Critical Weber Number Research Articles

Thin-liquid-film flow on three-dimensional topographically patterned rotating cylinders

Abstract

Study on melt jet breakup behavior with nonorthogonal central-moment MRT color-gradient lattice Boltzmann method

In this paper, the melt jet breakup behavior are numerically studied in 3D with nonorthogonal central-moment MRT color-gradient lattice Boltzmann method, which could significantly enhance the numerical stability and accuracy when applied to flows with very high Reynolds number. Firstly, the methodology to simulate immiscible two-phase flow is validated by conducting droplet oscillation tests. Then the ability of this model to accurately predict melt jet breakup in water is validated by simulating molten Wood's metal jet breakup experiments. Meanwhile, the breakup mechanisms are clarified. For the leading edge, the breakup of the side part is due to large eddies, the main part of the leading edge starts breakup owning to Rayleigh-Taylor instability. For the jet column, small droplets and filaments are stripping due to Kelvin-Helmholtz instability, segment breakup of the jet column is owning to Rayleigh-Taylor instability. Finally, the model is employed to simulate molten corium jet breakup in water. The hydrodynamic characteristics such as jet penetration depth, jet breakup length and fragment size are analyzed in detail. It is found that the simulation results are basically consistent with the dimensionless jet breakup length predicted by Epstein et al.‘s correlation when E0=0.1, but relatively shorter. RTI theory significantly overestimates mass median diameter while critical Weber number and KHI theories underestimate it.

Single drop breakage in a reciprocating plate column

Single drop breakage was investigated in a lab-scale reciprocating plate column. A high-speed camera was used to capture the drop breakage process and drop interactions with the plate. Image processing was completed to collect information on breakage location, breakage probability, breakage time and number of daughter drops under different operating conditions. The flow structure near the reciprocating plate was calculated using a computational fluid dynamics simulation with a moving reference frame. Two breakage mechanisms were observed experimentally, those mainly due to shear stress and those due to plate wettability. Spatial and temporal analysis was completed for the numerical shear stress distribution, and were compared to the breakage locations observed in the experiments. Breakage probability results showed that drops were more likely to breakup at higher reciprocating intensities, for lower interfacial tension systems and for a plate with fewer holes. Initial breakage time was measured but consistent values were not obtained. The number of daughter drops was influenced by the operating conditions and higher energies added to the system, resulting in the formation of more fragments. Finally, a correlation for breakage probability and an estimate of the critical Weber number were proposed.

Wind- and gravity-forced drop depinning

Liquid drops adhere to solid surfaces due to surface tension but can depin and run back along the surface due to wind or gravity forcing. This work develops a simple mechanistic model for depinning by combined gravity and high-Reynolds-number wind forcing and tests that model using water drops on a roughened aluminum surface. On non-inclined surfaces, drops depin at a constant critical Weber number, $W\!e_{\mathrm{crit}}=7.9$, for the present wettability conditions. On inclined surfaces, $W\!e_{\mathrm{crit}}$ decreases linearly with the product of the Bond number and the width-to-height aspect ratio of the unforced drop. The linear slope is different in distinct wind- and gravity-dominated forcing regimes above and below $W\!e_{\mathrm{crit}}=4$. Contact line shapes and drop profile shapes are measured at depinning conditions but do not adequately explain the differences between the two forcing regimes.

A mechanism for the amplification of interface distortions on liquid jets

Abstract

Analytical modelling of laminar drag and freestream turbulence eddies on droplet breakup criterion for internal combustion engines

The paper presents novel analytical droplet breakup criteria, on Weber number (We)-relative turbulence intensity and We-Ohnesorge (Oh) representations, based on the critical Weber number. The We-Oh analytical criterion stressed the importance of turbulence effects on We-Oh breakup criterion at high We-Oh applications. In developing the analytical models the energy criterion for a disturbed parent droplet to disintegrate and the dual-timescale for turbulent shear in droplet dispersion were considered. The present model has an advantage over to two popular droplet breakup criterion models (Pilch-Erdman and Kolev) because the present model has the ability to support a parametric investigation of droplet breakup characteristics in turbulent flow fields. The Weber-relative turbulence intensity and We-Oh analytical breakup criteria are in good agreement with published experimental data. It is envisaged that the analytical model will be incorporated into larger CFD codes for spray simulation. The continuous research in this important area will present the next generation fuel injectors for improved fuel economy of internal combustion engines, especially high-pressure direct injection engines. The model has the potential to be applied in other natural and engineering systems.

