A gradient-based framework for maximizing mixing in binary fluids

Abstract

A computational framework based on nonlinear direct-adjoint looping is presented for optimizing mixing strategies for binary fluid systems. The governing equations are the nonlinear Navier-Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a spectral Fourier-based method. The stirrers are embedded in the computational domain by a Brinkmanpenalization technique, and shape and path gradients for the stirrers are computed from the adjoint solution. Four cases of increasing complexity are considered, which demonstrate the efficiency and effectiveness of the computational approach and algorithm. Significant improvements in mixing efficiency, within the externally imposed bounds, are achieved in all cases.

Identifying vortical network connectors for turbulent flow modification

“…Multiple pulses of perturbation under-performs compared with even the single connector-based perturbation. According to the studies on mixing enhancement using stirrers (Aref 1984; Eggl & Schmid 2018), we expect the perturbation to achieve better mixing. The present results are in agreement with these studies.…”

Efficiency of laminar and turbulent mixing in wall-bounded flows

“…It is interesting in the light of the present investigation to mention the recent study [26], where optimization algorithms are applied to determine the most efficient stirring protocols in a setup similar to the one in the present study. In their work, the authors successfully optimize the mixing speed, changing the rod shape and the trajectory.…”

Mixing enhancement in binary fluids using optimised stirring strategies

“…The above formalism allows the efficient treatment of objects moving through a background grid on which the motion of the surrounding fluid is described. Details of this approach and its numerical implementation can be found in Eggl & Schmid (2018). The set-up shown in (2.1 c ) imposes no-slip velocity boundary conditions on the stirrers and no-flux Neumann conditions for the passive scalar on the solid bodies.…”

“…While mathematically equivalent, the projection technique is easier to implement and presents more flexibility in treating inequality constraints. Details of the numerical implementation of this procedure can be found in Eggl & Schmid (2018).…”