Mixing metrics for turbulent multi-scalar flows*

The mixing of scalars (i.e., temperature, chemical species concentration, etc.) in turbulent flows plays a vital role in many engineering and scientific fields, examples of which include combustion, environmental pollution dispersion, oceanography, and atmospheric science. In applications involving only a single scalar, mixing may be quantified using mixing metrics such as the unmixedness, a non-dimensional parameter characterizing the scalar variance. (Danckwerts 1952; Dimotakis and Miller 1990). However, approaches to quantify the degree of mixing in flows transporting multiple scalars are less developed. Using both theoretical arguments and experimental data obtained from turbulent coaxial jets in which two scalars are mixed, we investigate the suitability of commonly employed mixing metrics – such as the correlation coefficient, segregation parameter, and unmixedness – in describing multi-scalar mixing. We find that the aforementioned mixing metrics are limited in their ability to fully describe the state of mixing in flows in which more than one scalar is present, necessitating development of a new multi-scalar mixing metric.