Electrochemical Mass Transfer in Impinging Swirl Jets

Ind. Eng. Chem. Res. 2009, 48, 1593–1602

1593

Electrochemical Mass Transfer in Impinging Swirl Jets Mehmet E. Arzutug˘* and Sinan Yapıcı ¨ niVersitesi, Mu¨hendislik Faku¨ltesi, Kimya Mu¨hendislig˘i Bo¨lu¨mu¨, 25240 Erzurum, Tu¨rkiye Atatu¨rk U

The local mass transfer coefficients between an impinging swirl jet flow and a flat circular surface in a cylindrical cell were measured by the electrochemical limiting diffusion current technique. Helical-type swirl generators were used to generate swirl flow with intensities in the range of S ) 0-0.73. The experiments were carried out for a jet Reynolds number range of 10 950-43 800, a nozzle-to-surface distance range of 2-10, and a dimensionless radial distance range of 0-15. The measured local mass transfer distributions in the radial direction exhibited an increase first and then a decrease and a converging behavior as the radial distance increased. It was observed that increasing Reynolds number increased the mass transfer rate, but its effect was reduced with an increase in swirl intensity. Increasing swirl intensity decreased transfer coefficients but increased their uniformity over the disk surface. The change in the nozzle-to-surface distance affected mass transfer coefficients up to a dimensionless radial distance of approximately r/dj < 8, and beyond this distance, they converged in almost one line, showing no effect of this parameter. Mass transfer correlations for Sherwood numbers whose average was taken over the surface and for Sherwood numbers at the stagnation point were developed as a function of the experimental parameters. Introduction Impinging jets are one of the techniques widely used in many engineering applications to improve convective heat/mass transfer rates, as high transfer rates occur between the jet flow and impingement surface. Conventional impinging jets, which generally consist of a circular nozzle, are also widely used in some engineering applications and industrial processes, notably in nuclear power stations needing cooling with high heat flux, for cooling microelectrical circuits, in systems that require fast surface drying, etc. Some experimental studies of heat/mass transfer have shown that important increases in heat/mass transfer rates can be obtained by conventional impinging jets.1-4 These jets give a transfer rate behavior that is higher around the stagnation point and then decreases exponentially in the radial direction. As a result, the distribution of local transfer rates in the radial direction exhibits quite a nonuniform distribution.1,3,4 Therefore, these jets are not suitable tools to increase transfer rates in processes for which both high and uniform heat/mass transfer distribution are required. A few papers that present the heat transfer characteristics of impinging swirl jets have been published in the literature. Ward and Mahmood5 determined the heat/mass transfer coefficients between an impinging swirl jet flow and a flat surface. They employed a swirl generator that consisted of a straight tube fitted with four tangential inlets to produce swirl jet flow, and they measured the convective transfer coefficients by a naphthalene sublimation technique. They reported that increasing swirl intensity decreased the heat transfer rate while the uniformity of distribution of local transfer rates increased. In another work, heat transfer and flow visualization experiments were conducted by Huang and El-Genk6 to investigate and compare the performance of swirl, multichannel, and conventional impinging jets. The swirl jet flow was obtained by using a swirl generator consisting of a tube and a solid swirl generator insert that had four narrow grooves machined on a cylindrical rod at a certain angle with the rod axis. They also observed a significant enhancement in the radial uniformity of the heat transfer, but * To whom correspondence should be addressed. Tel: (+90) 442 2314559. Fax: (+90) 442 2314544. E-mail: [email protected].

