4354
Ind. Eng. Chem. Res. 1996, 35, 4354-4359
Effect of Surface Roughness Induced by Woven Metallic Screens Wrapped on the Inner Surface of an Annulus on the Rate of Turbulent Flow Mass Transfer M. M. Zaki† and I. Nirdosh* Department of Chemical Engineering, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1
G. H. Sedahmed Department of Chemical Engineering, Alexandria University, Alexandria, Egypt
Rates of mass transfer were measured at the inner surface of an annulus wrapped with a woven metallic screen under developing flow conditions using an electrochemical technique which involved measuring the limiting current of the cathodic reduction of potassium ferricyanide. Variables studied were screen characteristics, solution velocity, and physical properties of the solution. Mass-transfer rates based on the projected area of the annulus were found to increase by a factor ranging from 1.2 to 3 depending mainly on Re. The degree of mass-transfer enhancement was found to decrease with an increase in Re. Rates of mass transfer based on the true active area of the annulus and the screen were found to be smaller than the values at the smooth surface, the higher the Re the higher being the percentage decrease in the rate of mass transfer compared to the values at the smooth annulus. Practical implications of the present work in the design and operation of catalytic and electrochemical reactors used to conduct diffusion-controlled reactions have been highlighted. Introduction
Experimental Techniques
The effect of surface roughness on the rates of heat and mass transfer under fully developed flow has been the subject of many studies in order to improve the performance of industrial heat- and mass-transfer equipment.1-4 In these studies, different patterns of roughness were imparted to the transfer surface by machining. Creating surface roughness by machining is laborious and expensive especially for hard and refractory alloys. The objective of the present work was to explore the possibility of using woven metallic screens overlaid on the transfer surface as a means for enhancing the rate of mass transfer under turbulent flow conditions. The use of woven plastic screens (inactive) as turbulent promoters to enhance the rate of mass transfer under laminar flow conditions has been studied by Kim et al.5 and Winograd et al.6 Gabe and Makanjuola7 studied the effect of surface roughness induced by woven metallic screens on the rate of turbulent flow mass transfer at a rotating cylinder coated with the screen. In view of the industrial importance of the short annuli in the design of heat- and mass-transfer equipments such as double tube heat exchangers, dialyzers, and electrochemical reactors used to conduct diffusioncontrolled reactions, the present study was undertaken to investigate the rate of turbulent flow mass transfer at the inner surface of an annulus under developing flow. The rate of mass transfer was measured by an electrochemical technique which involves measuring the limiting current of the cathodic reduction of potassium ferricyanide. The technique has the advantage that the rough surface remains unaltered during experiments.
The experimental apparatus is shown in Figure 1 and consisted of a 30 L Plexiglass storage tank, a plastic centrifugal pump, a vertical annular cell, and the electrical circuit. The annular cell consisted of a 4.7 cm inside diameter and 50 cm long outer stainless steel tube which acted as an anode and an inner nickel-plated copper cylinder of 2.5 cm diameter and 50 cm length, out of which only the first 20 cm was used as a cathode and the remaining upper 30 cm was insulated with a Teflon tape. Roughness to the smooth cathode was induced by wrapping it with a sleeve of a nickel-plated stainless steel screen of 20 cm length. Five different screens of mesh numbers, respectively 10, 14, 20, 30, and 40 wire/in., were used. The screen characteristics are given below in Table 1. The anode and cathode were held coaxially in position using Plexiglass inlet and outlet sections. The stainless steel tube was connected to the inlet and outlet sections by threading. A 1.5 cm diameter Plexiglass entrance nozzle positioned on the center line of the annulus perpendicular to the annular flow was used; i.e., the flow in the annulus was an axial-developing turbulent flow. The outlet section was fitted with a similar tube. The electrical circuit consisted of a multirange ammeter and a 10 V dc power supply with a voltage regulator connected in series with the annular cell. A highimpedance voltmeter was connected in parallel with the cell to measure the cell voltage. The measuring accuracies were 1 µA for current and 0.1 mV for voltage. In view of the high anode area compared to the cathode area, the anode was used as a reference electrode against which the cathode potential was measured in constructing the current-voltage curves from which the limiting current was obtained. This obviated the need for an external reference electrode. A total of 20 L of electrolyte was circulated between the Plexiglass stor-
* To whom correspondence should be addressed. † Permanent address: Department of Chemical Engineering, Zagazig University, Zagazig, Egypt.
