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Procedía Engineering 99 (2015) 198 - 207

Procedía Engineering

www.elsevier.com/locate/procedia

"APISAT2014", 2014 Asia-Pacific International Symposium on Aerospace Technology,

APISAT2014

Conceptual Design of Single-stage Rocket Using Hybrid Rocket by

Means of Genetic Algorithm

Masahiro Kanazakia*, Atthaphon Ariyairtb, Kazuhisa Chibab, Koki Kitagawac,

ToruShimadac

aTokyo Metropolitan University, 6-6, Hino, Tokyo 191-0065, Japan bHokkaido University of Science, 7-15-4-1, Maeda, Teine, Sapporo 006-8585, Japan cJapan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara 001-0010, Japan

Abstract

In this study, a multi-objective genetic algorithm (MOGA) was applied to the multidisciplinary design optimization (MDO) of a hybrid rocket. A swirling-oxidizer-type hybrid rocket engine (HRE) with a single cylindrical grain port was designed. It was considered that this HRE could temporarily stop combustion via oxidizer throttling; this feature is called multi-combustion. The MOGA was applied to solve the multi-objective problem using real-number coding and the Pareto ranking method. In this study, three design problems were considered. First problem was the maximization of the flight altitude and minimization of the gross weight. Second problem was the minimization of the maximum acceleration and minimization of the gross weight. Third problem was the maximization of the duration time over the target flight altitude and minimization of the gross weight. Each objective function was empirically estimated. In addition, this study compared two types of HREs to investigate the emects of the multi-combustion: one type was able to carry out the multi-combustion, and the other was not. Many non-dominated solutions were obtained using the MOGA, and a trade-off was observed between the two objective functions. To understand the design problem, the MOGA results were visualized using a parallel coordinate plot (PCP). © 2015TheAuthors. PublishedbyElsevierLtd.Thisis an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA) Keywords: Hybrid rocket engine; Single-stage launch vehicle; Multi-disciplinary design; Genetic algorithm

* Corresponding author. Tel.: +81-42-585-830; . E-mail address: kana@tmu.ac.jp

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA) doi: 10.1016/j.proeng.2014.12.526

1. Introduction

The hybrid rocket engine (HRE) [1] was successfully put to practical use for SpaceShipOne [2], which completed the first private manned space flight. In Japan, the hybrid rock-et research working group (HRErWG) has been part of the Japan Aerospace Exploration Agency (JAXA),and several studies [3][4][5] have been conducted on the HRE. These stud-ies are characterized by a combination of propellants to lower the environmental impact and to increase the safety level by throttling of the liquid oxidizer. In addition, a HRE can temporarily stop its combustion during engine driving by throttling the oxidizer. This feature, which is called multi-combustion, has the potential to allow efficient engine design by controlling thrust as required.

On the other hand, the HRE has a remarkably different combustion mechanism from a conventional liquid or solid rocket. O/F can be controlled in these conventional rockets before it is ignited, but the mixture of fuel and oxidizer in the HRE is initiated after ignition. Combustion occurs in the boundary layer diffusion flame adjacent to the surface of the solid propellant. 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 com-bined to design an efficient HRE rocket.

In an HRE, which supplies the solid fuel to the gas oxi-dized via a single port, O=F is affected by aspects of the solid fuel design, such as the port diameter, fuel length, and mass flow of the oxidizer. As a result, multi-disciplinary optimization (MDO) is desirable in designing HREs, which have to consider the rocket weight, the thrust, and the flight altitude as part of the design. Thus, ref [6] has developed an MDO methodology that includes a technique for an evaluation of the HRE performance. Using the devel-oped methodology, a global design of the launch vehicle (LV) using HRE has been explored the multi-objective genetic algorithm (MOGA) for a small rocket which was same scale as the solid-propellant rocket S-210 used by JAXA.

In this study, three design problems for a single stage launch vehicle (LV) using an HRE are solved using an evaluation method developed in this study. In addition, the effects of multi-combustion are also investigated. The first design problem considers the maximization of the flight altitude the maximization and gross weight minimization. The second design problem considers the minimization of maximum acceleration and the minimization of gross weight. The third design problem considers maximization of the duration time over the target altitude, the minimization of maximum acceleration and minimization of gross weight. For the second and the third problems, the optimization is carried out under the constraint that the LV should reach an altitude of 50.0 km.

Fuel (Solid grain)

^Oxidizer (Liquid) tank

Figure 1. Conceptual illustration of the HRE.

