ロケットターボポンプ用タービンの最適設計に関する研究

Abstract

This paper describes the optimization results for a rocket turbopump turbine obtained by using the “Robust Design Process” and “Multi-Objective Genetic Algorithm” (i.e., MOGA). The results of the study contributed to the improvement of the design capability of a rocket turbopump turbine. || A large liquid rocket system uses a turbopump to pressurize the propellant fed to the engine. A turbopump, characterized as one of main components of the liquid rocket engine, is a fluid machine for pumping the propellant into the combustion chamber by suctioning low-pressure cryogenic propellant from the propellant tank. Therefore, aturbopump is considered to be the heart of the rocket engine. A turbopump consists of a turbine and a centrifugal impeller, which are connected by coaxial and supported by two sets of ball bearings. The role of a rocket turbopump turbine is to convert the enthalpy of working fluid of the turbine to the enthalpy of the working fluid of the pump. || In the development of a turbopump, shaft vibration is one of the most important problems, and the rotor dynamic force in the turbine (i.e., Thomas Force) is one of the causes of shaft vibration of the turbopump. Thomas Force is due to fluid-structure interaction in a turbine with non-axisymmetric tip clearance. In a turbine undergoing transverse vibrations, the portion of the blading with the smaller tip gap would produce a greater tangential driving force than its 180 deg opposite portion. Upon integration, this difference in work extraction results in a cross force tending to promote forward whirl. This can be a powerful positive feedback mechanism, leading to rotor dynamic instability. Actually, in the past engine development in Japan, there was a shaft vibration problem due to Thomas Force. Reducing the Thomas force is a valid approach from the view point of reducing the shaft vibration of a turbopump. A number of studies related to Thomas Force have been made over the years, however, because there have been few previous studies on the reduction of the Thomas Force, the effect of turbine design parameter for Thomas force remains unclear. || There is also another problem related to designing a rocket turbopump turbine. In recent rocket engines, the expander bleed cycle tends to be selected in order to simplify the engine system and improve reliability of the whole engine. Due to its special specifications, many turbopump turbines are designed as impulse turbines which have higher loading and blades with an extremely low aspect ratio. In such a situation, it is difficult to predict turbine efficiency accurately in the system design phase of the rocket engine. Therefore, further improvement in turbinedesign techniques is needed because turbine performance directly affects engine performance and reliability in a liquid rocket propulsion system. Given this background, the purpose of the present study was to perform multi-objective optimization for reducing Thomas Force by using a newly proposed optimization process that combines Quality Function Deployment (i.e., QFD) and the Robust Design Process (i.e., Parameter Design). || Firstly, in order to evaluate the accuracy of the existing one-dimensional loss model, one-dimensional analysis by using the specifications of existing rocket turbopump turbines was carried out. Furthermore, by using steady three-dimensional CFD analyses, parametric studies of the major design variables such as tip clearance, blade loading, and blade aspect ratio were carried out. The results clarified the cause of the reduction of accuracy of one-dimensional prediction of turbine efficiency. The one-dimensional loss model was found to underestimate the loss under the condition of a blade with a low aspect ratio. From comparison between the existing one-dimensional loss models, it was also found that the "Craig & Cox model" could reproduce the tendency for blade loading correctly. Since an optimum turbine would be selected based on the analysis results for over 10,000 points in this optimization process, it was necessary to shorten the calculation time by using one-dimensional analysis. Therefore, from this result, the Craig & Cox model was selected as the one-dimensional loss model for use in the optimization. || In this optimization process, QFD was performed as the first step, and Parameter Design and MOGA optimization were performed as the second step. Therefore, the purpose of QFD was to visualize “the Voice of the Market” (i.e., Market Needs) which were essential for optimization of rocket turbopump turbines to identify important design parameters. The procedure of QFD was as follows. Firstly, acquisition of quality requirements was performed. “Market Needs” for rocket turbopump turbine of various stakeholders should be understood and also visualized. Therefore, interviews and an AHP survey of the stakeholders such as turbopump designers, rocket engine designers, manufacturer and inspectors were conducted. Based on the results of the AHP survey, the