S0888-5885(96)00215-1 CCC: $12.00
© 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4355
Figure 1. (a) Apparatus: (1) valve, (2) storage tank, (3) centrifugal pump, (4) rotameter, (5) nickel-plated copper cylinder coated with screen (cathode), (6) stainless steel pipe (anode), (7) dc power supply, (8) Plexiglass inlet section, (9) Plexiglass outlet section, (10) insulated part of the cathode cylinder, (11) bypass. (b) Contact between the screen and the surface of the inner cylinder. Table 1. Screen Parameters wire mesh no. diameter aperture, (wire/in.) (cm) a (cm) porosity 40 30 20 14 10
0.0254 0.033 0.0356 0.0508 0.0508
0.042 0.059 0.084 0.141 0.2
0.667 0.665 0.767 0.746 0.823
RH (cm) 0.051 0.0656 0.117 0.149 0.236
surface area area/cylinder (cm2) area 414 427 292 330 219
2.62 2.7 1.85 2.1 1.39
age tank and the cell. The solution was 0.025 M each in ferricyanide and ferrocyanide of potassium dissolved in a large excess of sodium hydroxide as the supporting electrolyte. Three different sodium hydroxide concentrations were used, namely, 1, 2, and 4 M. All solutions were prepared using deionized water and A.R.-grade chemicals. Before each run dissolved oxygen was removed from the solution by bubbling nitrogen gas, and nitrogen bubbling was maintained during each experiment to prevent the interference of oxygen reduction at the cathode with the reduction of ferricyanide. Cathodes were activated before each run by allowing electrolytic H2 to evolve on the cathode from a sodium hydroxide solution under conditions mentioned elsewhere.8 Current-voltage curves from which the limiting current was determined were constructed by increasing the current stepwise and measuring the corresponding cell voltage. Flow velocities ranging from 30 to 90 cm/s were regulated by means of a bypass and were measured by a rotameter. During experiments, temperature was adjusted at 25 ( 1 °C by passing cold water through a stainless steel cooling coil immersed in the Plexiglass storage tank. Each run was repeated once or twice. Physical properties of the solution used in data correlation were taken from the literature.9 The area of the screen was calculated from the number of apertures per linear centimeter and the wire diameter using the method of Armour and Cannon.10 Results and Discussion Figure 2 shows typical current-potential curves with well-defined limiting current plateaus. The masstransfer coefficient was calculated from the limiting current using the equation
K ) I/zFAC
(1)
Following previous studies on the effect of surface roughness on the rate of heat and mass transfer, the projected area of the inner cylinder cathode rather than
Figure 2. Typical polarization curves obtained using a cylinder roughened by a 20 mesh screen.
Figure 3. Comparison of the present data for a smooth cylinder with previous data obtained under developing flow conditions.
the true surface area was used in calculating the masstransfer coefficient at the inner rough surface of the annulus. Rai et al.11 obtained the following equation for mass transfer at smooth annuli under axially developing turbulent flow conditions similar to that used in the present work by correlating the experimental data of Singh et al.12
[
Sh ) 0.032 1 +
( )] d L
2/3
Re0.8Sc0.33
() do di
0.53
(2)
The above equation correlates data for Re > 6000 and L/d e 7 with an average deviation of (15%. Figure 3 shows a comparison between the present mass-transfer
4356 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Figure 4. Effect of flow velocity on the mass-transfer coefficient at different cylinder roughnessess for three different Sc.
