Mass Transfer to Finite Areas at the Wall in Swirling Pipe Flow in the

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Ind. Eng. Chem. Res. 1998, 37, 643-651

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Mass Transfer to Finite Areas at the Wall in Swirling Pipe Flow in the Transition Region Sinan Yapici* and R. Ebru Ozbahar Department of Chemical Engineering, Engineering Faculty, Ataturk University, 25240 Erzurum, Turkey

This paper presents a work on mass transfer to finite areas at the wall in decaying swirl flow in a circular pipe, generated by short helical swirl generators. Four swirl generators with angles at the outer edge between 15 and 60° to the duct axis were used to introduce a tangential velocity component to the axial flow. The experiments were carried out in the Reynolds number range 1730-8650 and at a Schmidt number of 1692. The axial distribution of the mass transfer to circular finite areas at the wall was measured using the electrochemical limiting current technique. Flow visualization observations showed that no circulation nor dead zone occurs from the leading edge of the swirlers to the end of the system. The local mass transfer data were correlated in the form of Sh Sc-1/3 ) 0.3058Re0.759(x/d)-0.400(1 + tan θ0)0.271, for the whole range of experimental conditions. 1. Introduction Intensification of convective transfer processes is done for many reasons such as reduced size, improved efficiency, improved safety, lower weight, lower cost, lower energy and material consumption, etc. There are many methods, some more practical than others, for the intensification of convective processes in operations. These applications in mass and heat transfer are normally called heat/mass transfer enhancement. Many techniques have been used for the enhancement of the convective processes known to be effective in enhancing transfer rates. These can be classified mainly into two groups: (a) passive techniques, which do not need additional external power and include the use of treated surfaces, rough surfaces, extended surfaces, displaced enhancement devices, swirl flow devices, surface tension devices, porous structures, grooves/rivulets, surface catalysis, coiled tubes, and additives for liquids and gases, and (b) active techniques, which require an extra external power source and include mechanical aids, surface vibration, fluid vibration, electrostatic fields, injection/suction, jet impingement, rotation, and pulsed flow (Bergles and Webb, 1985; Reay, 1991). Enhancement in the convective transfer rate is accompanied by an increase in the energy consumption, dissipated by further friction caused by nonsmooth surfaces and insertions, or by the necessary external power. Swirl flow has a wide range of technological applications in various engineering areas either in reacting or nonreacting cases, including heat and mass separation (Schultz-Grunow, 1963; Lin et al., 1990), particle separation and classification in cyclones, nuclear propulsion systems, agricultural spray machines, and industrial furnaces and internal combustion engines to obtain clean and efficient combustion and to control flame size and shape, in addition to enhancing convective transport properties in circular ducts (Gupta et al., 1984). In swirl flow, the tangential velocity component is of comparable magnitude with the mean axial flow velocity. Swirl flow in circular pipes may be classified into two main groups * Telephone: +90-442-2184120. Fax: +90-442-2336961. E-mail: [email protected].

(King et al., 1969): (a) continuous swirl flow, in which the swirling motion persists along the whole length of the pipe, and (b) decaying swirl flow, in which the swirl is generated at the entry of the pipe and decays along the flow path. The present research is concerned with the axial distributions of mass transfer to finite areas at the wall without a developing concentration boundary layer in a long small-diameter circular pipe. Although the enhancement of heat transfer in decaying swirl flow has received considerable attention, very little is known about mass transfer in this type of flow. Pipe-flow heat transfer in decaying swirl flow generated by various types of swirl generators has been investigated by many researchers (Blackwelder and Kreith, 1970; Klepper, 1973; Blum and Oliver, 1975; Hay and West, 1975; Sparrow and Chaboki, 1984; Du Plesis and Kroger, 1987; Razgatis and Holman, 1976; Zaherzade and Jagadish, 1975; Algifri et al., 1980; etc.). Only a few studies have been reported in the literature on mass transfer in decaying swirl flow. Shoukry and Shemilt (1985) investigated mass transfer enhancement in decaying annular pipe flow generated by a single tangential inlet, using the electrochemical limiting diffusion current technique to measure average mass transfer coefficients. These workers found that a smaller tangential inlet diameter gave higher enhancement in mass transfer due to the large tangential velocities and that the mass transfer enhancement decreased with axial distance. De et al. (1991) extended the above study to the investigation of mass transfer in the entrance region of decaying annular swirl flow using the same experimental technique. Legentilhomme and Legrand (1990, 1991) carried out very similar studies to the above, including the effect of varying annulus ratio. It was found that the effect of initial swirl intensity, which was defined as the ratio of the fluid velocity in the tangential inlet duct to that in the annular gap, is negligible and that varying the annulus ratio had little effect on mass transfer in decaying annular swirl flow. These workers also found that, with tangential inlet diameters smaller than or equal to the annular gap, mass transfer was higher than that for tangential inlet diameters larger than the annular gap. Using point

