Ind. Eng. Chem. Process Des. Dev.
K’ = constant in eq 11 K” = constant in eq 10 K, = constant in eq 8 K, = constant in eq 9 m = exponent in eq 11 n = power index N = exponent in eq 10 p = exponent in eq 9 S2 = variance t = time t , = characteristic time (see eq l l ) , s W = water/plaster weight ratio, dimensionless Greek Letters
i. = shear rate, s-l
4, = critical shear rate (see eq 9), s-l q = viscosity, Pa-s qp = plastic viscosity, Pa-s qr = relative viscosity, dimensionless qo = disperding medium viscosity, Pa-s [ q ] = intrinsic viscosity, dimensionless X = structural parameter, dimensionless u,2 = experimental error variance T = shear stress, Pa T~ = equilibrium shear stress, Pa T~ = peak shear stress, Pa T, = steady shear stress, Pa
T~
53
1985,2 4 , 53-56
= yield value, Pa
9 = nominal solid volume fraction, dimensionless
9,ff= effective solid volume fraction am = maximum solid volume fraction, dimensionless 9 p = ~ volume fraction of particles in a floc, dimensionless O0 = constant in eq 4 Registry No. Calcium sulfate hemihydrate, 26499-65-0.
Literature Cited Alessandrini, A.; Kikic, I.; Lapasln, R. “Proceedings, 3rd Austrian-Italian-Yugoslav Chemical Engineering Conference”, Graz. 1982; Voi. 11, p 71. Aiessandrini, A.; Lapasin, R.; Papo, A. Cbem. Eng. Commun. 1983, submitted for publication. Caufin, B.; Lapasln, R.; Papo, A. Paper presented at the “XVI Colloque National Annuel du Groupe Franpls de Rheologle”, Paris, 1981; Cahlers du Groupe Franpls de Rheologle, 1983; Voi. 6, p 125. Cheng, D. C-H.; Evans, F. Br. J. Appl. phvs. 1965, 18, 1599. Colussi, I.; Lapasin, R.; Pap, A. I d . Eng. Chem. Process Des. D e v . 1982. 2 1 , 514. Eilers, H. Kol/oM 2. 1941, 9 7 , 313. Firth, B. A,; Hunter, R. J. J. Cdldd Interface Scl. 1978, 5 7 , 248. Kato. Y.; Matsui. M.; Umeya, K. Gypsum Llm 1961, 107, 13. Lin, 0. C. C. Chem. Tech. 1975, 5 , 51. Quemada, D. Rheol. Acta 1978. 17, 632. Smith, T. L.; Bruce, C. A. J. ColbM Interface Sci. 1979, 72, 13. Thomas, D. G. A I C M J . 1984, 10, 517. Thomas, D. 0. J. ColloM Scl. 1965, 2 0 , 267.
Received for review March 14, 1983 Accepted December 21, 1983
Mass Transfer Enhancement in Swirling Annular Pipe Flow Ehsan Shoukry and Leslle W. Shemllt” Department of Chemical Englnwing, McMaster Unlversi?v, Hamilton, Ontario, Canada, L8S 4L 7
Experimental measurements have been made by the electrochemical mass transfer technlque for annular pipe flow subjected to inlet swirling turbulent flow. For a Reynolds number range of 2000-15 000, the average mass transfer coefficients have been determined. Enhancement of mass transfer up to 300% was achieved. Correlations are presented.
Introduction Swirl flow may be classified into two types: continuous swirl and decayed or damped swirl. In the first type, the swirling motion persists over the entire length of the tube, while in the second type, the swirl is generated at the inlet section and decays freely along the flow path. Continuous swirl is usually achieved by inserting coiled wires, twisted taps, spiral fins, etc., along the entire length of the tube. Decaying swirl may be induced by tangential inlet slots or tubes, tangential vanes, short lengths of helical inserts, and rotating cylinders or propellers. Although augmentation of heat transfer by swirl flow has received attention, with results on both continuous and decayed swirl reported in the literature, very little is lmown about mass transfer improvement by this process. The purpose of this paper is to present experimental results of mass transfer in turbulent decaying swirl flow in an annulus. The swirling motion was induced by introducing the fluid through tangential inlet tubes. The electrochemical mass transfer method was applied to determine the average maw transfer coefficient to the surface of the annular core, at different heights from the inlet section.
