Large eddy simulation of spray atomization with a probability density function method

•New LES-PDF model for atomization using liquid volume and surface density.•The model uses an Eulerian Monte Carlo approach.•The method resolves both dense and dilute regions of spray.•The solution provides instantaneous sub-grid droplet size distribution.•Surface density and liquid dispersion results are in good agreement with DNS.

Despite recent advances in numerical methods for multiphase flows, the complete simulation of a liquid spray is still an illusive goal. There are few models that can describe accurately both the primary and secondary atomization simultaneously. The biggest difficulty is the wide range of length scales involved; from millimetres in the largest liquid structures close to the smallest micron-size droplets. This wide range makes Direct Numerical Simulation of sprays very expensive all scales need to be resolved and expensive algorithms are required to reconstruct accurately the interface. Large eddy simulations are becoming increasingly popular in turbulent flows due to their better description of turbulence and the relative robustness of sub-grid stress models. Despite its advantages, large eddy simulation cannot describe accurately fluid structures that occur at sub-grid levels. This paper presents a new model to describe the atomization process. The method consist of solving a joint sub-grid probability density function of liquid volume and surface using stochastic methods. The approach can simulate both dense and dilute regions of the spray. The proposed model can determine instantaneous sub-grid liquid structures (droplets) distributions as well as to capture the primary break-up. The results of the simulations are compared to a Direct Numerical Simulation of a Diesel Jet break-up. The mean liquid volume and surface density are well predicted; The modelling of the sub-grid scales is shown to be fundamental in the dilute regions of the spray.