Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Hui Hu
Rye M Waldman
Department of Aerospace Engineering, Iowa State University
Ames, Iowa 50011, U.S.A
Lecture # 16: Review for Final Exam
AerE 344 Lecture Notes
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Dimensional Analysis and Similitude
Commonly used non-
dimensional parameters:
force tension surface
force inertial WeNumber,Weber
force inertial
force lcentrifugaStr Number, Strohal
forcelity compressib
force inertialM Number,Mach
forcegravity
force inertial
lgFr Number, Froude
force viscous
force inertialRe number, Reynolds
force inertial
force pressureEu number,Euler
2
2
lV
V
l
c
V
V
VL
V
p
Similitude:
• Geometric similarity: the model
has the same shape as the
prototype.
• Kinematic similarity: the velocity
ratio is a constant between all
corresponding points in the flow
field.
• Dynamic similarity: Forces which
act on corresponding masses in
the model flow and prototype
flow are in the same ratio
through out the entire flow
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Measurement Uncertainties
• “Error” is the difference between the experimentally-determined value and its true value;
therefore, as error decreases, accuracy is said to increase.
• Total error, U, can be considered to be composed of two components:
– a random (precision) component,
– a systematic (bias) component,
– We usually don’t know these exactly, so we estimate them with P and B,
respectively.
222 PBU
X
True value
X=100
Bias error
precision error
measured value
X=101
Repeatability Precision Error
Reproducibility Both Bias and Precision Errors
truemtruemeasurederror AAEAAA true
errorrelative
A
AE
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Measurement Uncertainties
222
RRR PBU
Uncertainty in derived quantities:
J
i
i
i
R
J
i
i
i
R PX
RPB
X
RB
1
2
2
1
2
2 ;
Total uncertainties in multivariate are computed like a vector norm
12
2
1 1
1 1;
N N
i i i i ik kk k
S X X X XN N
JXXXXRR ,,,, 321
1 2
1 2
J
J
R R RdR dX dX dX
X X X
Uncertainties in a single measurement can be estimated from the standard deviation of the
ensemble measurements, S.
2i iP S
X
S
Mean X
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Components of a Wind Tunnel
• Test section
• Contraction section
• Diffuser section
• Setting chamber
• Screens and similar structures
• Cooling system / radiators
• Motors /fans
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Function of Contraction
Va
ΔVa
ΔVb =?
a
b
Ac
A
2
2 2
2 2
1
2
1 1
2 2
1( 1)
2
x x
a a b b
b a a
p V const
p V p V
p p V c
a a b b
b a
V A V A
V cV
Aa
Ab
ΔVb
Mass cons:
Bernoulli:
At the perturbation:
2 2 2 2
2
2 2
1
a a a a a b
a a a b
a a a b a b
a b a b
c V V V c V cV V
V V cV V
V V cV V V V
cV V c V V
2 2 2 2
2 2 2
1 1 1( ) ( 1) ( )
2 2 2
1 1( 2 ) ( 2 )
2 2
a a a a a b b
a a a b b b
p V V p V c V V
c V V V V V V
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Pressure Measurement Techniques
• Deadweight gauges:
• Elastic-element gauges:
• Electrical Pressure transducers:
• Wall Pressure measurements
– Remote connection
– Cavity mounting
– Flush mounting
• Pressure Measurements inside Flow Field:
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
)(2
)(,2
1
0
2
0
stat
stat
ppV
BernoulliVpp
• Advantages:
• Simple
• Cheap
• Disadvantages:
• Averaged velocity only (slow response)
• Single point measurements
• High measurement uncertainties, especially
at low velocity
Velocity measurement techniques – Pitot –Static Probe
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Velocity measurement techniques – Hotwire Probe
• Advantage:
• High accuracy
• High dynamic response
• Disadvantage:
• Single point measurements
• Fragile, easy to break
• Much more expensive compared
with pitot-static probe.
• Requires frequent calibration.
Flow Field
Current flow
through wire
The rate of which heat is removed from
the sensor is directly related to the
velocity of the fluid flowing over the
sensor
V
• Constant-current anemometry
• Constant-temperature
anemometry
),(2
www TVqRi
dt
dTmc
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
The nature of light
• Light as electromagnetic waves.