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644 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998

mass transfer flux is dependent on the limiting current as follows

NA )

Ilim nFA

(1)

Mass flux can also be expressed in terms of the mass transfer coefficient as follows

NA ) k(c∞ - cs)

(2)

For limiting current conditions, the concentration of reacting species at the cathode, cS ) 0, from eq 1 and 2, the following expression relating the mass transfer coefficient directly to the limiting current can be written

k)

Figure 1. Schematic diagram of experimental rig and design of swirl generator.

electrodes embedded into both the inner and outer walls of an annular pipe, Yapici et al. (1994, 1995) made detailed mass transfer measurements (including circumferential mass transfer measurements and current fluctuations) in a decaying annular swirl flow generated by short axial vanes to clarify the axial distribution of local mass transfer coefficients. The above studies on mass transfer in decaying swirl flow are the only studies of that kind known to the authors, and all of them have been carried out in annular systems; no study was found on mass transfer in decaying swirl flow in smooth circular pipes. Studies on swirl flow have been concentrated on heat transfer, and the above-mentioned studies on mass transfer in swirl flow, except the work of Yapici et al. (1994, 1995), do not provide information on truly local mass transfer behavior, since they used Ni rode cathodes as the inner wall of the annular systems. The aim of this work is to get some information on mass transfer in decaying swirl flow in a circular pipe in the transition region and to make a comparison with the results of annular systems for the similar flow regime range, with emphasis on better understanding of local characteristics. 2. Experimental Section A schematic diagram of the experimental rig used in the investigation and the design of swirl generators is given in Figure 1. All piping sections were made of PVC to ensure chemical inertness to the test electrolyte, and to avoid the adverse effects of light. For mass transfer measurements the electrochemical limiting diffusion current technique was used (Mizushina, 1971; Selman and Tobias, 1978). The electrode/electrolyte system employed was potassium ferricyanide with a ferrocyanide couple supported with aqueous sodium hydroxide solution using Ni anodes and cathodes as electrodes. The

Ilim nFAc∞

(3)

where k is the mass transfer coefficient, Ilim is the limiting diffusion current, n is the number of electrons exchanged in the electrochemical reaction, F is the Faraday constant, A is the area of the active electrode surface, and c∞ and cs are the bulk and surface concentrations of the active species, respectively. So the mass transfer coefficient can be directly determined from the measurement of limiting current in the electrolyte system. The physical properties of the electrolyte solution which consisted of 0.5 M sodium hydroxide, 0.01 M potassium ferricyanide, and 0.02 M potassium ferrocyanide are F ) 1027.23 kg m-3, ν ) 1.123 N s m-2, and Dferri ) 6.455 × 10-10 m2 s-1, at 20 °C (Bourne et al., 1985). The temperature of the electrolyte was kept constant at 20 °C within (1 °C, using a glass coil immersed in the reservoir. Four short helical swirl generators were manufactured from steel SS 316 rod of 12 mm diameter with helical channel angles of 15, 30, 45, and 60° to the pipe axis. They were manufactured by machining four grooves, with a certain angle to the pipe axis, in a rod, leaving a hub 2.5 mm in diameter in the center. To reduce the effect of the sudden expansion after the swirler, the hub was extended conically, tapering to a point, as seen Figure 1. The geometric characteristics of the swirl generators are also given in this figure. The whole length of the experimental section was approximately 90 equivalent diameters; 55 equivalent diameters of this was the entry section, and approximately 35 diameters was the test section, made of Teflon PTFE of 8.5 mm i.d., so allowing a fully developed flow before the test section for all experiments. The test section was equipped with 20 Ni electrodes 1 mm in diameter flush with the inner surface of the pipe at certain intervals beginning from 3 to 33.6 diameters. Only one electrode was used as cathode while all the others were used as anode to ensure a cathodic controlled process. For the mass transfer measurements, the necessary preparatory steps were performed to ensure the most accurate possible measurements, as reviewed by Berger and Ziai (1983). After these precautions the experiments could be repeated within a deviation of approximately (8%. Flow visualization experiments were carried out by injecting nitrogen gas through a needle into the test section, made of glass with the same inside diameter as that of the Teflon PTFE pipe, to see whether flow

Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 645

photographs, the streak line follows a helical path around the center line due to tangential motion introduced to the fluid flow as it passed through the swirler. For the flow from 60° swirlers, a twisted flow motion around the pipe center is observed in the first one-third of the test section. 3.2. Local Mass Transfer Measurements. Mass transfer between a fluid flow and a surface in forced convection can be written as a function of three dimensionless parameters

Sh ) f(Re,Sc,x/d)

(4)

where Sh ) kd/DAB, Re ) dU/ν, Sc ) ν/DAB, and x/d is a dimensionless distance. For laminar flow in a duct the relative velocity and concentration boundary layer thickness are proportional to the Schmidt number as follows

Figure 2. Flow visualization photographs at Re ) 9000 for different swirlers.

δ ≈ Scn δc

(5)

Equation 4 is generally written in the following form reversal or a stagnation point occurred. Nitrogen gas was injected into the flow stream through a needle just upstream of the swirler. First the system was operated and the flow rate was set, and nitrogen gas was then fed into the system, and the gas flow rate was adjusted until a clear vision of flow behavior was obtained. Then the photograph of the gas line, enlightened with a light source, along the pipe was taken. While liquid flow was continuing, the gas injection into the system was stopped to see whether gas was trapped in the system, that is, if any flow reversal or dead zone occurred in the test section. 3. Results and Discussion 3.1. Flow Visualization. The flow reversal occurrence in swirl flow is a function of swirl intensity and fluid velocity in addition to the system geometry, especially the swirler geometry. The possibility of its occurrence increases with increasing swirl intensity and flow velocity (Baker and Sayre, 1974; Ward-Smith, 1980). Due to the dependence of the hydrodynamics of swirl flow on the geometry, it is difficult to form a base for comparison between swirl flow studies using different geometries (Bradshaw, 1970). The flow visualization experiments were carried out by injecting nitrogen gas into the flow area just before the swirl generator to observe whether any flow reversal or dead zone occurs in the system. After a clear picture of the flow path of the injected gas was obtained, the injection was stopped to see if there was any trapped gas, that is any dead zone, in the swirling flow area. The flow visualization pictures for four swirlers at a Reynolds number of 9000, the upper limit of the Reynolds number range used in the present study, are given in Figure 2. The observations showed that no reverse flow or dead zone occurred in the system in the flow range. Nitrogen gas fed into the system before the swirler immediately moved toward the center of the pipe, as it passed through the swirler, at the trailing edge of the swirler due to the lower density of the gas and centripetal action. The streak line moved outward from the center to the pipe wall with increasing axial distance. As seen from the

Sh ) aRemScn(x/d)p

(6)

For most applications it was assumed that n ) 0.33 (Incropera and De Witt, 1985). For turbulent flow, analytical considerations showed that the value of n is between 0.5 and 0.62 depending on the details of the analysis. But empirical correlations in this form generally have suggested a value between 0.30 and 0.43. The Colburn j-factor analogy indicates that the Prandtl/ Schmidt number exponent should be 0.33 (Bennet and Myers, 1983). Since the most commonly used value for the Schmidt number exponent is 0.33, for the sake of comparison with the correlations from the literature, the power of the Schmidt number in the correlations of the present study was fixed as 0.33. Before carrying out mass transfer measurements for swirl flow, the mass transfer measurements were taken for fully developed axial flow. The averaged data from 20 electrodes fit the following correlation

ShavSc-0.33 ) 0.078Re0.764

(7)

with a regression coefficient of 0.9950. This expression represents the mass transfer to a small finite circular surface in fully developed axial pipe flow with no developing concentration boundary layer around, for a Reynolds number range of 1730-8650 and Sc ) 1692. For mass transfer to the inner rod of L/de ) 11.25 of an annular system in a fully developed turbulent flow for 4000 < Re < 15 000 and Sc ) 2604, Shoukry and Shemilt (1985) gave the following correlation, using the same measurement technique

ShavSc-0.33 ) 0.0135Re0.88

(8)

Sa et al. (1991) gave the following correlation for the mass transfer to the inner rod of L/de ) 10.14 in the entrance region of an annular system for the Reynolds number range 1800-12500

ShavSc-0.33 ) 0.24Re0.69

(9)

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Figure 3. Axial distribution of the local mass transfer downstream of the 15-60° swirlers.

