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Bottom Pressure Method for the Determination of the Flooding/ Loading Transition in an Aerated Vessel Stirred by a Rushton Impeller Baoqing Liu, Fangyi Fan, Ruijia Cheng, Zilong Xu, Yijun Zheng, and Zhijiang Jin* College of Energy Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China ABSTRACT: A novel method to determine the flooding/loading transition point (Nf) was proposed based on the measurements of the bottom pressure. Experiments were carried out in an aerated vessel stirred with a Rushton impeller in single-phase and two-phase systems. The results showed that the bottom pressure (P) in the single-phase system had a parabolic decrease with the increasing impeller speed (N), which followed the Bernoulli Effect; the flooding/loading transition was defined by a sharp change in the P−N curve. The data were well consistent with the results obtained by the global gas holdup method, as well as the existing literature data on flooding/loading transition.

1. INTRODUCTION Different flow regimes existed in an aerated vessel have a correlation with the impeller speed and gas flow rate. The typical flow regimes are divided into three categories: flooding, loading, and complete dispersion (Figure 1).1 For an impeller speed under the critical speed which is always labeled as Nf, the gas flows up the middle of the vessel, and the impeller is flooded (Figure 1a). With the increase of the impeller speed, the fluid flows radially out of the impeller and reaches the vessel wall,2 and the impeller is loaded (Figure 1b). When the impeller speed is further increased, the gas will be dispersed in the upper and lower sections of the vessel (Figure 1c). Flooding is a characteristic feature of gas−liquid mixing equipment, and often occurs in the condition where the gas flow rate is high and the impeller speed is low. Because the gas distribution is extremely uneven in the vessel when the flooding occurs, it will badly affect the mass transfer and micromixing efficiency between gas and liquid.3,4 To maximize the stirred vessel performances, it is supposed to operate in the loading regime or the completely dispersed regime. Therefore, it is of critical importance to detect the transition. Previously, several authors2,5,6 had researched and described this “flooding” phenomenon, but its definition is still not well established. Simultaneously various kinds of experimental methods had been proposed to determine the flooding regime, which mainly fall into two broad categories. The first one is based on the measurements of global parameters. For instance, Warmoeskerken and Smith3 detected the impeller flooding by measuring the gassed power drawn, and found a linear relationship between the Froude number (Fr) and the Flow number (Fl) at the flooding/loading transition. Rewatkar and Joshi7−9 measured the critical impeller speeds of a pitched blade turbine downflow by visual observations, gauging power © XXXX American Chemical Society

consumption and mixing time, respectively. They also investigated the impact of gas sparger style and structure on the critical impeller speed. With the development of probe techniques and advanced statistic signal analysis techniques, local characteristics were measured for identification of the flooding/loading transition, such as the liquid velocity and the local void fraction of the impeller outflow. Applying a conical hot-film anemometer, Lu and Chen1 assumed that there was a sharp transition of fluctuation velocity of the impeller outflow at the beginning of the flooding/loading transition. Bombac and colleagues10−13 studied the gas cavity structure and the local void fraction by the time-series resistivity probe and provided a novel method to detect the flooding point of an individual impeller in single and multi-Rushton stirred vessels. They found that there was an appearance of ragged cavities behind impeller blades when impeller flooding occurred. Besides, there were other methods of determining the flooding/loading transition based on the local detection, such as the conductivity probe method,14,15 the acoustic emission (AE) method,16 the light transmission method,17 and the gamma-CT scan method,18 etc. However, these mentioned methods have their own limitations. For example, most of the local detection methods are intrusive and would interfere with the flow field in the stirred vessels, so these methods are not suitable for harsh industrial production environments. The global detection methods also have some insufficiencies. For instance, the visual observation method is simple and convenient, but its accuracy is not high and can only be used in transparent devices. The Received: Revised: Accepted: Published: A

April 19, 2017 September 13, 2017 September 15, 2017 September 15, 2017 DOI: 10.1021/acs.iecr.7b01625 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Sketches of the bulk flow patterns in stirred vessels.