in contrast to the work by Ward and Mahmood,5 they found that the swirling impinging jets caused large increases in Nusselt number (Nu) compared to multichannel and conventional impinging jets. Lee at al.1 used the liquid crystal measurement technique, which provides an image of the surface isotherms, to investigate the effect of a swirl jet on the heat transfer from an impinging swirl jet flow to a flat surface. The researchers introduced the swirl flow into the main jet flow with vane-type swirl generators having different swirl intensities in the range of 0-0.77. They stated that the variation of Nu for S ) 0.77 at H/dj ) 10 is smallest within (15-20% of the average Nu in the entire region. Therefore, they concluded that this configuration can be utilized for the purpose of uniform heating/cooling applications. The heat transfer between a plate and an impinging swirl jet was studied by Bilen et al.3 They investigated the performance of swirl jets and a multichannel jet. Four screwlike grooves were machined on a rod at a desired angle with the rod axis to obtain swirl flow at the exit of the housing tube. They found that the local and mean Nusselt numbers measured on the plate in multichannel jets were generally higher than those of swirl jets. However, the swirl jets resulted in a significant improvement in radial uniformity of the heat transfer compared to the multichannel one. The heat transfer characteristics of an impinging swirl jet were experimentally studied by a combination of particle image velocimetry and laser-induced fluorescence technique for simultaneous measurement of the velocity and temperature fields.7 The study showed that the radial width of the jet stretches with increasing swirl intensity. At the stagnation region, the flow near the heated surface was mixed intermittently by reverse flows toward upstream, and the spatial distributions of the temperature are correlated with instantaneous velocity vector maps. The dynamic behavior of the recirculation zone which is attributed to the intensity of the swirl number and impinging distance, mainly determined the turbulent heat transfer at the stagnation region. Arzutug et al.4 measured the local mass transfer behavior between jet flow from a circular jet and a flat surface, and between jet flow from a multichannel jet and a flat surface, by employing the electrochemical limiting diffusion current tech-

10.1021/ie0715097 CCC: $40.75  2009 American Chemical Society Published on Web 01/12/2009

1594 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009

Figure 1. Schematic view of experimental rig: (1) cell; (2) nozzle; (3) connection for local cathodes; (4) storage tank; (5) cooling coil; (6) constant temperature circulator; (7) thermocouple; (8) digital temperature displayer; (9) flowmeters; (10) N2 meter; (11) ammeter; (12) voltmeter; (13) DC power supply; (14) data acquisition card; (15) computer; (16) pump; (17) gas distributor.

nique. Comparison of the results showed that the multichannel jet gave more uniform mass transfer distributions than those obtained by conventional jets. The above summarized literature clearly shows that most studies on impinging swirl jets have been mainly concentrated on heat transfer employing air as working fluid. No mass transfer study with a swirl jet system having liquid as the working fluid was spotted in the literature. Clarification of the detailed heat/ mass transfer behavior of impinging swirl jets is very important to determine the advantages and disadvantages of applying swirl jets into liquid systems and to control heating/cooling of surfaces and mass transfer between surface and flow field when high transfer rates are required. Therefore, a detailed investigation is necessary to determine mass transfer behavior in impinging swirl jet systems. The aim of this work is to perform a detailed mass transfer study for better understanding of the behavior of local mass transfer coefficients in impinging swirl jets. Experimental Section The experimental work was performed by using the experimental rig shown in Figure 1, which was designed and constructed by Arzutug et al.4,8 The entire piping system, including fittings, valves, and reservoirs, was made of materials such as polyethylene, acrylic, stainless steel, nickel, and Teflon, which are inert to the electrochemical solution. In addition, to avoid the effect of light on potassium ferrocyanide, the entire piping system was also isolated against light. Nozzle and Cell. The cell was made of a cylindrical pipe of polyethylene having an inner diameter of 360 mm and a height of 180 mm, and its top and bottom were covered with acrylic plates, as shown in Figure 2. The swirl jet system is shown schematically in Figure 3. Four exits from the cell provided circulation of the solution coming from the nozzle back to the reservoir. The nozzle (housing tube) was made of polyoxymethylene having an inner diameter of 8.5 mm and a length of 300 mm. The nozzle was attached to the center of the top cover so that the impinging point matches the center of the nickel cathode. To be able to change the distance between the exit of the nozzle and the impingement surface, a scaled screw system was designed to move the nozzle vertically at desired intervals. Swirl Generators. Swirl generators were manufactured by machining four helical grooves on a cylindrical rod at a certain angle to its axial direction and then inserting this four-channeled rod, whose diameter was approximately 8.4 mm, into the nozzle or housing tube, as shown in Figure 4. The inserts made of

