Aerodynamic Breakup Research Articles

Aerodynamic breakup of emulsion droplets in airflow

AbstractAerodynamic breakup refers to the process where large droplets are fragmented into small droplets by the aerodynamic force in airflow, which plays a vital role in fluid atomization and spray applications. Previous research has primarily concentrated on the aerodynamic breakup of single‐component droplets, but investigations into the breakup of emulsion droplets are limited. This study experimentally investigated the aerodynamic breakup of water‐in‐oil emulsions in airflow, utilizing high‐speed photography to observe the breakup process and digital in‐line holography to measure fragment sizes. Comparative analyses between emulsion droplets and single‐component droplets are conducted to examine the breakup morphology, breakup regime, deformation characteristics, and fragment size distributions. The emulsion droplets exhibit higher apparent viscosity and shorter stretching lengths of the bag film and peripheral rim due to the presence of a dispersed phase. The breakup regime transitions of emulsions are modeled by integrating the viscosity model of emulsions and the transition model of the pure fluid. The fragment sizes of emulsion droplets are larger due to the shorter lengths of the bag film and peripheral rim.

Aerodynamic breakup of gel suspension droplets loaded with aluminum particles

The persistent and frequent space explorations are affected by the performance of propellants, among which the closely related gel propellants have been widely used due to their unique characteristics. Currently, research efforts primarily concentrate on the metallization and atomized combustion of gel propellants, emphasizing the combustion performance of metallized gel propellants. However, little attention has been given to the secondary breakup process that occurs just before combustion. By utilizing high-speed flow visualization technology, this study examines the key aerodynamic breakup process of gel suspension droplets loaded with micro aluminum particles, experimentally and theoretically investigating the droplet dynamics induced by particle volume fraction. The experimental confirmation of the three breakup behaviors exhibited by gel suspension droplets, namely oscillation mode, bag-stamen breakup, and hemline breakup, is presented along with the construction of a phase diagram. The impact of heterogeneous effects resulting from an increase in particle volume fraction on the critical breakup Weber number is revealed, with a concentration of 9 % as the turning point. Within the range of moderate Weber numbers, the tail flick deformation of suspension droplets in airflow is observed and reported for the first time. At different particle concentrations, there keeps a linear correlation between the dimensionless tail length and Weber number. Spherical suspension droplets will deform into thin disks in the airflow, with a nearly constant deformation rate regardless of changes in particle concentration. Additionally, the relationships between characteristic times and droplet parameters are discussed through statistical analysis of the results. As Ohnesorge number and particle volume fraction increase, the characteristic times both show a monotonically increasing trend. Moreover, a model of unstable growth rate associated with the particle volume fraction is established through linear instability analysis, accurately predicting the variation in critical Weber number for gel suspension droplet breakup. The congruence between our theoretical framework and experimental findings not only enhances comprehension of the impact of micro aluminum particles on the secondary breakup of gel suspension droplets but also provides valuable guidance for the aerospace applications of metallized gel propellants.

Improved semi-theoretical correlation to predict the Sauter mean diameter of swirl cups

The spray downstream of swirl cups involves complex two-phase flow. Comprehensively, understanding the flow physics of the spray to accurately predict the characteristics of the swirl spray is crucial for developing next-generation low-emission gas turbine combustors. The Sauter mean diameter (SMD) of the spray is an important design parameter in a gas turbine combustor, and the semi-theoretical method is among the most widely used approaches for predicting the SMD of atomizers. Of the available semi-theoretical models for predicting the SMD of prefilming-type atomizers, Shin's phenomenological three-step atomization (PTSA) model is a physics-based correlation. The PTSA model comprises three submodels: those of the pressure-swirl spray, impingement and film formation, and aerodynamic breakup. Based on similar physical mechanisms, the PTSA model can effectively predict the SMD for the spray shear layer of swirl cups. In this study, a new model, called the PTSA-V model, is proposed by introducing the viscosity of the liquid to the three submodels of PTSA. Additionally, the submodel of impingement and film formation was reconstructed, using a simplified model of a round water jet impinging on a cylindrical wall to predict the thickness of the liquid film on the Venturi surface. Experiments were carried out on a swirl cup under different pressures and temperatures of fuel as well as varying pressure drops in the air by using a two-component phase Doppler particle analyzer. The resulting uncertainty in predictions of the PTSA-V model was lower than ±7.4% under the 26 operating conditions considered here, compared with an uncertainty of ±20% in the outcomes of PTSA. Uncertainty in predictions of PTSA-V was lower than ±15% when it was applied to SMD data downstream of the swirl cup from the literature.

