Investigation of chaotic mixing in laminar fluid systems by the use of computational fluid dynamics

Abstract

This work presents significant development into chaotic mixing induced through periodic boundaries and twisting flows. Three-dimensional closed and throughput domains are shown to exhibit chaotic motion under both time periodic and time independent boundary motions, A property is developed originating from a signature of chaos, sensitive dependence to initial conditions, which successfully quantifies the degree of disorder withjn the mixing systems presented and enables comparisons of the disorder throughout ranges of operating parameters, This work omits physical experimental results but presents significant computational investigation into chaotic systems using commercial computational fluid dynamics techniques. Physical experiments with chaotic mixing systems are, by their very nature, difficult to extract information beyond the recognition that disorder does, does not of partially occurs. The initial aim of this work is to observe whether it is possible to accurately simulate previously published physical experimental results through using commercial CFD techniques. This is shown to be possible for simple two-dimensional systems with time periodic wall movements. From this, and subsequent macro and microscopic observations of flow regimes, a simple explanation is developed for how boundary operating parameters affect the system disorder. Consider the classic two-dimensional rectangular cavity with time periodic velocity of the upper and lower walls, causing two opposing streamline motions. The degree of disorder within the system is related to the magnitude of displacement of individual particles within these opposing streamlines. The rationale is then employed in this work to develop and investigate more complex three-dimensional mixing systems that exhibit throughputs and time independence and are therefore more realistic and a significant advance towards designing chaotic mixers for process industries. Domains inducing chaotic motion through twisting flows are also briefly considered. This work concludes by offering possible advancements to the property developed to quantify disorder and suggestions of domains and associated boundary conditions that are expected to produce chaotic mixing.