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In thermal spraying, molten YSZ (Yttria Stabilized Zirconia) drop impact is crucial to the understanding of formation of splats and hence coatings. However, existing studies hardly cast attention to the possible rebounding dynamics when successive molten YSZ drops impinge onto newly solidified splats whose temperature is still high so that freezing may be delayed. This work uses a newly developed numerical model based on the conservative level set method to probe into the rebounding dynamics of YSZ drops in practical thermal spraying conditions. The free-energy-based surface tension model in the phase field method was introduced to avoid the computing of curvature, which is however necessary in the continuum surface tension model. The projection method was invoked to solve the Navier–Stokes equations. The model was validated against an experiment of drop impact with rebounding, showing reasonable agreement. Moreover, the model was applied to both dense and hollow YSZ drop impact, with the details of fluid flow being analyzed. The maximum spread factor was found in agreement with existing scaling laws. [ABSTRACT FROM AUTHOR]

Drop impact-freezing on an incline is omnipresent in nature and industrial applications like 3D (three-dimensional) printing, but most current research concentrates on the impact instead of the interaction between impact and freezing. This paper thus developed an OpenMP-paralleled phase field model to probe into the underlying physics in 3D printing conditions. The finite difference solution to the Cahn–Hilliard equation helps track the evolving liquid–gas interface, and the liquid fraction is defined over the whole computational domain to distinguish between solid and fluid. The model was first validated against two experiments, showing agreeable consistency. Then, it was applied to inclined impact without and with phase change. The effect of inclination angles was also examined. It was found that increasing inclination angles can extend contact time, and that solidification cannot retard the gravity-driven fluid flow down the incline at an inclination angle of 45° but can at an inclination angle below 30°. Besides, the retracting speed declines with increased inclination angles. [ABSTRACT FROM AUTHOR]

Drop impact dynamics with solidification has been a hot topic of research recently. However, numerical studies to that end mainly concentrate on spherical drops, paying less attention to non-spherical ones that are ubiquitous in industrial applications like additive manufacturing and plasma spraying. Therefore, a phase field model accelerated with the shared-memory parallelism OpenMP is proposed to simulate the impact of a non-spherical heavy metal droplet in actual additive manufacturing conditions. The tracking of the gas–liquid interface is realized by the finite difference solution of the Navier–Stokes equation and the Cahn–Hilliard equation. We use the liquid fraction defined all over the computational domain to distinguish between solid and fluid. The model was then employed to predict the impact and freezing dynamics of non-spherical droplets, with the focus on the effects of the aspect ratio, of the contact angle, and of the phase field mobility. It shows that the established model could well capture the axis switching process, that rebounding accompanying the axis switching process could be hindered by solidification, and that larger phase field mobility could smooth drop profile, rendering it round in the axis switching process. [ABSTRACT FROM AUTHOR]

Air entrapment in drop impact onto solid surfaces has riveted the attention of the scientific community since it could drastically influence heat rate and splat porosity in additive manufacturing or thermal spraying processes. Due to the limitations of experimental methods, numerical methods have been gaining popularity in probing into air entrapment dynamics. To that end, this paper developed a paralleled phase field model. The model couples the Navier–Stokes equations with the Cahn–Hilliard equation to capture the liquid–gas interface, and adopts the liquid fraction, defined all over the computational domain, to distinguish between solid and liquid. The model is discretized using a finite difference method on a half-staggered grid. The model was first compared with experimental data, achieving reasonable agreement. Afterward, it was applied to a couple of cases. The air entrapment process was captured entirely and the interaction between solidification and air entrapment was also given. It shows that under the parameters studied here air entrapment may occur twice, one in the impacting center in the form of a bubble and the other in the form of a bubble ring. Besides, the effect of phase field mobility on air entrapment was examined as well. [ABSTRACT FROM AUTHOR]

A comprehensive numerical model has been developed, which is capable of predicting the spreading of a high-speed yttria-stabilized zirconia (YSZ) droplet with solidification microstructure formation under a horizontal electric field in plasma spraying processes. The numerical model entails the explicit finite difference solution of the Navier–Stokes equations and the energy balance equation, coupled with the Cahn–Hilliard equation to track the liquid–gas two-phase interface and with a phase field model for solidification microstructure formation involving polycrystalline growth. The electric force is added as a source term in the Navier–Stokes equations, and the fluids are assumed to be perfect dielectrics. The in-house code is written in Fortran and run in parallel. The results reveal that the retracting process could be completely inhibited using a horizontal electric field and that solidification time is greatly reduced. A new mechanism to suppress droplet breakup/splash could be realized, featuring reduction of the rising angle the spreading front makes with a substrate. All the cases show columnar grains within a splat. Besides, the model is validated against experimental results, with gratifying agreement achieved. [ABSTRACT FROM AUTHOR]

