Experimental and Computational Study of Scalar Modes in a Periodic Laminar Flow

Scalar fields can evolve complex coherent structures under the action of periodic laminar flows. This comes about from the competition between chaotic advection working to create structure at ever finer length scales and diffusion working to eliminate fine scale structure. Recently analysis of this competition in terms of spectra of eigenfunctions of the advection-diffusion equation (ADE) has proven fruitful because these spectra contain both fundamental information about how mixing processes create emergent Lagrangian coherent structure and also clues about how to optimize flows for heat and mass transfer processes in industry. While theoretical and computational studies of ADE spectra exist for several flows, experiments, to date, have focused either solely on the asymptotic state or on highly idealized flows. Here we show a coupled experimental and computational study of the spectrum for the scalar evolution of a model of an industrially relevant viscous flow. The main results are the methods employed in this study corroborate the eigenmode approach and the outcomes of different methods agree well with each other. Furthermore, this study employs a Lagrangian formalism for thermal analysis of convective heat transfer in the representative geometry to determine the impact of the fluid motion in the thermal homogenization process. The experimental/numerical methods and tools used in the current study are promising for further qualitative parameter studies of the mixing/heat transfer characteristics of many inline mixers and heat exchangers.