Initial Droplet Research Articles

Simulation of a sessile nanofluid droplet freezing with an immersed boundary-lattice Boltzmann model

The freezing process of a sessile nanofluid droplet has been reported to behave differently from a pure sessile water droplet in terms of freezing dynamics and the final shape of the ice droplet. When nanoparticles are added to the water droplet, instead of forming a pointed tip on the top, the completely frozen droplet exhibits a flat plateau shape. To investigate this unique scenario, we developed a lattice Boltzmann (LB) model that combines the multiphase solidification model (MSM) with the immersed boundary method (IBM). The MSM is based on our previous work of simulating the freezing of a pure droplet, while the IBM is used to handle the interaction forces between the suspended particles and the different phases in the freezing droplet. Using this LB model, we succeeded in simulating the formation process of the frozen plateau shape. The simulation takes into account the dynamics of the dispersed particles, including their expulsion from the propagation freezing front and their segregation, which brings the liquid water to the edge. We compared the simulated freezing shape profiles with the experimental images and found that the shape forms in a similar manner. We then used the developed model to explore more cases, considering the effects of droplet contact angles and particle volume concentration. Results show that the distribution of particles and final droplet height depend on the surface wettability, as the freezing front exhibits a concave/convex shape on hydrophilic/hydrophobic surfaces, resulting in different particle separation distributions on the freezing front interface. Furthermore, our simulation results confirm the experimental conclusion that the plateau size on the frozen top increases with particle concentration and appears to be independent of the initial droplet contact angle.

Effects of surface temperature and Weber number on the dynamic and freezing behavior of impacting water droplets on a superhydrophobic ultra-cold surface

The dynamic and freezing behavior of a water droplet impacting a superhydrophobic cold surface is worthy of investigation. In this study, experiments are conducted to examine the impact and freezing of a water droplet on a cold superhydrophobic surface whose temperature changes in a wide range between −10 °C and −60 °C. A numerical model that introduces a continuous energy balance equation is developed to investigate the process numerically. The effects of surface temperature, Weber number, and initial droplet temperature on the droplet morphology, spread factor, contact time, and rebound height are investigated. The droplet exhibits three different behaviors as the surface temperature decreases: full rebound, partial rebound, and full adhesion. For the full rebound case, the results indicate that the growth rate of the contact time with decreasing surface temperature increases as the Weber number decreases. For the full adhesion case, the variation in the surface temperature minimally affects the dynamic behavior of the droplet impacting on an ultracold superhydrophobic surface (below −40 °C). The effect of surface temperature on the maximum spread factor is more pronounced at higher Weber numbers. Additionally, the ice nucleation rate is analyzed theoretically. The results show that the nucleation rate of droplets impacting an ultracold surface remains almost constant regardless of the surface temperature and surface roughness. Moreover, a regime map showing the different droplet morphologies correlating with the surface temperature and Weber number is established. The critical surface temperatures for different droplet morphologies of supercooled and room-temperature droplets are analyzed. This study allows us to better understand the dynamic and heat transfer mechanisms involved in the impact and freezing of a water droplet on a superhydrophobic surface.

Are Most Micrometer Droplets (>10 μm) Wasted in Electrospray Ionization? An Insight from Real-Time High-Speed Imaging.

Electrospray ionization (ESI) is one of the main techniques used in mass spectrometry (MS) of nonvolatile compounds. ESI is a disordered process, in which a large number of polydisperse droplets are projected from a fluctuating Taylor cone and jet protruding ESI emitter. Here, we disclose a system for sectioning electrospray plumes to discrete packets with millisecond and submillisecond lifetime, which are introduced to the MS orifice, one at a time. A high-speed camera was triggered at 10,000 frames per second to capture consecutive images of the electrospray packets transmitted to the mass spectrometer. We further correlated the high-speed images of electrospray packets with MS signals of a test analyte (acetaminophen). Following computational treatment of the images, we determined the number of droplet observations (<300), average diameter of droplets (∼10-20 μm), and average volume of droplets (few tens of picoliters) in the individual electrospray packets. The result shows that most micrometer droplets (>10 μm) do not have any significant contribution to the MS signals. This finding is in agreement with the prior conjecture that most of the MS signals are mainly attributed to nanodroplets. Based on this finding, one can deduce that only a small number of the initial microdroplets effectively carry analyte molecules that undergo ionization. We discuss that, in future, one may propose a way to "recharge" the emitted initial micrometer droplets to increase the efficiency of conventional ESI setups.

