numerical modelling of turbulent flows : introduction numerical modelling of turbulent flows e....

NUMERICAL MODELLING OF TURBULENT FLOWS : Introduction

NUMERICAL MODELLING OF TURBULENT NUMERICAL MODELLING OF TURBULENT FLOWSFLOWS 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: [email protected]


• 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.


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.


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


Introduction


• Most flows in nature & technical applications are turbulent

Pictures of Jupiter

Flow around propellers

Flow around a submarine


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


• Such flows occur when the source of kinetic energy moving the fluid >> to viscous forces opposed by the fluid to move.

• Conversely, flow in which the kinetic energy dies out due to the action of fluid molecular viscosity is called laminar flowlaminar flow.

axisymmetric base (Siegel et al. 2008)

sphere (Johnson & Patel 1999)

Examples of laminar flows


• 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?


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!


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


• 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=UaxialD/

No change in time, streamlines // pipe axis

Re >2300, turbulentOccurrence of small scales.

Generated by the inertial forces and dissipated by the viscous forces.

Flowing water


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)



•Turbulent flow: Large-scale structures + small-scale turbulence



Flow past a D-shaped cylinder

Experiments, Re=13000Parezanović & 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)


• 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,…


• 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 obstacledevelops turbulent wakes and generally increases the drag It has to be avoided to obtain better aerodynamics properties


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


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


Numerical examples

Actual flows: industrial applications (RANS)

Efflux pattern around an airplane at Ma=0.15


Actual flows: industrial applications (LES) for simpler geometries

Turbulent structures around propellers

Turbulent structures around wing


Academic flows: research interests (high-order LES)

Turbulent structures around a square cylinder (from Minguez et al. 2011)


In summary:

numerical modelling of turbulent flows : introduction numerical modelling of turbulent flows e....

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