Conditional statistics in a planar liquid jet with a second-order chemical reaction

Conditional statistics, conditioned on mixture fraction, are experimentally investigated in a planar liquid jet with a second-order isothermal chemical reaction A+B→R. Reactants A and B are contained in the jet and ambient flows, respectively, and are supplied into the test section under the non-premixed condition. Streamwise velocity, mixture fraction and concentrations of all reactive species are simultaneously measured by using an I-type hot-film probe and an optical fibre probe based on light absorption spectrometry. The cross-streamwise profiles of conditional mean concentrations and conditional mean reaction rate show that the conditional mean concentrations and the conditional mean reaction rate near the jet exit change with the cross-streamwise position, whereas they are independent of the cross-streamwise position in the downstream regions. On the jet centreline, the conditional mean reaction rate has a peak value on the condition that the conditional mean concentration of product R has a peak value. A comparison between the conditional mean reaction rate and the covariance of conditional concentration fluctuations shows that the covariance of conditional concentration fluctuations is so small that a first moment closure model for the conditional mean reaction rate is valid. The conditional mean streamwise velocity is almost linear to the mixture fraction for small mixture fraction fluctuations. The conditional scalar dissipation rate is calculated from the budget of the conditional moment closure equation. The results show that the conditional scalar dissipation rate has a single peak value in the upstream region, whereas in the downstream region, it has two peaks for the large and small mixture fraction values. The conventional mean scalar dissipation rate is calculated from the probability density function of the mixture fraction and the conditional scalar dissipation rate. The conventional mean scalar dissipation rate on the jet centreline decreases in the downstream direction as (x∗)-2.9 (where x∗ is the distance from the virtual origin), which is almost the same as that expected from scaling arguments.