THEORY OF PROPULSION 4' Nozzles

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THEORY OF PROPULSION 4. Nozzles

• P. M. SFORZA
• University of Florida

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Nozzle characteristics
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Pressure field along the nozzle
Drag
Friction
4CfL/D
Cf.005 CD0.1
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Flow in a nozzle with simple area change
0
Isentropic flow prgTg/(g-1)
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Pressure distribution in the nozzle
pp when M1
integrating
ppt when M0
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Temperature distribution in the nozzle
Adiabatic flow along a streamline
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Mass flow through the nozzle
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Maximum mass flow through the nozzle
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M1 Critical Mach number Mass flow maximized
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Area distribution in the nozzle
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Isentropic flow in a nozzle with simple area
change
pressure is double-valued at a given A
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Nozzle critical area
0 when M1
Critical area is a minimum
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Maximum mass flow in nozzle
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Nozzle area ratio
Subsonic branch
Supersonic branch
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Pressure distribution in converging-diverging
nozzle
Z
Matched nozzle
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Sample problem Nozzle pressure mismatch effects
Nozzle with pt2.76MPa and Aexit/Amin5.16 was
designed for h30.5km but launch takes place at
sea level (p101.3kPa). Find Flaunch/F30.5km
USAF AEDC Rocket Test Cell
5.16
Assuming g1.3 we may iterate to find Mexit3.
Then FA7p7(gM721)-p0 and Flaunch110.6A7 and
F30.5km125.2A7 Therefore Flaunch/F30.5km0.884,
a 12 reduction in thrust from the design value.
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Nozzle Design

• Specify Mach number or pressure distribution
• Determine nozzle area distribution as f(Z)
• Determine nozzle radius or height as a f(Z)
• Wall angle a at exit affects thrust
• lFg /mV7 sina/a for 2-D and (1cosa)/2 for
  round
• Check that throat radius of curvature d to 2d
• Length of nozzle may be three or more throat
  diameters

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Normal shock inside nozzle
As
pdown
Shock
Shock jump
Shock jump
pup
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Shock waves and exit pressure ratio
Z
Design exit Mach number is M73
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Locating a shock in a nozzle
pegiven Tt,7Tt,5 pt,7ltpt,5
Shock is adiabatic but not isentropic
Mu
Mdlt1
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Locating a shock in the nozzle

• Knowing geometry and pe/pt,5 calculate pt,7/pt,5
• From shock tables find Mupstream
• From Mupstream find Aupstream/AAupstream/A6
• From geometry locate the station Aupstream/A6

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Chart for locating a shock in nozzle
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Oblique shock wave angle vs flow deflection
(g1.4)
Mgtgt1
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Nozzle geometry requirements
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J47 Exhaust Nozzle
Courtesy NASA
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F-15 with 2-D Vectoring Nozzles
Courtesy NASA
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2-D Variable Area Nozzle
Courtesy NASA
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2-D Variable Area Nozzle
Courtesy NASA
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Over-expanded nozzle
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Underexpanded nozzle
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Nozzle regimes for fighter aircraft