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Noise analysis of transmitted light beams for determining bubble velocity and gas holdup profiles in a bubble column
Scievu-e. Vol. Chemical Engineering Printed in Great Britain.
NOISE
47.
ANALYSIS VELOCITY
No.
13/14.
pp.
3631-3638.
1992.
@
0009-2509/92 $5.00+0.00 1992 Pergamon Press Ltd
OF TRANSMITTED LIGHT BEAMS FOR DETERMINING BUBBLE AND GAS HOLDUP PROFILES IN A BUBBLE COLUMN R.F. Mudde, R.A.
Bakker, H.E.A.
van den Akker
Kramers Laboratorium voor Fysische Technologie Delft University of Technology Prins Bemhardlaan 6, 2628 BW Delft, The Netherlands
ABSTRACT Noise analysis techniques are used to construct bubble velocity and gas holdup profiles in an air/water bubble column. It is shown that the use of a laser renders reliable and consistent results. A comparison with local data obtained with a four-point glasfiber probe and the drift flux model of Bamea and Miirahi is made. The velocity profiles become steeper with increasing height in the column and with increasing gas flow rate. The holdup profiles are rather flat. The measurements are performed in a 50 mm inner-diameter tube and cover a holdup range from 2 % to 12 %.
KEYWORDS Bubble column; noise-analysis; cross-correlation; light-extinction; bubble velocity profile; holdup.
INTRODUCTION Bubble columns are widely used gas-liquid contactors. Among the advantages are the lack of mechanically moving parts, the low shear and the low operation costs. There are, however, important problems in engineering these reactors. An adequate description of the flow and holdup field in the column is still lacking. Hence, scale up rules are not very rigorous and there is still a need for experimental data. In this contribution we report on measurements of the local bubble velocity using correlation of two light beams. Furthermore, the extinction of one of the beams is used to obtain the local gas holdup. The measurements were done in a 50 nun inner-diameter air-water tube. The mean holdup ranged from 2 R to 12 96. Four different gas flows were investigated. All experiments reported here are confined to stagnant water.
BACKGROUND It is well known that in a bubble column the bubbles have a tendency to rise through the central part of the column. This does not only give rise to a holdup profile but at the same time generates a velocity profile. One reason is that due to the difference in mixture density between centre and periphery in the column a large circulation tends to set in (Rietema, 1982). Another reason is that in the wake of a bubble, a portion of water rises up to the surface and this flows back preferentially via the periphery.
3631
Bubble Velocity
D3
R. F. MUDDE et al.
3632
Profile
In order to measure the bubble velocity profile a cross-correlation technique is used. Two fluctuating signals are generated by passing two light beams through the column in a direction perpendicular to the flow direction. As long as the distance between the two beams is not too large the fluctuating signals are more or leas similar and only shifted in time. Via cross-correlation this time delay is obtained. In an extensive review Ltibhesmeyer (1984) has shown that in the case of bubbly flow, the velocity that can be constructed from the time delay and the known distance between the beams, is close to the bubble velocity. This finding is supported by experimental evidence, see e.g. Van der Hagen (1989) for an air/water loop, Miyzaki et al. (1973) for NJwater and Matsumoto et al. (1986) for solid particles suspensions. Furthermore, Ltibbesmeyer showed that there is a slight preference for the use of the peak in the cross-correlation function (CCF) rather than the slope of the cross power spectral density to determine the time delay. Hence, we use the CCF defined as
m CCF(r)
= lim T-0
f
/
s,(r)*S,(t-r)
dr
(1)
-m
with S,(t) and S,(t) the fluctuating signals (S, recorded upstream from SJ. Liibbesmeyer and Leoni (1983) report the influence of the so-called digitalisation parameter DP (= f.D/% with f,=signal sample frequency, D=distance between detectors, v,=velocity of the bubbles; this parameter should be chosen between 10 and 40, in our case DP-330-40). A radial velocity profile results in two or three side peaks in the CCF (Liibbesmeyer (1984)). Due to averaging of our CCFs we only found one peak in the CCFs which is assumed to represent the velocity averaged over the beam path. Ltibbesmeyer (1982) reports on numerical simulations of the velocity measurements using cross-correlation in the case a radial velocity profile is present, He concludes that cross-correlation of the signals does not lead to the area-averaged velocities. We also performed simulations using three bubbles trains with different velocities. We do arrive at a specific velocity which agrees reasonably with the arithmetic mean velocity we started from (see Fig.11 as long as the spread in velocities is not to high. The velocity profile itself can be constructed by dividing the cross-sectional area of the column in rings. The velocity in each ring i is Vi. A ring i is shone through over a length li and the holdup in the ring is ei. The number of bubble trains q in the segment li can now be estimated from the mean horizontal distance between the centres of two neighbouring bubbles ((rl6ei)l”dv for a locally homogeneous bubble swarm) and the length of the segment as
and according to the simulation we take for the measured velocity
v_
(3)
where the second equality holds when the bubble diameter and holdup only weakly depend on the radial position. This equation is used to obtain the velocity profile by scanning the column from wall to centre, Furthermore, we performed a numerical simulation in the case a velocity profile is present. The velocity profile is constructed according to the scheme given above. The result is shown in Fig.2. In this simulation the same behaviour is found as indicated in Fig.1: the larger the differences in the velocities of the bubble trains involved, the larger the deviation from the actual velocity value.
