Adjoint-based design optimization of a Kenics static mixer

Abstract

Mixing processes are important in many applications like food processing or in chemical reactors. Achieving homogeneous mixtures over short distances with a small pressure drop is a challenge. Kenics static mixers usually provide a good balance between pressure drop and mixing quality. Nevertheless, little attention has been paid to the use of this mixing device in mixing gases, and consequently relatively large pressure drops are obtained. In this paper, the discrete adjoint method is used to obtain optimized Kenics static mixer designs with a negligible increase in pressure drop. First, a framework of a composition-dependent model based on the ideal gas mixing laws for thermochemical properties is implemented and coupled to the existing discrete adjoint solver within SU2, which is an open-source software suite for multiphysics simulations and design optimization. Subsequently, in order to identify the key geometrical parameters that affect the pressure drop in the mixer, numerical simulations are performed for different aspect ratios, blade thicknesses, and Reynolds numbers. These results are compared with available simulations and correlations reported in the literature, showing good agreement. These simulations indicate that reducing the aspect ratio and increasing the blade thickness enhance the mixing process in the mixing units. However, a substantial increase in pressure drop is observed. The results of the parameter study are used as a starting point to optimize the blade designs inside the Kenics static mixer using a discrete adjoint approach. The objective is to minimize the variance of the mass fraction at the outlet, which is a measure of mixture homogeneity, without substantially increasing the pressure drop along the mixing device. The results indicate that an optimized design can be obtained with a negligible increase in pressure drop, highlighting the capabilities of the discrete adjoint design approach as an optimization tool for mixing devices.