CFD Simulations of Flow Characteristics in Pulsed-Sieve-Plate

Theoretically, it is this interface renewal effect, caused by the periodic coalescence and dispersion of droplets, that enhances the mass transfer in ...
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Ind. Eng. Chem. Res. 2011, 50, 1110–1114

CFD Simulations of Flow Characteristics in Pulsed-Sieve-Plate Extraction Columns Tang Xiaojin* and Luo Guangsheng State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua UniVersity, Beijing 100084, China

For better understanding the mass transfer and axial mixing characteristics, computational fluid dynamics software (CFX) is used to simulate the single-phase flow in a pulsed-sieve-plate extraction column (PSEC) with three different types of structures, including the standard PSEC structure and two types of coalescence-dispersion pulsed-sieve-plate extraction column (CDPSEC) structures. It was found that the simulation results may explain the axial mixing characteristics very well by comparing them with the experimental data. The simulation results show that the standard PSEC structure is of stable flow fields under different operating conditions. The CDPSEC structure as an improvement upon the standard PSEC structure shows complex flow characteristics and mass transfer performances. The CFD method can be applied to optimize the CDPSEC structure besides the practical experiments and be of the potential to reduce the experimental cost as low as possible. Introduction Extraction columns are widely used in chemical industry, but the understanding of the transport phenomena and axial mixing in extraction columns is limited for the complexities of the flow characteristics. Nowadays, the computational fluid dynamics (CFD) is applied more and more to investigate the disciplines of multiphase flow in chemical engineering as a powerful mathematical tool. With the help of CFD simulation, the flow fields of extraction columns can be visualized easily to provide valuable information, including formation of a single drop, drop free motions, and coalescence with the main phase interface in a pulsed-sieve-plate extraction column,1,2 the residence time distribution of droplets in a discs and doughnuts pulsed extraction column,3 the single-phase flow field in an agitated extraction column,4 and the 3D simulation of the two-phase flow in a rotating disk extraction column.5 The pulsed-sieve-plate extraction column (PSEC) is known as a contactor with high mass transfer performances. In addition, the coalescence-dispersion pulsed-sieve-plate extraction column (CDPSEC) is a modified PSEC. In the CDPSEC, the coalescence plates, made of Teflon, are periodically inserted into the PSEC. The droplets of the dispersed phase coalesce when they pass through the coalescence plates and then break up to provide a new interface area for mass transfer when they pass through the dispersion plates (standard steel plates). Theoretically, it is this interface renewal effect, caused by the periodic coalescence and dispersion of droplets, that enhances the mass transfer in the CDPSEC. It was reported that the CDPSEC with 50 mm in the plate spacing was of 120% overall mass transfer efficiency over the standard PSEC.6 However, when the plate spacing of the CDPSEC was reduced to 25 mm, it was reported that the mass transfer efficiency of the CDPSEC was only about 50% that of the standard PSEC,7 although the interface renewal frequency was doubled. From the point of the mass transfer enhancement, the influence of flow field must be considered carefully besides that of the interface renewal effect. In this study, CFD software (CFX) was used to simulate the steady single-phase flow fields in the PSEC with three types of * To whom correspondence should be addressed. Tel.: 86-1062783870. E-mail: [email protected].

structures under different operating conditions by the k-ε model with the following boundary conditions, a uniform radial velocity profile at the inlet, 0 Pa in average pressure at the outlet, and the no-slip wall condition. The tetrahedron mesh was used to simulate the calculation domain in the PSEC for the complex structure of the sieve plates. The mass transfer performances of the PSEC with different types of structures7 were explained by the simulation results, including the ‘true’ height of mass transfer unit Hox, and the axial dispersion coefficient of the continuous phase Ex. In addition, the influence of the flow field on the mass transfer and axial mixing characteristics in the PSEC was discussed. In the mass transfer experiments, the continuous phase is the heavy phase with the down-flow pattern and the dispersed phase is the light phase in the up-flow pattern. Therefore, the single-phase calculated results by CFD with the down-flow pattern could be used to simulate the flow field of the continuous phase and the single-phase calculated results by CFD with the up-flow pattern could be used to simulate the flow field of the dispersed phase. CFD Simulation Results 1. Structure of PSEC. To simulate single-phase flow in the PSEC, whose diameter is 150 mm, two types of the CDPSEC structures with 50 and 25 mm in plate spacing and the standard PSEC structure with 50 mm in plate spacing, shown in Figure 1, were chosen. Water at 25 °C was chosen as the fluid in the calculation domain.

Figure 1. Calculation domain of CDPSEC and PSEC: (a) CDPSEC structure, (b) PSEC structure, and (c) CDPSEC structure. Plate spacing ) 50 mm, plate spacing ) 50 mm, plate spacing ) 25 mm.