Figure 2. Design of impinging swirl jet cell.

brass were electroplated with nickel to avoid the corrosive effect of the electrolyte. Photographs of the inserts and the angles of the grooves machined on the rod with the corresponding swirl numbers are shown in Figure 5. The swirl generator at zero angle with the jet axis is called the swirl generator with S ) 0 instead of the multichannel jet in the present work. Swirl number was calculated from the following equation given by Kerr and Frazer9 since there is a geometric similarity between the swirl generators of the present work and the ones used by them: S)

[

]

3 2 1 - (ri/ro) tan θ 3 1 - (r /r )2 i o

(1)

where θ is the angle between groove and rod axis (in degrees), ri is the radius of the inner hub, and ro is the outer radius of the swirl generator. Main and Local Cathodes. Twenty-one local cathodes of 99.98% nickel with a nominal size of 2 mm diameter were attached on the main cathode of 99% nickel (diameter 256 mm) by inserting the nickel wires into the holes of 2.2 mm. The local electrodes were positioned in a region from the impingement point to a radial distance of approximately 15dj, where dj is the inner diameter of the jet housing. An epoxy resin was used to isolate electrically the local cathodes from the main cathode and stick them into the hole. The local electrodes were flushed with the surface of the main cathode. The main cathode was mounted on the bottom of the cell, and only its upper surface was electrochemically active. The anode (diameter 340 mm), which was also made of the same nickel material as that of the main cathode, was attached just under the top cover of the cell. To ensure a cathodic-controlled process, both surfaces of the nickel anode were used for the electrochemical reaction. This gave a surface area for the anode approximately 3.5 times larger than that for the main cathode. Electrolyte. The electrolyte solution was a mixture of 5 mol m-3 potassium ferricyanide and 20 mol m-3 potassium ferrocyanide, with a supporting electrolyte of 500 mol m-3 sodium hydroxide. A-grade chemicals were used for preparation of the electrolyte. The concentration of potassium ferrocyanide was 4

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times higher than that of potassium ferricyanide to ensure a cathodic-controlled electrochemical process. To avoid the oxidizing effect of oxygen on potassium ferrocyanide, the solution was saturated by nitrogen and was kept under a nitrogen blanket during the experiments. The physical properties of the electrolyte with a Schmidt number (Sc) of 1690 were taken from Bourne et al.10 The measurement method for the local mass transfer coefficients is based on driving the electrochemical reaction to its maximum possible rate, which is controlled by the mass transfer of active ions to the cathode surface. This condition corresponds to a current plateau (limiting current) on a current-potential diagram. The reactions, which take place in the system, are the reduction of ferricyanide to ferrocyanide on the cathode and the oxidation of ferrocyanide to ferricyanide on the anode as follows: [Fe(CN)6]3- + e- f [Fe(CN)6]4[Fe(CN)6]4- f [Fe(CN)6]3- + e-

cathodic reaction anodic reaction

So, the concentrations of the active species in the electrolyte remain constant during the process. Procedure. Before each series of experimental measurements, all the precautions reported by Berger and Ziai11 were taken and the active areas of the local cathodes were determined by use of the Cottrell equation.12 It was determined that these precautions provided a reading from the local electrodes with a deviation within (3.4%. A stabilized DC power supply was employed to apply a potential across the electrodes, and a computer equipped with a data acquisition card was used for data recording together with a package program called Genie for data processing. The experiments were carried out at a temperature of 20 ( 0.5 °C. The average of measurements of the electrical currents taken for 40 s was used to calculate local mass transfer coefficients. The mass transfer coefficients were calculated from the following equation derived for the electrochemical limiting current diffusion conditions:13,14 k)

Ilim nFA(C∞ - CS)

Figure 3. Schematic representation of electrochemical impinging jet flow and electrochemical measurement system.