Although their measurement includes a developing concentration boundary layer effect, they expressed that the concentration boundary layer was essentially fully developed over much of the rod, since for Sc ) 2604 the concentration boundary layer reaches fully developed conditions in a very short distance. In the mass transfer correlation for fully developed turbulent flow, the power of the Reynolds number has been recorded to be between 0.8 and 0.88, while this power changes to be between 0.58 and 0.88 for mass transfer in developing turbulent flow (Sa et al., 1991; Pickett, 1979). Despite the difference of not having a concentration layer around the finite area at which mass transfer occurs, in the present case, the power of the Reynolds number is close to the recorded range in the literature. The axial distribution of the local mass transfer coefficients for the 15-60° swirl generators is given in Figures 3 and 4 as Shs ) kd/DAB vs Re ) Ud/ν. The graphs of the distribution of the axial local mass transfer coefficient show that the decay of local mass transfer in the axial direction becomes more pronounced as the swirler angle increases. It is difficult to observe any obvious difference between the results of 15 and 30° swirlers, since they exhibit very similar behavior and very close results. The enhancement and decay of mass transfer along axial distance is more pronounced for the 45 and 60° swirlers. These graphs show increas-

Figure 4. Effect of swirlers on the axial distribution of the local mass transfer downstream for certain Reynolds numbers.

ing swirl number increases local mass transfer rates to the finite areas. The graphs given in Figure 6 shows the effect of swirler angle for certain Reynolds numbers. These graphs confirm that 15 and 30° give very close results for the whole range of Reynolds number. Although 45 and 60° swirlers gave close results to each other at lower Reynolds numbers, the difference between the mass transfer results for these swirl generators increased with increasing Reynolds number. These behaviors can be explained by the fact that the 15° swirler can produce enough turbulence to increase the mass transfer rate as much as the 30° swirler increase it with the swirl and turbulence effects. At low Reynolds numbers, the flow cannot gain enough tangential acceleration to show a pronounced difference between the mass transfer rates obtained from different swirlers. Figure 5 shows the increase in mass transfer relative to the axial mass transfer as Shs/Sha for some Reynolds numbers. These graphs show that the mass transfer rate has a rapid decay up to a dimensionless distance of approximately 15 for the swirlers of 15-45°, while this decay extends to a dimensionless distance of approximately 28 for the 60° swirler. After these axial distances it decays slowly but still has the effect of swirl

Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 647

Figure 6. Ratio of averaged Sherwood number over the whole length of the test section to that of the fully developed axial flow.

values used in the present work. An increase of up to 3.6 times the value in fully developed axial flow was obtained at the beginning of the test section for the 60° swirler. When considering the averaged values over the test section, approximately twice of the fully developed mass transfer rate can be reached, with the 60° swirler at a Reynolds number of 8650. The graph says that enhancement is better for lower Reynolds number for the 15-45° swirler, but the opposite is valid for the 60° swirler. The results were correlated for each individual swirler in terms of local Sherwood number as a function of the Reynolds number and the dimensionless axial distance as follows, with 160 values for each correlation

ShavSc-0.33 ) 0.4812Re0.704(x/d)-0.368 for 15° swirler (10) Figure 5. Increase in mass transfer relative to the axial mass transfer for some Reynolds numbers.

at a dimensionless axial distance of about 34. The 15 and 30° swirlers gave very close degrees of enhancement for whole ranges of Reynolds number; however, the enhancement increased with increasing swirler angle between 30 and 60°. 15-45° swirlers seem to give better enhancement at lower flow rates. But for the 60° swirler, the enhancement increases with increasing flow rate. This behavior can be seen more clearly in Figure 6 as the ratio of the averaged Sherwood number over the whole length of the test section to that of the fully developed axial flow. This can be explained by the outward spreading of flow, which hits the wall and therefore increases mass transfer for the 60° swirler. This effect can increase with increasing flow rate. Maxima in the ratios of Sherwood numbers occurred at a Reynolds number of 2700 for all swirl generators, as seen in the figure. The flow downstream of the swirler may not be classified as laminar or turbulent on the basis of the value of Reynolds number for ducts, since the behavior of flow can substantially change as it passes through the swirler. These maxima in the ratios of Sherwood numbers can be attributed to the relative increase in turbulence level of the flow after it passes through the swirler. Since this flow rate is in the low transition region, swirling flow may increase the turbulence intensity relative to that for the fully developed flow much more effectively than the other flow rate

