Advances in modelling of binary droplet collision outcomes in Sprays: A review of available knowledge

Abstract

The present article summarises the requirements for modelling droplet binary collisions in the frame of a Lagrangian point-particle tracking approach. The essential ingredients of such a collision model are the collision detection, done in a deterministic or stochastic way, the consideration of the impact efficiency (i.e. small droplets might move around larger ones with the relative flow), and the prediction of the droplet collision outcome based on the well-known collision maps (i.e. B = f(We), We is the Weber-number and B the non-dimensional impact parameter, both defined below). The different approaches used in Euler/Lagrange spray calculations for prescribing such collision maps with single or composite boundary lines are briefly reviewed.Then available experimental studies providing full collision maps including all possible collision outcomes with boundary lines are reviewed with special emphasis on higher liquid viscosities; however both droplets have the same fluid, and different sizes of colliding droplets. Most important for modelling the collision outcomes (i.e. in the lower We-regime up to about 150 – 200 these are bouncing, coalescence, stretching and reflexive separation) are physically-based theoretical boundary lines between the regimes which are not specific for certain boundary conditions (i.e. liquid properties, ambient gas conditions and droplet size ratio). The most commonly used correlations for boundary lines are presented and analysed with respect to their performance (i.e. effect of size ratio, liquid properties and included model constants or parameters).In this study the shift of boundary lines and characteristic points in the collision maps due to changes of fluid properties (i.e. the Ohnesorge-number) and size ratio are used as a modelling framework. Specifically, these are the critical Weber-number location (i.e. beginning of reflexive separation) and the triple-point (i.e. location where bouncing, coalescence and reflexive separation come together). Numerous available experiments on these characteristic point locations are collected showing that they very well correlate with the Ohnesorge-number (i.e. depending only of liquid properties and droplet size). For generalisation, the model of Jiang et al. (Jiang, Y. J., Umemura, A. and Law, C.K.: Journal of Fluid Mechanics, Vol. 234, 171–190, 1992) including viscous dissipation is used for the stretching separation-coalescence boundary and for the beginning of reflexive separation the Ashgriz and Poo (Ashgriz, N. and Poo, J.Y.: Journal of Fluid Mechanics, Vol. 221, 183–204, 1990) approach is applied. This boundary line is just shifted according to the critical Weber-number obtained from an elaborated correlation WeC = f(Oh). The Jiang et al. (1992) boundary could be very well adapted for different liquids through the involved constants which again depend on the Ohnesorge-number, differentiating between pure fluids and solutions. It is demonstrated that the suggested novel models capture the two boundaries extremely well for a variety of different liquids and also solutions.Eventually, the effect of droplet size ratio on the collision outcome is considered. Additional experiments were conducted for a polymer-water solution and a high viscous sunflower oil by varying the size ratio of colliding droplets in a wider range of 1.0 < Δ < 0.35 and for We < ≈ 200. The proposed reflexive separation boundary model using the shift due to different fluid properties, i.e. WeC, and including the size ratio compares very well with these measurements. For the boundary stretching separation-coalescence the Jiang et al. (1992) and the Brazier-Smith et al. (Brazier-Smith, P. R., Jennings, S. G. and Latham, J.: Proc. R. Soc. Lond. A, Vol. 326, 393–408, 1972) boundaries were combined to capture both influences, namely the liquid property and size ratio. The model parameters were adapted in the same way as done in the model only accounting for the type of liquid. For upper values of the size ratio, range of 1.0 < Δ < 0.5, the agreement with the measurements was found to be excellent.