Numerical study on spherical flame propagation in dispersed liquid ammonia droplets

Directly using liquid ammonia in combustion devices can simplify the fuel supply system and reduce equipment costs. However, the detailed ignition and propagation mechanisms of liquid ammonia flames have not been fully understood. This study aims to investigate the ignition and propagation of liquid ammonia flames numerically under various conditions. Spherically expanding liquid ammonia flames are studied using detailed chemistry. The effects of initial temperatures, droplet diameters, equivalence ratios, and heat fraction are investigated. The results indicate that the rapid flash boiling of liquid ammonia droplets leads to a strong local heat loss, hindering the ignition and propagation of the flame. Preheating can significantly increase the reaction rate, which compensates for the heat loss caused by phase change, allowing the flame kernel to ignite and propagate outwards. While droplet-flame interaction is present but not significant due to the rapid evaporation of liquid ammonia. The effect of droplet on the flame surface curvature is only distinguishable at conditions of large diameter. Equivalence ratio and ammonia heat fraction ratio change the amount of liquid ammonia. The more liquid ammonia, the more heat is absorbed by the phase change process, making the flame more difficult to be ignited.

Sensitivity analysis of nucleation and droplet growth models in the prediction of natural gas non-equilibrium condensation in Laval nozzle

Supersonic separation is a promising technology for purifying natural gas by removing impurities like H2O and heavy hydrocarbons. The condensation process of natural gas has obvious non-equilibrium characteristics, the accurate prediction of which is challenging and essential for efficient separators design. Euler-Euler two-fluid model was developed to investigate non-equilibrium condensation of four two-component gas mixtures: H2O, CO2, H2S and n-C9H20 in CH4. Various nucleation and droplet growth models were employed to analyze the sensitivity in predicted results. The obtained results show significant differences in condensation characteristics among four gas mixtures due to varying isentropic expansion coefficients. The choice of nucleation models had a pronounced impact on H2O and n-C9H20, especially using the internally consistent classical theory(ICCT). However, noticeable differences emerged for CO2 and H2S only when using ICCT compared to classical nucleation theory (CNT). Furthermore, results for H2O and n-C9H20 exhibits high sensitivity to calibration factors in the Gy and Yg droplet growth models. Conversely, due to the essentially continuous flow of initial droplet sizes for CO2 and H2S, the Nusselt number and results show minimal response to such calibrations. These results can provide a reference for determination or development of nucleation and droplet growth model for natural gas non-equilibrium condensation.

Investigating airborne transmission risks: A mathematical model of evaporating droplets with solid residue

The COVID-19 pandemic has spotlit the scientific field of fluid dynamics governing airborne transmission through virus-laden mucosal-salivary droplets. In this work, a mathematical model for airborne droplet dispersion and viral transmission centered on evaporating droplets containing solid residue was proposed. Droplet dynamics are influenced by factors such as initial velocity, relative humidity (RH), and solid residue, in agreement with analytical and experimental results. Interestingly, the maximum droplet dispersion distance depends strongly on initial droplet size and RH, such as 0.8-mm-diameter droplet at 0.3 RH, 1.0 mm at 0.6 RH, and 1.75 mm at 0.9 RH, but only weakly on initial projected velocity. Under realistic conditions, an evaporating sputum droplet can cover a dispersion distance at least three times than that of a pure water droplet. Based on Wells falling curves, the critical droplet size, the largest droplet that can remain suspended in air without settling due to gravity, ranges from 120 μm at 0.3 RH to 75 μm at 0.9 RH. Together, our results highlight the role of evaporation on droplet lifetime, dispersion distance, and transmission risks.

