Quantifying mixing in flows transporting multiple scalars: New mixing metrics describing three-scalar mixing

The present work investigates mixing metrics used to quantify multi-scalar mixing in turbulent flows. Whereas existing mixing metrics, such as the correlation coefficient or the segregation parameter, are capable of quantifying mixing between two scalars of interest, they fail to capture the interactions between these scalars and the surroundings in which they mix. To overcome such limitations, new multi-scalar mixing metrics derived from the invariants of a three-scalar unmixedness tensor are proposed and then evaluated in coaxial jets transporting multiple scalars. Application of these metrics in coaxial jets with varying momentum flux ratios provides clearer insights into the influence of initial flow conditions on scalar mixing, resolving contradictions observed using other metrics. In particular, these metrics can be used to concisely quantify the mixing of one scalar with another, as well as the mixing of the individual scalars with the surroundings (or, alternately, a third scalar field). • Many flows mix multiple scalars (e.g. temperature and humidity in the atmosphere). • Current mixing metrics provide incomplete information on the mixing in such flows. • This work proposes new metrics to quantify the mixing of two scalars in a flow. • The metrics are tested in coaxial jets in which helium and temperature are mixed in air.