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Aerodynamics
Masters of Mechanical Engineering
Transition from Laminar to Turbulent Flow
• Flow in pipes
Reynolds experiment
Aerodynamics
Masters of Mechanical Engineering
http://video.google.pt/videoplay?docid=18277021822
65329855&ei=po6TS7vmMMOt-
AbflejfAg&q=Transition+Laminar+to+Turbulent&hl=pt-PT#
http://www.youtube.com/watch?v=nl75BGg9qdA&feature=related
http://www.youtube.com/watch?v=U2IWE_jzwZo&fe
ature=related
Transition from Laminar to Turbulent Flow
• Flow in pipes
Reynolds experiment
Aerodynamics
Masters of Mechanical Engineering
Transition from Laminar to Turbulent Flow
• Flow in pipes
Aerodynamics
Masters of Mechanical Engineering
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Parameters that affect transition
• Pressure gradient
• Wall roughness
• Outer flow turbulence
Aerodynamics
Masters of Mechanical Engineering
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Critical Reynolds number
Transition Reynolds number
Aerodynamics
Masters of Mechanical Engineering
Transition from Laminar to Turbulent Flow
• Different stages of boundary-layer transition
1. Two dimensional instabilities of the
boundary-layer profile. Tollmien-Schlichtingwaves
2. Three-dimensional introduced by secondary
perturbations
3. Start of aleatory turbulent eruptions
4. “Fully-turbulent” flow
Aerodynamics
Masters of Mechanical Engineering
• α is the wavenumberof the perturbation(wavelength )
• Rcrit is the minimum
Reynolds number of the
line that divides the stable
and unstable regions of
the diagram
• Rtrans is the Reynolds
number where the
turbulent flow regime
starts
Rtrans>Rcrit
α
π2=
00 >Λ≤Λ
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Neutral stability of boundary-layer velocity profile
Aerodynamics
Masters of Mechanical Engineering
Viscous
instability
Inviscid
instability
Profile without
inflection point
Profile with
inflection point
∞→⇒∞→ ααe
R
0→⇒∞→ αe
R
00 >Λ≤Λ
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Neutral stability of boundary-layer velocity profile
Aerodynamics
Masters of Mechanical Engineering
• Adverse pressure
gradient, Λ>0, favours transition
• Favourable pressure
gradient, Λ<0, makestransition hardest
dx
dUe
ν
δ 2
−=Λ
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Aerodynamics
Masters of Mechanical Engineering
• The increase of the roughness height favours transition
Effect of roughness on thetransition Reynolds numberof a flat plate boundary-layer (zero pressure gradient)
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Aerodynamics
Masters of Mechanical Engineering
θ
δ *
=H
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Change of the velocity profile
Aerodynamics
Masters of Mechanical Engineering
• The shape factor, H, diminishes
• The momentum thickness, θ, remains approximatelyconstant, if xcrit�xtrans
• The displacement thickness, δ*, diminishes
• The skin friction coefficient,Cf, increases
• Empirical correlation to determine H at the end of transition to turbulent flow
( )9698,0
log
4754,1
10
+=
transeR
H
θ
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Change of the velocity profile
Aerodynamics
Masters of Mechanical Engineering
7546,0 1041022400
1174,1 ×<<
+=
exex
ex
eRR
RR θ
Rex
Re
θ
1.0x10+06
2.0x10+06
3.0x10+06
4.0x10+06
5.0x10+060
200
400
600
800
1000
1200
1400
1600
1800
2000
dp/dx=0
with
Cebeci&
Smith
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Empirical correlations
Aerodynamics
Masters of Mechanical Engineering
H
Lo
g1
0(R
ex)
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.95
5.5
6
6.5
7
7.5
8
8.5
9
dp/dx=0
with( ) 32
10 3819,37538,268066,644557,40log HHHRex
+−+−= 8.21.2 << H
exRH −
Transition from Laminar to Turbulent Flow
• Transition in boundary-layers
Empirical correlations