Experimental and numerical analysis of the emulsification of oil droplets in water with high frequency focused ultrasound

Focused high frequency ultrasound emulsification provides significant benefits such as enhanced stability, finer droplets, elevated focal pressure, lowered power usage, minimal surfactant usage and improved dispersion. Hence, in this study, the high frequency focused ultrasound emulsification of oil droplets in water was investigated through experiments and numerical modeling. The effect of transducer power (74–400 W), frequency (1.1 and 3.3 MHz), oil viscosity (10.6–512 mPas), interfacial tension (25–250 mN/m) and initial droplet radius (10–750 µm) on the emulsification process was assessed. In addition, the mechanism of droplet break-up was examined. The experiments showed that the acoustic pressure increased from 9.01 MPa to 26.24 MPa as the power was raised from 74 W to 400 W. At 74 W, the Weber number (We) at the surface and focal zone are 0.5 and 939.8, respectively. However, at 400 W, the We at the transducer surface and focal region reached 2.7 and 6451.8, respectively. Thus, bulb-like and weak catastrophic break up dominates the emulsification at 74 W. The catastrophic break up at 400 W is more vigorous because the ultrasound disruptive stress and We are higher. The time for the catastrophic dispersion of a single droplet at We = 939.8 and We = 6451.8 are 1.01 ms and 0.45 ms, respectively. The numerical model gives reasonable prediction of the trend and magnitude of the experimental acoustic pressure data. The surface and focal pressure amplitudes were estimated with errors of ∼ 6.5% and ∼ 10%, respectively. The predicted Reynolds number (Re) between 74 and 400 W were 8442 and 21364, respectively. The acoustic pressure at the focal region were ∼ 26 MPa and ∼ 69 MPa at frequencies of 1.1 MHz and 3.3 MHz, respectively. Moreover, the acoustic velocities were ∼ 16 m/s and ∼ 42 m/s at 1.1 MHz and 3.3 MHz, respectively. Hence, smaller droplets could be attained at higher frequency excitation under intense catastrophic modes. The Ohnesorge number (Oh) increased from 0.062 to 3.12 with the viscosity between 10.6 mPas and 530 mPas. However, the We remained constant at 856.14 for the studied range. Generally, higher critical We is required for the different breakup stages as the viscosity ratio is elevated. Moreover, the We increased from 25.68 to 1284.22 as the droplet radius was elevated from 15 to 750 µm. Larger droplets allow for higher possibility and intensity of breakup due to diminished viscous and interfacial resistance.

Multiple structures and transition mechanisms of laminar fuel-rich ethanol/air counterflowing spray flames

Structures of laminar non-premixed ethanol/air spray flames in the axisymmetric counterflow configuration are studied under fuel-rich conditions by means of numerical simulations. The monodisperse ethanol spray is carried by air and directed against an air stream. Both streams enter at 300 K, and the system is at atmospheric pressure. Up to three different structures of these flames for identical boundary and initial conditions are identified, and regime diagrams are presented that show their conditions of existence in terms of the gas strain rate on the spray side of the configuration, [Formula: see text], starting from 55/s at an initial spray velocity of 0.44 m/s. The equivalence ratio on the spray side, [Formula: see text], is varied between 1.1 and 1.6, and initial droplet radii, [Formula: see text], from 10 to 50 [Formula: see text]m are considered. The most stable spray flame structure is characterized by two chemical reaction zones. For some conditions, single chemical reaction zones on either side of the counterflow configuration are found. Conditions under which these different flame structures exist are analyzed. Previous studies identified only two different structures for non-identical boundary conditions, and in this study, three different structures are presented for the first time. Moreover, the transition mechanisms of one structure to another are analyzed. The competition between the energy-consuming spray evaporation and the exothermic chemical reaction rates as well as the location of the spray determines the existence of the different flame structures. This transition of the different flame structures may explain spray flame characteristics such as flame pulsation or flame instabilities.

