Igor Vušanović and Vaughan R Voller
When a multi component alloy solidifies the redistribution of solute components leads to the formation of macrosegregation patterns. Blending ideas from a number of recent…
Abstract
Purpose
When a multi component alloy solidifies the redistribution of solute components leads to the formation of macrosegregation patterns. Blending ideas from a number of recent publications the purpose of this paper is to provide a “best practice” on how grid convergence of a given macrosegregation simulation can be measured and determined.
Design/methodology/approach
The best practice is arrived at by considering a benchmark problem consisting of a 2D-casting simulation of an idealized Al-4.5%Cu alloy in a side cooled square (76×76 mm) cavity. The model for this simulation is based on a mixture treatment of the relevant heat and mass transfer equations. Simulations are made using three increasingly refined grid sizes.
Findings
The best practice to determine grid resolution involves two steps: first, a visual evaluation of predicted segregation images leading to the evaluation of solute profiles along selected transects; and second, the construction of a cumulative distribution function (CDF) of the predicted segregation field. On application to the benchmark problem, it is concluded that current computer resources are insufficient to grid resolve macrosegregation patterns but that the CDF provides a useful signal of the nature of macrosegregation in a given system.
Research limitations/implications
The benchmark is chosen to be representative. Exact convergence behavior, however, may depend on the system chosen.
Originality/value
In addition to establishing a best practice for measuring grid resolution of macrosegregation simulations the work also highlights, even in the absence of complete grid convergence, how the recently proposed CDF treatment can inform solidification modeling and process understanding.
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V.R. Voller, J.B. Swenson, W. Kim and C. Paola
To present a novel moving boundary problem related to the shoreline movement in a sedimentary basin and demonstrate that numerical techniques from heat transfer, in particular…
Abstract
Purpose
To present a novel moving boundary problem related to the shoreline movement in a sedimentary basin and demonstrate that numerical techniques from heat transfer, in particular enthalpy methods, can be adapted to solve this problem.
Design/methodology/approach
The problem of interest involves tracking the movement (on a geological time scale) of the shoreline of a sedimentary ocean basin in response to sediment input, sediment transport (via diffusion), variable ocean base topography, and changing sea level. An analysis of this problem shows that it is a generalized Stefan melting problem; the distinctive feature, a latent heat term that can be a function of both space and time. In this light, the approach used in this work is to explore how previous analytical solutions and numerical tools developed for the classical Stefan melting problem (in particular fixed grid enthalpy methods) can be adapted to resolve the shoreline moving boundary problem.
Findings
For a particular one‐dimensional case, it is shown that the shoreline problem admits a similarity solution, similar to the well‐known Neumann solution of the Stefan problem. Through the definition of a compound variable (the sum of the fluvial sediment and ocean depths) a single domain‐governing equation, mimicking the enthalpy formulation of a one‐phase melting problem, is derived. This formulation is immediately suitable for numerical solution via an explicit time integration fixed grid enthalpy solution. This solution is verified by comparing with the analytical solution and a limiting geometric solution. Predictions for the shoreline movement in a constant depth ocean are compared with shoreline predictions from an ocean undergoing tectonic subsidence.
Research limitations/implications
The immediate limitation in the work presented here is that “off‐shore” sediment transport is handled in by a “first order” approach. More sophisticated models that take a better accounting of “off shore” transport (e.g. erosion by wave motion) need to be developed.
Practical implications
There is a range of rich problems involving the evolution of the earth's surface. Many of the key transport processes are closely related to heat and mass transport. This paper illustrates that this similarity can be exploited to develop predictive models for earth surface processes. Such models are essential in understanding the formation of the earth's surface and could have a significant impact on natural resource (oil reserves) and land (river restoration) management.
Originality/value
For the most part the solution methods developed in this work are extensions of the standard numerical techniques used in heat transfer. The novelty of the work presented rests in the nature of the problems solved, not the method used. The particular novel feature is the time and space dependence of the latent heat function; a feature that leads to interesting analytical and numerical results.
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Robert Vertnik and Božidar Šarler
The purpose of this paper is to develop a new local radial basis function collocation method (LRBFCM) for one‐domain solving of the non‐linear convection‐diffusion equation, as it…
Abstract
Purpose
The purpose of this paper is to develop a new local radial basis function collocation method (LRBFCM) for one‐domain solving of the non‐linear convection‐diffusion equation, as it appears in mixture continuum formulation of the energy transport in solid‐liquid phase change systems.
