Scalar mixing optimisation in 3D pulsatile channel flow

The mixing of passive scalars in energetic flows is a complex and important process, and have many applications in industrial and environmental contexts. In our study, we aim to utilise forcings that can be physically achieved in realistic situations to control the mixing process of scalars in three-dimensional Poiseuille flow. We note that pulsatile channel flow has recently been shown to exhibit destabilising effects at certain frequencies, with the strongest destabilisation seen at Womersley number Wo ≃ 7 (see Pier & Schmid (2017), Kern et al. (2021)). Floquet analyses are used to identify the most unstable eigenvalues for flows at different Womersley numbers. The associated eigenfunctions could then be used as the initial conditions for DNS simulations. Mixing efficiency for a range of oscillation parameters is investigated, and the effect of different nonlinear pulsatile flow regimes (namely the ‘ballistic’ and ‘cruising’ regimes) on the scalar mixing process is discussed. Through the use of variational “direct-adjoint looping” methods, it is also possible to potentially identify “optimal” initial perturbations for the homogenisation of the scalar field for a given forcing mechanism.