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An Experimental Investigation of Adiabatic Two-Phase Flow in a Vertical Pipe at Different Temperatures
0263±8762/00/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 78, Part A, November 2000
AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW IN A VERTICAL PIPE AT DIFFERENT TEMPERATURES È LLER-STEINHAGEN (FELLOW) M. R. MALAYERI, J. M. SMITH (FELLOW) and H. MU Department of Chemical and Process Engineering, University of Surrey, Guildford, UK
T
his paper presents the experimental results on the effect of temperature on the void fraction and spatial evolution of the structure of air/water ¯ows. The experimental techniques are based on measuring void fraction using gamma ray attenuation together with video images taken from high speed video recordings. The independent variables are: liquid and gas ¯ow rates, temperature and axial position in the ¯ow direction. The results show the signi®cant effect of temperature on bubble size and shape as well as on void fraction. Bubble size and void fraction increase monotonically with temperature as a result of the partial saturation of air bubbles with water vapour. There are also changes in ¯ow regime and a reduction of bubble clustering at elevated temperatures. This phenomenon becomes more important as the system approaches its boiling point. Keywords: bubbly ¯ow; ¯ow regime; temperature; vertical; two-phase ¯ow.
INTRODUCTION Two-phase ¯ows play an important part in many industrial processes. In spite of the vast number of investigations to date, most two-phase parameters can only be predicted with poor accuracy1,2. This is ®rstly due to the deformable nature of the interfacial area, which prevents accurate estimation of transport phenomena between the phases. The second source of error is caused by ignoring the differences between gas/liquid and vapour/liquid systems or even the effect of temperature on gas/liquid ¯ows. A survey of the literature reveals that most investigations of gas/ liquid two-phase ¯ow simulation and regime recognition have not considered temperature effects, whereas commercial two-phase ¯ow systems often operate at elevated temperatures, particularly near to or at the liquid boiling point3. Relevant conditions arise in many tubular reactors in which exothermic reactions are carried out in a two-phase regime; perhaps thermal cracking provides the most spectacular example. A different application involving a similar physical situation is used in the heat exchangers in which fouling rates are reduced by increasing turbulence near the heat transfer surface by injecting inert gas into the hot liquid feed. Most investigations of inert gas injection have nevertheless been carried out at ambient temperature4. It has generally been believed that the effect of temperature could be ignored because of the much higher liquid ¯ow rates than those in bubble columns, together with the immiscibility of gas and liquid. Little or no fundamental work has been published in this respect. However, several investigators have looked at the effects of elevated temperature in bubble columns. There are large discrepancies between
the presented results. Grover et al.5 observed that with increasing temperature, the void fraction decreases substantially below about 508 C. Beyond this point, however, the effect of temperature is only marginal. Saxena et al.6 con®rmed the above results. In contrast, Renjun et al.7 showed that the effect of temperature on the void fraction can be divided into two stages. At ®rst, below about 758 C void fraction increases slowly with an increase of the temperature. Above that temperature void fraction increases considerably as the temperature rises. Much more experimental information is needed in order to characterize two-phase ¯ow structure at different temperatures. The present study aims to establish experimentally the effect of temperature on the void fraction at elevated temperature, particularly near to the boiling point. This is done with two-phase ¯ow at different axial positions along a vertical pipe. The experimental results at elevated temperature will help to see how the ¯ow structure changes as the air/ water system approaches a steam/water system. EXPERIMENTAL EQUIPMENT A closed ¯ow loop has been used to investigate the void fraction in air/water ¯ows through a cylindrical pipe at different temperatures. The experimental test rig is illustrated schematically in Figure 1. The loop has a 1.5 m vertical (V) measuring section of 24.2 mm inside diameter. The pipe is made from Pyrex glass, so that ¯ow visualization and high speed video photography are possible. The atmospheric pressure loop contains a circulating pump (P), a magnetic liquid ¯ow meter (E) and a supply tank (A) in which the bulk water temperature is regulated by an immersed electric heater and cooling coil. The test section has thermocouples (J type) to measure the input and output
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Figure 1. Schematic diagram of the experimental rig.
¯ow temperatures (J). Air enters the test section through a stainless steel tube and a cylindrical porous plug (S), which gives well-mixed gas distribution. Video images showed that, depending on the liquid ¯ow rate, the sparged air bubbles are in the 2 to 4 mm size range. The mixture of air and demineralized water (viscosity ml 0.001 Pa s; density rl 998 kgm 3 and surface tension j 0.072 N m 1 ), then passes through the test section where local void fraction can be measured. The air/water mixture is separated in the supply tank, with the water being recirculated. An Americium-214 gamma source densitometer (G) was employed for measuring the void fraction. The system has been designed to be sensitive to very small changes in the void fraction within a two-phase ¯ow, in the range from 0 to 2%. The slit collimator supplied with the system, provides a transverse beam 25 mm wide and 5 mm thick. The signals for measuring average void fraction are generated by a linear array of 100 detectors. The gamma densitometer can be traversed along the test section and this allows the void fraction to be measured along the test section at points separated by only 5 mm. This precise positioning allows the void fraction dynamics to be accurately assessed. The video images were recorded using a high speed video camera (Maximum frame rate 40500 frame/s). The full frame resolution is 256 ´ 256 pixels. Images were taken at two downstream length positions de®ned by the ratios, L/D 17 and 45, to observe the spatial evolution of ¯ow structure. The test section was surrounded by a rectangular polycarbonate block to reduce the effect of refraction on the recorded images. The video records were then analysed using the image analysis package (Optimas version 5.22) to determine area-based bubble size distribution and bubble size. Experimental Procedure and Error Analysis The measurements were carried out by varying liquid ¯ow rate, gas ¯ow rate, temperature and local downstream length ratio. The liquid ¯ow rate could be varied from 3 to 35 lit min ±1 (corresponding to 0.19±2.2 m s ±1) and the inlet gas ¯ow rate from 0 to 12 lit min ±1 (0±0.76 m s ±1). The temperature of the continuous phase was maintained at a speci®ed value by regulating the amount of heating load or cooling in the supply tank (A). An analogue to digital data conversion board with 8