Study on the Interface Instability of a Shock Wave–Sub-Millimeter Liquid Droplet Interface and a Numerical Investigation of Its Breakup

This study investigated the influence of instability on the interaction between sub-millimeter liquid droplets and shock waves. Experiments were conducted using 0.42 mm diameter droplets with varying shock wave Mach numbers. The investigation quantified the effects of Weber numbers and initial diameters on the development of Rayleigh–Taylor and Kelvin–Helmholtz instabilities at the shock wave–sub-millimeter liquid droplet interface. Three-dimensional numerical simulations were performed to investigate the deformation and breakup behaviors of sub-millimeter liquid droplets under the impact of a shock wave with a Mach number of 2.12. The post-shock gas flow environment in this condition was in a supersonic state. The simulations utilized the volume-of-fluid method to model the gas–liquid interface, employed unsteady Reynolds-averaged Navier–Stokes methods to simulate turbulence, and incorporated grid gradient adaptive technology to enhance computational efficiency. The results revealed that by increasing the Weber number or decreasing the initial diameter, both the growth rate and the wavenumber extremum of the Rayleigh–Taylor and Kelvin–Helmholtz instability waves increased. The variation in the K–H instability’s growth rate extremum increasing Weber number surpassed that of the R–T’s instability. This indicated that both the R–T and K–H waves on sub-millimeter liquid droplets tended to exhibit increased growth rates and reduced scales. Moreover, as the Weber number increased, the K–H instability became dominant in the aerodynamic fragmentation. The numerical simulations showed good qualitative agreement with the experimental data, affirming the viability of numerical methods for addressing such challenges. The evolution of the sub-millimeter liquid droplets was marked by two primary stages, flattening and shear stripping, signifying that the K–H instability-driven SIE mechanism governed the aerodynamic breakup in the supersonic post-shock airflow.

Physics-based reduced-order modeling of flash-boiling sprays in the context of internal combustion engines

Flash-boiling injection is one of the most effective ways to accomplish improved atomization compared to the high-pressure injection strategy. The tiny droplets formed via flash-boiling lead to fast fuel–air mixing and can subsequently improve combustion performance in engines. While most of the previous studies related to the topic focused on modeling flash-boiling sprays using three-dimensional (3D) computational fluid dynamics (CFD) techniques such as direct numerical simulations (DNS), large-eddy simulations (LES), and Reynolds-averaged Navier–Stokes (RANS) simulations, the present work introduces a reduced-order cross-sectionally averaged spray (CAS) model with significantly reduced computational cost. The proposed CAS model incorporates several physical submodels in flash-boiling sprays such as those for air entrainment, drag, superheated droplet evaporation, flash-boiling induced breakup, and aerodynamic breakup models. The CAS model is then applied to different fuels to investigate macroscopic spray characteristics such as liquid and vapor penetration lengths under flash-boiling conditions. It is found that the newly developed CAS model captures the trends in global flash-boiling spray characteristics reasonably well for different operating conditions and fuels. Moreover, the CAS model is shown to be faster by up to four orders of magnitude compared with simulations of 3D flash-boiling sprays. The novelty of the present work lies in providing a reduced-order flash-boiling spray model that offers cost-effective computational representations of complex phenomena. The proposed model can be very valuable for applications, such as experimental design, fuel screening, and creating digital twins, thus playing a crucial role in the advancement of research and development in the field of spray combustion.

