Multi-Stage Hybrid Rocket Design for Micro-Satellites Launch using Genetic Algorithm
1The 28th International Symposium on Space Technology and Science Chemical Propulsion 2011-a-35s Multi-Stage Hybrid Rocket Design for Micro Satellites Micro-Satellites Launch using Genetic Algorithm Yosuke Kitagawa Tokyo Metropolitan University
2Contents 1. Background 2. Objectives 3. Design methods g 4. Design problem 5. 5 Results 6. Conclusions
3Background Advantage of hybrid rocket engine (HRE) ・ Safety ・ Cost ・ EnvironmentL Launch Vehicle (LV) development with HRE h V hi l d l ih • HRE is employed in plan of private space travel using SpaceShipTwo by Virgin Galactic in America. America • Copenhagen Suborbitals develops small manned spacecraft using HRE, TychoBrahe SpaceShipTwo S Shi T Tycho Brahe Tycho Brahe www.scaled.com www.copenhagensuborbitals.com
4Background Disadvantage of HRE • Regression rate of solid fuel is slow. • LOX tank is required in the engine construction. construction • There is severe trade-off between flight altitude and gross weight. Thrust and weight are affected by Pressurized tank ・Pressure Nozzle LOX tank Chamber ・Expansion ratio Expansion ・Mass flow of oxidizer ・Pressure ・Pressure Solid fuel ・Length ・Port radius It is helpful for design of LV with HRE to apply multi disciplinary multi-disciplinary optimization (MDO) and knowledge discovery techniques.
5ObjectivesMDO of three-stage LV with HRE for deliveringmicro-satellitesmicro satellites using genetic algorithm (GA) • Evaluation method of multi-stage LV with HRE multi stage • Exploration of global solutions by genetic algorithm • Design knowledge discovery by data mining
6Flowchart of Evaluation Grain sizing INPUT Grain length Oxidizer mass flow Port radius Initial O/FFuel mass flow Coefficient of regression rate O/F Initial oxidizer mass flux O/F Combustion time Initial pressure of chamber Pressure and NASA CEA NASA-CEA Initial pressure of pressurized tank p p velocity at Isp Expansion ratio of nozzle nozzle exit C* Thrust Th t Mass M Thrust Gross mass Trajectory Kosugi, K., et al. "Multidisciplinary and Multi-objective Design g, , p y j g OUTPUT Exploration Methodology for Conceptual Design of a Hybrid Rocket," Infotech@aerospace, AIAA 2011-1634, 2011. Flight path, Rocket length and diameter etc.
7Grain Configuration Initial radius of grain port L fuel moxii rport 0 Go 0 r (t ) m fuel moxi rport (t ) ( Design D i variables i bl Grain length Grain moxi m fuel 0 O F 0 moxi : Oxidizer mass flow m fuel : Fuel mass flow f m fuel 0 rport : Radius of grain port L fuel 2rp 0 r 0 fuel port f r : Regression rate Go : Oxidizer mass flux r 0 a Gon 0 L fuel : Grain length Design variables fuel : Grain density
8O/F and Chamber Pressure Calculation L fuel Definition of O/F O moxi (t ) r (t ) F m fuel (t ) m fuel moxi moxii rport (t ) ( 2rport (t ) L fuel fuel r (t ) Grain n moxi r t a G t a n rport t o 2 p Pch Chamber pressure ： m prop Propellant mass flow p ： p Ch b pressure Chamber C：Characteristic velocity m prop (t ) C (t ) C C： Efficiency of characteristic velocity Pch (t ) t) Ath Ath Area of nozzle throat ：
9Mass Estimation Structural mass Design variables ・Chamber M ch PchVch 17 .3 10 4 same as motor case as solid ・Pressurized tank M pre Ppre V pre 17 .3 10 4 rocket, M V rocket M-V (CFRP) ・Oxidizer tank M res PresV res 4 .4 10 4 CFRP with aluminum liner 2 1 M prop 3 4 ・Nozzle* M noz 125 Empirical expression 5400 4 Structure* M st 1 . 3 M ch M res M pre M noz M He Propellant mass Design variables tburn M prop M oxi M fuel moxi tburn m fuel (t )dt 0 Gross mass M tot M prop M st M pay M pay : Payload mass * Ronald Humble, “Space Propulsion Analysis and Design”
10Trajectory Evaluation Thrust T t CF C* [ m prop u e ( Pe Pa ) Ae ] • C * ：thrust loss by incomplete combustion • CF ：thrust loss by friction at nozzle wall Drag 1.0 During combustion Estimation using flight data of solid rocket, S-520 0.8 After combustion CD,S-520 • Friction drag coefficient 0.6 0.455 1 0.4 C D f , Design 2.58 log10 Re 1 0.144M 2 0.655 0.2 02 0.0 • Pressure drag coefficient S wet , S 520 0.0 2.0 4.0 6.0 8.0 10.0 C D p , S 520 C D , S 520 C D f , S 520 Mach number S ref , S 520 • Drag of designed rocket S wet Rocket wet area ： 1 D V 2 S ref , DesignC D p , S 520 S wet , DesignC D f , Design 2 S ref Rocket reference area ： The effect of the longitude and diameter can be separately evaluated.
