Multi Objective Design Optimization of Rocket Engine Turbopump Turbine Naoki Tani , Akira Oyama and Nobuhiro Yamanishi [email protected] Japan Aerospace Exploration Agency JAXA is now planning to develop a next generation booster engine named LE-X, which is a successor of LE-7A. From an engine cycle study, the LE-X requires a high efficiency turbine. To achieve this requirement, a feasibility study of multi-objective design optimization with generic algorithm was applied to the turbine blade shape. The optimized results show strong tradeoff between axial-horsepower and entropy-rise within the stage. By use of Self-Organizing MAP (SOM) and correlation function, it is revealed that this tradeoff is primarily derived from outlet blade design, and inlet blade shape also has an influence to axial-horsepower improvement. INTRODUCTION The shape optimization is considered to be one of the best In order to achieve high-efficiency and high-robustness, the way to achieve the above objective. Usually, engineering expander-bleed cycle was chosen as an engine cycle for the problems are tradeoff problems, such as weight and next generation booster engine, called LE-X (Fig.1)[1][2]. structural strength. Presently, multi-objective generic The LE-X is considered to use the liquid-hydrogen as a fuel, algorithm (MOGA) was chosen as an optimization method and liquid-oxygen as an oxidizer. The energy source of the since MOGA can handle multi objective optimization turbo-pump driving gas is generated by the heat-exchange problem and can search through a large design space. In a around the main combustion chamber in expander-bleed gas-turbine, effectiveness of MOGA is widely demonstrated cycle, thus high efficiency pump and turbine are required. in applications such as a compressor [3], a turbine [4] and a According to the engine cycle study, turbine efficiency is cooling system [5]. However, compared to the gas-turbine, more sensitive for the engine total performance compared to the turbopump turbine is quite highly loaded, therefore, pump efficiency [1]. efficiency may not be particularly improved. Therefore, in the present study, to clarify whether the highly-loaded LH2 LOX turbine blade can be improved or not, MOGA was applied Main Fuel Mi xer on a trial base. Usually, it is quite difficult to show trade-off Val ve Oxidizer Main Oxidizer information in MOGA, especially more than three objective Tur bopump Val ve Main Igniter Fuel functions, so the Self Organizing Map (SOM) was used [6]. Tur bopump SOM can graphically show multi-dimensional trade-off Waste Valve information by projecting to a two-dimensional map. Main Combustion Chamber Chamber Cooling Val ve Table 1 Generic algorithm methods and parameters Mi xt ure Ra ti o Thrust Control Control Val ve Val ve Pareto Ranking Nozzle Fitness + Shearing Selection SUS Blending BLX-0.5 Alternation of Best-N Generation Mutation Rate 0.1 Generation No. 50 Population No. 16 COMPUTATIONAL METHOD Multi-Objective Generic Algorithm Fig.1 LE-X cycle diagram and 3D model [1] The presently used optimization method is a real-coded multi-objective generic algorithm with constraint-handling method by Oyama et al.[7]. One of the features of this method is more efficient and more robust search of the Baseline Shape optimized solution with multiple constraints. The parameters The overall and baseline shape of the present optimization of MOGA are listed in Table 1. is shown in Fig.2, and calculation condition is shown in Table 2. The turbine has two stages, and the first stage rotor Flow Direction is operated in supersonic condition. Figure 3 shows the result of entropy rise of the total stage CFD result. The calculation is at steady condition with a mixing-plane model. The other calculation conditions, such as boundary Nozzle 1st Rotor Stator conditions and turbulence model are the same as the 2nd Rotor optimization CFD which will be shown later. According to Fig.3, entropy rise of the first stage is the largest, therefore, this stage is selected as an optimization object. The original blade has two-dimensional blade design, however, the blade shape is changed three dimensionally during the optimization process. The turbine performance is expected to be improved by this three dimensionalized blade design. Fig.2 Baseline shape and grid. The first rotor is selected as an optimization baseline shape CFD Setting As a CFD solver, the commercial code FLUENT 6.3.29 1 was used. Presently, Mach number in the turbine is 0.9 considered to be not so high, thus the compressible SIMPLE 0.8 algorithm was applied with the Pressure-Velocity coupling 0.7 method. For the advection scheme, second order upwind 0.6 scheme was applied. 