1. Compressible Fluid Flow
Objectives of the Course
To develop the fundamental concepts of compressible
flow
To solve engineering problems such as diffusers and
nozzles of subsonic and supersonic airbreathing engines,
supersonic wind tunnels, rocket nozzles, lift and drag on
supersonic wings
– p.1
2. Textbook
It is not necessary to buy a textbook
If you really want a textbook, buy Compressible Fluid
Flow 2nd Edition by Michel Saad
You can save money by “writing your own book” based
on the lecture material
– p.2
3. English or Korean?
Lecture – in English
Assignments – in English
Midterm and Final exams – questions will be written in
english
The good news: Compressible Fluid Flow is an engi-
neering course and ... the “language of engineering” is
mathematics
– p.3
4. Grading
Grading
Mid-term – 40%
Final – 60%
Bonus – 15% Max.
or
Midterm – 20%
Final – 80%
Bonus – 15% Max.
(whichever gives the highest mark)
– p.4
5. Grading System: No Relative Scoring!
F if score30% (no upgrade possible, no exception)
F if 30%score50% (upgrade to D0 possible, but not
automatic. See below)
D0 if 50%score55% and if you come to my office
alone after the final exam and give very good reasons
why you failed (in english)
D+ if 55%score60%
C0 if 60%score65%
C+ if 65%score70%
B0 if 70%score75%
B+ if 75%score80%
A0 if 80%score85%
A+ if score85%
– p.5
6. Canadian Style Grading System
A0-A+ Great
B0-B+ Good
C0-C+ Fair
D0-D+ Hmmmm
F Not good enough to take more advanced courses
– p.6
7. Assignments
3-4 problems per week
Questions may depend on student number
Solutions will be given after due date
Assignment questions and answers are in english
Should require 5-7 hours of your time per week
No late assignment will be accepted
You must understand and remember the solutions
you hand in
– p.7
8. Bonus System
15 points Bonus given to all students
4 points penalty for missing a lecture
2 points penalty for coming late to the lecture
3 points penalty for not submitting an assignment
3 points penalty for submitting an assignment late
4 points penalty for disturbing the class
15 points penalty for not remembering your own solu-
tions to the assignments
Bonus can be positive, but can also be negative.
– p.8
9. Attendance
Missing one class = 4 point penalty
No certificate is accepted except those for job
interviews
For job interviews, you must notify me at least 48 hours
before the interview
I may call the company and verify if the certificate is
valid
In case you forged the certificate, you will get F
– p.9
10. Exams
Exams are closed book
Compressible Flow Tables will be handed out along
with the question sheet
Only simple calculators are allowed (not more than
20,000 wons, no SD stick)
Any attempt at cheating will result in F
Bring your calculator to every class – there will be sur-
prise exams
– p.10
11. Surprise Tests
Surprise tests will be given once in a while
The test will consist of solving one assignment problem
If your solution is significantly different from the one
you handed in, you will get a 15 points penalty
If your solution is more or less the same as the one you
handed in, you will get no penalty
Bring your calculator to every class – it will be needed
for the surprise test
– p.11
12. How to get a good mark
Never miss a lecture
Don’t disturb the others during the lecture
Do the assignments by yourself as much as possible –
There is no group work in the exams
Understand and remember the solutions you hand in
– p.12
13. Learn by Doing, not just by Watching
Nam Hyun-hee. Just
watching Nam Hyun-hee
foil won’t make someone
a good fencer. One also
needs to practice. The same
applies with learning Com-
pressible Flow.
– p.13
14. Don’t let a problem remain unsolved
First try to solve the problem by yourself – work
seriously on it
Discuss it with a friend
Get the solution from another student by bribing him
or her
Send the professor an email asking him a specific
question
Come to see the professor in his office – make sure you
are respectful of his time by preparing well your question
– p.14
15. Slides Shown Today
All the slides shown in the class today can be
downloaded in pdf format from
http://www.bernardparent.com/
– p.15
16. http://www.bernardparent.com
You have to create an account on my website to download
the slides, the assignments, the tables, and check your scores.
Note the following:
Your account login ID must be your student ID
Your account will become active only after I approve it
It may take a couple of days before your account is ap-
proved
– p.16
17. What is Compressibility?
In fluid mechanics, compressibility is a measure of the rel-
ative volume change of a fluid as a response to a pressure
change.
compressibility
1
V
@V
@P
where V is the volume and P is the pressure. Compressibil-
ity can also be thought to be a measure of the relative density
change of a fluid as a response to a pressure change. By def-
inition, the density corresponds to:
density
mass
volume
– p.17
18. Bullet
Schlieren photograph of
a bullet “flying” at a
speed of 1500 kilome-
ters/hour Schlieren photo-
graph shows change in air
density.
– p.18
19. Supersonic Engine Intake
Schlieren photograph of
the intake of the engines
of a supersonic aircraft.
The flow speed is Mach
1.95 (about 2000 kilome-
ters per hour).
– p.19
20. Space Shuttle Main Engine
Photograph of the exhaust of the Space Shuttle
Main Engine (SSME). The flow exiting the rocket
is steady and uniform but soon downstream ’diamond-
like’ features appear.
– p.20
21. Compressibility Effects in Aerodynamics
Compressibility is an important factor in aerodynamics. At
low speeds, the compressibility of air is not significant in re-
lation to aircraft design, but as the airflow nears and exceeds
the speed of sound, a host of new aerodynamic effects be-
come important in the design of aircraft. These effects, often
several of them at a time, made it very difficult for World War
II era aircraft to reach speeds much beyond 800 km/h (500
mph), since they resulted in changes to the airflow that lead
to problems in control. Such were observed on many World
War II aircraft such as the P38 Lighting, the Mitsubishi Zero,
the Supermarine Spitfire, and the Messerschmitt Bf 109.
– p.21
22. P38 Lighting
The P-38 Lightning with its thick high-lift wing had a particular
problem in high-speed dives that led to a nose-down condition.
Pilots would enter dives, and then find that they could no longer
control the plane, which continued to nose over until it crashed.
Maximum Mach number: Mach 0.6. – p.22
23. Recommended Approach to the Solution of a
Compressible Flow Problem
1. Outline of the laws of physics
2. Derivation of working relations from laws of physics
3. Statement of assumptions involved in obtaining the
working relations
4. Use of working relations to obtain a solution to a fluid
flow problem
5. Discussion of the problem solution and limitations of
physical model / working relations
Compressible flow physics can be particularly unintuitive.
Do not trust your intuition; rather, follow the steps above.
– p.23
24. Why Derivations of Working Relations from Laws of
Physics are Important
To learn about the assumptions related with the working
relations
To understand the limitations of the working relations
To increase confidence about a design based on the
working relations
– p.24
25. Ideal Gas Law
The state of an amount of gas is determined by its
pressure, volume, and temperature according to the
equation:
P D RT
P in Pa, in kg/m3
, R in J/kgK, and T in K.
What is pressure? What is temperature? – To
understand the latter, we need to derive the ideal gas
law from basic principles.
