- Email: [email protected]
The influence of particle Reynolds number on voidage at fluidization
Powder Technology, 66 (1991)
97
97-99
Letter The influence of particle Reynolds number on voidage at fluidization
where m is the mass of particles bed of diameter D.
of density
ps in a
Experimental
J. Beiia and I. Havalda Chemical Engineering Department, Slovak Technical University, Radlinskiho 9, 812 37 Bratislava (Czechoslovakia)
(Received January 2, 1990; in revised form October 22, 1990)
We wish to report an experimental investigation into whether the void fraction in a fluidized bed at the point of minimum fluidization, emf, varies systematically with the particle Reynolds number Red or Archimedes number Ar. The investigation was motivated by the suggestion, by various authors, that emf varies with temperature due to changes in Red or Ar. Analysis of our own measurements and data from the literature reveal no evidence that Ed varies with Re,,,*. Introduction
Some workers [l-6] have found that Em varies with temperature, and it has been suggested [4-6] that this phenomenon can be explained through the dependence of e,,,f on Re,r. Thus, Lucas et al. [4] found that, for silica sand between 15 and 950 “C, lmf was about 0.593 for Remf CO.75, decreased to 0.539 as Remf increased from 0.75 to 2, but remained constant for Remf> 2. Mathur et al. [6], working with beds of sand at temperatures between 27 and 977 “C, observed an effect of temperature over the range 1
Measurements have been carried out on fifteen types of glass ballotini, each representing the size range between two successive meshes in the standard sieve series. The Sauter mean diameter, obtained from microscopic measurements, was used as the characteristic dimension do of each particle bed. The values of d0 varied from 0.124 to 2.74 mm. Two Perspex fluidization columns were used, of internal diameter 0.060 and 0.110 m, respectively, with fritted glass discs of grade Gl(b) as distributors. A steel fluidization column of 0.143 m ID was also used, with two layers of filter cloth sandwiched between perforated brass discs as distributor. The plenum chambers of all columns were designed [8] to ensure uniform air distribution. The Perspex columns had side pressure taps at the distributor level, while the steel column had side taps also at various levels above the distributor. The pressure difference between bed and freeboard, Ap, was measured using a U-tube manometer filled with ethanol and damped by a capillary [9]. The pressure taps of the steel column were also connected by piezometric and/or induction sensors. At the point of minimum fluidization, the measured value of Ap was within 2% of the theoretical value of 4 mglwD’. Values of Ed were determined from eqn. (1) at the minimum fluidization velocity V,, determined from a standard log-log plot of Ap as a function of U. For the Perspex columns, hmf was measured directly. For the steel column, the bed depth was varied until its surface coincided with one of the side taps, determined by amplification of the pressure signal from the appropriate tap. Results and discussion
The resulting measurements are shown as the filled points in Fig. 1; they are in good agreement with corresponding measurements for spherical particles fluidized with water [lo]. The dependence of emf on Red was tested, using the correlation coefficients and t statistics in the Table. Data sets 1 and 2 clearly show that there is no dependence of emmr on Remf. Data set 3 suggests that emf and Reti could be related, but the dependence is negligible because emt only varies from 0.411 to 0.418 when Re, is varied from 0.21 to 6.4.
Q Elsevier Sequoia/Printed
in The Netherlands
98
m 0.35
0
0
1,111, ,,,,, ,,,,,, ,,,,,,,,,, ,,c,,,,,jJ,,,, 0.05
0.l
a2
05
1
2
5
10
,,,,,,,,,,,,,,,( 20
50
mo
2w
Remf
