Homework 2, part 2! ii) Calculate and plot design spike contour,
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1 Homework 2, part 2! 1) For Aerospike Nozzle use Sonic Throat section, assume axi-symmetric design, full spike length.. For Aerospike Nozzle use Sonic Throat section, assume axisymmetric. design, full spike length.. Design a Conical aerospike nozzle replacement for the RS-27A Nozzle i) First Compare RS-27A Nozzle Length with minimum length nozzle of same expansion ratio (assume conical nozzle with :1 expansion ratio,! θ exit = 30.5 deg.). Plot both Contours! ii) Calculate and plot design spike contour, iii) Calculate design altitude for this expansion ratio and plot design mach number and pressure profile along spike, assume :1 expansion ratio and chamber properties identical to RS-27A! iv) Plot delivered Thrust and I sp as a function of altitude for RS-27a Stage stage 1a: 0 to km altitude (RS-27A + 3 x Gem40) stage 1b: km altitude km altitude (RS-27A) Assume conventional Nozzles for Gem-40 boosters 1!
2 Homework 2 (2)! iv) Calculate mean I sp over the operating range of the First stage (use above generated data) Use 2/3rds rule Stage 1a Stage 1b Use I sp ( ) eff = 2 3 # % $ ( I sp )Rs 27 A+ 3x Gem40 & ( ' launch + 1 # 3 % I sp $ & ( )Rs 27 A+ ( 3x Gem40 ' Gem40 Burnout Use ( I sp ) eff = 2 ( 3 I sp ) R2 27 A initial (16.31km) I sp ( ) R2 27 A final (105.52km) v) Re-work delta II Homework problem (HW 2) using new mean I sp s for stage 1a and 1b with the RS-27A aerospike nozzle compare to earlier results using standard conical nozzle for stage 1 assume conventional nozzles for Both Gem-40 and AJ Second Stage Engine 2!
3 3-D Nozzle Algorithm" Aerospike Nozzle! tanφ x = R e R x X x φ x = ν e ν x + µ x X x = R x = R exit R exit R x ( ) tan ν e ν x + µ x 1 sin ( ν ν + µ e x x ) ε.' 2 * ( ) γ + 1+, ' 0 1+ γ 1 2 M x ( ) / 2 γ +1 * 1 2( γ 1) +, 3 2 sin ( µ ) x = 1 M x 3!
4 Stage 1 Properties! Boeing Delta II Rocket Stage 1!!- Sea Level Thrust: 890kN!!- Vacuum Thrust: kn!!- Nozzle Expansion Ratio: :1!!- Conical Nozzle, 30.5 deg exit angle! Combustion Properties:! (RS-27A Rocketdyne Engine)!!- Lox/Kerosene, Mixture Ratio: 2.24:1!!- Chamber Pressure (P 0 ): kpa!!- Combustion temperature (T 0 ): 3455 K!!- γ = !!- M W = kg/kg-mol! - Propellant Mass: Metric Tons! - Stage 1 Launch Mass: Metric Tons! 4!
5 Include 2-D Spike Contour on Plot!! 3-D flow! relief effect! Allows conical! Aerospike to! turn corner! faster than 2-D! spike and still! preserve isentropic! flow! 14!
6 Spike Design Characteristics! iii) Calculate design altitude for this expansion ratio and plot design mach number and pressure profile along spike, assume :1 expansion ratio and chamber properties identical to RS-27A! 5!
7
8 Compare RS-27A Nozzle to Minimum Length Nozzle! Slight Thrust! For Minimum Length! Nozzle Due to Higher! Exit Angle! Launch Thrust,! I sp Levels! 6!
9 Compare RS-27A Nozzle to Aerospike Nozzle! 7!
10 Spike Design Characteristics (1)! At Design Condition! Design! Sea Level! Vacuum! 8!
11 Spike Ramp Characteristics (1)! 9!
12 Nozzle Comparison Summary! Launch Thrust, knt Vacuum Thrust, kn Design Thrust, knt Launch I sp, sec Vacuum I sp, sec Design Isp, sec Length, cm RS-27A Normal Nozzle! RS-27A Minimum Length Nozzle! RS-27A Full Aerospike Nozzle! RS-27A Truncated Aerospike Nozzle, 61. 1% (RS-27A Length) RS-27A Truncated Aerospike Nozzle, 69.7% (Minimum Length) Spike Wins all Around!! 10!
13 Spike Performance Comparisons (1)!! 11!
14 Delta II Launch Analysis! iv) Plot delivered Thrust and I sp as a function of altitude for RS-27a Stage stage 1a: 0 to km altitude (RS-27A + 3 x Gem40) stage 1b: km altitude km altitude (RS-27A) Assume conventional Nozzles for Gem-40 boosters, full aerospike for RS-27A! Stage 1a! Full Aerospike Nozzle Thrust, I sp at Sea Level:!!!965.7 knt, sec Aerospike Nozzle Thrust, I sp at km (P amb = kpa):!!! knt, sec! Nozzle Mass Flow: kg/sec! 12!
