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A numerical study of non-isothermal turbulent coaxial jets

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Abstract

In this work, we propose to study non isothermal air–air coaxial jets with two different approaches: parabolic and elliptic approaches. The standard k−ε model and the RSM model were applied in this study. The numerical resolution of the equations governing this flow type was carried out for: the parabolic approach, by a “home-made” CFD code based on a finite difference method, and the elliptic approach by an industrial code (FLUENT) based on a finite volume method. In forced convection mode (Fr = ∞), the two turbulence models are valid for the prediction of the mean flow. But for turbulent sizes, k−ε model gives results closer to those achieved in experiments compared to RSM Model. Concerning the limit of validity of the parabolic and elliptic approaches, we showed that for velocities ratio r lower than 1, the results of the two approaches were satisfactory. On the other hand, for r > 1, the difference between the results became increasingly significant. In mixed convection mode (Fr ≅ 20), the results obtained by the two turbulence models for the mean axial velocity were very different even in the plume region. For the temperature and the turbulent sizes the two models give satisfactory results which agree well with the correlations suggested by the experimenters for X ≥ 20. Thus, the second order model with σ t = 0.85 is more effective for a coaxial jet study in a mixed convection mode.

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Abbreviations

g :

gravity constant (m s−2)

P :

static pressure (Pa)

x, y :

longitudinal and transverse coordinates, (m)

X, Y :

dimensionless longitudinal and transverse coordinates

\({\overline{u}}, {\overline{v}}\) :

mean velocity components along x and y directions, (m s−1)

\({\overline{U}}, {\overline{V}}\) :

dimensionless mean velocity components

u′, v′:

fluctuating velocity components, (m s−1)

\({\overline{{U'}}}, {\overline{{V'}}}\) :

dimensionless fluctuating velocity components

\({\overline{T}}, \hbox{T}^{'}\) :

mean and fluctuating temperature (K)

D:

nozzle diameter (m)

k:

turbulent kinetic energy (m2 s−2)

r :

velocities ratio \((\frac{{\overline{{u_{{02}}}}}}{{\overline{{u_{{01}}}}}})\)

rD :

diameters ratio \((\frac{{D_{{2in}}}}{{D_{{1in}}}})\)

Re :

Reynolds number \({\left({\frac{{\overline{u}_{{02}} D_{{2\operatorname{int}}}}}{\nu}} \right)}\)

Pr :

Prandtl number \({\left({\frac{{\mu C_{p}}}{\lambda}} \right)}\)

Fr i :

Froude number \(\frac{{\overline{u} ^{2}_{{02}}}}{{g_{i} \beta D_{{2\operatorname{int}}} (\overline{{T_{{02}}}} - \overline{{T_{\infty}}})}}\)

ε:

dissipation rate of the turbulent kinetic energy, (m2 s−3)

\(\overline{\theta}\) :

dimensionless temperature \(\overline{\theta} = \frac{{{\left({\overline{T} - \overline{{T_{\infty}}}} \right)}}}{{{\left({\overline{{T_{{02}}}} - \overline{{T_{\infty}}}} \right)}}}\)

\(\overline{{\theta '}}\) :

dimensionless fluctuating temperature

ρ:

density (kg m−3)

μ:

molecular dynamic viscosity (kg s−1 m−1)

ν t :

turbulent viscosity (m2 s−1)

σ t :

turbulent prandtl number

β:

thermal expansion coefficient (K−1)

C:

jet axis

0:

nozzle exit

1:

inner nozzle

2:

outer nozzle

3, ∞:

ambiant middle (air)

in:

inner

out:

outer

max:

maximum

′:

fluctuation

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Authors and Affiliations

  1. Laboratoire de Mécanique des Fluides et Thermique, Ecole Nationale d’Ingénieurs de Monastir, Route de Ouardanine, Monastir, 5000, Tunisie

    Wassim Kriaa, Kamel Abderrazak & Hatem Mhiri

  2. Institut de Mécanique de Marseille, 60 rue Juliot Curie Technopôle de Château-Gombert, Marseille Cedex 13, 13453, France

    Georges Le Palec & Philippe Bournot

Authors
  1. Wassim Kriaa
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  2. Kamel Abderrazak
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  3. Hatem Mhiri
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  4. Georges Le Palec
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  5. Philippe Bournot
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Correspondence to Wassim Kriaa.

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Kriaa, W., Abderrazak, K., Mhiri, H. et al. A numerical study of non-isothermal turbulent coaxial jets. Heat Mass Transfer 44, 1051–1063 (2008). https://doi.org/10.1007/s00231-007-0343-7

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  • DOI: https://doi.org/10.1007/s00231-007-0343-7

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