Section1:

Compressible Flow: Historical Perspective

and Basic Definitions

Anderson: Chapter 1 pp. 1-19

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 De Laval Nozzle
• High Speed flows often seem “counter-intuitive” when
Compared with low speed flows

• Example: Convergent-Divergent Nozzle (De Laval)

QuickTime™ and a
In 1897 Swedish Engineer Gustav De Laval designed
TIFF (Uncompressed) decompressor
are needed to see this picture.
A turbine wheel powered by 4- steam nozzles

De Laval Discovered that if the steam nozzle

Credit: NASA GSFC first narrowed, and then expanded, the efficiency of
the turbine was increased dramatically
flow
Furthermore, the ratio of the minimum area
to the inlet and outlet areas was critical for achieving
maximum efficiency … Counter to the “wisdom” of the day
Convergent / Divergent Nozzle

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 De Laval Nozzle (cont’d)
• Mechanical Engineers of the 19’th century were
Primarily “hydrodynamicists” .. That is they were
Familiar with fluids that were incompressible … liquids
and Low speed gas flows where fluid density was
Essentially constant

• Primary Principles are Continuity and Bernoulli’s Law

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 De Laval Nozzle (cont’d)
• When Continuity and Bernoulli are applied to a
De Laval Nozzle and density is Assumed constant
High Pressure Inlet
pI pt pe
VI A I At Vt Ae Ve
AI At Ae
 At Throat 


• Pressure Drop
• Velocity Increases

Continuity
Bernoulli
“classic” Venturi 4
 De Laval Nozzle (cont’d)
• When Continuity and Bernoulli are applied to a
De Laval Nozzle and density is Assumed constant
High Pressure Inlet
pI pt pe
VI A I At Vt Ae Ve
AI At Ae
  
At Exit

• Pressure Increases
• Velocity Drops

Continuity
Bernoulli
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 De Laval Nozzle (concluded)
High Pressure Inlet
pI pt pe
VI A I At Vt Ae Ve

AI At Ae
  
• But De Laval Discovered that when the Nozzle throat
Area was adjusted downward until the pressure ratio became
pt / pI < 0.5484 -> then the exit Pressure dropped (instead of
Rising … compared to the throat pressure)
And the exit velocity rose (instead of dropping)…
Which is counter to What Bernoulli’s law predicts
… he had inadvertently ,,, Generated supersonic flow! …
• fundamental principle that makes rocket motors possible
6
 Effects of Compressibility
Example 2: “Mach Tuck”
• Driven by Combat Needs in WWII, Aircraft airspeeds
became increasingly faster.

• P-51s, Spitfires and other types were reaching speeds close

to that of sound, especially in dives to catch, or escape from,
the enemy.

• Pilots began to report control difficulties and unexpected

problems, including a strong nose down pitch and a loss of
pitch control authority. Often took all of pilot’s strength to
correct. Some did not make it and dove into the ground, or
broke up, as their aircraft exceeded the maximum design
speed.

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 Effects of Compressibility
Example 2: “Mach Tuck” (cont’d)

• Nose down pitching moment was a result of Localized Supersonic Flow and
Air Compressibility

• At low speeds airfoils have an aerodynamic center that isApproximately at

the 25% chord point.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.

• However, as the aircraft moves into supersonic flight the induced wash ahead
of the wing disappears … we’ll learn Why later … As a result the aerodynamic
center moves back to the 50% chord point.

QuickTime™ and a
Credit: Selkirk College Professional Aviation Program TIFF (LZW) decompressor
are needed to see this picture.
8
 High Speed Flight: Historical Perspective (cont’d)

• As the aircraft moves into supersonic flight the aerodynamic center suddenly
moves back from 25% chord to 50%, the resolved Moment is strongly nose down
… a phenomenon known as “Mach Tuck”

• Modern Supersonic aircraft compensate for “Mach Tuck” Using the flight
control system, and the effect is insignificant to the pilot.

• However, if the aircraft was never designed to enter supersonic flight (like
early subsonic fighters) the nose would pitch down Is severe during the
transition through the transonic speed range.

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 High Speed Flight: Historical Perspective (cont’d)

• Nose down pitching moment was a result of Localized Supersonic Flow and Air
Compressibility

• Reduced control authority was a result of the movement of the Aerodynamic

center aft on the aircraft.

• In 1940 NACA commissioned Bell aircraft company to build a special research

aircraft for exploring speed range beyond the speed of sound … the Bell X-1.
Instrumental in proving these effects.