Simultaneous measurements of deforming Hinze-scale bubbles with surrounding turbulence

Abstract

Numerical simulation on partial coalescence of a droplet with different impact velocities* *Project supported by the National Natural Science Foundation of China (Grant No. 51876102) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51621062).

Partial coalescence is a complicated flow phenomenon. In the present study, the coalescence process is simulated with the volume of fluid (VOF) method. The numerical results reveal that a downward high-velocity region plays a significant role in partial coalescence. The high-velocity region pulls the droplet downward continuously which is an important factor for the droplet turning into a prolate shape and the final pinch-off. The shift from partial coalescence to full coalescence is explained based on the droplet shape before the pinch-off. With the droplet impact velocity increasing, the droplet shape will get close to a sphere before the pinch-off. When the shape gets close enough to a sphere, the partial coalescence shifts to full coalescence. The effect of film thickness on the coalescence process is also investigated. With large film thickness, partial coalescence happens, while with small film thickness, full coalescence happens. In addition, the results indicate that the critical droplet impact velocity increases with the increase of surface tension coefficient but decreases with the increase of viscosity and initial droplet diameter. And there is a maximum critical Weber number with the increase of surface tension coefficient and initial droplet diameter.

Droplet breakup and coalescence of an internal-mixing twin-fluid spray

Droplet breakup and collision dynamics of an internal-mixing twin-fluid (air-assisted) spray were investigated experimentally. Time-resolved spray morphological evolutions were obtained by employing a high-speed spray visualization system, while droplet size and velocity were measured by using a phase-Doppler particle analyzer. The results show that the air-assisted spray is composed of a bulk of tiny droplets entrained by high-speed gas-phase flow. Droplets with a diameter of less than 5 µm account for the majority of samples on the basis of the distribution function. The calculated Stokes numbers of selected tracer droplets (0 µm–5 µm) show that these droplets tend to follow the air flow faithfully and thus can be used to estimate the local air flow velocity. By comparing with the critical Weber number, we found that droplet shear breakup is absent, but some droplets may undergo turbulent breakup. A theoretical analysis accounting for the effects of the turbulent dissipation rate on both droplet breakup and coalescence was performed, and the critical equilibrium length of breakup and coalescence is found to be less than 3.0 mm. In terms of droplet collision dynamics in the spray far-field, coalescence dominates droplet collision outcomes; therefore, the droplet size increases linearly as the spray downstream distance X increases. Particularly, the influence of the droplet size ratio [C. Tang, P. Zhang, and C. K. Law, “Bouncing, coalescence, and separation in head-on collision of unequal-size droplets,” Phys. Fluids 24, 022101 (2012)] was adopted to quantify the droplet coalescence probability. When compared to the n-octane spray, the n-dodecane spray accounts for more droplet bouncing (II) since n-dodecane possesses a relatively larger bouncing (II) region.

Coalescence of Al droplet impacting on a melt surface

The droplet falling into its bulk liquid surface is very common but complex which widely exists in nature and industry. In this case, the impact behavior is almost simultaneous with the coalescence. To deeply understand the dynamics and mechanism of this phenomenon, molecular dynamics simulations have been performed to study the characteristics of the impact coalescence process under different conditions. Results show that four coalescence behaviors, including rebound, calm coalescence, deformation and coating, are mainly determined by the impact velocity. Interestingly, a cavity is observed in the liquid bulk when the impact velocity is big enough, which can be explained by the momentum transfer. Beyond that, the mixing degree increases with Weber number and there is a critical Weber number between rebound and coalescence. The study illustrates how the temperature and impact velocity affects the coalescence behavior and provides opportunity to well understand the droplet impact process towards its melt surface.