Figure 2. Experimental apparatus.

power method is a noninvasive measurement method, but its sensitivity is not high. To overcome these limitations, a simple and reliable technique for detecting the flooding/loading transition is required in academia as well as industry. In this research, only the transition from impeller flooding to loading was considered, and the purpose is to propose a novel method to estimate the flooding of a Rushton impeller in an aerated vessel based on the measurements of the bottom pressure.

Figure 3. Rushton impeller.

2. EXPERIMENTAL SECTION 2.1. Experimental apparatus. The experiments were done in a cylindrical perspex vessel equipped with a standard elliptical bottom, and its diameter T was 380 mm. To eliminate the circular flow, four baffles of width 38 mm were installed perpendicularly to the vessel wall with a gap of 10 mm. A Rushton impeller with a diameter of 133 mm (D = 0.35T) was positioned with an off-bottom clearance (C) of 160 mm. A gas sparger of diameter 110 mm was located with an off-bottom clearance 70 mm. The gas sparger was made of a stainless steel tube of external diameter 18 mm. There were 24 equidistant holes of diameter 2 mm on the bottom side. The experimental apparatus is shown in Figure 2, and the Rushton impeller is depicted in Figure 3.

The pressure was measured by a customized flat membrane pressure sensor (Figure 4). The measurement error of this pressure sensor was ±10 Pa, which ensured sufficient measurement accuracy. The pressure sensor was installed on

Figure 4. Flat membrane pressure sensor. B

DOI: 10.1021/acs.iecr.7b01625 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research the vessel bottom allowed pressure reading to be taken, and its membrane of diameter 20 mm was flush with the inner surface of the stirred vessel. The selected point was located on a diametral line at 45° between subsequent baffles, at a radial location 50 mm from the center of the vessel. The experimental results were also determined using the step change of the global gas holdup under the same experimental conditions. The global gas holdup was defined by the ratio between the gas phase and the liquid phase volume and could be transformed into a ratio of heights (εg = 1 − H/Hg). 2.2. Bottom Pressure Method. The output of the pressure sensor provided a time series {Pn}nM= 1, sampled with a frequency of 1 Hz and kept a record of a time span for 120 s, which corresponded to M = 120 points. A characteristic timeseries is shown in Figure 5. The data were sufficient for the

Figure 6. Relationship between P and N in the single-phase system.

indicate that the pressure signals respond to the dynamic characteristics of fluids in the stirred vessel. It is noteworthy that the pressure sensor is placed at the point of the vessel bottom shown in Figure 2, and the local pressure can be actually read. In agitation conditions, this local pressure includes the hydrostatic pressure, dynamic pressure, and other vertical forces. Because of the negligible density of the air, the presence of gas would not affect the hydrostatic pressure on the vessel bottom. Meanwhile, other vertical forces are small compared with the hydrostatic pressure, so the bottom pressure variations are mainly affected by the dynamic head effects. 3.2. Identification of Flooding/Loading Transition of the Rushton Impeller. Figure 7 shows the P−N curves at five different superficial gas velocities (Vg): 2.45 × 10−3 m/s, 4.90 × 10−3 m/s, 7.35 × 10−3 m/s, 9.80 × 10−3 m/s, and 12.25 × 10−3 m/s, separately, when tap water and compressed air are used as working fluids. Under the conditions without the agitation of the impeller, an axial fluid flow similar to that in a bubble-cap column was induced by the buoyancy effects of the bubbles. The liquid circulation generated by gas sparger was upward in the central region and downward near the vessel wall (Figure 1a). Because of a frictional loss from the vessel wall, the downward flow near the wall was reduced, and the volume below the impeller formed a dead zone. In this case, the value of P did not change, compared with that without gas. As the impeller speed increased (N < Nf), there was an axial flow of fluid (gas and liquid) through the impeller up to the free surface, and the flow pattern was still a single cycle shown in Figure 1a. As the impeller speed increased, the axial force produced by the impeller increased. This axial force was transmitted to the vessel bottom, causing a pressure increase. However, a radial impeller was used in experiments, so the axial force was very weak, and P increased slightly. Meanwhile, with the increase of the radial flow generated by the impeller, the axial bubble flow gradually expanded, but the degree of radial motion was very limited. In these cases, the velocity of the downflow near the wall was greater, and minor liquid flows would gradually reach the vessel bottom, resulting in a little reduction of P. The combined effect of the axial force and the dynamic head effects was that P increased slightly, with the increase of the impeller speed, followed by the slight decrease.

