Liquid Film Dynamic on the Spray Impingement Modelling

The present paper addresses a liquid film sub-model included into a computational model that aims at reproducing the spray impingement phenomena. This numerical extension incorporates the spread of the liquid film over the neighbouring nodes due to the dynamic motion induced by the film inertia but also the exchange of mass between the liquid layer and the incident and splashing particles. Moreover, the dimensionless film thickness parameter is introduced into the sub-model by mean of an experimentally-deduced correlation that can be fitted and updated to specified conditions. In order to realize how the model behaves with different influencing parameters, a thorough investigation is performed: the results that are obtained with and without the liquid film sub-model are compared against the experimental data for two crossflow rates. The integration of the computational extension with the spread/splash transition criterion is also evaluated by considering two types of transition criteria: one that takes into account the effect of the film thickness and one that does not. The results show that the latter option in combination with the sub-model do not distinctly enhance the simulation results, contrary to what happens using the transition criterion that considers the film thickness as an influencing parameter. In this case, the model with the computational extension reveals better prediction results than the one without it, which indicates the necessity of considering the liquid film formation for spray impingement simulations but also a splash threshold that takes into account the influence of the film thickness. Introduction The dynamic of droplets impacting onto a dry or wet solid surface plays an important role in a wide variety of fields, such as in ink-jet printing technologies, spray painting and coating, raindrops impacting on the ground and in liquid-fuelled combustors. However, it has only been in the near decade that a major scientific effort has been pursued in order to acquire a detailed and comprehensive knowledge about the mechanisms underlying the spray impingement process. Yet, this complete physical understanding is still lacking due to the host of parameters that influence the outcome. One of those parameters, which, curiously, is often neglected in spray impingement models, is the liquid film accumulated on the wall due to the deposition of the incident drops. The correct understanding of the film dynamic is of utmost importance for the accurate modelling of the spray impingement phenomenon. In fact, it is a key influencing parameter in several specific applications: if, on the one hand it is important to avoid as far as possible the liquid layer over the surface in situation of diesel engines cold-starting, on the other hand the presence of this liquid film is desired in cooling systems applications. In a general way, the formation of a liquid film and its interaction with the incident spray strongly affects the mixing process by taking effect on such properties as the splashing threshold and the secondary droplets characteristics. Despite the new boundary conditions promoted by the liquid/liquid interaction, the surface characteristics may still have significant influence on the outcome depending on the thickness of the film [1]. In fact, given the depth of the liquid over the solid surface, Tropea and Marengo [2] considered four categories (very thin film, thin film, thick film and deep pool) in which they defined a dependence between the influence of the surface topography and the dimensionless film thickness (ratio of the film liquid thickness to the incident drop diameter). The authors found that only in the case of a deep pool, which is not the condition reported in this study, the impact depend neither on the surface roughness nor on the film thickness. The present work aims at developing and integrating a liquid film extension in a multiphase computational model. This paper follows on from a set of previous studies [3–5] that seek to refine a flexible dispersion model in some aspects that would allow converging towards the best computational solution with minimum time constraints through the use of adapted and more suitable empirical correlation that fit specific configurations. Therefore, the liquid film formation sub-model is proposed by considering some basic principles (conservation of mass and volume between impinging and adhered parcels) but also an empirical correlation deduced from experimental data [6] for the average film thickness which allows a connection to the phenomenological experience that can easily be fitted and updated to specific settings. This model is incorporated into the code originally proposed by Bai et al. [7], *Corresponding author: [email protected]