Lecture # 07: Laminar and Turbulent Flowshuhui/teaching/2019-08Fx/AerE344x/class-no… · The small...
Transcript of Lecture # 07: Laminar and Turbulent Flowshuhui/teaching/2019-08Fx/AerE344x/class-no… · The small...
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Dr. Hui Hu
Dr. Rye M Waldman
Department of Aerospace Engineering
Iowa State University
Ames, Iowa 50011, U.S.A
Lecture # 07: Laminar and Turbulent Flows
AerE 344 Lecture Notes
Sources/ Further reading: Munson, Young, & Okiishi, “Fundamentals of Fluid
Mechanics,” 4th ed, Ch 8
Tropea, Yarin, & Foss, “Springer Handbook of Experimental
Fluid Mechanics,” Part C Ch 10
Tritton, “Physical Fluid Dynamics,” 2nd ed, Chs 2, 19–21
Sources/ Further reading: Schlichting, “Boundary Layer Theory,” any ed
White, “Viscous Fluid Flow,” 3rd ed.
Kundu & Cohen, “Fluid Mechanics,” 3rd ed.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Turbulence
“Big whorls have little whorls
That feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.”
-LF Richardson
Leonardo Da Vinci
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Reynolds’ experiment
DUReReynolds number:
Empirically, when Re < 1000, laminar flow,
and when Re > 3000, turbulent flow.
ReC ~ critical Reynolds number above
which flow exhibits turbulent
characteristics
For external flows (e.g., flow around airfoil)
(ReC)L ~ 3 ∙ 105
For internal flows (e.g., pipe flow)
(ReC)δ ~ 3 ∙ 103
From Pradtl: boundary layer (δ) vs body
size (L) scales like L/δ ~ (Re)L1/2.
Thus (Re)L / (Re)δ ~ 102.
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Turbulence
ReLU
Reynolds number:
At the large scales, the flow is determined
by the reference length scale, L, and the
reference time scale, τ0 = L/U.
The small length scales are governed by
the Kolmogorov scales η = (ν3 / ε)1/4, and
τη = (ν / ε)1/2.
ε is the turbulent energy dissipation rate.
Scaling:
For a flow with Re ~ 10,000:
Flow scales span 3 orders of magnitude in
length and 2 orders of magnitude in time.
Turbulent flows contain a vast range of
length and time scales that must be
resolved!!! Difficult!!
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Laminar Flows and Turbulence Flows
• Laminar flow, sometimes known as streamline flow, occurs
when a fluid flows in parallel layers, with no disruption
between the layers. Viscosity determines momentum
diffusion.
– In nonscientific terms laminar flow is "smooth," while
turbulent flow is "rough."
• Turbulent flow is a fluid regime characterized by chaotic,
stochastic property changes. Turbulent motion dominates
diffusion of momentum and other scalars. The flow is
characterized by rapid variation of pressure and velocity in
space and time.
– Flow that is not turbulent is called laminar flow
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VDRe
Turbulent flows in a pipe
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Characterization of Turbulent Flows
'';' wwwvvvuuu
Tt
t
Tt
t
Tt
t
dttzyxwT
wdttzyxvT
vdttzyxuT
u0
0
0
0
0
0
),,,(1
;),,,(1
;),,,(1
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Turbulence intensities
0'0';0' wvu
0)'(0)'(;0)'(1
)'( 2222
0
wvdtuT
u
Tt
t
o
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Turbulent Shear Stress
y
ula m
Laminar flows:
''vuy
utu rblam
Turbulent flows: ''vutu rb
(a) laminar flow (b) turbulent flow
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Quantification of Boundary Layer Flow
y
Uu 99.0
, yat
Displacement thickness:
Momentum thickness:
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Boundary Layer Theory
X
X
X
X
f
X
X
X
X
C
XU
Re
664.0
Re
72.1*
Re
0.5
Re
328.1
Re
0
y
p
X
Y Blasius solution for laminar
boundary layer:
wa ll
wy
U
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Boundary Layer Theory
5/1
5/1
)(Re
37.0
)(Re
074.0
Re
X
X
f
X
X
C
XU
0
y
p
X
Y
Turbulent boundary layer:
wa ll
wy
U
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Boundary Layer Flows
wa ll
wy
U
X
Y
Which one will induce more
drag?