Flow Regime Transition in the Post-CHF Flow Regimes under Subcooled and Low-quality Conditions

Post critical heat flux (post-CHF) heat transfer may occur during loss of coolant accidents (LOCAs) in water-cooled nuclear reactors when makeup water quenches the uncovered portion of fuel rods in the reactor cores. Post-CHF flow regimes include inverted annular film boiling (IAFB), dispersed flow film boiling (DFFB), and a transition regime between these two, i.e., inverted slug film boiling (ISFB) for low mass fluxes or agitated inverted annular film boiling (AIAFB) for high mass fluxes. Flow regime transition is important for modeling heat transfer characteristics in the post-CHF flow regimes. Breakup of the liquid core in the IAFB regime represents the flow regime transition from the IAFB to ISFB/AIAFB regimes. This paper first presents a literature review of previous experimental and theoretical studies of the mechanisms of breakup of the liquid core in the IAFB regime and flow regime transition in the post-CHF regimes. To physically explain the breakup of the liquid core in the IAFB regime, the Weber number is calculated from the experimental data obtained from steady-state post-CHF experiments at subcooled and low-quality conditions and a critical Weber number is obtained to describe the flow regime transition from the IAFB to ISFB/AIAFB regimes. Parametric effects of the inlet subcooling, mass flux, and system pressure on the critical Weber number are then studied, based on which a new correlation for the critical Weber number is proposed to predict the flow regime transition from the IAFB to ISFB/AIAFB regimes. Due to the different flow patterns in the transition regime, i.e., ISFB and AIAFB respectively for low and high mass fluxes, the heat transfer characteristics show different trends. The indication of the flow regime transition from the IAFB to ISFB/AIAFB regimes by the critical Weber number criterion matches well with the trend of the wall heat transfer coefficient.

A model of droplet breakup in a turbulent flow for a high dispersed phase holdup

A model of droplet breakup during formation of a dense emulsion in a turbulent flow is developed. Droplet fluctuation velocities, eventually causing breakup, are determined using the kinetic theory of granular media. For model validation, an experimental Couette device is employed. The dispersed and continuous phases are deionized water and mineral oil, respectively. Droplet coalescence is suppressed by a surfactant. A series of experiments is conducted for different Couette device rotation speeds and water holdups. For identification of the major droplet breakup model parameter, the critical Weber number, droplet dispersion in the Couette device is modelled by CFD-population balance A-MuSiG method implemented into the developer’s version of the Simcenter STAR-CCM+® commercial code. A good agreement between the computational and experimental data is obtained for the dispersed phase holdups in the range of 10–30%, commonly encountered in production logging of oil and water producing wells.

Experimental Investigation of Water Droplet Impact on the Electrospun Superhydrophobic Cylindrical Glass: Contact Time, Maximum Spreading Factor, and Splash Threshold.

The impinging of water droplets on superhydrophobic cylindrical glasses has been investigated experimentally by using a high-speed camera. The superhydrophobic cylindrical surfaces were fabricated by electrospinning technique combined with silane treatment. The effects of the diameter ratio of cylindrical glass and Weber number on the postimpact regime, contact time, maximum spreading factor, and splash threshold were investigated in the ranges 3.5-16 and 27-161, respectively. The results were compared with impact droplets on superhydrophobic flat glass and uncovered hydrophilic cylindrical glass. Three types of regimes were observed on hydrophilic and superhydrophobic cylindrical glasses including coating, splash, and splash-rebound. Results showed that contact time on the cylindrical surface is up to 50% less than the flat one. Moreover, the splash regime was started at the critical Weber number = 134 on high-diameter-ratio superhydrophobic cylindrical and flat surfaces while happening earlier when the diameter ratio is below D* < 4.

