Mixing enhancement in binary fluids using optimised stirring strategies

Abstract

Abstract

Fluidic shaping of optical components

“…To showcase the efficacy and applicability of the direct-adjoint framework, we present three distinct optimization cases: (i) optimization of the cross-sectional shape of the moving stirrers, (ii) optimization of the velocity along a circular path of the shape-modified stirrers (from step (i)) and (iii) compound and simultaneous optimization of both the shape and path velocity for both stirrers. The constraints include energy, velocity and energy bounds for any path velocity optimization (see, e.g., Eggl and Schmid, 2020a), area-conservation and untwisting for the shape optimization (see, e.g. Eggl and Schmid, 2020b) and both sets of constraints for the third case.…”

“…The constraints include energy, velocity and energy bounds for any path velocity optimization (see, e.g., Eggl and Schmid, 2020a), area-conservation and untwisting for the shape optimization (see, e.g. Eggl and Schmid, 2020b) and both sets of constraints for the third case. In all cases presented here, we achieve enhanced mixing and a significant decrease in the mix-norm at the end of the optimization horizon, attesting to the effectiveness of an objective optimization approach to reach a more homogeneous mixture through unorthodox stirrer designs and improved stirring protocols.…”

“…In addition, we have to specify the total amount of energy 0 exerted by the stirrers, as well as the limits on the stirrers' velocities, , , and accelerations, , . For an argument for this set of constraints, the reader is referred to Eggl and Schmid (2020b). The full optimization problem can then be stated as…”

“…In this manner, we produce 'hydrodynamic' stirring elements, beyond the two obvious solid stirrers. As a consequence of this degree of freedom, we have to impose additional bounds on the energy, velocity and acceleration of the stirrers to avoid divergences in the optimization scheme and, instead, arrive at a converged and realizable mixing strategy (see Eggl and Schmid (2020b) for details). But even with these bounds in place, we achieve a dramatic decrease in the mix-norm, indicating a superior mixing result.…”

Frequency response analysis of a (non-)reactive jet in crossflow

“…Extensions to nonlinear systems have allowed the analysis of high-lift airfoils, mixing enhancement and minimal seeds for transition to turbulence (Schmidt et al. 2013; Foures, Caulfield & Schmid 2014; Rabin, Caulfield & Kerswell 2014; Eggl & Schmid 2020), among many other applications. Recently, the same techniques have also been applied to reactive flows, either by aiding the adaptive mesh refinement in steady-state Reynolds-averaged Navier–Stokes calculations (Duraisamy & Alonso 2012), or in detailed simulations of one- and two-dimensional laminar configurations with decoupled reactive equations (Braman, Oliver & Raman 2015).…”