Multi-Objective Optimization of Three-Dimensional Blade Shape for an Axial Compressor Rotor in Transonic Stage

A three-dimensional (3D) blade design method for an axial compressor transonic stage to optimize the aerodynamic performance is presented in this paper. The blade is defined by three profiles and a radial stacking line. Each profile is a multi circular arc (MCA), and the stacking line is defined as a B-spline curve with six design parameters. To ensure the off-design performance, a multi-objective genetic algorithm (MOGA) is applied. The objective functions are the efficiency, shock position and leading edge pressure difference at the design point. Because shock position and leading edge pressure difference can evaluate the potential for stalling, the method can generate blades with a wide operating range with just one performance prediction. This method is applied in a transonic blade design. The result shows that the efficiency of the optimized blade at the design point is increased and the operation range is expanded compared with the original blade. NOMENCLATURE C Chord length [mm] DPL Normalized pressure difference at leading edge [-] G Mass flow rate [kg/s] H Blade height [mm] i Incidence angle [deg] Pt Total pressure [MPa] S Slope of stacking line [-] Tt Total temperature [degC] X Axial coordinate [mm] Xm Maximum thickness position [%] Xc Combination position of arcs [%] Xs Shock position [%] Y Circumferential coordinate [mm] Specific heat ratio [-] Efficiency [%] Pressure ratio [-] Central angle of arc [deg] c Centrifugal stress [MPa] g Gas bending stress [MPa] -Subscripts1 Inlet of the cascade 2 Outlet of the cascade d Design point h Blade hub t Blade tip INTRODUCTION In recent years, use of highly loaded axial compressor blades with high efficiency is essential to achieve both performance improvement and cost reduction. To apply these blades for transonic stages, the shock wave on the blade surface should be alleviated because a high load causes stronger shock wave. For reduction of shock loss, control diffusion airfoils and 3D blades were developed. These performances were studied in detail by Denton and Xu (2002) and Bonaiuti et al. (2007). Recently, Iwatani et al. (2007) and Zheng et al. (2010) studied the performance of a sweep blade, which was a kind of 3D blades. They showed that an S-shaped stacking line could reduce the shock loss. However, adopting sweep blades will increase the total design time because more design parameters are needed than for conventional blades. To reduce design time, a lot of researchers have carried out optimization of 3D blades using computational fluid dynamics (CFD). In these studies, multi-objective optimizations were used in order to achieve more than two design goals. For example, Li et al. (2006) applied a new geometry deformation approach called ‘aerodynamic mode shape’ in an aero-mechanical optimization to reduce the number of design parameters. Luo et al. (2009) used the Multi-objective Differential Evolution (MDE) algorithm as an optimizer to find the Pareto solutions of an aero-mechanical problem easily. However, most of the design goals of these researchers were usually for aerodynamic performance at the design point, blade stress and vibration. Few researchers have used aerodynamic performance at off-design points as the design goal of the optimization, because additional performance calculations at off-design points should be carried out. In this paper, a 3D blade design method to optimize the aerodynamic performance at both the design point and off-design points by only one calculation at the design point is presented. This method is applied in an aerodynamic design of a blade, for which specifications are almost the same as the first stage rotor of a conventional axial compressor. To validate the method, optimized blades are compared with a blade optimized by the method just with an objective function related to the performance at the design point. THREE-DIMENSIONAL BLADE DESIGN SYSTEM Flow diagram The flow diagram of the developed system is shown in fig.1. In this system, the optimization procedure consists of the blade definition, structural analysis, flow analysis, and evaluation of the objective functions by the optimization algorithm. All the processes are done using the optimization support program modeFRONTIER 4.2. 0. The optimization is finished when the generation number N reaches the maximum generation number Nmax defined in advance. International Journal of Gas Turbine, Propulsion and Power Systems December 2013, Volume 5, Number 1 Presented at International Gas Turbine Congress 2011 Osaka, November 13-18, Osaka, Japan, IGTC2011-0055 Review completed on December 25, 2013 Copyright © 2013 Gas Turbine Society of Japan