Quantitative investigation of sooting dynamics in droplet combustion using an automated image analysis algorithm

This paper reports an image analysis approach using a newly-developed open-source program to extract quantitative measurements of soot volume fraction (SVF) from digital video images of burning n-heptane droplets. The automated program developed in this work can analyze images of fixed and untethered droplets to quantify sooting dynamics. The images analyzed in the program were taken from experiments carried out in the Multi-user Droplet Combustion Apparatus (MDCA) onboard the International Space Station (ISS). In these experiments, video imaging of burning droplets was obtained using backlighting by a laser diode with a wavelength of 653 nm. The light was collimated before it passed through the droplet and soot-containing region, after which the light was then attenuated and projected onto the camera’s sensors. This technique facilitates the measurements of SVF based on the principles of the full field light extinction method (FFLEM). The measurements provide quantitative data that reveal the sooting dynamics of liquid fuels during droplet combustion processes.The analyses of a soot-attenuating image (ISS n-heptane, untethered droplet) at an instant during the burning show that the SVF distribution has a peak at the soot shell location. It then decreases due to soot oxidation when the location is further away from the burning droplet. Regarding temporal effects on the maximum SVF (SVFmax), results show that SVFmax first increases after the burning is initiated until a peak value is reached, after which SVFmax decreases. The SVFmax values identified in this study for n-heptane are quantitatively consistent with previously reported values for fiber-supported droplets and are reached relatively early in the burning history. n-Heptane images are also analyzed to show the effects of initial droplet sizes on the maximum soot volume fraction. Results show that SVFmax decreases with increasing initial droplet size, which is consistent with visual observations of less soot formed and dimmer flame brightness as Do increases.

Directional control of the size and velocity of micro-droplets ejected after impacting a super-hydrophobic surface

Impact velocity plays a crucial role in the control of droplet ejection when producing micro-droplets with directed diameters and velocities from millimetre-sized droplets. In this study, high-speed photography is used to experimentally investigate the characteristics of the ejection of micro-droplets after impacting a super-hydrophobic surface with different impact velocities ranging from 0.16 to 2.34 m/s. The results indicate that droplet ejection only occurs at impact velocities ranging from 0.26 to 1.31 m/s. Furthermore, it is found that the droplet ejection process can be classified into five stages based on the Weber number. In Stages 1–3, the ratio of the ejected to initial droplet diameters changes only slightly with the Weber number. In Stage 4, the ratio first increases, then decreases, and finally increases again. In Stage 5, the ratio decreases linearly. An equation describing the decrease in the ratio during Stage 5 is obtained and the correlation between the ratio of the ejection to impact velocities and the Weber number for the same stage is investigated. It is concluded that the formation of the central liquid column and the final characteristics of droplet ejection are mainly the result of the competition among inertial force, reaction force from the surface, gravity, and surface tension; and the formation of the jet is determined by the collapse of the air cavity.

Natural extract-polymer monodisperse submicron particles from Plateau-Rayleigh microjets

Particles of interest in food, pharmaceutical, and nutraceutical sectors are often formulated with a polymer and one or more natural or synthetic active compound. The two components frequently have distinct hydrophilicity. Submicrometric particles with narrow size dispersion can be made by the droplet-to-particle route by electrospray. In the steady cone-jet mode a liquid Taylor cone (TC) continuously emits a Plateau-Rayleigh microjet which breaks up spontaneously and periodically into tiny droplets, which later dry up to form solid particles. To achieve a stable process of this kind, we argue that it is necessary to: (i) operate near the minimum solution flow rate compatible with TC stability, (ii) prevent the drying of the TC by surrounding it with a gentle gas stream saturated in solvent vapor, and (iii) monitor the electric current and image the TC. We demonstrate this process in the preparation of curcumin (CUR) loaded polyvinylpyrrolidone (PVP) submicrometric particles as a function of solution composition and ambient relative humidity. In the atomization step (jet and droplet formation), the initial droplet size and charge are determined by the liquid properties and flow rate. The particles’ shapes were spherical (with or without internal voids), corrugated due to shell buckling (with compact interiors), and filamented due to Coulombic instabilities, depending on the interplay of different factors at the droplet drying step. These included the droplet size and charge, solvent evaporation, solute diffusion, water uptake from the ambient, mechanical forces, and solution thermodynamics. The electric current and droplet size are suitably predicted by scaling laws developed for simple Newtonian fluids. Hence, our particle sizes lie always between the predicted droplet and compact-sphere sizes, at a distance which depends on the particle morphology. CUR-loaded PVP quasi-monodisperse submicron particles could be an interesting model for drug delivery and biomedical applications.

