1. Design and analysis of Parabolic nozzle using MOC and CFD

2. Outline Introduction Literature Review MOC Contoured nozzle
Conical nozzle
Conclusions
Future Plans

3. Introduction

4. Nozzle

5. Method of characteristics (MOC)
In MOC nozzle’s physical boundaries are found as a solution
MOC is used to predict the contour of a parabolic rocket nozzle with a design exit Mach number
The designed nozzle contour is then analysed using the Computational Fluid Dynamics (CFD)
Different nozzle contours are be compared

6. Development of Rockets
In 600 AD, Chinese prepared fire arrows using propellants
Understanding and development of the rocket began in 19th century
In 1920 it was concluded that a rocket needs no air to work thus it can work even in vacuum conditions also
Rocket of 10 feet length was launched in 1926
During post-World War II era, Germany developed the A-4 rocket
The Space Shuttle Main Engine is the mile stone in the development

7. Indian Rockets - History
The first indian built sounding rocket, Rohini-75, was a small 75-diameter model that shot off in 1967, from Thumba.
The first of India's satellite launch vehicles was SLV-3 to place 40-kg satellites into orbit.
Followed by the Augmented Satellite Launch Vehicle (ASLV) that could place 100-kg satellites into orbit.
It was followed by the Polar Satellite Launch Vehicle (PSLV) to launch 1000-kg remote sensing satellites in a 900 kilometer polar Sun Synchronous Orbit.
GSLV is 40,000 times heavier than Rohini-75.
GSLV can lob 2-ton satellites into a orbit

8. Rocket Engine Thrust chamber Propellant feed system
Propellant control system
Thrust vector control system

9. Literature Review Mach number is a function of area ratio
𝑨 𝑨 ∗ = 𝟏 𝑴 𝟐 𝜸+𝟏 (𝟏+ 𝜸−𝟏 𝟐 𝑴 𝟐 𝜸+𝟏 𝟐(𝜸−𝟏)
Conical nozzle – loss of performance
Contoured nozzled – better than conical nozzles

10. Method of characteristics is used to design the wall contour to cancel the expansion waves in the near exit region.
In 1929, Ludwig Prandtl and Adolf Busemann implemented the method of characteristics successfully for nozzle design.
Solutions to axis-symmetric supersonic streams using a method of characteristics approach was proposed by Foelsch
G.V.R. Rao used the method of characteristics to develop contour nozzle designs.

11. Rao’s Approach

12. Shock Formation in Nozzles- Need of MOC

13. Flow Regimes at Nozzle Throat

14. MOC Equations

15. MOC

16. Comparison of co ordinates

17. Basics
𝑭= 𝒅𝒎 𝒅𝒕 𝑽 𝒆 = 𝒎 𝑽 𝒆 (𝟏)
𝑭= 𝒎 𝑽 𝒆 + 𝒑 𝒆 − 𝒑 𝒂 𝑨 𝒆

18. Basics

19. Logic of nozzle development

20. Contoured Nozzle

21. CFD domain

22. Code validation

23. Grid

24. Mach number distribution

25. Flow development

26. Full nozzle simulation

27. Effect of downstream pressure
Effect of number of characteristic lines
Comparison with isentropic values

28. Conical nozzle

30. Flow development

31. Effect of wall divergence angle

32. Comparison between contoured and conical nozzle

33. Conclusions
The main objective of this study is to design the contoured nozzle having the exit Mach number of 5.
A contoured nozzle is designed using method of characteristics (MOC) . The designed nozzle is analysed using computational fluid dynamics (CFD).
A code validation was done against the published experimental result and found that the CFD results matches closely with the experimental result.
It was found that the grid size plays an important role during CFD analysis. The grid of proper resolution is required to capture the flow correctly.
The Mach number calculated by CFD is lesser than the Mach number expected. This is because the MOC approach does not include the viscous effects and thus the nozzle contour to be corrected to accommodate the boundary layer on the wall.
An unsteady analysis shows that the flow takes about 0.5 seconds to fully develop and the contoured nozzle gives a thrust of 50 KN.
The range of number of characteristic lines has a least impact on the designed nozzle performance.
With increase in downstream pressure the flow expands more in the downstream region of the contoured nozzle as expected.
A conical nozzle having the same area ratio and the length was designed.
The exit Mach number of conical nozzle is higher than the contoured nozzle.
The flow angle varies from minimum to maximum from center line to the wall. This happens because the flow direction near the wall should match that of wall.
With variation in wall divergence angle of conical wall for the same area ratio, minor difference in nozzle thrust and the nozzle exit Mach number was found.
The thrust of the conical and contoured nozzle were compared and found the contoured nozzle is offering 20% higher thrust.
It is concluded that the contoured nozzle is superior in performance.

34. Future Plans
This analysis is done for 2D. 3D analysis for the same geometry to be done.
The effect of mass flow rate by changing the upstream conditions on the thrust to be found out.
Since the wall angles chosen for the conical nozzle does not offer separation, further increase in wall angle to be studied. This will reduce the nozzle length and weight.

35. Thank You