Delayed Leidenfrost phenomenon during impact of elastic fluid droplets

This article highlights the role of non-Newtonian (elastic) effects on the droplet impact phenomenon at temperatures considerably higher than the boiling point, especially at or above the Leidenfrost regime. The Leidenfrost point (LFP) was found to decrease with an increase in the impact Weber number (based on the velocity just before the impact) for fixed polymer (polyacrylamide) concentrations. Water droplets fragmented at very low Weber numbers (approx. 22), whereas the polymer droplets resisted fragmentation at much higher Weber numbers (approx. 155). We also varied the polymer concentration and observed that, up to 1000 ppm, the LFP was higher than that for water. This signifies that the effect can be delayed by the use of elastic fluids. We have shown the possible role of elastic effects (manifested by the formation of long lasting filaments) during retraction in the increase of the LFP. However, for 1500 ppm, the LFP was lower than that for water, but had a similar residence time during the initial impact. In addition, we studied the role of the Weber number and viscoelastic effects on the rebound behaviour at 405°C. We observed that the critical Weber number up to the point at which the droplet resisted fragmentation at 405°C increased with the polymer concentration. In addition, for a fixed Weber number, the droplet rebound height and the hovering time period increased up to 500 ppm, and then decreased. Similarly, for fixed polymer concentrations like 1000 and 1500 ppm, the rebound height showed an increasing trend up to certain a certain Weber number and then decreased. This non-monotonic behaviour of rebound heights was attributed to the observed diversion of the rebound kinetic energy to rotational energy during the hovering phase. Finally, a relationship between the non-dimensional Leidenfrost temperature and the associated Weber and Weissenberg numbers is developed, and a scaling relation is proposed.

Experiments on splashing thresholds during single-drop impact onto a quiescent liquid film

The process of normal impingement of a single drop onto a quiescent liquid film was investigated experimentally to determine the thresholds of the early and late splashes. Seven liquids of different hydraulic properties were used and the liquid film thickness was varied within about 0.2–3 times the impacting drop diameter. It was found that the critical Weber number for the early splash to occur is dependent on the liquid properties (more specifically, the Ohnesorge number) but not on the liquid film thickness. On the other hand, the critical Weber number of the late splash was influenced by both the liquid properties and the liquid film thickness. It increased gradually with an increase in the liquid film thickness in a thin film range and jumped to a constant value when the critical film thickness was reached. The critical film thickness was 0.7 times the impacting drop diameter in average in the present experiments. Using the present experimental data, dimensionless correlations were developed for the thresholds of the early and late splashes. The predictive performances of the proposed correlations were tested against the experimental databases available in the literature. Due to the complexity of the drop impact process, noticeable disagreements remained between the experimental data and the predictions even in the simple situation explored in this work. Nonetheless, the present dimensionless correlations succeeded to express the overall trends of the splashing thresholds fairly well.

Collision dynamics of SDS solution drops on a smooth wood substrate: Role of surface tension

Drop impact has been widely studied as it plays a key role in numerous scientific and industrial applications. Despite an extensive trove of literature, only a limited number of studies have investigated the behavior of liquid drops impinging on polished wood. Subsequently, to better ascertain how surface tension (ST) influences the drop impact behavior on smooth wood surfaces, the impingement of SDS solution drops on a polished Diospyros crassiflora substrate (Rq = 0.60 μm) was investigated in this study. The results revealed a distinct absence of recoil amongst the impinging SDS solution drops (γ = 72–40 mN/m) when the maximum wetting diameter was reached. However, a decrease in ST did correspond to the formation of more prominent finger-like projections and an increase in the extent up to which it spread on the wood surface. Interestingly, similar behavior was observed amongst impinging water/SDS solution drops when the impact velocity was increased (0.44–2.9 m/s); thus, indicating that in general, the drop impact behavior of SDS solution drops on wood was significantly dependent on its Weber number. A decrease in the ST also corresponded to an increase in the critical Weber number or a decrease in the critical impact height (Hc). An increase in the impact height (>Hc) was marked by an increase in the number of emitted droplets. The volume and propagation velocities of these droplets were dependent on the time (after impact) at which they were formed.

Experimental study of droplet impact on superheated cylindrical surfaces

In this study, droplet impact dynamics on superheated cylindrical surfaces are investigated experimentally, through high-speed imaging. The outcome regimes of impacting droplets observed in the experiments are mapped and described. Four distinguishable regimes are identified, namely rebound-transition boiling, rebound-film boiling, breakup-transition boiling, and breakup-film boiling. In addition, the effects of Weber number, surface temperature and curvature diameter on boiling mode, film thickness, droplet spreading and contact time are examined. The scaling laws of maximum spreading ratio and liquid film thickness with the impact Weber number are established. The larger film thickness on the concave surface reduces the dynamic Ledifenfrost temperature, meanwhile improves the critical Weber number for droplet breakup. Under the effect of the tangential gravity component, the spreading of droplets in the circumferential direction is suppressed on the concave surface, while is promoted on the convex surface. Increasing the curvature diameter, the maximum spreading increases on the concave surface, but decreases on the convex surface. The maximum spreading on both surfaces decreases with the wall temperature in the transition boiling state. Noticeable reduction in the contact time of droplets in the rebound regimes are observed on both surfaces, especially on the concave surface. The contact time is shown to generally decrease with the wall temperature, but increase with the curvature diameter.

