Multiobjective Optimization of Circumferential Casing Grooves for a Transonic Axial Compressor

R ECENTLY, casing treatments using grooves or slots have been applied to axial compressors to prevent surge and enhance stall margin (SM). However, this is accompanied by a loss near the blade tip region, which leads to a decrease in efficiency of the axial compressor. Therefore, a systematic design of the casing treatment using multiobjective optimization techniques in conjunction with a flow analysis using three-dimensional Reynolds-averaged Navier– Stokes equations (RANS) was used to investigate a compromise between the SM and the efficiency of the compressor. Various types of grooves have been suggested by many researchers, and it has been reported that using grooves increases SM by delaying stall. Huang et al. [1] studied the effects of the configuration, width, and depth of circumferential groove casing treatment on SMby numerical analysis, and suggested that the stall mechanism was substantially influenced by tip clearance.Muller et al. [2] studied the effects of the number and depth of the grooves on SM by threedimensional numerical analysis. Houghton and Day [3] examined the effect of grooves on rotor outflow blockage, and the near casing flowfield was studied using experimental and computational methods. Many engineering designs involve multiple disciplines and simultaneous optimization of multiple objectives related to each discipline. These design problems, usually known as multiobjective problems, require simultaneous consideration of all objective functions to optimize the system. The nondominated sorting genetic algorithm (NSGA-2) by Deb [4] generates a Pareto-optimal solution using an evolutionary algorithm. Shape optimization of a hydraulic turbine diffuser was performed with multiple objectives by Marjavaara et al. [5]. Kim et al. [6] reported a multiobjective optimization of a centrifugal compressor impeller with four design variables that defined the impeller hub and shroud contours in meridian terms. Samad and Kim [7] reviewed the performance of the surrogate models applied to turbomachinery design optimization, and introducedmulti and single-objective optimization techniques in conjunction with three-dimensional RANS analysis. In this study, based on previous work [8] for a single-objective optimization, a hybridmultiobjective evolutionary algorithm (hybrid MOEA) [9] coupledwith the Kriging (KRG)model [10] was applied to obtain a global Pareto-optimal front for the design of circumferential casing grooves in an axial compressor with NASARotor 37 [11]. To the best of the authors’ knowledge, no previous study has reported on the optimization of the design of circumferential casing grooves. The present multiobjective optimization was motivated to provide an efficient tool for the design of an axial compressor with circumferential casing groove treatment, and it is expected for designers to meet their design requirements with regard to the SM and adiabatic efficiency from the Pareto-optimal designs (PODs) obtained in this work. Numerical solutions at the selected design points were obtained by three-dimensional RANS analysis. The shape of the grooves was optimized by considering width and depth as designvariables in order to improve the SM and the peak adiabatic efficiency. The tradeoff between these two competing objective functions is explored and discussed with respect to the design variables.