Optimization of mixing in stirred, binary fluids

Mixing is a process that is present in a wide-range of industrial applications, and optimization of mixing under time and energy constraints is a research area of great interest. We employ a computational framework based on nonlinear direct-adjoint looping for the optimization of mixing processes in a binary fluid system. By optimizing the stirring protocol of two cylindrical stirrers on circular paths, we seek to improve the mix-norm of the binary fluid system and ultimately generate a more homogeneous mixture. A Fourier-based pseudo-spectral numerical approach coupled to a Brinkman penalization of the immersed bodies is used to solve the direct and adjoint problem. The extracted gradient information is then processed in an optimization algorithm to gradually improve the stirring strategy. This optimization is attempted while observing a prescribed finite time horizon and an upper bound on the expended control energy.

Several cases of mixing enhancement, covering different time horizons and energy budgets, will be presented to demonstrate the effectiveness, efficiency and flexibility of the computational direct-adjoint approach. In all cases, significant improvements in mixing can be observed.