Numerical study of oblique droplet impact on a liquid film

Abstract

The dynamic characteristics of droplet obliquely impact on a liquid film are investigated numerically by using the Coupled Level Set and Volume of Fluid method (CLSVOF), with the impact angle ranging from 0° to 60°. The influence factors as film thickness and Weber number on the splashing formation and the crown evolution are also systematically investigated. Results showed that the crown radius on the behind side of the advancing droplet decreases as the impact angle increases, while the crown radius on the front side of the advancing droplet appears to be an opposite trend. Furthermore, the crown diameter is almost unchanged when the impact angle increases from 30° to 45°. However, when the impact angle increases to 60°, the crown lamella on the front side of the advancing droplet is completely suppressed. It is found that the crown height does not linearly change with the film thickness. With an increase in the film thickness, the right crown height first increases and then decreases, indicating the presence of a critical film thickness under the studied conditions. An increase in Weber number results in a transition from non-splashing to partial splashing and even to entire splashing.

Introduction

The dynamic characteristics of droplet impact on a liquid film are a fascinating physical phenomenon and have been widely studied due to its various nature and industry applications, such as raining, spray cooling, fuel injection, ink-jet printing and desalination. In these applications, droplets initially impact on a dry solid surface, as the studies have been conducted in the references [1], [2], [3], [4], while this solid surface will be quickly covered with a liquid film formed by the prior droplets. Thus, the impact of droplet on a liquid film is more common. In addition, like the spray cooling, the droplets will impact on the liquid film obliquely but not always normally. Liquid crown will be formed and even splash after a droplet impact on a liquid film, while these morphological features will be different for the case of oblique impact with the normal impact, which needs an extensive and in-depth research.

Numerous studies have been conducted to investigate the normal impact of droplet on a stational liquid film [5], [6], [7], [8], [9], [10]. Weiss and Yarin [5] focused on the initial stage of a normal impact. They found that a jet will be formed at the neck between the droplet and the liquid film after droplet impact, which can detach or reconnect with the liquid film. Lee et al. [6] used the Level Set (LS) method to simulate the normal impact. Their results showed that the larger the Weber number, the higher the crown height. However, the effect of the film thickness is opposite. Guo et al. [7] studied the effects of impact velocity and film thickness on crown evolution by using the CLSVOF method. Their results indicated that the crown diameter decreases as the film thickness increases, and a larger impact velocity enhances the splashing. Shetabivash et al. [8] numerically investigated the droplet normally impact on a thin liquid film. They found that the evolution rates of crown radius and crown height decrease with increasing the liquid film thickness, while the crown radius is not affected by viscosity. Liang et al. [9] experimentally and numerically studied the droplet impact on a very thin spherical liquid film. Their results showed that the splashing can be suppressed by decreasing Weber number and Reynolds number, and that an increase in film thickness is unfavorable to the splashing onset. Rahmati and Zarareh [10] employed a modified pseudopotential lattice Boltzmann model to simulate the splashing phenomenon after droplet impact. Their results showed that as the Weber number increases, the crown height increases, while the crown radius slightly decreases at the early stage of the droplet impact. Nikolopoulos et al. [11] used the Volume of Fluid (VOF) method to simulate the normal impact. They pointed out that there are two mechanisms for secondary droplet formation, Rayleigh instability and surface tension.

For the case of oblique impact, a significant difference from the case of normal impact is that the flow characteristics will be asymmetrical. In order to gain a better understanding of these differences, several experimental and numerical studies have been conducted [12], [13], [14], [15], [16]. Okawa et al. [12] experimentally studied the effect of impact angle on the secondary droplets after droplet impact on a stationary liquid film. They found that when the impact angle is less than 50°, increasing the impact angle can significantly increase the total mass of the secondary droplets. However, when the impact angle exceeds 70°, no secondary droplet appears. Liu [13] experimentally investigated the effect of wind on droplet impact and found that the critical value of dimensionless K number is affected by the wind velocity and the impact angle. Cheng and Lou [14] investigated the crown evolution during droplet obliquely impact on a liquid film by using the lattice Boltzmann method (LBM). Their results showed that the impact angle can significantly influence the evolution of the splashing. The authors also indicated that a critical impact angle exists on the behind side of the advancing droplet. Guo and Lian [15] used a moment-of-fluid (MOF) method to simulate the high-speed oblique impact of droplet on a thin liquid film. Their results revealed that crown height and radius on the behind side of the advancing droplet will be lower with a higher tangential velocity. Liu et al. [16] numerically simulated the dynamics of droplet impact on a liquid film with a given horizontal velocity. They found that the larger the Weber number, the higher the crown height on the front side of the advancing droplet but the lower the crown height on the behind side. Here, we should be noticed that when droplet normally impact on a flowing liquid film, the flow characteristics are also obviously asymmetrical and have fascinated researchers [17], [18], [19], [20]. However, this asymmetry is different with that in oblique impact case and has been analyzed by Cheng and Lou [14].

Although a great deal of numerical studies on crown evolution and splashing have been done, most of them are restricted to the normal impact. Therefore, more researches on oblique impact should be carried out, and more influence factors should be considered. In this study, we qualitatively and quantitatively investigate the morphological features of droplet obliquely impact on a stationary liquid film by using the CLSVOF method. By considering the influence factors of impact angle, film thickness and Weber number, we also intend to find the typical values for the evolution of the liquid crown and the splashing.