Post on 01-Oct-2020
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
Kundu & Cohen, “Fluid Mechanics,” 3rd ed, Chs 3 & 13
Tritton, “Physical Fluid Dynamics,” 2nd ed, Chs 2, 19–21
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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!!
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
VDRe
Turbulent flows in a pipe
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Characterization of Turbulent Flows
'';' wwwvvvuuu
Tt
t
Tt
t
Tt
t
dttzyxwT
wdttzyxvT
vdttzyxuT
u0
0
0
0
0
0
),,,(1
;),,,(1
;),,,(1
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Turbulence intensities
0'0';0' wvu
0)'(0)'(;0)'(1
)'( 2222
0
wvdtuT
u
Tt
t
o
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Turbulent Shear Stress
y
ulam
Laminar flows:
''vuy
uturblam
Turbulent flows: ''vuturb
(a) laminar flow (b) turbulent flow
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Laminar Flows and Turbulence Flows
AU
DCd
2
2
1
DURe
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Flow Around A Sphere with laminar and turbulent boundary
layers
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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
-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
)
Laminar and turbulent flows
Re=100,000
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Automobile aerodynamics
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Automobile aerodynamics
Mercedes Boxfish Vortex generator above a Mitsubishi rear window
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
-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 )
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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!
Stall Hysteresis Phenomena
• Stall hysteresis, a phenomenon where stall inception and stall recovery do not occur at the same
angle of attack, has been found to be relatively common in low-Reynolds-number airfoils.
• When stall hysteresis occurs, the coefficients of lift, drag, and moment of the airfoil are found to be
multiple-valued rather than single-valued functions of the angle of attack.
• Stall hysteresis is of practical importance because it produces widely different values of lift coefficient
and lift-to-drag ratio for a given airfoil at a given angle of attack. It could also affect the recovery from
stall and/or spin flight conditions.
Increasing AOA
decreasing AOA
AOA – Angle of Attack
Lift
coeffic
ient
Lift coefficient curve of a “typical” airfoil Lift coefficient curve with stall hysteresis
AOA – Angle of Attack
Increasing AOA
decreasing AOA
Lift
coeffic
ient
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Measured airfoil lift and drag coefficient profiles
-0.2
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
-4 -2 0 2 4 6 8 10 12 14 16 18 20
AOA increasingAOA decreasing
Angle of Attack (degree)
Lift
Co
eff
icie
nt,
Cl
Hysteresis
loop
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
-4 -2 0 2 4 6 8 10 12 14 16 18 20
AOA increasingAOA decreasing
Angle of Attack (degree)
Dra
g C
oe
ffic
ien
t, C
d
Hysteresis loop
• The hysteresis loop is clockwise in the lift coefficient profiles, and counter-clockwise in the drag coefficient
profiles.
• The aerodynamic hysteresis resulted in significant variations of lift coefficient, Cl, and lift-to-drag ratio, l/d,
for the airfoil at a given angle of attack.
• The lift coefficient and lift-to-drag ratio at AOA = 14.0 deg were Cl = 1.33 and l/d = 23.5 when the angle was
in the increasing angle branch of the hysteresis loop.
• The values were Cl = 0.8 and l/d = 3.66 for the same AOA=14.0 degrees when the angle was at the
deceasing angle branch of the hysteresis loop
GA(W)-1 airfoil, ReC = 160,000
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
8 9 10 11 12 13 14 15 16 17 18 19 20
AOA decreasing
AOA increasing
Angle of Attack (degree)
Lift
Co
eff
icie
nt,
Cl
PIV Measurement results
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
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
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
separation bubble
X/C *100
Y/C
*10
0
-40 -20 0 20 40 60 80 100 120 140
-60
-40
-20
0
20
40
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
(Hu, Yang, Igarashi, Journal of Aircraft, Vol. 44. No. 6 , 2007)
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
8 9 10 11 12 13 14 15 16 17 18 19 20
AOA decreasing
AOA increasing
Angle of Attack (degree)
Lift
Co
eff
icie
nt,
Cl
Refined PIV Measurement Results
X/C *100
Y/C
*10
0
-5 0 5 10 15 20 25 30 35
-10
-5
0
5
10
15
20
25
-18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0
GA(W)-1 airfoil 25 m/s
X/C *100
Y/C
*10
0
-5 0 5 10 15 20 25 30 35
-10
-5
0
5
10
15
20
25
vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0
GA(W)-1 airfoil 25 m/s
X/C *100
Y/C
*10
0
-5 0 5 10 15 20 25 30 35
-5
0
5
10
15
20
vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0
GA(W)-1 airfoil25 m/s
X/C *100
Y/C
*10
0
-5 0 5 10 15 20 25 30 35
-10
-5
0
5
10
15
20
vort: -18.0 -14.0 -10.0 -6.0 -2.0 2.0 6.0
GA(W)-1 airfoil25 m/s
(Hu, Yang, Igarashi, Journal of Aircraft, Vol. 44. No. 6 , 2007)
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
y
x
Lab 6: Airfoil Wake Measurements and Hotwire Anemometer
Calibration
2
2
2
2
2
2
;
21
)])(
1()(
[
)]1)(
()(
[
)( Since
)(
)ˆ(
dAU
yU
U
yUUD
dAU
yU
U
yUUDF
DF
pyppp
dAypdApD
dAnpDF
X
X
up
up
CS
XX
2
2
2
2
2
2
)])(
1()(
[2
2
1
)])(
1()(
[
2
1
dyU
yU
U
yU
CC
CU
dAU
yU
U
yUU
CU
DC
D
D
Compare with the drag coefficients obtained based on airfoil surface pressure
measurements at the same angles of attack!
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Required Measurement Results
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