Numerical Investigation into Characteristics of WIPCC and Distortion of S-shaped Intake

Water injection pre-compressor cooling technology can efficiently increase the engine thrust and expand the flight envelope of the aircraft. Changes in the curvature of the intake and the evaporative cooling of the spray medium naturally distort the total pressure, total temperature, and characteristics of the swirl of the flow before it enters the engine. This study conducts numerical research on the aerothermal process of the WIPCC in an S-shaped intake using the Eulerian-Lagrangian method. The spatial evolution of critical variables along the flow direction and specific cross-sections were obtained by analyzing the statistical time-averaged results of multiphase flow. The transient distortion descriptors were quantified and analyzed following the SAE standard, which revealed the characteristics of various distortions and their spatial-temporal changes. Furthermore, the variables reflecting the transient flow structure were decomposed using the POD method to obtain the coherent structure of each mode and its frequency and energy characteristics. The results showed that aerodynamic breakup was the main cause of droplet size reduction and led to a decrease of 74.4% and 63.8% in Sauter droplet size under two conditions, respectively. The downstream mixing of flows in the S-duct mitigated the distortions caused by the intake's changing curvature and droplet evaporation. After the mixing of flows under specific conditions, the total pressure distortion coefficient decreased from 0.30 to 0.12, the swirl intensity decreased from 4°-6° to 2°-4°, and the high total temperature extent decreased from 0.65 to 0.35. The POD mode of the variables exhibited broadband characteristics with multiple spikes and energy dispersion. The main modes of the drop coefficients in total pressure and temperature corresponded to large- and small-scale structures, respectively, with Strouhal number ranges of 0.079-0.394 and 0.362-1.260. These results reveal the effects of WIPCC on the aerothermal processes in the S-shaped intake and the mechanism of generation and evolution of distortions. Moreover, the results provide reasonable boundary conditions for numerical investigations of wet compression under intake distortions.

Simulation and modeling of the vaporization of a freely moving and deforming drop at low to moderate Weber numbers

The vaporization of a freely moving drop in a uniform, high-temperature gas stream is investigated through direct numerical simulation. The incompressible Navier-Stokes equations with surface tension and phase change are solved in conjunction with the energy equations of each phase. The sharp liquid-gas interface is tracked using the geometric Volume-of-Fluid (VOF) method and an immersed Dirichlet boundary condition for temperature is imposed at the interface. The simulation approach is validated by simulating water and acetone drops at nearly zero Weber numbers, and the simulation results agree very well with the empirical relation for spherical drops. Parametric simulations were conducted to investigate the aerodynamic breakup of vaporizing drops at low to moderate Weber and Reynolds numbers. The range of Weber numbers considered has covered the vibrational and bag breakup regimes. Through the simulation results, we have characterized the impact of drop deformation and breakup on the drop vaporization rate. When the drop Weber number increases, the windward surface area increases more rapidly over time. As a result, the rate of drop volume reduction also increases. The correlation between the vaporization rate and the windward surface area is examined for different Weber and Reynolds numbers. Using the approximate correlation between the drop vaporization rate and the windward surface area and the TAB model for drop deformation, a new time-dependent drop vaporization model is proposed. The present model agrees well with the simulation results and shows a significant improvement over the conventional model for spherical drops.

Numerical simulations of droplet evaporation and breakup effects on heterogeneous detonations

Evaporation and breakup of droplets are critical phenomena in the liquid-fueled, multiphase detonation process. Understanding the relevant conditions and times for each process is crucial for predicting real world behavior. In this paper, the effects of evaporation and breakup on the multiphase detonation process will be explored through Euler-Lagrange (EL) simulations. Various droplet sizes of n-dodecane (C12H26) are reacted with oxygen (O2) utilizing a single-step global reaction mechanism. Droplet processes are modeled using temperature dependent thermophysical properties through the liquid-gas phase change and into the supercritical regime. Two aerodynamic breakup models are considered (based on theorized hydrodynamic instability mechanisms) from both empirical and theoretical approaches. Detonation wave velocity deficits are observed to be sensitive to breakup and evaporation time. It is shown that droplets redistribute fuel vapor mass over their lifetime, perturbing the equivalence ratio and creating vapor rich regions that cannot fully react. It was shown that as the total evaporation time decreases (shorter breakup time), the detonation structure becomes more like the idealized gaseous detonation case.

