, are the jet power and mixing zone volume respectively.
P.H.M.R. Cramers et al. / Hydrodynamics
The local energy dissipation rate of the mixing zone region can be found by considering what happens to the entrained’ gas. Therefore a scheme of the mixing zone is given in Fig. 7. Where the high velocity jet discharges into the mixing zone, the resulting submerged jet will expand to occupy the entire cross-sectional area of the tube [9, lo]. In our opinion the effective volume of the mixing zone equals the conical volume of the submerged two-phase jet as shown in Fig. 7. Once the submerged jet occupies the entire cross-sectional area of the tube, the mixing zone is completed. Assuming that the energy is dissipated uniformly throughout the mixing zone (submerged jet region), the specific energy dissipation rate is given by EDIS=
-
flJ
(6)
PMvMZ
PJ= ; PL(v,)3(dJ>2
(7)
VM= ; (dd2L,
(8)
ejectors
cf gas-liquid
71
No theoretical model is available in the open literature that predicts the mixing zone length. Therefore a model has been developed in our laboratories. It predicts this length as a function of the operating and geometrical parameters of the ejector. In this paper we will show some predictions; an extensive derivation of the model will be published elsewhere [ 8 1. That our model predicts the experimental data very well is seen from Figs. 5(a) and 5(b). Further, it is concluded from our model that the ratio dJ/ dM,where dJis the actual jet diameter at the plunging point, has a significant effect on the mixing zone length (and hence on V& and consequently on cn,s (eqns. (6) and (8)). The influence of the d,/d, ratio on the mixing zone length (&Z>, the local energy dissipation rate (ED& and the mass transfer characteristics (kL and a) is shown in Figs. 8(a) and 8cb). These figures show that d,/d, has a signillcant effect on the local energy dissipation rate within the mixing zone and consequently on the local kL and a values within this zone. Further, it is seen 8
1.0
K is the fraction of the jet power (PJ) which is effectively dissipated for “mixing” of both phases in the mixing zone, pi is the two-phase mixture density @M = p~(1 - co)) and I;Mzis the mixing zone length.
0.6
0.0
0.2
0.4
0.6
0.6
1.0
d, 1%
04 20000
0.0°4
I
16000 A 7 <
LIZ
12000
3
$
8ooo
V two
ph+e
flow
zq3e 0.0
> pressure
f
> 4
Fig. 7. Schematic representation of the mixing zone: expansion of the submerged jet.
0)
0.2
0.4
“,
0.6
0.0
1 .o
/=L
Fig. 8. Influence of d,/d, at the point of impact on the local mixing zone characteristics (calculations: &/QL= m s-‘, dM= 29 mm).
1,
U, = 16.8
P.H.M.R.
72
Crammers et al. / Hpdrodpamics
that there exists an optimum value at a d.,/dM ratio of approximately 0.4. Prom these model calculations it can be concluded that the actual d,/d, ratio at the plunging point is of crucial importance for the local kL a values of the mixing zone and consequently for the overall mass transfer characteristics of ejectors. An interesting illustration of this effect is presented by some experiments with and without a swirl device in the upstream section of the nozzle. The effect of the swirl device on the local (k,a),, values is illustrated in Pig. 9. This figure shows that the ejector configuration without the swirl device in the nozzle creates k,a values which are approximately twice as high, although the dNdM ratio and initial jet power are constant. The physical explanation for the observed phenomenon is in fact very simple. F’igure 3 showed that the swirl device forces the jet to disintegrate much faster than in the absence of the swirl device. Thus with a swirl device in the nozzle the actual jet diameter at the point of impact is wider. The dN/dM ratio used in the experiments was 0.41. Thus, when a swirl device is used, the d,/d, ratio is larger than without a swirl device, resulting in a decrease in the local (kLa)MZ value (see Fig. 8(b)). The main conclusion that can be drawn from the theoretical and experimental observations is that the ratio of the actual jet and mixing tube diameters is of crucial importance for the local volumetric mass transfer coefficient of the mixing zone, since it determines the mixing zone length and hence its local volumetric mass transfer coefficient in this region. This indicates that the mass transfer performance of ejectors should not be related directly to ejector dimensions such as dN/dM as is done in all the existing literature.