Figure 4. Design of swirl generator.

(2)

An error analysis, which was carried out according to the method given by Holman,15 indicated that the uncertainties involved in Sh, Re, and k were (15.32%, (12.65%, and (13.79%, respectively. Results and Discussion The effects of four parameterssjet Reynolds number Re () djumF/µ, where F is the electrolyte density and µ is electrolyte viscosity), swirl number S, nozzle-to-plate distance H/dj, and dimensionless radial distance r/djson the values and radial uniformity of local mass transfer coefficients, represented by the Sherwood number, Sh ) kdj/D, were investigated in the present work. The experiments were carried out for a jet Reynolds number range of 10 950-43 800, a nozzle-to-plate distance range of 2-10, a swirl number range of 0-0.73, and a dimensionless radial distance range of 0-15. Effect of Reynolds Number. The effect of Re on the distribution of local mass transfer coefficients is shown in Figure 6 for H/dj ) 4 and S ) 0. As seen in Figure 6a for S ) 0, an increase in Re increases the transfer coefficients. The radial distribution of coefficients exhibits an increasing behavior first, and then a decreasing and converging behavior as the radial distance increases. It gives two peaks at low swirl intensities,

Figure 5. Photos of nickel-plated swirl generators.

one for radial distances r/dj of 0-2 and the other at approximately r/dj ) 4. The location of the second maximum remains almost unchanged with increasing Re. For different Re values, the mass transfer coefficients are presented in Figure 6b-e for swirl jets with S ) 0.26, 0.43, and 0.73. For H/dj ) 4, the radial distributions of coefficients exhibit an increasing behavior up to the location of a peak value at first, and then decreasing and converging behavior as the radial distance increases. The distributions of transfer coefficients for swirl jets with different S values have similar


Figure 6. Effect of Re on radial distribution of local mass transfer coefficients for swirl jets with different swirl intensity and H/dj.

behavior; they exhibit minimum mass transfer at the stagnation region, increase with increasing dimensionless radial distance up to a peak value, and then decrease by exhibiting a tendency to converge. For S ) 0.26, the distribution shows a bit more complicated behavior, especially at higher Re values. However, the effect of Re on mass transfer decreased with increasing S, and almost no increase in the mass transfer was observed for S ) 0.73 with increasing Re; all values converged in almost one line at H/dj ) 4. The increasing effect of Re becomes

more visible at constant S as H/dj increased. This behavior can be explained by the jet flow radially spreading rather than impinging directly on to surface with increasing S, which produces a higher tangential velocity component than the axial one. In addition, high swirl intensities can produce a recirculation region, as reported by Lee at al.,1 Chigier,16 and Ward and Mahmood,5 which is effective especially at small H/dj values and can have a decreasing effect on the mass transfer. With increasing Re, the difference between the mass transfer coefficients in the stagnation region and


Figure 7. Effect of swirl intensity on radial distribution of local mass transfer coefficient for swirl jets with different H/dj at Re ) 29 780.

those in the peak values also increased for all swirl intensities. The location of the peak values generally shifted as H/dj values increased. Effect of Swirl Intensity. Figure 7 shows the effect of S on the radial distribution of mass transfer coefficients on the impingement surface for different H/dj values at Re ) 29 780. As seen from this figure, the distribution for the jet with S ) 0 exhibits some fluctuations around r/dj ) 0.24, 1.76, and 3.86 and then smoothly decreases, converging to a certain value together with the distributions for jets having different swirl intensities. These fluctuations, which are seen for the whole

range of H/dj in the present work and also seen in the works by Bilen et al.3 and Lee et al.,1 can be caused by the wall of grooves and the central hub of the jet. The jet with S ) 0 always gave higher coefficients than the other jets having swirl intensity different from zero; the mass transfer coefficients decreased but their uniformity over the impingement surface increased with increasing swirl intensity. Higher transfer coefficients for the jet having S ) 0 can be attributed to direct impingement of the jet flow, which has mainly axial momentum onto the surface.


