Farrace, D., Panier, R., Schmitt, M., Boulouchos, K. et al., "Analysis of Averaging Methods for Large Eddy Simulations of Diesel Sprays," SAE Int. J. Fuels Lubr. 8(3):568-580, 2015, doi:10.4271/2015-24-2464.
Large Eddy Simulations (LES) provide instantaneous values indispensable to conduct statistical studies of relevant fluctuating quantities for diesel sprays. However, numerous realizations are generally necessary for LES to derive statistically averaged quantities necessary for validation of the numerical framework by means of measurements and for conducting sensitivity studies, leading to extremely high computational efforts. In this context, the aim of this work is to explore and validate alternatives to the simulation of 20-50 single realizations at considerably lower computational costs, by taking advantage of the axisymmetric geometry and the Quasi-Steady-State (QSS) condition of the near nozzle flow at a certain time after start-of-injection (SOI). Three different approaches are proposed and carefully investigated: the first combines ensemble with spatial averaging techniques based on the estimation of the azimuthal integral length scales to assess the maximal number of independent profiles; the second proposes in addition a time averaging technique that relies on the QSS assumption, whereas a third approach merges all the mentioned techniques together. Results show that for axisymmetric constant volume geometries, converged statistics (mean and standard deviation values) can be obtained from one single LES realization with up to 252 statistically independent samples. These results are very promising and could potentially reduce computational costs up to 50 times, allowing for numerical setup optimizations and sensitivity studies at computational efforts comparable to Reynolds-averaged Navier-Stokes (RANS) simulations.