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CFD evaluation of the influence of the draft tube on solids circulation in conical spouted beds

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Abstract

The particle circulation is important to guarantee process homogeneity and efficiency in conical spouted beds. This work investigated the influence of the draft tube on the solids circulation of conical spouted beds using a Computational Fluid Dynamics (CFD) Euler–Euler multiphase model. The solids mass flow in the spout and the particle cycle time were estimated for different conditions of solids bed height and inlet air velocities. Validation of the mathematical model was performed comparing the minimum spouting velocity according to experimental data from the literature, presenting deviations of 1.6% and 7.5%. Simulation results indicated a reduction in the minimum spouting velocity between 46.7 and 53.0% after the insertion of the draft tube in the equipment. However, the draft tube reduced the solids mass flow rate in the spout by approximately 70.5–78.0% when compared to configurations without the tube, hence causing a pronounced increase in solids cycle time. CFD performed a detailed and physically coherent analysis of the behavior of particle circulation parameters that are difficult to obtain experimentally.

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Abbreviations

a,  f exact ,  p′:

GCI test parameters

C D :

Drag coefficient

d s :

Particle mean diameter (m)

D o :

Spouted bed inlet diameter (m)

D T :

Diameter of the draft tube (m)

e ss :

Restitution coefficient

f exact :

GCI response

g:

Gravity (m/s2)

g 0,ss :

Radial distribution function

H o :

Static bed height (m)

H T :

Height of the draft tube (m)

I :

Identity tensor

k θ :

Diffusion coefficient for the energy fluctuation

K :

Inter-phase momentum exchange coefficient (kg/m3.s)

L T :

Length of the draft tube (m)

p :

Pressure (Pa)

ΔP :

Static pressure (Pa)

Res :

Relative reynolds number

R j :

Spout radius (m)

\(\mathop v\limits^{ \to }\) :

Velocity vector (m/s)

u :

Superficial gas velocity (m/s)

u ms :

Superficial gas velocity at minimum spouting based on Do (m/s)

W s :

Solid phase mass flow in the spout at x = Hc (kg/s)

α :

Volume fraction

α s ,max :

Maximum volume fraction of solids

\(\phi\) :

Energy exchange between phases

γ θ :

Collisional dissipation of energy (kg/m s3)

μ :

Dynamic viscosity (Pa s)

ρ :

Density (kg/m3)

τ :

Stress tensor (Pa)

θ :

Granular temperature (m2/s2)

f:

Gas phase

s:

Solid phase

col:

Collisional

kin:

Kinetic

fr:

Frictional

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Acknowledgements

This study was financed in part by the Coordenacão de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. This work was also supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico – Brasil (CNPq) under Grant No. (142102/2019-9).

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  1. Drying Center of Pastes, Suspensions and Seeds, Department of Chemical Engineering, Federal University of São Carlos, São Carlos, SP, Brazil

    Amarílis S. Souza & Rodrigo Béttega

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  1. Amarílis S. Souza
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Souza, A.S., Béttega, R. CFD evaluation of the influence of the draft tube on solids circulation in conical spouted beds. J Braz. Soc. Mech. Sci. Eng. 45, 462 (2023). https://doi.org/10.1007/s40430-023-04364-x

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