Figure 8. Effect of H/dj on radial distribution of local mass transfer coefficient for swirl jets with different swirl intensities at Re ) 10 950.

The mass transfer distribution for jets with finite swirl intensity exhibits a behavior with a maximum at a dimensionless radial distance between approximately 2 and 6 and then decreases with increasing radial distance. The reason for this maximum behavior can be the occurrence of the impingement regions away from the stagnation point at the center of the disk due to the geometry of the swirl generators.3 The location of the maximum mass transfer coefficients shifted radially outward in the rangeH/dj ) 6-10 with increasing swirl intensity, while it exhibited no clear shift for H/dj ) 2-4; all occurred at a dimensionless radial distance of approximately 0.7-6.0. As seen in Figure 7, around the stagnation region, the jet with S ) 0.43 is generally much more effective than the one with S ) 0.26 in producing higher local mass transfer coefficients up to the location where the maximum value takes place for H/dj ) 2-8. Beyond this point, the values of the coefficients for S ) 0.43 and 0.26 are almost the same for H/dj ) 2-4. Among all jets except the one with no swirl, the jet with S ) 0.43 exhibited the highest maximum values except for the case of H/dj ) 10, for which the jet with S ) 0.26 had the highest maximum value. Generally speaking, the mass transfer coefficients decreased with increasing swirl intensity. All the distributions exhibited a tendency to converge toward the edge of the disk at a given Reynolds number. However, they exhibited some irregular behaviors when the distributions for swirl intensity of 0.26 and 0.43 were considered; for some cases, the jet with S ) 0.43 gives higher coefficients than the one with S ) 0.26.

When it comes to energy considerations, the power input will increase as the swirl intensity gets higher, because higher swirl intensity produces more pressure drop. Therefore, for the same Reynolds number, higher pumping power input is required when the swirl intensity increases. In the present work no pressure drop measurement was taken; however, for the effect of increasing swirl intensity on the pressure drop and energy considerations for the similar swirl generators, the interested reader can refer to works by Yapıcı et al.17 and Yapıcı.18 Effect of Dimensionless Nozzle-to-Plate Distance. Figure 8 shows the distribution of local mass transfer coefficients for different H/dj values at Re ) 10 950. As seen from this figure, the effect of H/dj on mass transfer coefficients is more pronounced at radial distances of approximately r/dj < 8. After this distance, all values converged to almost one line, showing no effect of H/dj on mass transfer. For all swirl intensities, the coefficients increased with decreasing H/dj for dimensionless radial distances between approximately 0 and 8. The highest mass transfer distribution was obtained for the jet with H/dj ) 2 for all swirl intensities. The maximum values occurred at a position of approximately r/dj ) 0.5 for S ) 0 for all H/dj values. In a conventional impinging jet system with a complete circular cross section, the position of the maximum coefficient is expected to be at the stagnation point. The shift of the maximum values from the stagnation point can be explained by the fact that the nozzle used in the present work has a hub in the center. For S ) 0.26, the location of the maximum value shifted outward from r/dj


Figure 9. Effect of H/dj on radial distribution of local mass transfer coefficient for swirl jets with S ) 0.43 at Re ) 29 780.

Figure 10. Comparison of local Nusselt numbers for circular impinging jets from the present work8 with literature values for Re ) 19 270-23 000 and H/dj ) 10.