Figure 5. Pressure fluctuations vs time n.

time-scales of the flow regimes to obtain statistically independent results. The bottom pressure measurement was extracted from the data of time series by the pressure sensor, and if the bottom pressure (P) is the mean value of time series, then P=

1 M

M

∑ Pn n=1

(1)

Measurements were conducted in the same manner, which started from low to high gas flow rates, with stepwise increase of the impeller speed at a constant gas flow rate. The measurement of bottom pressure was repeated twice for each impeller speed, and the repeatability error was less than 1%.

3. RESULTS AND DISCUSSION 3.1. Bottom Pressure Analysis in the Single-Phase System. Figure 6 shows a relationship between the bottom pressure (P) and the impeller speed (N) of the Rushton impeller in the single-phase system. It can be seen that P drops with the increase of N. A fitting is applied to the data of P and N, which shows a quadratic relationship, and it has a correlation coefficient of 0.997, which means a good degree of fitting. The changes in the pressure value are proportional to the square of impeller speed. This phenomenon is caused by the Bernoulli Effect in which the pressure within the fluid (liquid or gas) decreases when the velocity of fluid flow increases. Hence the pressure changes with the increase of the impeller speed C


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Figure 7. P−N curve in the two-phase system.

Table 1. Value of Nf Obtained from the Data of Figure 7

At a certain impeller speed (N = Nf), a sharp reduction of P could be seen within a lesser range of impeller speeds along the P−N curve. The flow pattern under this condition was shown in Figure 1b. It could be seen that the fluid was ejected in the radial direction and divided into two circular flows as it reached to the vessel wall, and the flow pattern changed from original single cycle into double circulations. Because of forming a lower circulation, the velocity of liquid flow in the vessel bottom sharply increased, so P decreased suddenly at this point. Because of the obvious slope change in the P−N curve at the transition from the flooding regime to loading regime, the flooding/loading transition was defined by a sharp change in the P−N curve. Table 1 sums up the value of Nf in Figure 7, as well as the corresponding Froude number and Flow number.

superficial gas velocity

flooding/loading transition point

Froude number

flow number

Vg (m/s)

Nf (rpm)

Frf

Flf

0.0564 0.0774 0.0968 0.1178 0.1383

0.055 0.117 0.168 0.202 0.229

−3

2.45 × 10 4.90 × 10−3 7.35 × 10−3 9.80 × 10−3 12.25 × 10−3

120 175 210 230 245

(±5) (±5) (±5) (±5) (±5)

With the further increasing of impeller speed (N > Nf), the flow generated by the impeller increased continuously, and the velocity of liquid circulation in the lower part of the vessel was greater. Hence P decreased continuously along the P−N curve. D


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Industrial & Engineering Chemistry Research All in all, through the analysis of the average pressure across the pressure sensor returned signal, a simple, objective, and physically based way of flow-regime identification in stirred vessels was provided. And it was found that the values of Nf obtained by the bottom pressure method were in good agreement with the visual observation. 3.3. Global Gas Holdup Method. Figure 8 shows that the global gas holdup εg changed with the impeller speed N which

Figure 9. Comparison of our experimental results in the flooding/ loading transition with those from the literature.

were obtained by measuring the local gas holdup in the aerated vessel, combining with computational fluid dynamics (CFD). It is observed that our data based on the bottom pressure method agree with those predicted by Nienow et al.19 and Wang et al.20 As a matter of fact, it could be seen that if the diameter of the stirred vessel is identical to that in present study (T = 380 mm), the two sets of experimental results are in very good accordance with each other. In consequence, the data of flow pattern discrimination obtained by analyzing the bottom pressure are consistent with the results in the existing literature data on flooding/loading transition by other methods.

