Rocket Propulsion Basics Thrust

Transcription

1 Rockets 101: A Quick Primer on Propulsion & Launch Vehicle Technologies Steve Heister, Professor School of Aeronautics and Astronautics Purdue University Presentation to AFSAB, 13 January, 2010 Rocket Propulsion Basics Thrust The thrust (F) of a rocket propulsion device can be related to conditions in the combustion chamber and at the nozzle exit: F = mv ɺ + ( p p ) A Jet Thrust e e a e Pressure Thrust The Specific Impulse, Isp, is the gas mileage of a rocket propulsion system as it measures the propellant flowrate required to attain a certain thrust level: F Ae Isp = = ve/ g ( pe pa ) mg ɺ + mg ɺ System Typical Isp, sec Solid Rocket Motor Liquid Rocket Engine Hybrid Rocket Engine Nuclear Thermal Engine Arcjet The nozzle exit velocity is determined from a Ion ,000 balance of thermal energy in combustion chamber and kinetic energy at the nozzle exit: 2 2γ RuTc ( 1)/ ve = [1 ( pe / p ) γ γ c ] M( γ 1) Since high Ve gives us high Isp, we can see we want propellants with large T c / M 1

2 Rocket Propulsion Basics - Weights The propellant mass fraction, λ, measures the structural efficiency of the system Mp λ = Mp + Mi M pl M p = M i = Useful propellant (that which is burned to provide acceleration in desired direction.) Sum of all inert masses associated with the propulsion system. Includes engines, tanks, pumps, lines, reactors, pressurant bottles, gas generators, insulation, etc. M p The best possible design in this sense would be a consumable rocket made entirely from propellant (λ=1) M i In general, λ increases with system size due to structural efficiency Mass Fractions for Several Launch Vehicle Stages Mass fractions increase with system size In general, SRMs have higher mass fractions than liquid stages 2

3 System Trades Both Isp and λ Matter The best system would have both high Isp and high λ. Unfortunately, these items are somewhat mutually exclusive Hot propellants give good Isp but require additional insulation (lowers λ). Large nozzle gives good Isp but reduces λ. High pressures give better Isp but require thicker-walled structures. Our consumable rocket would give high λ but lousy Isp. The Rocket (or Tsiolkovsky) Equation m(t) v(t) F(t) m g = Weight D = Drag (atmospheric) Newton s 2 nd Law F D mg = ma = dv m dt Using definition of Isp, juggling a bit, can integrate this equation to give the velocity gain, v: t b D v = g Isp ln ( Mo / M f ) dt g t b actual m velocity gain imparted 0 gravity or vel. gain by the propulsion system drag loss " g t" loss sensed by the payload This equation is the fundamental expression used in Rocket Design. It links mission requirements v, propulsion system performance Isp, and vehicle masses (Mo/Mf). To attain a low earth orbit, we need a v of about 25,000 f/s, but drag and gravity losses are near 5000 f/s so our propulsion system must provide 30,000 f/s velocity change! 3

4 Determining Propellant Required (Mp) for Given Mission Rearranging the rocket equation, we can solve for the v that must be imparted by the propulsion system: ( ) v = v + v + v = g Isp ln M / M Solving for the Mass Ratio, MR: MR = exp( v / g Isp ) = M / M id Drag grav o f id o f Propellant Required to Accelerate a 1 lb Payload, λ =0.9 And since Mo=Mpl+Mp/ λ., Mf=Mpl+Mi we can write: MR 1 M p = M pl MR ( MR 1) / λ Staging Multiple stages permits us to drop some inert mass midway through the process Allows higher v missions such as space access at the expense of development of more stages Results from detailed sizing studies generally look like this: Gross Liftoff Weight (GLOW) 1 stage 2 stages 3 stages 1 Stage Optimal 2 Stages Optimal 3 Stages Optimal V 4

5 Typical Ascent Sequence to High Orbits Delta II Launch h V Vehicle le Payload fairing (4 min; 74 mi) Stage 1 & Stage 2 (5 min; 89 mi) Apogee Burn 113-sec duration No. 2 (6 hr 28 min; 22,000 mi) Standard fairing cutoff No. 2 Stage 2 shutdown (9 min; 105 mi) Elliptical transfer orbit Stage 2 (9 min 9 sec; 105 mi) Satellite GPS Satellite Satellite orientation and deployment LEO Parking orbit cutoff No. 1 No. 1 (1 hr 9 min; 120 mi) Perigee Burn 147-sec duration Stage 1 (2 min; 28-mi high) Solid rocket (2 min, 9 sec; 32-mi high) Interstage Second stage Third stage Stage 0 TITAN IV/IUS Delta II THE AEROSPACE CORPORATION Launch Vehicle Sizing, an Example Consider a two-stage launch vehicle with the following attributes: Stg 1: LOX/RP-1, λ=0.91, Isp=300 sec. Stg 2: LOX/LH2, λ=0.89, Isp=450 sec. Vehicle is to deliver 50,000 lbf to LEO with ideal V of 30,000 f/s Assume equal V splits (15,000 f/s each) From Eq *, get Mp1=1074, Mp2=117 Klbf., GLOW=1362 Klbf A frightening (and typical) notion: Mpl is only 3.7% of GLOW MR 1 M p = M pl Eq. * MR ( MR 1) / λ 5

6 Understanding the sensitivities Can conduct differential analysis (or construct a set of partial derivatives) to assess the sensitivity of the design to changes in parameters Payload losses assuming a 1% decrease in λ or Isp: 1% Drop in % Loss in Payload % Change in Inert Mass λ λ Isp Isp Questions/Acknowledgements 6