**Pavlos Alexias †,\* and Kyriakos C. Giannakoglou**

Parallel CFD & Optimization Unit, School of Mechanical Engineering, National Technical University of Athens, Irroon Polytechniou 9, Zografou 15780, Greece; kgianna@mail.ntua.gr


Received: 28 November 2019; Accepted: 6 January 2020; Published: 8 January 2020

**Abstract:** In this paper, the continuous adjoint method is used for the optimization of a static mixing device. The CFD model used is suitable for the flow simulation of the two miscible fluids that enter the device. The formulation of the adjoint equations, which allow the computation of the sensitivity derivatives is briefly demonstrated. A detailed analysis of the geometry parameterization is presented and a set of different parameterization scenarios are investigated. In detail, two different parameterizations are combined into a two-stage optimization algorithm which targets maximum mixture uniformity at the exit of the mixer and minimum total pressure losses. All parameterizations are in conformity with specific manufacturability constraints of the final shape. The non-dominated front of optimal solutions is obtained by using the weighted sum of the two objective functions and executing a set of optimization runs. The effectiveness of the proposed synthetic parameterization schemes is assessed and discussed in detail. Finally, a reduced length mixer is optimized to study the impact of the length of the tube on the device's performance.

**Keywords:** mixing devices; two-phase flows; shape optimization; continuous adjoint method