The ideal gas law mathematically follows from a
statistical mechanical treatment of primitive identical
particles which do not interact, but exchange
momentum in elastic collisions
Applicable to cases where the intermolecular forces are
negligible – not applicable to gases with relatively high
pressure and low temperature – p.25
26. Benoit Paul Emile Clapeyron
French engineer born in Paris in
1799
Clapeyron studied at the Ecole
polytechnique and the Ecole des
Mines
First stated the ideal gas law as
the equation of state of a
hypothetical ideal gas in 1834.
In 1843, Clapeyron further devel-
oped the idea of a reversible pro-
cess to what is now known as the
second law of thermodynamics
– p.26
27. Pressure
The pressure is the average in time of the force per unit area
acting on a surface due to molecular collisions
P
R t
0
Fdt
At
D
F
A
with
P the pressure (in Pa)
F the force acting on a wall due to elastic molecular
collisions (in N)
A the cross sectional area on which the force is acting (in m2
)
– p.27
28. Blaise Pascal (1623–1662)
French mathematician, physicist,
and philosopher born in 1623
Clarified the concepts of pressure
and vacuum
At the time, most scientists did
not believe in the possibility of
vacuum
Established the principle and
value of the barometer
His work in the calculus of proba-
bilities laid important groundwork
for Leibniz’s formulation of the
infinitesimal calculus
– p.28
29. Temperature
Temperature is proportional to the average kinetic energy of
the molecules.
T
mq2
3k
D
q2
3R
(in degrees K, Kelvin)
with
k the Boltzmann constant (1:38 10 23
J/K)
m the mass of one molecule in kg
q the speed of a molecule in m/s
R the gas constant (equals k=m in J/kgK)
– p.29
30. Mass Conservation in Quasi-1D
Mass Conservation Equation:
d Av D 0
or
2A2v2 D 1A1v1
where the density is in kg/m3
, the cross-section area A in
m2
, and v in m/s
Applies to steady one-dimensional flow in ducts with
area change
– p.30
31. Momentum Conservation in Quasi-1D
Momentum Conservation Equation:
vd v C d P D 0
where the density is in kg/m3
, the velocity v in m/s and P
in Pa
Derived from Newton’s second law F D ma
Applies to steady one-dimensional flow in streamtubes
or ducts with area change
– p.31
32. Energy Conservation Equation
(or First “Law” of Thermo)
d e’
change of system energy
D P d .1=/š
work done on system
C ıq‘
heat added to system
Based on what was discovered in the 19th century, the
First Law of Thermo is now not a Law since it can be
shown from other laws
It can be shown by taking the dot product between the
velocity vector and Newton’s law in vector form applied
to a molecule, summing over a large number of
molecules, and then taking the average in time.
Not always necessary for incompressible flows unless
heat transfer or viscosity is present
Always necessary for compressible flows to find the den-
sity+pressure distribution
– p.32
34. James Prescott Joule (1818–1889)
English physicist born in Salford,
Lancashire, England in 1818
Studied the nature of heat, and
discovered its relationship to
mechanical work.
Fascinated by electricity. He and
his brother experimented by
giving electric shocks to each
other and to the family’s servants.
Found the relationship between
the current through a resistance
and the heat dissipated
– p.34
35. Types of Energy Modes in a Gas
Translational energy, etr D 3
2
RT
Rotational energy, erot D RT
Vibrational energy
Electronic energy
The latter can be shown from statistical thermodynamics.
Atoms only have translational and electronic energy.
– p.35
36. Types of Thermodynamic Processes
Isobaric. Constant pressure process.
Isovolumetric. Constant volume process.
Isothermal. Constant temperature process.
Isentropic. Constant entropy process.
Adiabatic. A process in which there is no energy added
or subtracted by heating or cooling.
Reversible. A process which is both adiabatic and isen-
tropic.
– p.36
37. Energy Conservation in Quasi-1D
1st “Law” of Thermo:
d e C P d .1=/ D 0 or d h d P= D 0
Energy conservation equation:
d
h C
v2
2
D 0
holds for adiabatic and isentropic process (reversible)
along a one-dimensional duct with varying
cross-section area
v is the velocity in m/s
h is the enthalpy in J
h e C P=
the enthalpy is the potential of the flow to do work – p.37
39. Specific Heats
The specific heats at constant pressure and volume are de-
fined as:
CP
d h
d T
and CV
d e
d T
For many gases (such as N2, O2, H2, air), the vibrational and
electronic energies can be neglected when the temperature is
less than about 800 K. Then, the specific heats and the spe-
cific heat ratio
become:
CV CP
molecule 5
2
R 7
2
R 7
5
atom 3
2
R 5
2
R 5
3
– p.39
40. Calorically Perfect Gas
A calorically perfect gas is a gas where the specific heats CP
and CV are constant.
This yields the following relationships:
h D CP T
e D CV T
A calorically perfect gas should not be confused with a
thermally perfect gas.
A calorically perfect gas entails constant CP and CV . A ther-
mally perfect gas is one which is governed by the ideal gas
law P D RT .
– p.40
41. Terminal (or Exit) Velocity
The terminal velocity is the velocity that is obtained when
a gas is expanded isentropically to a vacuum (that is, when
the terminal pressure approaches zero).
For a calorically perfect gas, the terminal velocity corre-
sponds to:
vterminal D
p
2CP Tı
where vterminal is in m/s, CP is in J/kgK, and Tı is in K.
– p.41
42. Speed of Sound
Speed of an infinitesimal wave propagating isentropically in
a gas:
c D
s
@P
@
ˇ
ˇ
ˇ
ˇ
s
In the case of a calorically perfect and thermally perfect gas,
the sound speed becomes:
c D
p
RT
– p.42
43. Compressible Flow Tables and Charts
http://www.bernardparent.com/
Contains most used equations as well as tables and
charts for solving problems
The same document will be distributed during the mid-
term and final exams
– p.43
44. Stagnation Pressure – Definition
The stagnation pressure can either refer to the static pressure
at a stagnation point in a fluid flow or can refer to the pres-
sure that would be obtained if the flow would be reversibly
decelerated to stagnation conditions.
The stagnation pressure can be obtained by integrating along
an adiabatic and isentropic path the momentum equation
from the point under consideration to a state of vanishing
velocity.
– p.44
45. Stagnation Pressure Expressions
Stagnation pressure for incompressible flow (Bernoulli
Equation):
Pı D P C
v2
2
Stagnation pressure for compressible flow:
Pı D P
1 C
1
2
M2
1
where M D v=c is the Mach number and v is the flow speed
(magnitude of velocity). The gas is assumed calorically per-
fect and thermally perfect throughout the path to stagnation.
– p.45
46. Daniel Bernoulli (1700–1782)
Swiss mathematician
Best known for his application of
mathematics to mechanics and his
pioneering work in probability
and statistics
Earliest writer who attempted to
formulate a kinetic theory of
gases, and he applied the idea to
explain Boyle’s “law”.