channels is interfaced with an IBM-486 compatible digital computer for data collection. This data acquisition system is used to record the gamma ray attenuation, liquid and gas ¯ow rates and the temperatures at different positions of the gamma densitometer using a Thurning-LoÈffel code. With 95% con®dence the uncertainties are estimated to be less than 1% of full scale for the liquid ¯ow meter and 0.75%, for the gas ¯ow meter. In this study the most important variable is the void fraction, which was determined as follows: 100 detectors are available to measure the average void fraction at a given axial position. The results of these detectors are integrated to provide a value for the instantaneous mean void fraction over the cross section in question. To achieve reliable results, several matrices of data were collected to calculate the time averaged void fraction, at different time sequences. To check the accuracy of the void fraction measurements, and to provide an independent calibration, attenuation data were also collected for the empty and full pipe. The results showed that the mean average error was 1.3%. All data have been taken at least one minute after the sampling time bringing the average error to less than 1.5%. This sampling time is higher for highly unstable ¯ow regimes such as slug and churn ¯ows. RESULTS AND DISCUSSION The Effect of Temperature on the Void Fraction Key phenomena related to the variation of void fraction are bubble growth/coalescence or collapse as a result of change in ¯ow rates at room temperature. When two air bubbles coalesce, the resistance to drainage of the liquid ®lm between them must be overcome. The coalescence of a pair of bubbles occurs essentially in two stages: (i) the draining of the intervening ®lm of the continuous phase liquid to a critical thickness (ii) the rupture of the remaining ®lm. In the case of pure water, this resistance is caused by the intermolecular forces of water (hydrogen bonds) which keep water molecules bound together. Jamialahmadi and MuÈller-Steinhagen8 stated that if the intermolecular forces are relatively weak, then the chance of bubble coalescence should increase. It is shown that in the absence of vibration and agitation, temperature has a considerable effect on the rate of bubble coalescence. An increased temperature leads to a lowering of surface tension and viscosity together with a dramatic increase in vapour pressure. Any effect leading to increased drainage and evaporation of the liquid ®lm between the bubbles will lead to more rapid coalescence. The In¯uence of Gas and Liquid Flow Rates For the processing of the experimental results, it is conventional, and usually meaningful, to plot the data as a function of the inlet volumetric ¯ow ratio, which is de®ned as: Qg b 1 Qg Ql In this equation Qg and Ql are the inlet gas and liquid volume ¯ow rates, respectively. The effect of inlet volumetric ¯ow ratio on the void fraction at different temperatures is depicted in Figure 2 at a given liquid ¯ow rate. It is obvious that rising temperature causes void fraction to Trans IChemE, Vol 78, Part A, November 2000
AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW
Figure 2. Effect of temperature on the void fraction at low liquid ¯ow rate.
increase, especially between 898 C and 958 C, while in the range from 248 C to 608 C the variation of void fraction is marginal. Figure 3 illustrates the variation of void fraction as a function of temperature at approximately constant inlet volumetric ¯ow ratio for 6.65 lit min ±1 liquid ¯ow rate. At ®rst the void fraction increases slowly until a substantial rise at about 608 C. It can also be seen that the variation of void fraction is more pronounced near the boiling point. The signi®cant change in void fraction with temperature may result in a change in the ¯ow regime. A comparison of the variation of void fraction at temperatures 248 C and 958 C reveals that there is a difference between the dependence of void fraction on the inlet volumetric ¯ow ratio at ambient and elevated temperatures. Of the parameters, which may in¯uence this phenomenon, one of the most important is the liquid vapour pressure. Table 1 gives the physical properties of water and air at different temperatures, which shows the signi®cant variation of vapour pressure, especially near to the boiling point. The above results have been presented as a function of inlet b. Nevertheless, a modi®ed value of the volumetric ¯ow ratio should be used since the injected bubbles will increase in volume as they quickly saturate with water vapour at the operating temperature, (a 3 mm bubble reaches 95% saturation within about 1 second of exposure to hot water). Therefore, it is logical and convenient to de®ne a modi®ed volumetric ¯ow ratio as: Qg ´i b 2 Qg i QL in which: i
pa pa
rgh rgh pv
3
Equation (2) shows that the modi®ed volumetric ¯ow ratio changes in response to vapour pressure and local
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Figure 3. Variation of void fraction as a function of temperature at constant volumetric ¯ow ratio.
hydrostatic pressure. In this equation pa is atmospheric pressure, pv vapour pressure, g the gravitational acceleration, h the local submergence below the free surface of the measurement point and r the liquid density. Substitution of equation (3) into (2) yields: b
i 1 b
4 i
1
It is apparent that at ambient temperature (i < 1) the modi®ed volumetric ¯ow ratio (b ) reduces to the ordinary b. The in¯uence of temperature on the modi®ed inlet gas ¯ow rate required to achieve a given void fraction is shown in Figure 4. This ®gure highlights that the inlet gas ¯ow rate required to achieve a void fraction of 0.15, decreases from 1.52 lit min ±1 to 0.4 lit min ±1 for a temperature change from 208 C to 908 C, while the modi®ed gas ¯ow rate, including the effect of vapour pressure at the operating temperature is almost constant. This ®gure also indicates that at higher temperature, especially near the boiling point, the ordinary volumetric ¯ow ratio de®nition does not re¯ect the actual volume of the gas ¯ow rate at different temperatures. Equation (4) is also validated by comparing the data shown in Figures 2 and 4 with the drift ¯ux correlation 9. The results showed the mean average error of 6.8%, which veri®es the suitability of equation (4) at higher temperatures. Malayeri et al.10 studied the effect of liquid ¯ow rate on the void fraction and experimentally showed that in vertical ¯ow at ambient temperature with a constant inlet gas ¯ow rate the void fraction decreases as the liquid ¯ow rate goes up. Figure 5 illustrates the effect of temperature on the void fraction as a function of liquid ¯ow rate at constant inlet gas ¯ow rate. Void fraction varies remarkably at ambient temperature, while at 958 C variation of void
Table 1. Physical properties of air/water at different temperature. Temperature (8 C) 25 95
rg (kgm 3 )
102 mg (mPa s)
rl (kgm 3 )
ml (mPa s)
pv (105 Pa)
j (Nm 1 )
1.185 0.962
1.833 2.163
998.23 960.96
0.894 0.295
0.0313 0.8813
0.072 0.061
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Figure 6. Effect of temperature on the variability of the void fraction measurement.