Design/methodology/approach
The method is structured on multiquadrics radial basis functions. The collocation is made locally over a set of overlapping domains of influence and the time stepping is performed in an explicit way. Only small systems of linear equations with the dimension of the number of nodes in the domain of influence have to be solved for each node. The method does not require polygonisation (meshing). The solution is found only on a set of nodes.
Findings
The computational effort grows roughly linearly with the number of the nodes. Results are compared with the existing steady analytical solutions for one‐dimensional convective‐diffusive problem with and without phase change. Regular and randomly displaced node arrangements have been employed. The solution is compared with the results of the classical finite volume method. Excellent agreement with analytical solution and reference numerical method has been found.
Practical implications
A realistic two‐dimensional non‐linear industrial test associated with direct‐chill, continuously cast aluminium alloy slab is presented.
Originality/value
A new meshless method is presented which is simple, efficient, accurate, and applicable in industrial convective‐diffusive solid‐liquid phase‐change problems with non‐linear material properties.
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Guillaume Houzeaux and Ramon Codina
To develop a numerical methodology to simulate the lost foam casting (LFC), including the gas back‐pressure effects.
Abstract
Purpose
To develop a numerical methodology to simulate the lost foam casting (LFC), including the gas back‐pressure effects.
Design/methodology/approach
Back‐pressure effects are due to the interactions of many physical processes. The strategy proposed herein tries to model all these processes within a simple formula. The main characteristic of the model consists of assuming that the back‐pressure is a known function of the external parameters (coating, temperature, gravity, etc.) that affects directly the heat transfer coefficient from the metal to the foam. The general framework of the simulation is a finite element model based on an arbitrary Lagrangian Eulerian (ALE) approach and the use of level set function to capture the metal front advance.
Findings
After experimental tunings, the model provides a way to include the back‐pressure effects in a simple way.
Research limitations/implications
The method is not completely predictive in the sense that a priori tuning is necessary to calibrate the model.
Practical implications
Provides more realistic results than classical models.
Originality/value
The paper proposes a theoretical framework of a finite element method for the simulation of LFC process. The method uses an ALE method on a fixed mesh and a level‐set function to capture metal front advance. It proposes an original formula for the heat transfer coefficient that enables one to include back‐pressure effects.
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Roland W. Lewis, Eligiusz W. Postek, Zhiqiang Han and David T. Gethin
To present a numerical model of squeeze casting process.
Abstract
Purpose
To present a numerical model of squeeze casting process.
Design/methodology/approach
The modelling consists of two parts, namely, the mould filling and the subsequent thermal stress analysis during and after solidification. Mould filling is described by the Navier‐Stokes equations discretized using the Galerkin finite element method. The free surface is followed using a front tracking procedure. A thermal stress analysis is carried out, assuming that a coupling exists between the thermal problem and the mechanical one. The mechanical problem is described as an elasto‐visco‐plastic formulation in an updated Lagrangian frame. A microstructural solidification model is also incorporated for the mould filling and thermal stress analysis. The thermal problem is solved using enthalpy method.
Findings
During the mould‐filling process a quasi‐static arbitrary Lagrangian‐Eulerian (ALE) approach and a microstructural solidification model were found to be applicable. For the case of the thermal stress analysis the influence of gap closure, effect of initial stresses (geometric nonlinearity), large voids and good performance of a microstructural model have been demonstrated.
Research limitations/implications
The model can also be applied to the simulation of indirect castings. The final goal of the model is the ability to simulate the forming of the material after mould filling and during the solidification of the material. This is possible to achieve by applying arbitrary contact surfaces due to the sliding movement of the cast versus the punch and die.
Practical implications
The presented model can be used in engineering practice, as it incorporates selected second‐order effects which may influence the performance of the cast.
Originality/value
During the mould‐filling procedure a quasi‐static ALE approach has been applied to SQC processes and found to be generally applicable. A microstructural solidification model was applied which has been used for the thermal stress analysis only. During the thermal stress analysis the influence of gap closure and initial stresses (geometric nonlinearity) has been demonstrated.
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Oleg Iliev, Joachim Linn, Mathias Moog, Dariusz Niedziela and Vadimas Starikovicius
This study proposes to develop and investigate different iterative solvers for non‐Newtonian flow equations.
