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Annexe Chapitre 2Figure (5) shows, for example, thenumerical results of the turbulent passive'scalar flux v'θ obtained with the twomodels. Once again a good agreement is2.52observed between the DNS data ofRogers et al. [1] and the numerical resultsobtained with the first and second ordermodels.DNS(Rogers et al.,[1])second orderfirst order1.51v'θ'0.50-0.5-1-1.50 5 10 15StFigure 5: Development of the turbulent passive scalar flux v'θ '. Comparison between the numerical results andDNS data of Rogers et al. [1].43.5DNS(Rogers et al.,[1])second orderfirst order32.5R21.510.500 5 10 15StFigure 6: Development of the dimensionless parameter R . Comparison between the numerical results and DNSdata of Rogers et al. [1].A comparison between the predictedlength and time scales characterising thebehaviour of the velocity and scalarfields is presented in figures (6) and (7).173
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
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N° d’ordre : 2454Thèseprésent
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RemerciementsLe travail présenté
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ResuméCe travail vise l’amélior
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Sommaire2.5.2 Equations de transpor
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Sommaire4.6.4 Profils de vitesse mo
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Nomenclatureu' ' ( S )Liu LjLk , in
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Chapitre 1: Introduction générale
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Chapitre 1: Introduction générale
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Chapitre 2: Modélisation à deux f
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Page 170 and 171: Bibliographiefor simulating hydrody
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Page 174 and 175: BibliographieOxygen sensor manuel,
Page 176 and 177: BibliographieVoinov O. V., 1973. Fo
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Page 180 and 181: Annexe Chapitre 2equation of the sc
Page 182 and 183: Annexe Chapitre 210864u'v' v' 220-2
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Page 188 and 189: Annexe Chapitre 2[3] K. Abe, T. Kon
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