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Experimental assessment of subgrid-scale mixing models for large-eddy simulation (LES)
Student: Olivia Sun (osun: jhu.edu)
(Figures: sample data sample results) (Publications)
For computing realistic combustion systems, significant attention is being paid to large-eddy simulation (LES), in which large flow length scales are resolved and computed explicitly, while small scales are unresolved and entrusted to subgrid-scale (SGS) models. Combustion processes are dependent on molecular mixing, so accurate representation of subgrid scale mixing is essential for combustion simulations. Denoting a conserved scalar quantity as C, and representing LES filtering with an overbar, the evolution equation for the LES-filtered scalar field is
where the u_i are the velocity components and D is the scalar diffusivity. The τ (tau) term on the right side of the equation represents a scalar flux, and is defined as
This term is unresolved in an LES and must be modeled. Particularly for combustion applications, other scalar quantities of interest include the subgrid scalar variance, defined as
and the subgrid scalar dissipation, defined as
For both the subgrid variance and dissipation, the filtered products appearing in the definitions are unresolved in LES and require modeling.
In this work, we assess SGS models for scalar mixing, including models for the subgrid scalar flux, variance and dissipation, using highly resolved experimental measurements of simultaneous, planar velocity and scalar fields. The data allow both for a priori testing, in which model predictions are tested directly, and for direct assessment of modeling assumptions. The data used here are from a turbulent crossflowing jet (reported by L.K. Su and M.G. Mungal, Journal of Fluid Mechanics 513, 2004, at JFM online). Figure 1 shows a sample scalar field image, obtained using planar laser-induced fluorescence (PLIF), from this data set.
Figure 1. A sample scalar field image from the turbulent crossflowing jet. The present work focuses on window 8 (upper right).
The jet issues from left to right in the image, and the crossflow moves from bottom to top. The jet exit Reynolds number is approximately 5000 and the jet-to-crossflow velocity ratio is 5.7. The simultaneous velocity field measurements, performed using particle image velocimetry (PIV), use the eight windows shown superimposed on the scalar field image. For the present work we use the data from window 8, which offers the best spatial resolution.
Among the SGS models considered are three models for the subgrid scalar dissipation, χ (chi):
Figure 2. Scatterplots of modeled vs. measured results for the SGS scalar dissipation. Results for (a) the gradient-based model, (b) the model of Jimenez et al., and (c) the dynamic structure model.
The simulated LES filter for these cases has linear dimension eight times the measurement grid spacing. The plots make clear that the model of Jimenez et al. offers superior correlation. The assumption that the mechanical and scalar time scales are proportional thus seems to be more robust than either the assumption of equilibrium between subgrid variance production and dissipation, or the assumption of scale similarity in the dissipation. Further analysis is required to evaluate the dependence of these results on filtering methods and other considerations. More extensive discussion of these results, as well as of the results for the subgrid scalar flux and scalar variance models, can be found in the reference below.
Publications (inquiries: email Olivia Sun, osun: jhu.edu)
All materials © 2008 Applied Fluid Imaging Laboratory. Last page update 1.2.08.
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