| Course label : | Turbulent flows and small-scale turbulence |
|---|---|
| Teaching departement : | CMA / |
| Teaching manager : | Mister JEAN-MARC FOUCAUT |
| Education language : | |
| Potential ects : | 2 |
| Results grid : | |
| Code and label (hp) : | MR_TUR_CMA_TFS - Turbulent flows and small-scal |
Education team
Teachers : Mister JEAN-MARC FOUCAUT
External contributors (business, research, secondary education): various temporary teachers
Summary
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.
Educational goals
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
Sustainable development goals
Knowledge control procedures
Final Exam
Comments: The evaluation will be done by a terminal written exam.
Online resources
Written turbulence course notes Exercises
Pedagogy
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.
Sequencing / learning methods
| Number of hours - Lectures : | 20 |
|---|---|
| Number of hours - Tutorial : | 0 |
| Number of hours - Practical work : | 0 |
| Number of hours - Seminar : | 0 |
| Number of hours - Half-group seminar : | 0 |
| Number of student hours in TEA (Autonomous learning) : | 0 |
| Number of student hours in TNE (Non-supervised activities) : | 0 |
| Number of hours in CB (Fixed exams) : | 0 |
| Number of student hours in PER (Personal work) : | 0 |
| Number of hours - Projects : | 0 |
Prerequisites
Good level in vector calculus and mathematics in general, and a prior introduction to fluid dynamics