10.1021/ie101788b  2011 American Chemical Society Published on Web 12/16/2010

Ind. Eng. Chem. Res., Vol. 50, No. 2, 2011

Figure 2. Axial profile of velocity in structure I (u ) 0.00133 m/s).

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Figure 4. Axial profile of velocity in structure II (u ) 0.00133 m/s).

Table 1. List of PSEC Structure no.

I

II

III

structure plate spacing/mm

CDPSEC 50

PSEC 50

CDPSEC 25

Table 2. Specifications of Dispersion Plate and Coalescence Plate

name

material

plate thickness, mm

dispersion plate coalescence plate

stainless steel Teflon

1 2

free area, % 23 23

hole diameter, mm 3 Figure 5. Radial profile of velocity in structure II (u ) 0.00133 m/s).

Table 3. Variances of Axial Profiles in Structure I u (m/s) σ2 (m2/s2)

0.00133 0.327

0.00206 0.309

0.00270 0.302

Table 5. Variances of Axial Profiles in Structure II 0.00462 0.302

As shown in Figure 1, there is a coalescence plate under three dispersion plates in the CDPSEC, but there is only the dispersion plate in the standard PSEC. For simplicity, these three types of structures are numbered as shown in Table 1. The same specifications of the coalescence plate and dispersion plate in our previous work7-10 are used in this study, shown in Table 2. 2. Single-Phase Up-Flow Fields. To simulate the dispersed phase flow, the fluid enters the calculation domain from the bottom and leaves the calculation domain from the top. 2.1. Flow Field in Structure I. Figure 2 shows the axial profile of the up-flow field in structure I. The variances of the axial profiles under different operating conditions are shown in Table 3. Figure 3 shows the radial profile of the flow field, whose position is 15 mm above the coalescence plate. The variances of the radial profiles under different operating conditions are shown in Table 4. In Figures 2 and 3, u is the superficial velocity at the inlet, which locates at the bottom of the calculation domain, and σ2 is the variance of the velocity distribution. From Tables 1 and 2, it can be found that σ decreases and the velocity distribution

u (m/s) σ2 (m2/s2)

0.00133 0.229

0.00206 0.246

0.00270 0.259

0.00462 0.288

Table 6. Variances of Radial Profiles in Structure II u (m/s) σ2 (m2/s2)

0.00133 0.0900

0.00206 0.0899

0.00270 0.0866

0.00462 0.0797

in Structure I is uniform with the increase of u, meaning the dispersed phase distribution is uniform with an increase of u under practical operation. 2.2. Flow Field in Structure II. Figure 4 shows the axial profile of the up-flow field in structure II. The variances of the axial profiles under different operating conditions are shown in Table 5. Figure 5 shows the radial profile of the flow field, whose position is 15 mm above the coalescence plate. The variances of the radial profiles under different operating conditions are shown in Table 6. The flow fields in structure II are very similar, even u changes in a wide range, meaning the dispersed phase flows in a relatively stable style in the standard PSEC structure compared with the CDPSEC structure. In addition, in the axial direction, σ in structure II is smaller than that in structure I, which means the flow field in structure II is more uniform than that in structure I. 2.3. Flow Field in Structure III. Figure 6 shows the axial profile of the up-flow field in Structure III. The variances of the axial profiles under different operating conditions are shown in Table 7. Figure 7 shows the radial profile of the flow field, whose position is 15 mm above the coalescence plate. The

Figure 3. Radial profile of velocity in structure I (u ) 0.00133 m/s). Table 4. Variances of Radial Profiles in Structure I u (m/s) σ2 (m2/s2)

0.00133 0.0256

0.00206 0.0235

0.00270 0.0221

0.00462 0.0214

Figure 6. Axial profile of velocity in structure III (u ) 0.00133 m/s).

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Figure 7. Radial profile of velocity in structure III (u ) 0.00133 m/s).

Figure 9. Radial profile of velocity in structure I (u ) 0.00100 m/s).

