Adjoint-based mixing enhancement for binary fluids

Abstract

Mixing is a fundamental fluid process that dominates {a} great many natural phenomena and is present in a wide variety of industrial applications. Therefore, studying the characteristics and optimisation of this process may lead to a significant impact in many fields. This thesis presents an analytical and computational framework for optimising fluid mixing processes using embedded stirrers based on a non-linear direct-adjoint looping approach. The governing equations are the non-linear Navier-Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a Fourier-based spectral method. Stirrers are embedded in the computational domain by a Brinkman-penalisation technique, and shape and path gradients for the stirrers are computed from the adjoint solution. The relationship between this penalisation approach and the adjoint will be examined through the derivation of a dual system of equations, and three different optimisation scenarios of increasing complexity, each focusing on different optimisation parameters, are considered. Within the limits of the parameterisations of the geometry and the externally imposed bounds, significant improvements in mixing efficiency are achieved in all cases.