Influence of droplet collision modelling in Euler/Lagrange calculations of spray evolution

Abstract

The numerical computation of spraying systems is favourably conducted by applying the Euler/Lagrange approach. Although sprays downstream of the breakup region are very often rather dilute, droplet collisions may still have a significant influence on the spray evolution and especially the produced droplet size spectrum. Consequently, they have to be reliably modelled in the Lagrangian tracking approach. For this purpose, the fully stochastic droplet collision model is applied, which is numerically very efficient. It is demonstrated that this model is largely independent of the considered flow mesh and hence grid size, as well as the number of tracked parcels and the Lagrangian time step size. Moreover, this model includes the impact efficiency which may remarkably reduce collision rates for a wide droplet size spectrum. An essential ingredient of any droplet collision model is the proper description of the collision outcome through the so-called collision maps (i.e. the non-dimensional impact parameter plotted versus collision Weber number; B = f(We)), where the outcome regions (i.e. bouncing, coalescence and stretching or reflexive separation) are demarked by appropriate, mostly theory-based boundary lines. There are a number of different correlations available which may be applied for this purpose. The structure of the collision maps strongly depends on the kind of liquid being atomised. Different types of boundary lines and collision map structures are analysed here in detail with regard to the conditional collision rates or numbers within a rather simple hollow cone spray. The comparison of the averaged Sauter mean diameters along the spray demonstrates the importance of droplet collisions and how strongly this result is affected by the presumed droplet collision maps. Crude approximations to such collision maps may result in large errors and wrong predictions of the produced droplet size spectrum. Moreover, it is demonstrated that the effective PDF (probability density function) of the colliding droplet size ratio has typically a maximum in the range 0.1 < Δ < 0.3, a condition where no experimental data are available so far and some of the commonly used boundary lines are not suitable. Naturally, the spray simulations are compared to experimental data for a water hollow-cone spray, showing excellent agreement if the droplet collision map is selected properly. This concerns profiles of both gas and droplet velocities as well as droplet concentration development and local droplet size distributions. Expectedly, the prediction of the velocities is less sensitive with respect to the presumed droplet collision map.