Table 7. Variances of Axial Profiles in Structure III u (m/s) σ2 (m2/s2)

0.00133 0.328

0.00206 0.355

0.00270 0.341

0.00366 0.330

0.0462 0.324

Table 8. Variances of Radial Profiles in Structure III u (m/s) σ2 (m2/s2)

0.00133 0.0334

0.00206 0.0318

0.00270 0.0308

0.00366 0.0309

0.00462 0.0319

variances of the radial profiles under different operating conditions are shown in Table 8. In a different way, the influence of u on the flow fields of structure III does not coincide with that of structure I, although the similar CDPSEC structure is used and the only difference is the plate spacing between these two types of structures. When u ranges between 0.00270 and 0.00366 m/s, an optimal flow field can be obtained with the minimum value of σ (σ2 ) 0.0308 m2/s2). In other words, the higher superficial velocity of the dispersed phase does not mean the more uniform flow field in structure III. 3. Single-Phase Down-Flow Fields. To simulate the continuous phase flow, the fluid enters the calculation domain from the top and leaves the calculation domain from the bottom. 3.1. Flow Field in Structure I. Figure 8 shows the axial profile of the down-flow field in structure I. The variances of the axial profiles under different operating conditions are shown in Table 9. Figure 9 shows the radial profile of the flow field, whose position is near the bottom of the calculation domain. The variances of the radial profiles under different operating conditions are shown in Table 10. From Tables 9 and 10, the increase of σ with the increase of u means that the flow fields of the continuous phase are nonuniform when u increases. Furthermore, one thing that must be noted is that the flow field below the coalescence plate is not uniform. Near the central axis, the fluid velocity is much smaller than the average value. This apparent velocity distribution leads to a nonuniform residence time distribution. 3.2. Flow Field in Structure II. Figure 10 shows the axial profile of the down-flow field in structure II. The variances of

the axial profiles under different operating conditions are shown in Table 11. Figure 11 shows the radial profile of the flow field, whose position is near the bottom of the calculation domain. The variances of the radial profiles under different operating conditions are shown in Table 12. From the flow field simulation results of structure II it is can be found that the flow fields of the continuous phase are nonuniform when u increases because of the increase of σ with the increase of u. The value of σ in structure II is much smaller than that in structure I, which means the flow field of the continuous phase in structure II is more uniform than that in structure I. 3.3. Flow Field in Structure III. Figure 12 shows the axial profile of the down-flow field in structure III. The variances of the axial profiles under different operating conditions are shown in Table 13. Figure 13 shows the radial profile of the flow field, whose position is near the bottom of the calculation domain. The variances of the radial profiles under different operating conditions are shown in Table 14.

Figure 8. Axial profile of velocity in structure I (u ) 0.00100 m/s).

Figure 11. Radial profile of velocity in structure II (u ) 0.00100 m/s).

Table 9. Variances of Axial Profiles in Structure I

Table 12. Variances of Radial Profiles in Structure II

u (m/s) σ2 (m2/s2)

0.00100 0.526

0.00133 0.525

0.00206 0.532

0.00279 0.541

Figure 10. Axial profile of velocity in structure II (u ) 0.00100 m/s). Table 10. Variances of Radial Profiles in Structure I u (m/s) σ2 (m2/s2)

0.00100 0.0542

0.00133 0.0521

0.00206 0.0535

0.00279 0.0573

Table 11. Variances of Axial Profiles in Structure II u (m/s) σ2 (m2/s2)

u (m/s) σ2 (m2/s2)

0.00100 0.215

0.00100 0.0345

0.00133 0.226

0.00133 0.0345

0.00206 0.247

0.00206 0.0385

0.00279 0.261

0.00279 0.0420

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Figure 12. Axial profile of velocity in structure III (u ) 0.00100 m/s). Table 13. Variances of Axial Profiles in Structure III u (m/s) σ2 (m2/s2)

0.00100 0.642

0.00133 0.646

0.00206 0.652

0.00279 0.654

Table 14. Variances of Radial Profiles in Structure III u (m/s) σ2 (m2/s2)

0.00100 0.0753

0.00133 0.0846

0.00206 0.105

0.00279 0.112

The flow fields in structure III are also nonuniform, which are similar to those in structure I. In addition, the values of σ in structure III are the highest of the three types of structures, which means the flow field in structure III is the most nonuniform. 4. Discussion In this section, the flow field simulation results, mentioned above, are used to explain the mass transfer performances of the PSEC with three types of structures. Figure 14 is the comparison of Hox in the PSEC.7 The experimental system is 30% tributyl phosphate (TBP) (in kerosene)-nitric acid-water. The water phase is the continuous phase, and the organic phase is the dispersed phase. Generally, Hox decreases with an increase of the superficial velocity of the dispersed phase, uy, because the holdup of the dispersed phase, φ, increases. From the point of the flow field influence on the mass transfer process, the uniform flow field of the dispersed phase is of

Figure 13. Radial profile of velocity in structure III (u ) 0.00100 m/s).

Figure 14. Comparison of Hox with different structure (Af ) 2.5 cm/s, ux ) 0.00133 m/s).

