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A computational work on turbulent flow and heat transfer in a channel fitted with inclined baffles

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Abstract

Numerical studies of momentum and heat transfer characteristics have been investigated of a steady incompressible turbulent flow of air through channel. The channel has inclined baffles which are arranged on the walls in a periodically staggered way. The governing equations, namely, continuity, Navier–Stokes and energy, based on k–ω turbulence model to describe the turbulence phenomenon are solved using the finite volume method and the SIMPLE algorithm. Calculations are performed for a Reynolds number between 12,000 and 38,000. The axial velocity profiles, the velocity fields, the local and average coefficient of friction and the Nusselt number distribution were obtained for all the geometry considered and for different sections selected, upstream, downstream and between the two inclined baffles. Simulation results which were obtained by the use of baffles are validated by an experimental study. Good agreement is observed between numerical and experimental results data in the literature.

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Abbreviations

a:

Sound speed

Cp :

Specific heat at constant pressure (J/kg K)

D:

Distance between two baffles (m)

Dh :

Hydraulic diameter of channel, (Dh = 2H) (m)

Dω :

Crossing the diffusion term (m2/s)

e:

Width of plate baffle (m)

f :

Friction factor

f 0 :

Friction factor in smooth pipe at the same Reynolds number

F(M t ):

The compressibility function

Gk :

Production of turbulent kinetic energy due to velocity gradient through (m2/s2)

Gω :

Kinetic energy production due to buoyancy (m2/s2)

h:

Baffle height (m)

H:

Height of air tunnel in pipe (m)

k:

Turbulent kinetic energy (m2/s2)

L:

Channel length (m)

L1 :

Distance upstream of the first baffle (m)

L2 :

Distance downstream of the second baffle (m)

\( \overline{Nu} \) :

Averaged Nusselt number

\( Nu_{x} \) :

Local Nusselt number

P:

Pressure (pa)

Pr:

Prandtl number

Prt :

Turbulent Prandtl number

Re:

Reynolds number

\( \text{Re}_{t} \) :

One of the constants of the k–ω turbulence model

R k :

One of the constants of the k–ω turbulence model

\( \text{Re}_{\omega } \) :

One of the constants of the k–ω turbulence model

Sk, Sω :

Source term for k and ω

T:

Temperature (°C)

ui :

Velocity components in the xi-direction (m/s)

uj :

Components in the xj-direction (m/s)

Uin :

Inlet velocity (m/s)

\( \overline{U} \) :

Mean velocity in channel (m/s)

u, v:

Fluid velocity in the x, y direction (m/s)

\( \overrightarrow {V} \) :

Velocity vector (m/s)

x:

Longitudinal nodal increments (m)

xi, xj :

Cartesian coordinates (m)

Yk, Yx :

Dissipation of k and ω (m2/s)

ω:

The specific dissipation rate of turbulence energy (m2/s)

\( \Upgamma_{k} \), \( \Upgamma_{\omega } \) :

Effective diffusivity of k and ω

ρ:

Linear density of the air (kg/m)

λ :

Thermal conductivity (w/m °C)

μ:

Dynamic viscosity (kg/ms)

μ l , μ t :

Laminar, turbulent viscosity (kg/ms)

μf :

Dynamic viscosity of fluid (kg/ms)

μ e :

Effective viscosity (Pa s)

ν :

Kinematics viscosity (m2/s)

σk :

Model constant for the k-equation

σω :

Model constant for the ω-equation

τ w :

The shear stress to the wall (kg/(s2 m))

Δp :

Pressure losses

α :

Coefficient of thermal expansion (K−1)

δ ij :

Stress tensor

\( \alpha^{ * } \) :

Coefficient of the turbulent viscosity causing a low-Reynolds-number correction

\( \alpha_{\infty }^{ * } \) :

One of the constants of k–ω turbulence model

\( \alpha_{0}^{ * } \) :

One of the constants of k–ω turbulence model

f β :

One of the constants of k–ω turbulence model

χ ω :

One of the constants of k–ω turbulence model

\( \zeta^{*} \) :

One of the constants of the model k−ω

\( M_{t}^{2} \) :

One of the constants of k–ω turbulence model

\( M_{t0} \) :

One of the constants of k–ω turbulence model

ϕ :

Represents the dependent variables of u, v, p, k, ω, and T

\( \phi^{ * } \) :

Denote values of the previews iterations

δ :

Prescribed error

in, out :

Inlet, outlet of the test section

b:

Bulk

t :

Turbulent

w :

Wall

e :

Effective

f :

Fluid

s :

Solid

i, j :

Refers coordinate direction vectors

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Authors and Affiliations

  1. Laboratoire d’Energétique et Thermique Appliquée (ETAP), Université Abou Bekr Belkaid, Tlemcen, BP 230, 13000, Tlemcen, Algeria

    Rachid Saim

  2. Département de Génie Mécanique, Faculté de Technologie, Université Abou Bekr Belkaid, Tlemcen, BP 230, 13000, Tlemcen, Algeria

    Rachid Saim & Rachid Bouchenafa

  3. Département de Génie Mécanique, Faculté de Génie Mécanique, Université des Sciences et de Technologies (USTO), BP 1505, El M’naouar Oran, Algeria

    Hamidou Benzenine

  4. Department of Mechanical Engineering, Technology Faculty, Firat University, 23119, Elazig, Turkey

    Hakan F. Oztop

  5. Department of Mechanical Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia

    Khaled Al-Salem

  6. IRTES-M3M - EA 7274, Université de Technologie de Belfort-Montbéliardsite de Sévenans, 90010, Belfort cedex, France

    Said Abboudi

Authors
  1. Rachid Saim
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  2. Rachid Bouchenafa
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  3. Hamidou Benzenine
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  4. Hakan F. Oztop
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  5. Khaled Al-Salem
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  6. Said Abboudi
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Corresponding author

Correspondence to Hakan F. Oztop.

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Saim, R., Bouchenafa, R., Benzenine, H. et al. A computational work on turbulent flow and heat transfer in a channel fitted with inclined baffles. Heat Mass Transfer 49, 761–774 (2013). https://doi.org/10.1007/s00231-013-1121-3

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  • DOI: https://doi.org/10.1007/s00231-013-1121-3

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