The continuous adjoint method is formulated and utilized for the optimization of a static mixing device. The CFD tool used for the simulations is based on a two-phase model governing flows of two miscible fluids. The formulation of the corresponding continuous adjoint problem is presented and the computed gradients are utilized in an optimization loop. In specific, a multi-objective optimization problem is formulated and solved for maximum mixture uniformity at the outlet and minimum total pressure losses inside a static mixing device. The weighted sum of these two quantities of interest is the objective function to be minimized by solving a single-objective problem. Through the solution of a number of optimization problems, with different weights each, the Pareto front of optimal solutions is computed. Two optimization approaches are employed taking the manufacturability of the final shape into consideration, giving rise to different optimal designs to be discussed and compared. Differences in the efficiency and the optimal shapes between the two approaches are thoroughly discussed and compared.

中文翻译：

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使用连续伴随的两相混合模型优化静态混合装置

制定了连续伴随方法，并将其用于优化静态混合设备。用于仿真的CFD工具基于控制两种可混溶流体流动的两相模型。提出了相应的连续伴随问题的公式，并在优化循环中利用了计算出的梯度。具体而言，制定并解决了一个多目标优化问题，以实现出口处最大的混合物均匀性和静态混合设备内部的最小总压力损失。这两个感兴趣的量的加权和是通过解决单目标问题而要最小化的目标函数。通过对每个具有不同权重的多个优化问题的求解，可以计算出最优解的帕累托前沿。考虑到最终形状的可制造性，采用了两种优化方法，从而产生了需要讨论和比较的不同优化设计。彻底讨论和比较了两种方法之间效率和最佳形状的差异。