Figure 8. Relation between εg and N for different Qg.

corresponded to Figure 7. It can be seen that there is a remarkable increment of εg in the flooding/loading transition. In the flooding states, there was an axial flow of fluid through the impeller up to the free surface. The flow pattern was under the control of the gas flow, which would be an extreme nonhomogeneous distribution. In the flooding/loading transition, gas bubbles were radially discharged from the impeller plane and impinged the wall lightly. In this case, the bubbles had an approximately homogeneous distribution within the vessel and occupied more liquid volume. Thus, there was a rapid increase of εg in the flooding/loading transition. With further enlargement of N, εg increased continuously, because more and more bubbles became entrained in the downflow. The same values of Nf were obtained by two methods (the global gas holdup and the bottom pressure method), therefore, verifying the correctness and validity of the bottom pressure method. 3.4. Comparison of Literature Correlations. On the basis of the equation proposed by Warmoeskerken and Smith,3 Nienow et al.19 analyzed the function of the geometrical structures as for impeller configuration and diameter, tank to impeller diameter ratio, and gas sparger on the flooding/ loading transition, and further modified this equation, postulating a correlation including different geometrical ratios (1/3 < D/T < 1/2) as well as vessel scale size (0.29 < T < 1.2 [m]): ⎛ D ⎞3.5 Fl f = 30⎜ ⎟ Fr f ⎝T ⎠

4. CONCLUSIONS A novel method has been developed for measuring the flooding/loading transition point (Nf) in the aerated vessel stirred by a Rushton impeller. Measuring the mean pressure on the bottom of the stirred vessel based on the pressure sensor does not affect flow field in the vessel, and is reliable, objective, quantitative, and also can be applied to nontransparent industrial reactors. Because of the Bernoulli Effect, the pressure difference across the pressure sensor returned a signal directly related to the liquid flow velocities on the bottom of the vessel. Through analysis of the bottom pressure, the flooding/loading transition point (Nf) could be obtained, and the flooding/loading transition was defined by a sharp change in the P−N curve. The data were fully consistent with the results obtained by the global gas holdup method, as well as the existing literature data on flooding/loading transitions.

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AUTHOR INFORMATION

Corresponding Author

(2)

*Tel.: +86 571 87952729. E-mail: [email protected].

Figure 9 compares the present experimental data with those of Nienow et al.19 and Wang et al.,20 which is displayed in the dimensionless plot Frf −Flf. Nienow et al.19 obtained the experimental data by analyzing impeller torque in relation to the impeller speed and gas flow rate. The data of Wang et al.20

ORCID

Zhijiang Jin: 0000-0002-1173-112X Notes

The authors declare no competing financial interest. E


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(16) Wang, Y.; Wang, B.; Ren, C.; Wang, J.; Yang, Y. Identification of flooding-loading transition in stirred vessel based on acoustic method. CIESC J. 2009, 60, 1148−1155. (17) Babalona, E.; Markopoulos, J. The light transmission method as a new technique for determining flooding characteristics in gas-liquid contactors. Chem. Eng. Technol. 2010, 33, 654−657. (18) Kong, L.; Li, W.; Han, L.; Liu, Y.; Luo, H.; Al Dahhan, M.; Dudukovic, M. P. On the measurement of gas holdup distribution near the region of impeller in a gas-liquid stirred Rushton tank by means of γ-CT. Chem. Eng. J. 2012, 188, 191−198. (19) Nienow, A. W.; Warmoeskerken, M. M. C. G.; Smith, J. M.; Konno, M. On the flooding-loading transition and the complete dispersal condition in aerated vessels agitated by a Rushton turbine. Proceedings of the 5th European Conference on Mixing, Wüzburg, Germany, 1985; BHRA: Cranfield, U.K., 1985. (20) Wang, W.; Mao, Z.; Yang, C. Experimental and numerical investigation on gas holdup and flooding in an aerated stirred tank with Rushton impeller. Ind. Eng. Chem. Res. 2006, 45, 1141−1151.

