研究者詳細 - 北川　幸樹

Construction of the Calculation Model to Clarify the Energy Conversion Ratio in the Entire Area of an LSD Wave 査読有り

ARAI Ten, MATSUI Kohei, KITAGAWA Koki

Journal of Evolving Space Activities ( 宇宙技術および科学の国際シンポジウム ) 2 ( 0 ) n/a 2024年01月

担当区分：最終著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

In laser propulsion, there is a method that uses the atmosphere as a propellant and laser energy from the ground. This method utilizes Laser Supported Detonation (LSD) in which a laser is absorbed and thrust is generated by detonation. To estimate the thrust of laser propulsion with LSD, the energy conversion ratio is an important parameter. The energy conversion ratio is the ratio of energy conversion from laser to working fluid. In a previous study, the energy conversion ratio was obtained experimentally and analytically, but the results have a large discrepancy. To eliminate the discrepancy, it is necessary a new calculation method for the energy conversion ratio. The purpose of this study is to establish a new method for calculating the energy conversion ratio across the entire LSD wavefront using the specific heat ratio of LSD obtained theoretically under the assumption of the Chapman-Jouguet state, and to evaluate the calculation method. The results show that the energy conversion ratios are 0.25 and 0.38 at the termination time under the laser energy of 8 and 10 J, respectively, which are close to the experimental values. This agreement could indicate that the newly proposed method for calculating energy conversion ratios is useful in laser propulsion.

DOI： 10.57350/jesa.191

Evaluation of Radiative Heat-Transfer Effect on Paraffin-Wax Regression Rate in Hybrid Rocket 査読有り国際誌

Naka G., Carmicino C., Messineo J., Kitagawa K., Shimada T.

Journal of Propulsion and Power 39 ( 2 ) 258 - 273 2023年03月

記述言語：英語掲載種別：研究論文（学術雑誌）

A numerical setup has been developed to rebuild the axial profile and time history of the regression rate of a paraffin-wax-based fuel in a hybrid rocket, with the main target of investigating the effect of the local radiative heat transfer from both the combustion gas molecules and soot particles. The numerical approach is based on a quasi-one-dimensional computational fluid dynamic strategy, which is coupled with chemical equilibrium combustion; the vaporization and entrainment components of the wax-fuel regression rate have been estimated with an established liquefying-fuel model. The increase of the convective heat-transfer blocking due to radiation and the effect of recirculation flow due to oxidizer injection have been introduced. Numerical results are compared with experimental data. When radiative heat transfer, blocking-effect correction, and recirculation flow effect are taken into account, the calculated and measured fuel regression rates agree well in both values and axial profiles.

DOI： 10.2514/1.B38728

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85150484554&origin=inward

Function Test of Experimental System to Obtain Laser Ignition Characteristics of Low-Temperature Boron/Potassium Nitrate 査読有り国際誌

MATSUI Kohei, MATSUURA Yoshiki, TOKUDOME Shinichiro, KITAGAWA Koki

Journal of Evolving Space Activities ( 宇宙技術および科学の国際シンポジウム ) 1 ( 0 ) n/a 2023年01月

担当区分：最終著者記述言語：英語掲載種別：研究論文（学術雑誌）

In order to use laser ignition systems for solid rocket motors operating in deep space environments, it is necessary to elucidate the laser ignition characteristics of the ignition charge in low-temperature environments. This study aims to design an experimental system that can confirm the ignition threshold, ignition delay, and ignition temperature by irradiating an ignition charge with a diode laser in a low-temperature environment. Ignition experiments at room temperature were conducted. The data were evaluated statistically to obtain an ignition threshold with the maximum likelihood method. The relationship between the laser irradiation duration and the laser power with respect to the ignition threshold was obtained. The target value of the low-temperature environment temperature was determined as -50 °C. We examined the requirements of the experimental system and conceptually designed the system to simulate the low-temperature environment. It was confirmed that the constructed experimental system cooled the ignition charge to -50 °C. In the ignition experiment, the ignition charge was successfully ignited at room temperature and at low temperature. The ignition delay, the ignition temperature, and the high-speed image were obtained. Eventually, the validity of the experimental system was confirmed through the function tests.