2. Design Method

2.1. Procedure for HRE Performance Evaluation

This study considers the conceptual design of the LV of a single-stage HRE rocket, which has a thrust chamber, an oxidizer tank, a nozzle, and a payload (Fig. 1). The combustion chamber has solid fuel with a single port to supply the oxidizer. The performace of HRE can be estimated by the regression rate which decided by the mass flux. Figure 2 shows the evaluation procedure [6]. Generally, the regression rate of the fuel in the radial direction r port(t) governs the thrust and decide the performance of the LV. rport(t) is expressed by the mass flux of the oxidizer throug the fuel port Goxi(t) as follows.

rm = aG"oxl(t) (1)

The coe fficient a and index n are evaluated by an experiment with several propellants and Eq. 1 is empirically defined. Using Eq. 1, rport(t) can be used to estimate the oxidizer-to-fuel ratio O/F(t), while changing the design parameters The coefficient a and index n are evaluated by an experiment with several propellants and Eq. 1 is empirically defined. Using Eq. 1, rport(t) can be used to estimate the oxidizer-to-fuel ratio O/F(t), while changing the design parameters, such as the fuel shape and oxidizer mass flow, as stated below.

O / F(t) = —— (2)

mfuel is estimated from r port(t) as

(0 (3)

Lf uei and rport (t) are two of the design parameters in the proposed evaluation module. rport(t) is aquired by subtracting the integrated value of the fuel reduction due to combustion, duration time t, from rport(0):

rport (0 = rport (0) - £ rport (t)Jt (4)

Using 0=F(t) obtained from Eq. 2, the thrust T(t) can be calculated as

T{t) = n, (Ym ue + (P - Pa)Ae) (5)

Here, the mass flow of the propellant m prop is obtained by adding m oxi and m fuel:

^OK + Mfuel (6)

ue and Pe can be obtained from Pc ehich is a design variable and O=F(t) using the NASA Chemical Equilibrium with Applications (NASA-CEA) program [7]. t stop and tinter are introduced for oxidizer throttling and the multi-combustion can be simulated. Goxi(t) is given as

^.(0 = 0.0 for tstop<t<tstop+tmXer

Goxl{t) = — M 0.0 <t<t^9 tstop+tmter<t<tburn (?)

nrport

In the case when Goxi(t) = 0:0, the thrust becomes 0.0. Using the expression by Eq. 7, the multi-combustion can be simulated.

2.2. Non-dominated sorting genetic algorithm-II (NSGA-II)

GA is a popular holistic optimization technique that uses operators such as the selection, the crossover, and the muta-tion, as shown in Fig. 4(a). The non-dominated sorting genetic algorithm-II (NSGA-II)[8] used in this study can be explained as follows. NSGA-II is one type of MOGA, and is widely used to solve multi-objective problems. NSGA-II is characterized by non-dominated sorting and crowding distance sorting. The individuals of the next

generation are selected by elitism. The new generation is fi lled by each front sequentially until the population size exceeds the cur-rent population size (see Fig. 4(b)). In this study, the blend-ed crossover-0.5 (BLX-0.5) and the simple mutation are also applied.

2.3. Parallel Coordinate Plot (PCP)

Parallel coordinate plot (PCP) is a statistical visualization technique used to convert high-dimensional data into two-dimensional graphs. [6] [5] To generate the PCP, the attribute values in the design problem, such as design variables, ob-jective functions and constraint value, have to be normalized for comparison in the same axis as shown in Fig. 5. After the normalization, axes are arranged in consistent parallel lines. Generally, the distances between a line and the next are equivalent. With PCP, it is easy to inspect the design problem at a glance.

Fuel mass flow

O/F calculation

NASA-CEA

Pressure and velocity i at nozzle exit

Thrust estimation

Thrust

Flight altitude calculation

LOX mass flow Grain length Radius of initial port Burn time

Pressure of chamber Nozzle

Design of the oxidizer tank, the chamber, and the nozzle

Weight estimation

y/ Gross weight

OUTPUT

Flight altitude/Maximum acceleration/ Gross weight/Length and diameter of rocket

NASA-CEA: NASA Chemical Equilibrium with Applications

Figure 2. The evaluation procedure of the LV using the HRE

3.Formulation

In this study, a swirling-oxidizer-type HRE proposed in [3] is designed for two design problems. In [3], polypropylene is used as a fuel containing a single port, with a swirling vaporized oxidizer. r port(t), as expressed in Eq. 1, is written as

/^(0 = 0.08260^(0 (8)

A single-stage LV is designed under the assumption that a 40-kg payload is carried. Design variable ranges without multi-combustion are defined in Table 1. Design variable ranges with multi-combustion are defined in Tables 1 and 2.

t =t +tf

*burn lstop ® burn

Figure 3. Schematic illustration of multi-combustion and usage of tstop and tinter.

Figure 4. Overview of the MOGA. (a)Flowchart of the GA, and (b)Ranking by NSGA-II (minimization of f1 and f2).