Laminar boundary layer?
Turbulent boundary layer?
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Boundary Layer Flows
wa ll
wy
U
Which one will induce more drag?
Laminar boundary layer? Turbulent boundary layer?
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Laminar Flows and Turbulent Flows
AU
DCd
2
2
1
DURe
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Flow Around A Sphere with laminar and Turbulence
Boundary Layer
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Aerodynamics of a golfball
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved! X/D
Y/D
-101234
-1
0
1
2
U m/s: -10 -5 0 5 10 15 20 25 30 35 40
X/D
Y/D
-101234
-1
0
1
2 U m/s: -10 -5 0 5 10 15 20 25 30 35 40
X/D
Y/D
-101234
-1
0
1
2 U m/s: -10 -5 0 5 10 15 20 25 30 35 40
Smooth ball Rough ball Golf ball
Laminar and turbulent flows
Re=100,000 -0.4
-0.2
0
0.2
0.4
0.6
0.8
1.0
-2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
smooth-ballrough-ballgolf-ball
Distance (X/D)
Ce
nte
rlin
e V
elo
city (
U/U
)
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Automobile aerodynamics
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Automobile aerodynamics
Mercedes Boxfish Vortex generator above a Mitsubishi rear window
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Flow Separation on an Airfoil
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Conventional vs Laminar Airfoils
• Laminar flow airfoils are usually thinner than the
conventional airfoil.
• The leading edge is more pointed and its upper
and lower surfaces are nearly symmetrical.
• The major and most important difference
between the two types of airfoil is this, the
thickest part of a laminar wing occurs at 50%
chord while in the conventional design the
thickest part is at 25% chord.
• Drag is considerably reduced since the laminar
airfoil takes less energy to slide through the air.
• Extensive laminar flow is usually only
experienced over a very small range of angles-of-
attack, on the order of 4 to 6 degrees.
• Once you break out of that optimal angle range,
the drag increases by as much as 40%
depending on the airfoil
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Aerodynamic performance of an airfoil
X/C *100
Y/C
*10
0
-20 0 20 40 60 80 100 120
-40
-20
0
20
40
60
vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
shadow region
GA(W)-1 airfoil
25 m/s
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 2 4 6 8 10 12 14 16 18 20
CL=2
Experimental data
Angle of Attack (degrees)
Lift
Co
eff
icie
nt,
C
l
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 2 4 6 8 10 12 14 16 18 20
Experimental data
Angle of Attack (degrees)
Dra
g C
oe
ffic
ien
t,
Cd
X/C *100
Y/C
*10
0
-40 -20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
60
vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
shadow region
GA(W)-1 airfoil
25 m/s
Airfoil stall
Airfoil stall
Before stall
After stall
cV
DCd
2
2
1
cV
LCl
2
2
1
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Flow Separation and Transition on Low-Reynolds-number
Airfoils
• Low-Reynolds-number airfoil (with Re<500,000)
aerodynamics is important for both military and
civilian applications, such as propellers, sailplanes,
ultra-light man-carrying/man-powered aircraft, high-
altitude vehicles, wind turbines, unmanned aerial
vehicles (UAVs) and Micro-Air-Vehicles (MAVs).
• Since laminar boundary layers are unable to
withstand any significant adverse pressure gradient,
laminar flow separation is usually found on low-
Reynolds-number airfoils. Post-separation behavior
of the laminar boundary layers would affect the
aerodynamic performances of the low-Reynolds-
number airfoils significantly
• Separation bubbles are usually found on the upper
surfaces of low-Reynolds-number airfoils .
Separation bubble bursting can cause airfoil stall at
high AOA when the adverse pressure gradients
become too big.