11Optimization MethodsMulti-objective Genetic Algorithm (MOGA) Searching global non-dominated solutions hi l b l d i d l i based on global explorations E l i and selection (P Evaluation d l i (Pareto ranking method) ki h d) • When a solution #xi is dominated by #ni solutions, rank(xi)=1+ ni. • Penalty method When a solution xi don’t meet constraints, rank(xi)= rank(xi)+p (p>0). Optimum direction
12Optimization Method Crossover（BLX-α） • Children are generated based on interpolation or extrapolation based on selected two parents. • In BLX-α, children are generated between the range which is extended equally on both sides determined by a parameter, α.Children2 Children1 Mutation x1 x2 x3 x4 x5 • Mutation generate children that cannot be Parent generated from the present population. • Children are generated by a uniform Child random number.
13Data Mining Method Parallel Coordinate Plot (PCP) • One of statistical visualization techniques from high dimensional high-dimensional data into two dimensional graph. • Normalized design variables and objective functions are set parallel in the normalized axis. • Global trends of design variables can be visualized using PCP. g g 1.0 0.8 0.6 0.4 0.2 0.0 dv1 d 1 dv2 d 2 dv3 d 3 dv4 d 4 dv5 d 5 H W L/D
14Design Problem Design target: Design of three-stage rocket which can deliver micro-satellites to the Sun-synchronous orbit (SSO) (perigee is 250km, apogee is 800km) Obj ti f Objective functions ti • maximize Payload mass/Gross mass (Mpay/Mtot) • minimize Gross mass (Mttott) Constraints • After combustion of third stage, Height > 250km Angular momentum > 52413.5km2/s -0.5deg. < Fli ht path angle < 0.5deg. 0 5d Flight th l 0 5d • Rocket aspect ratio < 20 • Radius of nozzle exit < Radius of rocket • Area of grain port > 2・(Area of nozzle throat) Combustion type • Swirling oxidizer type engine • Oxidizer：LOX, Fuel：WAX (FT-0070)
15Design Problem (design space) 1st stage 2nd stage 3rd stage Design variables Min Max Min Max Min Max Oxidizer O idi mass flow [k / ] fl [kg/s] moxi,1st moxi,1st moxi,2nd moxi,2nd 50 150 (moxi) ×1/10 ×1/3 ×1/10 ×1/3 Initial O/F [-] 2 3 2 3 2 3 Coefficient of regression rate 6.224 15.61 6.224 15.61 6.224 15.61 equation, a* [×10-3] Initial oxidizer mass flux 200 800 200 800 100 800 [kg/m2s] Combustion time [s] (tburn) 40 80 tburn,1st+0 tburn,1st+50 tburn,2nd+0 tburn,2nd+50 Initial pressure of 0.5 5.0 0.5 5.0 0.5 5.0 chamber [MPa] Initial pressure of 10 47 10 47 10 47 pressurized tank [MPa] Expansion ratio of nozzle [-] 2 15 15 60 50 100 Coasting time [s] 0 300The range of the a for each stage is empirically decided*. ( r t a Gon t ) * Hikone,S., et al, “Regression Rate Characteristics and Combustion Mechanism of Some Hybrid Rocket Fuels ,”Asian Joint Conference onPropulsion and Power 2010.
17MOGA Results Optimum direction O ti di ti Epsilon rocketMpay/Mto [%] Mpay [kg] ot [ Mtot [ton] Mtot [ton] • There is trade-off between Mtot and Mpay/Mtot. • Maximum Mpay/Mtot is 1.30% (Mpay is 232kg, Mtot is 17.8ton). • Maximum Mpay/Mtot of solid rocket, Epsilon* is about 1.3%. ⇒ LV with HRE considered here have enough capability compared with the solid rocket. ih h lid k • Mpay is approximately proportional to Mtot (Mtot=0.0619Mpay+3.427). ⇒When Mpay increases by 1kg, Mtot must increase by 61.9kg. *Epsilon rocket: Next generation solid rocket developed by JAXA and IA.