DOI： 10.57350/jesa.17

Evaluation of Measurement System for Heat Transfer Characteristics ofLiquid Oxygen Flow in a Thin Tube under High Heat Flux Conditions 査読有り国際誌

KITAGAWA Koki, MATSUI Kohei

Journal of Evolving Space Activities ( 宇宙技術および科学の国際シンポジウム ) 1 ( 0 ) n/a 2023年01月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

Heat transfer characteristics of liquid oxygen under high pressure and high heat flux should be elucidated to design a regenerative cooling nozzle for a hybrid rocket. Previously, we developed an experimental system using Joule heating to a thin tube in which liquid oxygen flows. The objective of this study is the evaluation of the measurement system to obtain the heat transfer characteristic under high pressure and high heat flux. We conducted a cold flow experiment and an experiment of heat transfer characteristic measurement. The friction factor of the tube is estimated with the Colebrook-White equation. The heat transfer coefficient was calculated by solving the heat conduction equation in the tube and the conservation laws of the fluid. The calculated heat transfer coefficient is in the same order as the experimental value. Consequently, we confirmed that experimental and analytical methods are appropriate to obtain heat transfer characteristics.

DOI： 10.57350/jesa.45

進化計算法によるWAX燃料を用いた強度可変酸化剤流旋回型ハイブリッドロケットエンジンによる単段打ち上げ機の性能評価

金崎雅博, 北川幸樹, 嶋田徹

最適化シンポジウム講演論文集 ( 一般社団法人日本機械学会 ) 2022.14 ( 0 ) U00073 2022年01月

記述言語：日本語掲載種別：研究論文（研究会，シンポジウム資料等）

To improve the thrust by the O/F shift, which is one of the weak points of the hybrid rocket, a method with a variable oxidizer strength has been proposed. In this study, the superiority of this type of hybrid rocket over the conventional hybrid rocket without variable oxidizer supply was compared through several launch vehicle designs, such as altitude maximization by vertical launch and downrange extension problems with an optimized launch angle. A multi-objective evolutionary algorithm and the multi-disciplinary evaluation method of the launch vehicle were applied.

DOI： 10.1299/jsmeoptis.2022.14.u00073

Flight Results of Solid Propulsion Systems for Epsilon-4 査読有り国際誌

KITAGAWA Koki, TOKUDOME Shinichiro, HORI Keiichi, UI Kyoichi, KINOSHITA Masahiro, HASHIMOTO Junichi, ICHIMURA Kotaro

TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN ( 一般社団法人日本航空宇宙学会 ) 19 ( 3 ) 400 - 406 2021年01月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

Epsilon-4, which was the Enhanced Epsilon launch vehicle optional configuration with a multi-satellite mount structure, was successfully launched with seven satellites in January 2019. The seven satellites consist of 200 kg-class small-satellite, three micro-satellites and three CubeSats in the Innovative Satellite Technology Demonstration-1 program. The post flight analysis was conducted. The chamber pressure and thrust of three main motors and chamber pressure of SMSJ and SPM were analyzed to confirm the effectiveness of design and production methodologies. All solid propulsion systems for Epsilon-4 showed a very good behavior during the flight. As a result, the validity of the design and operation of the Enhanced Epsilon launch vehicle was confirmed.

