1. Stagnation Properties
B.GOVINDHARAJAN
J.PARTHIBAN
Capacity of A Resource…..

2. Stagnation Properties of Isentropic Flow1

3. What was Stagnation Temperature At Columbia Breakup
Loss Of Signal at:
61.2 km altitude
~18.0 Mach Number
T∞ ~ 243 K

4. Ideal & Calorically perfect Gas
Ideal Gas with Variable Properties
Real Gas with Variable Properties

5. Capacity of A Cross Section
Mass flow rate through any cross section of area A
Maximum Capacity is obtained when sonic velocity occurs at throat !

6. Calorically perfect gas:

10. Specific Mass flow Rate
Mass flow rate per unit area of cross section:

11. Design of Supersonic Intake / Nozzle
B.GOVINDHARAJAN
J.PARTHIBAN
From the Beginning to the Peak or Vice Versa….

12. Quasi-One-Dimensional Flow

13. Distinction Between True 1-D Flow and Quasi 1-D Flow
• In “true” 1-D flow Cross sectional area is strictly constant
• In quasi-1-D flow, cross section varies as a Function of the longitudinal coordinate, x
• Flow Properties are assumed
constant across any cross-section
• Analytical simplification very useful for evaluating Flow properties in Nozzles, tubes, ducts, and diffusers.
Where the cross sectional area is large when compared to length

14. Specific Mass flow Rate
Mass flow rate per unit area of cross section:

15. Maximum Capacity of An Intake/Nozzle
• Consider a discontinuity at throat “choked-flow” Nozzle … (I.e. M=1 at Throat)
• Then comparing the massflow /unit area at throat to some other station.

16. Take the ratio of the above:

19. Design Analysis
For a known value of Mach number, it is easy to calculate area ratio.
Throat area sizing is the first step in the design.
If we know the details of the resource/requirements, we can calculate the size of throat.

20. Cryogenic Rocket Engines
A ratio of LO2:LH2 =6:1
T0 = 3300 K.
P0 = 20.4 Mpa

21. Specifications of A Rocket Engine
• Specific Impulse is a commonly used measure of performance
For Rocket Engines,and for steady state-engine operation is defined
As:
• At 100% Throttle a RE has the Following performance characteristics
Fvacuum = kNt
Ispvacuum = 450 sec.
Fsea level = 1600 kNt

22. Specific impulse of various propulsion technologies
Engine
"Ve" effective exhaust velocity (m/s, N·s/kg)
Specific impulse (s)
Energy per kg (MJ/kg)
Turbofan jet engine
300
3000 43
Solid rocket
2500
250
3.0
Bipropellant liquid rocket
4400
450
9.7
Plasma Rocket
29 000
430
VASIMR
290 000
30 000
43 000

23. Design Procedure
Select a technology : Isp & Fthrust

24. SEA Level Performance
One needs to know the Mach number distribution for a given geometric design!
Find the roots of the non-linear equation.

25. Numerical Solution for Mach Number Caluculation
• Use “Newton’s Method” to extract numerical solution
• Define:
• At correct Mach number (for given A/A*) …
• Expand F(M) is Taylor’s series about some arbitrary Mach number M(j)

26. • Solve for M

27. • From Earlier Definition , thus
Still exact expression
• if M(j) is chosen to be “close” to M
And we can truncate after the first order terms with “little”
Loss of accuracy

28. • First Order approximation of solution for M
“Hat” indicates that solution is no longer exact
• However; one would anticipate that
“estimate is closer than original guess”

29. • If we substitute back into the approximate expression
• And we would anticipate that
“refined estimate” …. Iteration 1

30. • Abstracting to a “jth” iteration
Iterate until convergence
j={0,1,….}
• Drop from loop when

31. Plot Flow Properties Along Nozzle Length
• A/A*

32. • Mach Number

33. • Temperature
T0 = 3300K
Tthroat = K

34. • Pressure
P0 = 20.4Mpa
Pthroat = MPa

35. Operating Characteristics of Nozzles
B.GOVINDHARAJAN
J.PARTHIBAN
Realizing New Events of Physics…….

36. Converging Nozzle
pb = Back Pressure
Design Variables:
Outlet Condition: p0 pb

37. Designed Exit Conditions
Under design conditions the pressure at the exit plane of the nozzle is applied back pressure.

38. Profile of the Nozzle
At design Conditions:

39. Full Capacity Convergent Nozzle

40. Remarks on Isentropic Nozzle Design
Length of the nozzle is immaterial for an isentropic nozzle.
Strength requirements of nozzle material may decide the nozzle length.
Either Mach number variation or Area variation or Pressure variation is specified as a function or arbitrary length unit.
Nozzle design attains maximum capacity when the exit Mach number is unity.

41. Converging Nozzle p0
Pb,critical

42. Operational Characteristics of Nozzles
A variable area passage designed to accelerate the a gas flow is considered for study.
The concern here is with the effect of changes in the upstream and downstream pressures
on the nature of the inside flow and
on the mass flow rate through a nozzle.
Four different cases considered for analysis are:
Converging nozzle with constant upstream conditions.
Converging-diverging nozzle with constant upstream conditions.
Converging nozzle with constant downstream conditions.
Converging-diverging nozzle with constant downstream conditions.

43. Pressure Distribution in Under Expanded Nozzle
pb=p0 p0
pb,critical<pb3<p0
pb,critical<pb2<p0
pb,critical<pb1<p0
Pb,critical
At all the above conditions, the pressure at the exit plane of nozzle, pexit = pb.

44. Variation of Mass Flow Rate in Exit Pressure1 1

45. Variation of in Exit Pressure1 1

46. Variation of in Mass Flow Rate1

47. Low Back Pressure Operation

48. Convergent-Divergent Nozzle Under Design Conditions

50. Convergent-Divergent Nozzle with High Back Pressure
p*< pb1<p0
pthroat> p*

51. Convergent-Divergent Nozzle with High Back Pressure
When pb is very nearly the same as p0 the flow remains subsonic throughout.
The flow in the nozzle is then similar to that in a venturi.
The local pressure drops from p0 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.

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

56. At exit with high back pressure pb
At throat with high back pressure pb

57. 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.
An decreasing exit pressure produces lowering throat pressure

58. Variation of Mass Flow Rate in Exit Pressure1 1

59. Variation of in Mass Flow Rate1