Figure 4. Effect of temperature on the gas ¯ow rate needed to attain a speci®ed void fraction.
on the reproducibility of a void fraction even in a speci®ed ¯ow regime such as bubbly ¯ow. The details are also summarized in Table 2. It is apparent that there is a signi®cant in¯uence of temperature, which increases the void fraction from 0.04 to 0.18. Moreover there is a remarkable gap when the temperature is raised from 758 C to 908 C. The reproducibility of the measured void fraction also deteriorates as the temperature goes up. This variability is closely related to bubble growth/coalescence and the generation of bigger and unstable bubbles at higher temperature, giving rise to a change in ¯ow regime.
fraction with liquid ¯ow rate is small as the void fraction is about 0.92, (in the annular ¯ow regime). This can be related to the fact that the most important parameter at low temperatures is the liquid ¯ow rate. However, at high temperatures the contribution of water vapour is the main parameter which changes the initial gas ¯ow rate from 8 lit min ±1 (at 158 C) to 45 lit min ±1 (at 958 C). The bubble growth/coalescence occurring at higher operating temperatures can minimize the effect of liquid ¯ow rate and change the ¯ow regime. Variability of the Void Fraction Measurements The transition from a speci®ed ¯ow regime to another one can be identi®ed using gamma densitometer. In order to do this reproducibly, the measurements of the instantaneous void fraction taken at different times have to be reliable. In bubbly ¯ow, because of the approximate uniformity of bubble size, void fraction cannot be independently varied, but it changes substantially as the ¯ow pattern moves to slug or annular ¯ow when large bubbles develop across the pipe section. The results of a sequence of experiments at ®xed inlet air and water rates (b 0.067) and different temperature are shown in Figure 6. This ®gure is also intended to demonstrate the effect of growing bubble size
Void Fraction at Different Axial Position A set of experiments have been undertaken to investigate the importance of vapour pressure on the void fraction and also to discern how quickly air bubbles will be saturated with the hot water at different axial positions. Great care has been taken to generate bubbles with diameters as small as possible at very low void fraction (« 0.02) and at high liquid ¯ow rate to avoid the bubble coalescence which may occur at lower liquid and higher gas ¯ow rates. Accordingly, a single metal tube with 1.4 mm inside diameter replaced the former porous gas sparger. The generated bubbles were within the range of 2.0±3.0 mm. More experimental data were collected within a range of 908 C to 988 C, due to the importance of vapour pressure near to the boiling point. Figure 7 represents the variation of void fraction as a function of temperature at two different axial positions. It can be seen that void fraction changes slightly up to 608 C and increases monotonically thereafter. The results are consistent with those shown in Figure 3. Table 2. The statistical void fraction results for different temperatures. Symbol e
n s
Figure 5. Effect of liquid ¯ow rate on the void fraction at different temperature.
Temperature (8 C)
Number of data
a (average)
6 a
18 45 60 75 90
14 12 9 11 20
0.040 0.057 0.078 0.104 0.180
0.006 0.005 0.020 0.014 0.060
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Figure 7. Comparison of the void fraction at different axial position with respect to temperature.
When the comparison of the void fraction is made at different axial position, there is a slightly lower void fraction at the point L/D 45 at lower temperature. Contrariwise, there is a higher void fraction at the point L/D 45 at higher temperatures, particularly above 908 C. These results imply that i) as expected, bubbles contain more vapour at higher temperatures and ii) the signi®cant change of void fraction at L/D 45 compared to the L/D 17, is because of a further increase in bubble size as a result of approaching saturation as well as a lower pressure level at L/D 45. This ®gure also shows that the volume fraction of the gas phase in the test section can be changed 7 times. Effect of Temperature on the Development of Flow Structure Although the primary intention of this work is to consider the characteristics of void fraction, consideration of the spatial evolution of the ¯ow structure at different temperature is also of interest. Grover et al.5 reported that in bubble columns, increasing temperature leads to a decrease in the gas velocity at which the ¯ow regime changes from bubbly to slug ¯ow. This can only be a result of bubble growth and/or coalescence. Saxena et al.6 observed that as the temperature goes up, the bubble size increases. This effect is attributed to the in¯uence of vapour pressure near the boiling point. On the contrary, Renjun et al.7 found that bubble size is smaller at the elevated temperatures. It can be concluded that with ®xed ¯ow conditions, the effect of temperature is the key parameter describing bubble size and shape and consequently the spatial evolution of the ¯ow structure. The results which were recorded using a high speed video camera are presented in this section. Figure 8 shows the recorded images of ¯ow structure at two different positions with respect to the variation of gas ¯ow rate. It is obvious from this ®gure that i) not only bubble size, but the tendency of the bubbles to cluster increases as the gas ¯ow rate rises, ii) the change of bubble shape from spherical to ellipsoidal shape and subsequently distorted shape, which is one of the most important parameters in the process of bubble coalescence, becomes more and more distinct as either gas ¯ow rate increases or liquid ¯ow rate decreases, and iii) smaller bubbles as well as bubbles which Trans IChemE, Vol 78, Part A, November 2000
Figure 8. Spatial evolution of the ¯ow structure at different gas ¯ow rate and room temperature.
are ¯owing down through a liquid ®lm around the large bubbles enter into the wake of large bubbles as a result of predominant updraft force. Tomiyama et al.11 and Zun et al.12 showed that the presence of shear-induced turbulence near the wake of large bubbles is the main cause of the clustering of the smaller bubbles. It should also be noted that the cluster of bubbles at L/D 17 is likely to develop into a Taylor bubble at L/D 45, as a result of the coalescence of many of the bubbles in the cluster. The coalescence of bubbles and formation of a larger cluster or a Taylor bubble are generally seen at different gas ¯ow rates, but typically take place at lower L/D as the gas ¯ow rate rises. Figure 8 also implies that in spite of almost constant void fraction at low temperature (Figure 7) the structure of the ¯ow is entirely different at the different axial positions. Figure 9 shows the effect of temperature on the void fraction at a given liquid ¯ow rate and different axial positions. The highest possible liquid ¯ow rate has been taken to minimize the effect of initial bubble coalescence at the entrance. From 178 C to 608 C the variation of bubble size is small, but it becomes more and more distinct between 908 C and 958 C. A comparison of bubble shape at different positions also shows that bubbles have been continuously saturated at higher position along the ¯ow direction as the bubbles become bigger in the upstream of the ¯ow direction. This distinctive behaviour is more dominant at 958 C. On the contrary, the variation of bubble size is much smaller at lower temperature, due to the limited effect of vapour pressure. The interesting result is that the bubble clustering as seen in Figure 8 was not observed at higher temperatures. This can be related to the partial saturation of air bubbles with water vapour. Since the air bubbles have been saturated at higher temperature, the resistance of the interface between the phases becomes weaker while this resistance is stronger due to existence of pure air bubbles at lower temperatures.
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Figure 11. Effect of temperature on the spatial ¯ow structure at constant void fraction.
Figure 9. Spatial evolution of the ¯ow structure at different temperature.
