High Fidelity Spectral-FDF-LES of Turbulent Scalar Mixing

ABSTRACT

The fidelity of the hybrid spectral-filtered density function (FDF) methods is assessed for large eddy simulation of turbulent scalar mixing. Both continuous and discontinuous spectral-element methods are considered on domains furnished by structured & unstructured grids. A parametric study is conducted of the effects of the spectral polynomial approximation ($p$), the grid size ($h$), and the LES filter width ($\mathrm{\Delta }$). The simulated results are appraised via comparisons with high resolution direct numerical simulation (DNS) data. It is shown that the amount of energy resolved by LES depends on the magnitude of $\mathrm{\Delta }$, but the total energy is predicted reasonably well for all $\mathrm{\Delta }/h$ values. Also, for a fixed filter width, the LES results converge to DNS data with both $h\mathrm{\&}p$- refinements. At lower $\mathrm{\Delta }/h$ values, the rate of convergence to DNS is faster as $p$ increases. Within the range of parameters considered, $h\approx \mathrm{\Delta }$ provides the optimum LES resolution. The consistency of the hybrid spectral-FDF for LES of complex flows is demonstrated; warranting future applications of the methodology for combustion engineering.

KEYWORDS:

• Large eddy simulation
• filtered density function
• grid resolution
• spectral-elements
• discontinuous Galerkin

Acknowledgments

We are grateful and indebted to Professor William A. Sirignano for his mentorship and leadership in this research area. This work is part of an effort sponsored by the National Science Foundation under Grant CBET-1603131. Computational resources are provided by the University of Pittsburgh Center for Research Computing.

Additional information

Funding

This work was supported by the National Science Foundation [CBET-1603131].