Shape optimisation of stirring rods in mixing binary fluids

TL;DR

This paper develops a computational framework using nonlinear direct-adjoint looping to optimize the shape and motion of stirrers for improved mixing efficiency in binary fluids, demonstrating the discovery of non-intuitive, highly effective stirrer geometries.

Contribution

It introduces a Fourier-based shape and motion optimization method for stirrers in mixing processes, incorporating a Brinkman-penalisation technique and adjoint sensitivity analysis.

Findings

Non-intuitive stirrer shapes significantly enhance mixing efficiency.

The framework effectively optimizes stirrer geometry and motion within constrained time and velocity.

Optimized stirrers outperform traditional designs in mixing performance.

Abstract

Mixing is an omnipresent process in a wide-range of industrial applications, which supports scientific efforts to devise techniques for optimising mixing processes under time and energy constraints. In this endeavor, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the non-linear Navier-Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman-penalisation technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is in turn used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilise a Fourier-based approach for parameterising and optimising the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We consider a restricted optimisation space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes are found which produce significantly enhanced mixing efficiency.