1.
28th International Symposium on Space Technology and Science
2011-o-1-10v Hybrid Rocket: A Safe and Green Space Propulsion Evolution 3
Knowledge Discovery for Hybrid Rocket Conceptual Design
Based on Evolutionarily Algorithm
Masahiro Kanazaki
Tokyo Metropolitan University (TMU)
Yosuke Kitagawa
Tokyo M t
T k Metropolitan University (TMU)
lit U i it
Koki Kitagawa
Japan Aerospace Exploration Agency
Masashi Nakamiya
Japan Aerospace Exploration Agency
Toru Shimada
Japan Aerospace Exploration Agency

2.
Contents 2
 Background
 Conceptual design of launch vehicle (LV) with hybrid rocket (HRE)
 Evolutionally algorithm for aircraft design
 Overview of genetic algorithm (GA)
 Demonstrations of GA for multi objective problems
multi-objective
 Two-objective problem
 Three-objective problem
 Design problem of sub-orbital LV with HRE
sub orbital
 Formulation
 Evaluation of LV with HRE
 Design variables
 Objective functions
 Results
Design results

Visualization of non-dominated solutions

Addition of the constraint in relation to the rocket sizing

Design knowledge

 Conclusions *The application to the design of the three-stage rocket
will presented in session a-8-s.

3.
Background1 Advantage of hybrid rocket 3
Hybrid Rocket Engine(HRE) ： propellant stored in two kinds of phases
It can adopt the beneficial features of both the liquid and solid rockets.
Solid fuel + Liquid oxidizer :
Advantage of HRE
・Simple construction and mechanism
・Higher specific impulse (ISP) than solid rocket engine
・Ability to stop/restart the combustion ⇒ safet
Abilit comb stion safety
・Low environmental impact and low cost

4.
Background2 Design of HRE 4
 Solid rocket：Preliminary mixed solid propellant
 Liquid rocket：Control of mass flow of fluid propellant
→ Easy to maintain a constant oxidizer and mass -
fuel ratio (O/F) and to g a stable thrust
( ) get
 HRE：The mixture of fuel and oxidizer is initiated after ignition.
Combustion occurs in the boundary layer diffusion flame.
→ Because O/F is decided in this part of combustion process, the solid fuel
geometry and the supply control of the oxidizer have to be optimally
combined.
combined
⇔With too much mass flow of oxidizer, the
rocket achieves higher thrust, but structural
weight should be heavier .
Importance to find optimum fuel geometry and oxidizer supply
⇒ Optimizer for non linear problem is desirable
non-linear desirable.

5.
Aircraft design using evolutionally algorithm 5
Evolutionary algorithm based design exploration
Application of Mitsubishi Regional Jet (MRJ)
Targets
•Wing design
•High-lift Airfoil design
•Nacelle chine design
Design Exploration
•Genetic Algorithm
•Surrogate model
•Data mining
・Chiba, K., Obayashi, S., Nakahashi, K., and Morino, H., "High-Fidelity Multidisciplinary Design Optimization of Aerostructural Wing
Shape for Regional Jet," AIAA Paper 2005-5080, AIAA 23rd Applied Aerodynamics Conference, Toronto, Canada, June 2005.
・Kanazaki, M., and Jeong, S., “High-lift Airfoil Design Using Kriging based MOGA and Data Mining,” The Korean Society for
Aeronautical & Space Sciences International Journal, Vol. 8, No. 2, pp. 28-36, November 2007.
・Kanazaki, M., Yokokawa, Y., Murayama, M., Ito, T., Jeong, S., and Yamamoto, K., “Nacelle Chine Installation Based on Wind Tunnel
Test Using Efficient Design Exploration,” Transaction of Japan Society and Space Science, Vol.51, No. 173, pp. 146-150, November
2008. … etc.
Design Exploration is also expected in MDO for hybrid rocket.

6.
Genetic Algorithm (GA)1 6
 Genetic algorithm (GA)
 One of evolutionally algorithm proposed by
Prof. John Henry Holland
 Inspired by evolution of life
 Crossover, mutation
 Global search → meta heuristic approach
meta-heuristic
 Arbitrary evaluations can be integrated.
 Easy to use in computer science

