LAUSR

A sub-grid model accounting for the interaction of spray and sub-grid turbulence was developed and tested. The model predicts the sub-grid scale dispersion velocity used for calculating the slip velocity in Lagrangian–Eulerian Large-eddy simulation spray models. The dispersion velocity is assumed to be decomposed into a deterministic and a stochastic part, and it is updated in every turbulence correlation time for each computational parcel. The model was validated against two datasets: volume-of-fluid simulations and Engine Combustion Network experiments. The volume-of-fluid data showed that dispersion velocities at the centerline are anisotropic. This qualitative feature is well captured by the current model. For the Engine Combustion Network Spray A cases, it was found that sub-grid scale dispersion has profound impact on the prediction of the spatial distribution of liquid mass. Neglecting the sub-grid scale dispersion model results in underprediction of the width of the lateral projected liquid mass density profiles. Also, the prediction of the projected liquid mass density is sensitive to the two model constants determining the sub-grid scale dispersion velocity magnitude and turbulence time scale. However, the predictions of resolved gas-phase statistics are relatively insensitive to different sub-grid scale dispersion model setups. The primary reason for this was investigated. It was found that the motion of high-momentum liquid blobs in the near-nozzle region leading to air entrainment and subsequent gas jet development is minimally influenced by sub-grid scale dispersion. The importance of sub-grid scale dispersion inversely correlates with drag force magnitude: the larger the drag force, the less critical the sub-grid scale dispersion. Moving further downstream, quasi-equilibrium between the two phases is established, resulting in relatively small slip velocity and drag force.