Experimental study on secondary droplets produced during liquid jet impingement onto a horizon solid surface

https://doi.org/10.1016/j.expthermflusci.2020.110249Get rights and content

Highlights

  • The splash ratio of the jet impingement was expressed as a function of the impact Weber number and the Ohnesorge number.

  • The mean secondary droplet diameter was roughly proportional to the mean primary droplet diameter.

  • The size distribution of the secondary droplets was fitted with the log-normal distribution.

Abstract

Experiments were preformed to measure the mass and size of secondary droplets splashed during liquid jet impingement onto a horizontal solid surface. To explore the effects of liquid hydraulic properties such as viscosity and surface tension, pure water, two aqueous solutions of glycerin, and two aqueous solutions of ethanol were used as the test solutions. Using the experimental data accumulated in this work, dimensionless correlation was developed for the splash ratio (ratio of the droplet splash rate to the jet flow rate). Here, it was assumed that the mass of secondary droplets splashed per impact can be expressed as a function of the impact Weber number and the Ohnesorge number. The correlations for the Sauter mean diameter and the size distribution of secondary droplets were also proposed. It was shown that the size distribution of the secondary droplets can be fitted with the log-normal distribution. Two parameters determining the log-normal distribution profile were correlated by the impact Weber number.

Introduction

Liquid sodium is one of the most common coolants used in fast breeder reactors by the reason of its preferable features such as weak neutron moderation performance, high thermal conductivity, high boiling point, low density, and so on. However, since sodium reacts with the oxygen and moisture in the air easily, sodium fire may be caused if coolant leakage occurs [1]. The leaking sodium forms liquid pool on the floor and/or splutters as secondary droplets in the containment vessel. The intensity of combustion is supposed more significant when liquid sodium exists as secondary droplets than in liquid pool since the surface area of the liquid sodium per unit volume that serves as the reaction field is much greater for droplets [2]. When liquid jet collides with the solid structures in the containment vessel, splashing may take place to generate droplets of various sizes [3], [4]. However, since droplet splash is a very complex hydrodynamic phenomenon, considerable uncertainty still remains in the mass and size of secondary droplets assumed in the numerical analysis of sodium fire incident [5]. This indicates that to accurately evaluate the significance of the sodium fire encountered in fast reactors, understanding should be enhanced for the splashing of secondary droplets during liquid jet impingement onto a solid surface.

During liquid jet impingement, splashing of secondary droplets mainly occurs when the primary droplets produced following the jet breakup collide with the liquid film formed on the solid surface as discussed later. As for the drop impact on a liquid film, many studies have been conducted so far to understand the characteristics of secondary droplets. For instance, Stow and Stainer measured the size distribution of secondary droplets produced by the impact of single water droplet onto a thin water film [6]. Vander Wal et al. performed the experiments of droplet splashing during impacts onto various depths of liquid film [3]. Okawa et al. showed that the mass ratio of the secondary droplets to the impacting droplet is correlated well as a function of the impact Weber number and the Ohnesorge number [4]. Yarin and Weiss measured the total volume and size distribution of secondary droplets produced during successive impacts of micrometer-size droplets on a solid surface [7]. Zhang et al. studied the effects of the Weber number and the Reynolds number on spreading characteristics of a liquid crown and droplet splashing [8].

As the situation more similar to the liquid sodium leakage in fast reactors, droplet splashing caused by the liquid jet impingement on a solid surface has also been studied by many investigators. Kim et al. verified that the splash rate of droplets from the impingement point is governed by the initial velocity of liquid jet and the occurrence of breakup [9]. Bhunia and Lienhart investigated the growth of surface disturbances on turbulent liquid jets in air and measured the splash rate when a continuous turbulent jet impinges on a solid plate [10], [11]. Trainer demonstrated that in the drop impingement splatter mode, strong relation is present between the liquid splatter onset point and the jet breakup length [12]. These studies indicate that more secondary droplets are produced when the fall height is greater than the breakup length and consequently the liquid impacts on the solid surface as a broken jet. It is hence considered that the droplet splashing mainly occurs when primary droplets caused by a result of jet breakup impinge on a liquid film formed on a solid surface. The frequency of the impacts of the primary droplets is obviously zero if the fall height is shorter than the breakup length of the liquid jet and would increase asymptotically with an increase in the distance from the nozzle. The splash rate is expected proportional to the impact frequency [13]. This signifies that accurate prediction of the impact frequency of primary droplets is necessary in mechanistic evaluation of the splash rate of secondary droplets.

As one of the earliest studies regarding the jet breakup, Plateau conducted experimental and theoretical investigations on the breakup of circular jet into small droplets [14]. Rayleigh then developed a theoretical model for the instability of liquid jet neglecting the effects of gravity and viscosity [15]. In the theoretical analysis conducted by Weber, the effects of jet velocity, viscosity and density were taken into consideration to estimate the breakup length of the liquid jet [16]. Ohnesorge classified the type of liquid jet breakup into the Rayleigh regime, the two kinds of wind-induced regime and the atomization regime based on the Reynolds number and the Ohnesorge number [17]. Sterling and Sleicher extended Weber’s theory to account for the effect of ambient gas [18]. Lin and Reitz explained that the breakup length of the liquid jet can be expressed as a function of the jet exit velocity at the nozzle [19]. Grant and Middleman developed the correlations of breakup length for laminar and turbulent jets [20]. Wang et al. investigated the droplets generation by dripping from a capillary nozzle [21]. Lienhart and Day established a relation between the Reynolds number and the breakup length [22]. Shibata et al. established an empirical correlation for the breakup length taking into account the influence of gravity [23]. Cheong and Howes investigated the growth rate of disturbance of liquid jet and the size of droplets produced following the jet breakup [24].