0.5 Boundary conditions are important for appropriate 0.4 optimization, since the operating point may change during 0.3 0.2 the optimization process. Presently, mass flow rate, total 0.1 temperature and flow angle is set to be constant, and Entropy /Entropy Total Entropy Rise Rise 0 constant static-pressure condition was applied at the outlet Nozzle 1st Rotor Stator 2nd Rotor boundary condition. For the inlet velocity and temperature Fig. 3 Entropy rise of each stage and outlet static-pressure distribution, CFD result of total The entropy rise is normalized by total stage entropy rise. stage calculation was used. The Realizable k-ε model was applied as turbulence model, since the calculated result show the best agreement between experimental results. These conditions are also listed in Table 2. Table 2 Computational conditions Air Blade Surface Control Points Operating Fluid •Radial Position (Test Rig Condition) •Axial Position Rotation Speed 14000 rpm Mass Flow, total Inlet Boundary Temperature and flow Condition angle are fixed Outlet Boundary Static pressure is fixed Conditioin Leading / Trailing Edge Shape Total Design Variables : 58 •Curvature Radius Space Accuracy 2nd Order Upwind •Rotation •Radial Position Pressure-Velocity •Axial Position (Except Hub Surface) Compressible SIMPLE Coupling Fig.4 Control points of the design variables Turbulence Model Realizable k-e DESIGN PROBLEM The most important objective of the turbo-pump turbine is to OPTIMIZED RESULTS generate torque to drive the pumps with lower fluid loss. In Design Tradeoff addition, the matching of the following stage is also Figure 5 shows the plots of each objective functions of important from a viewpoint of the total turbine performance. optimization, namely, axial horsepower, entropy rise and As a result, the following three points are selected as next stage AOA. Each value is normalized by the baseline objective functions. shape result. The maximum improvement of z Axial horsepower [Axial-Horsepower]: Maximize axial-horsepower is about 8% increase, and entropy-rise and z Entropy rise within the stage next stage AOA are 30% and 40% reduction, respectively. [Entropy Rise]: Minimize According to Fig.5, it seems that there is a strong correlation z Angle of attack(AOA) of the next stage between axial horsepower and entropy rise, and a weak correlation between next stage AOA and axial horsepower. [Next Stage AOA]: Minimize However, it is difficult to clarify the relation between design Figure 4 shows control points of the design variables. variables and objective functions by these two-dimensional There are 8 control points in each hub, mean and tip blade plots. In order to know tradeoff information in section, and each control point moves to the axial and multi-objective optimization, Obayashi[6] proposed to use circumferential directions, except the leading and trailing Self-Organizing Map (SOM). The SOM projects edge control points at the hub. In addition to these two multi-dimensional information to two-dimensional surface, directional movements, scaling and rotating movements and can show tradeoff information more clearly. In addition were applied to the leading and trailing edge control points. to SOM visualization, correlation function is used to reveal The total design variables are 58. For the shape deformation, design tradeoff tendency. The correlation function Corr grid morphing software SCULPTOR1.8.7 was used. The shows the tendency of similarity between two data arrays. If grid morphing technique has several advantages as follows: the absolute value of the correlation function is large, one is that complicated grid re-generation method is not correlation between the selected two arrays is strong. And its necessary, and this method only needs initial grid generation sign shows tendency. and definition of the control points. The other is a system generality, since shape optimization can be carried out only 1 by defining morphing control points. 0.8 Constraint functions are often considered in optimization 0.6 0.4 problem, however, the present optimization is set to be 0.2 constraint free. 0 -0.2 1.4 Dominated solutions -0.4 Baseline -0.6 1.2 -0.8 Correlation Function 1 -1 Axial B.H.P. Axial B.H.P. Entropy Rise 0.8 vs vs vs r te Entropy Rise Nxst Stage AOA Next Stage AOA et 0.6 B Optimum Point 0.4 Optimum Point Optimum Point Parato solutions Relative Entropy Rise 0.2 0 0.9 0.95 1 1.05 1.1 Relative Axial-Horsepower 2.5 2 Baseline Dominated solutions Axial Entropy Rise Next Stage Horsepower AOA 1.5 Fig.6 Correlation function (upper) and SOM 1 (lower) of the objective functions 0.5 r te Relative NextRelative Stage AOA et Parato solutions B Figure 6 shows SOM and correlation functions of objective 0 0.9 0.95 1 1.05 1.1 functions. According to the Fig. 6, strong tradeoff can be Relative Axial-Horsepower observed between the axial horsepower and the entropy rise, Fig.5 Plots of dominated and parato solutions and the axial horsepower and the next stage AOA. On the has little influence to each objective function contrary, correlation between the entropy rise and the next stage AOA is weak since the correlation function between Table3 Design variables which have large correlation these two objective functions is small.