Quantification of mixing and mixing rate from experimental observations

A new measure of mixedness, based on entropy considerations, and a related mixing rate are introduced. It is argued that the time rate of change of the mixedness is proportional to the mixing rate. The new measures are applied to experimental observations on an axisymmetric jet and an array of jets in crossflow. The concentration field of an axisymmetric jet is measured at 10 downstream locations by optical imaging of Rayleigh scattering from a laser sheet. Mixedness and mixing rate are calculated for each of the locations. In agreement with theory, the mixedness of the self-similar jet is constant along the length of the jet. The measures allow us to locate the instantaneous realization that is most typical in terms of mixedness and mixing rate. Also analyzed is the mixing of a row of jets injecting fluid into a crossflow, The jets are sufficiently close that there is significant interaction between neighboring jets. The mixedness and mixing rate were calculated. Well-mixed regions have a low mixing rate, whereas poorly mixed regions tend to mix most rapidly. The mixedness and mixing rate allow the assessment of the effectiveness of different orifice shapes in promoting rapid mixing.