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Investigation of double-diffusive mixed convection effect on the particles dissolution in the shear flow using coupled SPM–LBM

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Abstract

In the present study, double-diffusive mixed convection related to the heat and mass transfer of the solid particles dissolution in a shear flow was numerically investigated. For this purpose, the study employed the combined two-dimensional thermal-concentration smoothed profile-lattice Boltzmann method scheme. The governing equations of the flow, concentration and temperature fields are solved by applying the LBM. The interplay amongst the fluid–solid particle and the boundary condition of the no-slip at the interface of the fluid–solid particle is treated by using the SPM. Initially, a comparison made amongst the results obtained in the present numerical method and to those that had been obtained in the previous works, showing a well compatibility. Then, the impacts of Reynolds number, thermal and concentration Grashof numbers and buoyancy ratio on the flow characteristics and dissolution process have been addressed. Following that, a comparison is made amongst the impacts of pure forced convection and double-diffusive mixed convection on the solid particle dissolution behavior. It is shown that different competitive mechanisms have impact on the migration of the solid particles under the double-diffusive mixed convection; these are the particle mass force, the buoyancy force resulting from the fluid weight, the thermal convection and finally, the concentration convection. The numerical results also revealed the identification of the critical buoyancy ratio, with the dissolution time of the solid particles being sensitive to it.

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Abbreviations

Br:

Buoyancy ratio

C(x, t):

Concentration field

C*(x, t):

Middle concentration

C ref :

Reference concentration

C s :

Speed of sound

C ij :

Force scale

e α :

Discrete velocity vector

f α :

Density distribution functions

f eqα :

Momentum equilibrium distribution function

F α :

Discrete force (hydrodynamic)

F Hi :

Hydrodynamic force on the ith particle

F ini :

Actual hydrodynamic force on the ith particle

f s :

Solid–fluid hydrodynamic force

f e :

External force

F exti :

External force on the ith particle

F ri :

Repulsive force on the ith particle

F wr,ij :

Collision force amongst a particle and wall

F pr,ij :

Collision force amongst a particle and other particles

g α :

Temperature distribution functions

g eqα :

Temperature equilibrium distribution function

G Tα :

Heat source term

GrC :

Concentration Grashof number

GrT :

Thermal Grashof number

I p :

Particle moment

j α :

Concentration distribution functions

j eqα :

Concentration equilibrium distribution function

J C α :

Concentration source term

Le:

Lewis number

M p :

Particle mass

N p :

Numbers of particles

P :

Dimensionless pressure

Pr:

Prandtl number

q C :

Solid–fluid mass transfer driving force

q T :

Solid–fluid heat transfer driving force

Re:

Reynolds number

Ri:

Rayleigh number

R i(t):

Position of the particles

R i :

ith particle location

R j :

jth particle location

R wj :

Position of the wall

Sc:

Schmidt number

T(x, t):

Temperature field

T*(x, t):

Middle temperature

T ref :

Reference temperature

\(T_{i}^{\text{H}}\) :

Torque exerted on the ith particle

\(T_{i}^{\text{ext}}\) :

External torque on the ith particle

\(T_{i}^{\text{in}}\) :

Actual torque on the ith particle

u(x, t):

Velocity field

u*(x, t):

Middle velocity

u p(x, t):

Particle velocity

v i(t):

Translational velocity on the ith particle

w i(t):

Angular velocity on the ith particle

x :

Coordinates of the grid points

ξ :

Dimensionless concentration

θ :

Dimensionless temperature

τ f :

Momentum relaxation time

τ g :

Thermal relaxation time

τ j :

Concentration relaxation time

φ(x, t):

Particle concentration function

ρ(x, t):

Density field

ρ p :

Particle density

ρ f :

Fluid density

v :

Fluid kinematic viscosity

α :

Thermal conductivity

Г :

Diffusion coefficient

Δt :

Time step

w α :

Mass coefficient

β T :

Temperature expansion coefficient

β C :

Concentration expansion coefficient

ε w, ε p :

Stiffness coefficients

ζ :

Interfacial thickness

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Authors and Affiliations

  1. Department of Chemical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Raziyeh Safa & Ataallah Soltani Goharrizi

  2. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Saeed Jafari

  3. Department of Energy, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran

    Ebrahim Jahanshahi Javaran

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  1. Raziyeh Safa
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  2. Ataallah Soltani Goharrizi
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  3. Saeed Jafari
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  4. Ebrahim Jahanshahi Javaran
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Correspondence to Saeed Jafari.

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Safa, R., Soltani Goharrizi, A., Jafari, S. et al. Investigation of double-diffusive mixed convection effect on the particles dissolution in the shear flow using coupled SPM–LBM. J Therm Anal Calorim 144, 2497–2514 (2021). https://doi.org/10.1007/s10973-020-10019-z

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