– p.46
47. Difference Between Compressible and Incompressible
Stagnation Pressure
The incompressible stagnation pressure can also be written
as:
P incomp
ı D 1 C 1
2
M2
Using Taylor series, it can be shown that the compressible
stagnation pressure is equal to:
P comp
ı D 1 C 1
2
M2
C 1
8
M4
C :::
At Mach 0.5, 0.8, and 1.0, the difference is around 1%, 7%,
and 18%.
– p.47
48. P38 Lighting
Maximum Mach number: Mach 0.6.
Famous for loss of control when the
flight Mach number approached 0.8 in
dives. – p.48
49. Ernst Mach (1838–1916)
Austrian physicist and
philosopher born in Chirlitz in the
Austrian empire, now Brno,
Czech Republic
Mach’s main contribution to
physics was his description of
shock waves
Using a so-called
schlierenmthod he and his son
Ludwig were able to photograph
the shadows of the invisible shock
waves
The Mach number is named after
him
– p.49
50. Stagnation Density and Temperature
The stagnation temperature and density of a compressible
gas:
Tı
T
D 1 C
1
2
M2
ı
D
1 C
1
2
M2
1
1
with ı and Tı the stagnation density and temperature and
with M the Mach number and
the ratio of the specific
heats.
– p.50
51. Impact of Cross-Sectional Area on Flow Properties
d v
v
D
1
M2
1
d A
A
d P
P
D
M2
1 M2
d A
A
d
D
M2
1 M2
d A
A
d T
T
D
.
1/M2
1 M2
d A
A
d M
M
D
2 C .
1/M2
2.M2
1/
d A
A
where
is the ratio of the specific heats, M the Mach num-
ber, A the flow cross sectional area, and v, P , T , the
velocity, pressure, temperature, and density.
– p.51
52. Nozzle and Diffuser
Nozzle: Expands and accelerates the gas
Diffuser: Compresses and decelerates the gas
The definitions of “nozzle” and “diffuser” do not entail spe-
cific shape characteristics. For instance, a diverging area
duct is a nozzle for supersonic flow but a diffuser for sub-
sonic flow. Likewise, a converging area duct is a diffuser for
supersonic flow but a nozzle for subsonic flow.
– p.52
53. de Laval Nozzle
A de Laval nozzle (or
convergent-divergent
nozzle, CD nozzle or con-di
nozzle) is a tube that is
pinched in the middle,
making an hourglass-shape.
It is used as a means of
accelerating the flow of a
gas passing through it to a
supersonic speed.
It is widely used in some
types of steam turbine and is
an essential part of the mod-
ern rocket engine and super-
sonic jet engines.
– p.53
54. Gustaf de Laval (1845–1913)
Swedish engineer and inventor born in
Orsa, Sweden
Enrolled at the Institute of Technology
in Stockholm in 1863, receiving a
degree in mechanical engineering in
1866
Completed a doctorate in chemistry in
1872 at Uppsala University (Sweden)
In 1890 developed a nozzle to increase
the steam jet to supersonic speed
Now known as a de Laval nozzle, the
nozzle is used in modern rocket en-
gines.
– p.54
55. Critical Mach Number
The critical Mach number is defined as the ratio be-
tween the flow speed and the critical sound speed. The
critical sound speed is the sound speed that would oc-
cur should the flow be accelerated or decelerated to
Mach 1. This yields a critical Mach number of:
M?
v
p
RT ?
which can be shown to be equal to:
M?
D
M
q
1C
2
q
1 C
1
2
M2
– p.55
56. Critical Area
The critical area A?
is the cross-sectional area of the
flow should the latter be accelerated or slowed down
isentropically to Mach 1. The ratio between the area
and the critical area can be shown to be equal to:
A
A?
D
1
M
2
C 1
1 C
1
2
M2
1C
2.
1/
– p.56
57. Critical Pressure, Temperature, Density
The critical pressure, temperature, and density corre-
spond to the pressure, temperature, and density of the
flow should the latter be accelerated or slowed down
isentropically to Mach 1. They can be expressed as a
function of the stagnation properties as follows:
P ?
Pı
D
1 C
1
2
1
T ?
Tı
D
1 C
1
2
1
?
ı
D
1 C
1
2
1
1
– p.57
58. Example of a Diffuser
The cross sectional area of
the engine increases before
the first blades
At subsonic speed, a
diverging area duct is a
diffuser since it compresses
the flow
The flow is hence
compressed before
encountering the first
turbine blades
The diffuser helps in obtain-
ing a high compressor effi-
ciency
– p.58
59. Effect of Back Pressure
Subsonic Nozzle. The exit pressure must be equal or
higher than the back pressure. If the nozzle is choked,
then the exit Mach number is 1 and the exit pressure is
greater than the back pressure. If the nozzle is not
choked, then the exit Mach number is less than 1 and
the exit pressure is equal to the back pressure.
Supersonic Nozzle. If the exit pressure is greater than
the back pressure, the flow will remain supersonic in the
nozzle. If the exit pressure is less than the back pressure,
then the flow may become subsonic at the nozzle exit.
– p.59
60. Choked Flow
Choked flow is a limiting condition which occurs when the
mass flux will not increase with a further decrease in the
downstream pressure environment.
Take for example a stagnant gas in a container with a higher
pressure than the environment. As the gas is released to the
environment, it goes through an expansion process through
a converging area duct. At the throat, the flow is said to be
choked if a further decrease in environment pressure will not
result in a higher mass flow rate. For an inviscid compress-
ible fluid, choking occurs when the Mach number reaches 1.
For a viscous compressible fluid, choking occurs for a Mach
number slightly less than 1. For a liquid, choking may be
caused by sudden cavitation.
– p.60
61. Mach Waves
Mach waves are formed around supersonic object
The flow Mach number can be found as M D
1
sin ˛
with
˛ the angle with respect to the flow streamline
– p.61
62. Nozzle Efficiency
The efficiency of a real nozzle is defined as the ratio
between the actual kinetic energy at the nozzle exit and
the one that would be obtained should the flow expand
isentropically through the nozzle:
nozzle
v2
e
v2
i
where ve is the actual flow velocity at the nozzle exit,
and vi is the velocity that would be obtained through
isentropic expansion from the same stagnation pressure
and temperature to the same nozzle exit pressure.
– p.62
64. C-D Nozzle in SSME – Discussion
The C-D nozzles intended for space propulsion have a di-
verging section with a length typically more than 10 times
the one of the converging section, hence resulting in a sub-
stantial weight gain. How much additional thrust is given by
a C-D nozzle compared to a standalone converging nozzle?
