Axial flow compressor blade optimization through flexible shape tuning by means of cooperative co-evolution algorithm and adaptive surrogate model

Abstract

The present study is to explore potential benefits of axial flow compressor blade optimization through a flexible tuning. Modifications of blade sectional profiles and their stacking line can control spanwise blade loading distribution, reduce shock losses, and extend operating flow range. Most previous studies focused on tuning either sectional profiles or stacking line, but little work was conducted by collaboratively varying both, which may be due to abrupt rise of optimization variables and complexity. An efficient optimization method is developed to handle highly nonlinear high-dimension blade optimization problem with simultaneous variation of both sectional profiles and stacking line. It incorporates an improved cooperative co-evolution algorithm optimizer and one-stage expected improvement based adaptive surrogate model. The former decomposes the high-dimension problem into low-dimension subproblems and they can be readily solved; the latter enables the optimizer to jump out of the local minima and conduct the aim-oriented optimal search toward global optimum. A coarse surrogate model is firstly constructed with some DOE samples but it is refined during optimization process with newly identified and evaluated samples. The model prediction accuracy is gradually improved, thus it captures the distinct features (especially global optimum) of optimization problem. Both blade sectional profiles and their spatial positions are simultaneously varied. Four sectional profiles of hub, 33% span, 67% span, and shroud are parameterized, and each is defined by a mean camber line and thickness distribution. Both of them are represented, respectively, by a third-order B-Spline curve. Spatial position of each profile varies in term of sweep and lean. Blade design optimization is conducted for Rotor67 at design flow on a single workstation of Dell 7500. Performance gains are significant: at design flow, overall efficiency and pressure ratio are increased, respectively, by 1.44 and 7.24%; off-design performances are also improved over the entire flow range.