Three-objective optimization of micromixer with Cantor fractal structure based on Pareto genetic algorithm

Abstract

Abstract This paper introduces the multi-objective optimization process of the micromixer with Cantor fractal baffle. The combination of fractal principle and multi-objective optimization is a main feature of this article. The three-dimensional Navier–Stokes equation is used to numerically analyze the fluid flow and mixing. The proxy modeling and Pareto genetic algorithm are used to optimize the shape of the Cantor fractal micromixer. We choose three parameters related to the geometry of the Cantor fractal baffle as design variables, and choose the mixing index, pressure drop and mixing sensitivity at the outlet of the micromixer as three objective functions. For the parameter study of the design space, the Latin hypercube sampling (LHS) method is used to select design points in the design space. We use response surface function (RSA) as a proxy modeling to approximate the objective function. A multi-objective genetic algorithm is used to find the Pareto optimal solution. K-means clustering is used to classify the optimal solution set, and then select representative design variables from it. The representative optimal design is analyzed by using numerical analysis method. The optimization results show that the Cantor fractal baffle is beneficial to promote faster mixing of the two fluids. At the same time, the suitable goal can be weighed in the Pareto optimal solution set. The mixing index and mixing sensitivity are increased by 13.55 and 3.91 %, respectively, compared with the reference design of the micromixer. And we have also proved that this multi-objective optimization method is applicable to any Reynolds numbers (Res).