| Libellé du cours : | Turbulent flows and small-scale turbulence |
|---|---|
| Département d'enseignement : | CMA / Chimie et Matière |
| Responsable d'enseignement : | Monsieur JEAN-MARC FOUCAUT |
| Langue d'enseignement : | |
| Ects potentiels : | 2 |
| Grille des résultats : | Grade de A+ à R |
| Code et libellé (hp) : | MR_TUR_CMA_TFS - Turbulent flows and small-scal |
Equipe pédagogique
Enseignants : Monsieur JEAN-MARC FOUCAUT
Intervenants extérieurs (entreprise, recherche, enseignement secondaire) : divers enseignants vacataires
Résumé
This course is taught by Prof. JC VASSILICOS Energy considerations motivate the need of two-point statistics for the understanding of the turbulence energy dissipation's independence on viscosity at high enough Reynolds number. The theory of two-point turbulence statistics is presented in a fully generalised Karman-Howarth framework which is then applied to locally homogeneous and locally stationary turbulence (equilibrium) to derive the main results of Kolmogorov 1941. The Taylor-Kolmogorov equilibrium relation for turbulence energy dissipation follows and its pivotal importance for turbulence phenomenology, theory and modeling is explained. This relation is then used to close the mass-momentum-energy equations for planar jets and planar wakes and it is shown how, on the basis of this relation, one can obtain the most basic and important properties of such boundary-free shear flows in cases where they are self-preserving: the jet/wake width growth with streamwise distance and the jet/width mean velocity/velocity deficit decay with streamwise distance. The course goes on to introduce the Turbulent/Non-Turbulent Interface (TNTI) and external intermittency, which is a remarkable phenomenon present very widely in turbulent shear flows. The TNTI is related to entrainment and jet/wake width growth and its mean speed relative to the flow is derived in terms of the Kolmogorov velocity. Finally, this second turbulence course also closes by demonstrating how some of this knowledge has been used in turbulence modelling, one-point turbulence model and the k-epsilon model in particular. Turbulence modelling requires some discussion of decaying homogeneous turbulence and homogeneous turbulence with uniform mean shear. This course's physical basis for two-point turbulence modelling such as Large Eddy Simulation is exploited in the turbulence simulation course.
Objectifs pédagogiques
At the end of the course, the student will be able to: - understand basic physics of interscale energy transfer, cascade and turbulence dissipation - understand the implications on these physics on turbulence dissipation scaling - derive from these physics and scalings theories of self-similar turbulent shear flows, use these theories broadly and apply their consequences to turbulence modeling - understand entrainment and the physics of the turbulent/non-turbulent interface and their consequences on turbulence prediction and modeling - know the caveats of current turbulence modeling and prediction methods
Objectifs de développement durable
Modalités de contrôle de connaissance
Contrôle Terminal
Commentaires: The evaluation will be done by a terminal written exam.
Ressources en ligne
Written turbulence course notes Exercises
Pédagogie
Class sessions with active student participation will be set up with classical blackboard teaching. Sessions will be followed by tutorial sessions with exercises to be done independently during class and/or prepared at home. At the next tutorial session, these exercises will be corrected.
Séquencement / modalités d'apprentissage
| Nombre d'heures en CM (Cours Magistraux) : | 20 |
|---|---|
| Nombre d'heures en TD (Travaux Dirigés) : | 0 |
| Nombre d'heures en TP (Travaux Pratiques) : | 0 |
| Nombre d'heures en Séminaire : | 0 |
| Nombre d'heures en Demi-séminaire : | 0 |
| Nombre d'heures élèves en TEA (Travail En Autonomie) : | 0 |
| Nombre d'heures élèves en TNE (Travail Non Encadré) : | 0 |
| Nombre d'heures en CB (Contrôle Bloqué) : | 0 |
| Nombre d'heures élèves en PER (Travail PERsonnel) : | 0 |
| Nombre d'heures en Heures Projets : | 0 |
Pré-requis
Good level in vector calculus and mathematics in general, and a prior introduction to fluid dynamics