D3
Noise
analysis
of transmitted
3633
light beams
Furthermore, it was found from the simulations that (as expected) the steeper the profile, the larger the deviations. A similar simulation with the velocity ranging from Y = 30 cm/s at the centre to v = 20 cm/s at the wall showed a reduction of the deviation by a factor of two. 0.5
0.3
input prot?le simulation
\
“sim
-
-
-
(mis)
0;2
0
vmeun (mls)
1
r
2
(cm)
Fig. 1. Exact calculation of correlation using three simulated bubble trains: v_ is the arithmetic mean of the three velocities (one is fixed at 0.2 m/s), v,, is the result from the correlation. Fig.2. Reconstruction of a radial velocity profile:
-
original profile, - - - correlation result.
Holduu Profile From either of the fluctuating signals the bubble holdup can be derived. Calderbank presented a formula for measuring the holdup by means of a light scattering technique:
(1958) (4)
with E = the holdup, 1 = the optical path length and dvF= a Sauter diameter calculated from the volume equivalent diameter (d,,) and the diameter based on the area of projection of the bubbles perpendicular to the light beam. Equation (4) holds for 6el/d,< 25, Ohba and Itoh (1978a, 1978b) considered attenuation of a light beam and showed that for e up to 12 % eq.4 can be used. Although cq.4 is derived for a homogeneous situation it can also be used to obtain holdup profiles. By again dividing the cross-sectional area in rings (i) with for each ring a holdup c the intensity of the beam that enters ring i is reduced by a factor exp(-3eJ;/(2dw)). Hence if only segment 1 and 2 are shone through one obtains
where it is assumed that the Sauter diameter d, is constant over the cross-sectional area of the column (this assumption is backed up by experiments of Frijlink (1987)). Comparison with the calculated from (4) is the (line-) average of the Calderbank equation (4) shows that the holdup E, values in the rings:
T =A e_
= -
c4
(6)
Thus the same procedure as in the case of the velodity profile is used. The only unknown is now d, since only l i/d, can be calcuIated. This problem is overcome by matching the results on ei and y to the known gas flow
R. F. MUDDE er al.
3634
Q. = ~=iVZIr
D3 CI)
with Q, = volume flow of gas, &= area of ring i. Thus finally we obtain the velocity profile, the holdup profile and the mean ‘Sauter’ diameter_
EXPERIMENTAL
SET UP
column The experimental rig consists of a glass tube. The inner diameter of the tube is 49.7 mm. The height of the tube is 5.0 m. The water in the column is stagnant, i.e. there is no net water flow through the column. The air sparger is located 35 cm above the bottom of the column. The sparger is made of a porous plate (material: Flexolith-H, porosity 40 96, mean pore diameter 4Opm; 10 mm thick and 35 mm in diameter). Air is supplied to the column via a pressure vessel (volume 1.6.10* m’) in order to reduce the effect of unwanted oscillations in the gas flow. The gas flow is controlled by a needle valve located downstream of the pressure vessel; the flow itself is measured by means of a set of rotameters. The pressure in the pressure vessel is 1.8 bar. There are pressure tabs at three locations along the column: 89. 192 and 294 cm above the gas distibutor .
Lipht Beams A 5 mW He-Ne laser is used for the generation of the parallel light beams. The laser was placed vertically and the light beam struck a perspex plate (thickness 14.0 mm). The normal of this plate made an angle of 45” with the incoming beam. Part of the beam was reflected at the upper surface of the plate, part at the bottom of the plate. In this way two parallel horizontal beams with a vertical distance of 10.7 mm were obtained. After transmission through the column the beams were detected by two photo diodes. The diameter of the laser beams is 0.5 mm. The laser system can be rotated around a vertical axis so that the beams can scan the radial distribution in the tube. Reference measurements were conducted with a four-point glass fiber probe prijlink (1987), Bakker (1991)]. It consists of one central glass fiber glued in between three fibers which form an equilateral triangle. The central fiber is 1.2 mm longer than the other three. Furthermore, values for the velocity were obtained from video pictures.
