Computing Statistical Averages from Large Eddy Simulation of Spray Flames

The primary strength of large eddy simulation (LES) is in directly resolving the instantaneous large-scale flow features which can then be used to study critical flame properties such as ignition, extinction, flame propagation and lift-off. However, validation of the LES results with experimental or direct numerical simulation (DNS) datasets requires the determination of statistically-averaged quantities. This is typically done by performing multiple realizations of LES and performing a statistical averaging among this sample. In this study, LES of n-dodecane spray flame is performed using a well-mixed turbulent combustion model along with a dynamic structure subgrid model. A high-resolution mesh is employed with a cell size of 62.5 microns in the entire spray and combustion regions. The computational cost of each calculation was in the order of 3 weeks on 200 processors with a peak cell count of about 22 million at 1 ms. In the first part of this study, the number of realizations required to obtain ensemble-averaged quantities is critically examined using relevance index analysis. This study showed that, for statistically axisymmetric flows, if the results are azimuthally averaged over 35-40 planes, only 5 realizations are required to obtain statistically converged profiles for the mean temperature, mixture fraction, OH and soot mass fractions. In the second part, two methods of perturbing the LES solutions are examined - changing a random seed in the spray sub-models and perturbing the initial turbulence intensity in the computational domain. It is shown that both these methods lead to similar realization-torealization variability in the flame structure.