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2D numerical simulation of impinging jet to the flat surface by \(k - \omega - \overline{{v^{2} }} - f\) turbulence model

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Abstract

In this article, the effects of dependent parameters such as inlet Reynolds number (4000 ≤ Re ≤ 20,000), nozzle-plate distance (4 ≤ H/D ≤ 10), plate diameter (18 < D/B < 40 based on other approaches), inlet flow type (fully developed, uniform and pulsed) and thermal boundary condition (constant heat flux and temperature) in confined and unconfined turbulent impinging jet are investigated considering constant inlet fluid (air). The obtained results are compared with other experimental and numerical results found in the literature. This investigation indicates that the \(k - \omega - \overline{{v^{2} }} - f\) model acquires appropriate performance in terms of thermal and dynamical fluid analysis compared to other turbulence models and experimental results.

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Abbreviations

ρ :

Fluid density (air)

k :

Turbulent kinetic energy

ω :

Specific dissipation rate

\(\overline{{v^{2} }}\) :

The turbulence stress normal to the wall

f :

Relaxation parameter in modelled \(\overline{{v^{2} }}\) pressure strain rate

μ :

Dynamic viscosity

μ t :

Turbulent eddy viscosity

x j :

Direction components

U j :

Velocity components

\({\text{P}}_{k}\) :

Production of the kinetic energy

β, β *, ζ, σ k , σ w , β o , f β , C μ , χ w , C 1, C 2, C L , C η :

Correlation coefficients

σ d :

Cross-diffusion

Ωij :

Mean rotation rate tensor

S ij :

Mean strain rate tensor

T :

Time scale

L :

Length scale

ν :

Kinetic viscosity

ν t :

Turbulent eddy kinetic viscosity

Nu :

Nusselt number

Re :

Reynolds number (=UD/ν)

u peak :

Maximum inlet velocity(=2 in nondimentional)

Pr, Pr t :

Laminar and turbulent Prandtl numbers

x :

Distance from stagnation point

y :

Distance from the target wall (impinging plate)

D :

Width of the slot nozzle

A :

Amplitude of pulsation

u avg :

Mean inlet velocity

fr :

Pulsation frequency

θ :

Temperature

τ :

Cyclic period time

H:

Distance between impinging plate and nozzle

X:

Width of the impinging plate

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yazd University, Yazd, Iran

    E. Khalaji, M. R. Nazari & Z. Seifi

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  1. E. Khalaji
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  2. M. R. Nazari
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  3. Z. Seifi
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Correspondence to M. R. Nazari.

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Khalaji, E., Nazari, M.R. & Seifi, Z. 2D numerical simulation of impinging jet to the flat surface by \(k - \omega - \overline{{v^{2} }} - f\) turbulence model. Heat Mass Transfer 52, 127–140 (2016). https://doi.org/10.1007/s00231-015-1688-y

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