RESULTS Velocity and holdup profiles are obtained for four different superficialgas velocities (0.52, 1.58, 2.09, 2.50 cm/s) and at four different heights above the gas distributor (h= 1.4, 2.4, 3.0, 3.5 m)_ The data on v_ and E, were first smoothed before vi and pi were calculated in order to reduce the effects of errors in the measured values near the wall. These errors would sum up in the calculations of the values for vi and ei located near the column centre. An example of the velocity profiles obtained at h= 1.4 m and h=3.0 m is shown in Fig.(3a) for v-=2.09 cm/s. In the plot also data from the glasfiber (h= 1.4, 3.0 m) and from the video pictures (h=3.0 m) are shown. The profiles for h= 1.4 m are mutually in excellent agreement. This also holds, to some extent, at h=3.0 m. A second example is shown inFig.(3b) for v- = 2.50 cm/s. A third one is given in Fig.(%) for vns,=0.52 cm/s. In this case the laser profile for h=3.0 m is unrealistically steep in view of the low holdup E- 2 R (the results at h =2.4 m and 3.5 m are much closer to the profile at h= 1.4 m). The velocity profiles for h=2.4 m and 3.5 m are not shown in the plots for the sake of clarity. The general trend of the velocity profiles is that the profiles become steeper with
R. F. MUDDE
3636
D3
et al.
Figure 4 shows a typical example (v_ =2.09 cm/s) of the obtained holdup profiles. Generally, the holdup profiles are overestimated. This is in accordance with the finding that the laser predicts too low velocity values close to the wall. The contribution to the total gas flow (see eq.7) of the latter region is tbe most important one in view of the large ring areas there. Hence, if the velocity close to the wall is too low, the calculated value for dW (obtained by matching 6 and vi to the total gasflow QJ is too large. Consequently, also ci is overestimated, since Ei/dvpis obtained from the attenuation measurements. As demonstrated in fig.4 it is thus of greatest importance to measure c and v as accurately as possible in the wall region. This also means that one has to measure as close to the wall as possible. In all holdup profiles little structure is found as function of the height. Furthermore, sometimes the profiles are convex, sometimes concave. The latter ones are presumably caused by an experimental error in the values obtained closest to the wall. Again this shows the need for accurate data close to the wall.
5-
h (ml 1.4 3.0
0
I 0
I
I 1
r
atten 0 fiber 0 pressure I
(cm)
I
l -
’
Fig.4. Typical example of holdup profiles at h= 1.4, 3.0 m for v-=2.09
cm/s.
Bubble Diameters As discussed above also the mean Sauter diameter dvp is obtained from the measurements. In the case of ellipsoidal bubbles this is equal to the (horizontal) long axis of the ellips. The glass fiber probe measures the (vertical ) short axis. For a single bubble the ratio Q of short to long axis is given by (Cl ift (1978)) E = (1 + 0.163 Eo~*‘~)-’
(8)
with Eo= E&v& number = g&d*/a, L\p= density difference of water and air, u= surface tension. In table 1 the mean values for the diameters as obtained by laser and glass fiber are presented together with the ratio E, from fiber and laser diameters and the prediction according to equation (8) when Eo is based on the laser diameter. The results of the ratio E shows that at increasing flow rates either bubbles in a swarm are deformed to more oblate ellipsis or that indeed the Sauter diameter (and thus the huldup) is overestimated in order to match eq.7.