Previous Work Mass transfer results reported (Richardson et al., 1976) for continuous swirl flow in the laminar region were based on microporous Teflon annuli with longitudinal grooves or splines on both inner and outer tube surfaces. Axial twisting of the tubes, making the splines helical, was found to enhance mass transfer. Counter-twisting was more effective than co-twisting. Experimental studies of heat transfer characteristics of decaying swirl flow were reported by Ivanova (1966). Hay and West (19751, using a single tangential slot at different angles of inclination to the pipe, found the swirl number (the ratio of the angular momentum to linear momentum flux) to decrease exponentially with the distance from the inlet section. The degree of decay was a function of the geometry of the swirl generator and Re through the pipe. The increase of the local heat transfer was found to be a function of the swirl number. Nerezhny and Sudarev (1971) obtained results for the local heat transfer to swirled flow of air obtained by short helically twisted inserts placed at the pipe inlet. The experimental data were described by the correlation Nu, = cRe,0.8,in which c was a function of the initial swirl angle and the relative tube length. Zaherzadeh and Jagadish
0196-4305f85f1 124-0053$OI.50/0 0 1984 American Chemical Society
54
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985 2000
B 1000 800 0
500
v)
300
'r"
,#'
200 W'
100 1000
i
2000
4000 6000 10,000 Re
20,000
Figure 3. Axial flow results for three cathodes: ( 0 )H / d e = 2.4; (0) H / d , = 36; (W) H / d e = 70; (A) Sh = 0.0135Re0.88S~0.33; (B) Sh = 0.41Re0-80S~0.33.
Figure 1. Experimental Apparatus: (A) nickel cathodes (30 cm) at 2.4de, 36de, and 70defrom inlet; (B) outer tube of annular test section, Ni 200,2.55 cm long, 5.2 cm i.d.; (C) acrylic rod inner core, 2.5 cm 0.d.; (D) inlet section; see Figure 2; (E) exit section; (F) temperature controlled electrolyte tank; (G) pump; (H) rotameters.
y""i'F
b
1" i.d.
- H I +
6
Figure 2. Dimensions of tangential and axial inlets.
(1975) determined the enhancement in the average heat transfer coefficient in decaying swirl flow created by tangential vane generators and presented the correlation N u / P ~ O=. ~&en, where both c and n depended on the geometry of the generator. Migay and Golukev (1970) carried out a theoretical analysis to predict the heat transfer coefficient based on the evaluation of equivalent friction factors for swirl flow, while a series solution for the decay of swirl in an annulus was presented by Scott (1972). Experimental Apparatus The experimental arrangement used is shown in Figure 1. The annular test section was constructed of a Ni200 outer tube, 255 cm in length and 5.21 cm i.d., which served as the anode. The inner core was made of an acrylic rod of 2.54 cm 0.d. Three Ni cathodes, each 30 cm long, formed parts of the core. These were placed with their lowest point at 6.5 cm (2.4de), 96.5 cm (36de), and 186.5 (70de) above the center of the inlet of the test section; 55 cm (204) was allowed as an exit length. The core was machined to ensure a continuous smooth surface throughout the flow. The outer annular tube was flanged at both ends to PVC inlet and outlet sections, which also held the annular core concentrically. Four different inlet sections were used. Three of them were swirl inducers with a tangential inlet pipe of 1/2, 3/4, 1 in. i.d. while the fourth section, which provided nonswirling (axial) flow, had a 1in. i.d. inlet tube (Figure 2). All other elements of the experimental apparatus were nonmetallic. The flow was controlled by a by-pass and measured by one of two rotameters to cover the range of flow rates. The temperature was controlled to 25 f 1"C. The electrolyte circulated through the system was an aqueous solution equimolar in K3Fe(CN), and K4Fe(CN),