) 2 to 6 as H/dj increased. These shifts range from 1.2 to 4.5 for S ) 0.43 and from 1.2 to 6.2 for S ) 0.73 at Re ) 10 950. When Re was increased to 29 780 at S ) 0.43, the shift of the maximum coefficient location was effected, showing a bit more shift outward up to a dimensionless radial distance of approximately 5, with higher mass transfer values, as seen in Figure 9. In general, the location of the peak values shifted outward with increasing H/dj and Re. Comparison and Discussion of Distributions of Transfer Coefficients. Although the impinging jets in heat transfer studies have exhibited a wide range of diversity, some convective local transfer measurements of the heat and mass transfer for especially circular impinging jets are given in Figures 10 and 11 in the form of local Nusselt numbers versus jet Reynolds number for confirmation of the accuracy of measurements in the present work. The conversion from Sh to Nu was performed by using heat-mass transfer analogy. As seen from these figures, the measurements taken from the same experimental rig of the present work4,8 show a good agreement with the results from the literature1,19-21 although the values of Reynolds number and dimensionless distance of nozzle-to-impingement surface are not the same; some of them were confined jets and some were unconfined, and the geometry of circular jets is not the same. Swirl flow is one of the most complex flows encountered in fluid mechanics, and its classification can be found elsewhere.22,23 The swirl flow characteristics depend on various factors such as system geometry and especially the methods of generating swirl. There is no standard way of designing swirl generators,

Figure 11. Comparison of local Nusselt numbers for circular impinging jets in the present work4 with literature values for Re ) 10 950-14 000 and H/dj ) 8-10.

but a general classification of the methods of generating swirl into three main categories can be found in the literature.24,25 When some swirl generating methods used only in impinging swirl jets in the literature1,3,5,6,22 are considered, it is seen that almost all of them have different geometrical specifications. The swirl generators used by Bilen et al.3 are very similar to the ones employed in the present work. Their work gives an important clue about the heat transfer characteristics of swirl jet flow. They measured heat transfer behavior in an impinging swirl jet flow, employing the liquid crystal technique, thus getting a temperature contour of the whole impingement surface, as shown in Figure 12. These photographs show that, in swirl jet flow, each groove on the swirl generator tends to behave as an individual jet and forms a separate impingement region depending on S, Re, and H/dj, while the four-channeled jet with no swirl behaves as if it were a single circular jet. In other works and the present work, local measurements were given for a line starting from the stagnation point at the disk center up to a certain radial distance. Although Ward and Mahmood5 employed the naphthalene sublimation technique and Lee et al.1 employed the liquid crystal technique for measurement of transfer coefficients, they do not give any information about detailed behavior of the transfer coefficients on the whole impingement surface. In these works, the swirl flow was accepted to be symmetrical and, therefore, resulted in a distribution type of the local transfer coefficients as shown in Figure 12c. In this case, the distribution from the center up to a given radial distance on the impingement surface does not change with angular position. However, in reality the flow can be quite unsymmetrical due to the wall of the inserts, vanes, grooves, slots, and hub in swirl generators, as given in Figure 12d. One can easily see that the behavior of the local transfer coefficients measured by sensors depends on the angular position at which the sensors are attached; for example, along the ways shown as I, II and III in Figure 12d. However, in general it can be expected that they exhibit similar behavior, increasing first up to a position corresponding to a maximum value and then decreasing with radial distance. When it comes to the distribution of local mass transfer coefficients, the minimum at the impingement point or the first peak can be explained by the presence of the central hub of the swirl generator, which avoids the occurrence of maximum local axial jet velocity at the center of the jet axis. Therefore, the maximum transfer rate occurs at a radial position on the impingement surface corresponding to the impingement position of the local maximum axial jet velocity of the individual groove. The high turbulence intensity at the nozzle edge and central


Figure 12. Liquid crystal photographs3 of impingement surface in (a) normal four-channeled jet and (b) four-channeled swirl jet, and (c, d) their representative temperature contours.