D3
Noise
analysis
of transmitted
3637
light beams
Table 1. Bubble diameters
laser
fiber
0.52
3.14
2.79
0.89
0.85
1.58
4.65
3.07
0.66
0.78
2.09
4.84
3.25
0.67
0.77
(cm/s)
5.20 3.37 0.65 0.77 2.50 Our results are also compared with the drift flux model of Bamea and Mizrahi (1973). This model takes mutual hindrance of the bubbles into account (for constant drag coefficient): W %!=c x (9) v, ( l+fP 1 with v,= rise velocity of a single bubble in water. The mean bubble velocity in the swarm is Finally from pressure measurements the mean holdup is simply obtained as =v,/e. obtained and the mean bubble velocity can be calculated. All is summarized in table 2 (< y > = area averaged bubble velocity, < e > = area averaged holdup). The drift flux model of Bamea and Miirahi shows the same trends as our laser results. Table 2. Comparison of area averaged velocity and holdup laser (cVZs)
drift flux model
tv,>
pressure
(c&s)
(96)
(96)
(c&s)
W)
0.52
23.2
2.25
21
2.5
25
2.1
1.58
21.5
7.29
19
8.2
26
6.0
2.09
20.6
9.91
19
11.3
25
8.4
2.50
20.1
12.1
18
13.8
23
10.9
CONCLUSIONS Our noise-analysis techniques (based on laser beam transmission) is a sound non-intrusive method for measuring velocity and holdup profiles. Its accuracy is comparable to that of other techniques (video, probe). It is of greatest importance to know the values of velocity and holdup close to the wall as accurately as possible since both influence the profiles in several ways. The drift flux model of Bamea and Mizrahi follows our noise-analysis results.
NOMENCLATURE
Ai
CCF d d, dv dw
area of ring i (m”) cross-correlation function bubble diameter (m) diameter based on projection of bubble area frontal to light beam volume equivalent diameter ::; dv’/dp2 (m)
CES47:13/14-EE
(m) distance between the two beams ratio of long to short axis of bubble (-) Ei3tWs number sample frequency accelaration of gravity : height above the distributor 1,11,12 transmitted light intensity D E Eo f.
R. F.
3638
I,
1,
li
&is L t vb
vVi
incidentlight intensity path length of light beam number of bubble trains in ring i flow rate(m’s-‘) radial position in cohunn fluctuating signals time
bubble velocity D/r, velocity from correlation velocity of bubbles in ring i
MUVDE
VW (7;-
V,
r 0
cross-sectional area averaged
e* Ci
e@I
(m 5-l) (m s-l) (m cl)
superficialgas velocity (m 6’) rise velocity of a single bubble (m s’) density difference water-air (kg m-9 gas holdup, gas holdup in ring i (-) holdup from measurementsee eq.4 (-) surface tension (kg s-9 time delay (s)
4’ Cm)
D3
t-r al.
0
REFERENCES Bakker, A. (1992). Hydrodynamics of stirred gas-liquid dispersions, thesis, TU Delft, The Netherlands. Bamea, E. Miirahi, J. (1973). A generalizedapproachto the dynamics of particulatesystems. Part I. Chem. Enp J, 5,171-189. Calderbank,P.H. (1958): Physical rate processes in industrialfermentation.Part I. Trans. Instn, Chem. Enzrs 3&443-459. Clift, R. Grace:’ J.R. Weber, M.E. (1978). Bubbles. droDs and uarticleg, Academic press, London. Frijlink, J.J. (1987). Physical aspects of gassed suspension reactors. thesis TU Delft, The Netherlands. Hagen van der, T.H.J.J. (1989). Stabilitymonitoringof a natural-circulation-cooled boiling water reactor. thesis, TU Delft, The Netherlands. Lilbbesmeyer, D. (1982). Uber den einfluss eines radial-symmetrischenGeschwindigkeitsProfds auf die Geschwindigkeitsmessung mit rauschanalytischen Methoden. ReDOIt EIR-473. Ltlbbesmeyer,D. (1984). Experimentalreactornoise - a review on noise-analyticmeasurements of thermo-hydraulicparametersin operatingBWRs and their interpretation.Proz_ Nucl. Energy, 14, 41-93. Liibbesmeyer, D. Leoni, B. (1983). Fluid-velocity measurementsand flow-patternidentification by noise-analysisof light-beam signals. Int. J. Multiohase Flow, 9, 665679. Matsumoto, S. Harakawa, H. Susuki, M. Ohtani, S. (1986). Solid particle velocity in vertical gaseous suspensionflows. Jnt. J. MultinhaseFlow, u, 445458. Miyzaki, K. Isogai, K. Fuziine, Y. Suita, T. (1973). Measurementsof propagationvelocities of pressureand voidfractionsin nitrogen-waterflow. J. Nucl. Sci. Techn,, 1Q, 323. Ohba, K. Itoh, T. (1978a). Light attenuationtechniquefor voidfractionmeasurementin two-phase . bubbly flow-Part I Theory. Technol. ReDt. Osaka Umv, a, 487494. Ohba, K. Itoh, T. (1978b). Light attenuationtechniquefor’voidfiaction measurementin two-phase bubbly flow-Part II Experiment. Technol. Rem. Osaka Univ., 28, 495-506. Rietema, K. (1982). Science and Technology of dispersed two-phase systems-I and II. Chem, Enz. Sci., 37, 1125-1150.
