1. Gas Dynamics for Study of Nozzles@ Off-Design
P M V Subbarao
Professor
Mechanical Engineering Department
Recognize the Surprises, if Any…..

3. Ideal Convergent-Divergent Nozzle Under Design Conditions

4. Ideal Convergent-Divergent Nozzle with High Back Pressure
pb1< pin, but > p*
pthroat > p*

5. Ideal Convergent-Divergent Nozzle with High Back Pressure
When pb is very nearly the same as pin the flow remains subsonic throughout.
The flow in the nozzle is then similar to that in a venturi.
The local pressure drops from pin to a minimum value at the throat, pthroat , which is greater than p*.
The local pressure increases from throat to exit plane of the nozzle.
The pressure at the exit plate of the nozzle is equal to the back pressure.
This trend will continue for a particular value of back pressure.

6. Ideal Subsonic Convergent-Divergent Nozzle with High Back Pressure
At all these back pressures the exit plane pressure is equal to the back pressure.
pthroat> p*

7. Mass Flow Rate at Higher Back Pressures

8. Mass flow rate at Variable back pressure
Throat pressure with high back pressure pb

9. Throat pressure as a function of Variable Back pressure
For a given value of high back pressure corresponding throat pressure can be calculated.
As exit area is higher than throat area throat pressure is always less than exit plane pressure.
A decreasing exit pressure produces lowering throat pressure

10. Exit Pressure Vs Back Pressure1 1

11. Variation of in Mass Flow Rate1

12. Further Decrease the Back Pressure till the throat is just choked….
Will this be design Back pressure only ???
If not???
Define the back pressure that generates choking at throat as critical back pressure, pb.critical.

13. Back Pressure for Choking Vs Design Back Pressure
This generates choked condition at the throat.
This is the back pressure which produces maximum (design) flow rate Through the nozzle.
Is this back pressure same as design back pressure?
If not??????

14. Pexit = pb,critical
Pthroat = p*

15. Variation of in Throat Pressure1 1

16. Variation of in Mass Flow Rate1

17. What Next? What happens if back pressure is further reduced?
Still the gas pressure at the exit plane is equal to the back pressure?
Is it possible to get further lower pressure at throat !?!?!

18. Convergent-Divergent Nozzle with Lower Back Pressure than the critical back pressure
It is impossible to have a pth- < p* ???
Pthroat = p*
pb< pb,critical <pin
Pthroat< p*????
However there will be a location in the diverging section where pressure can reach p*.

19. Find out another downstream location, x where p
Find out another downstream location, x where p* can be achieved with lower back pressures.
A=?
pb < pb,critical <p0
Feasible solution
Infeasible solution ?
M<1
M<1

20. Convergent-Divergent Nozzle Under Peculiar Off-Design Conditions

21. Standing Normal Shock in Diverging Section of CD Nozzle
Normal Shock : A large discontinuity
M<1
M>1
M<1