Weber Number Conditions Research Articles

Impact dynamics of non-spherical droplets on a thin water film

A droplet impinging on a liquid film finds numerous applications in diverse scientific fields. Although studies have primarily focused on spherical droplets, a droplet can present both spherical shape and non-spherical shape at the moment of impact. In the present study, the impact dynamics of a non-spherical droplet on a thin liquid film is investigated experimentally. The results show that, under the same film thickness and Weber number conditions, the splashing and deposition regimes are different for different droplet shapes such as prolate, sphere, and oblate. It is found that the splashing threshold (Ksp) is changed according to the shape of the droplet. Under the same condition when a spherical droplet is in the deposition mode, an oblate droplet is more likely to splash and form secondary droplets, while a prolate droplet is more splash-resistant even at higher Weber numbers. A modified theoretical model for crown radius evolution is developed. The predictions of theoretical model are found to agree well with the experimental results for spherical and non-spherical droplets. Moreover, at the same Weber number, a prolate droplet has a relatively higher maximum crown height than those of an oblate droplet and a spherical droplet.

Drop encapsulation and bubble bursting in surfactant-laden flows in capillary channels

We present a parametric study of the unsteady phenomena associated with the flow of elongated gas bubbles traveling through liquid-filled square capillaries under high Weber number conditions. These conditions induce the formation of an indentation at the back of the bubble that commonly gives way to a deep reentrant liquid jet penetrating the bubble. Subsequent steps include pinch-off events in the penetrating liquid to generate one or multiple encapsulated drops which may coalesce, in conjunction with the bursting of the bubble-liquid interface by either the liquid jet or the drops. Some of these interfacial instabilities have previously been reported experimentally and numerically for liquid-liquid flow in microchannels. We carry out three-dimensional direct numerical simulations based on a hybrid interface-tracking/level-set method capable of accounting for the presence and dynamic exchange of surfactants between the liquid bulk phase and the liquid-gas interface. Our results indicate that the delicate interplay among inertia, capillarity, viscosity, surfactant adsorption/desorption kinetics, and Marangoni stresses has a dramatic influence over the nonaxisymmetric morphological structures of the encapsulated drops-elongated bubble. This strong coupling also influences the pinch-off time, penetration depth of the liquid, and number, size, and velocity of the encapsulated drops across the bubble. The observed phenomena are summarized in three main morphological regimes based on surfactant-related parameters and dimensionless groups. A discussion of the flow regime maps is also provided. Published by the American Physical Society 2024

Application of Surface Wettability to Control Spreading of an Impacting Droplet.

While the simplest outcome of a normal impact on a flat stationary solid surface is radially symmetric spreading, it is important to note that asymmetric spreading can intrinsically occur with a tangential velocity along the surface. However, no previous attempt has been made to restore the symmetry of a lamella that intrinsically spreads asymmetrically. Adjusting the lamella's asymmetric shape to a symmetric one is achieved in this work by varying wettability to affect the receding velocity of the contact line, according to the Taylor-Culick theory. Here we theoretically and practically show how restoring the symmetry can be achieved. Theoretically we built a framework to map the needed receding velocity at every given point of the contact line to allow for symmetry to be restored, and then this framework was applied to generate a wetting map that shows how at each local the wettability of the surface needs to be defined. Simulated results confirmed the effectiveness of our framework and identified the envelope of its applicability. Next, to apply the idea experimentally, the wetting map was transformed to a single wettability contrast area dubbed the "patch". Experimental results showed the effectiveness of the patch design in correcting the asymmetric spreading lamella for water droplets impacting a surface for the following Weber number conditions: Wen ≤ 300, Wet ≤ 300, and 0.51 ≤ Wen/Wet ≤ 2.04.

