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

Annexe Chapitre 210864u'v' v' 220-2-4-6u'v' (DNS Rogers et al.[1])-8 v' 2 (DNS Rogers et al.[1])-10u'v' (RS Launder et al.[10])v' 2 (RS Launder et al.[10])-120 5 10 15StFigure 1: Development of the Reynolds stress tensor components of Reynolds stress tensor in a sheared turbulence(DNS by Rogers et al. [1])Once the Reynolds stress transport modelassessed, the analysis is then focussed onthe second order modelling of thetransport equation of the turbulentpassive scalar. For this purpose theclosure of the pressure-scalar gradientcorrelations and of the destruction ratetensor are evaluated, and the numericalresults are compared with the (DNS) dataof Rogers et al. [1].For this purpose different closures of thepressure-scalar gradient term were tested.In particular the three closures proposedby Wikström et al. [6] (models a, b, andc) were tested and an additionalformulation of the model is proposed.This model writes:DDt− C⎛' '' '⎜∂Ui ' 'uiθ= − ujθ+ uiuj⎝ ∂xjεu θ + Ck' 'θ1 i θ 4' ' ∂Θuiuj∂xj∂Θ ⎞⎟∂xj ⎠(15)In equation (15), the constants of theoriginal Wikström et al. [6] model arefixedtor + 1C1= 1.3 ; C 35θ θ 4= 0.rC C = C 0 .θ 2=θ 3 θ 5=andIn these simulations the transportequation of the destruction rate ε θof thescalar variance q is computed using thefollowing constants ( C = 2. 4 , C = 1. 89 ,γ 1 γ 2*=*C 0.1 and C = 0. 95 ). The results ofγ 1 γ 2these simulations are reported in figure(2) and compared to the (DNS) data ofRogers et al. [1]. Figure (2) shows a goodagreement between the DNS data ofRogers et al. [1] and the numerical results'of the turbulent passive scalar fluxes u'θ'and v'θ obtained with the second ordermodel as it is adjusted above.169