Spray dynamics as a multi-scale process

The analysis of the processes in sprays, taking into account the contribution of all spatial and temporal scales, is not feasible in most cases due to its complexity. The approach used in most applications is based on separate analysis of the processes at various scales, and the analysis of the link between these processes. This approach is demonstrated for the analysis of spray break-up and penetration in Diesel engine-like conditions, and vortex ring-like structures in gasoline engine-like conditions. The conventional WAVE, TAB, stochastic and modified WAVE (taking into account transient effects) models are reviewed. It is pointed out that the latter model leads to the prediction of spray penetration in Diesel engine-like conditions closest to the one observed experimentally. In gasoline engine-like conditions, spray penetration is often accompanied by the formation of vortex ring-like structures, the spatial scale of which is comparable with the scale of spray penetration. The general expression of the velocity of the vortex ring centroid can be simplified for short and long times, the latter simplification being particularly simple and useful for engineering applications. The thickness of the vortex ring is expressed as l = at(b), where a is an arbitrary constant and 1/4 <= b <= 1/2. The cases when b = 1/2 and b = 1/4 refer to laminar and turbulent vortex rings respectively. The model is compatible with the observation of vortex ring-like structures in gasoline engine-like conditions.