Superhydrophobic ceramic coatings with lotus leaf-like hierarchical surface structures deposited via suspension plasma spray process

In this work, superhydrophobic yttria-stabilized zirconia coatings were deposited via the suspension plasma spray process using a new water-based suspension. The new water-based suspension was prepared with the addition of surfactant, which showed a much lower surface tension than the conventional water-based suspension, and meanwhile was much cheaper and safer, and more environmentally friendly than the ethanol-based suspension. The coatings exhibited lotus leaf-like hierarchical surface structures of micron-sized protuberances with superimposed nanometer-sized splats/particles. After chemical modification, the coatings showed excellent water repellency with a water contact angle of ∼157°, a roll-off angle of ∼5°, and complete droplet rebound behaviors. The ethanol-based suspension and conventional water-based suspension were also prepared and used for coating deposition. Comprehensive characterizations of the suspension properties (surface tension, viscosity, atomization behaviors), surface structures, and wetting behaviors of different coatings were conducted for comparative investigation. The formation mechanism of different surface structures was elaborated by investigating the properties of suspensions and plasma gas flow, the aerodynamic breakup behaviors of suspensions, and the motion of impinging particles. The different wetting behaviors of coatings were correlated with the surface structures and wetting states. The study provides a rapid and cost-effective way to deposit hierarchically-structured superhydrophobic ceramic coatings via the water-based suspension plasma spray process.

An ammonia flash break-up model based on bubble dynamics with force and energy analysis on droplet

Ammonia flash break-up model was developed using bubble dynamics based on force analysis of surface tension and pressure forces in this study. The initial bubble radius was calculated by modifying bubble number density equation considering the superheat degree with assuming a single bubble in the droplet. The Rayleigh–Plesset equation with compressibility factor was employed to calculate bubble growth in the liquid ammonia droplet. Droplet disintegration was predicted by force analysis. The velocity change by flash break-up was assumed to be a product of the surplus energy between the surface-energy change and the pressure work, and the bubble growth rate. The simulation results were compared to results in a previous experimental study of ammonia spray behavior. The time constant of the thermodynamic breakup model was added to simulate the flash boiling condition that induces rapid spray changes. In this study, the time constant 12 is used through the verification process. Compared with previous experimental results of ammonia flash boiling spray, the proposed flash breakup model was superior in predicting radial spray development by the flash boiling compared to the conventional aerodynamic breakup model.

A consistent volume-of-fluid approach for direct numerical simulation of the aerodynamic breakup of a vaporizing drop

A novel simulation framework has been developed in this study for the direct numerical simulation of the aerodynamic breakup of a vaporizing drop. The interfacial multiphase flow with phase change is resolved using a consistent geometric volume-of-fluid method. The bulk fluids are viscous and incompressible with surface tension at the interface. The newly-developed numerical methods have been implemented in the Basilisk solver, in which the adaptive octree/quadtree mesh is used for spatial discretization, allowing flexibility in dynamically refining the mesh in a user-defined region. The simulation framework is extensively validated by a series of benchmark cases, including the 1D Stefan and sucking problems, the growth of a 3D spherical bubble in a superheated liquid, and a 2D film boiling problem. The simulation results agree very well with the exact solution and previous numerical studies. 2D axisymmetric simulations were performed to resolve the vaporization of a moving drop with a low Weber number in a high-temperature free stream. The computed rate of volume loss agrees well with the empirical model of drop evaporation. Finally, the validated solver is used to simulate the aerodynamic breakup of an acetone drop at a high Weber number. A fully 3D simulation is performed and the morphological evolution of the drop is accurately resolved. The rate of vaporization is found to be significantly enhanced due to the drop deformation and breakup. The drop volume decreases nonlinearly in time and at a much higher rate than the empirical correlation for a spherical drop.

Hybrid VOF–Lagrangian CFD Modeling of Droplet Aerobreakup

A hybrid VOF–Lagrangian method for simulating the aerodynamic breakup of liquid droplets induced by a traveling shock wave is proposed and tested. The droplet deformation and fragmentation, together with the subsequent mist development, are predicted by using a fully three-dimensional computational fluid dynamics model following the unsteady Reynolds-averaged Navier–Stokes approach. The main characteristics of the aerobreakup process under the shear-induced entrainment regime are effectively reproduced by employing the scale-adaptive simulation method for unsteady turbulent flows. The hybrid two-phase method combines the volume-of-fluid technique for tracking the transient gas–liquid interface on the finite volume grid and the discrete phase model for following the dynamics of the smallest liquid fragments. The proposed computational approach for fluids engineering applications is demonstrated by making a comparison with reference experiments and high-fidelity numerical simulations, achieving acceptably accurate results without being computationally expensive.

