lectures-intro-propulsion - 650:460 Aerodynamics...

650:460 Aerodynamics
Introduction to Propulsion
Prof. Doyle Knight
Tel: [phone], Email: [email protected]
Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment
Fall 2012
1

Introduction
• Afterburning turbojet engine
2

Introduction
• Conservation of mass
X
˙ m
in
=
X
˙ m
out
Thus
ρ
o
V
o
A + ˙ m
s
+ ˙ m
f
= ( ˙ m
o
+ ˙ m
f
) + ρ
o
V
o
( A
9
- A )
Note definition of ρ
o
, ˙ m
s
, ˙ m
o
, A . The above equation simplifies to
˙ m
s
= ˙ m
o
- ρ
o
V
o
A
9
3

Introduction
• Conservation of momentum
X
˙ mV
x
|
out
-
X
˙ mV
x
|
in
=
X
F
x
The net force is
X
F
x
= F |
thrust
| {z }
F
- ( p
9
- p
o
) A
9
The momentum fluxes are
X
˙ mV
x
|
out
= ( ˙ m
o
+ ˙ m
f
) V
9
+ ρ
o
V
2
o
( A - A
9
)
X
˙ mV
x
|
in
= ρ
o
V
2
o
A + ˙ m
s
V
o
4

Introduction
• Conservation of momentum
The equation simplifies to
( ˙ m
o
+ ˙ m
f
) V
9
- ˙ m
o
V
o
= F - ( p
9
- p
o
) A
9
Define
F = F
uninstalled
= ( ˙ m
o
+ ˙ m
f
) V
9
- ˙ m
o
V
o
+ ( p
9
- p
o
) A
9
and
D
ram
= ˙ m
o
V
o
For subsonic flow at exit, p
9
= p
o
.
For supersonic flow at exit, p
9
is not necessarily equal to p
o
.
p
9
< p
o
: overexpanded
p
9
= p
o
: perfectly expanded
p
9
. p
o
: underexpanded
5

Introduction
• Conservation of momentum
Define gross thrust
F
g
= ( ˙ m
o
+ ˙ m
f
) V
9
+ ( p
9
- p
o
) A
9
and thus
F = F
g
- D
ram
For multiple exhausts
F =
X
F
g
|
nozzles
- D
ram
|
inlets
For turbofan
F = ˙ m
9
V
9
+ ˙ m
19
V
19
+ ( p
9
- p
o
) A
9
+ ( p
19
- p
o
) A
19
- ˙ m
o
V
o
6

Introduction
• Takeoff thrust
At takeoff, the air speed V
o
is small and thus
F |
takeoff
≈ ( ˙ m
o
+ ˙ m
f
) V
9
+ ( p
9
- p
o
) A
9
7

Installed Thrust
• The installed thrust is the actual measured thrust when the engine is
installed on the pylon
• The uninstalled thrust is the thrust that would be measured if the
engine were isolated from the wing and pylon
• The uninstalled and installed thrust are related by
F |
installed
= F |
uninstalled
- D |
nacelle
• The text shows that a different choice of control volume yields the
same result for uninstalled thrust
8

Introduction
• The installed net thrust accounts for the effects of the engine
installation on the pylon
9