NozzlesNozzles

TerminologyTerminologyAmbient or TankChamber p

ChamberTank

pcpb

•

•

Ambient or 

Throat/Exit •

pc

TankChamber Throat

pb Ambient/Tank

•

•

•Exit pe

JetsJetsSubsonic Supersonic

Pressure at exit must be same as back pressure

Pressure at exit may ormay not be same as back pressureback pressure same as back pressure

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

M<1

pc

Throat/ExitM<1 pe=pb

Subsonic flow

p /p

1

pb /pcp /pc

0

Distance down the nozzleExit

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

M<1

pc

Throat/ExitM<1 pe=pb

Subsonic flow

p /p

1

pb /pcp /pc

0

Distance down the nozzleExit

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

M<1

pc

Throat/ExitM<1 pe=pb

Subsonic flow

p /p

1

/p /pc pb /pc

0

Distance down the nozzleExit

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

M=1

pc

Design/Flow just choked

Throat/ExitM=1 pe=pb

p /p

1

p /pcpb /pc

0

Distance down the nozzleExit

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

pcM>1 with waves

Underexpanded/Choked

Throat/ExitM=1 pe>pb

p /p

1

p /pc

pb /pc

0

Distance down the nozzleExit

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

M>1 with waves

pc

Underexpanded/Choked

Throat/ExitM=1 pe>pb

p /p

1

p /pc

pb /pc

0

Distance down the nozzleExit

Converging NozzleConverging NozzleAmbientChamber pb

Flow acceleratingM<1

Th t/E it

M>1 with waves

pc

Underexpanded/Choked

Throat/ExitM=1 pe>pb

p /p

1

p /pc

pb /pc0

Distance down the nozzleExit

pb /pc

Example‐ Converging NozzleExample Converging Nozzlepc=100kPaTc=300K (a) Find Me, pe, Te for pb=63kPa

pb

CL1 e

(b) Find Me, pe, Te for pb=40kPa

TABLES

Example‐ Converging NozzleExample Converging Nozzlepc=100kPaTc=300K (a) Find Me, pe, Te for pb=63kPa

pb

CL1 e

(b) Find Me, pe, Te for pb=40kPa

Example‐ Converging NozzleExample Converging Nozzlepc=100kPaTc=300K (a) Find Me, pe, Te for pb=63kPa

pb

CL1 e

(b) Find Me, pe, Te for pb=40kPa

1. Asked for M1, p1 ?Variations

2. Asked for mass flow rate?

3. Asked for max mass flow rate?

Example‐ Converging NozzleExample Converging Nozzlepc=100kPaTc=300K (a) Find Me, pe, Te for pb=63kPa

pb

CL1 e

(b) Find Me, pe, Te for pb=40kPa

4. Asked for pb/pc range for which nozzle choked?Variations

5. What if shock in nozzle?

6. Pressure range for which nozzle underexpanded?g p

7. Asked for design pressure ratio? design M?

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow deceleratingM<1

M<1

M<1

Exit M<1pe=pbSubsonic flowp /pc

1 pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow deceleratingM<1

M<1

M<1

Exit M<1pe=pbSubsonic flowp /pc

1 pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow deceleratingM<1

M<1

M<1

Exit M<1pe=pbSubsonic flowp /pc

1 pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow deceleratingM<1

M=1

M<1

Exit M<1pe=pbFlow just chokedp /pc

1pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow deceleratingM<1

M=1

M<1M>1

Exit M<1pe=pbp /pc Shock in Nozzle/Choked

1

pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow dec.M<1

M=1

M<1Flow acc.M>1

Exit M<1pe=pbp /pc Shock in Nozzle/Choked

1

pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

Flow dec.M<1

M=1

M<1Flow acc.M>1

Exit M<1pe=pbShock in Nozzle/Chokedp /pc

1

pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

M=1

M<1Flow acceleratingM>1

Exit M<1pe=pbShock at exit/Chokedp /pc

1

pb /pc

00

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1Supersonicor mixedsub/supersonicflow with waves

pc

Flow acceleratingM<1

M=1

Flow acceleratingM>1

f

Exit M>1Pe<pbp /pc Overexpanded/Choked

1

pb /p

0

pb /pc

0

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1Supersonicor mixedsub/supersonicflow with waves

pc

Flow acceleratingM<1

M=1

Flow acceleratingM>1

f

Exit M>1Pe<pbOverexpanded/Chokedp /pc

1

0

pb /pc

0

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

M=1

Flow acceleratingM>1

M>1

Exit M>1pe=pbDesign/Chokedp /pc

1

0

pb /pc

0

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

M=1

Flow acceleratingM>1

Supersonicflow with waves

Exit M>1pe>pbUnderexpanded/Chokedp /pc

1

0

pb /pc

0

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

M=1

Flow acceleratingM>1

Supersonicflow with waves

Exit M>1pe>pbUnderexpanded/Chokedp /pc

1

0pb /pc

0

Distance down the nozzleExitThroat

Converging‐Diverging NozzleConverging Diverging Nozzle

p

pbAmbientChamber Throat

M 1pc

Flow acceleratingM<1

M=1

Flow acceleratingM>1

Supersonicflow with waves

Exit M>1pe>pbUnderexpanded/Chokedp /pc

1

0 pb /pc0

Distance down the nozzleExitThroat

pb /pc

Example‐ Converging‐Diverging NozzleExample Converging Diverging Nozzlepc

pb Compute M,p at i etj

(a) For entirely subsonic flow 

CL i et j

( ) ywith  pb/pc =0.9

(b) For pb/pc just low enough to choke flow

( ) At d ij (c) At designAe =0.15m20.125m2 0.1m2 0.125m2

TABLES

Example‐ Converging‐Diverging NozzleExample Converging Diverging Nozzlepc

pb Compute M,p at i etj

(a) For entirely subsonic flow 

CL i et j

( ) ywith  pb/pc =0.9

(b) For pb/pc just low enough to choke flow

( ) At d ij (c) At designAe =0.15m20.125m2 0.1m2 0.125m2

Example‐ Converging‐Diverging NozzleExample Converging Diverging Nozzlepc

pb Compute M,p at i etj

(a) For entirely subsonic flow 

CL i et j

( ) ywith  pb/pc =0.9

(b) For pb/pc just low enough to choke flow

( ) At d ij (c) At designAe =0.15m20.125m2 0.1m2 0.125m2