degree of importance ofthe quality requirements was calculated. From these results, “Market Needs” of the rocket turbopump turbine as specified by each stakeholder was clarified. Secondly, conversion to the degrees of importance for quality characteristics was done by using a quality table. From these results, the “Market Needs” for a rocket turbopump turbine were translated into “Technical Words” which could be understood by rocket engineers. Finally, conversion to the degree of importance for design parameters was carried out by using technology deployment. From these results, important design parameters which reflect “Market Needs” for a rocket turbopump turbine, such as “pitch chord ratio of blade” and “axial blade gap”, were identified by using the technology deployment. From the results of QFD, criteria for selecting "important design parameters" were revealed. These "important design parameters" were used as design variables in the optimization calculation that was performed in the second step of this optimization process. || The LE-7 prototype Fuel Turbopump Turbine was selected as the design object in this optimization. In this optimization, both Parameter Design and MOGA optimization by using the one-dimensional loss model were employed. The procedure of multi-objective optimization considering the feasibility of the blade structure and Thomas Force was as follows. Firstly, Parameter Design was conducted. The purpose of Parameter Design was to reveal the design parameters that contribute to the reduction of Thomas Force. By performing Parameter Design for the reduction of Thomas Force with the use of an orthogonal array, it was found that the design parameters, such as the "exit angle of blade", and the "pitch chord ratio of blade", contribute to the reduction of Thomas Force. Secondly, MOGA optimization was conducted. In this optimization, both of "Blade Stress" and " Turbine Weight"were added to the objective functions in addition to reduction of Thomas Force. The approximation model of "Turbine Weight" and "Blade Stress" was created by using the response surface method. Multi-objective optimization that had three objective functions (i.e., turbine weight, blade stress, and Thomas Force) was performed after validation of the accuracy of these approximation models. In order to obtain trade-off information on multi-objective optimization, the results of the present optimization were visualized by using the Self-Organizing Map (i.e., SOM). The SOM is a data mining method, which can show trade-off information more clearly by projecting multi-dimensional information onto a two-dimensional surface. Since SOM of objective functions showed a trade-off relationship, it was indicated that the optimum solution that satisfied all of the objective functions could not be obtained. From this result, the turbine with the smallest weight was selected as the optimal solution. The optimum turbine by MOGA optimization was based on one-dimensional analysis, so the effect for reducing Thomas force was verified by using CFD analysis. In addition to the verification of Thomas force by CFD, by using FEM, it was also confirmed that the resonance of optimum turbine could be avoided at operating speed. From these evaluation results of the optimum turbine, it was found that optimized blade resulted in a reduction of 10% in weight, and 30% in Thomas Force, as compared with the original blade. || Furthermore, in order to evaluate the effect of Thomas Force on the stability of rotor system, a turbopump linear dynamic simulation was conducted by using the LE-7 prototype fuel turbopump rotor system. This rotor system was modeled by using the Finite Element Method (FEM). Its vibration characteristics were validated by the published data. The effect of rotor dynamic force (i.e., Thomas Force) on the dynamic characteristics of the rotor system was investigated. From this result, reduction of Thomas Force was found to be an effective measure for the suppression of rotor vibration. || Finally, consideration of the usefulness of this optimization process which was combined QFD and Parameter Design was conducted. The correspondence between the design parameters of the parameter design process and theimportant design parameters of QFD was good. Because criteria for selecting objective functions and design parameters were clarified from the result of QFD, the information obtained from the QFD could reinforce the weakness of the optimization process. Therefore, the optimization process herein proposed was useful in carrying out optimization for meeting the “Market Needs” of the stakeholders. || Through the present study, the ability to perform multi-objective optimization considering the rotor dynamic force of rocket turbopump turbine could be obtained. As a result, improvement of design flexibility and capability for rocket turbopump turbine was achieved. These achievements are also useful for progress in the development of general industrial turbo machinery in addition to the development of rocket turbopumps.