DOI： 10.2322/tastj.19.400

その他リンク： https://ci.nii.ac.jp/naid/130008034521

Development Results of Laser Ignition System for Solid Rocket Motor 査読有り国際誌

MINAMI Keisuke, MATSUURA Yoshiki, KITAGAWA Koki, ARAKAWA Satoshi, MORISHITA Naoki, TAKEMAE Toshiaki, IWABUCHI Shota, WADA Asato, TOKUDOME Shinichiro

TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN ( 一般社団法人日本航空宇宙学会 ) 19 ( 5 ) 807 - 811 2021年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

This paper describes the development status of a laser ignition system for a solid rocket motor. This system is being developed as a simple, lightweight, and small design with a high resistance to electrical disturbances and a high level of safety. The most notable advantage of this system is that its high level of safety can decrease the cost of launching rockets into space. A laser initiator and a laser safe-and-arm device (laser S/A), which are essential components of the proposed system, were developed. In particular, prototypes of the laser initiator and laser S/A for the ignition of an upper stage rocket motor were manufactured, and some environmental tests, which are required for space rocket devices, were conducted. In addition, the lowest laser energy that is needed to ignite the laser initiator was determined by changing the laser power and operating time of the laser S/A. Furthermore, a small rocket motor vacuum fire test was successfully conducted.

DOI： 10.2322/tastj.19.807

その他リンク： https://ci.nii.ac.jp/naid/130008084441

Reconstructed Ballistic Data Versus Wax Regression-Rate Intrusive Measurement in a Hybrid Rocket 査読有り国際誌

Jerome Messineo, Koki Kitagawa, Carmine Carmicino, Toru Shimada, Christian Paravan

Journal of Spacecraft and Rockets ( American Institute of Aeronautics and Astronautics ) 57 ( 6 ) 1295 - 1308 2020年07月

記述言語：英語掲載種別：研究論文（学術雑誌）

Burning tests of a laboratory-scale hybrid rocket engine were carried out with gaseous oxygen and a microcrystalline-wax-based fuel to look into the feasibility of using an intrusive resistor-based sensor for measuring the fuel regression rate. This initial screening was driven by the need for real-time control of the oxidizer-to-fuel ratio in altering-intensity swirling-flow-type hybrid rocket engines aiming at performance optimization. A traditional ballistic reconstruction technique was critically revised in order to build up a framework for comparison with the measured data; with the measured aft-chamber pressure and oxygen mass flow rate time histories, the fuel regression rate and port diameter were reconstructed over the firing by estimating the combustion efficiency with the constraint that calculated and measured fuel mass consumed are equal. This technique invariably suffers from the issue of presenting multiple solutions for the fuel mass flow rate in the proximity of the optimum mixture ratio, for which a novel variable-efficiency approach is proposed. Reconstructed data show that regression rate is nearly constant in each firing, yielding dependence upon the port diameter other than the mass flux. Resistor-sensor raw data displayed large deviation from the ballistic results for the slower burning rate of the sensor support. A detailed analysis is presented.

DOI： 10.2514/1.A34695

その他リンク： https://arc.aiaa.org/doi/10.2514/1.A34695

Prediction of space and time distribution of wax-based fuel regression rate in a hybrid rocket 査読有り

Naka G., Messineo J., Kitagawa K., Carmicino C., Shimada T.

AIAA Propulsion and Energy 2020 Forum 1 - 30 2020年01月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

A numerical set up has been developed to predict the axial distribution and time history of fuel regression rates with the aim of comparing numerical results with the experimental data. The numerical approach is based on a quasi-one-dimensional CFD strategy, which is coupled with chemical equilibrium combustion; the wax-fuel regression rate has been simulated with the liquefying fuel theory developed by Karabeyoglu. In this model, local radiation heat transfer from both the hot gas combustion molecules (CO, CO2, and H2O) and soot particles is considered. It is shown that, when radiation heating of the fuel is taken into account, the calculated fuel regression rates exhibit values and axial profiles close to the ones observed experimentally.