ShavSc-0.33 ) 0.3420Re0.748(x/d)-0.372 for 30° swirler (11) ShavSc-0.33 ) 0.5408Re0.724(x/d)-0.368 for 45° swirler (12) ShavSc-0.33 ) 0.1878Re0.862(x/d)-0.445 for 60° swirler (13) where Sh ) kd/DAB and Re ) Ud/ν. The regression coefficients of these equations are between 0.9685 and 0.9910. These correlation equations show that there is no regular change in the power of the Reynolds number, but the decay of mass transfer rate increases with increasing swirler angle, expressed as the power of x/d. Taking into consideration the initial swirl intensity, defined as the swirl number, which is the ratio of the axial flux of tangential momentum to the product of the axial flux of the axial momentum and the radius of the duct, which is proportional to the tangent of the initial swirl angle (Ahmed et al., 1985)

S0 ∝ tan θ0

(14)

then, all experimental data for the five swirl generators were correlated, using simultaneous multiple regression, by one general equation as a function of the Reynolds number, the dimensionless axial distance and

648 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998

tangential entry, using cathode rods as parts of the inner rod of the annular section. They correlated their results of mass transfer to the cathode rod of approximately 11.1de; the lower section was located at a distance of 2.4de from the tangential entry of the vertical test section, for 2000 < Re < 15000

ShavSc-0.33 ) 0.1169Re0.69 for tangential entry of 2.54 cm i.d. (17) ShavSc-0.33 ) 0.0950Re0.75 for tangential entry of 1.91 cm i.d. (18) ShavSc-0.33 ) 0.0778Re0.81 for tangential entry of 1.27 cm i.d. (19)

Figure 7. General correlation of local mass transfer.

the initial swirl angle expressed as (1 + tan θ0), and the dimensionless axial distance, as follows

ShavSc-0.33 ) 0.3058Re0.759(x/d)-0.400(1 + tan θ0)0.271 (15) with a regression coefficient of 0.9793. Here θ0 is the angle given in Figure 1. The relative mean squares of the errors between the experimental data and the predictions of the correlation were calculated from the following equation

[

E% ) 100

1

N

∑

Nj)1

]

ex 2 (Shpr j - Shj )

Shpr j

1/2

(16)

where N is the number of experimental data and Shpr is the calculated value and Shex the experimental value of the Sherwood number. The general correlation of the mass transfer in swirling pipe flow represents the experimental data with a relative root mean squares error of 9.69% (N ) 640). The correlation is represented graphically in Figure 7. Similarity between different decaying swirl flow experiments is almost impossible to achieve because of the strong dependency of the flow characteristics on the specific system geometry and because of the more complex flow structure and boundary conditions, compared with those for axial flow (Chigier and Beer, 1964; Bradshaw, 1970). Since swirl flow behavior is mainly determined by the swirl-generating method and because of the fact that authors define swirl intensity in different ways depending on their system, it is difficult to make a comparison between correlations. If a comparison is to be made, it has to take into consideration firstly the similarity in the generation of the swirl flow. As mentioned in the Introduction, all the studies on decaying swirl flow have been carried out in annular ducts, using the same experimental technique. Here the comparison with the studies from the literature has to be made by taking into consideration the Reynolds number ranges used in the experiments, since the swirlgenerating techniques of this work and those of the studies from the literature are different. Shoukry and Shemilt (1985) carried out a mass transfer study in decaying annular swirl flow, generated by single circular

A very similar study was carried out by Legentilhomme and Legrand (1990) but with three sequential cathode rods separated from each other with PVC elements as parts of the inner rod beginning from the entrance section, and using a tangential entry of the same diameter as the annular gap, i.e de/2, and for the experimental ranges of Reynolds number 2000-5900 and axial distance (1.5-19.3)de. They recorded the following correlation