The Effect of Weber Number on Spray and Vaporization Characteristics of Liquid Jets Injected in Air Crossflow

AbstractThis paper details a numerical investigation conducted to systematically evaluate the effects of aerodynamic Weber number, in the range from 68 to 136, on spray characteristics and gaseous fluid dynamics when liquid jets are injected in high-temperature air crossflow. The momentum flux ratio and air temperature for all the cases studied in this research effort are 9 and 573 K, respectively. The computations are conducted using an Eulerian–Lagrangian framework, where the gas phase is modeled by the compressible form of the Navier–Stokes equations and the liquid phase is treated in the Lagrangian frame with appropriate models to account for jet injection and breakup phenomena. A modified version of two-way coupling, which takes into account the finite size of the dispersed phase, is used to account for the exchange of mass, momentum, energy and species between the two phases. Turbulence closure is achieved using the large eddy simulation technique. As a first step, the framework is validated against measurements for non-vaporizing and vaporizing conditions—our results agree well with experimental data. Next, three computations in the range of Weber numbers mentioned above are conducted—the effect of Weber number is quantified in terms of the spatiotemporal evolution of the mass fraction of the vaporized liquid, detailed distributions of droplet sizes, their velocities, and volumetric fluxes. It is found that with an increase in the Weber number, the droplet sizes and the penetration depth monotonically decreased. As a result, at higher Weber number conditions, the vaporized liquid in the domain increases due to the overall enhancement in the effective surface area of the liquid phase.

Explosive lift-off triggering mechanism on a surface with micropillar arrays: Liquid-vapor interface behavior between micropillars during drop impingement

Generally, three classified hydrodynamic behaviors of impinging water drops involving corresponding boiling heat transfer regimes have been reported under low Weber number conditions (We < 20): contact boiling (nucleate boiling), transition rebound (transition boiling), and Leidenfrost rebound (film boiling). In previous studies of drop impingement on a structured surface, an explosive lift-off regime, which is characterized by lift-off from the surface within 1 ms without any disturbance at the top side of the drop, was reported, and the triggering hypothesis of explosive lift-off suggested had no quantitative evidence. In this study, the outcomes of water drop impingement onto a heated surface with micropillar arrays were investigated using a high-speed imaging system, for wall temperatures between 150 and 380 °C and a Weber number of approximately 4. Pool boiling experiments were conducted to validate the triggering hypothesis of explosive lift-off, as suggested by previous researchers. Based on the experimental results, the triggering mechanism of the explosive lift-off is discussed.

Investigation of Two-Phase Flow in a Hydrophobic Fuel-Cell Micro-Channel

This paper presents a quantitative visualization study and a theoretical analysis of two-phase flow relevant to polymer electrolyte membrane fuel cells (PEMFCs) in which liquid water management is critical to performance. Experiments were conducted in an air-flow microchannel with a hydrophobic surface and a side pore through which water was injected to mimic the cathode of a PEMFC. Four distinct flow patterns were identified: liquid bridge (plug), slug/plug, film flow, and water droplet flow under small Weber number conditions. Liquid bridges first evolve with quasi-static properties while remaining pinned; after reaching a critical volume, bridges depart from axisymmetry, block the flow channel, and exhibit lateral oscillations. A model that accounts for capillarity at low Bond number is proposed and shown to successfully predict the morphology, critical liquid volume and evolution of the liquid bridge, including deformation and complete blockage under specific conditions. The generality of the model is also illustrated for flow conditions encountered in the manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The experiments provide a database for validation of theoretical and computational methods.

Effect of breakup model on large-eddy simulation of diesel spray evolution under high back pressures