Figure 10 shows the quantitative variation of mean bubble diameter with temperature at different axial positions corresponding to the experimental runs which were shown in Figure 9. This ®gure also contains the minimum and maximum range of bubble size as well as the schematic bubble shape at a speci®ed temperature. The biggest bubbles are signi®cantly larger in the range from 908 C to 958 C than at lower temperatures. The size range is also wider and so depends on the operating temperature. The signi®cance of the saturation process becomes more evident when different axial positions are compared. Two factors in¯uence the growth of air bubbles in an upward ¯ow of hot water: the fast but not instantaneous saturation of the gas phase with water vapour and the probability of coalescence within clusters of small bubbles. Observation suggests that bubble clusters are more stable at lower temperatures, so that larger bubbles occur naturally in hotter conditions. In considering the data of Figure 7, at 958 C the void fraction increases from 13% to 16% in moving from L/D 17 to 45. This 30% increase in volume
may well re¯ect the ®nal stages of saturation of relatively large bubbles. However, the photographs of Figure 9 suggest that the individual bubble volumes may have increased as much as fourfold over this same distance. It seems very likely that saturation has had less in¯uence on the size of these large bubbles than enhanced coalescence at high temperature. Certainly the changes at lower temperature, also shown in Figure 9, are not as spectacular. In addition to the above observations in which the liquid and inlet gas ¯ow rates were kept constant, a set of experiments has also been undertaken, to establish the variability of bubble size at constant void fraction. Void fraction was maintained at a speci®ed value by adjusting the ¯ow rate of inlet gas at the appropriate temperature. Figure 11 shows pictures of bubbles at the operating temperature and a given void fraction. It is evident that the bubble shape and size are remarkably different at various temperatures. At low temperatures the bubbles tend to move as a cluster and are signi®cantly larger, while this is less so at elevated temperatures. The same results were also obtained as the experiment was repeated with different liquid and gas ¯ow rates. These observations are potentially important for the processes in stirred vessels where parameters such as relative power demand (RPD) is dependent on the shape and size of bubbles at elevated temperatures. CONCLUSIONS The results presented in this paper highlight some important features of the effect of temperature on void fraction and evolution of the ¯ow structure and provide useful information, which are summarized as follows:
Figure 10. Mean, minimum and maximum bubble size as a function of temperature.
· The effect of temperature on the void fraction of increasing vapour pressure at elevated temperatures cannot be ignored even at high liquid ¯ow rates. The experimental data show an excessive in¯uence of temperature, especially above 608 C. This effect becomes dominant near the boiling point. The modi®ed volumetric ¯ow ratio (equation (4)) adequately includes the effect of vapour pressure on the void fraction at higher ¯ow rates. The results also re¯ect a change in ¯ow regime as temperature rises due to a sharp increase of bubble size with temperature. Trans IChemE, Vol 78, Part A, November 2000
AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW
· The recorded images show that the chance of bubble clustering becomes unlikely at higher temperature. This is probably due to a weak boundary layer of the partially saturated air bubbles leading to rapid bubble coalescence (Figures 8 and 9). It is also shown experimentally that the change in ¯ow regime is caused by bubble coalescence at a lower temperature, however, it would be affected by growth and subsequent coalescence, as the air bubbles saturate at elevated temperatures. This phenomenon is more signi®cant at greater downstream distances. NOMENCLATURE D g h L Q Pa Pv T
pipe diameter, m gravitational acceleration, m s ±2 local submergence below the free surface, m distance from gas sparger, m volumetric ¯ow rate, m3 s 1 atmospheric pressure, N m ±2 vapour pressure, N m ±2 temperature, 8 C
Greek b b m r j
letters volumetric ¯ow ratio, Qg / Qg Qf modi®ed volumetric ¯ow ratio (equation (4)) viscosity, kg m ±1 s ±1 density, kg m ±3 surface tension, N m ±1
Subscripts gas g liquid l
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2. Whalley, P. B., 1987, Boiling, Condensation, and Gas-Liquid Flow (Clarendon Press, Oxford, UK). 3. Tribbe, C., 1998, Gas/liquid ¯ow in cylindrical and corrugated channels, PhD Thesis (University of Surrey, Guildford, UK). 4. Kuru, W. C. and Panchal, C. B., 1997, Application of single-phase fouling data to two-phase ¯ows, Convective Flow and Pool Boiling Conf (Kloster Irsee, Germany). 5. Grover, G. S., Rode, C. V. and Chaudhari, R. V., 1986, Effect of temperature on ¯ow regimes and gas hold-up in a bubble column, Can J Chem Eng, 64: 501±504. 6. Saxena, S. C., Rao, N. S. and Thimmapuram, P. R., 1992, Gas holdup in slurry bubble columns for two and three phase systems, Chem Eng J, 49: 151±159. 7. Renjun, Z., Xinzhen, J., Baozhang, L., Yong, Z. and Laiqi, Z., 1988, Studies on gas holdup in a bubble column operated at elevated temperature, Ind Eng Chem, 27: 1901±1916. 8. Jamialahmadi, M. and MuÈller-Steinhagen, H., 1993, Effect of energy input on bubble coalescence, Technical report (University of Auckland, New Zealand). 9. Wallis, G. B., 1969, One Dimensional Two-Phase Flow (McGraw-Hill, New York). 10. Malayeri, M. R., Smith, J. M. and MuÈller-Steinhagen, H., 1998, Effect of bubble size on two-phase ¯ow behaviour in vertical up-ward ¯ow, The 3rd Iranian Congress of Chem Eng, Ahwaz, Iran, 258±261. 11. Tomiyama, A., Tamai, H., Makino, Y. and Miyoshi, K., 1998, Modelling and Real-Time Simulation of a Developing Bubble Flow in a Vertical Pipe, Japan-UK mini workshop. 12. Zun, I., Kljenak, I. and Moze, S., 1993, Space-time evolution of the non-homogeneousbubble distribution in upward ¯ow, Int J Multiphase Flow, 19(1): 151±172.
ADDRESS
REFERENCES 1. Hewitt, G. F., 1996, In search of two-phase ¯ow, J Heat Transfer, 118: 518±527.
Trans IChemE, Vol 78, Part A, November 2000
Correspondence concerning this paper should be addressed to Professor H. MuÈller-Steinhagen, Institut fuÈr Technische Thermodynamik, German Aerospace Center, Pfaffenwaldring 38-40, D-70569 Stuttgart, Germany. E-mail: [email protected] The manuscript was received 13 September 1999 and accepted for publication after revision 17 August 2000.
AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW IN A VERTICAL PIPE AT DIFFERENT TEMPERATURES È LLER-STEINHAGEN (FELLOW) M. R. MALAYERI, J. M. SMITH (FELLOW) and H. MU Department of Chemical and Process Engineering, University of Surrey, Guildford, UK
T
his paper presents the experimental results on the effect of temperature on the void fraction and spatial evolution of the structure of air/water ¯ows. The experimental techniques are based on measuring void fraction using gamma ray attenuation together with video images taken from high speed video recordings. The independent variables are: liquid and gas ¯ow rates, temperature and axial position in the ¯ow direction. The results show the signi®cant effect of temperature on bubble size and shape as well as on void fraction. Bubble size and void fraction increase monotonically with temperature as a result of the partial saturation of air bubbles with water vapour. There are also changes in ¯ow regime and a reduction of bubble clustering at elevated temperatures. This phenomenon becomes more important as the system approaches its boiling point. Keywords: bubbly ¯ow; ¯ow regime; temperature; vertical; two-phase ¯ow.
INTRODUCTION Two-phase ¯ows play an important part in many industrial processes. In spite of the vast number of investigations to date, most two-phase parameters can only be predicted with poor accuracy1,2. This is ®rstly due to the deformable nature of the interfacial area, which prevents accurate estimation of transport phenomena between the phases. The second source of error is caused by ignoring the differences between gas/liquid and vapour/liquid systems or even the effect of temperature on gas/liquid ¯ows. A survey of the literature reveals that most investigations of gas/ liquid two-phase ¯ow simulation and regime recognition have not considered temperature effects, whereas commercial two-phase ¯ow systems often operate at elevated temperatures, particularly near to or at the liquid boiling point3. Relevant conditions arise in many tubular reactors in which exothermic reactions are carried out in a two-phase regime; perhaps thermal cracking provides the most spectacular example. A different application involving a similar physical situation is used in the heat exchangers in which fouling rates are reduced by increasing turbulence near the heat transfer surface by injecting inert gas into the hot liquid feed. Most investigations of inert gas injection have nevertheless been carried out at ambient temperature4. It has generally been believed that the effect of temperature could be ignored because of the much higher liquid ¯ow rates than those in bubble columns, together with the immiscibility of gas and liquid. Little or no fundamental work has been published in this respect. However, several investigators have looked at the effects of elevated temperature in bubble columns. There are large discrepancies between
the presented results. Grover et al.5 observed that with increasing temperature, the void fraction decreases substantially below about 508 C. Beyond this point, however, the effect of temperature is only marginal. Saxena et al.6 con®rmed the above results. In contrast, Renjun et al.7 showed that the effect of temperature on the void fraction can be divided into two stages. At ®rst, below about 758 C void fraction increases slowly with an increase of the temperature. Above that temperature void fraction increases considerably as the temperature rises. Much more experimental information is needed in order to characterize two-phase ¯ow structure at different temperatures. The present study aims to establish experimentally the effect of temperature on the void fraction at elevated temperature, particularly near to the boiling point. This is done with two-phase ¯ow at different axial positions along a vertical pipe. The experimental results at elevated temperature will help to see how the ¯ow structure changes as the air/ water system approaches a steam/water system. EXPERIMENTAL EQUIPMENT A closed ¯ow loop has been used to investigate the void fraction in air/water ¯ows through a cylindrical pipe at different temperatures. The experimental test rig is illustrated schematically in Figure 1. The loop has a 1.5 m vertical (V) measuring section of 24.2 mm inside diameter. The pipe is made from Pyrex glass, so that ¯ow visualization and high speed video photography are possible. The atmospheric pressure loop contains a circulating pump (P), a magnetic liquid ¯ow meter (E) and a supply tank (A) in which the bulk water temperature is regulated by an immersed electric heater and cooling coil. The test section has thermocouples (J type) to measure the input and output
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Figure 1. Schematic diagram of the experimental rig.
¯ow temperatures (J). Air enters the test section through a stainless steel tube and a cylindrical porous plug (S), which gives well-mixed gas distribution. Video images showed that, depending on the liquid ¯ow rate, the sparged air bubbles are in the 2 to 4 mm size range. The mixture of air and demineralized water (viscosity ml 0.001 Pa s; density rl 998 kgm 3 and surface tension j 0.072 N m 1 ), then passes through the test section where local void fraction can be measured. The air/water mixture is separated in the supply tank, with the water being recirculated. An Americium-214 gamma source densitometer (G) was employed for measuring the void fraction. The system has been designed to be sensitive to very small changes in the void fraction within a two-phase ¯ow, in the range from 0 to 2%. The slit collimator supplied with the system, provides a transverse beam 25 mm wide and 5 mm thick. The signals for measuring average void fraction are generated by a linear array of 100 detectors. The gamma densitometer can be traversed along the test section and this allows the void fraction to be measured along the test section at points separated by only 5 mm. This precise positioning allows the void fraction dynamics to be accurately assessed. The video images were recorded using a high speed video camera (Maximum frame rate 40500 frame/s). The full frame resolution is 256 ´ 256 pixels. Images were taken at two downstream length positions de®ned by the ratios, L/D 17 and 45, to observe the spatial evolution of ¯ow structure. The test section was surrounded by a rectangular polycarbonate block to reduce the effect of refraction on the recorded images. The video records were then analysed using the image analysis package (Optimas version 5.22) to determine area-based bubble size distribution and bubble size. Experimental Procedure and Error Analysis The measurements were carried out by varying liquid ¯ow rate, gas ¯ow rate, temperature and local downstream length ratio. The liquid ¯ow rate could be varied from 3 to 35 lit min ±1 (corresponding to 0.19±2.2 m s ±1) and the inlet gas ¯ow rate from 0 to 12 lit min ±1 (0±0.76 m s ±1). The temperature of the continuous phase was maintained at a speci®ed value by regulating the amount of heating load or cooling in the supply tank (A). An analogue to digital data conversion board with 8