19PCP Visualization (to deliver 150kg payload) Effect of combustion process a：Coefficient of regression rate equation Go：Oxidizer mass flux 1：1st stage 2：2nd stage 3：3rd stage Max Min Average Required regression rate a1 [×10-3] [ 0 1.44 . 1.34 .3 1.37 .37 14.6mm/s 14 6 / Go1 [kg/m2s] r t a Gon t 488 357 428 a2 [×10-3] 1.16 1.13 1.09 9.1mm/s 9 1mm/s Go2 [kg/m2s] 211 208 209 a3 [×10-3] 1.34 1.29 1.31 8.8mm/s Go3 G 3 [k / 2s] [kg/m ] 141 126 130
20PCP Visualization (to deliver 150kg payload) Effect of internal pressure of chamber/ pressurized tanks Pc：Chamber pressure Pp：Pressure of pressurized tank Max Min Average Structural mass/Gross mass Pc1 [MPa] [ ] 2.90 .90 2.27 . 7 2.63 .63 20.7% 20 7% Pp1 [MPa] 43.5 37.9 41.0 Pressure：Large Pc2 [MPa] 1.00 0.98 0.99 ⇒Thickness： Increase 11.9% 11 9% ⇒ Structural mass：Increase Pp2 [MPa] 21.8 19.6 21.3 Pc3 [MPa] 0.80 0.72 0.75 14.5% Pp3 [MPa] P 3 [MP ] 12.8 12 8 10.9 10 9 11.9 11 9
21Selected Design from Non-dominated Solutions Non- Design variables 1st 2nd 3rd Oxidizer mass flow [kg/s] 100.3 28.3 4.3 O/F [-] 2.47 2.88 2.87 Coefficient of regression rate [×10-3] 1.34 1.16 1.32 I iti l oxidizer mass flux [k / 2s] Initial idi fl [kg/m ] 445 209 128 Combustion time [s] 43.0 90.2 96.0 Initial pressure of chamber [MPa] 2.90 2 90 0.98 0 98 0.73 0 73 Initial pressure of pressurized tank [MPa] 43.5 21.7 12.8 Nozzle expansion ratio [-] p  6.3 22.1 72.4 Mpay/Mtot [%] Mtot [ton]
22Selected Design from Non-dominated Solutions Non- Engine parameter of selected rocket 1st t 1 t stage 2nd t 2 d stage 3rd t 3 d stage Thrust (after ignition ⇒ [kN] 342 ⇒ 415 95 2 ⇒ 123 95.2 17 8 ⇒ 20 1 17.8 20.1 after combustion) Isp [s] 248 ⇒ 284 256 ⇒ 316 334 ⇒ 344 Regression rate [mm/s] 14.5 ⇒ 7.08 9.33 ⇒ 3.70 8.75 ⇒ 2.64 Length of grain [m] 2.18 1.06 0.35 Inside diameter of grain [m] 0.54 0.42 0.21 Outside diameter of grain [m] 1.34 1.35 0.96 To realize space transportation using HRE with existent fuel, engine of thrust 400kN must be developed. developed
23Selected Design from Non-dominated Solutions Non- Selected rocket size Length of rocket [m] 20.8 Diameter of rocket [m] 1.46 1 46 Aspect ratio of rocket [-] 14.3 Gross mass [ton] 13.0 Payload mass [kg] 152 Payload mass/Gross mass [%] 1.17 1st stage 2nd stage 3rd stage Length [m] 8.22 6.57 6.06 Diameter [m] 1.45 1.46 1.07 Gross mass [ton] 8.07 4.09 0.70 Structural mass [ton] 1.78 0.49 0.10 Structural mass ratio [%] 22.1 11.9 14.5 20.8 8.22 6.57 6.06 1.35 1.36 0.97 1.46 1.21 2.18 3.21 1.61 2.29 1.06 2.11 1.11 2.06 0.35 0.99 0.64 2.02
24Flight History Start of combustion in 2nd stage Start of coasting Start f St t of combustion b ti in 3rd stage • Maximum acceleration is 9G less than 10G. • Load to satellites is lower than that of solid rocket. (M-V ： About 12G in 3rd stage)
25Conclusions MDO of LV using HRE for space transportation • Development of performance evaluation method • The design of three-stage rocket for delivering micro-satellites to SSO maximize i i Payload P l d mass/Gross mass /G minimize Gross mass • Exploration of global non-dominated solutions using MOGA non dominated There is trade-off between Mtot and Mpay/Mtot. Maximum Mpay/Mtot is 1.30%. • Design knowledge discovery using PCP Maximum regression rate should be about 15mm/s in first stage. In first stage, pressure of chamber, LOX tank and pressurized tank should be large. In second stage and third stage press re of chamber LOX tank and stage, pressure chamber, pressurized tank should be low.
26Acknowledgement This presentation was supported by hybrid rocket research working group (HRrWG), ISAS/JAXA. gg p( ), I thank members of HRrWG in ISAS/JAXA for giving their experimental data and their valuable advices. p