Mixing mechanisms in the view of mixing indicators: from passive-scalar mixing to variable-density mixing

Abstract

<abstract><p>Mixing is the basis of stable and efficient combustion in air-breathing power systems, and it is also an important problem in fluid mechanics, which has been extensively studied from various perspectives. The purpose of this review is to investigate mixing mechanisms based on two commonly-used mixing indicators, namely $ c^i $ ($ c $ refers to concentration, and $ i $ is either 1 or 2, indicating first- or second-order statistics), with a focus on passive-scalar (PS) and variable-density (VD) mixing. For PS mixing, the flow is not influenced by the mixing process. By using first-order statistics with concentration as the core, the PS mixing mechanisms on lamella structures can be described as stretching enhancing diffusion and promoting mixing. On the other hand, second-order statistics represented by the scalar dissipation rate can investigate mixing mechanisms on specific type of flow structures described by the invariants of velocity gradient tensors and the rotation of principal strain axis. As such, it has been found that strain-dominated flow structures can promote mixing, while rotation-dominated flow structures hinder it. For VD mixing, it has two distinct characteristics: flow changes due to baroclinic vorticity, and the inherent velocity divergence alters the mixing indicators. Studies using first-order statistics center on the mixing time in different types of VD flows, leading to the discovery of new phenomena. For instance, the second baroclinic vorticity can promote stretching in shock bubble interactions. Studies on second-order statistics for VD mixing have defined several mixing indicators from the component-transport equation, which have been utilized in phenomenological studies on VD mixing. This review aims to provide an overview of mixing phenomena, mixing indicators, and mixing mechanisms, and proposes research directions for understanding the mixing characteristics, flow structures, and their relationship with specific combustion phenomena particularly by second-order statistics.</p></abstract>