Analyse expérimentale et modélisation du transfert de matière et du ...
Analyse expérimentale et modélisation du transfert de matière et du ...
Analyse expérimentale et modélisation du transfert de matière et du ...
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Annexe Chapitre 2First and second or<strong>de</strong>r mo<strong>de</strong>lling of turbulent scalar transportin homogeneous turbulenceH. Ayed 1,2* , J. Chahed 1 , and V. Roig 21 Ecole Nationale d’Ingénieurs <strong>de</strong> Tunis BPN°37, 1002 Le Belvédère, Tunis, Tunisia,2 Institut <strong>de</strong> Mécanique <strong>de</strong>s flui<strong>de</strong>s <strong>de</strong> Toulouse, UMR CNRS 5502, Av. C. Soula, 31400, Toulouse, France*Corresponding author. E-mail: ayed@imft.frAbstractThe present work aims at <strong>de</strong>veloping a full second or<strong>de</strong>r mo<strong>de</strong>l for turbulent transportof a passive scalar. A turbulent Prandtl number formulation is obtained by re<strong>du</strong>cing thesecond or<strong>de</strong>r mo<strong>de</strong>lling. A first or<strong>de</strong>r turbulence mo<strong>de</strong>l is than proposed with analgebraic formulation of the turbulent scalar flux. The mo<strong>de</strong>l is tested in homogeneousshear flow with an imposed mean scalar gradient. The Direct Numerical Simulation(DNS) data by Rogers <strong>et</strong> al. [1] were used in the validation of the first and second or<strong>de</strong>rmo<strong>de</strong>lling of the turbulent passive scalar transport. The comparison of the numericalresults with DNS data shows good agreements.Keywords: Passive scalar, turbulent flux, homogeneous shear flow, turbulence mo<strong>de</strong>lling1. Intro<strong>du</strong>ctionThe prediction of the transport of scalarssuch as temperature, chemical species orpollutants in turbulent flows is of greatimportance in the <strong>de</strong>sign and the controlof in<strong>du</strong>strial fluid systems. During thelast <strong>de</strong>ca<strong>de</strong>s, an important progress in thestatistical mo<strong>de</strong>lling of the turbulenttransport of passive scalar has beenachieved. Number of recent works was<strong>de</strong>voted to the <strong>de</strong>velopment of first andsecond or<strong>de</strong>r turbulence mo<strong>de</strong>ls, (Nagano<strong>et</strong> al. [2]; Abe <strong>et</strong> al. [3,4]; Kawamura <strong>et</strong>al. [5]; Wikström <strong>et</strong> al. [6]). The mo<strong>de</strong>l<strong>de</strong>veloped by Nagano <strong>et</strong> al. [2] is<strong>de</strong>veloped for heat transfer problems inboth wall and free turbulent flows. Abe <strong>et</strong>al. [3,4] proposed a modified version ofNagano mo<strong>de</strong>l. Furthermore, the mo<strong>de</strong>lcan also take into account the lowReynolds number effects in the near-wallregion and is also applicable to complexheat transfer fields with flow separationand reattachment by intro<strong>du</strong>cing theKolmogorov velocity scale. Kawamura <strong>et</strong>al. [5] proposed a transport mo<strong>de</strong>l for th<strong>et</strong>urbulent heat flux by intro<strong>du</strong>cing theinteraction b<strong>et</strong>ween the mean temperatureand velocity gradients in rapid term ofturbulent scalar flux equation.On the other hand, many experimentaland numerical simulation works were165