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Planar laser imaging measurements of differential molecular diffusion in turbulent jets
Student: Cody Brownell (cbrownell: jhu.edu)
(Figures: imaging schematic sample images quantitative results) (Publications)
The goal of this work is to study the role of differential molecular diffusion in turbulent mixing, and to estimate its importance in turbulent diffusion flames. The inherent complexity of turbulent combustion processes makes direct modeling of flame and flow field characteristics exceedingly difficult. To simplify the analysis of non-premixed turbulent flames, a single value of molecular diffusivity is typically assumed for all species involved in a reaction. A problem with this assumption is that chemical reactions require mixing at the molecular level, where diffusive effects - and, possibly, varying diffusivities among different species - are particularly important. For example, it has been shown that the rapid diffusion of hydrogen in turbulent jet diffusion flames can cause flame structure to differ significantly from predictions that assume uniform diffusion.
In this work planar laser Rayleigh scattering yields direct measurements of differential molecular diffusion in turbulent jets. Figure 1 shows a schematic of the imaging arrangement. The 532 nm, second-harmonic output of a Nd:YAG laser serves as the light source for the Rayleigh scattering.
Figure 1. Schematic of the laser imaging arrangement for propane-helium imaging.
A jet consisting of a propane-helium mixture issues into air. Propane diffuses relatively slowly, and has a large Rayleigh scattering cross-section, while helium diffuses rapidly and has a small scattering cross-section. The two gases are combined in such proportion that the scattering cross-section of the initial mixture is the same as that of air. In the absence of differential diffusion as the flow evolves, the scattering images are featureless; differential diffusion of the propane and helium into the surrounding air results in fluctuations in scattering intensities in the images.
Figure 2 shows sample Rayleigh scattering images from these experiments, at jet Reynolds numbers 1000 and 3000 (corresponding to outer-scale Reynolds numbers from 4300 and 13000). The jet moves upward in the images. The imaging windows span from approximately 2 to 20 jet nozzle diameters, d, downstream of the jet exit, and from the centerline to the jet outer boundary on at least one side.
Figure 2. Sample differential diffusion fields, obtained through planar Rayleigh scattering in the propane-helium jet, at (a) jet exit Re = 1000, and (b) Re = 3000.
The predominant grey color represents the scattering cross-section of both air and the initial jet mixture. The brighter regions indicate a larger local scattering cross-section, meaning that the local propane-helium ratio exceeds the initial jet value, while the dark regions indicate a smaller local cross-section, caused by a local propane-helium ratio lower than the initial value. The flow is laminar in the near-nozzle region at Re = 1000, and in the absence of turbulence the differential diffusion field takes on a characteristic large-scale structure, where the fast-diffusing helium is in excess to the outside of the jet, leaving a region with excess propane just to the inside of this, surrounding the unmixed jet core. With the onset of turbulence, features in the differential diffusion field become more uniformly distributed across the jet. The extent of the laminar part of the jet diminishes with increasing Reynolds number, and by Re = 3000, no distinct laminar region is evident. In that case, differential diffusion structures form primarily in an underlying turbulent flow. In the downstream, turbulent portion of the jet, the jet boundary sees a mean excess of propane, in a reversal of the laminar situation. This is true regardless of the extent of the laminar part of the jet. In the absence of velocity field measurements, we postulate that the presence of higher-density propane to the outside of the jet arises from an inertial mechanism, akin to cyclonic separation.
We can investigate the effect of differential diffusion quantitatively, by looking at probability distributions of the differential diffusion variable ξ (xi), conditional on different downstream and off-axis positions. The variable ξ (xi) is a conserved scalar, defined as
where the χ (chi) are the mole fractions of propane and helium, and the superscript 0 denotes the initial (jet exit) values. In a turbulent flow, the production of differential diffusion is assumed to be strongest at the smallest flow scales. Contrary, then, to typical turbulent spectra, in which energy input comes at large flow scales, the accepted thinking has been that the spectrum of ξ (xi) should have a peak at a wavenumber range that is intermediate to the molecular-diffusive scales of the two differentially diffusing species.
Figure 3. Spectra of the differential diffusion variable ξ (xi) determined from one-dimensional radial sections. (a) At x/d = 13 for Re = 1000, 2500 and 3000. (b) At x/d = 17 for Re = 2500 and 3000.
Figure 3 shows spatial spectra of ξ (xi), determined from one-dimensional radial profiles at (a) x/d = 13 for Re = 1000, 2500 and 3000, and (b) x/d = 17 for Re = 2500 and 3000. These spectra all resemble the spectra of conventional scalar variables, with no evidence of any intermediate peak values. The downstream spectra at the higher Re also show a clear (-5/3)-power inertial range, as would be expected in conventional scalar mixing at these relatively high outer-scale Reynolds numbers. It appears that differential diffusion in these flows is characterized by production at relatively large scales, for example in laminar flow regions or those regions with intermittently low turbulence intensity, with the resulting structures then being broken down through the familiar turbulent cascade process. These results may have important implications for flow systems where turbulence levels can vary significantly, such as reacting flows that are subject to local laminarization in high-temperature zones.
Additional analysis of these data includes investigations of the spatial structure of the differential diffusion fields, as well as further examination of their statistical properties. Full details are available in the references below.
Publications (inquiries: email Cody Brownell, cbrownell: jhu.edu)
All materials © 2008 Applied Fluid Imaging Laboratory. Last page update 1.8.08.
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