NOISE
47.
ANALYSIS VELOCITY
No.
13/14.
pp.
3631-3638.
1992.
@
0009-2509/92 $5.00+0.00 1992 Pergamon Press Ltd
OF TRANSMITTED LIGHT BEAMS FOR DETERMINING BUBBLE AND GAS HOLDUP PROFILES IN A BUBBLE COLUMN R.F. Mudde, R.A.
Bakker, H.E.A.
van den Akker
Kramers Laboratorium voor Fysische Technologie Delft University of Technology Prins Bemhardlaan 6, 2628 BW Delft, The Netherlands
ABSTRACT Noise analysis techniques are used to construct bubble velocity and gas holdup profiles in an air/water bubble column. It is shown that the use of a laser renders reliable and consistent results. A comparison with local data obtained with a four-point glasfiber probe and the drift flux model of Bamea and Miirahi is made. The velocity profiles become steeper with increasing height in the column and with increasing gas flow rate. The holdup profiles are rather flat. The measurements are performed in a 50 mm inner-diameter tube and cover a holdup range from 2 % to 12 %.
KEYWORDS Bubble column; noise-analysis; cross-correlation; light-extinction; bubble velocity profile; holdup.
INTRODUCTION Bubble columns are widely used gas-liquid contactors. Among the advantages are the lack of mechanically moving parts, the low shear and the low operation costs. There are, however, important problems in engineering these reactors. An adequate description of the flow and holdup field in the column is still lacking. Hence, scale up rules are not very rigorous and there is still a need for experimental data. In this contribution we report on measurements of the local bubble velocity using correlation of two light beams. Furthermore, the extinction of one of the beams is used to obtain the local gas holdup. The measurements were done in a 50 nun inner-diameter air-water tube. The mean holdup ranged from 2 R to 12 96. Four different gas flows were investigated. All experiments reported here are confined to stagnant water.
BACKGROUND It is well known that in a bubble column the bubbles have a tendency to rise through the central part of the column. This does not only give rise to a holdup profile but at the same time generates a velocity profile. One reason is that due to the difference in mixture density between centre and periphery in the column a large circulation tends to set in (Rietema, 1982). Another reason is that in the wake of a bubble, a portion of water rises up to the surface and this flows back preferentially via the periphery.
3631
Bubble Velocity
D3
R. F. MUDDE et al.
3632
Profile
In order to measure the bubble velocity profile a cross-correlation technique is used. Two fluctuating signals are generated by passing two light beams through the column in a direction perpendicular to the flow direction. As long as the distance between the two beams is not too large the fluctuating signals are more or leas similar and only shifted in time. Via cross-correlation this time delay is obtained. In an extensive review Ltibhesmeyer (1984) has shown that in the case of bubbly flow, the velocity that can be constructed from the time delay and the known distance between the beams, is close to the bubble velocity. This finding is supported by experimental evidence, see e.g. Van der Hagen (1989) for an air/water loop, Miyzaki et al. (1973) for NJwater and Matsumoto et al. (1986) for solid particles suspensions. Furthermore, Ltibbesmeyer showed that there is a slight preference for the use of the peak in the cross-correlation function (CCF) rather than the slope of the cross power spectral density to determine the time delay. Hence, we use the CCF defined as
m CCF(r)
= lim T-0
f
/
s,(r)*S,(t-r)
dr
(1)
-m
with S,(t) and S,(t) the fluctuating signals (S, recorded upstream from SJ. Liibbesmeyer and Leoni (1983) report the influence of the so-called digitalisation parameter DP (= f.D/% with f,=signal sample frequency, D=distance between detectors, v,=velocity of the bubbles; this parameter should be chosen between 10 and 40, in our case DP-330-40). A radial velocity profile results in two or three side peaks in the CCF (Liibbesmeyer (1984)). Due to averaging of our CCFs we only found one peak in the CCFs which is assumed to represent the velocity averaged over the beam path. Ltibbesmeyer (1982) reports on numerical simulations of the velocity measurements using cross-correlation in the case a radial velocity profile is present, He concludes that cross-correlation of the signals does not lead to the area-averaged velocities. We also performed simulations using three bubbles trains with different velocities. We do arrive at a specific velocity which agrees reasonably with the arithmetic mean velocity we started from (see Fig.11 as long as the spread in velocities is not to high. The velocity profile itself can be constructed by dividing the cross-sectional area of the column in rings. The velocity in each ring i is Vi. A ring i is shone through over a length li and the holdup in the ring is ei. The number of bubble trains q in the segment li can now be estimated from the mean horizontal distance between the centres of two neighbouring bubbles ((rl6ei)l”dv for a locally homogeneous bubble swarm) and the length of the segment as
and according to the simulation we take for the measured velocity
v_
(3)
where the second equality holds when the bubble diameter and holdup only weakly depend on the radial position. This equation is used to obtain the velocity profile by scanning the column from wall to centre, Furthermore, we performed a numerical simulation in the case a velocity profile is present. The velocity profile is constructed according to the scheme given above. The result is shown in Fig.2. In this simulation the same behaviour is found as indicated in Fig.1: the larger the differences in the velocities of the bubble trains involved, the larger the deviation from the actual velocity value.
D3
Noise
analysis
of transmitted
3633
light beams
Furthermore, it was found from the simulations that (as expected) the steeper the profile, the larger the deviations. A similar simulation with the velocity ranging from Y = 30 cm/s at the centre to v = 20 cm/s at the wall showed a reduction of the deviation by a factor of two. 0.5
0.3
input prot?le simulation
\
“sim
-
-
-
(mis)
0;2
0
vmeun (mls)
1
r
2
(cm)
Fig. 1. Exact calculation of correlation using three simulated bubble trains: v_ is the arithmetic mean of the three velocities (one is fixed at 0.2 m/s), v,, is the result from the correlation. Fig.2. Reconstruction of a radial velocity profile:
-
original profile, - - - correlation result.
Holduu Profile From either of the fluctuating signals the bubble holdup can be derived. Calderbank presented a formula for measuring the holdup by means of a light scattering technique:
(1958) (4)
with E = the holdup, 1 = the optical path length and dvF= a Sauter diameter calculated from the volume equivalent diameter (d,,) and the diameter based on the area of projection of the bubbles perpendicular to the light beam. Equation (4) holds for 6el/d,< 25, Ohba and Itoh (1978a, 1978b) considered attenuation of a light beam and showed that for e up to 12 % eq.4 can be used. Although cq.4 is derived for a homogeneous situation it can also be used to obtain holdup profiles. By again dividing the cross-sectional area in rings (i) with for each ring a holdup c the intensity of the beam that enters ring i is reduced by a factor exp(-3eJ;/(2dw)). Hence if only segment 1 and 2 are shone through one obtains
where it is assumed that the Sauter diameter d, is constant over the cross-sectional area of the column (this assumption is backed up by experiments of Frijlink (1987)). Comparison with the calculated from (4) is the (line-) average of the Calderbank equation (4) shows that the holdup E, values in the rings:
T =A e_
= -
c4
(6)
Thus the same procedure as in the case of the velodity profile is used. The only unknown is now d, since only l i/d, can be calcuIated. This problem is overcome by matching the results on ei and y to the known gas flow
R. F. MUDDE er al.
3634
Q. = ~=iVZIr
D3 CI)
with Q, = volume flow of gas, &= area of ring i. Thus finally we obtain the velocity profile, the holdup profile and the mean ‘Sauter’ diameter_
EXPERIMENTAL
SET UP
column The experimental rig consists of a glass tube. The inner diameter of the tube is 49.7 mm. The height of the tube is 5.0 m. The water in the column is stagnant, i.e. there is no net water flow through the column. The air sparger is located 35 cm above the bottom of the column. The sparger is made of a porous plate (material: Flexolith-H, porosity 40 96, mean pore diameter 4Opm; 10 mm thick and 35 mm in diameter). Air is supplied to the column via a pressure vessel (volume 1.6.10* m’) in order to reduce the effect of unwanted oscillations in the gas flow. The gas flow is controlled by a needle valve located downstream of the pressure vessel; the flow itself is measured by means of a set of rotameters. The pressure in the pressure vessel is 1.8 bar. There are pressure tabs at three locations along the column: 89. 192 and 294 cm above the gas distibutor .