Effects of liquid properties on atomization and spray characteristics studied by planar two-photon fluorescence

In this work, planar two-photon laser-induced fluorescence (2p-LIF) is applied for the first time to analyze the fluid dependent spray structure and atomization behavior of water and ethanol in a quantitative way. A commercial six-hole DISI (Direct-Injection Spark-Ignition) injector was studied at different injection pressures, operated with liquids containing the LIF dye fluorescein. Specifically for DISI-injectors, the fluid-dependent atomization is very complex and not fully understood due to the cavitating, turbulent nozzle flow that dominates the spray formation. Optical access and analysis of the near-nozzle spray are often challenging due to multiple light scattering in dense regions which is reduced by 2p-LIF measurements using a femtosecond laser. This allows high-contrast spray imaging close to the nozzle, resulting in an improved identification of single liquid structures of the spray. Thus, a higher accuracy of sizing is possible. Compared to water, the ethanol spray shape shows increased cone angles in the nozzle near-field of about 6%, which cannot be explained by classical atomization theory based on aerodynamic breakup. The larger cone angle of ethanol was attributed to its larger viscosity, which could decelerate the flow at the wall of the injection hole, affecting the velocity profile of the emerging jet. The atomization shows a main jet breakup distance of 7–10 mm in which the structure sizes decreased drastically, specifically for water. For the size of the liquid structures in the near-nozzle region, which show dimensions of about 80–130 μm, ethanol exhibited about 2% smaller Feret's diameters than water for the tested time steps at 20 MPa. This effect is even more distinct for other injection pressures and positions at a further distance to the injector. For all investigated conditions and measurement positions downstream of the nozzle, ethanol showed on average about 24% smaller structures compared to the water spray. Although this trend is in accordance with the classical atomization theory based on the aerodynamic breakup mechanism, other effects, such as cavitation and nozzle-flow induced breakup, contribute to this behavior.

Columnar-structured thermal barrier coatings deposited via the water-based suspension plasma spray process

Suspension plasma spray (SPS) has been developed as a rapid, facile and cost-effective process to deposit columnar-structured thermal barrier coatings (TBCs). In contrast to the most commonly used ethanol-based suspensions, water-based suspensions have not been used in the SPS process to deposit columnar-structured TBCs due to their high surface tension, although they are much cheaper and safer. In this work, a new water-based SPS process was prepared by adding surfactant to lower the surface tension. The optimum content of dispersant and surfactant added to the suspension was determined via measurements of viscosity, particle size, surface tension, contact angles, and atomized droplet size. Coatings deposited using suspensions with and without surfactant showed typical columnar-structured microstructures and vertically cracked microstructures, respectively. The coatings deposited using suspensions with surfactant also showed evolution from columnar-structured microstructures to mixed microstructures of columns and cracks, and to homogeneous microstructures with the increase in standoff distance. The formation of different coating microstructures was correlated to the size of droplets after aerodynamic breakup and the Stokes number of in-flight particles. The new water-based suspension together with the water-based SPS process show great potential to be a cheap and effective alternative to the ethanol-based SPS process.

Computational Evaluation of Shock Wave Interaction with a Liquid Droplet

This article represents the natural continuation of the work by Rossano and De Stefano (2021), dealing with the computational fluid dynamics analysis of a shock wave interaction with a liquid droplet. Differently from our previous work, where a two-dimensional approach was followed, fully three-dimensional computations are performed to predict the aerodynamic breakup of a spherical water body due to the impact of a traveling shock wave. The present engineering analysis focuses on capturing the early stages of the breakup process under the shear-induced entrainment regime. The unsteady Reynolds-averaged Navier–Stokes approach is used to simulate the mean turbulent flow field in a virtual shock tube device with circular cross section. The compressible-flow-governing equations are numerically solved by means of a finite volume method, where the volume of fluid technique is employed to track the air–water interface. The proposed computational modeling approach for industrial gas dynamics applications is verified by making a comparison with reference numerical data and experimental findings, achieving acceptably accurate predictions of deformation and drift of the water body without being computationally cumbersome.

