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Effect of Bubble Injection Pattern on the Bubble Size Distribution in a Gas-Solid Fluidized Bed

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Abstract

Three different bubble injection patterns including uniform, center oriented and corner oriented injection patterns over the gas distributor have been studied using a discrete bubble model in a 2-D gas solid fluidized bed. The results show that the bubble size and size distribution evolution through the bed are almost the same for uniform and corner oriented bubble injection patterns, but for the case of center oriented injection pattern, the area weighted average bubble diameter (d b,21) is greater than the others. The results show that in the center oriented injection pattern, many of the small bubbles leave the bed without coalescence and this leads to smaller d b,10 than two other cases. Moreover, in this work the size distribution evolution through the bed height is investigated in detail.

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Correspondence to Salman Movahedirad.

Appendices

Appendix: Comparison of the Results for Different Constants in Bubble Rising Velocity Correlation

According to Eq. 1, for 2-D bed Mudde et al. [23] proposed a constant coefficient of c = 0.5–0.6 for polymeric particles, whereas Shen et al. [24] proposed a coefficient between 0.8 and 1.0 for c in a bed filled with sand particles. Thus, there are very different reports on the constant value. Our simulations show that the bubble size distribution and the averaged emulsion phase velocity profiles don’t change considerably with varying c values. Actually, the effects of bubble-bubble interactions are more noticeable than the single bubble rising velocity correlation. Figure 16a and b show the total bubble size distribution and averaged emulsion phase velocity for three different constant values of c = 0.6, c = 0.711 and c = 0.8 in LRIP injection pattern. As can be observed from these figures there are no considerable deviation in the predictions. Moreover, simulation results show that the deviation for other injection patterns are not considerable. For other simulations the constant value of c = 0.711 were used.

Fig. 16
figure 16

a Total Bubble size distributions and b emulsion phase velocity profiles for different constant values in bubble rising equation

Notation

d b :

Bubble diameter, m

d b,10 :

Arithmetic mean bubble diameter, m

d b,21 :

Area-weighted mean bubble diameter, m

g :

Gravity acceleration, m/s 2

H :

Bed Height (m)

h :

Height above the distributor, m

h 0 :

Porous plate characteristic, (–)

H 0 :

Compact bed height, m

l i j :

Coefficient for modification of vertical velocity of bubble i due to the effect of vertical velocity component of bubble j

m i j :

Coefficient for modification of vertical (horizontal) velocity of bubble i due to effect of horizontal (vertical) velocity component of bubble j

n t :

Total number of bubbles in each section (y± Δy) of bed

R :

Radius, m

RH :

Inlet air relative humidity, %

t :

Time, s

v 0 :

Superficial gas velocity, m/s

v m f :

Minimum fluidization velocity, m/s

v :

Bubble velocity, m/s

v b r :

Single bubble rise velocity, m/s

v b ,i :

Bubble rise velocity in isolation, m/s

u x :

x component of the emulsion phase velocity, m/s

u y :

y component of the emulsion phase velocity, m/s

v x,i :

x component of the velocity of bubble (i), m/s

v y,i :

y component of the velocity of bubble (i), m/s

W :

Bed width, m

X A :

Conversion, %

Subscripts and superscripts

d :

Bubble-bubble distance

i :

Bubble number in x-direction

j :

Bubble number in y-direction

x :

Horizontal direction, m

y :

Vertical direction, m

0:

Initial position

Greek letters

α :

Shape parameter

β :

Shape parameter

δ :

Bed thickness, m

Δ:

Difference

ρ p :

Solid density, kg/m 3

Abbreviations

CeOIP:

Center Oriented Injection Pattern

CoOIP:

Corner Oriented Injection Pattern

G/S:

Gas-Solid

LRIP:

Linear Random Injection Pattern

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Probability density function

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Tavassoli-Rizi, M.H., Movahedirad, S. & Ghaemi, A. Effect of Bubble Injection Pattern on the Bubble Size Distribution in a Gas-Solid Fluidized Bed. Flow Turbulence Combust 98, 1133–1151 (2017). https://doi.org/10.1007/s10494-017-9800-7

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