Droplet breakup and rebound during impact on small cylindrical superhydrophobic targets

The impact behavior of a water droplet on small cylindrical superhydrophobic targets is studied numerically and theoretically. A numerical model using the volume of fluid method is developed to simulate the droplet impact process on small cylindrical superhydrophobic targets. The model is verified by comparing the calculated results with the experimental observations in our previous work and reference. The influences of the Weber number and the target-to-droplet diameter ratio (less than one) on the droplet impact behaviors, including the droplet profile and the deformation factor, are investigated. The results indicate that a larger Weber number accelerates the spreading and falling of the droplet and promotes the droplet breakup. An increase in the diameter ratio delays the spreading and falling of the droplet on the side of the target, thus enhancing the deformation and rebound of the droplet. Both the increases in the Weber number and the diameter ratio contribute to a larger maximum deformation factor. Furthermore, the droplet breakup criterion is analyzed theoretically based on the energy conservation. A formula describing the relationship between the critical Weber number and the diameter ratio for the droplet breakup is proposed, which shows high prediction accuracy compared with the numerical values. The critical Weber number for the droplet breakup becomes larger with the increase in the diameter ratio. The findings in this research deepen our understanding of the mechanism of droplet impact on small targets.

Deformation and regimes of liquid column during water exit of a partially submerged sphere using the front-tracking lattice Boltzmann method

When a solid sphere exits water at a given velocity, the liquid column is pulled out of a liquid reservoir. The present study focuses on the dynamic deformation of the liquid column and on the identification of the liquid column regime on the Weber number and dimensionless time (We-t*) map. The three-dimensional model of water exit has been established on the basis of the lattice Boltzmann method. A mass tracking algorithm was incorporated to capture the free surface, where the liquid–gas​ two-phase flow is simplified to a single-phase free surface flow. The surface tension is included by adding a perturbation term and the gravity as a body force is introduced in form of calculating the equilibrium distribution with an altered velocity. The contact angle condition in numerical simulation is not considered. The accuracy of the numerical results is demonstrated through the comparisons with the prior numerical and the experimental results in the literature. A parametric study has been conducted numerically on the radius and volume and of liquid column. Besides, the relationship between the pinch-off time of a liquid column and the Froude number has been obtained. Moreover, the evolution of the liquid column shape with a wide range of the Weber number and time scales are discussed based on the number of ligaments and droplets. The liquid column exhibits different characteristics and has been divided into three regimes. The transition between different regimes has been analyzed and the critical Weber number is given.

Effects of Turbulence on the secondary breakup of droplets in diesel fuel sprays

In this paper, the importance of turbulence effects on the procedure of droplet’s secondary breakup is studied. In the process of modeling the secondary breakup of a droplet, it is a common practice to presume that the droplet is moving in a laminar flow. However, it is evident that the critical Weber number is profoundly affected by the intensity of turbulence presented in the flow. As a result, the abovementioned supposition may lead to significant computational inaccuracy. This paper tends to perform a modification that considers the effects of turbulent flow on the secondary breakup of droplets. It is shown that the results obtained by the modified model are more precise and in a better agreement with experimental data. In this paper, spray behavior is predicted by a conventional breakup model and the one obtained by a modified model, which are both implemented in an in-house computer code. This CFD code accounts for engine simulation by solving the governing two-phase-flow equations using the Eulerian-Lagrangian approach in a three-dimensional coordinate system. To show the effects of turbulence, the changes in spray parameters such as droplet size distribution, spray tip penetration, and spray mean diameter, which is extracted from the two models are compared. Results have shown that the turbulence causes droplets to break in an earlier time, which leads to a higher rate of evaporation and lower penetration length. An interesting fact concluded in this paper is that the difference between the results of the two models decreases as the gas pressure is increased, which means the effects of turbulence become less important as the gas pressure increases.