data at the smooth surface and the above equation and indicates a reasonable agreement between the two. The negative deviation of the present data from the above equation at high Re may be attributed to the fact that the data used to derive the above equation were experimentally obtained by Singh et al.12 for the dissolution of the benzoic acid cylinder in water. This technique suffers from the shortcoming that, under the influence of the high shear stress which prevails at high Re, benzoic acid attrition may take place along with benzoic acid dissolution, thereby leading to exaggerated rates of mass transfer. Figure 4 shows that the presence of screens on the smooth annulus increases the mass-transfer coefficient (K) over that of the smooth annulus by a factor ranging from 1.2 to 3 depending on Re and screen parameters. Figure 5 shows that the degree of enhancement defined as the ratio of the mass-transfer coefficients for the rough and smooth annuli, respectively (Kr/K), decreases with increasing Re. Figure 5 also shows that the sensitivity of the degree of enhancement to screen parameters decreases with increasing Re.
Figure 5. Effect of Re on the enhancement ratio (Kr/K) at different Sc (Kr is based on the projected area of the cathode).
The present increase in the rate of mass transfer caused by the presence of the screens on the smooth surface may be attributed at first sight to the increase in the active area of the annulus and eddy formation downstream of the screen wires normal to the flow as a result of boundary layer separation. To elucidate the relative contribution of the surface area increase and hydrodynamic conditions to the mass-transfer enhancement, the surface area effect was eliminated by calculating the mass-transfer coefficient using the true total area of the screen and the smooth annulus. Figure 6 shows that the presence of screen wrapping
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4357
Figure 6. Effect of Re on the enhancement ratio (K′r/K) at different Sc (K′r is based on the true area of the screen and the cylinder).
on the annulus reduces the mass-transfer coefficient K′r (based on the true area) below that of the smooth surface. This result may be explained tentatively as follows: 1. It is probable that the solution wetting the contact area between the screen and the smooth surface is not well mixed, owing to the inaccessibility of this area to the bulk solution. 2. According to previous studies13-15 conducted to elucidate the nature of flow over a rough surface consisting of cavities cut in the smooth surface normal to the direction of flow, an entrapped slowly rotating vortex would form in the cavities and separate the cavity
bottom and sides from the main stream outside the cavity. The formation of the vortex inside the cavity would increase the resistance to the rate of mass transfer, owing to the presence of a thick diffusion layer at the cavity bottom and walls and another diffusion layer between the vortex and the main stream at the cavity mouth. Alkire et al.,18 who measured the rate of mass transfer at the bottom of a small rectangular cavity in the wall of a rectangular duct through which solution was flowing, found that the mass-transfer coefficient at the cavity bottom decreases with increasing cavity depth to an exponent of -0.83. Aggarwal and Talbot,19 who measured the rate of mass transfer inside a semicylindrical cavity machined in the wall of a rectangular duct under forced convection, found that the mass-transfer coefficient inside the cavity is less than the flat surface value by about 25%. In view of this picture it follows that the rate of mass transfer within the screen pores should be less than the value at the interface between the screen and the main stream where some enhancement may take place as a result of boundary layer separation downstream of the screen wires normal to the flow. The decrease in the enhancement ratio Kr/K with increasing Re agrees with the finding of Ross and Badhwar,16 Berger and Hau,17 and Gabe and Makanjuola,7 who found that Kr/K decreases with increasing bulk turbulent intensity. It would be of interest to relate the enhancement ratio Kr/K to the dimensionless roughness height which determines the position of the roughness elements with respect to the hydrodynamic boundary layer. The dimensionless roughness height, e+, was calculated in terms of the functional velocity u*. In view of the difficulty of measuring the pressure drop across the short section used in the present work using a simple manometer, the friction factor (f) needed to calculate the friction velocity at the rough surface was approximately determined from the Moody diagram.20 The peak to valley height of the roughness elements was taken as twice the screen wire diameter (screen thickness). The fact that the present flow is developing while the Moody diagram represents data for a fully developed flow does not incur significant error in the friction coefficient which changes slowly after a distance equal to twice the annulus equivalent diameter from the inlet.20 Figure 7 shows that the enhancement ratio Kr/K decreases with increasing e+. This is consistent with the fact that the present data lie in the fully rough region (e+ > 30) where the roughness elements extend in the turbulent boundary layer.2 In the fully rough region bulk turbulence becomes more influential in enhancing the rate of mass transfer compared to the turbulence generated downstream of the roughness elements as a result of boundary layer separation. This result agrees with the results of other researchers, who used other patterns of surface roughness.1-4 It is also noteworthy that for a given e+ the degree of masstransfer enhancement increases with increasing Sc, and this may be attributed to the following: With increasing Sc, the kinematic viscosity (ν) increases while the molecular diffusivity of the transferring substrate (D) decreases. The high value of ν leads to decreasing the value of e+ (e+ ) eu*/ν) with a consequent increase in the enhancement ratio as shown in Figure 7. The decrease in D at high Sc makes the rate of diffusion which controls the rate of mass transfer across the diffusion layer more sensitive to eddies which
4358 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Figure 8. Overall mass-transfer correlation at rough surfaces.
