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Influence of the grid on fluidized bed inhomogeneity
The Chemical Engineering Journal, 15 (1978) 165 - 168 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
Short Communication
Influence of the grid on fluidized bed inhomogeneity Part III: The inhomogeneity criterion as a measure of fluidixed bed @homogeneity LUBOMiR
NE&L
and BENITTO MAYRHOFER
Department of Chemical Engineering, hvlgue Institute of Chemical Technology, Prague (C’zechozIouakia) (Received 25 February 1977; in final form 14 November 1977)
1. Introduction In Part I of this work we proved by theoretical analysis that the condition Ino < 1 is satisfactory for ensuring a maximum damping effect on the grid side of disturbances occurring in a fluidized bed. We can write the inhomogeneity criterion Ino in the form [l] (there are other possibilities) Ino =
do&ildo)3 6~:s
- 1](P* - P&V26
Fig. 1. Plot of 6, = 6,.( In,) for corundum.
(I-37b)
ti(~I2)Pt
Experimental results and a discussion of the validity of this condition have been given in Part II [2]. This paper is devoted to examining the case when this condition is not met, i.e. when Ino > 1. We. also attempt to use Ino as a quantitative measure of fluidized bed inhomogeneity. As this contribution is closely associated with the previous papers, we refer to them [ 1, 21 for a detailed description of the physical quantities and the experimental data. 2. Using Ino as the inhomogeneity criterion Let the coefficient of variation 6, be the statistic measuring the local inhomogeneity of a concentration field of particles in a fluid&d bed. We have then 6, = s&
‘“G
(11-4)
Fig. 2. Plot of 6, = 6,( hG ) for glaaa spheres.
An interesting result is shown in Figs. 1 and 2, which give 6, = S&n,, h, v) at different distanCes h from the grid and at three dimensionless air velocities U (calculated using eqn . (11-6)). We obtained the numerical values of
& through eqk. (1-37~) by inserting 0.175 -for tan (a/2) and for iZJits deviations Ev2(h). The trend of the points in both graphs is 165
approximately the same. We can distinguish two regions: at higher Ino values we observe a pronounced dependence of the fluidized bed inhomogeneity 6 c on Ino ; at hver Ina values the inhomogeneity 6, is independent of Ino, and therefore independent of the grid type. The envelopes are only introduced for clarity and have not been obtained by calculation. 0.51
I
materials at different velocities. The theoretical treatment was directed merely towards the influence of the grid which can be explained by the criterion Ino. However; the quantity 6 C expresses the resulting inhomogeneity due to the interaction between the grid and the dispersed system (fluidized bed). On the basis of our experimental evidence we suggest that the total inhomogeneity 6, can be decomposed into two additive parts, at least as a first approximation :
I
6, ‘6B
I
I
I
I
,
1
A
10
+8G
where 6 z is the inhomogeneity contribution which cannot be reduced by grid design and 6 o is the contribution influenced by the grid design, and which eventually decreases to zero. Assuming the validity of eqn. (l), we can study separately the dependence of 6a and 6 o on various characteristics.
‘“G
Fig. 3. Plot of 6, = 6&nG) 0 mm.
I
I
1
I
for corundum
at h =
WfS,
-
I 10
“fs,
-.
wn3
I
I
Fig. 6. Plot of 6, = aB + 60 for grid types A and 2. ‘“G
Fig. 4. Plot of 6, = 6&nG) 0 mm.
for glass spheres at h -
For corundum particles (Fig. 3) the break in slope can be approximated for U = 0.2 by InG = 1, in accordance with the theoretical condition given by eqn. (I-36). It seems probable that a similar result would be obtained at U = 0.3. However, we have insufficient experimental data to confirm this. For glass spheres (Fig. 4) the break in slope occurs at a higher value of Ino . In this particular case it occurs at approximately Ino = 3 for u = 0.3 and at Ino = 5 for U = 0.2. A grid design based on the theoretical value Ino = 1 would then be on the safe side, as expected. It is also not surprising that the plots of 6, = s,(Ino) are not identical for different
Let us first show the dependence of 6.&on bed height h at different superficial velocities of the fluidizing fluid (three levels), for two grid types denoted by A and Z (Fig. 5). (The indices f and s are omitted for simplicity.) We have w1 < ws < ws. Let us consider the case when the fluidized bed exhibits minimum possible inhomogeneity for grid A at all velocities w considered, and for’the grid Z only at the highest velocity w8. Then we have ~G(A)(W>W1)=O
aG(Z)(W
2
%d=o
The inhomogeneity level 6 a of the fluidized bed increases with increasing fluid velocity w. Hence it follows (here the numerical index is identical with the velocity level index) that
167
The values of 6 B are identical with the 6 C values for grid type A, since ijcCA)(~ > wl) = 6 B(A)(~ 2 WI ) = 6 B. The same applies for grid type Z : 6 c(z)3 > 6 e(Z)2 > 6 et zj1. According to our experimental data [ 2 - 41, differences in 6 C decrease at higher velocities, i.e.