7.
Genetic Algorithm (GA)2 7
 R
Representation of individuals (
t ti f i di id l (gene t
type)
)
 Binary number cording
 Similar construction to the real organisms’ genes
 Advantage to represent discrete values (control optimization, topology optimization)
 Requirement the encode/decode continuous real numbers
1 1 0 1 0 1 0 0
 Real number (decimal number) cording
 Representation of gene by vector
 S it bl f problems with continues f
Suitable for bl ith ti functions
ti
x = (x1, x2 …., xn)
 Genetic operation
 Crossover (Blended crossover, BLX-α)  M t ti
Mutation
 Children are generated near the  Uniform mutation method adds a uniform
selected parents. random number to each component of an
xc = γ xa+(1 γ) xb
+(1-γ) individual’s vector
 Mutation has provability of about 0.1.
xd = γ xb+(1-γ) xa γ=(1+2α)ran-α  Maintaining the diversity in a population
 Promotion of searching in the solution
space that cannot be g
p generated from the
Child xc Child xd x present population
Parent xa Parent xb x = (x1, x2 …., xn) x = (x1+a1, x2+a2 …., xn+an)

8.
Genetic Algorithm (GA)3 8
 Multi-objective GA (MOGA)
 Pareto-ranking method
 Ranking of designs for multi-objective function
 Parents are selected based on the ranking.
Dominated solutions
Definition 1 D i
D fi i i 1: Dominance
Optimum direction
A vector u = (u1,….,u n) dominates v = (v1,….,vm) if u ≤ v and at least a set of ui ≤ vi.
p
Definition 2: Pareto-optimal
A solution x∈X is Pareto-optimal if there is no x’∈X for which f(x’) = (f1(x’),….,fn(x’))
dominates f(x) = (f1(x),….,fn(x)).
Minimize f1
Minimize f2
Non-dominated solutions
 A rectangle by yellow point i l d one i di id l ⇒ rank=2
t l b ll i t includes individual. k 2
 A rectangle by blue point includes two individuals. ⇒ rank=3
 Rectangles by Red points do not include any other individual. ⇒ non-dominated solutions

9.
Demonstrations of GA1 9
Two-objective case
Minimize f1=rcosθ
Minimize f2=rsinθ Non-dominated solutions
subject to
bj t t
0≦r ≦1, 0≦θ≦π/2
Pareto-optimal set must
foam a circle.

10.
Demonstrations of GA２ 10
Three-objective case
Minimize f1=rsinθcosγ
Minimize f2=rsinθsinγ Non-dominated solutions
Minimize
Mi i i f3=rcosθ θ
subject to
0≦r ≦1
0≦θ≦π/2, 0≦γ≦π/2
Pareto-optimal set must
foam a sphere.
f h
It is hard to observe multi-dimensional
data (solution and design space.)

11.
Demonstrations of GA２（Contd.） 11
Post process of MOGA
P f
Relation among objective functions
What kind of design can be optimum?
⇒ Knowledge discovery by data mining
Scatter matrix plot (SPM)
Parallel coordinate plot (PCP)
Self-organizing map (SOM)
Parallel coordinate plot (PCP)
Scatter matrix plot (SPM)
Self-organizing map (SOM)

12.
Demonstrations of GA２（Contd.） 12
Visualization example by SPM
Scatter plot
Correlation
SPM arranges two-dimensional scatter plots among attribute values like a matrix
・The present SPM shows scatter plots on the upper triangular, and
correlation coefficient on the lower triangular (Software R is used for statistical computing and graphics.)

13.
Design problem of LV with HRE1 13
Design target
the sounding rocket with assuming that the 40kg payload is carried.
Design variables (6)
Lower
L Upper
U
Mass flow of oxidizer [kg/s](dv1) 1.0 30.0
Fuel length [m] (dv2) 1.0 10.0
Port radius of fuel [m] (dv3) 0.01 0.30
Combustion time [s] (dv4) 10.0 40.0
Pressure of combustion chamber [MPa] (dv5) 3.0 6.0
aperture ratio of nozzle [-](dv6) 5.0 8.0
Objective functions (2)
Minimize Gross weight, Wgross
Maximize Maximum flight altitude Hmax
altitude,

14.
Design problem of LV with HRE1 (Cont’d) 14
Overview of the evaluation procedure
r port (t )  a  G oxi t 
 n

15.
Design problem of LV with HRE1 (Cont’d) 15
List of input/output by developed module
Input variable
p Output variable
p
* Mass flow of oxidizer [kg/s] * Flight altitude [km]
* Fuel length [m] * Gross weight [kg]
* Port radius of fuel [m] * Total oxidizer weight [kg]
* Comb stion time [s]
Combustion * Total f el weight [kg]
fuel eight
* Pressure of combustion chamber [MPa] * Nozzle length [m]
* aperture ratio of nozzle [-] * Combustion chamber length [m]
* Oxidizer tank length [m]
g [ ]
* Rocket radius [m]
* Rocket aspect ratio [-]
* Nozzle throat area [m2]
* Thrust at ignition [kN]
* Initial oxidizer mass flux [kg/m2s]
* History of flight, thrust, and
combustion chamber pressure
p

16.
Design problem of LV with HRE1 16
Swirling oxidizer type HRE
 Proposed by Prof. Yuasa, et al.
p y ,
 Swirling oxidizer is supplied into the fuel.
 Polypropylene is employed as a fuel.
r port t   0.0826Goxi55
This expression was
0.
p provided by Prof. Yuasa.
regression rate against the mass flux of the oxidizer
Yuasa, S., et al, “Fuel Regression Rate Behavior in Swirling-Oxidizer-Flow-Type Hybrid Rocket Engines,” Proc 8th International
Symposium on Special Topics in Chemical Propulsion, No. 143, 2009.