channels is interfaced with an IBM-486 compatible digital computer for data collection. This data acquisition system is used to record the gamma ray attenuation, liquid and gas ¯ow rates and the temperatures at different positions of the gamma densitometer using a Thurning-LoÈffel code. With 95% con®dence the uncertainties are estimated to be less than 1% of full scale for the liquid ¯ow meter and 0.75%, for the gas ¯ow meter. In this study the most important variable is the void fraction, which was determined as follows: 100 detectors are available to measure the average void fraction at a given axial position. The results of these detectors are integrated to provide a value for the instantaneous mean void fraction over the cross section in question. To achieve reliable results, several matrices of data were collected to calculate the time averaged void fraction, at different time sequences. To check the accuracy of the void fraction measurements, and to provide an independent calibration, attenuation data were also collected for the empty and full pipe. The results showed that the mean average error was 1.3%. All data have been taken at least one minute after the sampling time bringing the average error to less than 1.5%. This sampling time is higher for highly unstable ¯ow regimes such as slug and churn ¯ows. RESULTS AND DISCUSSION The Effect of Temperature on the Void Fraction Key phenomena related to the variation of void fraction are bubble growth/coalescence or collapse as a result of change in ¯ow rates at room temperature. When two air bubbles coalesce, the resistance to drainage of the liquid ®lm between them must be overcome. The coalescence of a pair of bubbles occurs essentially in two stages: (i) the draining of the intervening ®lm of the continuous phase liquid to a critical thickness (ii) the rupture of the remaining ®lm. In the case of pure water, this resistance is caused by the intermolecular forces of water (hydrogen bonds) which keep water molecules bound together. Jamialahmadi and MuÈller-Steinhagen8 stated that if the intermolecular forces are relatively weak, then the chance of bubble coalescence should increase. It is shown that in the absence of vibration and agitation, temperature has a considerable effect on the rate of bubble coalescence. An increased temperature leads to a lowering of surface tension and viscosity together with a dramatic increase in vapour pressure. Any effect leading to increased drainage and evaporation of the liquid ®lm between the bubbles will lead to more rapid coalescence. The In¯uence of Gas and Liquid Flow Rates For the processing of the experimental results, it is conventional, and usually meaningful, to plot the data as a function of the inlet volumetric ¯ow ratio, which is de®ned as: Qg b 1 Qg Ql In this equation Qg and Ql are the inlet gas and liquid volume ¯ow rates, respectively. The effect of inlet volumetric ¯ow ratio on the void fraction at different temperatures is depicted in Figure 2 at a given liquid ¯ow rate. It is obvious that rising temperature causes void fraction to Trans IChemE, Vol 78, Part A, November 2000
AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW
Figure 2. Effect of temperature on the void fraction at low liquid ¯ow rate.
increase, especially between 898 C and 958 C, while in the range from 248 C to 608 C the variation of void fraction is marginal. Figure 3 illustrates the variation of void fraction as a function of temperature at approximately constant inlet volumetric ¯ow ratio for 6.65 lit min ±1 liquid ¯ow rate. At ®rst the void fraction increases slowly until a substantial rise at about 608 C. It can also be seen that the variation of void fraction is more pronounced near the boiling point. The signi®cant change in void fraction with temperature may result in a change in the ¯ow regime. A comparison of the variation of void fraction at temperatures 248 C and 958 C reveals that there is a difference between the dependence of void fraction on the inlet volumetric ¯ow ratio at ambient and elevated temperatures. Of the parameters, which may in¯uence this phenomenon, one of the most important is the liquid vapour pressure. Table 1 gives the physical properties of water and air at different temperatures, which shows the signi®cant variation of vapour pressure, especially near to the boiling point. The above results have been presented as a function of inlet b. Nevertheless, a modi®ed value of the volumetric ¯ow ratio should be used since the injected bubbles will increase in volume as they quickly saturate with water vapour at the operating temperature, (a 3 mm bubble reaches 95% saturation within about 1 second of exposure to hot water). Therefore, it is logical and convenient to de®ne a modi®ed volumetric ¯ow ratio as: Qg ´i b 2 Qg i QL in which: i
pa pa
rgh rgh pv
3
Equation (2) shows that the modi®ed volumetric ¯ow ratio changes in response to vapour pressure and local
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Figure 3. Variation of void fraction as a function of temperature at constant volumetric ¯ow ratio.
hydrostatic pressure. In this equation pa is atmospheric pressure, pv vapour pressure, g the gravitational acceleration, h the local submergence below the free surface of the measurement point and r the liquid density. Substitution of equation (3) into (2) yields: b
i 1 b
4 i
1
It is apparent that at ambient temperature (i < 1) the modi®ed volumetric ¯ow ratio (b ) reduces to the ordinary b. The in¯uence of temperature on the modi®ed inlet gas ¯ow rate required to achieve a given void fraction is shown in Figure 4. This ®gure highlights that the inlet gas ¯ow rate required to achieve a void fraction of 0.15, decreases from 1.52 lit min ±1 to 0.4 lit min ±1 for a temperature change from 208 C to 908 C, while the modi®ed gas ¯ow rate, including the effect of vapour pressure at the operating temperature is almost constant. This ®gure also indicates that at higher temperature, especially near the boiling point, the ordinary volumetric ¯ow ratio de®nition does not re¯ect the actual volume of the gas ¯ow rate at different temperatures. Equation (4) is also validated by comparing the data shown in Figures 2 and 4 with the drift ¯ux correlation 9. The results showed the mean average error of 6.8%, which veri®es the suitability of equation (4) at higher temperatures. Malayeri et al.10 studied the effect of liquid ¯ow rate on the void fraction and experimentally showed that in vertical ¯ow at ambient temperature with a constant inlet gas ¯ow rate the void fraction decreases as the liquid ¯ow rate goes up. Figure 5 illustrates the effect of temperature on the void fraction as a function of liquid ¯ow rate at constant inlet gas ¯ow rate. Void fraction varies remarkably at ambient temperature, while at 958 C variation of void
Table 1. Physical properties of air/water at different temperature. Temperature (8 C) 25 95
rg (kgm 3 )
102 mg (mPa s)
rl (kgm 3 )
ml (mPa s)
pv (105 Pa)
j (Nm 1 )
1.185 0.962
1.833 2.163
998.23 960.96
0.894 0.295
0.0313 0.8813
0.072 0.061
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Figure 6. Effect of temperature on the variability of the void fraction measurement.
