During the operation of supercritical CO${}_2$ (sCO${}_2$) radial inflow turbines (RITs), sonic conditions may happen, which will decrease their efficiency. Non-standard design geometries are needed to reduce the losses. However, modifying the turbine geometry is a challenge, especially as the optimum shape may be non-intuitive; commercial computational fluid dynamics (CFD) software is not friendly towards automation by surrogate scripts, and the traditional design method for blade passage shape is not suited to the optimisation of aerodynamic turbine design. Hence, in this study, a stator nozzle for a 120 kW sCO${}_2$ RIT, whose geometries are obtained from in-house preliminary design code TOPGEN${}^{\mathrm{t}\mathrm{m}}$, has been optimised with a modularised geometry optimiser. To parametrise the geometry, a parametrised stator mesh generator based on a meridional streamline is developed. Bulk CFD simulations are carried out with OpenFOAM${}^{\circledR }$, to form a Pareto front with a vector of 14 variables. Three final stators have been selected: they are the optimised Mach number distribution (${\sigma }_M$), the optimised outlet flow angle distribution (${\sigma }_{\alpha }$) and a compromise case. The the outlet boundary properties of these stators are extracted and discussed. The optimised ${\sigma }_M$ case has the shortest divergent nozzle, returns the best ${\sigma }_M$ and the least loss; the optimised ${\sigma }_{\alpha }$ case has the longest divergent nozzle and returns a better-uniformed outlet flow; the compromise case has the medium length of the divergent case. All these stators have fixed mass flow rates to allow de-coupling of the upstream system from the rotor. This study will ultimately benefit the development of the sCO${}_2$ power cycle.

超临界CO运行过程中${}_{\mathrm{2个}}$（二氧化碳${}_{\mathrm{2个}}$) 径流式涡轮机 (RIT)，可能会发生声波条件，这会降低其效率。需要非标准设计几何形状来减少损失。然而，修改涡轮机的几何形状是一项挑战，尤其是当最佳形状可能不直观时；商业计算流体动力学（CFD）软件对代理脚本的自动化不友好，传统的叶片通道形状设计方法不适合气动涡轮设计的优化。因此，在这项研究中，用于 120 kW sCO 的定子喷嘴${}_{\mathrm{2个}}$RIT，其几何形状来自内部初步设计代码 TOPGEN${}^{\mathrm{吨}\mathrm{米}}$，已使用模块化几何优化器进行了优化。为了参数化几何结构，开发了基于子午流线的参数化定子网格生成器。使用 OpenFOAM 进行批量 CFD 模拟${}^{\circledR }$, 以形成具有 14 个变量的向量的 Pareto 前沿。选择了三个最终定子：它们是优化的马赫数分布（${\sigma }_{米}$), 优化的出口流角分布 (${\sigma }_{\alpha }$) 和折衷方案。提取并讨论了这些定子的出口边界特性。优化的${\sigma }_{米}$案例有最短的发散喷嘴，回报最好${\sigma }_{米}$损失最少；优化的${\sigma }_{\alpha }$案例有最长的发散喷嘴并返回更均匀的出口流量；妥协案例的长度与发散案例的长度中等。所有这些定子都具有固定的质量流量，以允许上游系统与转子分离。这项研究最终将有利于上合组织的发展${}_{\mathrm{2个}}$电源周期。