A breakup model has been developed and optimized for diesel spray simulation with a large-eddy simulation. Previously, diesel spray analysis has been carried out using a breakup model such as the Kelvin–Helmholtz and Rayleigh–Taylor model. The Kelvin–Helmholtz and Rayleigh–Taylor models are used for high Weber number conditions. However, even when fuel is injected at high pressures, the downstream region of spray corresponds to relatively low Weber number conditions. Hence, a hybrid breakup model that combines the Kelvin–Helmholtz and modified Taylor analogy breakup models (Kelvin–Helmholtz–modified Taylor analogy breakup) has been developed. The Kelvin–Helmholtz and modified Taylor analogy breakup models are used to model the primary and secondary breakup, respectively. The modified Taylor analogy breakup model is more suitable than the Rayleigh–Taylor model to describe secondary breakup. Spray simulations under non-evaporative and evaporative conditions were performed to validate the Kelvin–Helmholtz–modified Taylor analogy breakup model. It is found that the simulation results of Kelvin–Helmholtz–modified Taylor analogy breakup are in good agreement with experimental measurements of non-evaporative and evaporative spray.

Hydrodynamics and boiling phenomena of water droplets impinging on hot solid

The collision of single water droplets with a hot Inconel 625 alloy surface was investigated by a two-directional flash photography technique using two digital still cameras and three flash units. The experiments were conducted under the following conditions: the pre-impact diameters of the droplets ranged from 0.53 to 0.60 mm, the impact velocities ranged from 1.7 m/s to 4.1 m/s, and the solid surface temperatures ranged from 170 °C to 500 °C. When a droplet impacted onto the solid at a temperature of 170 °C, weak boiling was observed at the liquid/solid interface. At temperatures of 200 or 300 °C, numerous vapor bubbles were formed. Numerous secondary droplets then jetted upward from the deforming droplet due to the blowout of the vapor bubbles into the atmosphere. No secondary droplets were observed for a surface temperature of 500 °C at the low-impact Weber numbers (∼30) associated with the impact inertia of the droplets. Experiments using 2.5-mm-diameter droplets were also conducted. The dimensionless collision behaviors of large and small droplets were compared under the same Weber number conditions. At temperatures of less than or equal to 300 °C, the blowout of vapor bubbles occurred at early stages for a large droplet. At a surface temperature of 500 °C, the two dimensionless deformation behaviors of the droplets were very similar to each other.

Modeling of binary droplet collisions for application to inter-impingement sprays

In this paper, we focused on modeling the collision phenomenon between two liquid droplets for application in spray simulations. It has been known that the existing O’Rourke collision model widely used in CFD codes is inaccurate in determining collision outcomes and droplet behavior. In addition, since the collision probability of the model follows a statistical approach involving computational cell geometry, the prediction results should be strongly dependent on the cell size. As a result, to more accurately calculate droplet collisions, the technique for predicting the droplet velocity and its direction after collision must be extended for use in spray modeling. Further, it is also necessary to consider all the possible collision outcomes, such as bouncing, stretching separation, reflexive separation and coalescence. Therefore, this paper describes the appropriateness of a composite concept for modeling collision outcomes and the implementation of deterministic collision algorithms into a multidimensional CFD code for the calculation of post-collisional droplet movements. Furthermore, the existing model does not consider the formation of satellite droplets. For this reason, our present modeling concept includes a fragmenting droplet collision model. Using the present model, we have validated the collision interactions between liquid droplets under high Weber number conditions by comparing our calculations with experimental results from a binary droplet collision. This paper also deals with the application of the model to inter-impingement sprays by analyzing the atomization characteristics, such as mean droplet size and velocity, spray tip penetrations and spray-shapes of the impinging spray using the suggested collision algorithms and then comparing the results with available experimental data.