15 Stage 1a (4)! vi) Effective Specific Impulse!! (3 x Gem 40 + RS-27A/w aerospike over operating altitude range!!!! ( I ) sp launch = F + 3 F RS 27 A Gem40 ( I sp )Gem = 253.4sec! 40 burnout = = 289.8sec! ( ) launch g 0 ( ) = m RS 27 A + 3 m Gem40 ( F RS 27 A + 3 F Gem40 )Gem40 burnout g 0 m RS 27 A + 3 m Gem40 ( ) = ( I ) sp eff = 2 3 " $ # = sec! ( I sp )Rs 27 A+ 3x Gem40 % ' & Launch + 1 " 3 $ I sp # % ( )Rs 27 A+ ' 3x Gem40 & Gem40 Burnou = 13!
16 Delta II Launch Analysis! iv) Plot delivered Thrust and I sp as a function of altitude for RS-27a Stage stage 1a: 0 to km altitude (RS-27A + 3 x Gem40) stage 1b: km altitude km altitude (RS-27A) Assume conventional Nozzles for Gem-40 boosters, full aerospike for RS-27A! Stage 1b! Aerospike Nozzle Vacuum Thrust, I sp :!!! knt, sec ( I ) sp eff = 2 3 "( I ) # sp R2 27 A $ % Gem40 Burnou + 1 "( 3 I ) # sp R2 27 A $ % R2 27 A MECO = = sec! 14!
17 Required versus Available Delta V! At $250/oz! You just saved! ~$4.5 Mil! On Payload! Aerospike! 2688 kg! Original! 2175 kg!
18 Delta II Launch Analysis! iv) Plot delivered Thrust and I sp as a function of altitude for RS-27a Stage stage 1a: 0 to km altitude (RS-27A + 3 x Gem40) stage 1b: km altitude km altitude (RS-27A) Assume conventional Nozzles for Gem-40 boosters, full aerospike for RS-27A! Stage 1a! 61.1% Aerospike Nozzle Thrust, I sp at Sea Level:!!!953.8 knt, sec Aerospike Nozzle Thrust, I sp at km (P amb = kpa):!!! knt, sec! Nozzle Mass Flow: kg/sec! 16!
19 Stage 1a (4)! vi) Effective Specific Impulse for 61.1% Truncated Nozzle!! (3 x Gem 40 + RS-27A/w aerospike over operating altitude range!!!! ( I ) sp launch = F + 3 F RS 27 A Gem40 ( I sp )Gem = 252.1sec! 40 burnout = = 288.5sec! ( ) launch g 0 ( ) = m RS 27 A + 3 m Gem40 ( F RS 27 A + 3 F Gem40 )Gem40 burnout g 0 m RS 27 A + 3 m Gem40 ( ) = ( I ) sp eff = 2 3 " $ # = sec! ( I sp )Rs 27 A+ 3x Gem40 % ' & Launch + 1 " 3 $ I sp # % ( )Rs 27 A+ ' 3x Gem40 & Gem40 Burnou = 17!
20 Delta II Launch Analysis! iv) Plot delivered Thrust and I sp as a function of altitude for RS-27a Stage stage 1a: 0 to km altitude (RS-27A + 3 x Gem40) stage 1b: km altitude km altitude (RS-27A) Assume conventional Nozzles for Gem-40 boosters, full aerospike for RS-27A! Stage 1b! Aerospike Nozzle Vacuum Thrust, I sp :!!! knt, sec 61.1% truncated nozzle! ( I ) sp eff = 2 3 "( I ) # sp R2 27 A $ % Gem40 Burnou + 1 "( 3 I ) # sp R2 27 A $ % R2 27 A MECO = = sec! 18!
21 Required vs. Available Delta V! 61.1% Aerospike! 2600 kg! Original! 2175 kg! Still a reasonable $4 mil! gain!!
22 Examples: Current (2007) Launch Costs to LEO Soyuz booster ( Soyuz spacecraft, Progress) LEO (200 km) Payload: 7,000 kg; Launch vehicle price:$37.5 million; Payload cost: $5,357 per kilogram. ($151.9/oz) Space Transportation System (Space Shuttle) LEO Payload: 28,803 kg; Launch vehicle price (estimated, pre-columbia ): $300 million, Payload cost: $10,416 per kilogram ($295.4/oz) Post-Columbia, $1 billion per launch, Payload cost: $34,718 per kilogram Proton (ISS modules) LEO Payload: 19,760 kg; Launch vehicle price: $85 million; Payload cost: $4,302 per kilogram ($122.0/oz) Ariane 5ES (ATV vehicle) LEO Payload: 21,00 kg; Launch vehicle price: $176 million; Payload cost: $9,778 per kilogram ($277.6/oz) At $250/oz! You just saved! Zenit 2 LEO Payload: 13,740 kg; Launch vehicle price: $42,5 million; Payload cost: $3,093 per kilogram. ($87.7/oz) Space-X Falcon 9 LEO (185 mi) mission from CCAFS, 9,900 kg payload; Launch vehicle price: $35 million, Payload cost: $3,535 per kilogram. ($100.3/oz) Any way you slice it LEO Payload is worth Far More than its weight in pure Silver!
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