Is the extra weight always justified? – p.64
65. Force Exerted on Duct by Flow
The force exerted on a duct in the opposite direction of
the fluid flow path (i.e., the thrust) by a moving com-
pressible fluid at steady-state corresponds to the change
of momentum of the flow:
F D
Z 2
1
P d A D v2
A C PA
2
v2
A C PA
1
with
P the pressure
A the cross sectional area
the density
v the velocity of the flow
– p.65
66. Ramjet
Engine needs no moving parts – Flow is compressed entirely
through a converging-diverging diffuser
Can operate until Mach 5, but most efficient around Mach 3
Generally used for missiles
Invented and patented by René Lorin in 1913
– p.66
67. Leduc 0.10 Ramjet Aircraft
First successful ramjet powered flight vehicle, built by
Breguet Aircraft
First flight: 21 October 1947
Maximum flight Mach number: 0.85
Could not take-off unassisted
– p.67
68. Project Pluto
Mach 3 nuclear-powered ramjet developed by the
Lawrence Radiation Laboratory in 1961
Combustor consists of an unshielded nuclear reactor
heating the incoming air
Was intended to be a long-range bomber to strike the
Soviet Union with nuclear weapons
Was never massively produced – replaced by ICBMs
– p.68
69. Continuity, Momentum and Energy Equations with
Diffusion Terms for 1D Constant-Area Flow
Mass Conservation:
d
d x
v D 0
Momentum Conservation:
d
d x
v2
C P
d v
d x
D 0
Energy Conservation:
v
d
d x
h C
v2
2
d
d x
K
d T
d x
C v
d v
d x
D 0
where:
is the viscosity
K is the thermal conductivity
– p.69
70. First “Law” of Thermo for a 1D Constant-Area Duct
d h
d x
1
d P
d x
D
d Q
d x
with
d Q
d x
1
v
d
d x
K
d T
d x
C
v
d v
d x
2
The First “Law” of Thermo is not a law in gasdynam-
ics, rather it is simply a “working relation” which can
be derived from more basic principles. We have shown
that the first “law” of thermo can be obtained from one
(and only one) law of physics, namely Newton’s law
EF D d mEv=d t.
– p.70
71. Second “Law” of Thermo for a 1D Constant-Area Duct
s2 s1 D
Z 2
1
K
vT 2
d T
d x
2
d xC
Z 2
1
vT
d v
d x
2
d x
or
s2 s1 0 along the flow path
The entropy s is defined as
d s
1
T
d Q
Similarly to the first “law”, the second “law” of thermo
is a working relation and not a law in gasdynamics. The
second “law” of thermo has been here derived using
only Newton’s law EF D d mEv=d t.
– p.71
72. Lazare Carnot (1753–1823)
French politician, engineer, and
mathematician
In 1784 he published his first work
Essai sur les machines en général
which contained the earliest proof of
irreversible processes (entropy)
Participated to the creation of Ecole
Polytechnique in 1794.
In 1800 he was appointed Minister of
War by Napoleon
His son, Sadi Carnot, is the engineer
who invented the “Carnot Heat Engine”
and the “Carnot Cycle”
Was exiled as a regicide in 1814 during
the reign of Louis XVIII – p.72
73. Shock Wave or Shock
Like an ordinary sound wave, a
shock wave propagates through
a gas and carries energy
Shocks are characterized by an
abrupt change in the gas
properties
Across a shock, there is always
a relatively rapid change in
pressure, temperature, velocity
A shock travels through a gas at
a higher speed than a sound
wave
The thickness of the shock must
be small enough that viscous ef-
fects become important – p.73
74. Rankine-Hugoniot Shock Relations For a Calorically
and Thermally Perfect Gas
Pıy
Pıx
D
1
C 1
C
2
.
C 1/M2
x
2
C 1
M2
x
1
C 1
1=.
1/
Py
Px
D
2
C 1
M2
x
1
C 1
Ty
Tx
D
2
C 1
M2
x
1
C 1
1
C 1
C
2
.
C 1/M2
x
My D
M2
x C
2
1
=
2
1
M2
x 1
1=2
where the subscript “y” refers to the properties after the
shock and “x” refers to the properties before the shock.
My and Mx are measured in the shock reference frame.
– p.74
75. William John Macquorn Rankine (1820–1872)
Scottish engineer, born in Edinburgh in
1820
A founding contributor, with Clausius
and Kelvin, to the science of
thermodynamics
One of the first engineers to recognise
that fatigue failures of railway axles
was caused by the initiation and growth
of brittle cracks
Professor of civil engineering and
mechanics at the University of
Glasgow from 1855 until his death (as
a bachelor) in 1872
Best remembered for the Rankine cycle
and the Rankine-Hugoniot Eqs. – p.75
76. Pierre-Henri Hugoniot (1851-1887)
French engineer, born in 1851 in
Allenjoie, France
Graduated from Ecole Polytechnique in
1872
Professor of mechanics and ballistics at
the Lorient Artillery school in 1879
Appointed as auxiliary assistant in
mechanics at Ecole Polytechnique in
1884
Published in the proceedings of the
Ecole Polytechnique in Volume 57
(1887) and Volume 58 (1889) the shock
relations that now bear his name
– p.76
77. Pitot tube
The basic pitot tube consists of a tube
pointing directly into the fluid flow. The
moving fluid is brought to rest as there is
no outlet to allow flow to continue. The
pressure obtained within the pitot tube is
the so-called “pitot pressure”. The veloc-
ity of the flow can be estimated by com-
paring the difference between the pitot
pressure and the static pressure. Invented
by Henri Pitot in the early 1700s and
modified to its modern form in the mid
1800s by Henry Darcy, the Pitot tube is
now widely used to determine the air-
speed of an aircraft and to measure air
and gas velocities in industrial applica-
tions. – p.77
84. Henri Pitot (1695–1771)
French hydraulic engineer, born in
Aramon in 1695
Supervising engineer of the
construction of Aqueduc de Saint
Clément near Montpellier
Discovered that much contemporary
theory was erroneous – for example,
the idea that the velocity of flowing
water increased with depth
Inventor of the Pitot tube, originally
intended to measure the speed of the
water in La Seine river.
In 1724 he became a member of the
French Academy of Sciences, and in
1740 a fellow of the Royal Society. – p.84
85. Wind Tunnels
A wind tunnel is a research tool developed to assist with studying
the effects of air moving over or around solid objects. The wind-
speed and flow properties can be measured using threads, dye or
smoke, pitot tube probes, or particle image velocimetry. Different
wind tunnel configurations are used for different flow regimes:
Subsonic wind tunnels: used for operations at rather low
speeds, with a Mach number in the test section generally not
exceeding 0.5
Transonic wind tunnels: used to simulate a test section Mach
number between 0.5 and 1.0
Supersonic wind tunnels: produces a flow Mach number in
the test section in the range 1:2 M 4.
Hypersonic wind tunnels: produces a test section flow Mach
number in excess of 4
– p.85
86. Open Subsonic Wind Tunnel
The air is moved with a large axial fan that creates a pressure dif-
ference and essentially “sucks” the air in the tunnel from the en-
vironment. The working principle is based on the continuity and
Bernoulli’s equation (flow is incompressible throughout).
– p.86
87. Closed Subsonic Wind Tunnel
In a closed wind tunnel, a large actuator fan creates a pressure
difference which entrains air in the test section from the return
duct. The return duct must be properly designed to reduce the
pressure losses and to ensure smooth flow in the test section.
