1. Instructor: Dr. David R. Greatrix Dept. of Aerospace Engineering
AE 8129 Rocket Propulsion
Instructor: Dr. David R. Greatrix
Dept. of Aerospace Engineering
Ryerson University
Phone: ext. 6432
Office: ENG 145
Counselling hours: posted

2. Additonal Logistics Lecture in ENG LG12, Wed., 9 am – noon
Run first part of class from 9:10 am – 10:30 pm, break for half-hour, second part from 11:00 am – noon
Tutorial (sample problems) incorporated into lectures; counselling hours flexible, my office (ENG 145), if I’m available

3. Logistics (cont’d) Evaluation: 1 Indiv. Proj. Report 25%
Oct. 26 (9:10 – 10:00 am)1 Term Test, 50 min. 25%
Univ. will sched. in Dec Final Exam, 3 hr %
No official course textbook; recommended books are useful for project and filling in gaps in understanding
Tests are open lecture notes + practice problem/soln. set + regular calculator

4. Logistics (cont’d)
Project may involve computer programming and/or spreadsheet analysis, at your discretion
Zero marks for late project submission

5. Outline of Course: Introduction Solid-Propellant Rocket Motors
Liquid-Propellant Rocket Engines
Hybrid Rocket Engines
Air-Breathing Rocket Engines
Non-Chemical Space Propulsion Systems

6. Delta II Launch Vehicle

7. Introduction to Rocket Propulsion
One associates rocket propulsion with space flight, but applications range from lower atmosphere to outer space
Emphasis in this course on chemical systems, employing combustion as the means for heat generation; later, will look at less conventional non-chemical approaches
Thrust produced by exhausting a hot high-speed gas (conventional approach)

8. Mission Requirements
Range of applications for rocket-based systems is considerable, from low end (e.g., pilot ejection seat) to high end (e.g., heavy space launch vehicle)
Let’s consider a simpler example, where the flight dynamics equations are more readily calculated: vertical ascent by a rocket vehicle

9. Schematic diagram of single-stage rocket vehicle at sea level launch,
quadrant elevation angle o = 90.

10. Gravity:
Vertical ascent o.d.e. :
Propellant consumption :

11. Aerodynamic drag:
, neglect
Updated o.d.e. :
Integrate to arrive at:
, 0 < t < tB1

12. Further integration provides height attained:
Move to two motor stages:

13. First stage burn time:
Vehicle mass at beginning of 2nd stage firing:
Vehicle velocity at end of 2nd stage firing:

14. Vehicle velocity at end of 1st stage burn:
Vertical height at end of 2nd stage burn:
Vertical ascent apogee:

15. Saturn V (Apollo)

16. Flight trajectory of multi-stage launch vehicle up to orbital altitude & speed.

18. Soyuz launch vehicle

19. Ideal Rocket Equation:
Space Shuttle (STS) Delta-V Budget (3 stages):
Desired (nominal) orbital velocity m/s
Gravity losses m/s
Pitch angle trajectory adjustment m/s
Atmospheric drag losses m/s
Final orbital insertion m/s
Minor correction manoeuvres m/s
Inertial assist from Earth rotation, lat.  = 28.5 m/s
CCCCC
Total required mission velocity (V) m/s

20. Gasdynamics/Thermodynamics
Thrust:
Classic contour bell nozzle
Exit gas velocity and mass flow:

21. Quick Thermodynamics Review
, ideal gas equation
of state
, enthalpy of gas
, ratio of specific heats
, speed of sound in gas
, flow Mach number

22. Isentropic Flow

23. Area-Mach Number relation:
Exit pressure:
Thrust:

24. Flow characteristics in convergent/divergent nozzle as chamber pressure
is progressively increased relative to constant outside air pressure. Case
(1): subsonic flow throughout. Case (2): flow has become choked, with
flow ahead of upstream-facing standing normal shock S2 being
supersonic, and subsonic downstream (overexpanded nozzle). Case (3):
standing normal shock S3, with bigger pressure increase across it than
S2, is positioned very near to the nozzle exit plane (overexpanded
nozzle). Inviscid flow assumed.

25. Flow characteristics in convergent/divergent nozzle as chamber pressure
is progressively increased relative to constant outside air pressure. Case
(4): supersonic flow throughout internal nozzle region; upstream-facing
oblique shock S4 with supersonic flow upstream and downstream to
bring pressure up towards ambient level (overexpanded nozzle). Case
(5): flow has reached design point, exit-plane exhaust at ambient air
pressure. Case (6): exit-plane exhaust pressure now exceeds outside air
pressure, thus producing an upstream-facing Prandtl-Meyer rarefaction
(expansion) wave to bring pressure down (underexpanded nozzle).2
Inviscid flow assumed.

26. Nominal exhaust flow patterns for an overexpanded supersonic nozzle
(upper diagram; Case 4 of previous slide) and an underexpanded supersonic
nozzle (lower diagram; Case 6 of previous slide).

27. Example flow contour diagram (contours of velocity magnitude in m/s) of
steady channel gas flow passing through a choked 2D-axisymmetric
convergent-divergent nozzle moving from left to right into the open
atmosphere; viscous-flow CFD simulation via FLUENT V Diagram
shows upper half of flow field, with flow centerline along the bottom
boundary. A standing normal shock is evident in the nozzle divergence
section, indicative of an overexpanded nozzle. The flow is separated from
the nozzle expansion wall downstream of the nozzle throat, resulting in an
exhaust jet that is of relatively constant cross-sectional area as it extends
and expands downstream.

28. Specific impulse (instantaneous):
Average specific impulse:

29. Standard Nozzle Designs
SRM examples

30. LRE example (bell nozzle, Rocketdyne RS-51)

31. Alternative Nozzle Designs
E-D = expansion-deflection, R-F = radial-flow, H-F = horizontal-flow

32. Expansion-deflection nozzle (pintled nozzle variant; pintle forces flow outward to the nozzle expansion walls; flow moving left to right in diagram below)

33. Stepped nozzle variant (G. P
Stepped nozzle variant (G.P. Sutton design; nozzle expansion insert ejected later in flight, at higher altitude)

34. Alternative Nozzle Designs (cont’d)
NASA/Lockheed Martin X-33 (VentureStar orbital
spaceplane program, subscale technology
demonstrator), utilizing two side-by-side liquid-propellant
Rocketdyne XRS-2200 aerospike-nozzled engines

35. X-33 in orbital flight over Earth’s surface

36. Combustion Review 18 amu, water vapour 8 : 1
Reaction, ideal result:
8 : 1
stoichiometric oxidizer-to-fuel ratio
Molecular mass of ideal stoichiometric product of
combustion (reaction):
18 amu, water vapour
+ heat energy

37. Non-ideal chemical reaction:
Molecular mass of non-ideal product of combustion :

38. Resulting gas specific heat:
Resulting gas ratio of specific heats:

39. Flame Structure
Premixed laminar flame, first category; process of combustion is driven predominantly by pressure
Turbulent diffusion flame, second category; process of combustion is driven predominantly by mixing
Commonly in propulsion system combustors, flame is a combination of the above two