hub can also significantly contribute to the occurrence of the first maximum.26 In addition, the possibility of flow recirculation at the center of the jet flow can also result in a decrease in transfer rate at the impingement point. There is no general rule for the occurrence of reverse flow or recirculation because various factors such as the method of generating swirl, flow rate, and swirl intensity have an influence.23 However, as swirl number increases, the radial spread of the jet increases, and for jets with swirl number greater than a critical value, the forces due to the axial adverse pressure gradient exceed the forward kinetic forces. As a result, the flow reverses its direction in the central region of the jet.16 This phenomenon can also cause a reduction in the transfer rate at the stagnation region. The spread of the jet flow outward in the radial direction as the swirl number increases can be the reason for the shift in position of the maximum transfer coefficients with increasing swirl intensity. This phenomenon also results in the shift of these maxima outward as jet-to-disk distance is increased since the jet flow starts at the nozzle exit enlarging its area and it flows axially toward the impingement surface. The second maximum observed in all mass transfer distributions can be attributed to the transition from laminar to turbulent boundary layer in the spreading wall jet as suggested by Lee and Lee.26 The reduction in the effect of increasing Reynolds number on mass transfer with increasing swirl number can be attributed to an increasing tangential velocity component. In this case, the jet flow spreads more outward, affecting the sidewalls more instead of directly impinging onto the disk surface as the swirl number is increased. Transfer Coefficients at Stagnation Point. Figure 13 shows the behavior of the stagnation point Sherwood number (Shst) at r ) 0 with changes in S and H/dj. The highest value at this point belongs to the jet with no swirl. As the swirl intensity

Figure 13. Effect of swirl intensity and H/dj on Sh at r ) 0 and Re ) 19 270.

increases, the mass transfer at the disk center shows a general tendency to decrease for all H/dj values, except for the swirl intensities of 0.26 and 0.43 at H/dj ) 2-8 and 10. This behavior can be explained by the decrease in axial momentum with increasing S, reducing the effect of direct impingement of the jet flow on the disk surface.27 For the jet with S ) 0.43, higher values of Shst than those for S ) 0.26 were obtained. In the range of 5 e H/dj e 10, the distributions of Shst for the jets having S ) 0.43 and 0.26 intersect between H/dj ) 6 and 8. The jet with highest swirl intensity, which is S ) 0.73, gave the lowest Shst distribution. The decrease in Shst with increasing swirl intensity for the same H/dj may be associated with the corresponding reduction in jet arrival axial velocity and in axial momentum at the impinging surface. In general, this figure


Figure 14. (a) Effect of jet-to-impingement surface distance on Nu for different swirl intensities at Re ) 23 000.1 (b) Effect of jet-to-impingement surface distance on heat transfer coefficient for different swirl intensities.5

Figure 15. Correlation of experimental Sh values averaged over disk surface.

exhibited similar results, obtaining the highest Nu distribution for the jet with no swirl, as seen in Figure 14a. Ward and Mahmood5 also reported that the highest heat transfer coefficients occurred for S ) 0, as shown in Figure 14b. The differences in the results of Lee et al.1 for the case with no swirl and S ) 0 comes from the definition of the generators. They referred to the empty jet as no swirl and to the jet having straight grooves with no angle as S ) 0. The turbulence caused by the groove walls and central hub for the jet with S ) 0 can give higher transfer coefficients than the jet with no swirl. When it comes to the change in maximum transfer coefficients with the jet-to-surface distance at a given swirl intensity, the coefficients generally decreased with jet-to-surface distance for the present work. The same behavior was observed for S > 0.24 by Lee et al.1 and Ward and Mahmood.5 But for the case where S < 0.24, Lee et al.1 observed maximum values at a dimensionless jet-to-surface distance of about 6, while Ward and Mahmood5 observed maxima at around 4. Correlation of Results. An empirical correlation was developed for mean Sh over the disk surface as a function of Re, H/dj, and (1 + S) for the range of the parameters employed in the present work. The following equation, for which the dependence of Sh on Sc was accepted to be Sc1/3, was obtained, and the results are presented graphically in Figure 15. Shav ) 0.057Re0.63(H/dj)-0.05(1 + S)-1.19Sc1/3

(3)

