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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]

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]

A novel numerical model was developed to investigate air entrapment in binary droplet impact with solidification microstructure formation under practical plasma spraying conditions. The evolving liquid–gas interface was tracked by the explicit finite difference solution to the Cahn–Hilliard equation, coupled with the Navier–Stokes equations. Another diffuse interface model was invoked to trace solid–liquid and grain–grain boundaries. The model was discretized using an explicit finite difference method on a half-staggered grid. The velocity pressure coupling was decoupled with the projection method. The in-house code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. The time duration over which gas compressibility matters was estimated. Typical cases with air entrapment were studied with the model. The effect of droplet porosity on air entrapment was probed into as well: the larger the porosity of a droplet, the bigger the trapped air bubble. The grain growth near the air bubble is skewed. Moreover, a case without air entrapment was also shown herein to stress that air bubbles could be suppressed or even eliminated in plasma spraying by adjusting the landing positions of successive droplets. [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]

Successive impingement of droplets after refining in supersonic plasma jet generally yields a submicron-sized lamellar coating with excellent comprehensive properties. Nevertheless, physical insight into the flattening and rapid solidification with crystallization behavior of supersonic impingement of refined droplets is difficult to understand. In this research, the content of refinement droplets reached 90% and displayed the multi-scale distribution of equiaxed grains. The boundary migration of equiaxed grains and anisotropic coalescence was found in the dynamic temperature gradient. Furthermore, an optimized model was established in order to accurately reproduce the multi-physical coupling process of supersonic impingement of single or two refined droplets, which was based on the numerical calculation of nonlinear equations (including the Mass and momentum, energy balance, Cahn–Hilliard, phase-field and orientational field equations). The size distribution and growth orientation of columnar grains within single or two flattened droplets were in good agreement with the experimental results. Epitaxial growth of columnar grains was found in the two-flattened droplet interface during the extremely rapid cooling stage. This optimized model could be an effective method in predicting the flattening and solidification with crystallization behavior of droplets during plasma spraying. [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]