Heat and Mass Transfer

, Volume 49, Issue 5, pp 629–656

Temperature impact on the turbulence generated by the interaction of twin inline inclined jets in crossflow


  • A. Radhouane
    • TTPI, École Nationale d’Ingénieurs de MonastirUniversité de Monastir
  • I. Bhouri Baouab
    • TTPI, École Nationale d’Ingénieurs de MonastirUniversité de Monastir
    • LGM, Institut Préparatoire aux Etudes d’Ingénieurs de MonastirUniversité de Monastir
  • H. Mhiri
    • TTPI, École Nationale d’Ingénieurs de MonastirUniversité de Monastir
  • Ph. Bournot
    • IUSTI, UMR CNRS 7343, Technopôle de Château-Gombert
  • G. Le Palec
    • IUSTI, UMR CNRS 7343, Technopôle de Château-Gombert

DOI: 10.1007/s00231-012-1108-5

Cite this article as:
Radhouane, A., Baouab, I.B., Mahjoub Saïd, N. et al. Heat Mass Transfer (2013) 49: 629. doi:10.1007/s00231-012-1108-5


Consideration is given to the interaction of twin tandem jets with an oncoming uniform crossflow. A variable temperature is assumed for the emitted jets while the crossflow is maintained constant, equivalent to the ambient temperature. Both jet nozzles are elliptic, as initially inclined with an angle of 60°, placed three diameters apart in line with the crossflow and discharge a nonreactive fume. The handled configuration is numerically simulated in the present work, by means of the finite volume method together with a non uniform grid system. The model is first validated with reference to available experimental data, in the simple isothermal case of air jets in air crossflow. It is then upgraded by considering a nonreactive fume discharged at a variable temperature. The upgraded model turbulence is described by means of the Reynolds Stress Model second order turbulent closure model. The present work is to our knowledge pioneering in the introduction of this particular model is such a configuration and its introduction proved to be highly valuable since is described satisfyingly the turbulent behavior of the resulting flowfield. This behavior is, precisely, specified in terms of shear stress components whose evolutions, explored along the different directions of the domain, showed a more pronounced vertical mixing, and gave rise to more significant vortices in most characterizing zones: near the injection plane as well as within the discharging nozzles.

List of symbols

C p

Specific heat, J kg−1 K−1


Nozzles’ spacing, m

G k

Term of production due to buoyancy forces, kg m−1 s−3

P k

Term of production due to the mean gradients, kg m−1 s−3


Injection to mainstream velocity ratio (R = u i /U ), no unit

S i j

Mean strain sate, no unit


Temperature, K


Crossflow velocity, m s−1

V 0

Injection velocity, m s−1


Jet nozzle diameter, m

\( \tilde{f} \)

Mass fraction, no unit


Gravitational acceleration, m s−2


Kinetic energy of turbulence, m2 s−2

ũ i

Velocity component along i direction, ms−1

\( \overline{{{\text{u}}_{\text{i}}^{\prime \prime } {\text{u}}_{\text{j}}^{\prime \prime } }} \)

Reynolds stress, m2 s−2

x i

Coordinate along i direction, m

Greek symbols


Injection angle with reference to the free stream (x axis), °


Thermal expansion coefficient, K−1

δ ij

Kronecker symbol (=1 if i = j and 0 if i ≠ j), no unit


Dissipation rate of the turbulent kinetic energy, no unit


Thermal diffusivity, m2 s−1


Thermal conductivity, W (mK)


Kinetic viscosity, kg (m s)−1


Turbulent (or eddy) viscosity, kg (m s)−1


Kinematic viscosity, m2 s−1


Density, Kg m−3


Conditions in crossflow, no unit


Exit section of the jet, no unit



Reynolds average, no unit


Favre average, no unit

Dimensionless groups


Prandtl number (Pr = μCp/λ)


Reynolds number (Re = uid/ν)


Schmidt number (Sc = ν/κ)

Copyright information

© Springer-Verlag Berlin Heidelberg 2012