(6 c(Z)- 6 B)l =
>
t6 c(Z) -5B)2>
@c(Z)-+B)3
=
0
Nomenclature
This relation can be written according to eqn. (1) as aG(Z)l
>
hG(Z)2
>
6G(Z)3
= 0
Bands of 6 o values are indicated in Fig. 5, and at the velocity w3 they fit a single curve because of our stipulation that 6G(Z)3 = 0. These results indicate the possibility of using the criterion Ino, outside the limits of validity given by Ino < 1, to provide a quantitative measure of the inhomogeneity of a fluidized bed in terms of the quantity 6 o : InG
3. Conclusion We have examined the possibility of using In, as a quantitative measure of fluidized bed inhomogeneity. Experimental verification of our ideas, especially of the hypothesis presented in eqn. (l), would be a substantial contribution to the hydrodynamics of inhomogeneous fluidized beds.
mean volumetric concentration of the solid phase in a jet #?vi, cv2 estimates of expected values of i?J diameter of the grid openings & acceleration of gravity g inhomogeneity criterion for a fluidizInG ed bed standard deviation of the volumetric sc concentration pitch of the grid openings tG u dimensionless superficial fluid velocity superficial fluid velocity WfS EJ
= InG t6 G)
where Ino > 1
@G
>
hG
@G
= 0)
<
1
0)
The CritWiOn hG, analogous to other inhomogeneity criteria [ 51, represents correctly the’increase in fluidized bed inhomogeneity, in accordance with experimental observations [6] , for an increase in the ratio (pS pt)/pt. The dependence of Ino on the relative free area cp, OpeIIiI’&g pitch to and opening diameter dG iS of the same type as the dependence of the fluidized bed inhomogeneity on these quantities [ 7,8] . The same applies to the volumetric concentration iYJ because lower bed parts fluidize at lower inhomogeneity [8] (lower bed parts generally imply lower & concentrations in streamlines). At increased fluid rates the fluidized bed inhomogeneity generally increases. This follows also from the results published in ref. 6 and from our previous work [2 - 41. However, the range of heterogeneous jets also increases with increased velocity [9] and, according to us, their stability then increases. This opposite influence can possibly be eliminated by the method introduced here, i.e. by using the quantity 6 o.
Greek symbols (Y jet angle SB
6, 6G
Pf,Ps
Ip
part of the coefficient of variation 6 C that is not influenced by the grid type coefficient of variation of the volumetric concentration part of the coefficient of variation 6, that is dependent on the grid type fluid and solid phase densities relative grid free area
References B. Mayrhofer and L. Neuiil, Chem. Eng. J., 14 (1977) 167. B. Mayrhofer and L. Neutil, Chem. Eng. J., 14 (1977) 167. B. Mayrhofer, Influence of the grid on fluidized bed inhomogeneity, Thesis, Rague Institute of Chemical Technology, Prague, 1970. B. Mayrhofer, L. NeuZil, E. HamHkovB. and S. LuciusovA, Scientific Papers of the Prague Institute of Chemical Technology, K5 (1973) 111. 0. Mikula, J. B&a and J. Havalda, Coil. Czech. Chem. Commun., 37 (1972) 2345. J. F. Davidson and D. Harrison, Fluidized Particles,
168 Cambridge University Press, Cambridge, 1963. 7 M. 5. Yufa, G. Grigorjev and P. V. Varencov, Zh. Prikl. Khim., 38 (1965) 1520. 8 M. F. Maslovskii, Khim. Neft. Mauhinostr., 20 (9)
(1965). 9 V. A. Basov, V. I. Markhevka, T. Kh. MelikAchnazarov and D. I. Grotschko, Khim. Proniet (Moscow), 42 (1966) 439; 44 (1968) 619.