DOI： 10.2514/6.2020-3768

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85091289443&origin=inward

Development and Flight Results of Solid Propulsion System for Enhanced Epsilon Launch Vehicle 査読有り国際誌

KITAGAWA Koki, TOKUDOME Shinichiro, HORI Keiichi, TANNO Haruhito, NAKANO Nobuyuki

TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES, AEROSPACE TECHNOLOGY JAPAN ( 一般社団法人日本航空宇宙学会 ) 17 ( 3 ) 289 - 294 2019年01月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

The development of enhanced propulsion system for the next Epsilon rocket was progressed. The development of Enhanced Epsilon is mainly the renewal of the second stage, and also includes each subsystem's improvement. The second stage motor M-35 was newly designed and manufactured. In order to verify the design, the static firing test of the second motor M-35 under the condition of vacuum ambient was conducted in 2015. The JAXA successfully launched the first Enhanced Epsilon launch vehicle. All solid propulsion systems for the Enhanced Epsilon launch vehicle showed a very good behavior during the flight

DOI： 10.2322/tastj.17.289

その他リンク： https://ci.nii.ac.jp/naid/130007642475

Hybrid rocket firing experiments at various axial–tangential oxidizer-flow-rate ratios 査読有り

Ozawa K., Kitagawa K., Aso S., Shimada T.

Journal of Propulsion and Power 35 ( 1 ) 1 - 15 2019年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

A breadboard model (BBM) of an altering-intensity swirling-flow-type (A-SOFT) hybrid rocket engine was recently developed, and static firing experiments of the BBM were performed under various axial and tangential oxidizer mass-flow rates. A-SOFTs are intended to control thrust at an optimal oxidizer-to-fuel-mass ratio and achieve a high baseline of regression rates with a fixed motor configuration. This is possible by controlling both the oxidizer mass-flow rate and the effective geometric swirl number. A simple model based on a continuous and monotonic function of oxidizer mass flux and effective geometric swirl number was able to accurately predict the performance of experiments conducted on the A-SOFT BBM. The local fuel regression behavior in the axial direction of the A-SOFT BBM was shown to be like that of a swirling-oxidizer-flow-type hybrid rocket engine. Combustion efficiency was evaluated indirectly using equations for the efficiencies of thrust and specific impulse to eliminate errors due to local pressure shifts and the centrifugal force in swirling flows. In most cases, this indirect method compensated for the overestimations of c efficiency that resulted by directly using chamber-pressure data.

DOI： 10.2514/1.B36889

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85076482957&origin=inward

Evaluation of safety distance for blast of hybrid rocket propellants 査読有り

Takahashi A., Kitagawa K., Shimada T.

AIAA Propulsion and Energy Forum and Exposition, 2019 2019年01月

記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

For the purpose of constructing a reliable and reasonable evaluation method of the safety of hybrid rockets, the evaluation of the safety distance for blast wave is conducted. Physical phenomena leading to the blast of hybrid rocket propellants are extracted and modeled recognizing fuel fragmentation and dust explosion as key phenomena which cause blast waves. In order to evaluate the amount of fuel dust, of the particle size less than or equal to 500 μm, a particular correlation is used. The correlation between dust mass fraction and the ratio of the applied energy to the absorbed energy by the fuel is represented by utilizing existing experimental data. Also indefinite parameters, four energy efficiencies during the explosion processes, are identified by reproduction of existing experimental data of blast pressure measurement tests. It is found that, by using the adjusted model parameters, the present model can reproduce the existing safety distance data of hybrid rocket propellant blast for various impact velocities. The correlation about dust mass is valid for various fuels and, with this, it is also implied that the evaluation model for blast is applicable to various situations.

DOI： 10.2514/6.2019-3917

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85095967657&origin=inward

Image analysis for velocity profile estimation in A-SOFT hybrid rocket combustor 査読有り国際誌

Kimura N., Obata K., Kitagawa K., Shimada T.

