Tip geometry modification is frequently used to suppress the tip leakage flow in the turbine cascade however a universally beneficial tip geometry modification design has not been fully discovered. In this paper, the two-surface coupling arbitrary blade tip design method in three-dimensional physical space which satisfies the simple trigonometric function law is proposed and the mathematical parametric description is presented. The effects of different arbitrary blade tips on tip leakage flow have been studied numerically in a highly loaded axial turbine cascade. The aerodynamic performance of different tips is assessed by the tip leakage mass flow rate and the total pressure loss coefficient at the exit section. The Kriging model and genetic optimization algorithm are used to optimize the arbitrary blade tips to obtain the optimal arbitrary blade tip. Compared with the flat tip, the tip leakage mass flow rate is decreased by 10.57% and the area-average total pressure loss coefficient at the exit section is reduced by 8.91% in the optimal arbitrary blade tip.
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