Figure 4. Effect of temperature on the gas ¯ow rate needed to attain a speci®ed void fraction.
on the reproducibility of a void fraction even in a speci®ed ¯ow regime such as bubbly ¯ow. The details are also summarized in Table 2. It is apparent that there is a signi®cant in¯uence of temperature, which increases the void fraction from 0.04 to 0.18. Moreover there is a remarkable gap when the temperature is raised from 758 C to 908 C. The reproducibility of the measured void fraction also deteriorates as the temperature goes up. This variability is closely related to bubble growth/coalescence and the generation of bigger and unstable bubbles at higher temperature, giving rise to a change in ¯ow regime.
fraction with liquid ¯ow rate is small as the void fraction is about 0.92, (in the annular ¯ow regime). This can be related to the fact that the most important parameter at low temperatures is the liquid ¯ow rate. However, at high temperatures the contribution of water vapour is the main parameter which changes the initial gas ¯ow rate from 8 lit min ±1 (at 158 C) to 45 lit min ±1 (at 958 C). The bubble growth/coalescence occurring at higher operating temperatures can minimize the effect of liquid ¯ow rate and change the ¯ow regime. Variability of the Void Fraction Measurements The transition from a speci®ed ¯ow regime to another one can be identi®ed using gamma densitometer. In order to do this reproducibly, the measurements of the instantaneous void fraction taken at different times have to be reliable. In bubbly ¯ow, because of the approximate uniformity of bubble size, void fraction cannot be independently varied, but it changes substantially as the ¯ow pattern moves to slug or annular ¯ow when large bubbles develop across the pipe section. The results of a sequence of experiments at ®xed inlet air and water rates (b 0.067) and different temperature are shown in Figure 6. This ®gure is also intended to demonstrate the effect of growing bubble size
Void Fraction at Different Axial Position A set of experiments have been undertaken to investigate the importance of vapour pressure on the void fraction and also to discern how quickly air bubbles will be saturated with the hot water at different axial positions. Great care has been taken to generate bubbles with diameters as small as possible at very low void fraction (« 0.02) and at high liquid ¯ow rate to avoid the bubble coalescence which may occur at lower liquid and higher gas ¯ow rates. Accordingly, a single metal tube with 1.4 mm inside diameter replaced the former porous gas sparger. The generated bubbles were within the range of 2.0±3.0 mm. More experimental data were collected within a range of 908 C to 988 C, due to the importance of vapour pressure near to the boiling point. Figure 7 represents the variation of void fraction as a function of temperature at two different axial positions. It can be seen that void fraction changes slightly up to 608 C and increases monotonically thereafter. The results are consistent with those shown in Figure 3. Table 2. The statistical void fraction results for different temperatures. Symbol e
n s
Figure 5. Effect of liquid ¯ow rate on the void fraction at different temperature.
Temperature (8 C)
Number of data
a (average)
6 a
18 45 60 75 90
14 12 9 11 20
0.040 0.057 0.078 0.104 0.180
0.006 0.005 0.020 0.014 0.060
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AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW
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Figure 7. Comparison of the void fraction at different axial position with respect to temperature.
When the comparison of the void fraction is made at different axial position, there is a slightly lower void fraction at the point L/D 45 at lower temperature. Contrariwise, there is a higher void fraction at the point L/D 45 at higher temperatures, particularly above 908 C. These results imply that i) as expected, bubbles contain more vapour at higher temperatures and ii) the signi®cant change of void fraction at L/D 45 compared to the L/D 17, is because of a further increase in bubble size as a result of approaching saturation as well as a lower pressure level at L/D 45. This ®gure also shows that the volume fraction of the gas phase in the test section can be changed 7 times. Effect of Temperature on the Development of Flow Structure Although the primary intention of this work is to consider the characteristics of void fraction, consideration of the spatial evolution of the ¯ow structure at different temperature is also of interest. Grover et al.5 reported that in bubble columns, increasing temperature leads to a decrease in the gas velocity at which the ¯ow regime changes from bubbly to slug ¯ow. This can only be a result of bubble growth and/or coalescence. Saxena et al.6 observed that as the temperature goes up, the bubble size increases. This effect is attributed to the in¯uence of vapour pressure near the boiling point. On the contrary, Renjun et al.7 found that bubble size is smaller at the elevated temperatures. It can be concluded that with ®xed ¯ow conditions, the effect of temperature is the key parameter describing bubble size and shape and consequently the spatial evolution of the ¯ow structure. The results which were recorded using a high speed video camera are presented in this section. Figure 8 shows the recorded images of ¯ow structure at two different positions with respect to the variation of gas ¯ow rate. It is obvious from this ®gure that i) not only bubble size, but the tendency of the bubbles to cluster increases as the gas ¯ow rate rises, ii) the change of bubble shape from spherical to ellipsoidal shape and subsequently distorted shape, which is one of the most important parameters in the process of bubble coalescence, becomes more and more distinct as either gas ¯ow rate increases or liquid ¯ow rate decreases, and iii) smaller bubbles as well as bubbles which Trans IChemE, Vol 78, Part A, November 2000
Figure 8. Spatial evolution of the ¯ow structure at different gas ¯ow rate and room temperature.
are ¯owing down through a liquid ®lm around the large bubbles enter into the wake of large bubbles as a result of predominant updraft force. Tomiyama et al.11 and Zun et al.12 showed that the presence of shear-induced turbulence near the wake of large bubbles is the main cause of the clustering of the smaller bubbles. It should also be noted that the cluster of bubbles at L/D 17 is likely to develop into a Taylor bubble at L/D 45, as a result of the coalescence of many of the bubbles in the cluster. The coalescence of bubbles and formation of a larger cluster or a Taylor bubble are generally seen at different gas ¯ow rates, but typically take place at lower L/D as the gas ¯ow rate rises. Figure 8 also implies that in spite of almost constant void fraction at low temperature (Figure 7) the structure of the ¯ow is entirely different at the different axial positions. Figure 9 shows the effect of temperature on the void fraction at a given liquid ¯ow rate and different axial positions. The highest possible liquid ¯ow rate has been taken to minimize the effect of initial bubble coalescence at the entrance. From 178 C to 608 C the variation of bubble size is small, but it becomes more and more distinct between 908 C and 958 C. A comparison of bubble shape at different positions also shows that bubbles have been continuously saturated at higher position along the ¯ow direction as the bubbles become bigger in the upstream of the ¯ow direction. This distinctive behaviour is more dominant at 958 C. On the contrary, the variation of bubble size is much smaller at lower temperature, due to the limited effect of vapour pressure. The interesting result is that the bubble clustering as seen in Figure 8 was not observed at higher temperatures. This can be related to the partial saturation of air bubbles with water vapour. Since the air bubbles have been saturated at higher temperature, the resistance of the interface between the phases becomes weaker while this resistance is stronger due to existence of pure air bubbles at lower temperatures.
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Figure 11. Effect of temperature on the spatial ¯ow structure at constant void fraction.
Figure 9. Spatial evolution of the ¯ow structure at different temperature.