Experimental study on the droplet dynamics after impacting an inclined superhydrophobic surface

Super-hydrophobic surface has been widely studied, related to surface self-cleaning and liquid transport. In this study, effects of the inclined angle and impact velocity on the dynamic characteristics of droplet impact are experimentally investigated, using high-speed photography. When the spreading break-up does not occur, the effect of the inclined angle on the maximum spreading diameter is mainly determined by the competition between the decrease in the inertial force component normal to the surface and the increase in the gravity and inertial force component parallel to the surface. A formula has been developed to predict the maximum spreading factor under different inclined angles. The increasing inclined angle promotes the complete rebound. When the impact velocity is constant, there exists a critical inclined angle, at which the rebounding time is minimum. Furthermore, the critical inclined angle increases with the impact velocity. The increasing inclined angle can affect droplet ejection and potentially hinder its occurrence. Droplet ejection is classified into five stages based on the change in the ratio of the ejected to initial droplet diameter versus Weber number normal to the surface. For stage 5, an empirical formula that predicts the diameter of ejected droplets under different inclined angles is given out. This study can provide a novel idea for the generation and transport of microdroplets of directed size, as well as the recycling of the remaining liquid film after droplet ejection.

Numerical simulation of TTIP/[formula omitted]-xylene precursor solution spray flames in the counterflow configuration

Sprays of precursor solutions are used in flame spray pyrolysis (FSP) to produce functional nanoparticles with specific properties. The present study concerns the precursor titanium(IV) isopropoxide (TTIP) in p-xylene. A dilute monodisperse spray carried by an air stream is directed against an air stream to establish a counterflowing laminar spray flame. The complex thermophysical properties of the bi-component droplets are incorporated into the code as well as the detailed chemical reactions of the system with 213 chemical reactions among 52 species; the chemical reaction mechanism includes thermal decomposition of the TTIP and the combustion of p-xylene. The droplets are modeled using the multicomponent evaporation model. Drag and gravity forces are considered in the equation of droplet motion. Monodisperse spray flame structures are presented depending on the gas strain rate, the initial droplet size, the precursor mass loading as well as the equivalence ratio. The preferential evaporation of the more volatile p-xylene provides the gaseous fuel for combustion, and the thermal decomposition of the precursor TTIP considerably reduces the flame temperature.

The Effects of Vaporisation Models on the FCC Riser Reactor

This work presents a steady-state one-dimensional model of the FCC riser considering the vaporisation of the gas oil feed and subsequent cracking reactions. The evaporation of droplets is studied using three models: the classical homogeneous model and the heterogeneous vaporisation models from the literature. Droplets are modelled using the Lagrangian framework model for particles moving through a fluid. This was coupled with the gas–solid flow field describing the catalyst particulate transport in the riser. Cracking reaction kinetics are modelled using a four-lumped model. The model was then validated against published plant data. The model performed well in terms of gas oil conversion, gasoline yield, pressure drop, and phase temperature profiles. Therefore, it is suitable for use in the design and optimisation of new and existing FCC unit risers, particularly in cost–benefit analysis considering the current push away from petroleum energy sources. It was found that vaporisation models are largely insignificant in terms of gas oil conversion profiles and gasoline yield for usual operation conditions of FCC risers, which is a finding that had yet to be proven in the literature. Vaporisation models are shown to only affect conversion and yield when the initial droplet exceeds 2000 μm.