with excess of NaOH. The rate of mass transfer between the electrolyte and the annular core was determined by measuring the limiting current for the cathodic reduction of K3Fe(CN),. The electrolyte properties were determined according to the equations given by Gordon et al. (1966). At each flow condition, the applied voltage of each cathode independently was increased stepwise by means of a Wenbig potentiostat (HC70) until the limiting current was reached. Since the area of the anode was large compared with the cathode, the former constituted a convenient reference electrode. The mass transfer coefficient was then evaluated from the limiting current using the expression
K = Ii/ZFACb (1) Axial Flow Results The axial flow experiments served to check the experimental method and provide a basis for evaluating the degree of mass transfer enhancement. The results are plotted in Figure 3 for the three electrode positions in the form of Shd vs. Re. The flow at the uppermost electrode was fully developed turbulent flow ( H / d e= 70). Since the L / d e ratio of the electrode was 11.25, the concentration boundary layer was fully developed over most of the electrode length especially for Re > 4000. The mass transfer results for this electrode were correlated by Shd = 0.0135Re0*88S~0-33
(2)
K/U* = 0 . 0 6 2 2 S ~ - ~ / ~
(3)
or as
U*, the well-known friction velocity, is a function of the friction factor and the average velocity. It was calculated by using the equations of the friction factors in annuli presented by Knudsen (1962). Equation 3 is in good agreement with the results of Shaw and Hanratty (1977). The measured mass transfer coefficient for the middle electrode ( H / d e = 36) for Re > 4000 followed the same dependency on Re as eq 2, indicating that the flow was fully developed, although the values of K were 4.5% less than those predicted by eq 2. For both the higher and the middle electrodes at Re < 4000, the concentration boundary layer is not developed over an appreciable part of the electrode and this gives rise to an exponent of Re between -0.42 (the value in case of developing concentration boundary layer) and -0.12 (the value for fully developed concentration boundary layer). The mass transfer results for the lower electrode ( H / d e = 2.4) for 4000 > Re > 13000 were correlated by Shd = 0.41Re0.8Sc1/3
(4)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 1, 1985 2000
r
55
A
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-
o 500
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100 1000
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-
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Figure 4. Preliminary experimental results: (A) 1-in. axial inlet, Sh Figure 6. Swirl flow by 3/4-in.tangential inlet: (A) H / d , = 2.4, Sh = 0.0135Reo%'c0~"; (B) 1-in.tangential inlet, Sh = 0.0881Re0~776S~0~33.= 0.095Re0.7aS~0.33; (B) H / d e = 36, Sh = 0.0023Re1.0BBS~0.33; (C) H / d , = 70. Sh = 0.0135Re0.88S~0.33. 2000 2000 -
1000 800 p
r
-
A
1000 800 -
500 -
o 500 -
v)
?rJ
300 --
zoo
300 -
-
1000
200 t-
2000
4000 6000 10,000
I
20,000
1000
Re
2000
4000 6000 10,000
20,000
Re
Figure 5. Swirl flow by '/Jn. tangential inlet: (A) H / d , = 2.4, Sh = 0.0778Re0%!3c039;(B) H / d , = 36, Sh = 0.0069Re0.8BSc0.33; (C) H / d , = 70, Sh = 0.0135Re0?S~0.33.
Figure 7. Swirl flow by 1-in. tangential inlet: (A) H / d , = 2.4, Sh = 0.1169Re0.69S~0.33; (0)H / d , = 36; (w) H / d e = 70; (B) Sh = 0.0135Re0.8sS~0.33.