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-0.10
-0.05
0
0.05
0.10
0.15
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
X/C
Y/C
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
0.5
1.0
1.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
AOA = 06 degAOA = 08 degAOA = 09 degAOA = 10 degAOA = 11 degAOA = 12 degAOA = 14 deg
X / C
CP
Separation point
Transition
Reattachment point
Surface Pressure Coefficient distributions (Re=68,000)
Typical surface pressure distribution when a laminar
separation bubble is formed (Russell, 1979)
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Transition
Reattachment
Separation
X/C
AO
A (
degr
ee)
GA (W)-1 airfoil
(also labeled as NASA LS(1)-0417 )
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Laminar Separation Bubble on a Low-Reynolds-number Airfoil
PIV measurement results at AOA = 10 deg, Re=68,000
X/C*100
Y/C
*10
0
-5 0 5 10 15 20 25 30 35
0
5
10
-18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0 10.0 14.0 18.0
10 m/sGA (W)-1 airfoil
Spawisevorticity
X/C*100
Y/C
*10
0
-5 0 5 10 15 20 25 30 35
0
5
10
U m/s: 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
GA (W)-1 airfoil
reattachmentseparation
X/C*100
Y/C
*10
0
18 20 22 24 26 28 30 32 343
4
5
6
7
8
9
10
11
U m/s: 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00
10 m/s
Reattachment
X/C*100
Y/C
*10
0
18 20 22 24 26 28 30 32 343
4
5
6
7
8
9
10
11
-25.0 -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0
SpanwiseVorticity(1/s * 10
3)
10 m/s
Instantaneous flow field Ensemble-averaged flow field
(Hu et al., ASME Journal of Fluid Engineering, 2008)
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Active flow control: Plasma actuators
Corke et al, Annu. Rev. Fluid Mech.
2010. 42:505–529
Use methods to actively control boundary
layer separation:
•Suction
•Blowing
•Plasma actuators: Applies a body force
acting on weakly ionized air to couple
momentum into the flow
•Synthetic Jets
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Active flow control: Synthetic jets
Synthetic jets: zero mass flux
actuators that inject momentum into
the flow
Glezer & Amitay, Annu. Rev. Fluid Mech.
2002. 34:503–29
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Passive flow control: Shark Skin
Dean & Bhushan, Phil. Trans. R.
Soc. A (2010) 368, 4775–4806
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Vortex Structure over Riblets
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Shark Skin
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Shark Skin Swimming Suits
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y
x
Lab 6: Airfoil Wake Measurements and Hotwire Anemometer
Calibration
1 2
2
2
2
Forces on CV = Fluid momentum change
ˆForces on CV: ( ) ( )
Since , ( )
Momentum change: ( ) ( )
[
X X up
CS
up
X
X
F D pndA D p dA p y dA
p p p y p
F D
U y U y U dA F D
UD U
2
2
( ) ( )(1 )]
y U ydA
U U
2
2
2
2 2
2
( ) ( )[ (1 )]
1 1
2 2
2 ( ) ( ) [ (1 )]
D
D
U y U yU dA
U UDC
U C U C
U y U yC dy
C U U
Compare with the drag coefficients obtained based on airfoil surface pressure
measurements at the same angles of attack!
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y
x 80 mm
Pressure rake with 41 total pressure probes
(the distance between the probes d=2mm)
Lab 6: Airfoil Wake Measurements and Hotwire Anemometer
Calibration
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Lab 6: Airfoil Wake Measurements and Hotwire Anemometer
Calibration
CTA hotwire probe
Flow Field
Current flow
through wire
V
),(2
www TVqRi
dt
dTmc
• Constant-temperature anemometry
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Hotwire Anemometer Calibration
0
2
4
6
8
10
12
14
16
18
20
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
Curve fitting
Experimental data
y=a+bx+cx2+d*x
3+e*x
4 max dev:0.166, r
2=1.00
a=10.8, b=3.77, c=-26.6, d=13.2
voltage (V)
Flo
w v
elo
city (
m/s
)
• Quantify the relationship between the flow velocity and voltage output from the CTA
probe
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Required Measurement Results
NOTE: We will be using the GA(W)-1 airfoil from the previous lab for the wake pressure
measurements
Required Plots:
• Cp distribution in the wake (for each angle of attack) for the airfoil wake measurements
• Cd vs angle of attack (do your values look reasonable?) based on the airfoil wake
measurements
• Your hot wire anemometer calibration curve: Velocity versus voltage output of hotwire
anemometer (including a 4th order polynomial fit)
Please briefly describe the following details:
• How you calculated your drag—you should show your drag calculations
• How these drag calculations compared with the drag calculations you made in the
previous experiment
• Reynolds number of tests and the incoming flow velocity