Figure 10 shows the quantitative variation of mean bubble diameter with temperature at different axial positions corresponding to the experimental runs which were shown in Figure 9. This ®gure also contains the minimum and maximum range of bubble size as well as the schematic bubble shape at a speci®ed temperature. The biggest bubbles are signi®cantly larger in the range from 908 C to 958 C than at lower temperatures. The size range is also wider and so depends on the operating temperature. The signi®cance of the saturation process becomes more evident when different axial positions are compared. Two factors in¯uence the growth of air bubbles in an upward ¯ow of hot water: the fast but not instantaneous saturation of the gas phase with water vapour and the probability of coalescence within clusters of small bubbles. Observation suggests that bubble clusters are more stable at lower temperatures, so that larger bubbles occur naturally in hotter conditions. In considering the data of Figure 7, at 958 C the void fraction increases from 13% to 16% in moving from L/D 17 to 45. This 30% increase in volume
may well re¯ect the ®nal stages of saturation of relatively large bubbles. However, the photographs of Figure 9 suggest that the individual bubble volumes may have increased as much as fourfold over this same distance. It seems very likely that saturation has had less in¯uence on the size of these large bubbles than enhanced coalescence at high temperature. Certainly the changes at lower temperature, also shown in Figure 9, are not as spectacular. In addition to the above observations in which the liquid and inlet gas ¯ow rates were kept constant, a set of experiments has also been undertaken, to establish the variability of bubble size at constant void fraction. Void fraction was maintained at a speci®ed value by adjusting the ¯ow rate of inlet gas at the appropriate temperature. Figure 11 shows pictures of bubbles at the operating temperature and a given void fraction. It is evident that the bubble shape and size are remarkably different at various temperatures. At low temperatures the bubbles tend to move as a cluster and are signi®cantly larger, while this is less so at elevated temperatures. The same results were also obtained as the experiment was repeated with different liquid and gas ¯ow rates. These observations are potentially important for the processes in stirred vessels where parameters such as relative power demand (RPD) is dependent on the shape and size of bubbles at elevated temperatures. CONCLUSIONS The results presented in this paper highlight some important features of the effect of temperature on void fraction and evolution of the ¯ow structure and provide useful information, which are summarized as follows:
Figure 10. Mean, minimum and maximum bubble size as a function of temperature.
· The effect of temperature on the void fraction of increasing vapour pressure at elevated temperatures cannot be ignored even at high liquid ¯ow rates. The experimental data show an excessive in¯uence of temperature, especially above 608 C. This effect becomes dominant near the boiling point. The modi®ed volumetric ¯ow ratio (equation (4)) adequately includes the effect of vapour pressure on the void fraction at higher ¯ow rates. The results also re¯ect a change in ¯ow regime as temperature rises due to a sharp increase of bubble size with temperature. Trans IChemE, Vol 78, Part A, November 2000
AN EXPERIMENTAL INVESTIGATION OF ADIABATIC TWO-PHASE FLOW
· The recorded images show that the chance of bubble clustering becomes unlikely at higher temperature. This is probably due to a weak boundary layer of the partially saturated air bubbles leading to rapid bubble coalescence (Figures 8 and 9). It is also shown experimentally that the change in ¯ow regime is caused by bubble coalescence at a lower temperature, however, it would be affected by growth and subsequent coalescence, as the air bubbles saturate at elevated temperatures. This phenomenon is more signi®cant at greater downstream distances. NOMENCLATURE D g h L Q Pa Pv T
pipe diameter, m gravitational acceleration, m s ±2 local submergence below the free surface, m distance from gas sparger, m volumetric ¯ow rate, m3 s 1 atmospheric pressure, N m ±2 vapour pressure, N m ±2 temperature, 8 C
Greek b b m r j
letters volumetric ¯ow ratio, Qg / Qg Qf modi®ed volumetric ¯ow ratio (equation (4)) viscosity, kg m ±1 s ±1 density, kg m ±3 surface tension, N m ±1
Subscripts gas g liquid l
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2. Whalley, P. B., 1987, Boiling, Condensation, and Gas-Liquid Flow (Clarendon Press, Oxford, UK). 3. Tribbe, C., 1998, Gas/liquid ¯ow in cylindrical and corrugated channels, PhD Thesis (University of Surrey, Guildford, UK). 4. Kuru, W. C. and Panchal, C. B., 1997, Application of single-phase fouling data to two-phase ¯ows, Convective Flow and Pool Boiling Conf (Kloster Irsee, Germany). 5. Grover, G. S., Rode, C. V. and Chaudhari, R. V., 1986, Effect of temperature on ¯ow regimes and gas hold-up in a bubble column, Can J Chem Eng, 64: 501±504. 6. Saxena, S. C., Rao, N. S. and Thimmapuram, P. R., 1992, Gas holdup in slurry bubble columns for two and three phase systems, Chem Eng J, 49: 151±159. 7. Renjun, Z., Xinzhen, J., Baozhang, L., Yong, Z. and Laiqi, Z., 1988, Studies on gas holdup in a bubble column operated at elevated temperature, Ind Eng Chem, 27: 1901±1916. 8. Jamialahmadi, M. and MuÈller-Steinhagen, H., 1993, Effect of energy input on bubble coalescence, Technical report (University of Auckland, New Zealand). 9. Wallis, G. B., 1969, One Dimensional Two-Phase Flow (McGraw-Hill, New York). 10. Malayeri, M. R., Smith, J. M. and MuÈller-Steinhagen, H., 1998, Effect of bubble size on two-phase ¯ow behaviour in vertical up-ward ¯ow, The 3rd Iranian Congress of Chem Eng, Ahwaz, Iran, 258±261. 11. Tomiyama, A., Tamai, H., Makino, Y. and Miyoshi, K., 1998, Modelling and Real-Time Simulation of a Developing Bubble Flow in a Vertical Pipe, Japan-UK mini workshop. 12. Zun, I., Kljenak, I. and Moze, S., 1993, Space-time evolution of the non-homogeneousbubble distribution in upward ¯ow, Int J Multiphase Flow, 19(1): 151±172.
ADDRESS
REFERENCES 1. Hewitt, G. F., 1996, In search of two-phase ¯ow, J Heat Transfer, 118: 518±527.
Trans IChemE, Vol 78, Part A, November 2000
Correspondence concerning this paper should be addressed to Professor H. MuÈller-Steinhagen, Institut fuÈr Technische Thermodynamik, German Aerospace Center, Pfaffenwaldring 38-40, D-70569 Stuttgart, Germany. E-mail: [email protected] The manuscript was received 13 September 1999 and accepted for publication after revision 17 August 2000.