ACKNOWLEDGMENTS Thanks to the Zhejiang Provincial Natural Science Foundation of China (LY16B060003) and the National Natural Science Foundation of China (21776246) for their support.

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NOMENCLATURE C = impeller clearance above the bottom, mm D = impeller disk diameter, mm T = inner diameter of stirred vessel, mm Fl = Flow number, Qg/ND3 Fr = Froude number, DN2/g g = gravity acceleration constant, m/s2 H = liquid height, mm Hg = height of the two-phase free surface, mm H/T = aspect ratio N = impeller speed, rpm P = bottom pressure gauged by the pressure sensor, Pa Vg = superficial gas velocity, m/s R = regression coefficient

Subscripts

f = flooding/loading transition point

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REFERENCES

(1) Lu, W.; Chen, H. Flooding and critical impeller speed for gas dispersion in aerated turbine-agitated vessels. Chem. Eng. J. 1986, 33, 57−62. (2) Rushton, J. H.; Bmbinet, J. Holdup and flooding in air liquid mixing. Can. J. Chem. Eng. 1968, 46, 16−21. (3) Warmoeskerken, M. M. C. G.; Smith, J. M. Flooding of disc turbines in gas-liquid dispersions: A new description of the phenomenon. Chem. Eng. Sci. 1985, 40, 2063−2071. (4) Lin, W. W.; Lee, D. J. Micromixing effects in aerated stirred tank. Chem. Eng. Sci. 1997, 52, 3837−3842. (5) Calderbank, P. H. Physical rate processes in industrial fermentation. Trans. Inst. Chem. Eng. 1958, 36, 443−463. (6) Westerterp, K. R. Interfacial areas in agitated gas-liquid contactors. Chem. Eng. Sci. 1995, 50, 3959−3959. (7) Rewatkar, V. B.; Joshi, J. B. Role of sparger design in mechanically agitated gas-liquid reactors, part I: power consumption. Chem. Eng. Technol. 1991, 14, 333−347. (8) Rewatkar, V. B.; Joshi, J. B. Role of sparger design in mechanically agitated gas-liquid reactors, part II: mixing time. Chem. Eng. Technol. 1991, 14, 386−394. (9) Rewatkar, V. B.; Joshi, J. B. Role of sparger design on gas dispersion in mechanically agitated gas-liquid contactors. Can. J. Chem. Eng. 1993, 71, 278−291. (10) Bombač, A.; Ž un, I.; Filipič, B.; Ž umer, M. Gas-filled cavity structures and local void fraction distribution in aerated stirred vessel. AIChE J. 1997, 43, 2921−2931. (11) Bombač, A.; Ž un, I. A simple method for detecting individual impeller flooding of dual Rushton impellers. Proceedings of 10th the European Conference on Mixing, Delft, Netherlands, 2000; Elsevier: Amsterdam, 2000. (12) Bombač, A.; Ž un, I. Gas-filled cavity structures and local void fraction distribution in vessel with dual-impellers. Chem. Eng. Sci. 2000, 55, 2995−3001. (13) Bombač, A.; Ž un, I. Individual impeller flooding in aerated vessel stirred by multiple-Rushton impellers. Chem. Eng. J. 2006, 116, 85−95. (14) Paglianti, A.; Pintus, S.; Giona, M. Time-series analysis approach for the identification of flooding/loading transition in gas−liquid stirred tank reactors. Chem. Eng. Sci. 2000, 55, 5793−5802. (15) Paglianti, A. Simple model to evaluate loading/flooding transition in aerated vessels stirred by Rushton disc turbines. Can. J. Chem. Eng. 2002, 80, 660−664. F


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