Abstract
Purpose
This study proposes to develop and investigate different iterative solvers for non‐Newtonian flow equations.
Design/methodology/approach
Existing approaches for the time discretization of the flow equation and for an iterative solution of the discrete systems are discussed. Ideas for further development of existing preconditioners are proposed, implemented and investigated numerically.
Findings
A two‐level preconditioning, consisting of a transformation of the original system in the first step and subsequent preconditioning of the transformed system is suggested. The GMRES iterative method, which usually performs well when applied to academic problems, showed dissatisfactory performance for the type of industrial flow simulations investigated in this work. It was found that the BiCGStab method performed best in the tests presented here.
Research limitations/implications
The iterative solvers considered here were investigated only for a certain class of polymer flows. More detailed studies for other non‐Newtonian flows should be carried out.
Originality/value
The work presented in this paper fills a gap related to the usage of efficient iterative methods for non‐Newtonian flow simulations.
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Víctor D. Fachinotti and Michel Bellet
The paper seeks to present an original method for the numerical treatment of thermal shocks in non‐linear heat transfer finite element analysis.
Abstract
Purpose
The paper seeks to present an original method for the numerical treatment of thermal shocks in non‐linear heat transfer finite element analysis.
Design/methodology/approach
The 3D finite element thermal analysis using linear standard tetrahedral elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe ways to directly discourage the use of these elements. This is especially true in the case of solidification problems, in which melted alloys at very high temperature contact low diffusive mould materials. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M‐matrix form, which ensures an oscillation‐free solution.
Findings
The proposed “diffusion‐split” method consists basically of using a modified conductivity matrix. It allows for solutions based on linear tetrahedral elements. The performance of the method is evaluated by means of a test case with analytical solution, as well as an industrial application, for which a well‐behaved numerical solution is available.
Originality/value
The proposed method should be helpful for computational engineers and software developers in the field of heat transfer analysis. It can be implemented in most existing finite element codes with minimal effort.
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Sung In Choi, Jingyu Zhang and Yan Jin
This study provides real-world evidence for the relationship between strategic communication from a global/multinational perspective and the effectiveness of corporate message…
Abstract
Purpose
This study provides real-world evidence for the relationship between strategic communication from a global/multinational perspective and the effectiveness of corporate message strategies in the context of environment risk communication. Among sustainability issues, particulate matter (PM) air pollution has threatened the health and social wellbeing of citizens in many countries. The purpose of this paper is to apply the message framing and attribution theories in the context of sustainability communication to determine the effects of risk message characteristics on publics’ risk responses.
Design/methodology/approach
Using a 2 (message frame: gain vs loss) × 2 (attribution type: internal vs external) × 2 (country: China vs South Korea) between-subjects experimental design, the study examines the message framing strategies' on publics' risk responses (i.e. risk perception, risk responsibility attribution held toward another country and sustainable behavioral intention for risk prevention).
Findings
Findings include (1) main effects of message characteristics on participants’ risk responses; (2) the impact of country difference on participants’ differential risk responses and (3) three-way interactions on how risk message framing, risk threats type and country difference jointly affect not only participants’ risk perception and risk responsibility attribution but also their sustainable behavioral intention to prevent PM.
Research limitations/implications
Although this study used young–adult samples in China and South Korea, the study advances the theory building in strategic environmental risk communication by emphasizing a global/multinational perspective in investigating differences among at-risk publics threatened by large-scale environmental risks.
Practical implications
The study's findings provide evidence-based implications such as how government agencies can enhance the environmental risk message strategy so that it induces more desired risk communication outcomes among at-risk publics. Insights from our study offer practical recommendations on which message feature is relatively more impactful in increasing intention for prosocial behavioral changes.
Social implications
This study on all measured risk responses reveals important differences between at-risk young publics in China and South Korea and how they respond differently to a shared environmental risk such as PM. The study's findings provide new evidence that media coverage of global environmental issues needs to be studied at the national level, and cross-cultural comparisons are imperative to understand publics’ responses to different news strategies. Thus, this study offers implications for practitioners to understand and apply appropriate strategies to publics in a social way across different countries so as to tailor risk communication messaging.
Originality/value
This study offers new insights to help connect message framing effects with communication management practice at the multi-national level, providing recommendations for government communication practitioners regarding which PM message features are more likely to be effective in forming proper risk perception and motivate sustainable actions among at-risk publics in different countries.