but the dimensionless parameter RH/a was found to give the best fit. Conclusions The mass-transfer coefficient based on the projected cathode area is increased by the presence of roughness generating screens on the smooth annular surfaces by a factor of 1.2-3. The ratio of the mass-transfer coefficients at rough to smooth surface, however, decreases with increases in Reynolds number and the dimensionless roughness height. The results can be expressed as an empirical dimensionless correlation involving the ratio of the mass-transfer coefficients for rough and smooth surfaces, Reynolds number, and the ratio of the screen hydraulic diameter and aperture. The equation can be used in the design and operation of heat exchangers, catalytic and electrochemical reactors used to conduct diffusion-controlled reactions, e.g., electrochemical effluent treatment to remove toxic ions, and electroorganic and electroinorganic syntheses. Acknowledgment
Figure 7. Effect of the dimensionless roughness height on the relative mass-transfer coefficient at different screen geometries for different Sc.
penetrate the diffusion layer. The present effect of Sc agrees qualitatively with the previous studies.2,3 An overall mass-transfer correlation was envisaged to correlate the present data in terms of the dimensionless groups Kr/K, Re, and the screen parameter RH/a. Figure 8 shows that the data for the conditions 1585 < Sc < 5676 and 2580 < Re < 18 900 fit the equation:
K/Kr ) 0.0016Re0.62(RH/a)-0.116
(3)
with an average deviation of (2%. The hydraulic radius of the screen RH is defined as the ratio between screen porosity and the area density of the screen. The porosity is defined as the ratio of the total void space of the screen to the total screen volume. The area density is the ratio of the total screen surface area to the total screen volume, where the total screen volume is taken as the product of the screen frontal area and the screen thickness. The screen thickness is either measured directly or assumed equal to twice the wire diameter. In obtaining eq 3, different screen parameters were tried
Financial support for this research was provided by the Natural Sciences and Engineering Research Council of Canada. Thanks are due to Messrs. R. Mazzaferro and E. Drotar of the Lakehead University Science Machine Shop for making the apparatus. List of Symbols a ) screen aperture A ) surface area C ) ferricyanide concentration d ) equivalent diameter of the annulus (do - di) do ) outer diameter of the annulus di ) inner diameter of the annulus D ) diffusivity of ferricyanide ion e ) roughness height e+ ) dimensionless roughness height (eu*/ν) f ) friction factor F ) Faraday’s constant I ) limiting current K ) mass-transfer coefficient at the smooth surface Kr ) mass-transfer coefficient at the rough surface based on the projected cathode area K′r ) mass-transfer coefficient at the rough surface based on the true area of the screen and cylinder RH ) screen hydraulic radius Re ) Reynolds number (FVd/µ) Sc ) Schmidt number (µ/FD) Sh ) Sherwood number (Kd/D)
