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Investigation of the fine-scale structure of turbulent mixing via planar measurements of the three-dimensional scalar gradient vector
With Prof. Noel T. Clemens, University of Texas at Austin
(Figures: imaging schematic sample images quantitative results) (Publications)
Molecular mixing is important in a wide variety of engineering problems. Among these are non-premixed combustion systems, where the relevant mixing is typically between fuel and oxidizer in the gas phase. To quantify mixing rates, we can consider the scalar dissipation rate, χ (chi), defined as
where C is a conserved scalar field and D is the scalar diffusivity coefficient. In realistic turbulent flows, the gradients in the above equation will be highly three-dimensional. However, in gas-phase flows such as those relevant to combustion, three-dimensional scalar field imaging has proven to be a difficult challenge. This work presents an approach to three-dimensional scalar imaging using simultaneous planar laser-induced fluorescence (PLIF) and planar laser Rayleigh scattering in parallel planes.
Figure 1. Schematic of the three-dimensional scalar imaging arrangement in the planar turbulent jet.
Figure 1 shows a schematic of the imaging arrangement. A planar jet consisting of a propane-acetone mixture issues into air. The output of an Nd:YAG laser is split into 532 nm and 266 nm beams, which are formed into parallel sheets and introduced from opposite sides of the measurement area. One camera collects the Rayleigh scattering signal from the 532 nm sheet, while a second camera collects the acetone fluorescence excited by the 266 nm sheet. A third camera monitors the sheet energy profiles to ensure accurate processing of the raw images.
Figure 2. Sample images from the three-dimensional imaging. Scalar fields measured simultaneously by (a) PLIF and (b) Rayleigh scattering, in parallel planes separated by 200 microns in the out-of-plane direction. (c) The two-dimensional scalar dissipation rate computed from the PLIF image in (a), and (d) the full three-dimensional scalar dissipation computed using both the PLIF and Rayleigh scattering image planes.
Figure 2c shows the scalar dissipation computed from the PLIF image using only the two in-plane scalar gradient components, while Fig. 2d shows the χ (chi) field that results when the Rayleigh scattering field is added to allow the determination of the out-of-plane gradient component. It is clear that this third component contributes significantly both to the magnitude and the structure of the dissipation rate field.
Figure 3. (a) The probability distribution of the logarithm of the three-dimensional scalar dissipation, compared with a log-normal distribution. (b) The thickness of the dissipation structures as a function of the local outer-scale Reynolds number, showing the (-3/4)-power dependence.
The nature of the data set also permits direct measurement of the characteristic thickness of structures in the dissipation field (e.g. Fig. 2d), as well as the dependence of this thickness on the local outer-scale Reynolds number. The results, shown in Fig. 3b, confirm the (-3/4)-power dependence consistent with Batchelor-Kolmogorov scaling. No evidence is seen in the measurements of Taylor scaling (which would be manifested in a (-1/2)-power dependence). More extensive analysis and discussion of these measurements can be found in the references below.
Selected publications (inquiries: email Lester Su, lsu: jhu.edu)
All materials © 2004 Applied Fluid Imaging Laboratory. Last page update 8.16.04.
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