MAE 123 : Mechanical Engineering Laboratory II
Final Lecture
Dr. J. M. Meyers | Dr. D. G. Fletcher | Dr. Y. Dubief
1
• Airfoil Lift and Drag Lab: Additional notes and corrections
• Optical Characterization of Density Lab Demo Details
• Final Exam Review
2
Airfoil Lab Notes and Corrections
=
−
ℎ
−ℎ
=
ℎ
−ℎ
=
ℎ
−ℎ
NOT
=
=
=
−
−(
−
ℎ
−ℎ
) cos( )
=
=
−
cos( +
)
=
=
−
sin( +
)
NOT
=
=
−(
−
) sin( )
3
Airfoil Lab Notes and Corrections
2D vs 3D lift and drag coefficients
2D (Sectional) Lift Coefficient
3D Lift Coefficient
Based on wing planform area
and overall lift
=
! "
#
=
! "
The section lift coefficient is based on two-dimensional
flow over a wing of infinite span and non-varying crosssection so the lift is independent of span-wise effects
and is defined in terms of $ , the lift force per unit span
(let’s call the wing span length % ) of the wing
($ = /%)
'
=
$
! (
)
=
*
! (
4
Airfoil Lab Notes and Corrections
Upper
Surface
NACA 2415
Airfoil
Lower
Surface
Pressure Tap
+ (%c)
, (%c)
- [rad]
./ [m2]
Leading Edge
0
0
1
1.193
2.657
0.9006
0.002577
2
5.688
5.374
0.3688
0.003374
3
14.89
7.944
0.1838
0.004548
4
25.40
9.185
0.05831
0.00561
5
39.44
9.278
-0.03975
0.006633
6
54.25
8.155
-0.1037
0.006633
7
68.64
6.308
-0.1503
0.006785
8
84.16
3.628
-0.2111
0.01107
Trailing Edge
100
0
Pressure Tap
+ (%c)
, (%c)
- [rad]
./ [m2]
Leading Edge
0
0
9
1.451
-2.213
0.7282
0.002502
10
6.730
-4.301
0.2264!!!
0.002994
11
14.11
-5.353
0.08516
0.003411
12
21.70
-5.688
0.00835
0.00474
13
35.08
-5.467
-0.03805
0.006444
14
49.93
-4.673
-0.06709
0.006595
15
63.99
-3.585
-0.08428
0.00705
16
80.72
-2.083
-0.1027
0.01251
Trailing Edge
100
0
5
Airfoil Lab Notes and Corrections
•
Keeping track of surface normal direction, 01,
is key in order to properly extract lift and drag
•
Account for angle of attack
•
Reference from a single location
2
=
2
−
3
=4−
3
−
6
Airfoil Lab Notes and Corrections
56
1
2
=
3D Lift Coefficient
2D Lift Coefficient
=
'
−
9:
! "
;
−
!
=
#
$
=
! ( × (1>)
=
! "
)
=
*
! ( × (1>)
7
Airfoil Lab Notes and Corrections
?@
?@
Critical Angle
of Attack
B
?A
Reynolds number
dependent
8
Airfoil Lab Notes and Corrections
5.1) Lift and Drag
For a set airspeed you are to compare lift vs. angle of attack and to discuss stall characteristics of the airfoil at that
airspeed. You will do this for multiple airspeeds. Thus you will need to determine the lift and drag coefficients for
various air speeds and angles of attack.
• Plot
• Plot
vs. for your data set as well as 3 additional data sets from within your lab section (4 total)
) vs. for your data set as well as 3 additional data sets from within your lab section (4 total)
'
5.2) Pressure Distribution and Stall
For one airspeed you will also determine the pressure coefficient distribution over the airfoil for various angles of
attack. Show how the C distribution changes as the angle of attack increases and discuss what you see happening
as the airfoil transitions to a state of stall.
• Plot C vs. D/( for every angle of attack within your data set to show the evolution of the pressure coefficient. Take
note and discuss what is occurring as you approach the critical angle of attack. What is causing stall?
5.3) Comparison with LIterature
You must compare your data with existing literature and show that your results make sense. One of the first
standard resources regarding airfoil data presents plenty of data at Reynolds numbers of 3x106 and higher [5].
However, your experimental conditions will present lower Reynolds numbers than this. You are required to
determine your Reynolds numbers and to research and find relevant airfoil data (lift and drag coefficient vs. angle of
attack) near these Reynolds number values.
9
Airfoil Lab Notes and Corrections
?E
B = −F
?E
D/(
?E
B=F
B=H
B = −G
?E
D/(
?E
D/(
B=I
D/(
D/(
?E
D/(
?E
B=G
B = JH
?E
D/(
B = JF
D/(
10
Optical Characterization of Density
Method
Easy
Shadowgraph
What we measure
Second derivative
of density
Schlieren
First derivative
of density
Interferometry
Density
Difficult
11
Optical Characterization of Density
Schlieren
Shadowgraph
•
•
•
•
Displays a mere shadow
Shows light ray displacement
KG L
Illuminance level responds to G
K,
No knife edge used
•
•
•
•
Displays a focused image
Shows ray refraction angle, ε
Illuminance level responds to KL
K,
Knife edge used for cutoff
12
Optical Characterization of Density
•
Physical basis of optical measurements of density explained: index of refraction variation in gases
causes either physical deviation of light ray (shadowgraph), its trajectory angle (Schlieren), or its
arrival time (interferometry)
•
Applicable to compressible flows or to incompressible flows of different media having different
refractive index… DENSITY GRADIENT!
•
Interferometry and Schlieren approaches can provide quantitative information if appropriate
care taken
•
Shadowgraph is most often used for qualitative imaging
•
Sensitivity advantage of Schlieren explains its more frequent implementation
•
Information from application is extremely useful for interpreting measurements on test articles
13
Optical Characterization of Density
Show Video
14
Final Exam Review
OVERVIEW
• Definitions/short answers [20 pts]
• 4 problems [20 pts. Each]
• Total: 100 Pts. (30% of overall grade)
15
Final Exam Review
M
=
1 ;
+ Q + R = constant
2
•
Bernoulli Equation
•
Streamlines/streamtubes – what is constant along/through these?
NOP
2
streamlines
streamtubes
2
1
1
Incompressible Flow
(L = const.)
const.
•
Incompressible Flow
(L = const.)
const.
Venturi Effect
What happens to pressure when velocity increases?
What happens to pressure when area increases?
16
Final Exam Review
•
Uncertainty Analysis
VW =
V
X
;
Y
YD2
;
+V
Z
;
Y
YD;
;
+V
[
;
Y
YD\
;
+ ⋯+ V
•
Pitot and calculating Velocity from manometer heights
•
Pressure: dynamic, total, static, gauge, and absolute
•
Airfoil lab… definitions and short answer possibility
^
;
Y
YD_
;
Good example involving
density in Lecture 1
17
Final Exam Review
•
Hot wire: calibration, time response, sensitivity orientation for measurement, benefits and
drawbacks compared to Pitot technique
`; =
•
+ a ∙ : c.d
Calculation of a time averaged and an RMS value to a fluctuating signal
Ve ; =
f; − f1
;
i )G !!!!
Note that gG h (g
Doesn’t have to be velocity as
indicated… could be temperature,
pressure, voltage, … etc.
CLOSED BOOK… ALL NECESSARY EQUATIONS AND CONSTANTS WILL BE GIVEN
18