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4359 u* ) friction velocity (Vxf/2) V ) solution velocity Greek Symbols F ) solution density µ ) solution dynamic viscosity ν ) solution kinematic viscosity
Literature Cited (1) Postlethwaite, J.; Lotz, U. Mass Transfer at ErosionCorrosion roughened surfaces. Can. J. Chem. Eng. 1988, 66, 75. (2) Dawson, D. A.; Trass, O. Mass Transfer at rough surfaces. Int. J. Heat Mass Transfer 1972, 15, 1317. (3) Grimanis, M.; Abedian, M. Turbulent Mass Transfer in Rough Tubes at High Schmidt Numbers. Physicochem. Hydrodyn. 1985, 6, 775. (4) Sedahmed, G. H.; Shemilt, L. W. Forced Convection Mass Transfer at Rough Surfaces in Annuli. Lett. Heat Mass Transfer 1976, 3, 499. (5) Kim, W. S.; Park, J. K.; Chang, H. N. Mass Transfer in a Three Dimensional Net-type Turbulent Promoter. Int. J. Heat Mass Transfer 1987, 30, 1183. (6) Winograd, Y.; Solan, A.; Toren, M. Mass Transfer in Narrow Channels in the Presence of Turbulence Promoters. Desalination 1973, 13, 171. (7) Gabe, D. R.; Makanjuola, P. A. Enhanced Mass Transfer Using Roughened Rotating Cylinder Electrodes in Turbulent Flow. J. Appl. Electrochem. 1987, 17, 370. (8) Selman, J. R.; Tobias, C. W. Mass Transfer Measurement by the Limiting Current Technique. Adv. Chem. Eng. 1978, 10, 211. (9) Bourne, J. R.; Dell’Ava, P.; Dossenbach, O.; Post, T. Densities, Viscosities and Diffusivities in Aqueous Sodium HydroxidePotassium Ferri- and Ferrocyanide Solutions. J. Chem. Eng. Data 1985, 30, 160.
(10) Armour, J. C.; Cannon, J. N. Fluid Flow Through Woven Screens. AIChE J. 1968, 14, 415. (11) Rai, B. N.; Sinha, A. K.; Ghosh, U. K.; Gupta, S. N.; Upadhyay, S. N. Forced Convective Mass Transfer in Annuli. Chem. Eng. Commun. 1988, 68, 15. (12) Singh, S. K.; Upadhyay, S. N.; Tripathi, G. Mass Transfer from Cylinders to Parallel Flowing Water Streams. Ind. Chem. Eng. 1971, 13, 161. (13) Townes, H. W.; Sabersky, R. H. Experiments on the Flow Over a Rough Surface. Int. J. Heat Mass Transfer 1966, 9, 729. (14) Knudson, J. G.; Katz, D. L. Heat Transfer and Pressure Drop in Annuli. Chem. Eng. Prog. 1950, 46, 10. (15) Maull, D. J.; East, L. F. Three Dimensional Flow in Cavities. J. Fluid Mech. 1963, 16, 620. (16) Ross, T. K.; Badhwar, R. K. The Effect of Surface Roughness Upon Electrochemical Processes. Corros. Sci. 1965, 5, 29. (17) Berger, F. P.; Hau, K. F. Local Mass/Heat Transfer Distribution on Surface Roughened With Small Square Ribs. Int. J. Heat Mass Transfer 1979, 22, 1645. (18) Alkire, R. C.; Deligianni, H.; Ju, J. B. Effect of Fluid Flow on Convective Transport in Small Cavities. J. Electrochem. Soc. 1990, 137, 818. (19) Aggarwal, J. K.; Talbot, L. Electrochemical Measurement of Mass Transfer in Semicylindrical Hollow. Int. J. Heat Mass Transfer 1979, 22, 61. (20) Knudson, J. K.; Katz, D. L. Fluid Dynamics and Heat Transfer; McGraw-Hill: New York, 1958.
Received for review April 15, 1996 Revised manuscript received August 20, 1996 Accepted September 3, 1996X IE960215A
X Abstract published in Advance ACS Abstracts, October 15, 1996.
