Mesh Independence and Adaptive Mesh Refinement For Advanced Engine Spray Simulations

Numerical investigation of the spray–mesh–turbulence interactions for high-pressure, evaporating sprays at engine conditions

“…It is widely accepted (Lippert et al, 2005;Aneja and Abraham, 1998) that the accuracy of the Eulerian-Lagrangian spray simulations is related to the various sub-models involved and to the inadequate spatial resolution hindering the coupling between the gas and liquid phases. This second aspect is the most important since it often requires an unphysical adjustment of the spray sub-models coefficients.…”

Modelling of high-pressure dense diesel sprays with adaptive local grid refinement

“…Lippert et al (2005) distinguished the phase coupling into 'gas-to-liquid' and 'liquidto-gas'. The first comprises the interpolation process, whereby gas quantities known at Eulerian nodes are estimated at the parcel location.…”

“…The weighting scheme for the distribution of the liquid/gas source terms suggested by Golovitchev and Nordin (2001), based on the reciprocal of the distance between the parcel and the eight nearest nodes (in a hexahedral mesh) raised to an integer power, improves the dependency of predictions on the numerical grid. Furthermore, Lippert et al (2005) proposed a methodology for momentum coupling that can be applied to meshes of arbitrarily structure, shape and topology, utilising a least-square-based interpolation scheme for gas-to-liquid coupling and a kernel smoothing scheme for liquid-to-gas coupling. Simulations were performed without accounting for break-up, collision and evaporation processes in order to allow for the effect of the momentum coupling between the two phases to become clear.…”

“…Particular emphasis has been given in the last decade to the influence of the temporal and spatial resolution of the continuous air motion on the computational spray sub-models. Many studies have demonstrated the strong dependence of the method on the grid resolution, for example Abraham (1997), Subramaniam and O'Rourke (1998) and Lippert et al (2005), among others. The reason for such grid-dependence is that, on one hand, the volume of the cells introduced for the discretisation of the gas phase equations should be bigger than the volume of the droplets they contain, as imposed by the Eulerian-Lagrangian formulation, on the other hand, the grid size should be small enough to accurately resolve the gas phase development near the nozzle.…”

“…With this methodology, phenomenological sub-models are required to account for the various physical processes taking place in the sub-grid time and length scales. Nowadays the physical sub-models predicting the spray processes are still limited to specific flow conditions, thus, empirical to some extent (Lippert et al, 2005). The processes controlling the fuel spray development include a variety of parameters like the nozzle geometry, the characteristics of the fuel supply system and the liquid-gas aerodynamic interaction.…”