Analyse expérimentale et modélisation du transfert de matière et du ...

Annexe Chapitre 2Figure (6) represents the dimensionlesskε parameter R = θ that represents theεqratio between the hydrodynamicturbulence timescale to the scalarturbulence time scale. Figure (7)3.53represents the dimensionless parameterk SB = that represents the length scaleq S θof the fluctuating velocity field comparedto the fluctuating scalar field.DNS(Rogers et al.[1])second orderfirst order2.52B1.510.500 5 10 15StFigure 7: Development of the dimensionless parameter B . Comparison between the numerical results and DNSdata of Rogers et al. [1].5. ConclusionIn this study, we have analysed a fullsecond order model for turbulenttransport of passive scalar flux, inhomogeneous turbulence. The model hasbeen tested against the DNS data ofRogers et al. [1] in homogeneousturbulence. The passive scalar fluxequation incorporates a full modelling ofthe pressure-scalar gradient correlationproposed by Wikström et al. [6]. A firstorder modelling is deduced from areduction of a second-order model. Thismodel is based on two-equationturbulence model ( k − ε model withalgebraic relations) and modelling of thetransport equations of the scalar variance( q ) and of its dissipation rate ε θ. Thenumerical results clearly show that themodel reproduces correctly thedevelopment of the turbulent passivescalar flux.6. References[1] M. M. Rogers, P. Mansour, W. C. Reynolds, J.Fluid Mech. , 203, (1989),77.[2] Y. Nagano, M. Tagawa, T. Tsuji, InProceedings of the ASME/JSME ThermalEngineering Joint Conference, Vol.3, (1991), 233-240.174