Towards a deterministic composite collision outcome model for surface-tension dominated droplets

Abstract

The focus of the present study is on the modeling and simulation of coalescence of surface-tension dominated liquid droplets in a gaseous environment. In the framework of a four-way coupled Euler-Lagrange approach using the large-eddy simulation technique, an improved composite collision outcome model identifying the four regimes of binary collisions of such droplets (bouncing, fast coalescence, reflexive and stretching separation) is assembled based on well-known correlations. A specific feature is that a hard-sphere model in combination with a deterministic collision detection is applied and hence the stochastic parcel approach often used for spray simulations is obsolete. In this composite model the bounding curves between the regimes mentioned before are taken from available experiments and described by well-known analytic correlations. The main objective is to provide a compilation of the different modeling assumptions resulting in a consistent model for the entire regime. Furthermore, the composite model is improved by introducing an additional condition to consider the overlapping region of the stretching and reflexive separation regimes at high Weber numbers. The outcome of a binary collision is identified based on the collision Weber number, the dimensionless impact parameter and the droplet size ratio. The results of each collision is treated separately with regard to the collision regime found, whereas the formation of satellite droplets during stretching and reflexive separation is currently not taken into account. Additionally, a droplet injection model for spray systems is introduced to specify the injected mass, the position, the velocity and the diameters of the released droplets. In this model the initial droplet diameters mimicking the primary break-up (atomization process) of the jet are modeled by means of a number distribution function. The implementation of the composite collision outcome model is verified using the test case of an inter-impingement spray system consisting of two crossing conical water sprays. Besides correctly reproducing the experimental correlations the composite model predicts a coalescence rate which is within the experimental range found in the literature. Then, the composite collision outcome model is applied to simulate the injection process of a solid-cone non-evaporating diesel spray into a quiescent nitrogen environment and validated against experimental data. The validation study is carried out in terms of the spray tip penetration, since it is one of the most important characteristics of sprays. A detailed comparative study is carried out to investigate the effect of different simulation parameters on the spray tip penetration. The results clearly show that a four-way coupled simulation using the enhanced composite model leads to the best agreement with the experiment.