A Study on the Dynamic Collision Behaviors of a Hydrous Ethanol Droplet on a Heated Surface

This study uses high-speed imaging to investigate the dynamic collision behavior of a single hydrous ethanol droplet in different water/ethanol ratios on a heated horizontal glass surface. The initial droplet diameter varied from 3.3 to 4.1 mm, and the impact velocity was 0.57 m/s. The study covers a range of surface temperatures (373 K to 553 K) and ethanol mass fractions (0% to 100%) to reveal four regimes of droplet-impinging behaviors, including quiescent surface evaporation, puffing or partial boiling, explosive nuclear boiling, and the Leidenfrost effect. The addition of volatile ethanol to less volatile water shifts the droplet collision behavior toward explosive boiling and the Leidenfrost phenomenon. As the ethanol mass fraction increased from 0% to 100%, the superheat limit temperature decreased by approximately 80 K, while the Leidenfrost temperature decreased by at least 100 K. The dimensionless droplet diameter in the regime of droplet spreading with quiescent surface evaporation is influenced by surface temperature, surface tension, and viscosity. Meanwhile, the dimensionless diameter and height of a droplet in the regime of the Leidenfrost phenomenon are mainly influenced by its surface tension. The study concludes that a single parameter, such as the superheat level, Weber number, or Reynolds number, is difficult to describe droplet collision behavior, and multiple factors would be required to best describe droplet collision behavior and establish empirical correlations. However, it is feasible to predict partial collision behaviors by using one of the single parameters under certain conditions.

Investigation of the effects of parallel electric field on fog dissipation

Fog dissipation by charge and electric field has become a research hotspot due to its affordability and high efficiency compared with traditional technologies. However, the mechanism by which the electric field affects the temporal variation of droplet concentration is unclear. Therefore, a cylinder fog chamber with a radius of 0.15 m and a height of 1 m is established to analyze the influence of electric field on the concentration change of partially charged fog (50% of fog droplets are charged). The distribution of electric field in the fog chamber is simulated by an electrostatic model in COMSOL, and the electric field in the fog chamber is regarded as a parallel electric field. A percentage concentration α, the ratio of the real droplet concentration n, and the initial droplet concentration n 0 are introduced to describe the effects of fog dissipation. The results show that visibility can increase from 10 m to 150 m after applying the electric field. The shortest time is 12 s, which is much smaller than the natural settling time (102 s). Furthermore, α first increases, then decreases, and finally gets close to zero with electric field E regardless of the charged state (neutral or partially charged) at the beginning of applying the electric field (t = 60 s). Besides, α without charging is smaller than that with partially charging. Finally, α decreases with electric field E regardless of the charged state at the end of the applied electric field (t = 240 s). These findings can be explained by the relative strength of electrostatic force effect induced by the electric field on neutral and charged droplets and gravitational effect, which are quantified by the calculation analysis of various forces. The results can be used to guide and optimize the structure of experimental setups for outdoor fog dissipation in the future.

On evaporation dynamics of an acoustically levitated multicomponent droplet: Evaporation-triggered phase transition and freezing

HypothesisMulti-component droplet evaporation has received significant attention in recent years due to the broad range of applications such as material science, environmental monitoring, and pharmaceuticals. The selective evaporation induced by the different physicochemical properties of components is expected to influence the concentration distributions and the separation of mixtures, thereby leading to rich interfacial phenomena and phase interactions. ExperimentsA ternary mixture system containing hexadecane, ethanol, and diethyl ether is investigated in this study. The diethyl ether exhibits both surfactant-like and co-solvent properties. Systematic experiments were performed using acoustic levitation technique to achieve a contact-less evaporation condition. The evaporation dynamics and temperature information are acquired in the experiments, using high-speed photography and infrared thermography technologies. FindingsThree distinct stages, namely, ‘Ouzo state’, ‘Janus state’, and ‘Encapsulating state’, are identified for the evaporating ternary droplet in acoustic levitation. A self-sustaining periodic freezing & melting evaporation mode is reported. A theoretical model is developed to characterize the multi-stage evaporating behaviors. We demonstrate the capability to tune the evaporating behaviors by varying the initial droplet composition. This work provides a deeper understanding of the interfacial dynamics and phase transitions involved in multi-component droplets and proposes novel strategies for the design and control of droplet-based systems.