– p.87
88. Transonic Wind Tunnel
High subsonic wind tunnels (0:4 M 0:75) or transonic wind
tunnels (0:75 M 1:2) are designed on the same principles
as the subsonic wind tunnels. Transonic wind tunnels are able to
achieve speeds close to the speeds of sound. The Mach number is
approximately one with combined subsonic and supersonic flow
regions. Testing at transonic speeds presents additional prob-
lems, mainly due to the reflection of the shock waves from the
walls of the test section. Therefore, perforated or slotted walls are
required to reduce shock reflection from the walls. Since impor-
tant viscous or inviscid interactions occur (such as shock waves or
boundary layer interaction) both Mach and Reynolds number are
important and must be properly simulated.
– p.88
92. Supersonic Wind Tunnels
A supersonic wind tunnel is a wind tunnel that produces super-
sonic speeds (1:2 M 4) generally through the use of a
converging-diverging nozzle. The test section Mach number
is determined by the nozzle geometry while the Reynolds
number is varied by changing the stagnation pressure and
temperature of the flow in the settling chamber. To simulate
high Mach number flows typical of high speed flight, a high
pressure ratio is required between the settling chamber and the
test section (at M D 4 this ratio is about 200).
Supersonic wind tunnels can be regrouped in four categories:
Suck-down
Blow-down
Suck-down-Blow-down
Shock tunnel
– p.92
93. Nozzle and Test Section of a Supersonic Wind Tunnel
In a supersonic wind tunnel, the flow can be accelerated from sub-
sonic to supersonic speeds using a converging-diverging nozzle
(also known as a “De Laval nozzle”). One of the challenges in
designing a supersonic wind tunnel is to prevent a normal shock
from forming in the test section while the measurement is being
taken. – p.93
94. Suck-down Supersonic Wind Tunnel
Suck-down supersonic wind tunnels
are characterized by very large vac-
uum tanks “sucking” the air directly
from the atmosphere (typically at a
pressure of 101300 Pa and temperature
of about 300 K). While the flow can be
accelerated to Mach numbers greater
than 10 through a De Laval nozzle,
the stagnation pressure and stagnation
temperature are too low to simulate
properly flight conditions at M 1:5.
– p.94
95. Blow-down Supersonic Wind Tunnel
A blow-down supersonic wind tunnel consists of a high-pressure
tank in which compressed gas expands to ambient pressure
through a De Laval nozzle and reaches supersonic speeds in the
process. Similarly to the suck-down supersonic wind tunnel,
achieving realistic flow conditions at more than Mach 2 is difficult
due to the air in the tank having too low stagnation temperature.
– p.95
96. Blow-down-Suck-down Supersonic Wind Tunnel
Due to the very large pressure difference between the high-
pressure tanks and the vaccuum tanks, a blow-down-suck-down
wind tunnel can achieve very high Mach numbers (M 10) in
the test section. The air is heated through a pebble bed heater to
obtain in the test section the high Reynolds number characteristic
of hypersonic flight.
– p.96
97. Pebble-Bed Heater
Before entering the De Laval nozzle, the expanded air can be
heated through a pebble bed to increase its stagnation tempera-
ture. It is then possible to reproduce the high Mach number and
Reynolds number experienced in flight conditions up to Mach 6. – p.97
98. Shock Tunnel
A shock tunnel is typically used to produce high Reynolds number
and high Mach number flows characteristic of hypersonic flight or
atmospheric reentry. The duration of the testing is limited, though,
to a few milliseconds. – p.98
99. HIEST Free Piston Shock Tunnel
(Kakuda Research Center, Japan)
– p.99
100. HIEST Free Piston Shock Tunnel Schematics
The high enthalpy shock tunnel HIEST is the largest free-piston
shock tunnel in the world. The length and mass of the tunnel are
approximately 80 m and 300 ton, while the nozzle exit diameter is
of 120 cm, and the scale model length is of 50 cm.
Test section properties: u D 4 7 km/s, Tı D 10000 K, Pı D
150 MPa, Test time D 2:0 ms.
– p.100
101. Gerald Bull (1928–1990)
Canadian aerospace engineer, born in
North Bay, Canada
Obtained Ph.D. from the University of
Toronto Institute of Aerospace Studies
in 1952
His PhD topic was on continuous
supersonic wind tunnels
Professor of Mechanical Engineering at
McGill University in the 1960s
Inventor of the Supergun (project
Babylon)
Assassinated in 1990 at the entrance of
his Brussels hotel – possibly by the Na-
tional Intelligence Agency of Israel
– p.101
102. Supergun – Project Babylon
Project Babylon was intended to launch a projectile loaded
with explosives into orbit as a means to “blind” enemy spy
satellites. Financial support by Saddam Hussein.
– p.102
103. 1D Flow with Friction – Governing Equations
Conservation of Mass:
d
d x
v D 0
Conservation of Momentum:
d
d x
v2
C P
C
4f
DH
1
2
v2
D 0
Conservation of Energy:
d
d x
.vH/ D 0
with:
f w
ı1
2
v2
DH 4A =
wetted perimeter
A cross sectional area
w wall shear stress
– p.103
104. Fanning Friction Factor vs Darcy Friction Factor
In this course, f will always refer to the fanning
friction factor, ffanning. In the litterature, sometimes the
Darcy friction factor is used. The Darcy friction factor
corresponds to four times the fanning factor:
fDarcy D 4ffanning
For instance, for fully-developed laminar flow,
fDarcy D 64=Re
and
ffanning D 16=Re
– p.104
106. Henry Darcy (1803–1858)
French Engineer born in Dijon in 1803
Attended École Polytechnique and
École des Ponts et Chaussées in 1821
Married Englishwoman Hanriette
Carey in 1828
During the 1840s, was engineer in
charge of building pressurized water
distribution system in Dijon
Developed Darcy-Weisbach equation
and Darcy friction factor
Improved the design of the Pitot tube c.
1850
The unit of fluid permeability, darcy, is
named in his honour – p.106
107. 1D Flow with Friction – Working Relations
d M
M
D
M2
1 C
1
2
M2
2 .1 M2
/
4f
DH
d x
d P
P
D
d M2
M2
1 .
1/M2
2 C .
1/M2
d v2
v2
D
d M2
M2
1 C
1
2
M2
1
d T
T
D
d M2
M2
.
1/M2
2 C .
1/M2
d Pı
Pı
D
d M2
M2
M2
1
2 C .
1/M2
– p.107
108. 1D Flow with Friction – Critical Properties (Fanno-line
Relations)
4fL?
DH
D
1 M2
M2
C
C 1
2
ln
(
M2
2
C 1
1 C
1
2
M2
1
)
P
P ?
D
1
M
2
C 1
1 C
1
2
M2
1=2
T
T ?
D
a2
a?2
D
2
C 1
1 C
1
2
M2
1
?
D
v?
v
D
1
M
2
C 1
1 C
1
2
M2
1=2
– p.108
109. 1D Flow with Friction – Critical Stagnation Properties
(Fanno-line Relations)
Pı
P ?