ShavSc-0.33 ) 0.18Re0.77(L/de)-0.26f(N)-0.15S-0.0004 0 (20) where f(N) is the geometric factor of the annular system and S0 is the swirl parameter of the flow defined as the ratio of the flow velocity in the tangential inlet to that in the annular gap. The same workers (1991) gave another correlation for the same experimental parameters but for the tangential inlet diameter larger than the annular gap, de/2

ShavSc-0.33 ) 0.091Re0.80(L/de)-0.39S0.18 0

(21)

Sa et al. (1991) performed another study at the same geometry with de ) 2.86 cm and the tangential entry of 1.27 cm i.d., but this time using shorter single cathode rods at different lengths to measure mass transfer in the entrance region. For the ranges of experimental parameters Re ) 1500-14000 and L/de ) 1.75-10.14, they developed the following correlation

Sh ) 0.408Re0.727Sc0.284(L/de)-0.235

(22)

It has to be kept in mind that the mass transfer results for the present case are for a decaying swirl flow in a circular duct generated by short helical swirlers. The results of the 60° swirler can be comparable to the results from the literature recorded here, since it is expected that it can give flow behavior closer to that obtained by tangential entry. The power of the Reynolds number changes between 0.69 and 0.81. The power of the Reynolds number for the present study, 0.759, falls well in the range of these values. The power of the dimensionless axial distance changes from -0.235 recorded by Sa et al. (1991) to -0.40 of the present study, but it should be noted that the correlation developed by Legentilhomme and Legrand (1991) and the correlation developed in the present work have very close values to each other, -0.39 and -0.40, respectively. If eqs 15 and 20-22 are rearranged for L/de )

Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998 649 Table 1. Details for Figure 10 for Some Integrated Correlations for Decaying Swirl Flow line no. 1 2 3 4 5

system

correlation equation

averaged length

ref

annular inner wall annular inner wall annular inner wall annular inner wall tubular

Sh ) Sh ) 0.0973Re0.77Sc0.33 Sh ) 0.0783Re0.80Sc0.33 Sh ) 0.2375Re0.727Sc0.284 Sh ) 0.2496Re0.759Sc0.33

2.4 e L/de e 13.5 0 e L/de e 10 0 e L/de e 10 0 e L/de e 10 0.2 e L/d e 10.2

Shoukry and Shemilt (1985) Legentilhomme and Legrand (1990) Legentilhomme and Legrand (1991) Sa et al. (1991); Legrand (1991) present work

0.0950Re0.75Sc0.33

Figure 8. Comparison of swirling flow mass transfer correlations (See Table 1 for details).

10, S0 ) 2.5, and θ0 ) 60°, in order to make a comparison for the experimental ranges used in these investigations, the following correlations are obtained, respectively

Shav ) 0.2496Re0.759Sc0.33

(23)

Shav ) 0.0973Re0.77Sc0.33

(24)

Shav ) 0.0783Re0.80Sc0.33

(25)

Shav ) 0.2375Re0.727Sc0.33

(26)

3. The differences in the results can be explained by the length of the active cathode surface and the swirlgenerating method. Those workers expressed that the mass transfer boundary layer over the surface develops rapidly in a very short distance over the cathode, and therefore the mass transfer rate measured from the cathode represents the mass transfer rate in a developed mass transfer boundary layer. But when the results are compared in Figure 8, it can be seen that the effect of the developing boundary layer on the measured mass transfer was underestimated. Since the increasing order of the lines in the figure follows the dimensionless length of cathodes used in the experiments, Shoukry and Shemilt (1985) used cathode rods of approximately 11 equivalent diameters, while the length of the cathode rods used by Legentilhomme and Legrand (1990, 1991) was between approximately 2.95 and 7.14 equivalent diameters, and Sa et al. (1991) used cathode rods having 1.75-10 equivalent diameters. The further difference in the results of Legentilhomme and Legrand (1990, 1991) and Sa et al. (1991) despite the closeness of the cathode rod lengths can be explained by the difference of the tangential entrance diameter. In the first two studies, the tangential entry diameter was equal to and larger than the annular gap, respectively, but in the later studies, they used a tangential entry smaller than the annular gap, which can produce more intensive swirl flow, giving higher mass transfer rates. For the present case, it is expected that the correlation gives the highest results, since the mass transfer rates were measured with no mass transfer boundary layer over the local cathodes. 4. Conclusions

