Mixing and chemical reactions in a turbulent liquid mixing layer

Abstract

An experimental investigation of entrainment and mixing in reacting and nonreacting turbulent mixing layers at large Schmidt number is presented. In nonreacting cases, a passive scalar is used to measure the probability density function (p.d.f.) ofthe composition field. Chemically reacting experiments employ a diffusionlimited acid-base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques.Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

Passive scalar mixing in a planar shear layer with laminar and turbulent inlet conditions

“…11,13 Further, the relatively in- variant m across the layer width, and the triple inflection point behavior of the ave profile are also consistent with previous findings. 11,13 The peak value in the mixed fluid probability, P m , is higher than observed in liquid phase studies due to the lower Sc, and is not considered to be a resolution effect. 20 Finally, the PLIF images clearly show the large-scale Kelvin-Helmholtz structures, and their persistence past the turbulent transition.…”

“…In the recent literature a significant effort has been put forth to identify the asymptotic far-field PDF shape associated with shear layer development in planar [10][11][12][13] and axisymmetric 19,28 configurations. As shown by Slessor et al, 15 and confirmed in part by this work, there does not appear to be a unique shape that is independent of inlet conditions.…”

“…Typically viewed in terms of the probability density function ͑PDF͒, either nonmarching, 10,11 where a preferred composition extends across the layer, or marching, 12 where the most probable composition varies linearly across the layer, style PDFs have been observed in planar mixing a͒ Author to whom correspondence should be addressed. Telephone: ͑608͒ 263-1684; Fax: ͑608͒ 263-9870.…”

“…In liquid mixing layers, it has been suggested that the observed shift in PDF style from nonmarching to marching with turbulent inlet conditions or higher Re ␦ is not physical but is due to measurement resolution problems. 11,13 Thus, the effect of turbulent inlet conditions on scalar mixing is somewhat uncertain.…”

The influence of Reynolds number on a plane jet

“…Likewise, Gilbrech 24 found that the asymptotic state of the mixing field occurs near Re d Ϸ 2.0 ϫ 10 4 . Koochesfahani and Dimotakis 25 used scalar images of laser-induced fluorescence at Re d = 1.75ϫ 10 3 and 2.30ϫ 10 4 to show more qualitative and well-mixed state at Re d = 2.30ϫ 10 4 relative to Re d = 1.75ϫ 10 3 . Similar results were found by Michalke,26 who found that the growth of instability waves in jet shear layers can be reduced dramatically when the Reynolds number is increased sufficiently.…”