Fig. 1. Values of l,r ~1s.Re,f. l , Present work, narrowly screened glass bailotini-air, d (mm) E < 0.401, 2.740 > , p. (kg/m3) E <2 527.1, 2 996.2>, m =OSOO 0 kg, D =0.060 m, room temperature, atmospheric pressure above the bed: A, present work, narrowly screened glass ballotini-air, d (mm) E <0.126,0.442>, pr (kg/m’) E <2 615.3,2 697.9>, m (kg) E < 1.500,4.000>, D =O.llO m, room temperature, atmospheric pressure above the bed; T, present work, narrowly screened glass bailotini-air, d (mm) E cO.144, 0.521>, pr (kg/m3) E <2 646.4, 2 674.5>, m (kg) E ~3.378 1, 22.360 I>, D=O.143 m, room temperature, atmospheric pressure above the bed; 0, authors [12], glass beads-air, d (mm) E < 0.112 5, 2.125 >, ps= 2 635 kg/m3, m (kg) E < 0.250,2.000 > , D = 0.095 m, room temperature, atmospheric pressure above the bed; A, authors [13], styrene divinylbenzene copolymer beads-air, d (mm) E ~0.248, 2.000>, pr= 1 040 kg/m3, D =4.68 cm, 6.59 cm and 9.37
cm, -, authors [ll], eqn. (2), original raw measured data were not published. Independent measurements of c,,,f and Re,r from the literature [ll-131 are shown as open symbols in Fig. 1. The values of ~,,,r are somewhat different from those determined in the present work. Doichev and Boichev [ll] published only the dependence E,f = 0.478.4r - o.ols
(2)
valid for 177
TABLE. Data set
Statistical
evaluation
Range of Remf
of the dependence
Range of Glf
Column ID (4
1 2 3 4 5
3.53-241.1 0.14W.55 0.212-6.40 0.0673-165.8 0.443-90.0
0.415-0.421 0.411-0.418 0.411-0.418 0.355-0.485 0.408-0.436
0.060 0.110 0.143 0.095 0.0468 0.0659 0.0937
vary with Red. However, the surprisingly wide range of values for lmf in these data, from 0.355 to 0.485, illustrates the difficulty of determining cti even at ambient conditions. Thus, the data are too imprecise to be regarded as evidence of dependence of .zmfon Re,r. The data of Hsuing and Thodos [13] showed no signi8cant dependence of lmf on Reti Other workers [4-6] have suggested theoretical justification for a dependence of Ed on Re,*, based on transition from laminar to turbulent flow around the particles. However, this cannot occur at such low Reynolds numbers. For example, Befia et al. [14] reported that, at E= cmf and at 7.2~ Ar< 1.06 x 10’ and/or at 0.007
Analysis of data obtained in this work and presented in the literature gives no evidence for dependence of cmton Rema at least for spherical particles in Geldart’s Group B. While these conclusions do not exclude an irdluence of temperature on emt, they show that any such effect must result from other than purely hydrodynamic effects. List of symbols Ar Archimedes do D
: m r Re L-2
number, d 3gpf(ps - pf)lpz length characteristic of particles (Sauter mean diameter) diameter of the column acceleration due to gravity height of bed weight of particles in bed sample correlation coefficient particle Reynolds number, Udpflp value of Student’s distribution with n -2 degrees of freedom, in this case
of lmmr on Re,f for measurements
given in Fig. 1
No. of data points n
Correlation coefficient rfi.
Statistic t, _2
Critical t” -2.0.05
t" -2,om
Critical
8 17 15 26 7
0.5836 0.2306 - 0.5621 0.5522 0.2406
1.76 0.92 - 2.45 3.24 0.55
2.45 2.13 2.16 2.06 2.57
3.71 2.95 3.01 2.80 4.03
Source
l
Present work
WI
1131
99
tn-2=r
lJ
l-r2
n-2
superficial velocity
u
Greek symbols Ap E CL Pf
Ps
mf
pressure drop across bed voidage of bed viscosity of gas density of gas density of solid
Subscript minimum
particles
fluidization
conditions
References 1 S. C. Saxena and G. J. Vogel, Trans. Inst. Chem. Engrs., 55 (1977) 184. 2 A. Desai, H. Kikukawa and A. H. Pulsifer, Powder TechnoL, 16 (1977) 143.
3 J. S. M. Botterill, Y. Teoman and K. R. Yuregir, Powder Technol., 31 (1982) 110. 4 A. Lucas, J. Amaldos, J. Casal and L. Puigjaner, Chem. Eng. Commun., 41 (1986) 121. 5 A. Mathur and S. C. Saxena, Powder Technol., 45 (1986) 287. 6 A. Mathur, S. C. Saxena and Z. F. Zhang, Powder Technol., 47 (1986) 247. 7 R. R. Pattipati and C. Y. Wen, Znd. Eng. Chem. Process Des. Dev., 21 (1982) 785. 8 J. E. Idelchik, Aerodinamika promyshlennych apparatov, Energia, Moscow - Leningrad, 1964, p. 261. 9 I. Havalda and J. Bella, Chem. Eng. Commun., 52 (1987) 135. 10 J. Befia, Associate Professor Thesis, Chemical Faculty, Slovak Technical University, Bratislava (1959). 11 K. Doichev and G. Boichev, Powder Techno/., I7 (1977) 91. 12 V. Thonglimp, N. Hiquily and C. Laguerie, Powder Technol., 38 (1984) 233. 13 T. H. Hsiung and G. Thodos, Can. J. Chem. Eng., 55 (1977) 221. 14 J. Befia, J. Ilavsk$, E. Kossaczkjr and L. NeuZil, Collection Czechoslov. Chem. Commun., 28 (1963) 293.