Figure 15. Comparison of Ex with different structure (Af ) 2.5 cm/s, ux ) 0.00133 m/s).

benefit to reduce the axial mixing. As shown in Figures 2 and 3, the flow field of the dispersed phase in structure I is uniform with an increase of uy. In Figures 4 and 5, the flow field in structure II is more uniform than that in structure I despite the change of uy, so the axial mixing of the dispersed phase is well controlled or decreased with the increase of uy. Therefore, the increase of uy can enhance the mass transfer. As mentioned above, there is an optimal flow field in structure III when uy ranges from 0.00270 to 0.00366 m/s. Surprisingly, there is also a lowest value of Hox in structure III when uy is 0.00366 m/s, as shown in Figure 14. In this sense, the influence of flow field on the mass transfer process must be considered carefully besides the mass transfer interface and the interface renewable effect. With the aid of CFD, it is helpful to obtain the optimal operating condition and reduce the experimental cost as low as possible. Figure 15 is a comparison of the axial mixing coefficient of the continuous phase, Ex, in the PSEC with different structures.7 Generally, an increase of ux, the superficial of the continuous phase, leads to an increase of Ex, because the flow fields of the continuous phase are more nonuniform. This can be found in Figures 8-13: σ increases with an increase of u. To reduce the value of Ex, the more uniform flow field of the dispersed phase and the higher holdup of the dispersed phase are very helpful. For structures I and II, Ex decreases with an increase of uy, because of the increase of φ, which can reduce the axial mixing of the continuous phase efficiently. However, in structure III, Ex is almost fixed with the increase of uy instead of an apparent decrease. Moreover, when uy < 0.003 m/s, Ex of structure I is the highest and Ex of structure III is the lowest. When uy > 0.003 m/s, Ex of structure II is the lowest. From Figures 2 and 3, the flow field of the dispersed phase in structure I is uniform with the increase of uy, so Ex reduces by the influence of the flow field of the dispersed phase. From Figures 4 and 5, it can be found that the flow fields are relatively stable in structure II, so Ex of structure II decreases with the increase of φ. As for structure III, the high value of uy does not mean a more uniform flow field as shown in Figures 6 and 7, so Ex of structure III is fixed by the different influence of uy and φ. When uy < 0.003 m/s, the plate spacing is a main factor to reduce the axial mixing, so Ex of structure III is the lowest among three types of structures despite the most nonuniform flow field as shown in Figures 12 and 13. With the same plate spacing, Ex of structure II is smaller than that of structure I. As shown in Figures 8 and 9, the flow field of the continuous phase between the coalescence plate and the bottom of the calculation domain in structure I is of marked nonuniformity, which leads to the intense axial mixing of the continuous phase. In addition,

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Ex of structure II is relatively small because the flow field is more uniform than that in structure I. When uy > 0.003 m/s, the influence of the plate spacing is weakened markedly. The flow field of the dispersed phase in structure III becomes more nonuniform, as shown in Figures 6 and 7, which leads to the increase of Ex. On the other hand, the increase of φ can reduce Ex, so Ex in structure III is almost fixed by these two opposite effects. At the same time, Ex in structure II continues to decrease with the increase of φ and is the lowest one in the three types of structures. In a similar way, Ex in structure I also continue to decrease and get closer and closer to that in structure III because of the more uniform flow field and the higher value of φ, but its value is still higher than that in structure II for the axial mixing between the coalescence plate and the bottom of the calculation domain, shown in Figures 8 and 9. 5. Conclusions The single-phase flow fields in the PSEC with three different structures were simulated by CFD. In addition, the simulation results were successfully used to explain the mass transfer performances of these types of structures and explain the complex mass transfer and axial mixing characteristics. In the standard PSEC structure, the flow fields of the two phases are relatively stable in spite of the changes of superficial velocities of the two phases. With the simulation results and the mass transfer performances, the standard PSEC structure is a practical choice to be used for its robustness in operating conditions. The CDPSEC structure is an important improvement upon the standard PSEC structure to enhance the mass transfer performances, but the flow fields strongly depend on the geometry structure for the complex flow characteristics in the CDPSEC. It is possible that there is an optimal flow field in the range of operating conditions. From this point of view, the practical mass transfer experiments should be combined with CFD to obtain the optimal structure of the CDPSEC with better mass transfer performance over the PSEC structure. With the help of the CFD method, the experimental cost can be reduced as low as possible to investigate extraction columns with high performances.

Nomenclature A ) pulse amplitude, cm f ) pulse frequency, 1/s Ex ) dispersion coefficient of the continuous phase, m2/s Hox ) ‘true’ height of mass transfer unit, m u ) superficial velocity, m/s ux ) superficial velocity of the continuous phase, m/s uy ) superficial velocity of the dispersion phase, m/s σ2 ) variance φ ) holdup of the dispersion phase

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ReceiVed for reView August 25, 2010 ReVised manuscript receiVed November 29, 2010 Accepted December 3, 2010 IE101788B