E. Serre

1
E. Serre
NUMERICAL MODELLING OF TURBULENT FLOWS
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_at_L3m.univ-mrs.fr
2

• 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
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

• OUTLINE
• PARTI
• Introduction
• Nature of turbulent flows
• Statistical description of turbulent flows
• Homogeneous turbulence theory
• Turbulent flow equations

• PART II
• - Numerical modellingDNS, RANS, LES

5
Introduction
6

• Most flows in nature technical applications are
  turbulent

Flow around a submarine
Flow around propellers
Pictures of Jupiter
7

• Whats 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

• Such flows occur when the source of kinetic
  energy moving the fluid gtgt 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 flow.

Examples of laminar flows
sphere (Johnson Patel 1999)
axisymmetric base (Siegel et al. 2008)
9

• 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
Non turbulent flow, Van Goghs clouds have no
small scales!
Turbulent illustrates by this sketch of a free
water jet issuing from a square hole into a pool
11
The world's first use of visualization as a
scientific tool to study turbulence
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.
Leonardo da Vinci
12

• 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
No change in time, streamlines // pipe axis
Flowing water
Re gt2300, turbulent Occurrence of small scales.
Generated by the inertial forces and
dissipated by the viscous forces.
ReUaxialD/n
13
From laminar to turbulent flow
2D cylinder (Williamson 1996)

• Dynamics of large scale structures

• Hydrodynamic stability (cf. lecture F. Gallaire)
  explains how structures of a specific frequency
  and scale are selected and emerge

14
From laminar to turbulent flow

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

15
From laminar to turbulent flow
Flow past a D-shaped cylinder
Experiments, Re13000 Parezanovic Cadot
2011-2012
Separated mean flow
Large scale dynamics (low frequency)
Instantaneous flow
Periodic flow dominated by vortex shedding
small scales dynamics (high frequency)
Power spectra
16

• 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

• - Needs to understand
• Meteo forecast,

• 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 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
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

• 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 examples

• Actual flows industrial applications (RANS)
• Efflux pattern around an airplane at Ma0.15

21

• Actual flows industrial applications (LES) for
  simpler geometries

Turbulent structures around wing
Turbulent structures around propellers
22

• Academic flows research interests (high-order
  LES)
• Turbulent structures around a square cylinder
  (from Minguez et al. 2011)

23
In summary