97
97-99
Letter The influence of particle Reynolds number on voidage at fluidization
where m is the mass of particles bed of diameter D.
of density
ps in a
Experimental
J. Beiia and I. Havalda Chemical Engineering Department, Slovak Technical University, Radlinskiho 9, 812 37 Bratislava (Czechoslovakia)
(Received January 2, 1990; in revised form October 22, 1990)
We wish to report an experimental investigation into whether the void fraction in a fluidized bed at the point of minimum fluidization, emf, varies systematically with the particle Reynolds number Red or Archimedes number Ar. The investigation was motivated by the suggestion, by various authors, that emf varies with temperature due to changes in Red or Ar. Analysis of our own measurements and data from the literature reveal no evidence that Ed varies with Re,,,*. Introduction
Some workers [l-6] have found that Em varies with temperature, and it has been suggested [4-6] that this phenomenon can be explained through the dependence of e,,,f on Re,r. Thus, Lucas et al. [4] found that, for silica sand between 15 and 950 “C, lmf was about 0.593 for Remf CO.75, decreased to 0.539 as Remf increased from 0.75 to 2, but remained constant for Remf> 2. Mathur et al. [6], working with beds of sand at temperatures between 27 and 977 “C, observed an effect of temperature over the range 1
Measurements have been carried out on fifteen types of glass ballotini, each representing the size range between two successive meshes in the standard sieve series. The Sauter mean diameter, obtained from microscopic measurements, was used as the characteristic dimension do of each particle bed. The values of d0 varied from 0.124 to 2.74 mm. Two Perspex fluidization columns were used, of internal diameter 0.060 and 0.110 m, respectively, with fritted glass discs of grade Gl(b) as distributors. A steel fluidization column of 0.143 m ID was also used, with two layers of filter cloth sandwiched between perforated brass discs as distributor. The plenum chambers of all columns were designed [8] to ensure uniform air distribution. The Perspex columns had side pressure taps at the distributor level, while the steel column had side taps also at various levels above the distributor. The pressure difference between bed and freeboard, Ap, was measured using a U-tube manometer filled with ethanol and damped by a capillary [9]. The pressure taps of the steel column were also connected by piezometric and/or induction sensors. At the point of minimum fluidization, the measured value of Ap was within 2% of the theoretical value of 4 mglwD’. Values of Ed were determined from eqn. (1) at the minimum fluidization velocity V,, determined from a standard log-log plot of Ap as a function of U. For the Perspex columns, hmf was measured directly. For the steel column, the bed depth was varied until its surface coincided with one of the side taps, determined by amplification of the pressure signal from the appropriate tap. Results and discussion
The resulting measurements are shown as the filled points in Fig. 1; they are in good agreement with corresponding measurements for spherical particles fluidized with water [lo]. The dependence of emf on Red was tested, using the correlation coefficients and t statistics in the Table. Data sets 1 and 2 clearly show that there is no dependence of emmr on Remf. Data set 3 suggests that emf and Reti could be related, but the dependence is negligible because emt only varies from 0.411 to 0.418 when Re, is varied from 0.21 to 6.4.
Q Elsevier Sequoia/Printed
in The Netherlands
98
m 0.35
0
0
1,111, ,,,,, ,,,,,, ,,,,,,,,,, ,,c,,,,,jJ,,,, 0.05
0.l
a2
05
1
2
5
10
,,,,,,,,,,,,,,,( 20
50
mo
2w
Remf
