Compared with the traditional actuator, the fluid momentum controller actuator based on magnetohydrodynamics (MHD) has some unique advantages and characteristics. In this paper, a method is proposed for the shape optimization of fluid momentum ring cross section. Based on the engineering situation, this article proposes a mathematical model of angular momentum that can be used for analytical calculations. Second, the two shapes obtained are unified and mathematically expressed in terms of maximum power and minimum resistance, respectively. Finally, the particle swarm algorithm is used to optimize the parameters of the proposed shape in combination with finite element method (FEM). Compared with the common rectangular section scheme, the attitude adjustment performance of fluid momentum ring can be effectively improved. Specifically, for the same area of cross section, the fluid momentum rings with the proposed shape provide the angular momentum values that exceed those of the rectangular shape by 14%-17% for the cases considered. This method avoids the huge computation of computational fluid dynamics and multidisciplinary topology optimization.

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