The above literature survey indicates that to elucidate the characteristics of liquid jet, effects of various parameters including the nozzle diameter, jet velocity and fluid properties have been explored by many researchers. However, understanding is still insufficient to achieve accurate evaluations of the impact frequency of the primary droplets and the splash rate of the secondary droplets. In view of this, in order to improve the accuracy of the mass and size of secondary droplets assumed in the numerical analysis of sodium fire incident, Zhan et al. conducted experiments of liquid jet to develop dimensionless correlations for the impact frequency of primary droplets and the splash rate of secondary droplets [25]. Measurements were then conducted for the thickness of liquid film formed on the solid surface and the size of secondary droplets [26]. As the first step, pure water was used as the test liquid in these experiments. In the model proposed by Zhan et al. [25], the splashing rate and the size of secondary droplets are dependent significantly on the impact frequency. For example, it was postulated that the splashing mainly occurs during drop impact and consequently the splashing rate is proportional to the impact frequency. Therefore, in the subsequent study, the effects of the viscosity and surface tension were explored experimentally using five test liquids to propose an improved impact frequency correlation [13]. The quantities required in the numerical analysis of sodium fire incident are the amount and size of secondary droplets. Hence, in the present work, the splash rate and the secondary drop size are experimentally measured using multiple test liquids of different values of viscosity and surface tension. Based on the impact frequency correlation developed in the previous work [13], improved dimensionless correlations are developed for the splash rate, the mean diameter, and the size distribution of the secondary droplets.

Section snippets

Experimental apparatus

The experimental apparatus used in this work is delineated in Fig. 1. Since this is the same apparatus used in Zhan et al. [13], it is described briefly. In the lower reservoir, about 40 L of test solution was prepared firstly. Then, using a liquid pump, the test solution was conveyed to the upper reservoir. Next, the upper reservoir was pressurized by the nitrogen cylinder. The needle valve equipped on the vertical discharge line beneath the upper reservoir was used to set the liquid flow

Splash ratio

Spatial development of a liquid jet from a discharge nozzle supposed by Zhan et al.’s [25] is explained schematically in Fig. 7. First, in the region A, the jet is still continuous and consequently the impact frequency of primary droplets is zero. As depicted in the right-hand-side photo, it can be seen that droplet splashing is negligible if the target plate is present in this region. Next, in the region B, the liquid jet breakup begins to produce primary droplets. The impact frequency

Conclusions

The mass and size of secondary droplets generated during liquid jet impingement onto a horizontal solid surface were experimentally measured to develop state-of-the-art dimensionless correlations for the splash rate, the mean diameter, and the size distribution of the secondary droplets. To explore the effects of liquid hydraulic properties, the five liquids (water, two aqueous solutions of glycerin, and two aqueous solutions of ethanol) were used as the test solutions in the experiments. It

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (31)

  • A.L. Yarin et al.

    Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity

    J Fluid Mech

    (1995)
  • H. Zhang et al.

    Experiment study of droplet impacting on a static hemispherical liquid film

    Exp Comput Multipha Flow

    (2020)
  • Y. Kim, K. Amagaya, G. Ogiwara, M. Arai, Wall impingement phenomena of a liquid jet, (1st Report, impingement behavior...
  • S.K. Bhunia et al.

    Surface disturbance evolution and the splattering of turbulent liquid jets

    J Fluids Eng

    (1994)
  • S.K. Bhunia et al.

    Splattering during turbulent liquid jet impingement on solid targets

    J Fluids Eng

    (1994)
  • Cited by (11)

    • Fundamental characteristics of secondary drops produced by early splash during single-drop impingement onto a thick liquid film

      2022, Experimental Thermal and Fluid Science
      Citation Excerpt :

      Splashing, or the ejection of secondary drops during drop impact onto a liquid film is an important fundamental phenomenon in a variety of technical applications including spray cooling of high-temperature solid surface [1,2], fuel injection in internal combustion engines [3–5], mass transfer between droplets and a liquid film in annular two-phase flow [6], separation of vapor and liquid in boiling water reactors [7,8] and in chemical plants [9,10], aerosol production during nuclear reactor severe accident [11], and sodium fire accident following coolant leakage in fast reactors [12].

    • Splashing generation by water jet impinging on a horizontal plate

      2022, Experimental Thermal and Fluid Science
    • Droplet generation during spray impact onto a downward-facing solid surface

      2021, Experimental Thermal and Fluid Science
      Citation Excerpt :

      Dimensionless correlations for the splashing threshold during drop impact on a liquid film were developed by several investigators [16–18]; the Weber number and the Ohnesorge number were used to express the threshold in these correlations. For the impingement of liquid jet, the present authors developed phenomenological dimensionless correlations for the size and the amount of splashing droplets generated during the collision of downward liquid jet onto a horizontal solid surface [19–21]. Recently, Kim et al. experimentally investigated the fraction of splashing droplets during the impingement of horizontal liquid jet onto a vertical wall [22].

    View all citing articles on Scopus
    View full text