Figure 5. Schematic illustration of the PCP.

3.1. Design Probleml

Two objective functions are considered: one is maximization maximum altidufe, Altmax and the other is minimization the total mass, Mtot. Aspect ratio of the vehicle L=D is limited to 25.0. The design problem can be expressed as

3.2. Design Problem2

Two objective functions are considered: one is minimization of the maximum accelaration of LV, accmax and the

other minimization of the Mtot . L=D is limited to 25.0 as well as Probleml. In addition, Altmax must be above Alt

Maximize Altmax

Minimize Mt„t

The design problem can be expressed as

In this study, Alttajget is set to 50. 0km.

Subjectto L /D < 25.0

Minimize accmax Minimize Mtot Subjectto L /D < 25.0

Subjectto Altmax > Alttarget

target

3.3. Design Problem3

Three objective functions are considered: one is the maximization of the duration time above Altterget, one is the minimization accmax and the other minimization of the Mtot. L=D is limited to 25.0 as well as Problemsl and 2. In addition, Altmax must be above Alttarget . The design problem can be expressed as

Maximize dU,Ui,on Minimize acc

Minimize M

Subjectto L /D < 25.0 Subjectto Altmx > Ahtarget

In this study, Alttarget is set to 50. 0km as well as Problem2

Table 1. Design variables for engine size.

Table 1. Similarity consideration

Design variables Unit Lower bound Upper bound

dv1 moxi kg 1.0 30.0

dv2 lfuel m 2.0 8.0

dv3 Vrt(0) m 0.05 0.5

dv4 /burn s 10.0 60.0

dv5 Pc bar 30.0 60.0

dv6 £ - 5.0 8.0

Table 2. Design variables for multi-combustion.

Design variables

Lower bound

Upper bound

dv7 Dv8

/stop £

60.0 60.0

4. Results

In this study, the generation number is set to 200, and the population number is set to 100 for GA execution. The non-dominated solutions are compared between the designs with and without multi-combustion for each design problem. The non-dominated solutions are also visualized by a PCP. For the PCP visualization, design variables are normalized by the upper and lower bounds, as shown in Tables 1 and 2. The objective functions and other evaluated values are also normalized by the upper and lower bounds, as shown in Table 3. The initial elevation angle is 90.0 degrees.

4.1. Result of Design Problem 1

Figure 6 shows the comparison of non-dominated solutions of Problem 1 for HREs with and without -multi combustion. According to this figure, solutions of the same quality could be obtained for both methods when Altmax was in a range of approximately 60.0-100.0 km. On the other hand, better solutions at higher Altmax could be auired by the HRE without multi-combustion than with multi-combustion. This result suggests that multi-combustion is not effective to gain higher Altmax because the temporary cessation of combustion causes a reduction in the acceleration. Figure 7 shows the comparison by a PCP of all solutions to Design Problem 1, and 8 shows the comparison by a

PCP of solutions for which Altmax 100.0km. According to Fig. 7, more varied solutions were explored for the HRE with multi-combustion (Fig. 7(b)) than for the HRE without multi-combustion (Fig. 7(a)), due to the introduction of the extra design variables, dv7 and dv8. According to Fig. 8(b), dv7 (tstop) assumed a high value and dv8 (tinter) assumed a low value. This result suggests that the combustion is stopped at the end of the total combustion time(tburn). This is equivalent to the HRE without multi-combustion, which shows that multi-combustion is not effective for allowing the LV to reach higher Altmax. This is a reasonable result, because the altitude of the LV should be reduced by stopping combustion.

4.2. Result of Design Problem 2

Figure 9 shows the comparison of non-dominated solutions of Problem 2 for HRE 's with and without-multi combustion. From this comparison, accmax is effectively reduced in the case of the HRE with multi-combustion, especially when Mtot is over 1000.0 kg. For example, the design that Mtot is 1500.0 kg could reduce accmax by approximately 10.0 km/s2 (equivalent to gravitational acceleration (=1G) on the Earth) compared to the HRE without multi-combustion. Such a design can reduce the load on the payloads. Figure 10 shows the comparison by a PCP of all solutions to Design Problem 2, and Fig. 11 shows the comparison by a PCP of solutions for which accmax < 170:0m/s2. According to Fig. 11(b), the non-dominated solutions can be separated into two clusters by dv4 (tburn) and dv5(Pc): one cluster with low dv4 and high dv5, and another cluster with high dv4 and low dv5. In addition, dv7 (tstop) and dv8 (tinter) of non-dominated solutions are also widely distributed in the design space. This suggests that the design result of Problem 2 strongly depends on the multi-combustion strategy decided by dv7 and dv8. On the other hand, 11(a) suggests that the design result using the HRE without multi-combustion is nearly limited to one trend, in which the accmax is higher than that of the HRE with multi-combustion.