Sustainable Production of Stable Lignin Nanoparticle-Stabilized Pickering Emulsions via Cellulose Nanofibril-Induced Depletion Effect

Spherical lignin nanoparticles (SLNs) are able to formulate Pickering emulsions with various applications. However, SLN-stabilized emulsions commonly comprise droplets in the micron range, resulting in inevitable instability upon storage. Herein, nonadsorbing cellulose nanofibrils (CNF) are shown to induce stabilization of the diluted SLN-stabilized Pickering emulsions via concentration-dependent depletion effects. Two regimes for such depletion interactions are established, including depletion flocculation-induced droplet aggregation at intermediate CNF concentrations and depletion stabilization of micron-sized droplets over critical CNF concentrations (0.2 wt %). The long-term stability of the SLN-based emulsions against creaming is over two months. The universality of the findings is tested with different initial oil volume fractions and droplet diameters. Overall, this study unveils the depletion effects in SLN-stabilized Pickering emulsions induced by renewable CNF, offering a simple, sustainable route for tailoring their phase behavior and creating ultrastable systems that are available for formulating green products.

Numerical study of the process of liquid droplets impacting the curved wall surface

The impact of droplets on the solid wall is a typical free surface flow phenomenon that widely exists in nature, industry, and daily life. According to the change of the droplet’s center thickness, the droplet, the spreading process of the droplet is usually divided into three unique stages: the initial droplet deformation stage, the inertia-dominated stage, and the viscosity-dominated stage with the increase of the impact time. The problem of the liquid droplet spreading under different impact conditions is simulated by the smoothed particle hydrodynamics (SPH) method. Firstly, the dynamic process of droplet spreading is simulated and compared with relevant experimental results to verify the effectiveness of the proposed method. Then, the effects of the Weber number and the diameter ratio of the droplet to the curved wall surface on the droplet’s maximum spreading diameter and central thickness were studied and analyzed. On this basis, the key coefficient in the existing relationship between the Weber number and maximum spreading diameter is fitted. Finally, the fitting equation of the center thickness and the impact time in the third stage of droplet spreading is assessed.

Combustion of 10–100 μm aluminum droplets in detonation products gases

AbstractWe describe a two‐phase model of combustion effects in aluminized high explosive (HE) charges. It is based on: (i) a Gas Dynamic Model of the expansion of the detonation product gases and their turbulent combustion with air; and (ii) a Heterogeneous Continuum Model of aluminum (Al) droplets and their combustion with the detonation product gases. Initial conditions are based on an analytical similarity solution for a cylindrical Chapman‐Jouguet (CJ) detonation propagating at the CJ detonation velocity. The CJ jump conditions are computed at the thermodynamic equilibrium state by the Cheetah code, assuming the Al droplets are inert. We assume that the Al is 10 % of the charge mass and occurs as droplets at the CJ state. Different initial droplet diameters, ranging from 10 to 100 microns, are studied. A hydrodynamic combustion model based on large Damköhler numbers is employed in this study, . It has a square‐root dependence on the Reynolds number (Re) and inversed‐squared dependence on the droplet diameter ( ). The burnout time ( ) of the Al droplets has a three‐halves dependence on the droplet diameter, . After burnout, the detonation products act as detonation products of the HE charge with active Al. They turbulently mix with air and form a combustion layer on the outer edge of the fireball. Details of the two‐phase model, initial conditions and evolution of the flow field will be described.