Fig. 1. Values of l,r ~1s.Re,f. l , Present work, narrowly screened glass bailotini-air, d (mm) E < 0.401, 2.740 > , p. (kg/m3) E <2 527.1, 2 996.2>, m =OSOO 0 kg, D =0.060 m, room temperature, atmospheric pressure above the bed: A, present work, narrowly screened glass ballotini-air, d (mm) E <0.126,0.442>, pr (kg/m’) E <2 615.3,2 697.9>, m (kg) E < 1.500,4.000>, D =O.llO m, room temperature, atmospheric pressure above the bed; T, present work, narrowly screened glass bailotini-air, d (mm) E cO.144, 0.521>, pr (kg/m3) E <2 646.4, 2 674.5>, m (kg) E ~3.378 1, 22.360 I>, D=O.143 m, room temperature, atmospheric pressure above the bed; 0, authors [12], glass beads-air, d (mm) E < 0.112 5, 2.125 >, ps= 2 635 kg/m3, m (kg) E < 0.250,2.000 > , D = 0.095 m, room temperature, atmospheric pressure above the bed; A, authors [13], styrene divinylbenzene copolymer beads-air, d (mm) E ~0.248, 2.000>, pr= 1 040 kg/m3, D =4.68 cm, 6.59 cm and 9.37
cm, -, authors [ll], eqn. (2), original raw measured data were not published. Independent measurements of c,,,f and Re,r from the literature [ll-131 are shown as open symbols in Fig. 1. The values of ~,,,r are somewhat different from those determined in the present work. Doichev and Boichev [ll] published only the dependence E,f = 0.478.4r - o.ols
(2)
valid for 177
TABLE. Data set
Statistical
evaluation
Range of Remf
of the dependence
Range of Glf
Column ID (4
1 2 3 4 5
3.53-241.1 0.14W.55 0.212-6.40 0.0673-165.8 0.443-90.0
0.415-0.421 0.411-0.418 0.411-0.418 0.355-0.485 0.408-0.436
0.060 0.110 0.143 0.095 0.0468 0.0659 0.0937
vary with Red. However, the surprisingly wide range of values for lmf in these data, from 0.355 to 0.485, illustrates the difficulty of determining cti even at ambient conditions. Thus, the data are too imprecise to be regarded as evidence of dependence of .zmfon Re,r. The data of Hsuing and Thodos [13] showed no signi8cant dependence of lmf on Reti Other workers [4-6] have suggested theoretical justification for a dependence of Ed on Re,*, based on transition from laminar to turbulent flow around the particles. However, this cannot occur at such low Reynolds numbers. For example, Befia et al. [14] reported that, at E= cmf and at 7.2~ Ar< 1.06 x 10’ and/or at 0.007
Analysis of data obtained in this work and presented in the literature gives no evidence for dependence of cmton Rema at least for spherical particles in Geldart’s Group B. While these conclusions do not exclude an irdluence of temperature on emt, they show that any such effect must result from other than purely hydrodynamic effects. List of symbols Ar Archimedes do D
: m r Re L-2
number, d 3gpf(ps - pf)lpz length characteristic of particles (Sauter mean diameter) diameter of the column acceleration due to gravity height of bed weight of particles in bed sample correlation coefficient particle Reynolds number, Udpflp value of Student’s distribution with n -2 degrees of freedom, in this case
of lmmr on Re,f for measurements
given in Fig. 1
No. of data points n
Correlation coefficient rfi.
Statistic t, _2
Critical t” -2.0.05
t" -2,om
Critical
8 17 15 26 7
0.5836 0.2306 - 0.5621 0.5522 0.2406
1.76 0.92 - 2.45 3.24 0.55
2.45 2.13 2.16 2.06 2.57
3.71 2.95 3.01 2.80 4.03
Source
l
Present work
WI
1131
99
tn-2=r
lJ
l-r2
n-2
superficial velocity
u
Greek symbols Ap E CL Pf
Ps
mf
pressure drop across bed voidage of bed viscosity of gas density of gas density of solid
Subscript minimum
particles
fluidization
conditions
References 1 S. C. Saxena and G. J. Vogel, Trans. Inst. Chem. Engrs., 55 (1977) 184. 2 A. Desai, H. Kikukawa and A. H. Pulsifer, Powder TechnoL, 16 (1977) 143.
3 J. S. M. Botterill, Y. Teoman and K. R. Yuregir, Powder Technol., 31 (1982) 110. 4 A. Lucas, J. Amaldos, J. Casal and L. Puigjaner, Chem. Eng. Commun., 41 (1986) 121. 5 A. Mathur and S. C. Saxena, Powder Technol., 45 (1986) 287. 6 A. Mathur, S. C. Saxena and Z. F. Zhang, Powder Technol., 47 (1986) 247. 7 R. R. Pattipati and C. Y. Wen, Znd. Eng. Chem. Process Des. Dev., 21 (1982) 785. 8 J. E. Idelchik, Aerodinamika promyshlennych apparatov, Energia, Moscow - Leningrad, 1964, p. 261. 9 I. Havalda and J. Bella, Chem. Eng. Commun., 52 (1987) 135. 10 J. Befia, Associate Professor Thesis, Chemical Faculty, Slovak Technical University, Bratislava (1959). 11 K. Doichev and G. Boichev, Powder Techno/., I7 (1977) 91. 12 V. Thonglimp, N. Hiquily and C. Laguerie, Powder Technol., 38 (1984) 233. 13 T. H. Hsiung and G. Thodos, Can. J. Chem. Eng., 55 (1977) 221. 14 J. Befia, J. Ilavsk$, E. Kossaczkjr and L. NeuZil, Collection Czechoslov. Chem. Commun., 28 (1963) 293.