Mie scattering measurements of scalar probability density functions in compressible mixing layers

Pianar Mie scattering from condensed ethanol droplets has been employed in an investigation of the probability density functions of passive scalar transport in compressible mixing layers. Ensembles of digital images were collected at two different flow conditions with relative Mach numbers of 0.63 and 1.49, respectively. The measured total mixed fluid probability for the case of product formation of ethanol droplets within the mixing layer was used to determine the accuracy of the scalar transport PDFs. A simple model for the nucleation, and subsequent growth, of ethanol droplets as a function of mixture fraction in the core of a large scale structure permitted the evaluation of the range of mixture fractions that were within the sensitivity limits of detection. Integration of the scalar transport PDF over this limited range of mixture fractions resulted in a close match of the estimated total mixed fluid probability in the mixing layer with the product formation values. The form of the PDFs themselves clearly exhibits a translating peak probability of preferred mixture fraction across the mixing layer, in contrast to a number of previous low Reynolds number experiments. The translating PDF form is concluded to be indicative of fully developed compressible mixing layers. Damkohler number estimates range from ‘slow chemistry’ to ‘fast chemistry’ for varying mixture fractions, offering an explanation for an observed bimodal variance profile in the product formation case.