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NUMERICAL SIMULATIONS OF A PASSIVE SCALAR TRANSPORT IN A JET FLOW Laboratoire de Modlisation en Hydraulique et Environnement Prepared by : Nabil MRABTI Presented by : Zouhaier HAFSIA Slide 2 2 Plan Introduction. Mathematical model (chen profile at the inlet). Numerical results. Conclusions. Rodi adjusments of the standard k- constants Slide 3 3 INTRODUCTION It is necessary to validate the transport model in a simple case : monophasic jet, 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 on the 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 with Gaussian profile Slide 4 4 THE JET FLOW PARAMETERS D= 30 mm; Win = 0.20 m/s Slide 5 5 GOVERNING EQUATIONS - equation : - Mass conservation For a stationary single-phase flow and with no buoyancy for a quasi-parallel flow having axial symmetry, the transport equations is : - Momentum - Scalar transport equation : - Kinetic equation : Slide 6 6 The model in its form described previously has been applied with success in a lot of type of flow but the universality of its constants cannot be expected. The field of application of this model can be extended thus if its constants are substituted by functions 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 users to place in their files of entry, the formulas for which it cannot have an equivalent there in the source program. Slide 7 7 Wc is the longitudinal mean velocity on the axis of the jet and is the width 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: Slide 8 8 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 the experimental data. Slide 9 9 Longitudinal variation of Slide 10 10 Longitudinal variation of Slide 11 11 Fig. 4 : Velocity Profile at : Z=2D. Mean velocity profiles Slide 12 12 Fig. 5 : Velocity Profile at : Z=3D. Mean velocity profiles Slide 13 13 RESULTS OF SIMULATIONS Fig. 6 : Velocity Profile at : Z=4D. Mean velocity profiles Slide 14 14 Turbulence Intensity profiles Fig.(5-a): Velocity fluctuations profiles at Z=2D. Slide 15 15 Turbulence Intensity profiles Fig.(5-a): Velocity fluctuations profiles at Z=3D. Slide 16 16 Turbulence Intensity profiles Fig.(5-a): Velocity fluctuations profiles at Z=4D. Slide 17 17 Concentrations profiles Fig.(5-a): Concentration profiles at Z=2D Slide 18 18 Concentrations profiles Fig.(5-a): Concentration profiles at Z=3D Slide 19 19 Concentrations profiles Fig.(5-a): Concentration profiles at Z=4D Slide 20 CONCLUSIONS * The monophasic jet transporting a passive scalar is affected by the conditions at the injection which describe the nature of the nozzle. * The Rodi adjustments for the jet flow provided significant improvements of hydrodynamic jet structure : for the mean velocity profiles and of the turbulent intensity at three sections in the establishment zone; however the concentrations profiles remain not acceptable. * Although, the modelling of the scalar transport by models which are based on a direct proportionality between diffusivities of momentum and that of the passive scalar appears insufficient. In fact, many authors such us Feath and al (1995) showed that the Schmidt number is variable through the cross-section of the stream discharge. Slide 21