l ehrstuhl für modellierung und simulation university of rostock | chair of modelling and...
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Lehrstuhl für
Modellierungund Simulation
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
Physics of turbulenceLecture 2
Experiments of Osborne Reynolds
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Re_transition=2400 in the pipe flow Re_transition=2400 in the pipe flow
ReUD
Reynolds numberReynolds number
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
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
4UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
Confined jetsConfined jets
DiffuserDiffuser
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Vortex structures in a free jet close to the nozzle
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Vortex structures in a free jet in a far field
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Vortex Structures in a free jet with acoustic impact
With acoustic With acoustic waveswaves
Free jetsFree jets
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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
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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.
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
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?
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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
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
Vortex cascade. Laminar-turbulent transition.
12UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
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
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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
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Structure of the turbulent Structure of the turbulent boundary layer.boundary layer.
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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).
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
17UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
From Smith&Walker (1995)Fluid vorticesFrom Smith&Walker (1995)Fluid vortices
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Coherent structuresCoherent structures
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
From Smith&Walker (1995)Fluid vorticesFrom Smith&Walker (1995)Fluid vortices
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Coherent structures. Hairpin vorticesCoherent structures. Hairpin vortices
From Vincent and Meneguzzi (2001)From Vincent and Meneguzzi (2001)
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
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u
Vorticity is solenoidalVorticity is solenoidal ( u ) 0
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
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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 !
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION
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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 !!!
UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION