Numerical methods for solid-liquid phase-change problems

Zeneli, Myrto; Nikolopoulos, A.; Karellas, Sotiriοs; Νikolopoulos, Nikos

doi:10.1016/b978-0-12-819955-8.00007-7

Cited by 26 publications

(19 citation statements)

References 115 publications

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“…The phase changes are considered by using the apparent heat capacity method which includes an additional term for latent heat as shown in Eq. ( 2) [43] where c p,solid (J kg −1 K −1 ) is the heat capacity of the solid phase, c p,liquid (J kg −1 K −1 ) is the heat capacity of the liquid phase, L s→l (J kg −1 ) is the latent heat, and f l is the phase transition function. For pure solid f l = 0, and for pure liquid f l = 1.…”

Section: Governing Equationsmentioning

confidence: 99%

Numerical modelling of thermal quantities for improving remote laser welding process capability space with consideration to beam oscillation

Mohan

Ceglarek

Auinger

2022

Int J Adv Manuf Technol

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This research aims to explore the impact of welding process parameters and beam oscillation on weld thermal cycle during laser welding. A three-dimensional heat transfer model is developed to simulate the welding process, based on finite element method. The results obtained from the model pertaining to thermal cycle and weld morphology are in good agreement with experimental results found in the literature. The developed heat transfer model can quantify the effect of welding process parameters (i.e. heat source power, welding speed, radius of oscillation, and frequecy of oscillation) on the intermediate performance indicators (IPIs) (i.e. peak temperature, heat-affected zone (HAZ) volume, and cooling rate). Parametric contour maps for peak temperature, HAZ volume, and cooling rate are developed for the estimation of the process capability space. An integrated approach for rapid process assessment, and process capability space refinement, based on IPIs is proposed. The process capability space will guide the identification of the initial welding process parameters window and helps in reducing the number of experiments required by refining the process parameters based on the interactions with the IPIs. Among the IPIs, the peak temperature indicates the mode of welding while the HAZ volume and cooling rate represent weld quality. The regression relationship between the welding process parameters and the IPIs is established for quick estimation of IPIs to replace time-consuming numerical simulations. The application of beam oscillation widens the process capability space, making the process parameter selection more flexible due to the increase in distance from the tolerance boundaries.

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Section: Governing Equationsmentioning

confidence: 99%

Numerical modelling of thermal quantities for improving remote laser welding process capability space with consideration to beam oscillation

Mohan

Ceglarek

Auinger

2022

Int J Adv Manuf Technol

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“…FDM is one of the oldest numerical methods used to solve differential equations, which are difficult or impossible to solve analytically. It is simple and well understood to convert differential equations into linear algebraic equations as Taylor series to obtain the approximations of the real solutions, but FDM is still difficult or not adaptable to higherdimensional and irregular geometries, which are actually widely existing in geotechnical engineering [11,12]. Compared to FDM, as another numerical method to solve partial differential equations (PDEs), FEM is more adaptable to high-dimensional problems, and it is versatile for all complex and irregular geometries.…”

Section: Introductionmentioning

confidence: 99%

“…The main advantage of the method is that the local physical conservation law can be maintained. So it has been extensively used in computational fluid dynamics [12,16]. BEM is also a powerful and efficient method for solving PDEs [17].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, a Stefan problem can be solved without depending on moving or fixed grids as in FDM or FEM. Integration of PDEs is performed with classical Green's function, while boundary conditions are applied in a way similar to that in FEM and FDM [12]. For FEM, FEM, FVM and BEM, all the methods share some similarities, since they all represent a systematic numerical method for solving PDEs.…”

Section: Introductionmentioning

confidence: 99%

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Methods for Solving Finite Element Mesh-Dependency Problems in Geotechnical Engineering—A Review

et al. 2022

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The instabilities of soil specimens in laboratory or soil made geotechnical structures in field are always numerically simulated by the classical continuum mechanics-based constitutive models with finite element method. However, finite element mesh dependency problems are inevitably encountered when the strain localized failure occurs especially in the post-bifurcation regime. In this paper, an attempt is made to summarize several main numerical regularization techniques used in alleviating the mesh dependency problems, i.e., viscosity theory, nonlocal theory, high-order gradient and micropolar theory. Their fundamentals as well as the advantages and limitations are presented, based on which the combinations of two or more regularization techniques are also suggested. For all the regularization techniques, at least one implicit or explicit parameter with length scale is necessary to preserve the ellipticity of the partial differential governing equations. It is worth noting that, however, the physical meanings and their relations between the length parameters in different regularization techniques are still an open question, and need to be further studied. Therefore, the micropolar theory or its combinations with other numerical methods are promising in the future.

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“…To capture this physical phenomenon, or at least the most essential parts of its effects, one of the simplest approaches is the so-called Apparent Heat Capacity method, Bonacina et al [112] and Muhieddine et al [113]. According to Zeneli et al [114], the work of Hashemi and Sliepcevich [115] was the first to propose this technique, distributing the latent heat over a finite temperature interval to deal with numerical instabilities arising from strong discontinuities in specific heat capacity values during the phase change. In this method, the energy necessary to put forth the phase change is considered by gradually and continuously raising the specific heat of the material in a small interval of temperature (  ) around the melting or vaporization temperature, while keeping the original governing equations of the problem.…”

Section: Phase Changementioning

confidence: 99%

A coupled thermo-mechanical model for the simulation of discrete particle systems in advanced manufacturing.

Ruiz¹

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Modern industry, such as in aerospace, automotive, biomedical and military fields, has adopted advanced manufacturing (such as particle sintering-like processes and other 3D printing) as a rapid and efficient alternative for manufacturing industrial parts. Also, state-of-the-art techniques in the civil engineering industry include 3D concrete printing and cement-based additive manufacturing processes. All these techniques invariably include thermally-active particles, such as sintering powders and functionalized cementitious materials. The purpose of this work is to present a thermo-mechanical model for the simulation of problems involving thermo-mechanically-active particles forming discrete particles systems in advanced manufacturing. Our approach is based on the Discrete Element Method (DEM), combined with lumped heat transfer equations to describe the various thermal phenomena that may take place for such systems. Particles' motion and their thermal states over time are computed under the influence of body (e.g., gravitational) forces, contact and friction forces (and the related moments w.r.t. the particles' centers), adhesive forces as well as applied heat from external devices, heat transfer through conduction (upon contact with other particles and objects), convective cooling and radiative effects. Phase transformation, which may be critical in certain applications, is also considered. A numerical scheme is presented for solution of the model's equations. We then develop direct, large-scale numerical simulations to illustrate the validity of the proposed scheme and its practical use to the simulation of modern advanced manufacturing processes.Keywords: Particles, thermo-mechanical effects, multiphysical particle systems, advanced manufacturing and 3D printing, discrete element method (DEM) v QUINTANA RUIZ, Osvaldo Dario. Um modelo acoplado termo-mecânico para a simulação de sistemas discretos de partículas em manufatura avançada. 2021. Num de Pág. 151 f. Tese (Doutor em Ciências) -

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Numerical methods for solid-liquid phase-change problems

Cited by 26 publications

References 115 publications

Numerical modelling of thermal quantities for improving remote laser welding process capability space with consideration to beam oscillation

Numerical modelling of thermal quantities for improving remote laser welding process capability space with consideration to beam oscillation

Methods for Solving Finite Element Mesh-Dependency Problems in Geotechnical Engineering—A Review

A coupled thermo-mechanical model for the simulation of discrete particle systems in advanced manufacturing.

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