2

In this statistical analysis, the value of R was calculated to be 0.92. Another empirical correlation was developed for Shst as a function of Re, H/dj, and (1 + S): Shst ) 2.74Re0.37(H/dj)-0.28(1 + S)-1.75Sc1/3

(4)

2

Figure 16. Correlation of experimental Sh values at stagnation point.

shows that Shst has a strong dependency on the swirl intensity and a weaker dependency on H/dj, especially when S increases. Similar behaviors were observed by Lee at al.1 and Ward and Mahmood.5 The results for the stagnation point from the work of Lee at al.,1 who used the same H/dj values as the present work,

In this case, the value of R was found to be 0.91, and the correlation is given graphically in Figure 16. It should be expressed that the correlations developed here hold for the conditions of the present work for the reasons mentioned above, in the section about comparison of distributions and of transfer coefficients. Conclusions The general conclusions from this work can be summarized as follows:


• Radial distributions of the local mass transfer coefficients exhibited increasing behavior up to a location at which the coefficient had a maximum value at first, and then decreasing and converging behavior as radial distance increased. • With increasing Re, the difference between coefficients in the stagnation region and the maximum values increased for all swirl intensities, and the location of peak values shifted radially outward as H/dj values increased. • Increasing Re had an increasing effect on mass transfer, but its effect was diminished with increasing swirl intensity; almost no effect of Re was observed with the swirl generator having S ) 0.73. • Transfer coefficients decreased but the uniformity of their distribution increased with increasing swirl intensity. • When average transfer coefficient was considered, the jet with S ) 0 gave higher values than those with S * 0. • Some fluctuations were observed around the stagnation point for all swirlers. • The effect of H/dj on mass transfer coefficients was observed for radial distances up to approximately r/dj < 8. Beyond this distance, all the values converged to almost one line, showing no effect of H/dj. • When one needs high mass transfer rates together with a uniform mass transfer distribution on the surface, the swirl jet with S ) 0.26 or 0.43 can be a good alternative. • Due to the complexity of swirl flow, the variety of swirl generating methods, and the differences in geometry of flow system and swirl generator, it is difficult to make a precise comparison between literature results on heat/mass transfer in impinging swirl jets, but a general comparison can be done. Acknowledgment This research was sponsored by the Atatu¨rk University Research Foundation under Contract 1997/45. Especially, the help of Professor Adnan Derdiyok for the measurement of data by a computer via data acquisition card is appreciated. Nomenclature A ) active electrode surface (m2) C∞ ) bulk concentration of reacting species (mol/m3) CS ) surface concentration of reacting species (mol/m3) D ) diffusion coefficient (m2/s) dj ) jet diameter (m) d ) diameter of main cathode disk (m) F ) Faraday constant (96 485 C/mol) H ) distance between jet exit and impingement surface (m) h ) heat transfer coefficient (W/m2 · °C) Ilim ) electrochemical limiting current (A) k ) mass transfer coefficient (m/s) kf ) thermal conduction coefficient (W/m · °C) n ) electron number associated with electrochemical reaction R ) correlation coefficient r ) radial distance, radius (m) um ) mean flow velocity in nozzle (m/s) S ) swirl intensity ) 2/3{[(1 - (ri/ro)3]/[1 - (ri/ro)2]} tan θ Re ) jet Reynolds number (djumF/µ) Sc ) Schmidt number (µ/FD) Sh ) Sherwood number (kdj/D) Nu ) Nusselt number (hdj/kf)

Literature Cited (1) Lee, D. H.; Won, S. Y.; Kim, T. T.; Chung, Y. S. Turbulent Heat Transfer from a Flat Surface to a Swirling Round Impinging Jet. Int. J. Heat Mass Transfer 2002, 45, 223.

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ReceiVed for reView November 6, 2007 ReVised manuscript receiVed October 24, 2008 Accepted November 4, 2008 IE0715097

Electrochemical Mass Transfer in Impinging Swirl Jets

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