• Light as photons.
• Color of light
• Index of reflection
1/ 0
vcn
sm /3x10c 8
0
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Laser Doppler velocimetry
Fringe spacing: 2sin( / 2)
2 sin( / 2)
Frequency of the scattering light :
2sin( / 2)
Frequency shift according to Doppler theory:
2sin( / 2)
T TD f
Vf V
f V
• Measures velocity in the direction of the fringe pattern
• Can be configured for 2 or 3 components
• Better temporal resolution than pressure transducer
• Non-intrusive measurement
• Assumes particles accurately follow local flow velocity
2-component LDV
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
• In shadowgraphy, as light rays pass through the
measurement region, the deflection of the light rays
as they interact with variations in the optical index
lead to an intensity distribution:
• For weak refraction, and applying the Gladstone-Dale
formula reveals a dependence on the second partial
derivatives of density.
Shadowgraphy
Shadowgraph of a bullet (by Andrew
Davidhazy )
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
• In Schlieren, as light rays pass through index
variations in the measurement region, the deflection
of the light rays cause them to be either blocked or
avoid a knife edge:
• For small angles of deflection, and applying the
Gladstone-Dale formula reveals a dependence on the
partial derivatives of density.
Schlieren
Shadowgraph of a bullet (by Andrew
Davidhazy )
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Visualization of a shockwaves using Schlieren technique
Before turning on the Supersonic jet
After turning on the Supersonic jet
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Schlieren vs. Shadowgraphy
Shadowgraphy
• Displays a shadow
• Shows light ray displacement
• Contrast level responds to
• No knife edge used
Schlieren
• Displays a focused image
• Shows ray refraction angle,
• Contrast level responds to
• Knife edge used for cutoff
yn
2
2
y
n
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Particle Image Velocimetry (PIV)
Seed fluid flows with small tracer particles (~µm), and assume
the tracer particles moving with the same velocity as the low
fluid flows.
Measure the displacements (L) of the tracer particles
between known time interval (t). The local velocity of fluid flow
is calculated by U= L/t .
A. t=t0 B. t=t0+10 s Classic 2-D PIV measurement
C. Derived Velocity field X (mm)
Y(m
m)
-50 0 50 100 150
-60
-40
-20
0
20
40
60
80
100
-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9
5.0 m/sspanwisevorticity (1/s)
shadow region
GA(W)-1 airfoil
t=t0 t
LU
t= t0+t L
• Advantage:
• Whole flow field measurements
• Non-intrusive measurements
• Disadvantage:
• Low temporal resolution
• Very expensive compared with
hotwire anemometers and
pitot-static probes.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
PIV system setup
Illumination system
(Laser and optics)
camera
Synchronizer
seed flow with
tracer particles
Host computer
Particle tracers: to track the fluid movement.
Illumination system: to illuminate the flow field in the interest region.
Camera: to capture the images of the particle tracers.
Synchronizer: the control the timing of the laser illumination and
camera acquisition.
Host computer: to store the particle images and conduct image
processing.
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Laminar Flows and Turbulent 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!
Laminar Flows and Turbulent Flows
'';' wwwvvvuuu
...),,,(1 0
0
Tt
t
dttzyxuT
u
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!
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!
Boundary Layer Flow
y
Uu 99.0
, yat Displacement thickness:
Momentum thickness:
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
“macro-scale” aircraft:ReC = 106 ~108
MAVs: ReC = 104 ~105
•“Scale-down” of conventional airfoils
could not provide sufficient
aerodynamic performance for MAV
applications.
•It is very necessary and important to
establish novel airfoil shape and wing
planform design paradigms for MAVs
Low Reynolds number aerodynamics (e.g., MAVs)
X/C*100Y
/C*1
00
0 10 20 30 40 50
-5
0
5
10
15
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
-5.50
Spanwisevorticity(1000*1/s)
X/C*100
Y/C
*10
0
0 10 20 30 40 50
-5
0
5
10
15
0.085
0.075
0.065
0.055
0.045
0.035
0.025
0.015
0.005
T.K.E
X/C*100
Y/C
*10
0
0 10 20 30 40 50
-5
0
5
10
15
0.085
0.075
0.065
0.055
0.045
0.035
0.025
0.015
0.005
T.K.E.