• X1 became the first aircraft to fly faster than the speed of sound on October, 14
1947 when Chuck Yeager flew to Mach 1.08

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 Flow Regimes
• In compressible flow regimes, flow properties vary significantly
From those of lower speed flows

• Understanding these differences is the primary topic of this course

1. Subsonic - All flow everywhere on the aircraft less than local speed of sound.

2. Transonic - Some flow is subsonic and some is supersonic.

3. Supersonic - All flow everywhere on the aircraft is supersonic.

4. Hypersonic - Fluid flows that are Much Higher than sonic velocity

• Key Parameter: Mach number --> ratio of airspeed and local speed of sound.
Mach 1~ 573.8 knots at -56 C (the typical stratosphere temperature.)

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 Flow Regimes (cont’d)
• As an object moves through a fluid medium it creates
pressure waves.

• Pressure waves travel out at the speed of sound which in term depends
on gas properties and temperature (more on this later)

• If the object is traveling significantly slower than sonic velocity, then

pressure waves travel out uniformly similar to waves on the surface of
a pond.

Credit: Selkirk College Professional Aviation Program 12

 Flow Regimes (cont’d)
• As the object approaches the speed of sound, it begins to catch up with the
pressure waves and creates an infinitesimally weak flow discontinuity
just ahead of the aircraft

Credit: Selkirk College Professional Aviation Program

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 Flow Regimes (cont’d)
• As the vehicle breaks the speed of sound, the infinitesimally weak Shock
waves begin to add up along a “Mach Line” and form a strong pressure wave
with highly compressed air, called a shockwave.

• We’ll spend
a considerable
Portion of the
course
Understanding
The properties of
shockwaves

Credit: Selkirk College Professional Aviation Program

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 Flow Regimes (cont’d)
• As Mach number increases, the strength of the shock wave increases and
the Angle of the shockwave becomes increasingly severe

• Mach Angle

1

 sin M 

Credit: Selkirk College Professional Aviation Program

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 Flow Regimes (concluded)
• Finally as mach number becomes very large the shock wave Is bent so severely
that it lies right against the vehicle; resulting flow field referred to as a shock layer.

• Within the shock layer the air is heated so much by friction and its own kinetic
energy that the air molecules ionize.

• This thin layer can produce many complications in vehicle design, and gas
dissociation chemistry is essential part of the Flow calculations

• In this Course we will only consider simple approximations for Hypersonic flow

QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.

Credit: www.aerospaceweb.org
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 Mathematical Definition of Compressible
Flow
• Compressibility is a fluid property
Liquids are largely incompressible
Gasses are more highly compressible

• Fractional change in volume as pressure is increased

1 dv
 
v dp
-> compressibility, v gas volume, p

Incompressible gas --- infinite 

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 Speed of Sound in a Gas

control
volume p p + dp
C C- d v A
c

 + d

• Consider the flow across an infinitesimal strength Shock wave

• Result is a compression with pressure and density rise And drop in

velocity

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 Speed of Sound in a Gas (cont’d)

control
volume p p + dp
C C- d v A
c

 + d

• Across the control volume we apply Newton’s Second law

(assuming constant mass within control volume)

• Letting the volume become infinitesimally small

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 Speed of Sound in a Gas (cont’d)

control
volume p p + dp
C C- d v A
c

 + d

• The constant mass flow through the control volume is

• Combining terms and simplifying

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 Speed of Sound in a Gas (cont’d)

control
volume p p + dp
C C- d v A
c

 + d

• Applying Continuity (conservation of mass) across control volume

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 Speed of Sound in a Gas (cont’d)

control
volume p p + dp
C C- d v A
c

 + d

• Collecting terms

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 Speed of Sound in a Gas (cont’d)

control
volume p p + dp
C C- d v A
c

 + d

• Because shock wave is infinitesimal, process is

1) Adiabatic … no heat loss or addition
2) Reversible … no dissipative phenomena occur
i.e. entropy is constant
Reversible adiabatic process is referred to as isentropic, and sonic
velocity is written as

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 Speed of Sound in a Gas (cont’d)
• Incompressible Gas … speed of sound is infinite

• Incompressible gas …Mach number is zero

M = V/c --> V/∞ = 0

• Later we’ll get a More workable expression for Sonic velocity for
a “perfect gas”

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 Summary
• Key Concepts:
i) High Speed flows often seem “counter-intuitive” when
Compared with low speed flows

ii) Flow regimes

Subsonic - All flow everywhere on the aircraft less than local speed of sound.
Transonic - Some flow is subsonic and some is supersonic.
Supersonic - All flow everywhere on the aircraft is supersonic.
Hypersonic - Fluid flows that are Much Higher than sonic velocity

iii) Mach number - ratio of true airspeed to local speed of sound

iv) Mach Angle … angle of shock wave generated by “point object”

1
v) Sonic Velocity in a gas 
sin M 

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 Next:
The Equation of State and a Review of
Thermodynamics

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