A hybrid particle volume-of-fluid method for curvature estimation in multiphase flows

We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic fitting that is employed in such cases. The curvature is computed from the equilibrium positions of particles constrained to circular arcs and attracted to the interface. The proposed particle method is combined with the method of height functions at higher resolutions, and it is shown to outperform the current combinations of height functions and parabolic fitting. The algorithm is conceptually simple and straightforward to implement on new and existing software frameworks for multiphase flow simulations thus enhancing their capabilities in challenging flow problems. We evaluate the proposed hybrid method on a number of two- and three-dimensional benchmark flow problems and illustrate its capabilities on simulations of flows involving bubble coalescence and turbulent multiphase flows.Comment: 25 pages, 33 figure

Computing curvature for volume of fluid methods using machine learning

In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface separating two immiscible fluids, given the volume fraction in the cell and the adjacent cells. Currently, the most accurate approach is to fit a curve (2D), or a surface (3D), matching the volume fractions and finding the curvature by differentiation. Here, a different approach is examined. A synthetic data set, relating curvature to volume fractions, is generated using well- defined shapes where the curvature and volume fractions are easily found and then machine learning is used to fit the data (training). The resulting function is used to find the curvature for shapes not used for the training and implemented into a code to track moving interfaces. The results suggest that using machine learning to generate the relationship is a viable approach that results in reasonably accurate predictions

Comparison of methods for curvature estimation from volume fractions

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. The numerical studies presented in this work find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost for dynamic interfaces when the interface reconstruction and advection are coupled to a two-phase Navier-Stokes solver

Deep learning of interfacial curvature: a symmetry-preserving approach for the volume of fluid method

Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform conventional methods on coarser grids but diverge with grid refinement. Furthermore, unlike conventional methods, data-driven methods are sensitive to coordinate system and sign conventions, thus often fail to capture basic symmetry patterns in interfaces. The present work proposes a new data-driven strategy which conserves the symmetries in a cost-effective way and delivers consistent results over a wide range of grids. The method is based on artificial neural networks with deep multilayer perceptron (MLP) architecture which read volume fraction fields on regular grids. The anti-symmetries are preserved with no additional cost by employing a neural network model with input normalization, odd-symmetric activation functions and bias-free neurons. The symmetries are further conserved by height-function inspired rotations and averaging over several different orientations. The new symmetry-preserving MLP model is implemented into a flow solver (OpenFOAM) and tested against conventional schemes in the literature. It shows superior performance compared to its standard counterpart and has similar accuracy and convergence properties with the state-of-the-art conventional method despite using smaller stencil.Comment: Preprint under review in Journal of Computational Physic

Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes

This paper proposes a method to estimate the curvature of an interface represented implicitly by discrete volume fractions on an unstructured two-dimensional mesh. The method relies on the computation of local parabolic reconstructions of the interface. The parabolic reconstruction of the interface in a given computational cell is obtained by solving a local non-linear minimisation problem, and only requires additional information from two neighbouring cells. This compactness ensures a robust behaviour on poorly-resolved interfaces. The proposed method is proven to be analogous to the height-function method for Cartesian configurations with consistent heights, and can be interpreted as a generalisation of the height-function method to meshes of any type. Tests are conducted on a range of interfaces with known curvature. The method is shown to converge with mesh refinement with the same order of accuracy as the height-function method for all three types of meshes tested, i.e. Cartesian, triangular, and polygonal

On estimating the interface normal and curvature in PLIC-VOF approach for 3D arbitrary meshes

Volume of fluid (VOF) method with its Piecewise Linear Interface Calculation (PLIC) reconstruction algorithm is one of the most popular approaches in numerical simulation of interfacial flows with a wide range of applications in different areas. In an effort to evaluate the similarity of the PLIC-generated planes in comparison with the exact interface, a point-cloud, based on the polygon centers of PLIC planes is extracted, which later is used to form a triangular grid that represents the estimated interface. The main objective of this article is to evaluate the interface geometrical properties based on the extracted triangular grid of the interface. The methods presented in this article, characterized by a higher spatially convergence ratio, are compared with the commonly used methods. The proposed methods are tested for two 3-dimensional general test cases, where an evident improvement is seen in calculation accuracy and spatial convergence of the errors of interface normal vector and curvature.This work has been financially supported by MCIN/AEI/10.13039/ 501100011033 Spain, project PID2020-115837RBI00. E. Schillaci acknowledges the financial support of the Programa Torres Quevedo (PTQ2018-010060).Peer ReviewedPostprint (author's final draft

An Overview of Additive Manufacturing Technologies—A Review to Technical Synthesis in Numerical Study of Selective Laser Melting

Additive Manufacturing (AM) processes enable their deployment in broad applications from aerospace to art, design, and architecture. Part quality and performance are the main concerns during AM processes execution that the achievement of adequate characteristics can be guaranteed, considering a wide range of influencing factors, such as process parameters, material, environment, measurement, and operators training. Investigating the effects of not only the influential AM processes variables but also their interactions and coupled impacts are essential to process optimization which requires huge efforts to be made. Therefore, numerical simulation can be an effective tool that facilities the evaluation of the AM processes principles. Selective Laser Melting (SLM) is a widespread Powder Bed Fusion (PBF) AM process that due to its superior advantages, such as capability to print complex and highly customized components, which leads to an increasing attention paid by industries and academia. Temperature distribution and melt pool dynamics have paramount importance to be well simulated and correlated by part quality in terms of surface finish, induced residual stress and microstructure evolution during SLM. Summarizing numerical simulations of SLM in this survey is pointed out as one important research perspective as well as exploring the contribution of adopted approaches and practices. This review survey has been organized to give an overview of AM processes such as extrusion, photopolymerization, material jetting, laminated object manufacturing, and powder bed fusion. And in particular is targeted to discuss the conducted numerical simulation of SLM to illustrate a uniform picture of existing nonproprietary approaches to predict the heat transfer, melt pool behavior, microstructure and residual stresses analysis