ı
D
1
M
2
C 1
1 C
1
2
M2
.
C1/=2.
1/
Tı
T ?
ı
D 1
ı
?
ı
D
Pı
P ?
ı
– p.109
110. Gino Girolamo Fanno (1888–1960)
Italian Engineer
Obtained Bachelor’s degree in
Mechanical Engineering in Venice,
Italy
Moved to Zurich, Switzerland in 1900
to attend graduate school for his
Master’s degree
Developed the Fanno-line flow model
as part of his Master’s thesis (1904)
Returned to Italy for a job in the
industry
Later obtained a Ph.D. from Regio Isti-
tuto Superiore d’Ingegneria di Genova
– p.110
111. 1D Flow with Heat Transfer – Governing Equations
Conservation of Mass:
d
d x
v D 0
Conservation of Momentum:
d
d x
v2
C P
D 0
Conservation of Energy:
d
d x
.vH/ D
d
d x
.vCP Tı/ D qin
with:
qin average heat
flux in W/m2
duct perimeter at a
given x-station through which
heat flux takes place
– p.111
112. 1D Flow with Heat Transfer – Critical Properties
(Rayleigh-line Relations)
P
P ?
D
C 1
M2
C 1
T
T ?
D
a2
a?2
D
M2
.
C 1/
2
.
M2
C 1/
2
?
D
v?
v
D
M2
C 1
M2
.
C 1/
Pı
P ?
ı
D
C 1
M2
C 1
2 C .
1/M2
C 1
1
Tı
T ?
ı
D
.
C 1/ M2
.2 C .
1/M2
/
.
M2
C 1/
2
– p.112
113. John Strutt, 3rd Baron Rayleigh (1842–1919)
English physicist, awarded the Nobel prize
of physics in 1904 for discovering argon
Obtained BA and MA degrees in
Mathematics from Cambridge (1861–1868)
Became the second Cavendish Professor of
Physics from 1879 to 1884 at the University
of Cambridge, following James Clerk
Maxwell
Was first to describe dynamic soaring by
seabirds in 1883 in the British journal
Nature
“Rayleigh-line flow” and the “Rayleigh
number” associated with buoyancy driven
flow are named in his honour
– p.113
114. 2D Subsonic Flow Around Airfoil
Smoke-jets visualization. Since the flow is subsonic, pressure
waves can travel upstream. Well upstream of the airfoil, the flow
is “aware” of it approaching and adapts in consequence. – p.114
115. 2D Supersonic Flow Around Blunt Bullet
Schlieren photograph.
Flow becomes subsonic
through quasi-normal
shockwave and then ad-
justs to the shape of the
object.
– p.115
116. Detached Shock Ahead of Blunt Body
Schlieren photograph reveals a detached normal shockwave ahead
of the body. “Attached” to the normal shock are two oblique
shockwaves.
– p.116
117. 2D Supersonic Flow Around Wedge
Schlieren photograph. Experiments reveal two “oblique” shock-
waves attached to the leading edge of the wedge, with no normal
shockwave upstream of the body.
– p.117
118. 2D Oblique Shockwaves – Governing Equations
Conservation of Mass:
.vN/2 D .vN/1
Conservation of N-Momentum:
v2
N C P
2
D v2
N C P
1
Conservation of T-Momentum:
.vT/2 D .vT/1
Conservation of Energy:
h C
1
2
v2
N
2
D
h C
1
2
v2
N
1
with:
vT the velocity component
transverse to the shockwave
vN the velocity component
normal to the shockwave
Subscripts “1” and “2” refer to
the properties before and after
the shockwave, respectively
– p.118
119. 2D Oblique Shockwaves – Working Relation
Starting from the governing equations, we can show that the
working relation linking the shock incoming Mach number
with the deflection angle corresponds to:
tan./
tan. ı/
D
.
C 1/M2
1 sin2
2 C .
1/M2
1 sin2
where
ı is the flow turning angle
M1 is the incoming flow Mach number
is angle of the shockwave with respect to the incoming
flow
– p.119
125. F14 Inlet Schematic
F14 inlet configuration in supersonic flight. The role
of the inlet is to slow the flow down to subsonic speeds
before it reaches the turbine. Effectively, the Mach number
at the turbine entrance is maintained to Mach 0.5–0.7 in
supersonic flight.
– p.125
126. Shock Polar Relationship
v2
c?
D ˙
v
u
u
u
u
u
u
u
t
M?
1
u2
c?
2 u2
c?
1
M?
1
1
M?
1
2
!
1
M?
1
2
u2
c?
1
M?
1
C
2
C 1
where u2 and v2 are the velocity components after the oblique
shock and M?
1 is the reduced Mach number ahead of the oblique
shock. M?
1 can be expressed as:
M?
1 D
s
.
C 1/M2
1
2 C .
1/M2
1
– p.126
129. Ludwig Prandtl (1875–1953)
German aeronautical engineer born near
Munich in 1875
His father – a professor of engineering –
encouraged him to observe nature and
analyze his observations
Obtained his PhD in Solid Mechanics from
the Technische Hochschule Munich
His first job was as an engineer designing
factory equipment
In 1901, became a professor of fluid
mechanics at the Technical Univesity
Hannover.
In 1904, he joined the University of Gottin-
gen
– p.129
130. Ludwig Prandtl (1875–1953)
Wrote a groundbraking paper on the
boundary layer in 1904 entitled Fluid Flow
in Very Little Friction in which the
boundary layer is described along with its
impact on body drag and flow streamlines
Developed with his student Theodor Meyer
the first theories of supersonic shock waves
and flow in 1908
Worked closely with Hermann Goring’s
Reich’s Air Ministry during World War II
Investigated the problem of compressibil-
ity at high subsonic speeds (Prandtl-Glauert
correction), which was used near the end
of World War II when German aircraft ap-
proached sonic speeds
– p.130
132. Lift and Drag Coefficients
CL D
FL
1
2
1q2
1Aplanform
CD D
FD
1
2
1q2
1Aplanform
where
FL is the lift force
FD is the drag force
q1 is the freestream air speed
1 is the freestream air density
Aplanform is the planform area
– p.132
135. Overexpanded Nozzle Flow While Testing the Space
Shuttle Main Engine
While the flow is uniform
at the nozzle exit, the exit
pressure of the nozzle is
less than the back pres-
sure. This is referred to as
an overexpanded nozzle
flow, and is accompanied
by an interaction between
the exit flow and the envi-
ronment in form of oblique
shocks and expansion fans.
– p.135
136. SR71 Blackbird at Take-off
Despite the flow being uniform at the nozzle exit, some di-
amonds appear downstream due to overexpansion.
