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

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

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. 50% 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

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

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

Delta II Launch Vehicle

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)

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

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

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

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

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

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

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

Saturn V (Apollo)

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

Soyuz launch vehicle

Ideal Rocket Equation: Space Shuttle (STS) Delta-V Budget (3 stages): Desired (nominal) orbital velocity 7790 m/s Gravity losses 1220 m/s Pitch angle trajectory adjustment 360 m/s Atmospheric drag losses 118 m/s Final orbital insertion 145 m/s Minor correction manoeuvres 62 m/s Inertial assist from Earth rotation, lat.  = 28.5 - 408 m/s CCCCC Total required mission velocity (V) 9347 m/s

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

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

Isentropic Flow

Area-Mach Number relation: Exit pressure: Thrust:

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.

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.

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).

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 V5.4 . 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.

Specific impulse (instantaneous): Average specific impulse:

Standard Nozzle Designs SRM examples

LRE example (bell nozzle, Rocketdyne RS-51)

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

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

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

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

X-33 in orbital flight over Earth’s surface

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

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

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

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