1. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction NUMERICAL MODELLING OF TURBULENT FLOWS E. Serre Laboratoire de Modélisation, Mécanique et Procédés Propres M2P2 UMR7340 CNRS / Aix –Marseille Université Technopôle de Château-Gombert; F-13451 Marseille Cedex 20, France LES of a turbulent flow over a square cylinder Email: eric.serre@L3m.univ-mrs.fr

2. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction BOOKS: Pope (2003, Cambridge). Part I provides a general introduction to turbulent flows: behaviour, quantitative description, fundamental physical processes… Part II is concerned with different approaches for modeling and simulating, turbulent flows.

3. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Lesieur (1997) Reviews the main characteristics and general theorems of rotational fluids (liquids or gases), with applications to aerodynamics and geophysical fluid dynamics. Emphasis is placed both on unpredictability, mixing, and coherent vortices or structures.

4. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction OUTLINE PARTI –Introduction –Nature of turbulent flows –Statistical description of turbulent flows –Homogeneous turbulence theory –Turbulent flow equations PART II - Numerical modelling:DNS, RANS, LES

5. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Introduction

6. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Most flows in nature & technical applications are turbulent Pictures of Jupiter Flow around propellers Flow around a submarine

7. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction What’s turbulence? Intuitively: turbulent flow= flow which is disordered in time and space+ many spatial and temporal scales. State of fluid motion which is characterized by apparently random and chaotic vorticity. Turbulence usually dominates all other phenomena

8. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Such flows occur when the source of kinetic energy moving the fluid >> to viscous forces opposed by the fluid to move. laminar flowConversely, flow in which the kinetic energy dies out due to the action of fluid molecular viscosity is called laminar flow. axisymmetric base (Siegel et al. 2008) sphere (Johnson & Patel 1999) Examples of laminar flows

9. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction You are a fluid dynamicist visiting the Louvre in Paris and are asked by the curator to comment on the paintings below. What do you say?

10. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Turbulent illustrates by this sketch of a free water jet issuing from a square hole into a pool Non turbulent flow, Van Gogh’s clouds have no small scales!

11. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Leonardo da Vinci “…thus the water has eddying motions, one part of which is due to the principal current, the other to the random and reverse motion." L. da Vinci Da Vinci provided the earliest reference to the importance of vortices in fluid motion: Finally, da Vinci's words "... The small eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by both small eddies and large.." presage Richardson's cascade, coherent structures, and large-eddy simulations, at least. The world's first use of visualization as a scientific tool to study turbulence

12. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Demonstrated by an experiment first reported by O. Reynolds (1883) Flow inside a pipe becomes turbulent every time a single parameter Re would increase Dye injected on the centerline Re=U axial D/ No change in time, streamlines // pipe axis Re >2300, turbulent Occurrence of small scales. Generated by the inertial forces and dissipated by the viscous forces. Flowing water

13. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction From laminar to turbulent flow Dynamics of large scale structures Hydrodynamic stability (cf. lecture F. Gallaire) explains how structures of a specific frequency and scale are selected and emerge 2D cylinder (Williamson 1996)

14. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction From laminar to turbulent flow Turbulent flow: Large-scale structures + small-scale turbulence

15. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction From laminar to turbulent flow Flow past a D-shaped cylinder Experiments, Re=13000 Parezanović & Cadot 2011-2012 Separated mean flow Instantaneous flow Power spectra Periodic flow dominated by vortex shedding Large scale dynamics (low frequency) small scales dynamics (high frequency)

16. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Significance of studying turbulence –The vast majority of flows are turbulent Meteorology: Transport processes of momentum, heat, water as well as substances and pollutants Health care: Pollution Engineering: Wind,…

17. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction In a flow stream, it has a consequence on the sediment transport Small-scale turbulence in the atmosphere can be an obstacle towards the accuracy of astronomic observations - Needs to understand Meteo forecast, … - Needs to control Promote or vanish turbulence, … Any rapid fluid passing an obstacle develops turbulent wakes and generally increases the drag It has to be avoided to obtain better aerodynamics properties

18. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction The study of turbulent flows Discovery: expe or simulation to provide qualitative and quantitative information Modelling: theoretical or modelling studies to dv tractable mathematical models that can predict properties Control: to manipulate or control the flow or the turbulence in a beneficial way

19. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Numerical modelling Any complete solution must resolve accurately these fine- scale motions + the large scale overall flow picture  Only feasible for relatively simple turbulent flows Two broad strategies for modelling engineering flows - Large-eddy simulation (LES): one resolves as large a proportion of the turbulent fluctuations as one judges necessary (or can afford) and applies a model - Reynolds averaged Navier-Stokes (RANS): the effect of all turbulent fluctuations are subsumed within the model

20. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction Numerical examples  Actual flows: industrial applications (RANS) Efflux pattern around an airplane at Ma=0.15

21. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction  Actual flows: industrial applications (LES) for simpler geometries Turbulent structures around propellers Turbulent structures around wing

22. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction  Academic flows: research interests (high- order LES) Turbulent structures around a square cylinder (from Minguez et al. 2011)

23. NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction In summary: