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The traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvature‐driven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a half‐staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation. [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]

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]

A recently developed conservative level set model, coupled with the Navier-Stokes equations, was invoked to simulate non-spherical droplet impact in three dimensions. The advection term in the conservative level set model was tackled using the traditional central difference scheme on a half-staggered grid. The pressure velocity coupling was decoupled using the projection method. The inhouse code was written in Fortran and was run with the aid of the shared memory parallelism, OpenMP. Before conducting extensive simulations, the model was tested on meshes of varied resolutions and validated against experimental works, with satisfyingly qualitative and quantitative agreement obtained. The model was then employed to predict the impact and splashing dynamics of non-spherical droplets, with the focus on the effect of the aspect ratio. An empirical correlation of the maximum spread factor was proposed. Besides, the number of satellite droplets when splashing occurs was in reasonable agreement with a theoretical model. [ABSTRACT FROM AUTHOR]

A phase field model enhanced with the shared memory parallelism OpenMP was proposed, capable of modeling the impact of a heavy metal droplet under practical plasma spraying conditions. The finite difference solution of the Navier-Stokes equations, coupled with the Cahn-Hilliard equation, tracks the gas-liquid interface. The liquid fraction, defined over the computational domain, distinguishes fluid from solid. The model is employed for Ni and YSZ drop impacts after ruling out the effect of mesh size. The model exhibits a reasonable parallel-computing efficiency, and the predicted maximum spread factors agree well with analytical models. [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]

Bubble-droplet interaction is essential in the gas-flotation technique employed in wastewater treatment. However, due to the limitations of experimental methods, the details of the fluid flow involved have not been fully understood. Therefore, a phase field model for a three-phase flow was developed to study the rise of a single bubble and bubble-droplet interactions. The fluid-fluid interfaces are tracked by the Cahn-Hilliard equation, which is coupled with the Navier-Stokes equations with an equivalent volumetric force substituted for interfacial tensions. The model was discretized using an explicit finite difference method on a half staggered grid, and the pressure velocity coupling was tackled using the projection method. The in-house code was written in Fortran and run with the help of OpenMP, a shared memory parallelism. The model was validated against experiments with gratifying agreement achieved. Bubble-droplet interaction was simulated in two distinct situations: the first features a gas bubble crossing the interface between two other phases, and the second features a gas bubble chasing from behind an oil droplet in a surrounding fluid of the third phase., Competing Interests: None declared., (This journal is © The Royal Society of Chemistry.)