The exponent on Re agrees with that suggested for developing turbulent flow, but the value of the constant is about 80% higher than that predicted by the work of Pickett and Ong (1974). This is probably due to the high degree of turbulence created by sudden change of direction of flow and the jetting effect caused when the inlet stream hits the annular core at right angles. Swirl Flow Results Preliminary experiments on swirl flow were carried out using one cathode (25.4 cm long) positioned at H/de = 15.5, and the 1in. i.d. tangential inlet tube. The experimental value of the average mass transfer coefficients were compared with those obtained for axial flow, using the same electrode at the same position. The results are shown in Figure 4. An enhancement of 50 70% was obtained. The mass transfer coefficient of the swirl flow was correlated for 2000 C Re < 15000 by Shd = 0.0581Re0.775S~0.33 (5) while the results of the axial flow fitted eq 2. The experimental results obtained using the ll2,3/q, and 1 in. tangential inlets are shown in Figures 5, 6, and 7, respectively. The data for the fully developed axial flow are also shown for comparison. At a given Re, the average mass transfer coefficient is found to decrease with the distance of the electrode from the inlet section, which is a result of swirl decay along the flow path. The values of the mass transfer coefficients at the higher electrode are virtually the same as the one for developed axial flow for the three different tangential inlets used. This indicates that the swirl is completely decayed as the flow reaches the upper electrodes ( H / d e= 70). For the same electrode position, decreasing the inlet pipe di-
ameter increases the degree of mass transfer enhancement due to higher tangential velocities at the inlet. The swirl flow data for the lower electrode position were correlated for different swirl generators for 2000 < Re < 12000 by
-
Shd = cR,"+'SC'/~ (6) Both c and n depend on the diameter for the tangential inlet. For the 'l2-in. tangential inlet the values of K were 190 210% greater than the axial value at the same position, while the enhancement based on K for fully developed flow was 300 320%. [ K I K , = 3 3.21. For the 3/4-in.inlet, K I K , values were 2.1 2.3, and for the inlet, K I K , values were 1.5 1.8. The results of the swirl mass transfer at the middle electrode were correlated for the 1/2-in.inlet by
-
-
-
Shd = 0.0069Re0~99Sc0~33 and for the 3/4-in. inlet by
(7)
Shd = 0.0023Re1~0986S~0~33 (8) while the data obtained with the 1-in. tangential inlet indicated completely decayed swirl at the middle electrode. Figures 8 and 9 give the values of ShlSh, as a function of electrode position for the three dimensions of swirl generator at Re 5000 and 10000 respectively. The Shd represents an average value for the particular electrode length and position. The decrease in enhancement and hence the decay of swirl motion with distance from the inlet depends on the inlet conditions and Re in the annulus. Finally, it should be noted that for the tangential inlets 3 / 4 and 1 in. id., part of the inlet system hits the annular
56
Ind. Eng. Chem. Process Des. Dev., Vol. 24,
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No. 1, 1985
Jd = 0.102Re4.'
Re 5000
e
1 2
T A N G E N T I A L INLET
, 3 4
A
(12)
which may be compared with the results obtained for the 'I2-in. swirl generator
1
Jd = 0.0778Re4,192
(13)
The data prepared by Zaherzadeh and Jagadish for the average heat transfer coefficient of water flowing in a tube (Lld = 90) at Re of 20000 to 100000 were correlated by Ol 10
20
40
30
50
60
70
H/de
Figure 8. Entrance effects. Dimensionless hydrodynamic entrance related to Sh as a ratio of Sh, (fully developed flow length, H/d,, value). 40
30
-9a
-L?p
Re 10000
.,
1
z
T A N G E N T I A L IP.LE-
.3 4 A
1
20
1c
C 10
20
40
30
50
60
70
Hide
Figure 9. Entrance effects (details as in Figure 8).
