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Effect of shapes of particle on flow and heat transfer in confined flow

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Abstract

The particles found in diverse processes such as in pneumatic conveying, food processing, drilling operations, etc., may or may not be spherical in shape. Different types of non-spherical shapes are known to play an important role in fluid–particle interactions in terms of hydrodynamics and thermal behavior. The shape effect is studied in this work for a spherical cap and circular disc having the same projected area, in cylindrical confinement of λ (≡base diameter of particle to diameter of the tube) = 0.5 for the Poiseuille flow of air (Pr = 0.72) over a Reynold number range 1 ≤ Re ≤ 100 in steady state regime. The momentum and energy equations are solved for this problem using finite element-based techniques using COMSOL Multiphysics. The obtained results for both spherical cap and circular disc are compared with a spherical shape under otherwise identical conditions. The results show that drag experienced by spherical cap is lowest in comparison to other considered shapes at low Reynolds numbers. However, this trend gets reversed at high inertial flow (Re = 100). Although, the heat transfer rate in the case of spherical cap is observed to be higher than that of the circular disc and sphere. Especially, at Re = 1 rate of heat transfer from spherical cap is ~3 times higher than the sphere. Furthermore, correlations have been proposed for drag coefficient and average Nusselt number over the range of Reynold number 1 ≤ Re ≤ 100 incorporating both the non-spherical shapes along with a sphere thereby enabling interpolation for the intermediate values in the various applications.

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Abbreviations

a, b :

Coefficients in Eq. 6 (–)

A p :

Projected area of the particle (m2)

C D :

Total drag coefficient (–)

C :

Thermal heat capacity of air (J/kgK)

C P :

Pressure coefficient (–)

C Pl :

Local pressure coefficient (–)

D :

Diameter of the particle (m)

d eq :

Volume equivalent diameter of the particle (m)

D sphere :

Diameter of sphere (m)

F D :

Drag force (N)

H :

Height of the particle (m)

h l :

Local heat transfer coefficient (W/m2K)

K :

Thermal conductivity of the air (W/mK)

L d :

Downstream length of the pipe (m)

L u :

Upstream length of the pipe (m)

Nu :

Nusselt number (–)

Nu l :

Local Nusselt number (–)

P :

Pressure (Pa)

Pr :

Prandtl number (–)

r, z :

Cylindrical coordinate (–)

Re :

Reynolds number (–)

S :

Surface area of the particle (m2)

T :

Non-dimensional temperature (–)

T o :

Temperature of the air at inlet (K)

T w :

Temperature at the particle surface (K)

U :

Velocity of the fluid (m/s)

V z :

Dimensionless velocity in z-direction (m/s)

V r :

Dimensionless velocity in r-direction (m/s)

λ :

Confinement ratio (–)

μ :

Viscosity of the air (Pa s)

ρ :

Density of the air (kg/m3)

τ :

Devioteric part of Cauchy stress tensor (Pa)

Ψ :

Sphericity of the particle

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India

    Preeti Suri & Swati A Patel

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  1. Preeti Suri
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  2. Swati A Patel
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Correspondence to Preeti Suri.

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Fluid Mechanics and Fluid Power

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Suri, P., Patel, S.A. Effect of shapes of particle on flow and heat transfer in confined flow. Sādhanā 48, 242 (2023). https://doi.org/10.1007/s12046-023-02289-8

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