CHARACTERISTICS OF WATER DROPLET IMPACTION BEHAVIOR ON A POLISHED STEEL HEATED SURFACE: PART I

This paper, which is in two parts, presents the results and analysis of droplet impaction on a hot stainless steel surface. Part I of this study reports the results of analysis of high-speed visualizations of droplet impaction phenomena on a hot stainless steel surface, including the characteristics of reatomized droplets that are produced at high impact Weber numbers. The investigation extends to ranges of smaller droplets and higher velocities compared with published research. Part II will then provide the results and analysis of the droplet impaction heat transfer on a hot surface. The 3.0 mm diameter flat stainless steel surface was heated to temperatures of 140°C < Tw < 400°C, and water sprays were produced from a droplet generation system based on an 80 mm diameter rotary cup. Droplet sizes in the range 20 µm < D < 160 µm were used, impacting with velocities of 5 ms-1 < U < 18 ms-1 . Previous research relevant to the topic is reviewed. Physical models for different forms of droplet breakup in different regimes are developed from the new experiments and compared with existing models. Data are presented for the droplet spreading characteristics, as well as reatomized droplet characteristics, under relatively high impact Weber number conditions (i.e., 100 < We < 750), and for different boiling regimes. These data are correlated well using equations that can be justified by physical arguments.

Thermal Interaction between Molten Metal Jet and Sodium Pool: Effect of Principal Factors Governing Fragmentation of the Jet

To clarify the effects of the principal factors that govern the thermal fragmentation of a molten metallic fuel jet in the course of fuel-coolant interaction, which is important in evaluating the sequence of core disruptive accidents (CDAs) for metallic fuel fast reactors, basic experiments were carried out using molten metallic fuel simulants (copper and silver) and a sodium pool.Fragmentation of a molten metal jet with a solid crust was caused by internal pressure produced by the boiling of sodium, which is locally entrapped inside the jet due to hydrodynamic motion between the jet and the coolant. The superheating and the latent heat of fusion of the jet are the principal factors governing this type of thermal fragmentation. On the other hand, the effect of the initial sodium temperature is regarded as negligible in the case of thermal conditions expected to result in CDAs for practical metallic fuel cores. Based on the fragmentation data for several kinds of jets (Cu, Ag, SUS, U, and U-5 wt% Zr alloy), an empirical correlation is proposed that is applicable to the calculation of a mass median diameter of fragments produced by the thermal fragmentation of the jet with a solid crust under low ambient Weber number conditions.

Deformation process of a droplet impinging on a hot oxide‐scaled surface above the Leidenfrost temperature

This paper is concerned with the collision dynamics of a water droplet impinging on a hot surface heated to above the Leidenfrost temperature, focusing upon the case where the impingement side is rough (oxide‐scaled) with an oxide film. The rough surface has been artificially made by rapidly quenching as‐rolled stainless steel by water spraying, after it has been heated to 1000°C in a furnace. A sequence of photographs showing the progressive stages of droplet deformation have been taken on several Weber number conditions. It has been found that the droplet configuration is not axially symmetric around the initial impact point even at an early stage immediately after collision and that the irregularity of the droplet configuration is amplified as the droplet deformation proceeds. With increasing Weber number, the irregularity has been seen to be more remarkable in the later stage and finally the droplet breaks up into some parts. Therefore, the critical Weber number to specify whether or not the droplet is disintegrated on the rough surface has been found to become small compared with the smooth surface case.

The rate of coalescence in a suspension of high Reynolds number, low Weber number bubbles

The interactions between bubbles of nearly equal size (size ratio less than 1.1 at Re=100, and size ratio less than 1.07 at Re=200) in a suspension of bubbles rising due to gravity were analyzed under high Reynolds number, low Weber number conditions. The potential flow interaction between a pair of bubbles was studied using the equations of motion derived by Kumaran and Koch [Phys. Fluids A 5, 1123 (1993)]. If the horizontal distance between the bubbles is smaller than a critical value, the bubbles approach each other along the horizontal plane and collide. Previous studies suggest that in a collision, the bubbles could either coalesce or bounce off each other. If it is assumed that the bubbles bounce when they collide, they continue to collide repeatedly. The amplitude of the oscillations decrease due to viscous drag, and ultimately the bubbles rise as a horizontally aligned pair. In this configuration, scaling arguments indicate the bubbles coalesce in finite time. The coalescence frequency in a suspension of bubbles was calculated by averaging over pair interactions. This procedure is valid for V≪18/Re, where V is the volume fraction of the bubbles. The coalescence frequency is proportional to V Re−2/5 in this limit.