Rocket Propulsion Fundamentals 2
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https://ntrs.nasa.gov/search.jsp?R=20140002716 2019-08-29T14:36:45+00:00Z Liquid Propulsion Systems – Evolution & Advancements Launch Vehicle Propulsion & Systems LPTC Liquid Propulsion Technical Committee Rick Ballard Liquid Engine Systems Lead SLS Liquid Engines Office NASA / MSFC All rights reserved. No part of this publication may be reproduced, distributed, or transmitted, unless for course participation and to a paid course student, in any form or by any means, or stored in a database or retrieval system, without the prior written permission of AIAA and/or course instructor. Contact the American Institute of Aeronautics and Astronautics, Professional Development Program, Suite 500, 1801 Alexander Bell Drive, Reston, VA 20191-4344 Modules 1. Rocket Propulsion Fundamentals 2. LRE Applications 3. Liquid Propellants 4. Engine Power Cycles 5. Engine Components Module 1: Rocket Propulsion TOPICS Fundamentals • Thrust • Specific Impulse • Mixture Ratio • Isp vs. MR • Density vs. Isp • Propellant Mass vs. Volume Warning: Contents deal with math, • Area Ratio physics and thermodynamics. Be afraid…be very afraid… Terms A Area a Acceleration F Force (thrust) g Gravity constant (32.2 ft/sec2) I Impulse m Mass P Pressure Subscripts t Time a Ambient T Temperature c Chamber e Exit V Velocity o Initial state r Reaction ∆ Delta / Difference s Stagnation sp Specific ε Area Ratio t Throat or Total γ Ratio of specific heats Thrust (1/3) Rocket thrust can be explained using Newton’s 2nd and 3rd laws of motion. 2nd Law: a force applied to a body is equal to the mass of the body and its acceleration in the direction of the force. F ma 3rd Law: For every action, there is an equal and opposite reaction. Fa Fr In rocket propulsion, a mass of propellant (m) is accelerated (via the combustion process) from initial velocity (Vo) to an exit velocity (Ve). The acceleration of this mass is written as: a Ve Vo / t Thrust (2/3) Combining terms, we get: F m(V V ) /t e o Which can be rearranged: m F (Ve Vo ) t The term of mass of propellant divided by time is referred to as mass flow rate (m-dot), expressed as F m (Ve Vo ) Substituting weight flow rate for mass flow rate and assuming a zero initial velocity, the thrust produced by propellant flow (momentum thrust, F1) is shown as m F (V ) 1 g e Thrust (3/3) Another component of thrust (pressure thrust, F2) comes from the force exerted by external pressure differences on the system. This is described by the difference of the pressure of the flow leaving the engine (Pe) through the exit area (Ae) compared to the external (ambient) pressure (Pa). F2 (Pe Pa )Ae In space, Pa is assumed to be zero (which explains why thrust rated at vacuum is higher than at sea level). Combining the two thrust components gives m F (V ) (P P )A g e e a e Specific Impulse (1/4) The total impulse (It) is the thrust integrated over the run duration (time, t) t I Fdt t 0 Assuming constant thrust and negligible transients (i.e., start and shutdown), this becomes I Ft t The specific impulse, (Isp) is the total impulse generated per weight of propellant t Fdt This is really what you need to know about I . F sp I 0 If you want to learn some more, stay seated. sp t m The rest of you can go get some coffee for g mdt about 10 minutes… o 0 Specific Impulse (2/4) Substituting the thrust equation for F gives V A e e Isp (Pe Pa ) g w Under optimal conditions the pressure of the flow exiting the nozzle is equal to that of the C =molar specific heat of exhaust gas ambient pressure (i.e., optimally expanded). pm M = molecular weight of exhaust gas The Isp equation then becomes Ps= isentropic stagnation pressure of the flow at the throat (almost always equivalent Ve to chamber pressure, Pc) I sp g γ= ratio of specific heats of exhaust gas Where the flow exit velocity is calculated by Don’t be intimidated by this 1 – just understand that Ve (and hence I ) is enhanced by sp Pe high release of energy from Ve 2gC pmTc / M 1 the combustion process (high Ps C ) and low molecular pm weight (low M) of the exhaust Specific Impulse (3/4) By definition The equation for Isp then becomes C C 1 p pm 2C pmTc P C C e v vm I sp 1 gM Ps and Cpm Cvm R From this, optimum Isp becomes Where R is the universal 1 gas constant, then 2 RTc Pe Cpm / 1R I spopt 1 1 gM Ps Primarily a function of the Primarily a function of the expansion of combustion process, which is the exhaust gases through the nozzle, influenced by the propellants, which is influenced by back pressure and the mixture ratio and area ratio Specific Impulse (4/4) From an empirical standpoint, determining Isp from test results involves calculating the total impulse generated by the engine and dividing it by the weight of the propellant consumed. t Fdt 0 I sp wconsumed The Isp for flight engines is established (i.e., tagged) on the test stand under simulated flight conditions to ensure acceptance of engine operation and adequate propellant loading of the vehicle. Other primary performance parameters J-2X Acceptance Test Profile (i.e., Thrust, MR) are also tagged during acceptance testing. Mixture Ratio Rocket propellants are mixed in relative quantities to produce the highest possible system Isp. This ratio of propellant consumption is called mixture ratio, MR. w MR o w f In most cases, MR is selected for maximum energy release per weight of propellant. This can be achieved by mixing the propellants in a stoichiometric reaction in the combustion chamber, where all the propellants are thoroughly combusted. However, a stoichiometric MR does not necessarily provide an optimized Isp. The SSME uses a MR of ~6 (stoichiometric for LO2/ LH2 combustion is 8) to reduce the internal and plume temperatures, but also to allow a small amount of H2 to remain in the exhaust. The lighter molecule is able to accelerate to a higher velocity and generate higher kinetic 2 energy (KE = ½ mV ) than a H2O steam exhaust. Isp vs. MR VACIDEAL VACIREAL 480 W inPlot v4.54 460 440 2X - J SSME • “Ideal” for SSME-like fluid 420 2 Vacuum Isp (sec) Isp Vacuum LH conditions (for LO2/LH2 combustion) / 2 and nozzle having ε = 77 used with LO CEA FORTRAN code. 400 • “Real” obtained by accounting for Stoichiometric Stoichiometric typical LO2/LH2 combustion/nozzle efficiencies. 380 1 2 3 4 5 6 7 8 9 10 Mixture Ratio Density vs. Isp . Liquid bipropellant combinations offer a wide . As an example, the densities range of performance capabilities. and Isp performance of the . Each combination has multiple factors that following propellant should be weighed when selecting one for a combinations will be vehicle. compared. • Performance (I ) Density Density sp 3 • Density (higher is better) (g/ml) (lb/ft ) • Storability (venting?) Hydrogen 0.07 4.4 • Ground Ops (hazards?) Methane 0.42 26.4 • Etc. RP-1 0.81 50.6 . One of the more critical trades is that of Oxygen 1.14 71.2 performance versus density. P = 300 psia . LO2/LH2 offers the highest Isp performance, c expanded to MR Isp but at the cost of poor density (thus increasing 14.7 psia (O/F) (sec) tank size). LO /LH 3.5 347(1) . Trading Isp versus density is sometimes 2 2 referred to as comparing “bulk impulse” or LO2/CH4 2.33 263(2) “density impulse”. LO2/RP-1 2.4 263(2) (1) SC (2) FC Propellant Mass vs. Volume 3500000 160000 3000000 140000 ) 3 -24% 120000 2500000 -54% -66% 100000 2000000 80000 1500000 60000 1000000 40000 Total Propellant Volume (ft Volume Propellant Total Total Propellant Mass (lbs) Propellant Total 500000 20000 0 0 1 2 3 LO2/LH1 2 LO2/CH2 4 LO2/RP3 -1 LO2/LH2 LO2/CH4 LO2/RP-1 . For an impulse requirement similar to . When the propellant mass is the 3 SSME’s used on the Shuttle compared against the tank volume, (~1.5 Mlbf for 520 seconds), the there is a significant disparity from required propellant masses are the low hydrogen density that can calculated. adversely impact the size (and total weight) of the vehicle. LO2/LH2 requires 24% less propellant mass than the others. Lesson: Isp isn’t everything – . However… especially with boost stages. Area Ratio (1/2) The parameter that determines exit velocity and pressure of the exhaust gases is area ratio or nozzle expansion ratio, MR A e At • As ε increases, the exit velocity increases and the exit pressure decreases (higher Isp). • When possible, ε is selected so that Pe = Pa and the engine operates at optimum thrust. • For in-space propulsion (i.e., J-2X), the ε is made as large as the weight requirements or volume limitations permit. • If Pe > Pa , then the nozzle is identified as underexpanded and will not provide optimal performance as the plume will continue to expand after exiting the nozzle. • If Pe < Pa , then the nozzle is identified as overexpanded and will not provide optimal performance as the exit shock will migrate inside the nozzle. This can be hazardous from thrust imbalances and damage to the nozzle. Area Ratio (2/2) • Criteria to be considered for selecting a design ε can include the following: • ε provides the optimal integrated performance over the engine operating period. Trajectory analysis is used to determine the altitudes (and Pa) that the engine will operate, which can be used to provide an integrated Isp based on ε.