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Solids Mixing Intensification in Tapered Fluidized Beds with an Inlet Jet: Experimental Validation and CFD Simulation

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Abstract

In this article, the intensification of solids mixing in tapered fluidized beds equipped with an inlet jet and varying apex angles (2.86°, 5.71°, and 8.53°) has been investigated. In this regard, a particle segregation number (PSN) and multi-fluid modeling (MFM) approach were employed to analyze the mixing process. The study utilized solid mixtures composed of particles with a density of 2500 kg/m3 and diameters of 240 and 510 µm. Simulation results were validated against our experimental data obtained using a small tapered bed without an inlet jet and those obtained using a larger tapered bed with an inlet jet, as Huilin et al. (2003) reported. This validation demonstrates satisfactory agreement between the simulation results and experimental data. The solids mixing process in a columnar fluidized bed was found to resemble that in a tapered bed with an apex angle of 2.86°. Increasing the apex angle leads to a larger equilibrium mixing value. In addition, the influences of inlet jet velocity and nozzle diameter on the solids mixing process were investigated. The simulation results indicated that higher inlet jet velocities and larger nozzle diameters enhance the equilibrium mixing index value. Notably, inlet jet velocities of 0.7 and 0.8 m/s exhibited three distinct solids mixing stages: rapid, slow, and equilibrium, whereas higher jet velocities only involved rapid and equilibrium mixing stages. Moreover, this study further examined how the initial arrangement of solid particles affects the mixing index, providing valuable insights into optimizing the solids mixing process. Furthermore, the present work sheds light on the factors influencing the mixing of solids in tapered fluidized beds, offering valuable insights for further research and industrial applications.

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Abbreviations

C D :

Drag coefficient

C f :

Friction coefficient

d m :

Average solids mixture diameter, m

D 0 :

Bottom diameter of the bed, m

D 1 :

Top diameter of the bed, m

e :

Restitution coefficient

e a :

Approximate relative error

E fr :

Rate of frictional dissipation energy

f :

Drag correlation parameter

Fr :

Empirical constant, Pa

\(\vec{g}\) :

Gravitational acceleration, m s–2

g 0,ss :

Radial distribution function

H 0 :

Static bed height, m

H exp :

Height of the expanded bed, m

h k :

Distance of the kth cell center from the gas distributor

I :

Unit stress tensor

I gm :

Momentum transfer between the gas phase and the mth solid phase

I mk :

Momentum exchange between solid–solid phases

I 2D :

Second invariant of the deviatory stress tensor, s–2

J coll :

Dissipation of granular energy via inelastic collisions, kg m–1 s–3

J vis :

Dissipation of granular energy via viscous dissipation of the gas phase, kg m–1 s–3

k :

Turbulence kinetic energy, m2 s–2

k Θs :

Diffusion coefficient of granular energy, kg m–1 s–1

K fs :

Momentum exchange coefficient between fluid and solid phase, kg m–3 s–1

MI :

Mixing index

N :

Number of grid cells

P :

Pressure, Pa

P g :

Gas pressure, Pa

P m :

Solid phase pressure, Pa

P 0 :

Atmospheric pressure, Pa

ΔP :

Pressure drop, Pa

–∆P N :

Net pressure drop, Pa

–∆ P fr :

Frictional term of pressure drop, Pa

–∆ P kin :

Kinetic term of pressure drop, Pa

∆ P top :

Pressure drops in tapered bed, Pa

∆ P col :

Pressure drops in columnar bed, Pa

PSN :

Particle segregation number

∆h :

Bed height, m

q :

Pseudo-thermal energy flux vector

S m :

Solid phase source term, Pa m–1

t :

Time, s

U 0 :

Superficial gas velocity, m s–1

u g :

Velocity of the gas phase, m s–1

u m :

Velocity of the mth solid phase, m s–1

u g,z :

Gas velocity component in the axial direction, m s–1

V k :

Volume of the kth cell

ε :

Dissipation rate, m2 s–3

ε g :

Volume fraction of gas phase

ε m :

Volume fraction of mth solid phase

ε* :

Maximum solid packing in binary solid mixtures

ε s ,k :

Volume fraction of the solid phase (flotsam or jetsam) in the kth cell

Θs :

Granular temperature, m2 s–2

μ b :

Bulk viscosity, Pa s

μ m :

Shear viscosity, Pa s

μ t :

Turbulent viscosity, Pa s

ρ :

Density, kg m–3

ρ g :

Density of gas phase kg m–3

ρ j :

Density of jetsam particles kg m–3

ρ f :

Density of jetsam particles kg m–3

ρ m :

Density of mth solid phase kg m–3

β gm :

The interphase momentum exchange coefficient between the gas phase and the mth solid phase

β mk :

Rate of exchange of solid–solid momentum

εo :

Bed voidage

τ g :

Stress tensor of gas phase, Pa

Γ slip :

Production of granular energy through the slip between the phases, kg m–1 s–3

col:

Collisional

con:

Conventional bed

f :

Fluid phase

fr:

Frictional

kin:

Kinetic

max:

Maximum

min:

Minimum

s :

Solid phase

t :

Turbulent

T :

Transpose

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Acknowledgements

The present authors would like to thank Sharif University of Technology (Tehran, Iran) for supporting this work

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  1. Department of Chemical and Petroleum Engineering, Sharif University of Technology, P. O. Box 11155–9465, Tehran, Iran

    Esmaeil Jabbari, Peyman Mardanloo, Kiana Sarafan & Asghar Molaei Dehkordi

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  1. Esmaeil Jabbari
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Correspondence to Asghar Molaei Dehkordi.

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Jabbari, E., Mardanloo, P., Sarafan, K. et al. Solids Mixing Intensification in Tapered Fluidized Beds with an Inlet Jet: Experimental Validation and CFD Simulation. Korean J. Chem. Eng. 41, 357–374 (2024). https://doi.org/10.1007/s11814-023-00011-2

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