X/C*100
Y/C
*10
0
0 10 20 30 40 50
-5
0
5
10
15
10.0
8.0
6.0
4.0
2.0
0.0
Velocity(m/s)
X/C*100
Y/C
*10
0
0 10 20 30 40 50
-5
0
5
10
15
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
-5.50
Spanwisevorticity(1000*1/s)
X/C*100
Y/C
*10
0
0 10 20 30 40 50
-5
0
5
10
15
10.0
8.0
6.0
4.0
2.0
0.0
Velocity(m/s)
0
0.2
0.4
0.6
0.8
1.0
0 2 4 6 8 10 12 14 16 18 20
Flat Plate
Profiled Airfoil
Corrugated Airfoil
Angle of Attack (Deg.)
CL
0
0.2
0.4
0.6
0.8
1.0
1.2
0 2 4 6 8 10 12 14 16 18 20
Flat Plate
Profiled Airfoil
Corrugated Airfoil
Angle of Attack (Deg.)
CL
interest for
MAV
applications
310 610410 510
010
110
210
310
710
CURe
MAXD
L
C
C
Streamlined airfoil
rough
surface
airfoil
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Review of Quasi-1D Nozzle Flow
0V S
dV U ndSt
viscous
V S S V
UdV U n UdS pdS fdV Ft
2 2
2 2V S S V V
U U qe dV e U ndS pU ndS dV f U dV
t t
Assumptions:
• Steady-state
• Inviscid
• No body forces
Quasi-1D:
• Area is allowed to vary but flow variables
are considered a function of x only
X
Mass conservation
Momentum conservation
Energy conservation
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Review of Quasi-1D Nozzle Flow
u
duM
A
dA)1( 2
M<1 M>1
Throat
M=1
u increasing
M>1 M<1
Throat
M=1
u decreasing
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Review of Quasi-1D Nozzle Flow
12 2 2
1 1 1
2 2 2
00
20
2 10
1
2 10
(Thermodynamics) :
( ) ( )
:
11 1
2 2 2
11
2
1(1 )
2
1(1 )
2
P P
P
Isentropic relations
P T
P T
Energy Equation
TV V VC T C T
T C T RT
TM
T
PM
P
M
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Review of Quasi-1D Nozzle Flow
20
2 2 2 2 2 2 20
0
2 110
2 1
2
1
2 10
* * *
u** section: M 1 * *
*
11 * * * *
2 ( ) ( ) ( ) ( ) ( ) ( ) ( )*
1(1 ) 1 2 1
2 [ (1 )]1 2
1(1 )
2
y
u A uA
at A u aa
isentropic relation
TM A a a a
TA u u a
PM
P MM
M
M<1 M>1
Throat
A*
P*,T**
M*=1
u*=a*=(KRT*)1/2
A
P,T,
M
u
1
1
2
2
2 )]2
11(
1
2[
1)
*(
yMMA
A
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
1st, 2nd and 3rd critic conditions
1st critic
condition
2st critic
condition
3st critic
condition
P0 in
crea
sin
g
P0 in
crea
sin
g
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Pressure Distribution Prediction within a De Laval Nozzle
by using Numerical Approach
atme PP
M<1 M>1
PT1 P1 P
T2
P2
M<1
Shock
AS
Ae
Throat ,
A* or At
atme PP
1
1
2
2
2
* 2
11
1
21
M
MA
A
• Using the area ratio, the Mach number
at any point up to the shock can be
determined:
• After finding Mach number at front of
shock, calculate Mach number after
shock using: 2
12
22
1
11
21
2
MM
M
• Then, calculate the A2*
1
122 2 2
2 2 2
2 11
1 2sA M A M
which allows us calculate the remaining
Mach number distribution
1
1
2
2
2
* 2
11
1
21
M
MA
A
2
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Streamlines (experiment)
Flow visualization by using smoke wind tunnel
• Path line
• Streak lines
• Streamline
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
2
2
1*
*
VC
qC
ppp
T
EA
Test section
Contraction
section
A
E
V
Settling
chamber
0
20
40
60
80
100
120
140
0 20 40 60 80 100 120 140
Linear curve fittingExperimental data
P = PA-P
E (Pa)
q =
0.5
*V
2
Wind Tunnel Calibration
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Pressure Sensor Calibration and Uncertainty Analysis
• Task #1: Pressure Sensor Calibration experiment
– A pressure sensor – Setra pressure transducer with a range of +/- 5 inH2O
• It has two pressure ports: one for total pressure and one for static (or reference) pressure.