Modeling drop impact in 3D in thermal spraying conditions poses a great challenge, since it requires first of all an accurate interface tracking model and an efficient numerical scheme to solve the governing equations. This paper thus put forward an integrated model, in the framework of the conservative level set equation, to simulate drop impact in real thermal spraying conditions. The model couples the conservative level set equation with the Navier–Stokes equation and is discretized using the finite difference method on a half-staggered grid. The model was validated against experimental data, showing reasonable agreement. Then it was applied to real impact in thermal spraying conditions. Nickel drop impact with solidification was simulated first. Subsequently, effects of contact angle, thermal contact resistance, and substrate materials, were examined. It shows that lower contact angle does not lead to larger contact area, since solidification commences faster around the contact line, thereby pinning its movement, and that thermal contact resistance exerts a huge impact on final splat shape. The smaller the contact resistance, the more violent the splash. [ABSTRACT FROM AUTHOR]

In the drop-on-demand 3D printing technique, molten drop impact is crucial to the understanding of the formation of the building block of a part. However, existing studies cast less due attention to the rebounding dynamics of molten drops. This paper thus develops a phase field method to that end. The model consists of the Cahn-Hilliard equation, coupled with the Navier-Stokes equation to track the evolving liquid-gas interface. A heat source is added to the energy balance equation to distinguish between solid and fluid. The model is discretized using a finite difference method on a semi-staggered grid, and is paralleled based on the shared memory parallelism, OpenMP. The model was first compared with an experiment before being applied to various impacts. The agreement is reasonable. Typical impacts in 3D printing conditions were considered. The major findings are that the Tin drop rebounds off the substrate with a dimpled bottom when the impact velocity is 1 m/s, but with a rounded one when the impact velocity is reduced by half, and that the dimpled bottom is caused by an entrapped bubble during the receding process. Besides, effect of solidification on drop rebounding was examined as well. [ABSTRACT FROM AUTHOR]

• A free-energy-based surface tension model used in the conservative level set modeling. • Distinct impact regimes in 3D printing conditions considered. • Parallel computing based on OpenMP employed. The recently developed conservative level set method is second order in nature, thus making it amenable to explicit finite difference solutions in three dimensions. Due to a lack of efficient numerical models in simulating impact-freezing problems in 3D printing conditions, this paper puts forward a model based on the coupling of the conservative level set equation and the Navier-Stokes equations. The interfacial tension is represented by the free-energy-based model, which is free from the cumbersome computation of curvature that may induce parasitic flows. The model is further augmented with the thermal field to deal with phase change. The model is discretized on a half-staggered grid, is written in FORTRAN, and is accelerated with the shared-memory parallelism, OpenMP. Furthermore, a simple yet effective dynamic contact angle is applied. Three validation tests were conducted, corresponding to different impacting regimes. It shows that the model could well predict the full rebounding, and especially, the splashing occurring in drop impact onto solid surfaces. [Display omitted] [ABSTRACT FROM AUTHOR]

In plasma spraying, copious heterogeneous nucleation starts when a molten ceramic droplet spreads on a cold surface under rapid cooling. Some nuclei will survive and grow, eventually forming a splat of grains of distinct crystalline orientations. This paper aims to predict the dynamic process of yttria-stabilized zirconia (YSZ) droplet impact with solidification microstructure formation under various plasma spray conditions. A diffuse interface model was developed to track the evolving liquid–gas and solid–liquid interfaces. Continuously dense YSZ droplet impacts with different impacting angles were conducted, along with a hollow droplet impact. Results reveal that competitive growth among crystals is limited in the planar solidification, and that columnar structure dominates all the tests performed owing to a large thermodynamic driving force, and that given the rapid spreading of YSZ droplets along a solid surface, solidification may be safely assumed to take place mostly after spreading. Besides, typical crystal growth velocities are around 1 m/s, and local equilibrium can be assumed in the bulk. [ABSTRACT FROM AUTHOR]

