The lack of established optimal design guidelines for turbomachinery operating in the nonideal flow regime (e.g., organic Rankine cycle turbines, ${\mathrm{CO}}_2$ compressors, compressors for refrigeration systems) demands for effective and efficient automated design methods. Past research work focused on gradient-free methods applied to computational fluid-dynamic simulations. The application of the adjoint method is a cost-effective alternative as it enables gradient-based optimization irrespective of the number of design variables. This paper presents the application of a fully turbulent unsteady adjoint method for the automated design of multirow turbomachinery partly operating in the nonideal flow regime. The method therefore allows for the solution of constrained unsteady fluid-dynamic optimization problems, in which the thermodynamic properties of the working fluid need to be modeled by means of complex equations of state. The optimal designs computed with unsteady simulations obtained with the harmonic balance method are then compared with optimal design resulting from mixing-plane simulations. The method is applied to the optimization of 1) a two-dimensional turbine cascade subject to time-varying inlet conditions, and 2) a two-dimensional turbine stage of an organic Rankine cycle power system. The results demonstrate the importance of computing fluid properties using accurate thermodynamic models and of using unsteady simulations for shape optimization of these machines.

在非理想流动状态下运行的涡轮机械缺乏既定的最佳设计指南（例如，有机朗肯循环涡轮机， ${\mathrm{二氧化碳}}_2$压缩机、制冷系统压缩机）需要有效和高效的自动化设计方法。过去的研究工作侧重于应用于计算流体动力学模拟的无梯度方法。伴随方法的应用是一种具有成本效益的替代方法，因为它可以实现基于梯度的优化，而与设计变量的数量无关。本文介绍了一种完全湍流非定常伴随方法在非理想流态下部分运行的多排涡轮机械自动化设计中的应用。因此，该方法允许求解受约束的非定常流体动力学优化问题，其中需要通过复杂的状态方程对工作流体的热力学特性进行建模。然后将使用谐波平衡方法获得的非稳态模拟计算的最佳设计与混合平面模拟产生的最佳设计进行比较。该方法应用于1）受时变入口条件影响的二维涡轮叶栅，和2）有机朗肯循环电力系统的二维涡轮级的优化。结果证明了使用精确的热力学模型计算流体特性和使用非定常模拟对这些机器进行形状优化的重要性。和2)有机朗肯循环动力系统的二维涡轮级。结果证明了使用精确的热力学模型计算流体特性和使用非定常模拟对这些机器进行形状优化的重要性。和2)有机朗肯循环动力系统的二维涡轮级。结果证明了使用精确的热力学模型计算流体特性和使用非定常模拟对这些机器进行形状优化的重要性。