17.
Design problem of LV with HRE1 (Cont’d) 17
 MOGA result colored by rocket’s aspect ratio (length/diameter)
After 100 generation started with
Non-dominated solutions 64 i di id l
individuals
The solutions which archive Hmax over
150km become heavier Wgross than the
solutions which archive Hmax not exceeding
150km.
To achieve high flight altitude, the rocket’s
aspect ratio becomes high.
Optimum direction
-There is trade off between Wgross and Hmax.
There trade-off
-Maximum Hmax is about 180km.

18.
Design problem of LV with HRE1 (Cont’d) 18
Visualization of non-dominated solution by SPM
dv3(port diameter in the fuel) of non-
dominated solutions becomes lower.
→ slender chamber
There a e co e at o a o g dv1(mass
e e are correlation among d ( ass
flow of oxidizer), dv2(fuel length), and two
objective functions. Aspect ratio is too high.
→ Requirement to control the rocket size
size.
The
Th rockets’ aspect ratio and th A
k t ’ t ti d the Acc_max
are correlative relation.

19.
Design problem of LV with HRE 19
Handling of constraints
Penalty function is added to the rank, if the
y ,
design i is infeasible.
rank(i) = rank(i) +p(i)
Optimum direction
 When the design is not feasible, the Pareto ranking get
worse, even if the design achieves better objectives.
, g j

20.
Design problem of LV with HRE2 20
Design variables (6)
Lower Upper
Mass flow of oxidizer [kg/s](dv1) 1.0 30.0
Fuel length [m] (dv2) 1.0 10.0
Port radius of f l [ ] (d )
di f fuel [m] (dv3) 0.01 0.30
Combustion time [s] (dv4) 10.0 40.0
Pressure of combustion chamber [MPa] (dv5) 3.0 6.0
aperture ratio of nozzle [-](dv6) 5.0 8.0
Objective functions (2)
Minimize Gross weight, Wgross
Maximize Maximum flight altitude Hmax
a e a u g t a t tude
Subject to Rocket’s aspect ratio <25.0

21.
Design problem of LV with HRE2 (Cont’d) 21
 MOGA result colored by rocket’s aspect ratio (length/diameter)
After 100 generation started Aspect ratio
with 64 individuals Non-dominated
Non dominated solutions
Non-dominated solutions
(satisfies the constraint)
Many solutions which satisfy the
constraint are obtained around Hmax
100km.
Optimum direction
- The rocket considered here is suitable for the sub-orbital flight around 100km altitude.

22.
Design problem of LV with HRE2 (Cont’d) 22
Visualization of non-dominated solution by SPM
dv1 still correlate with the altitude.
dv6(aperture ratio of nozzle) should be
larger to achieve higher altitude for
lower aspect ratio rockets.

23.
Design problem of LV with HRE 23
Design k
D i knowledge from non-dominated solution
l d f d i t d l ti
 There are trade-off between objective functions.
trade off
 The rockets which is higher aspect ratio achieve higher
g p g
flight altitude by reducing the aerodynamic drag.
 The rockets which is lower oxidizer mass flow, the
diameter of the combustion chamber becomes smaller. As
this result, the required material volume for the
combustion chamber also becomes lower.
 Aperture ratio of nozzle) is key parameter for lower aspect
ratio rockets.

24.
Conclusions 24
 Theory of MOGA, and how MOGA is working.
 Meta-heuristic approach for real world problems
 Pareto optimal theory for multi-objective design
 Two test problems
p
 Demonstration of knowledge discovery of conceptual design of
g y p g
LV with HRE
 High aspect ratio rocket is better for the present design
problem.
 Aperture ratio of nozzle should be larger to achieve higher
altitude for lower aspect ratio rockets.
 With proper definition of the design problem, the useful
design knowledge can b di
d i k l d be discovered.d

25.
Acknowledgement 25
We thank members of the hybrid rocket engine
research working group in ISAS/JAXA for giving
their experimental data and their valuable advices.
This paper and presentation was supported by
ISAS/JAXA.
Evaluation module (cygwin script) is open to the
p
public,,
http://www.sd.tmu.ac.jp/aerodesign/eng.htm#hte.
Thank you very much for your kind attention
attention.