As seen in Fig. 11(b), dv7 (tstop) should be half the value of dv4 (tburn), implying that the combustion should be temporarily stopped in the middle of tburn to avoid high acceleration. dv8 (t^) assumes a value of approximately dv4(tburn) - dv7 (tstop). This means that setting tstop, tinter and tburn to similar values is effective for reducing the accmax (see also Fig. 3). This is a reasonable result because the LV cannot reach Alt target with high t^, and accmax and should be maintained with a high accstop (that is, too much initial combustion time).

4.3. Result of Design Problem 3

Figure 12 shows the comparison of non-dominated solutions of Problem 3 for HRE 's with and without multi-combustion. Because this problem has three objective functions, three plots can be drawn with projecting 3-D plot,

that is accmax vs. Tduration, Tdulation vs.Mtot and accmax vs.Mtot. According to these plots, there are no difference betweenHRE 's with and without multi-combustion regarding accmax vs. Tduration and Tdulation vs. Mtot. This result suggest that the similar Tduration can be carried out whether the multi-time combustion is used or not. On the other hand, there is trade-off between accmax and Mtot. This trade-off is caused by the same reson compared with Problem 2.

Figure 13 shows the comparison by a PCP of all solutions to Design Problem 3, and 14 shows the comparison by a PCP of solutions for which accmax < 170.0m/s2and Tduration > 195.0m/s2. According to Fig. 13(b), dv4 (tburn) of the non-dominated solutions becomes higher in the design range. This result should be caused by the maximization of Tduration, because the visualization result is a different result from problem 2(Fig. 10). Comparing to 14(a) and (b), dvs1-6 which decide the LV geometries shows the similar trend between the HRE with and without multi-combustion. This result suggests that the geometry is decided by the maximization of Tduration and the minimization of Mtot. However, it is also found that the dv4 (tburn) of the HRE with multi-combustion is 10[sec.] higher than that of the HRE without multi-combustion. Such design can reduce the acceleration with lower combustion speed. (that is lower thrust.) According to Fig. 14(b), dv8 (t^) of non-dominated solutions are widely distributed in the design space. This result is different from the result of Problem 2 (Fig. 11). It is also found that the dv7 (tstop) should be approximately over 25[sec.] Because dv4 (tburn) is over 30[sec.], the combustion should be temporally stopped 5[sec.] to reduce the acc„,x.

* w/o multi-combustion

w/ multi-combustion » » 9

® ê » w

atf»»*®

100.0 120.0 All [km]

Fig 6. Comparison of non-dominated solution of Problem 1 for HRE with and without multi-combustion. Table 3. The upper and lower bounds of the objective functions and other evaluated values for PCP.

Design variables

Lower bound

Upper bound

Alt max

aCCmax Zduration

m/ s2 r

0.0 50.0 10.0

0.0 0.0

38000.0

400.0 300.0

5. Conclusions

In this study, a multi-disciplinary evaluation method for an LV with an HRE was developed, and multi-objective design was carried out by means of NSGA-II. The result was analyzed with design space visualization by PCP. The evaluation developed in this study can be used to consider the case where the LV is able to stop and restart combustion while in flight. This study investigated the e ffects of multi-combustion, which is one of the beneficial features of the HRE.

The first case was the maximization of the maximum altitude and the minimization of the total mass. The result by the MOGA suggested that multi-combustion is not effective for the maximization of the altitude, because the altitude is reduced when the HRE is stopped. The second case was the minimization of the maximum acceleration and the minimization of the total mass. In this case, an LV capable of delivering the payload to an altitude of 50.0 km was considered. The result by MOGA suggested that multi-combustion is effective for the maximization of the altitude and minimization of the maximum acceleration, because the temporary engine stop can reduce the acceleration. According to the design space visualization by PCP, it was found that the HRE should be stopped temporarily halfway through the total combustion time (the LV flies by momentum while the engine is stopped) to reduce the acceleration. If the duration of the engine stop is too long, the LV cannot reach the target altitude, and the fuel weight will be higher. On the other hand, if the dura-tion of the engine stop is too short, the acceleration cannot be sufficiently reduced. Such knowledge regard-ing the engine ignition timing is useful for the operation of the LV.

The third case was the maximization of the duration time over 50km altitude, the minimization of the maximum acceleration and the minimization of the total mass. In this case, there is little difference between the HRE with multi-combustion and the HRE without multi-combustion regarding the maximization of the duration time and the

minimization of the maximum acceleration. According to the visualization of the design problem by PCP, a LV geometry can be decided by the maximization of the duration time. In addition, it was also found that the maximum acceleration can be reduced to optimize the combustion time and the time of the combustion temporary stop

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