Effects of fuel properties and aerodynamic breakup on spray under flash boiling conditions

• Sprays of four single component fuels under flash boiling conditions were studied. • Spray collapses at R p of 0.28 for isooctane, hexane and ethanol, and 0.18 for pentane. • Ethanol has relatively larger near-field angle, far-field angle and SMD. • Aerodynamic breakup still plays an important role under low flash boiling conditions. • Isooctane, hexane and pentane under R p of 0.28 show a similar SMD value of 10 µm. The main purpose of this work is to conduct detailed comparisons of spray behavior among four important components of gasoline and to investigate the effects of fuel properties and aerodynamic breakup on spray behavior under flash boiling conditions. Isooctane, hexane, pentane, and ethanol were used as test fuels. Pressure ratio ( R p ) was used as an indicator for the superheated degree and varied from 0.14 to 1.1 by adjusting the ambient pressure. Both Diffused Backlight Imaging (DBI) and Phase Doppler Anemometry (PDA) measurements were used to obtain macroscopic and microscopic characteristics of sprays. Four dimensionless numbers were used to evaluate the aerodynamic breakup processes. The results showed that as the reduction of R p , the flash boiling intensity increased, leading to dramatic spray morphology changes and smaller droplet size, regardless of fuel type. Spray plumes merged into the spray center when lowering R p from 1.0. Spray collapsed at an R p of 0.28 for isooctane, hexane, and ethanol, and at an R p of 0.18 for pentane. Fuel properties also had significant effects on spray behaviors. Spray with pentane had the smallest penetration length, and a dramatic far-field angle reduction was observed at R p between 0.2 and 0.4, due to its higher vapor pressure and lower latent heat of vaporization. Under the same R p , ethanol sprays had relatively larger near-field angles, far-field angles, and Sauter mean diameter (SMD), due to its high latent heat of vaporization. All the dimensionless numbers showed that the spray with pentane had the largest aerodynamic breakup intensity, followed by hexane and isooctane, while ethanol had the lowest aerodynamic breakup intensity under the tested conditions. Aerodynamic breakup still played an important role under low flash boiling intensity conditions ( R p over 0.8). Microscopic results showed that SMD of isooctane, hexane, and pentane under an R p of 0.28 had a similar value of 10 µm.

A Consistent Volume-of-Fluid Approach for Direct Numerical Simulation of the Aerodynamic Breakup of a Vaporizing Drop

A Consistent Volume-of-Fluid Approach for Direct Numerical Simulation of the Aerodynamic Breakup of a Vaporizing Drop

Droplet aerobreakup under the shear-induced entrainment regime using a multiscale two-fluid approach

A droplet exposed to a high-speed gas flow is subject to a violent fragmentation, dominated by a widespread mist of multiscale structures that introduce significant complexities in numerical studies. The present work focuses on capturing all stages of the aerodynamic breakup of a waterlike droplet under the shear-induced entrainment regime. The numerical investigation is conducted within a physically consistent multiscale framework, which provides insight into the mist dynamics and the distribution of the produced secondary droplets under different postshock conditions.

Computational Evaluation of Shock Wave Interaction with a Cylindrical Water Column

Computational fluid dynamics was employed to predict the early stages of the aerodynamic breakup of a cylindrical water column, due to the impact of a traveling plane shock wave. The unsteady Reynolds-averaged Navier–Stokes approach was used to simulate the mean turbulent flow in a virtual shock tube device. The compressible flow governing equations were solved by means of a finite volume-based numerical method, where the volume of fluid technique was employed to track the air–water interface on the fixed numerical mesh. The present computational modeling approach for industrial gas dynamics applications was verified by making a comparison with reference experimental and numerical results for the same flow configuration. The engineering analysis of the shock–column interaction was performed in the shear-stripping regime, where an acceptably accurate prediction of the interface deformation was achieved. Both column flattening and sheet shearing at the column equator were correctly reproduced, along with the water body drift.

Parameter Scaling of the Aerodynamic Breakup of the Acoustic Levitated Droplets in an Air Jet Flow

The aerodynamic breakup of the droplet has been intensely studied in this paper. We aim to establish a unified relationship between dimensionless kinematic parameters such as displacement, spreading diameter, Weber number, time, and so on. The breakup characteristics of the acoustic levitated ethanol droplet are experimentally investigated when exposed to an air jet flow. The breakup phenomenons were recorded with a high-speed camera. The breakup characteristics were analyzed, and the physical models of the moving and transforming behaviors were established to explain the breakup mechanisms. We found that the displacement of the windward side of the droplet follows free acceleration rule, with the displacement, acceleration, and time in the dimensionless form. The spreading of the diameter during deformation can also be written in a simple equation as a function of Weber number and displacement. We also discussed more details.