• The solution of the Cahn-Hilliard equation to track moving boundaries. • A heat source term added in energy equation to trace solidification profile. • Thermal contact resistance studied to find its effect on maximum spread factor. • A supersonic impact of ceramic particles examined. A modified phase-field three-dimensional model has been developed to simulate the spreading of an impacting droplet undergoing solidification. The model is based on the numerical solution of the Cahn-Hilliard equation coupled with the Navier-Stokes equations for fluid flow and the energy balance equation for heat transfer. The solidification profile is tracked by treating the latent heat as a source term in the energy equation, which is modified to work with the Cahn-Hilliard equation. To verify the model, five cases were tested and matched well with experiments. Also, the effect of thermal contact resistance on the maximum spread factor of a solidifying droplet is discussed. One case was taken from practical thermal spraying conditions where a solidifying ceramic droplet spreads on a cold surface at a supersonic impact velocity; computed results are consistent with available measurements. [ABSTRACT FROM AUTHOR]

• The solution of the Cahn-Hilliard equation to track moving liquid-gas boundaries. • Drop impact under a horizontal electric field considered. • Drop splashing suppressed using electric force. A 3-D diffuse interface model has been developed to simulate impact of a dielectric droplet under the influence of a horizontal electric field. The Cahn-Hilliard equation, coupled with the Navier-Stokes equations, is employed to track liquid-gas interface. The model is discretized utilizing the finite difference method on a half staggered grid and solved using the projection method with the aid of OpenMP. Mesh independence test was also performed to choose an appropriate grid size. After validating the model, extensive simulations were conducted. The paper takes into account various factors influencing drop impact dynamics under real conditions, such as contact angle and impacting velocity. Numerical results show that for a moderate electric field, the electric force stretches a droplet in the direction of the applied electric field, and that a horizontal electric field can be useful to suppress splashing by reducing the rising angle made by the lamella with the substrate. [ABSTRACT FROM AUTHOR]

• Sequential droplet impact with grain growth and impingement is modelled. • Typical velocities of crystal growth are within 2 m/s. • Solidification time of a single splat on a stainless steel substrate is about 0.5 μs. • The undercooling in crystal growth ranges approximately from 150 K to 500 K. A coupled CFD and diffuse interface model was developed to predict the dynamic process of solidification microstructure formation of sequential yttria-stabilized zirconia (YSZ) droplet impact under supersonic plasma spraying. The numerical model relies on the explicit finite difference solution of the Navier-Stokes and energy balance equations, coupled with the Cahn-Hilliard equation, to track liquid-gas interface, and of a phase field model for solidification microstructure formation involving polycrystalline growth to trace solid-liquid interface. Extensive simulations, differing in the status of the first droplet and the impacting parameters of the second one, were carried out. The results reveal that solidification microstructure still follows a columnar pattern if the second droplet lands on the first that is just starting spreading, and that the growth direction around the contact region in the second splat will be obviously skewed by fluid flow if the first has been solidified, owing to earlier and easier nucleation on the top surface of the first splat, thus confirming the epitaxial growth across the splat-splat interface. Computed results are also compared with thermal spray experiments, with gratifying agreement obtained. [ABSTRACT FROM AUTHOR]

• The solution of the Cahn-Hilliard equation to track moving liquid-gas boundaries. • A phase field model for polycrystalline growth used to track solid-liquid interface and grain boundaries. • Supersonic YSZ droplet impact considered. • Convection effect on solidification microstructure investigated. A comprehensive numerical model has been developed, which is capable of representing the impact and spreading of a high-velocity yttria-stabilized zirconia (YSZ) molten droplet with microstructure formation in plasma thermal spraying processes. The numerical model entails the explicit finite difference solution of the Navier-Stokes equations and the energy balance equations, coupled with the Cahn-Hilliard equation to track the liquid-gas two phase interface and with a phase field model for solidification microstructure formation involving the polycrystalline growth. Numerical model procedures are given. The model, after being checked for mesh-independence, was applied to study the spreading and solidification of a high-temperature high-velocity YSZ droplet impinging upon a preheated substrate surface under the conditions typical of supersonic plasma thermal spraying processes. Extensive numerical simulations were carried out and results reveal that the solidification microstructure formed in the spreading droplet consists primarily of columnar grains. Computed results are also compared with thermal spray experiments, and gratifying agreement is obtained. [ABSTRACT FROM AUTHOR]