Lipht Beams A 5 mW He-Ne laser is used for the generation of the parallel light beams. The laser was placed vertically and the light beam struck a perspex plate (thickness 14.0 mm). The normal of this plate made an angle of 45” with the incoming beam. Part of the beam was reflected at the upper surface of the plate, part at the bottom of the plate. In this way two parallel horizontal beams with a vertical distance of 10.7 mm were obtained. After transmission through the column the beams were detected by two photo diodes. The diameter of the laser beams is 0.5 mm. The laser system can be rotated around a vertical axis so that the beams can scan the radial distribution in the tube. Reference measurements were conducted with a four-point glass fiber probe prijlink (1987), Bakker (1991)]. It consists of one central glass fiber glued in between three fibers which form an equilateral triangle. The central fiber is 1.2 mm longer than the other three. Furthermore, values for the velocity were obtained from video pictures.
RESULTS Velocity and holdup profiles are obtained for four different superficialgas velocities (0.52, 1.58, 2.09, 2.50 cm/s) and at four different heights above the gas distributor (h= 1.4, 2.4, 3.0, 3.5 m)_ The data on v_ and E, were first smoothed before vi and pi were calculated in order to reduce the effects of errors in the measured values near the wall. These errors would sum up in the calculations of the values for vi and ei located near the column centre. An example of the velocity profiles obtained at h= 1.4 m and h=3.0 m is shown in Fig.(3a) for v-=2.09 cm/s. In the plot also data from the glasfiber (h= 1.4, 3.0 m) and from the video pictures (h=3.0 m) are shown. The profiles for h= 1.4 m are mutually in excellent agreement. This also holds, to some extent, at h=3.0 m. A second example is shown inFig.(3b) for v- = 2.50 cm/s. A third one is given in Fig.(%) for vns,=0.52 cm/s. In this case the laser profile for h=3.0 m is unrealistically steep in view of the low holdup E- 2 R (the results at h =2.4 m and 3.5 m are much closer to the profile at h= 1.4 m). The velocity profiles for h=2.4 m and 3.5 m are not shown in the plots for the sake of clarity. The general trend of the velocity profiles is that the profiles become steeper with
R. F. MUDDE
3636
D3
et al.
Figure 4 shows a typical example (v_ =2.09 cm/s) of the obtained holdup profiles. Generally, the holdup profiles are overestimated. This is in accordance with the finding that the laser predicts too low velocity values close to the wall. The contribution to the total gas flow (see eq.7) of the latter region is tbe most important one in view of the large ring areas there. Hence, if the velocity close to the wall is too low, the calculated value for dW (obtained by matching 6 and vi to the total gasflow QJ is too large. Consequently, also ci is overestimated, since Ei/dvpis obtained from the attenuation measurements. As demonstrated in fig.4 it is thus of greatest importance to measure c and v as accurately as possible in the wall region. This also means that one has to measure as close to the wall as possible. In all holdup profiles little structure is found as function of the height. Furthermore, sometimes the profiles are convex, sometimes concave. The latter ones are presumably caused by an experimental error in the values obtained closest to the wall. Again this shows the need for accurate data close to the wall.
5-
h (ml 1.4 3.0
0
I 0
I
I 1
r
atten 0 fiber 0 pressure I
(cm)
I
l -
’
Fig.4. Typical example of holdup profiles at h= 1.4, 3.0 m for v-=2.09
cm/s.
Bubble Diameters As discussed above also the mean Sauter diameter dvp is obtained from the measurements. In the case of ellipsoidal bubbles this is equal to the (horizontal) long axis of the ellips. The glass fiber probe measures the (vertical ) short axis. For a single bubble the ratio Q of short to long axis is given by (Cl ift (1978)) E = (1 + 0.163 Eo~*‘~)-’
(8)
with Eo= E&v& number = g&d*/a, L\p= density difference of water and air, u= surface tension. In table 1 the mean values for the diameters as obtained by laser and glass fiber are presented together with the ratio E, from fiber and laser diameters and the prediction according to equation (8) when Eo is based on the laser diameter. The results of the ratio E shows that at increasing flow rates either bubbles in a swarm are deformed to more oblate ellipsis or that indeed the Sauter diameter (and thus the huldup) is overestimated in order to match eq.7.