The details for these correlations are given in Table 1. The reason to take S0 ) 2.5 is that in swirling flow by short helical vanes the axial velocity is accelerated to a velocity Us ) Ua/cos θ0; for θ0 ) 60°, Us ) 2Ua. By taking into consideration the blockage of the flow area by the swirler, it can be approximated as S0 ) Us/Ua ) 2.5. It is difficult to interpret the power of the Reynolds number because swirl-generating methods are different for the present case and for those from the literature. Even if the methods were the same for the studies from the literature, the ratios of tangential entry diameter to annular gap, de/2, would still be different for eqs 2426. So, the possibility of the hydrodynamic behavior of swirl flow on mass transfer being different for each study could result in different values of Reynolds number power. The comparison of these correlations is made graphically in Figure 8, for the Reynolds number range 2000-6000 within the experimental ranges used in these studies. As seen from the figure, the correlation of Shoukry and Shemilt (1985), shown with line 1, gave the lowest results, while the correlation of the present study, line 5, gave the highest results. Despite the difference in tangential entrance diameter, the correlations of Legentilhomme and Legrand (1990, 1991) gave very close results, as shown with lines 2 and

The present work was performed to obtain information on the axial mass transfer to local electrodes at the wall in a decaying tubular swirl flow in the transition region. It was observed by flow visualization that no reverse flow nor dead zone occurred in the system in the range of experimental parameters used. It was determined that increasing swirler angle increased local mass transfer rates to the finite areas. The experiments showed that the decay of local mass transfer in the axial direction became more pronounced as the swirler angle increased. It was difficult to observe any obvious difference between the results of 15 and 30° swirlers, since they exhibited very closer behavior and results. The enhancement and decay of mass transfer along axial distance were more pronounced for the 45 and 60° swirlers. The mass transfer rate had a rapid decay up to a dimensionless distance of approximately 15 for the 15-45° swirlers, while this rapid decay extended to a dimensionless distance of approximately 28 for the 60° swirler, and after these axial distances it decayed slowly, still having the effect of swirl at a dimensionless axial distance of 34. Although 45 and 60° swirlers gave close results to each other at lower Reynolds number, the difference between the mass transfer results for these swirl generators

650 Ind. Eng. Chem. Res., Vol. 37, No. 2, 1998

increased with increasing Reynolds number. The enhancement in mass transfer rate compared with the mass transfer in fully developed axial flow increased with increasing swirler angle between 30 and 60°. 1545° swirlers gave better enhancement in lower flow rates of the present range. But for the 60° swirler, the enhancement increased with increasing Reynolds number. An increase of up to 3.6 times the value in fully developed axial flow was obtained at the beginning of the test section for the 60° swirler, and approximately twice the fully developed mass transfer rate could be reached with the 60° swirler at a Reynolds number of 8650. Comparison of the studies from the literature showed a pronounced effect of the cathode length, that is, of the developing mass transfer over the surface and the swirl-generating method, on the mass transfer rate. Nomenclature A ) cathode surface area (m2) c ) concentration (mol m-3) D ) diffusion coefficient (m2 s-1) d ) duct diameter (m) F ) Faraday constant (96 487 C mol-1) I ) current (A) k ) local mass transfer coefficient (m s-1) k ) average mass transfer coefficient (m s-1) L ) axial length (m) N ) mass flux (mol m2 s-1) n ) number of electrons exchanged in electrochemical reaction U ) average velocity (m s-1) u ) local velocity (m s-1) r ) radial distance (m) x ) axial distance (m) w ) tangential velocity (m) Dimensionless Groups Re ) Reynolds number [(Ud/ν)] R 2 2 S ) swirl number ∫R 0 Fuwr dr/R∫0 Fu r dr Sc ) Schmidt number [(ν/DAB)] Sh ) Sherwood number [(kd/DAB)] Greek Letters θ ) vane angle at outer edge (deg) µ ) dynamic viscosity (kg m-1 s-1) ν ) kinematic viscosity (m2 s-1) F ) density (kg m-3) Subscripts and Superscripts a ) axial, annular av ) average e ) equivalent lim ) limiting o ) outer s ) swirl, surface conditions ti ) tangential inlet x ) axial w ) wall ∞ ) bulk conditions

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Received for review June 9, 1997 Revised manuscript received October 22, 1997 Accepted October 26, 1997X IE970411X

X Abstract published in Advance ACS Abstracts, December 15, 1997.