Statistical approach on visualizing multi-variable interactions in a hybrid breakup model under ECN spray condition

The Direct Numerical Simulation (DNS) approach to solving the fundamental transport equations down to the smallest scales of motion is favorable should the requirement be a truly predictive solution of fluid dynamic problems, but the simulation run times are unacceptable for most practical industrial applications. Despite the steadily increasing computational capabilities, Reynolds Averaged Navier-Stokes (RANS) based frameworks remain the most commercially viable option for high volume sectors, like automotive. The sub models within RANS simplify the description of key physical phenomena and include several numerical constants. These so-called “tuning constants” introduce multivariable dependencies that are almost impossible to untangle with local sensitivity studies. This paper addresses the prevailing difficulties in setting up an adequate diesel spray simulation which arise from the mentioned multi-variable interactions of these “tuning constants”, by applying a statistical approach named Design of Experiments (DoE). Often combined with an optimizer, DoE is commonly used to find an optimum set of engine parameters for set criteria at reduced experimental effort. In this case, the methodology was applied to determine an optimal set of “tuning constants” for the simulations which best matched experimental data at five conditions taken from the Engine Combustion Network (ECN) database. Multi-variable DoE were run for each condition. Stochastic response models (SPM’s) highlighted crucial simulation sensitivities of the turbulent dissipation constant C2and liquid/gas-phase momentum transfer at injection pressure swings. Further, a comparison of the breakup models which produced matching simulations exhibited patterns which correspond with physical processes. Lastly, it was shown that while a single set of the constants can give reasonable results in the space explored, there is merit in adjusting key constants to suit the operating condition in the search for accuracy.