Journal of Fluid Science and Technology ( 一般社団法人日本機械学会 ) 13 ( 4 ) JFST0029 - JFST0029 2018年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

Altering-intensity Swirling-Oxidizer-Flow-Type (A-SOFT) hybrid rocket engine (HRE) was proposed as a technique to solve problems of current hybrid rockets. It uses axial and tangential oxidizer injections and their mass flow rates are manipulated independently to control the thrust and O/F. The visualization experiment of combustion of gaseous oxygen (GOX) and polymethyl methacrylate (PMMA) of A-SOFT HRE is carried out under combustion pressure of 1 bar. Combustion gas flow in the combustor is captured by high speed cameras whose fps is 30000. In order to capture the nature of the flow field quantitatively, obtaining velocity profiles by image analysis applied to its visualization images is effective. Basic image analysis method is Direct Cross Correlation method and, for high precision and spatial resolution, Correlation Based Correction is applied recursively. Averaged velocity profiles are obtained by averaging the calculation results of 10000 images corresponding to the actual time duration of 0.3 s. Flames with strong white light emission are characteristic of hybrid rockets and regarded as traceable markers for the image analysis. These luminous flames are considered to flow in the boundary layer and velocity of flames in the boundary layer is important to capture the characteristics of combustion flow field. Axial velocity of the luminous flame is proportional to the total mixed mass flow rate for each location x. Tangential velocity is proportional to angular momentum given by tangential GOX injection and inversely proportional to the total mixed mass flow rate for each location x. And how much GOX injected in axial and tangential directions are mixed is speculated by velocity profiles. It is found that mixing of GOX injected in axial and tangential directions occurs at almost the same constant rate regardless of the ratio of GOX mass flow rate injected in axial and tangential directions.

DOI： 10.1299/jfst.2018jfst0029

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85057189423&origin=inward

Flight results of solid propulsion system for epsilon launch vehicle from the third flight 査読有り

Kitagawa K., Tokudome S., Hori K., Ui K., Kinoshita M., Hashimoto J., Ichimura K.

Proceedings of the International Astronautical Congress, IAC 2018-October 2018年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

The third Epsilon launch vehicle, which was the Enhanced Epsilon launch vehicle optional configuration, was successfully launched with the payload of ASNARO-2 in January 2018. The post flight analysis was conducted. The chamber pressure and thrust include residual thrust of three main motors and chamber pressure of SMSJ and SPM were analysed to confirm the effectiveness of design and production methodologies. All solid propulsion systems for the third Epsilon launch vehicle showed a very good behaviour during the flight.

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85065301986&origin=inward

Design Methodology of a Hybrid Rocket-Powered Launch Vehicle for Suborbital Flight 査読有り

Kanazaki M., Yoda H., Chiba K., Kitagawa K., Shimada T.

Journal of Aerospace Engineering 30 ( 6 ) 2017年11月

記述言語：英語掲載種別：研究論文（学術雑誌）

A multidisciplinary design methodology for a launch vehicle (LV) with a hybrid rocket was proposed in order to obtain qualitative design knowledge. In this study, a propulsion system performance and aerodynamic performance were empirically evaluated using a theoretical approach, and flight evaluation was performed by solving equations of motion to evaluate the motion along the horizontal/vertical directions and rotation around the body axis. To demonstrate the applicability of the proposed method, two types of multiobjective design problems were solved using multiobjective evolutionary algorithms, and the results were visualized using the parallel coordinate plot, which is a data mining technique. The first design problem has two objective functions: the maximization of the highest altitude and the minimization of the total mass. In this case, the effect of the constraint related to the body length and diameter ratio was evaluated. The second design problem also had two objective functions and two constraints for a realistic LV design: the maximization of the downrange and the minimization of the total mass. The target altitude was different for these problems although the objective functions were identical. As a result, the trade-off information was successfully acquired for each design problem. It was also found that the body length and diameter ratio were key factors in deciding the maximum altitude. Furthermore, during the downrange maximization, the characteristic geometries observed in the obtained nondominated solutions revealed the design required to fulfill the constraint related to the target altitude.

DOI： 10.1061/(ASCE)AS.1943-5525.0000778

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85027881923&origin=inward

Performance and regression rate characteristics of 5-kN swirling-oxidizer-flow-Type hybrid rocket engine 査読有り

Sakurai T., Yuasa S., Ando H., Kitagawa K., Shimada T.