Short Communication
Influence of the grid on fluidized bed inhomogeneity Part III: The inhomogeneity criterion as a measure of fluidixed bed @homogeneity LUBOMiR
NE&L
and BENITTO MAYRHOFER
Department of Chemical Engineering, hvlgue Institute of Chemical Technology, Prague (C’zechozIouakia) (Received 25 February 1977; in final form 14 November 1977)
1. Introduction In Part I of this work we proved by theoretical analysis that the condition Ino < 1 is satisfactory for ensuring a maximum damping effect on the grid side of disturbances occurring in a fluidized bed. We can write the inhomogeneity criterion Ino in the form [l] (there are other possibilities) Ino =
do&ildo)3 6~:s
- 1](P* - P&V26
Fig. 1. Plot of 6, = 6,.( In,) for corundum.
(I-37b)
ti(~I2)Pt
Experimental results and a discussion of the validity of this condition have been given in Part II [2]. This paper is devoted to examining the case when this condition is not met, i.e. when Ino > 1. We. also attempt to use Ino as a quantitative measure of fluidized bed inhomogeneity. As this contribution is closely associated with the previous papers, we refer to them [ 1, 21 for a detailed description of the physical quantities and the experimental data. 2. Using Ino as the inhomogeneity criterion Let the coefficient of variation 6, be the statistic measuring the local inhomogeneity of a concentration field of particles in a fluid&d bed. We have then 6, = s&
‘“G
(11-4)
Fig. 2. Plot of 6, = 6,( hG ) for glaaa spheres.
An interesting result is shown in Figs. 1 and 2, which give 6, = S&n,, h, v) at different distanCes h from the grid and at three dimensionless air velocities U (calculated using eqn . (11-6)). We obtained the numerical values of
& through eqk. (1-37~) by inserting 0.175 -for tan (a/2) and for iZJits deviations Ev2(h). The trend of the points in both graphs is 165
approximately the same. We can distinguish two regions: at higher Ino values we observe a pronounced dependence of the fluidized bed inhomogeneity 6 c on Ino ; at hver Ina values the inhomogeneity 6, is independent of Ino, and therefore independent of the grid type. The envelopes are only introduced for clarity and have not been obtained by calculation. 0.51
I
materials at different velocities. The theoretical treatment was directed merely towards the influence of the grid which can be explained by the criterion Ino. However; the quantity 6 C expresses the resulting inhomogeneity due to the interaction between the grid and the dispersed system (fluidized bed). On the basis of our experimental evidence we suggest that the total inhomogeneity 6, can be decomposed into two additive parts, at least as a first approximation :
I
6, ‘6B
I
I
I
I
,
1
A
10
+8G
where 6 z is the inhomogeneity contribution which cannot be reduced by grid design and 6 o is the contribution influenced by the grid design, and which eventually decreases to zero. Assuming the validity of eqn. (l), we can study separately the dependence of 6a and 6 o on various characteristics.
‘“G
Fig. 3. Plot of 6, = 6&nG) 0 mm.
I
I
1
I
for corundum
at h =
WfS,
-
I 10
“fs,
-.
wn3
I
I
Fig. 6. Plot of 6, = aB + 60 for grid types A and 2. ‘“G
Fig. 4. Plot of 6, = 6&nG) 0 mm.
for glass spheres at h -
For corundum particles (Fig. 3) the break in slope can be approximated for U = 0.2 by InG = 1, in accordance with the theoretical condition given by eqn. (I-36). It seems probable that a similar result would be obtained at U = 0.3. However, we have insufficient experimental data to confirm this. For glass spheres (Fig. 4) the break in slope occurs at a higher value of Ino . In this particular case it occurs at approximately Ino = 3 for u = 0.3 and at Ino = 5 for U = 0.2. A grid design based on the theoretical value Ino = 1 would then be on the safe side, as expected. It is also not surprising that the plots of 6, = s,(Ino) are not identical for different
Let us first show the dependence of 6.&on bed height h at different superficial velocities of the fluidizing fluid (three levels), for two grid types denoted by A and Z (Fig. 5). (The indices f and s are omitted for simplicity.) We have w1 < ws < ws. Let us consider the case when the fluidized bed exhibits minimum possible inhomogeneity for grid A at all velocities w considered, and for’the grid Z only at the highest velocity w8. Then we have ~G(A)(W>W1)=O
aG(Z)(W
2
%d=o
The inhomogeneity level 6 a of the fluidized bed increases with increasing fluid velocity w. Hence it follows (here the numerical index is identical with the velocity level index) that
167
The values of 6 B are identical with the 6 C values for grid type A, since ijcCA)(~ > wl) = 6 B(A)(~ 2 WI ) = 6 B. The same applies for grid type Z : 6 c(z)3 > 6 e(Z)2 > 6 et zj1. According to our experimental data [ 2 - 41, differences in 6 C decrease at higher velocities, i.e.