– p.136
138. Rotational Vortex Flow
In a rotational vortex, the viscous effects are significant
enough to have created substantial vorticity which itself in-
duces rotational flow. The vorticity ! is defined as:
! D
@u
@y
@v
@x – p.138
139. Irrotational Vortex Flow
In an irrotational vortex, the viscous effects are insignificant
and the vorticity is negligible:
@u
@y
@v
@x
! 0
– p.139
140. Potential Equation for Irrotational Compressible Flow
For an irrotational, isentropic, compressible fluid, it can be
shown that the potential equation becomes:
1
2
x
c2
xx C
1
2
y
c2
yy 2
xy
c2
xy D 0
where is a potential function defined such that:
x D
@
@x
D u
y D
@
@y
D v
– p.140
141. Linearized Potential Equation for Irrotational
Compressible Flow
Let’s decompose the velocity into a freestream component
and a perturbation component:
u D u1 C u0
and v D v0
Then, assuming that u0
and v0
are much smaller than u1, the
potential equation becomes linear:
1 M2
1
xx C yy D 0
where is a potential function defined such that:
x D
@
@x
D u0
y D
@
@y
D v0
– p.141
142. Linearized Potential Equation for Irrotational
Compressible Supersonic Flow
In the case of supersonic flow the linearized potential equa-
tion
1 M2
1
xx C yy D 0
is of hyperbolic type since the coefficients preceding the xx
and yy terms have alternating signs.
Since the equation is hyperbolic, the solution for corre-
sponds to a sum of f and g waves:
.x; y/ D f x C y
p
M2
1 1
C g x y
p
M2
1 1
– p.142
143. Pressure Coefficient for Linearized Irrotational
Supersonic Flow
Not to be confused with the specific heat at constant
pressure, the pressure coefficient CP is defined as:
CP
P P1
1
2
1q2
1
with q1 the freestream flow speed. In the case of supersonic
flow, the linearized potential equation yields the following
expression for CP :
CP D
2defl
p
M2
1 1
for the g waves
CP D
2defl
p
M2
1 1
for the f waves
– p.143
144. Swept Wings
A swept-wing is a wing planform common on jet aircraft capa-
ble of near-sonic or supersonic speeds. The wings are swept back
instead of being set at right angles to the fuselage which was com-
mon on propeller driven aircraft and early jets. This is a useful
drag-reducing measure for aircraft flying just below the speed of
sound, though straight wings are still favored for slower cruise and
landing speeds and aircraft with long range or endurance. Swept-
wings also provide a degree of inherent stability and it was for
this reason that the concept was first employed in the designs of
J.W.Dunne in the first decade of the 20th century, e.g. the Dunne
D.1. Swept wings as a means of reducing aerodynamic drag were
first used on bombers and jet fighter aircraft. Today, they have
since become almost universal on all but the slowest jets, and most
faster airliners and business jets.
– p.144
145. Swept Wings on Boeing B47 Stratojet (1947)
The Boeing B-47 Stratojet jet bomber was a medium-range and
medium-size bomber capable of flying at high subsonic speeds
and primarily designed for penetrating the airspace of the Soviet
Union. A major innovation in post-World War II combat jet de-
sign, it helped lead to the development of modern jet airliners. – p.145
146. Boeing B47 Stratojet Taking Off (1947)
Many people consider the B-47 as “the most influential jet aircraft
of all time.” All of Boeing’s jetliners adopted the same swept-wing
configuration and most of them also fitted their engines on the
wings just like the B-47. Other transonic airplane manufacturers
also adopted this configuration. The better performance of swept
wings at high speeds is due to their abeyance of the “area rule”. – p.146
147. What is the Area Rule?
At high-subsonic flight speeds, local supersonic airflow
can develop in areas where the flow accelerates around
the aircraft body and wings. The resulting shock
waves formed at these points of supersonic flow can
form a sudden and strong form of drag, called wave
drag. The area rule states that in order to reduce the
number and strength of these shock waves, an aerody-
namic shape should change in cross-sectional area
as smoothly as possible. It was developed at NACA
Langley by Richard Whitcomb and Adolf Busemann.
– p.147
148. Richard T. WHITCOMB (1921–)
American aeronautical engineer born in
Evanston, Illinois, in 1921
1943 graduate in Mechanical Engineering
from Worcester Polytechnic Institute
Spent most of his career at the Langley
Laboratory of the NACA and NASA
Proposed in the 1950s the “area rule” to
minimize shock drag in transonic flight
In the 1960s, developed the “supercritical
airfoil” which effectively extends the
supersonic region over a transonic wing
In the 1970s, developed the “winglets”
which reduce wingtip vortices and the in-
duced drag such vortices create
– p.148
149. Adolf BUSEMANN (1901–1986)
German aeronautical engineer born in
Lubeck, Germany in 1901
Received PhD in Aerospace Engineering at
the Technical University Braunschweig in
1924
In 1924, became aeronautical research
scientist at the Max-Planck Institute under
Ludwig Prandtl
Busemann originated the concept of swept
winged aircraft, presenting a paper on the
topic at the Volta Conference in Rome in
1935
Moved to NACA Langley in 1947 and
helped develop the area rule with Whitcomb
– p.149
150. McDonnell Douglas MD11 (Cruise Mach number of
0.85)
The profile of the MD11 nose shows clearly the application
of the area rule.
– p.150
151. NASA Convair 990 (Cruise Mach Number of 0.91)
Antishock bodies can be added to the wings of transonic air-
craft to make the aircraft cross-section obey the area rule.
– p.151
152. Anti-Shock Bodies Impact on Transonic Flow Over a
Wing (Using Oilflow Visualization)
To reduce the adverse effects of the shockwave in transonic
flight, anti-shock bodies are added according to the “area
rule” – p.152
153. Breaking the Sound Barrier
Vapor cone surrounding
a F18 aircraft.
In certain atmospheric
conditions when the
aircraft approaches the
speed of sound, the
rapid condensation of
water-vapor due to the
sonic shock creates a
visible vapor cone.
– p.153
154. Supersonic Flight
One difficulty associated with supersonic flight is the
rather low lift to drag ratio (L/D ratio) of the wings. At
supersonic speeds, airfoils generate lift in an entirely differ-
ent manner than at subsonic speeds, and are invariably less
efficient. For this reason, considerable research has been put
into designing planforms for sustained supersonic cruise. At
about Mach 2, a typical wing design will cut its L/D ra-
tio in half (e.g., the Concorde vehicle managed a ratio of
7.14, whereas the subsonic Boeing 747 has an L/D ratio of
17). Because an aircraft’s design must provide enough lift to
overcome its own weight, a reduction of its L/D ratio at su-
personic speeds requires additional thrust to maintain its air-
speed and altitude. Another difficulty associated with su-
personic flight is the too-high pressure on a leading edge
of the aircraft designed according to the area rule. This
lead to the adoption of the “Haack body” shape.
– p.154
155. Haack Body
The shock wave drag can be further decreased in supersonic
flight by imposing a pointed leading edge while minimizing
the area change difference along x. This results in the
Haack body:
Acs D .Acs/max
4
x
L
x2
L2
3
2
where:
x is the streamwise distance from the leading edge
L is the distance from the leading edge to the trailing edge
Acs is the cross-sectional area of the aircraft
.Acs/max is the maximum cross-sectional area of the aircraft,
located at x=L D 0:5
– p.155
156. Haack Body – Figure
Despite appearances, the cross sectional area of most super-
sonic airplanes follows the Haack body distribution.