Journal of Propulsion and Power 33 ( 4 ) 891 - 901 2017年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

Burning tests were carried out for the 5-kN-Thrust swirling-oxidizer-flow-Type hybrid rocket engine to establish the engine technology and to obtain the fuel regression characteristics. The engine attained stable burning without any combustion oscillation and C efficiencies of more than 98% under the 5-kN-Thrust conditions. The maximum timeaveraged thrust realized was 4.4 kN, which was lower than 5 kN. This was attributed to the regression rate being lower than the value estimated by regression rate correlation. The fuel regression behavior of this engine was characterized as the flow-development region near the grain leading edge and the fully developed turbulent flow region. The axial length of the flow-development region varied from that observed in the laboratory-scale engine, and it depended on the oxidizer mass flow rate, grain initial port diameter, and swirl strength. The controlling parameter of the regression rate in the fully developed flow region was modified to correlate with the grain port diameter. By effecting these modifications, the accuracy of the regression rate prediction was improved. The range of the applicable controlling parameter of the modified regression rate correlations was extended for use for larger-scale engines.

DOI： 10.2514/1.B36239

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85021289537&origin=inward

Development of solid propulsion system for enhanced epsilon launch vehicle and epsilon's second launch results 査読有り

Kitagawa K., Tokudome S., Hori K., Hashimoto J., Nakano N., Tanno H.

Proceedings of the International Astronautical Congress, IAC 13 8590 - 8596 2017年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

The development of Enhanced Epsilon is mainly the renewal of the second stage, and also includes each subsystem's improvement. The second-stage motor M-35 was newly designed and manufactured. In order to verify the design, the static firing test of the M-35 under the condition of vacuum ambient was conducted in 2015. The Epsilon's second flight, which was the first Enhanced Epsilon launch vehicle, was successfully conducted with the payload of Exploration of energization and Radiation in Geo-space (ERG) in Dec., 2016. After the flight, chamber pressure and thrust include residual thrust were analysed to confirm the effectiveness of design and production methodologies. All solid propulsion systems for the Enhanced Epsilon launch vehicle showed a very good behaviour during the flight.

その他リンク： https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85051500255&origin=inward

Structurisation and visualisation of design space for launch vehicle with hybrid rocket engine 査読有り国際誌

Kazuhisa Chiba; Masahiro Kanazaki; Shin'ya Watanabe; Koki Kitagawa; Toru Shimada

International Journal of Automation and Logistics 2 ( 1/2 ) 26 - 44 2016年02月

Design optimization of launch vehicle concept using cluster hybrid rocket engine for future space transportation 査読有り

KANAZAKI Masahiro, ITO Shoma, KANAMORI Fumio, NAKAMIYA Masaki, KITAGAWA Koki, SHIMADA Toru

Journal of Fluid Science and Technology ( 一般社団法人日本機械学会 ) 11 ( 1 ) JFST0003 - JFST0003 2016年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

This paper reports on the conceptual design of a three-stage launch vehicle (LV) with a clustered hybrid rocket engine (HRE) through multi-disciplinary design optimization. This LV is a space transportation concept that can deliver micro-satellites to sun-synchronous orbits (SSOs). To design a high-performance LV with HRE, the optimum size of each component, such as an oxidizer tank containing liquid oxidizer, a combustion chamber containing solid fuel, a pressurizing tank, and a nozzle, should be determined. In this study, paraffin (FT-0070) is used as a propellant for the HRE, and three cases are compared: In the first case, HREs are optimized for each stage. In the second case, HREs are optimized together for the first and second stages but separately for the third stage. In the third case, HREs are optimized together for each stage. The optimization results show that the performance of the design case that uses the same HREs in all stages is 40% reduced compared with the design case that uses optimized HREs for each stage.

DOI： 10.1299/jfst.2016jfst0003