– A computer data acquisition system to measure the output voltage from the manometer.
– A manometer of known accuracy
• Mensor Digital Pressure Gage, Model 2101, Range of +/- 10 inH2O
– A plenum and a hand pump to pressurize it.
– Tubing to connect pressure sensors and plenum
• Lab output:
– Calibration curve
– Repeatability of your results
– Uncertainty of your measurements
Setra pressure
transducer
(to be calibrated)
Mensor Digital
Pressure Gage A computer A plenum hand pump
tubing
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Measurements of Pressure Distributions around a Circular
Cylinder
2
2
2
2
2
2
sin41)sin2(
1
1
2
1
V
V
V
V
V
PPCp
R
P
Incoming flow
X
Y
-3
-2
-1
0
1
0 100 200 300 400
Angle, Deg.
Cp
Cp distribution around a cylinder
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7
theta (rad ) -->
cp
-->
EFD
CFD
AFD
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Airfoil Pressure Distribution Measurements
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
cV
LCl
2
2
1
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
cV
DCd
2
2
1
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)
Airfoil Wake Measurements and Hotwire Anemometer
Calibration
y
x
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
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Hot wire measurements in the wake of an airfoil
y
x
80 mm
Pressure rake with 41 total pressure probes
(the distance between the probes d=2mm)
Hotwire probe
Lab#3
Lab#4
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
PIV in an airfoil wake
Experimental setup for the PIV measurements
U∞
Instantaneous velocity field
• Mean velocity components in x, y directions:
•Turbulent velocity fluctuations:
• Turbulent Kinetic energy distribution:
NUuuN
i
i /)('1
2
N
i
i Vvv1
2)('
N
i
i NuU1
/
N
i
i NvV1
/
)''(2
1 22
vuTKE
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Visualization of Shockwaves using Schlieren technique
Under-
expanded
flow
Flow
close to
3rd critical
Over-
expanded
flow
2nd critical –
shock is at
nozzle exit
1st critical –
shock is
almost at the
nozzle throat.
Tank with compressed air Test section
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Set up a Schlieren and/or Shadowgraph System to Visualize a Thermal
Plume
Point Source
Candle plume
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Tank with compressed air Test section
Pressure Measurements in a de Laval Nozzle
Tap No. Distance downstream of throat (inches) Area (Sq. inches)
1 -4.00 0.8002 -1.50 0.5293 -0.30 0.4804 -0.18 0.4785 0.00 0.4766 0.15 0.4977 0.30 0.5188 0.45 0.5399 0.60 0.56010 0.75 0.58111 0.90 0.59912 1.05 0.61613 1.20 0.62714 1.35 0.63215 1.45 0.634
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Aerodynamic forces on an icing airfoil
Force transducer–wing model configuration
Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!
Final exam
Next week:
• Final exam on Tuesday December 13 7:30-9:30 a.m. in room
Hoover 1312
AERE 344 final exam specifics
• Open book and open class notes
• 20 multiple-choice problems (2 points each)
• 4 short answer problems related to lab design (15 points each)
• Exam time is 120 minutes
• You may use a calculator
• You cannot use any computer, smartphone, tablet, or network
connected device
• Don’t forget to fill out course evaluations!
First contact Scheduled final exam
Tues., 9:00-10:00 a.m.
Hoover 1312
Tues. Dec. 13 7:30-9:30 a.m..
Hoover 1312