NUMERICAL SIMULATIONSOF A PASSIVE SCALARTRANSPORT IN A JET FLOW
Laboratoire de Modélisation en Hydraulique et Environnement
Prepared by :
Nabil MRABTI
Presented by :
Zouhaier HAFSIA
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Plan
Introduction.
Mathematical model (chen profile at the inlet).
Numerical results.
Conclusions.
Rodi adjusments of the standard k-ε constants
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INTRODUCTION
It is necessary to validate the transport model in a simple case : monophasicjet, for example
An important progress was made in the CFD
It is possible to simulate a very large varieties of flow transport processes
We use the CFD code PHOENICS for numerical simulations.
Since 1980, Rodi showed that the constants of the (k-eps) model depends onthe decelaration of axial velocity
Numerical results are compared to experimental data of Hu (2000)associated with the establishment zone of the jet flow.
Chen in 1979 adjust turbulence intensity at the inlet of the jet flow withGaussian profile
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THE JET FLOW PARAMETERS
D= 30 mm; Win = 0.20 m/s
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GOVERNING EQUATIONS
- ε equation :
- Mass conservation
For a stationary single-phase flow and with no buoyancy for a quasi-parallelflow having axial symmetry, the transport equations is :
- Momentum
- Scalar transport equation :
- Kinetic equation :
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The model in its form described previously has been applied with success in a lotof type of flow but the universality of its constants cannot be expected. The field ofapplication of this model can be extended thus if its constants are substituted byfunctions of parameters of the flow. In this context comes the setting of Rodi and al.(1980) relative to jet flows which the constants are replaced by the equations:
: Maximal velocity
: (c: center and e: ambient fluid)
The manipulation of the constants of the model can be done by the technique"PLANT" relative to PHOENICS.
PLANT is an attachment to the PHOENICS-SATELLITE that allows the usersto place in their files of entry, the formulas for which it cannot have anequivalent there in the source program.
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Wc is the longitudinal mean velocity on the axis of the jet and is thewidth of the jet when the W is equal to 1%.
The gradient of velocity term is approximated by :
RODI ADJUSMENTS
Thus, we can modify the term directly source of the dissipation rate while substituting,in the expression of, by:
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BOUNDARY CONDITIONS :
- Standard inlet conditions :
- For a plane of symetry :
For the kinetic energy and the dissipation rate at the inlet :
- Chen profile at inlet (gaussian profile ) :
These two coefficients are adjusted numerically in order to reproduce theexperimental data.
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Longitudinal variation of
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Longitudinal variation of
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Fig. 4 : Velocity Profile at : Z=2D.
Mean velocity profiles
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Fig. 5 : Velocity Profile at : Z=3D.
Mean velocity profiles
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RESULTS OF SIMULATIONS
Fig. 6 : Velocity Profile at : Z=4D.
Mean velocity profiles
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Turbulence Intensity profiles
Fig.(5-a): Velocity fluctuations profiles at Z=2D.
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Turbulence Intensity profiles
Fig.(5-a): Velocity fluctuations profiles at Z=3D.
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Turbulence Intensity profiles
Fig.(5-a): Velocity fluctuations profiles at Z=4D.
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Concentrations profiles
Fig.(5-a): Concentration profiles at Z=2D
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Concentrations profiles
Fig.(5-a): Concentration profiles at Z=3D
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Concentrations profiles
Fig.(5-a): Concentration profiles at Z=4D
CONCLUSIONS
* The monophasic jet transporting a passive scalar is affected by theconditions at the injection which describe the nature of the nozzle.
* The Rodi adjustments for the jet flow provided significantimprovements of hydrodynamic jet structure : for the mean velocityprofiles and of the turbulent intensity at three sections in theestablishment zone; however the concentrations profiles remain notacceptable.
* Although, the modelling of the scalar transport by models which arebased on a direct proportionality between diffusivities of momentum andthat of the passive scalar appears insufficient. In fact, many authors suchus Feath and al (1995) showed that the Schmidt number is variablethrough the cross-section of the stream discharge.