D3
Noise
analysis
of transmitted
3637
light beams
Table 1. Bubble diameters
laser
fiber
0.52
3.14
2.79
0.89
0.85
1.58
4.65
3.07
0.66
0.78
2.09
4.84
3.25
0.67
0.77
(cm/s)
5.20 3.37 0.65 0.77 2.50 Our results are also compared with the drift flux model of Bamea and Mizrahi (1973). This model takes mutual hindrance of the bubbles into account (for constant drag coefficient): W %!=c x (9) v, ( l+fP 1 with v,= rise velocity of a single bubble in water. The mean bubble velocity in the swarm is Finally from pressure measurements the mean holdup is simply obtained as
drift flux model
tv,>
pressure
(c&s)
(96)
(c&s)
W)
0.52
23.2
2.25
21
2.5
25
2.1
1.58
21.5
7.29
19
8.2
26
6.0
2.09
20.6
9.91
19
11.3
25
8.4
2.50
20.1
12.1
18
13.8
23
10.9
CONCLUSIONS Our noise-analysis techniques (based on laser beam transmission) is a sound non-intrusive method for measuring velocity and holdup profiles. Its accuracy is comparable to that of other techniques (video, probe). It is of greatest importance to know the values of velocity and holdup close to the wall as accurately as possible since both influence the profiles in several ways. The drift flux model of Bamea and Mizrahi follows our noise-analysis results.
NOMENCLATURE
Ai
CCF d d, dv dw
area of ring i (m”) cross-correlation function bubble diameter (m) diameter based on projection of bubble area frontal to light beam volume equivalent diameter ::; dv’/dp2 (m)
CES47:13/14-EE
(m) distance between the two beams ratio of long to short axis of bubble (-) Ei3tWs number sample frequency accelaration of gravity : height above the distributor 1,11,12 transmitted light intensity D E Eo f.
R. F.
3638
I,
1,
li
&is L t vb
vVi
incidentlight intensity path length of light beam number of bubble trains in ring i flow rate(m’s-‘) radial position in cohunn fluctuating signals time
bubble velocity D/r, velocity from correlation velocity of bubbles in ring i
MUVDE
VW (7;-
V,
r 0
cross-sectional area averaged
e* Ci
e@I
(m 5-l) (m s-l) (m cl)
superficialgas velocity (m 6’) rise velocity of a single bubble (m s’) density difference water-air (kg m-9 gas holdup, gas holdup in ring i (-) holdup from measurementsee eq.4 (-) surface tension (kg s-9 time delay (s)
4’ Cm)
D3
t-r al.
0
REFERENCES Bakker, A. (1992). Hydrodynamics of stirred gas-liquid dispersions, thesis, TU Delft, The Netherlands. Bamea, E. Miirahi, J. (1973). A generalizedapproachto the dynamics of particulatesystems. Part I. Chem. Enp J, 5,171-189. Calderbank,P.H. (1958): Physical rate processes in industrialfermentation.Part I. Trans. Instn, Chem. Enzrs 3&443-459. Clift, R. Grace:’ J.R. Weber, M.E. (1978). Bubbles. droDs and uarticleg, Academic press, London. Frijlink, J.J. (1987). Physical aspects of gassed suspension reactors. thesis TU Delft, The Netherlands. Hagen van der, T.H.J.J. (1989). Stabilitymonitoringof a natural-circulation-cooled boiling water reactor. thesis, TU Delft, The Netherlands. Lilbbesmeyer, D. (1982). Uber den einfluss eines radial-symmetrischenGeschwindigkeitsProfds auf die Geschwindigkeitsmessung mit rauschanalytischen Methoden. ReDOIt EIR-473. Ltlbbesmeyer,D. (1984). Experimentalreactornoise - a review on noise-analyticmeasurements of thermo-hydraulicparametersin operatingBWRs and their interpretation.Proz_ Nucl. Energy, 14, 41-93. Liibbesmeyer, D. Leoni, B. (1983). Fluid-velocity measurementsand flow-patternidentification by noise-analysisof light-beam signals. Int. J. Multiohase Flow, 9, 665679. Matsumoto, S. Harakawa, H. Susuki, M. Ohtani, S. (1986). Solid particle velocity in vertical gaseous suspensionflows. Jnt. J. MultinhaseFlow, u, 445458. Miyzaki, K. Isogai, K. Fuziine, Y. Suita, T. (1973). Measurementsof propagationvelocities of pressureand voidfractionsin nitrogen-waterflow. J. Nucl. Sci. Techn,, 1Q, 323. Ohba, K. Itoh, T. (1978a). Light attenuationtechniquefor voidfractionmeasurementin two-phase . bubbly flow-Part I Theory. Technol. ReDt. Osaka Umv, a, 487494. Ohba, K. Itoh, T. (1978b). Light attenuationtechniquefor’voidfiaction measurementin two-phase bubbly flow-Part II Experiment. Technol. Rem. Osaka Univ., 28, 495-506. Rietema, K. (1982). Science and Technology of dispersed two-phase systems-I and II. Chem, Enz. Sci., 37, 1125-1150.