School of Aerospace Engineering

Isentropic Nozzles
Apply equations for isentropic flow with area change
to nozzles
Nozzles
increases velocity of fluid (no work)
converts thermal energy to KE (Tu)
For conventional (wall-bounded) nozzles, two types:
converging
1
M

converging-diverging (CD)

0<M<

AE3450
Isentropic Nozzles -1

Copyright 2001 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Converging Nozzles
Reservoir
po A pb 0
1.1
To
0.2
At
Assume choked
T/T o, p/p o, / o

0.9 Temperature
0.4
Solution of Pressure
Density
M

VI.17 (M v. A/A*) Mach Number 0.6

VI.6-8 (T/To, p/po, 0.7
/o v. M) 0.8

=1.4
Large change in 1
pressure and density 0.5
0 5 10 15
as approach throat
Area Ratio (A/A*)

AE3450
Isentropic Nozzles -2

Copyright 2001 by Jerry M. Seitzman. All rights reserved.

1
 School of Aerospace Engineering

Converging Nozzle and Back Pressure

pe
What determines whether Reservoir
flow get choked (goes sonic)? po A pb
To
back pressure (po/pb)
pressure is driving force, x
At
0
e.g., if po=pb, no flow p/po
1 pb=po
What happens as we pb<po
lower pb (initially =po) p*/po pb=p*
Mach # at exit keeps rising pb<p*
pe=p*
until flow is choked (Me=1)
pe=p*, max. mass flow rate 0 x

AE3450
Isentropic Nozzles -3

Copyright 2001 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

Critical Back Pressure

What is pb/po required to go Reservoir
sonic? po pb
To
pb/po = p*/po

po 1 2 1
= 1 + M (from VI.7)
p 2

p* 1 2 1
= 1 1 + 1
po 2
0.487 = 5 / 3
p* 2 1
= (VI.20) = 0.528 = 1.4
po + 1 0.546 = 1.3

AE3450
Isentropic Nozzles -4

Copyright 2001 by Jerry M. Seitzman. All rights reserved.

2
 School of Aerospace Engineering

Converging-Diverging Nozzles
Reservoir
0
po A pb
1.2
To =1.4
1 1
At

T/T o, p/p o, / o
0.8 Temperature
Assume choked Pressure 2
Density

M
0.6
Solution of Mach Number
3
VI.17 (M v. A/A*) 0.4
VI.6-8 (T/To, p/po, 4
0.2
/o v. M)
0 5
Very large change in
0 5 10 15
pressure and density Area Ratio (A/A*)

AE3450
Isentropic Nozzles -7

Copyright 2001 by Jerry M. Seitzman. All rights reserved.

School of Aerospace Engineering

CD Nozzle and Back Pressure

pe
At
What happens as we Reservoir
lower pb (initially =po)? po pb
To
Me keeps rising until Ae
flow is choked (Mt=1)
still subsonic at exit p/po pb=po
1
If lower pb enough, can pb<po
pb=
get isentropic Me>1 p*/p p(Ae/A*,M<1)
o
solution
pb=
pb in between, get p(Ae/A*,M>1)
nonisentropic flow 0 x

AE3450
Isentropic Nozzles -8

Copyright 2001 by Jerry M. Seitzman. All rights reserved.