(6 c(Z)- 6 B)l =
>
t6 c(Z) -5B)2>
@c(Z)-+B)3
=
0
Nomenclature
This relation can be written according to eqn. (1) as aG(Z)l
>
hG(Z)2
>
6G(Z)3
= 0
Bands of 6 o values are indicated in Fig. 5, and at the velocity w3 they fit a single curve because of our stipulation that 6G(Z)3 = 0. These results indicate the possibility of using the criterion Ino, outside the limits of validity given by Ino < 1, to provide a quantitative measure of the inhomogeneity of a fluidized bed in terms of the quantity 6 o : InG
3. Conclusion We have examined the possibility of using In, as a quantitative measure of fluidized bed inhomogeneity. Experimental verification of our ideas, especially of the hypothesis presented in eqn. (l), would be a substantial contribution to the hydrodynamics of inhomogeneous fluidized beds.
mean volumetric concentration of the solid phase in a jet #?vi, cv2 estimates of expected values of i?J diameter of the grid openings & acceleration of gravity g inhomogeneity criterion for a fluidizInG ed bed standard deviation of the volumetric sc concentration pitch of the grid openings tG u dimensionless superficial fluid velocity superficial fluid velocity WfS EJ
= InG t6 G)
where Ino > 1
@G
>
hG
@G
= 0)
<
1
0)
The CritWiOn hG, analogous to other inhomogeneity criteria [ 51, represents correctly the’increase in fluidized bed inhomogeneity, in accordance with experimental observations [6] , for an increase in the ratio (pS pt)/pt. The dependence of Ino on the relative free area cp, OpeIIiI’&g pitch to and opening diameter dG iS of the same type as the dependence of the fluidized bed inhomogeneity on these quantities [ 7,8] . The same applies to the volumetric concentration iYJ because lower bed parts fluidize at lower inhomogeneity [8] (lower bed parts generally imply lower & concentrations in streamlines). At increased fluid rates the fluidized bed inhomogeneity generally increases. This follows also from the results published in ref. 6 and from our previous work [2 - 41. However, the range of heterogeneous jets also increases with increased velocity [9] and, according to us, their stability then increases. This opposite influence can possibly be eliminated by the method introduced here, i.e. by using the quantity 6 o.
Greek symbols (Y jet angle SB
6, 6G
Pf,Ps
Ip
part of the coefficient of variation 6 C that is not influenced by the grid type coefficient of variation of the volumetric concentration part of the coefficient of variation 6, that is dependent on the grid type fluid and solid phase densities relative grid free area
References B. Mayrhofer and L. Neuiil, Chem. Eng. J., 14 (1977) 167. B. Mayrhofer and L. Neutil, Chem. Eng. J., 14 (1977) 167. B. Mayrhofer, Influence of the grid on fluidized bed inhomogeneity, Thesis, Rague Institute of Chemical Technology, Prague, 1970. B. Mayrhofer, L. NeuZil, E. HamHkovB. and S. LuciusovA, Scientific Papers of the Prague Institute of Chemical Technology, K5 (1973) 111. 0. Mikula, J. B&a and J. Havalda, Coil. Czech. Chem. Commun., 37 (1972) 2345. J. F. Davidson and D. Harrison, Fluidized Particles,
168 Cambridge University Press, Cambridge, 1963. 7 M. 5. Yufa, G. Grigorjev and P. V. Varencov, Zh. Prikl. Khim., 38 (1965) 1520. 8 M. F. Maslovskii, Khim. Neft. Mauhinostr., 20 (9)
(1965). 9 V. A. Basov, V. I. Markhevka, T. Kh. MelikAchnazarov and D. I. Grotschko, Khim. Proniet (Moscow), 42 (1966) 439; 44 (1968) 619.