l ehrstuhl für modellierung und simulation university of rostock | chair of modelling and...

Lehrstuhl für

Modellierungund Simulation

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Physics of turbulenceLecture 2

Experiments of Osborne Reynolds

2

Re_transition=2400 in the pipe flow Re_transition=2400 in the pipe flow

ReUD

Reynolds numberReynolds number


Definition

3UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Turbulent motion is the three dimensional unsteady flow motionTurbulent motion is the three dimensional unsteady flow motion•with chaotical trajectories of fluid particles, with chaotical trajectories of fluid particles, •fluctuations of the velocity and fluctuations of the velocity and •strong mixingstrong mixingarisen at large Re numbers due to unstable vortex dynamics. arisen at large Re numbers due to unstable vortex dynamics.

Difference between vorticity and concentrated vorticesDifference between vorticity and concentrated vortices

0u

Vortex motion Vortex structuresVortex motion Vortex structures

Turbulence in free flows


Confined jetsConfined jets

DiffuserDiffuser

5

Vortex structures in a free jet close to the nozzle


6

Helmholtz Kelvin Instability


7

Vortex structures in a free jet in a far field


8

Vortex Structures in a free jet with acoustic impact

With acoustic With acoustic waveswaves

Free jetsFree jets


9

Resolution Grid points

31 µm 23 000 000 000

300 µm 23 000 000

LES: Knots number versus resolutionLES: Knots number versus resolution

2.72 mm2.72 mm

2.0

8 m

m2

.08

mmResolution 31 Resolution 31 µmµm

90000 points in 90000 points in measur. windowmeasur. window

50 m

m5

0 m

m

Resolution 300 Resolution 300 µµ

2D2D

Vortices in a jet mixerVortices in a jet mixer


10

Fascinating world of vortices

x/D=1x/D=1 x/D=2x/D=2

x/D=3x/D=3 x/D=5x/D=5

Spatial Spatial ResolutionResolution 3131µ.µ.


Smallest Smallest vortices of vortices of the flow- the flow- kolmogorov kolmogorov vorticesvortices

PLIF Measurement of the LTT RostockPLIF Measurement of the LTT Rostock

What vortices are present in the flow?

11

50 m

m5

0 m

m

Resolution 300 Resolution 300 µµ

2D2D

x/D=3x/D=3

From scales compared to macrosizeFrom scales compared to macrosizeof the flow (pipe diameter) …..of the flow (pipe diameter) …..

to Kolmogorov scales (microns)to Kolmogorov scales (microns)

0 2 4 6 8 10x/D

0

50

100

150

200

250

Kol

mog

orov

laen

ge, m

km

G eschw indigkeit

0.9 m /s

1.2 m /s

1.75 m /s


Vortex cascade. Laminar-turbulent transition.


One of the possible schemes of the laminar One of the possible schemes of the laminar turbulent transition in the boundary layer. turbulent transition in the boundary layer.

Near Wall Turbulence Near Wall Turbulence

13

Structure of the turbulent boundary layer.

/ 0dp dx

0ττ

2 2

/ / 2x xT x y ux uy

du duτ ρ ρRl l ρl

dy dyu u

* 0τuρ

*

xdu

dy y

u

l y

*

x 0lny lnCu

u

* *

lnu u

* **

0ln lnC Cu u

u

+x*

1lny C

u

u

*yu

y

0.41; 5.0C

Far from the wall where the viscous stresses are much less compared with Far from the wall where the viscous stresses are much less compared with turbulent onesturbulent ones


14

Structure of the turbulent Structure of the turbulent boundary layer.boundary layer.


15

Coherent structuresCoherent structures

Smoke visualization of streaks in transition under the high-Smoke visualization of streaks in transition under the high-level free-stream turbulencelevel free-stream turbulencein a boundary layer (from Matsubara & Alfredsson, 2001).in a boundary layer (from Matsubara & Alfredsson, 2001).


16

Coherent structures

StreaksStreaks



From Smith&Walker (1995)Fluid vorticesFrom Smith&Walker (1995)Fluid vortices

18

Coherent structuresCoherent structures


From Smith&Walker (1995)Fluid vorticesFrom Smith&Walker (1995)Fluid vortices

19

Coherent structures. Hairpin vorticesCoherent structures. Hairpin vortices

From Vincent and Meneguzzi (2001)From Vincent and Meneguzzi (2001)


20

u

Vorticity is solenoidalVorticity is solenoidal ( u ) 0


21

Vector algebra. Operator Nabla of Hamilton

Exercise. Prove the following expressions

( A ) 0,

( f ) 0,

1A ( A ) ( AA ) ( A )A,

2

( A B ) ( B )A ( A )B A( B ) B( A ).

u 1u( u ) f p ( )u

t

NS equations:NS equations:

a mistake is here !!!! Pls correct !a mistake is here !!!! Pls correct !


22

Vorticity transport equation

( u ) ( )u ( )t

D( )

Dt

D0

Dt

NS equations:NS equations:

Vortex stretchingVortex stretchingVortex diffusionVortex diffusionVortex convectionVortex convection

D( )u

Dt

D( )u ( )

Dt

Vortex convectionVortex convection

Rotation and amplificationRotation and amplification

Diffusion (thickening)Diffusion (thickening)

Source of the Source of the turbulence !!!turbulence !!!


23

Vortex induced velocities


24

Vortex cascado. Vortex reconnection


25

Sample of the Vortex reconnection. Crow Instability (1971)


l ehrstuhl für modellierung und simulation university of rostock | chair of modelling and...

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