topic 6 - nozzles - students - virginia techdevenpor/aoe3114/6 - nozzles.pdf · pressure range for...
TRANSCRIPT
![Page 1: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/1.jpg)
NozzlesNozzles
![Page 2: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/2.jpg)
TerminologyTerminologyAmbient or TankChamber p
ChamberTank
pcpb
•
•
Ambient or
Throat/Exit •
pc
TankChamber Throat
pb Ambient/Tank
•
•
•Exit pe
![Page 3: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/3.jpg)
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
![Page 4: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/4.jpg)
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
![Page 5: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/5.jpg)
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
![Page 6: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/6.jpg)
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
![Page 7: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/7.jpg)
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
![Page 8: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/8.jpg)
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
![Page 9: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/9.jpg)
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
![Page 10: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/10.jpg)
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
![Page 11: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/11.jpg)
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
![Page 12: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/12.jpg)
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
![Page 13: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/13.jpg)
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?
![Page 14: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/14.jpg)
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?
![Page 15: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/15.jpg)
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
![Page 16: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/16.jpg)
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
![Page 17: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/17.jpg)
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
![Page 18: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/18.jpg)
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
![Page 19: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/19.jpg)
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
![Page 20: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/20.jpg)
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
![Page 21: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/21.jpg)
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
![Page 22: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/22.jpg)
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
![Page 23: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/23.jpg)
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
![Page 24: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/24.jpg)
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
![Page 25: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/25.jpg)
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
![Page 26: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/26.jpg)
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
![Page 27: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/27.jpg)
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
![Page 28: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/28.jpg)
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
![Page 29: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/29.jpg)
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
![Page 30: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/30.jpg)
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
![Page 31: Topic 6 - Nozzles - Students - Virginia Techdevenpor/aoe3114/6 - Nozzles.pdf · Pressure range for which nozzle underexpanded? 7. Asked for design pressure ratio? design M? ... Shock](https://reader034.vdocument.in/reader034/viewer/2022042708/5ad8ae487f8b9a32618dd901/html5/thumbnails/31.jpg)
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