core thus acting as a jet. Although this increases the degree of turbulence at the inlet and hence enhances the mass transfer at that position, it interferes with the swirling motion. Thus, ideally, the inlet pipe for swirl generation for the present annulus dimensions should be I 1/2-in.i.d. Discussion of Results a n d Comparison with Other Work In decaying swirl flow, the hydrodynamic and concentration boundary layers start developing after leaving the swirl generator. The reference dimension in calculating any criteria for swirl flow is the distance from the swirl generator exit to the given section, which takes into account the increase in the boundary layer thickness. In this study the average mass transfer for moderately long electrodes positioned at various distances from the inlet section was measured. The length of the working electrode used (30 cm) is large enough so that the effect of mass transfer entry on the measured mass transfer coefficient may be neglected. The lower electrode in this study was placed very close to the inlet (Hld, = 2.4) so that the concentration and hydrodynamic boundary layers may be assumed to develop simultaneously. Comparison of the experimental values of the average mass transfer coefficient with those estimated using the expression for local heat transfer coefficient for swirl flow is thus possible. Hay and West (1975) correlated their results for heat transfer in air flowing through a tube (L/d, = 18) using various dimensions of tangential slots in the form Nu, = 0.119Re,o~8 (9) which could be written for mass transfer as Sh, = 0.134S~l/~Re,0.~ (10) Upon integration over the electrode length L and expressing the integration in terms of shd and Re gives Shd = 0.167Re0.8(d/L)o.2Sc1/3 or J d =0.167Re-0.2(d/L)o.2 (11)
Applying the value of ( d / L ) used in the present study gives
Nu = (14) where n ranged from 0.89 to 1.026. This compares with the values of 0.99 and 1.098 obtained here for the middle electrode. The maximum enhancement in Zaherzadeh's results was 80% over the axial values. From the above results the dependence of the local mass transfer coefficient in Re seems to vary with the different phases of swirl motion decay along the flow path. Conclusions 1. Enhancement of the average mass transfer coefficient of up to 320% (compared with the value for developed axial flow) was obtained using tangential inlet tubes and short mass transfer sections (L= 30 cm). 2. The smaller the diameter of the tangential inlet, the higher the degree of enhancement due to large tangential velocities. 3. The decay of swirl, and hence the decrease in mass transfer augmentation along the flow path, depends on the inlet conditions and Re in the annulus. Nomenclature A = cathode area, cm2 Cb = bulk concentration, mol L D = diffusion coefficient, cm /s d = diameter, cm de = equivalent diameter, cm F = Faraday's constant H = hydrodynamic entrance length (distance of the electrode from the inlet section), cm 11= limiting current, A Jd = J factor for mass transfer = ( K / U ) S C ~ / ~ K = average mass transfer coefficient, cm/s K, = fully developed mass transfer coefficient, cm/s K, = local mass transfer coefficient, cm/s L = cathode length, cm U = mean velocity in the annular space, cm/s U* = friction velocity, cm/s x = axial distance from the inlet of test section, cm Z = number of electrons exchanged in the reduction reaction fi = dynamic viscosity, Pa s p = density, g/cm3
d
Dimensionless Groups Re = (Ppdg)/p; Re, = ( p w x ) / h Shd = K d / D ; Sh, = k x / D
SC = p / p D
Literature Cited Gordon, S.L.; Norman, J. S.;Tobias, C. W. Ber. Bunsenges. Fhys. Chem. 1966, 70. 414. Hay, N.; West, P. D. J. Heat Transfer 1975, 9 7 , 411. Ivanova, A. V. "Proceedings 2nd AlCSoviet Unlon Conference on Heat and Mass Transfer"; Gazley, C.; Hartnett, J. P.; Eckert. E. R. G., Ed.; Rand Corp.: Santa Monica, CA, 1966; Vol. 1, pp 243-250. Knudsen, J. 0. AICh€ J. 1962, 8 , 565. Mlgay, V. K.; Golubev. L. K. Heat Transfer. Soviet Res. 1970. 2(3). 68. Narezhnyy, E. G.; Sudarev. A. V. Heat Transfer. Soviet Res. 1971, 3(2),62. Pickett, D. J.; Ong, K. L. Electrochim. Acfa 1974, 19, 875. Richardson, P. D.; Tanishlta. K.; QUetti, P. M. Len. Heat Mass Transfer 1076, 2 , 445. Scott, C. J. J. Appl. Mech. 1072, 3 9 , 289. Shaw, D. A.; Hanratty, T. J. AIChE J. 1977, 2 3 , 28. Zaherzadeh, N. H.; Jagadlsh, B. S. Int. J. Heat Mass Transfer 1075, 18. 941.
Received for review September 3, 1982 Accepted February 10, 1984
