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Numerical Analysis of Double-Diffusive Natural Convection in Shallow and Deep Open-Ended Cavities Using Lattice Boltzmann Method

  • Research Article - Mechanical Engineering
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Abstract

In this work, the double-diffusive natural convection was studied in an open-ended cavity with the help of the lattice Boltzmann method. In this study, the driven force is developed by a change in the temperature gradient and concentration gradient on the left side of the cavity, which is the closed end. The temperature and concentration are maintained high at this end. The study is carried out for various parameters such as Rayleigh number (Ra) ranging from 103 to 106, aspect ratio (Ar) of 0.5, 1 and 2 and constant Prandtl number (Pr) of 0.7 and Lewis number (Le) of 2. The results are concentrated on for different buoyancy ratios (N = − 1, 0, 1) also. The results obtained are validated with existing literature results. The results show that when N value is negative, two buoyancy forces oppose each other and also the influence of concentration buoyancy force on fluid flow behavior gets dominant, and for aspect ratios 1 and 2, this effect was suppressed when Ra is increased but for the shallow cavity increasing in Ra helps the concentration force to become more dominant.

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Abbreviations

Ar:

Aspect ratio

C :

Nondimensional concentration

D :

Mass diffusivity (m2/s)

e :

Discrete lattice speed

F :

External force

f :

Distribution function for flow field

g :

Distribution function for temperature or concentration field

g y :

Gravitational acceleration (m/s2)

Le :

Lewis number

M :

Grid size

Ma :

Mach number

w :

Weight function

N :

Buoyancy ratio

Nu :

Local Nusselt number

Pr :

Prandtl number

Ra :

Rayleigh number

Sh :

Sherwood number

T :

Nondimensional temperature

u∙v :

Velocity components in x- and y-directions, respectively (m/s)

β C :

Concentration expansion coefficient (m3/kg)

β T :

Thermal expansion coefficient (K−1)

υ :

Kinematic viscosity (m2/s)

α :

Thermal diffusivity (m2/s)

ρ :

Fluid density (kg/m3)

ω :

Relaxation factor

avg:

Average

c :

Cold

f :

Flow

g :

Temperature or concentration

h :

Hot/high

i :

ith direction in the lattice structure

l :

Low

eq:

Equilibrium

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Authors and Affiliations

  1. Department of Thermal and Energy Engineering, School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    S. Arun & A. Satheesh

  2. Mechanical Engineering Department, Prince Mohammad Bin Fahd University (PMU), Al-Khobar, 31952, Saudi Arabia

    Ali J. Chamkha

Authors
  1. S. Arun
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  2. A. Satheesh
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  3. Ali J. Chamkha
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Correspondence to A. Satheesh.

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Arun, S., Satheesh, A. & Chamkha, A.J. Numerical Analysis of Double-Diffusive Natural Convection in Shallow and Deep Open-Ended Cavities Using Lattice Boltzmann Method. Arab J Sci Eng 45, 861–876 (2020). https://doi.org/10.1007/s13369-019-04156-3

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