24 I l
Swrl O(i)= 1.E l/S
of gas-liquid
ejectors
6. Conclusions The experiments have shown that it is essential to consider the mixing and bubble flow zones in ejectors as a system of two separate units in series, each requiring separate modelling. Further, the phenomena occurring in ejectors should be related to the actual jet diameter at the impact position (d,l d,) instead of the ejector configuration (dN/dM). Prom the experimental results it is concluded that the use of a swirl device has several advantageous results, i.e. stabilization of the mixing zone position and improvement in the maximum gas suction rates. However, it was also shown that for a given gas-liquid flow ratio the ejector with a swirl device in the upstream section of the nozzle creates lower k,a values in the mixing zone (approximately 50%), which is disadvantageous for creating maximal mass transfer. Acknowledgments The authors are gratefully indebted to DSM Research (Geleen, Netherlands) and Buss AG. (Pratteln, Switzerland) for their financial and technical support of this research programme. The experimental work of the present investigation was carried out using the facilities of the Process Engineering Division of the BHR Group Limited (Cranfield, UK). References 1 M.Z. Zhu, J. Harmon and A. Green, Chem. Eng. Sci., 47 (1992) 2847-2852. 2 C.L. Briens, L.X. Huynh, J.F. Farge, A. Catros, J.R. Berbard and M.A. Bergougnou, Chem. Eng. Sci., 47 (1992) 3549-3556. 3 P.H.M.R. Cramers, A.A.C.M. Beenackers and L.L. van Dierendonck, Chem. Eng. Sci., 47 (1992) 3557-2564. 4 C.A.M.C. Dirix and K. Van de Wiele, Chent. Eng. Sci., 45 (1990) 2333-2340. 5 H.J. Henzler, VT Verfahrenstechnik, 15 (1981) 738-749. 6 H. Jekat and T. Pilhofer, VT [email protected], II (1981) 572-577. 7 X. Changfeng, L. Remie and D. Game, Chem. React. Eng. Technol., 7 (1991) 143-149. 8 P.H.M.R. Cramers, Ph.D. Thesis, to be published. 9 G.M. Evans, Ph.D. Thesis, Department of Chemical Engineering, University of New Castle, NSW, 1990. 10 S. Ogawa, M. Kobayashi, S. Tone and T. Otake, J. C&m. Eng. Jpn., 15 (1982) 469-474.
01 0.0
0.4
0.8
1.2
1.6
2.0
Appendix
A: Nomenclature
Q&t
9. Influence of swirl device on the local k,a mixing zone.
Fig.
value in the
U
volumetric gas-liquid area (m’ mW3)
specific
interfacial
P.H.M.R.
CG CL
cm G 6 dPrl dN He
kL (kLa),m (kL a)m
Cramers
et al. / Hydrodynamics
oxygen concentration in gas phase (km01 mP3) oxygen concentration in liquid phase (km01 rnm3) oxygen concentration in liquid phase at inlet (km01 m-“) oxygen concentration in liquid at G-L interface (km01 rnd3) jet diameter at moment of impact (m) mixing tube diameter (m) nozzle diameter (m) Henry number, C,*/Co physical mass transfer coefficient (m s-‘) local volumetric mass transfer coefficient in BFZ (s-l) overall volumetric mass transfer coefficient of ejector (s-l)
(kLu)MZ
2 PJ
QG QL
UJ V VBE2 VE.l VMZ
of gas-liquid
ejectors
local volumetric mass transfer coefficient in MZ (s-l) mixing zone length (m) pressure differential (N rne2) jet power (W) volumetric gas flow rate (m3 s-l) volumetric liquid flow rate (m3 s- ‘) jet velocity (m s-r) volume (m”) two-phase flow volume (m’) ejector volume (m”) mixing zone volume (m3)
Greek letters energy dissipation rate (W kg- ‘) EDIS EC
PL
PM TEJ
73
gas
fraction,
QG/&G+ QJ
liquid density (kg m- 3, two-phase mixture density (kg rnm3) residence time (s)