– p.156
157. Nose Cone Drag versus Mach Number for Various
Shapes
Comparison of drag characteristics of various nose cone
shapes in the transonic to low-supersonic regions. Rankings
are: superior (1), good (2), fair (3), inferior (4).
– p.157
158. Wolfgang Haack (1902–1994)
German engineer and mathematician born
in Gotha, Germany in 1902
Obtained bachelor’s degree in Mechanical
Engineering in Hanover
Obtained Ph.D. in mathematics at the
Friedrich-Schiller-Universitat Jena in 1926
During World War II worked in the arms
industry for the Projektildesign
In 1941, published in a classified tech.
report an equation for projectile nose cone
shapes that minimize wave drag
In 1949, became a professor in the Depart-
ment of Mathematics and Mechanics at the
Technische Universitat Berlin (Berlin Tech-
nical Univ.) – p.158
159. Convair F106 “Delta Dart”
The cross section of
the aircraft follows
the Haack body
distribution
Deployed in the
1950s by the USAF
in Alaska, South
Korea, Germany, and
Iceland to intercept
bombers from the
Soviet Union
– p.159
160. CF-105 Avro Arrow Inauguration,
Toronto, Canada, 1958
Mach 2.0 Canadian aircraft deployed in 1958 to intercept soviet
bombers.
– p.160
161. CF-105 Avro Arrow in Flight,
Avro Aircraft Company (Canada), 1958
The aircraft body and delta wing are designed following the
Haack body to minimize wave drag.
– p.161
162. Avro Arrow – Choice of Delta Wing over Swept Wing
“At the time we laid down the design of the CF-105, there
was a somewhat emotional controversy going on in the
United States on the relative merits of the delta planform ver-
sus the straight wing for supersonic aircraft... our choice of
a tailless delta was based mainly on the compromise of at-
tempting to achieve structural and aeroelastic efficiency
with a very thin wing, and yet, at the same time, achieving
the large internal fuel capacity required for the specified
range.”
James C. Floyd
Chief Design Engineer of Avro Arrow Aircraft
– p.162
163. Avro Arrow in Royal Canadian Air Force Hangar,
Toronto, 1958
The Arrow had several world’s firsts, such as fly-by-wire technol-
ogy (hydraulic system to move the various flight controls along
with “artificial feel” added to the control stick) and computer-
controlled stability augmentation system (long, thin aircraft
have coupling modes that can lead to departure from stable flight
if not damped out quickly). – p.163
164. Avro Arrow Cockpit, Canada Aviation Museum,
Ottawa, Canada, 2004
The Arrow program was cancelled in 1959 with instructions given
to the Canadian military to immediately seize and destroy all air-
craft and blueprints and to shut down Avro Aircraft Company.
– p.164
165. Avro Arrow Wing, Canada Aviation Museum, Ottawa,
Canada, 2004
All that was left was a blow-torched cockpit and a wing. Well
preserved at the Canadian Aviation Museum.
– p.165
166. Jim Chamberlin (1915–1981)
Canadian aerospace engineer born in
Kamloops, British Columbia, 1915
Took Mechanical Engineering degrees at
the University of Toronto and the Imperial
College in London
In 1945, joined Avro Aircraft Ltd. and was
chief of technical design for the Arrow
Joined NASA in 1959 after the collapse of
Avro Aircraft and contributed to the design
of the NASA Gemini space capsule and the
Apollo Lunar Module (LM)
Recipient of several NASA awards includ-
ing Exceptional Scientific Achievement, Ex-
ceptional Engineering Achievement, and
Gold Medal – p.166
167. Scramjet: Supersonic Combustion Ramjet
Ground test of hydrogen-fuelled X43 at Dryden Center
in Dec. 1999
Successful flight at Mach 10 on November 16, 2004 – p.167
168. X43 Wind Tunnel Test
Wind tunnel testing of X43 at Mach 7 in NASA Langley
HTT (High Temperature Tunnel)
– p.168
169. The Renewal of Scramjet Research (1988-now)
U.S.A.: Hystep, Hyper X/X43A (one flight attempt),
Hytech (X43C), Hyset, X51A
France: PREPHA, ONERA-DLR JAPHAR, DGA
PROMETHEE
Germany: MTU, DLR/TsAGI
Australia: Hyshot
Russia: Kholod test flights (1991-1998), Igla project
China: Institute of Mechanics, Chinese Academy of
Sciences
Japan: NAL
– p.169
170. X51 Project
X51 scramjet engine firing in NASA Langley HTT. The
X51 is planned to fly by 2009 at Mach 7.
The X51 differs from the X43 through the use of hydro-
carbons (kerosene or a variant) rather than hydrogen
– p.170
171. Typical Scramjet Flowfield
Need of an isolator and shocktrain when using kerosene
fuel
Combustion takes place both subsonically and
supersonically
Long combustor required due to high flow speed induc-
ing slow mixing and combustion
– p.171
172. Antonio Ferri (1912–1975)
Italian aeronautical engineer born in 1912
in Norcia, Italy
Obtained PhD in Electrical Eng. (1934) and
PhD in Aeronautical Eng. (1936) at the
Univ. of Rome
Became the head of the Supersonic Wind
Tunnel of Guidonia (near Rome) in 1937
In 1944, moved to NACA Langley and
became Head of Gasdynamics branch
Authored the book Elements of Supersonic
Aerodynamics in 1949
Most known for pioneering supersonic com-
bustion, the scramjet, and self-restarting su-
personic inlets in the 1950s-60s
– p.172
173. Computational Fluid Dynamics (CFD)
The idea behind CFD is to transform the governing equa-
tions from the differential form into an approximate dis-
crete form and then solve the discrete form using a computer
– p.173
174. Method of Characteristics (MOC)
The MOC (method of characteristics) consists in reducing
a partial differential equation to a family of ordinary differ-
ential equations along which the solution can be integrated
from some initial data given on a suitable hypersurface.
In the case of linear equations, the MOC would collapse
to the linearized theory equations with the f waves and g
waves being the so-called characteristics. But contrarily
to linearized theory, the MOC can be also applied to non-
linear hyperbolic equations and can offer an exact solution
to the unsteady Euler equations or the steady supersonic Eu-
ler equations.
The MOC is particularly useful when designing supersonic
nozzles or to offer an exact solution to which a CFD method
can be validated against.
– p.174
175. Émile Coué (1857–1926)
French psychologist of Breton stock
born in Troyes, France, in 1857
Obtained degree in pharmacology in
1876
His book, Self-Mastery Through
Conscious Autosuggestion was
published in England (1920) and in the
United States (1922)
Coué’s Fundamental Theory is a U-turn
to what almost everyone thinks (By
will power we can do anything)
Rather, Coué’s Theory is that any idea
exclusively occupying the mind turns
into reality as long as the idea is within
the realms of possibility – p.175
