A Front Tracking Model for Transient Solidification of Al–7wt%Si in a Bridgman Furnace

Mooney, Robin P.; McFadden, Shaun; Rebow, Marek; Browne, David J.

doi:10.1007/s12666-012-0201-2

Cited by 15 publications

(23 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The BFFTM code of Mooney et al [15] has been verified for a steady state scenario using the order verification method given by Knupp and Salari [2] by way of demonstrative example, specifically, steady state solidification of high purity titanium. The model is first order accurate in space.…”

Section: Resultsmentioning

confidence: 99%

“…In this section we outline how the Bridgman furnace front tracking model (BFFTM) of Mooney et al [15] was implemented to solve our test problem. Then we determine the theoretical order of accuracy of the model.…”

Section: Numerical Solutionmentioning

confidence: 99%

“…The BFFTM was previously demonstrated for a transient solidification problem, involving a binary alloy, where step changes in the withdrawal velocity occurred [15]. It was shown how the model could be used to determine a steady state temperature profile, for a fixed withdrawal velocity, and assuming some arbitrary initial temperature profile in the sample.…”

Section: Implementation Of the Bfftmmentioning

confidence: 99%

“…This yields the explicit finite difference scheme used in the BFFTM. Refer to [15] and [24] for a further description of the BFFTM algorithm.…”

Section: Theoretical Order Of Accuracy Of the Bfftmmentioning

confidence: 99%

“…FTMs have been used to track the solidification interface in simple phase change problems involving pure materials [11], and also in more complex problems involving binary alloys [12], for example, where columnar dendritic growth occurs [13], or to predict columnar to equiaxed transition [14]. In this paper, we will verify the Bridgman furnace FTM (or BFFTM) of Mooney et al [15], for steady state Bridgman solidification of high purity titanium.…”

Section: Introductionmentioning

confidence: 96%

See 4 more Smart Citations

Order verification of a Bridgman furnace front tracking model in steady state

Mooney

McFadden

2014

Simulation Modelling Practice and Theory

View full text Add to dashboard Cite

Numerical model verification is a prerequisite to model validation. However, verification can be difficult if an analytical solution is not available for the normally complex problem that the numerical model is setting out to address. This article aims to formally verify a Bridgman furnace solidification front tracking model code in a steady state scenario. To do this an order verification procedure is applied using an established analytical solution from the literature. The model is verified as first order accurate in space for steady state Bridgman solidification. Highlights A Bridgman furnace front tracking model code is verified for a steady-state solution.  An order verification procedure is outlined and demonstrated.  The model is verified as first order accurate in space.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

Section: Implementation Of the Bfftmmentioning

confidence: 99%

“…This yields the explicit finite difference scheme used in the BFFTM. Refer to [15] and [24] for a further description of the BFFTM algorithm.…”

Section: Theoretical Order Of Accuracy Of the Bfftmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 3 more Smart Citations

Order verification of a Bridgman furnace front tracking model in steady state

Mooney

McFadden

2014

Simulation Modelling Practice and Theory

View full text Add to dashboard Cite

show abstract

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

Zimmermann

Sturz

Nguyen-Thi

et al. 2017

JOM

Self Cite

View full text Add to dashboard Cite

During casting often a dendritic microstructure is formed, resulting in a columnar or equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). Especially the detailed knowledge of the critical parameters for CET is important, because the microstructure determines significantly the materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the ESA MAP project CETSOL. Reduced gravity allows for pure diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station ISS Al-7wt%Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed columnar growth in case of non-refined alloy. CET was detected 2 only for refined alloys, either as a sharp CET in case of a sudden increase of the solidification velocity, or as a progressive CET in case of a continuous decrease of the temperature gradient. The unique experimental data were used for numerical modelling of CET with three different approaches: (i) a front tracking model using an equiaxed growth model, (ii) a 3D CAFE model, (iii) a 3D dendrite needle network (DNN) method. Each model allows predicting the columnar dendrite tip undercooling and the growth rate with respect time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements.

show abstract

An experimental–numerical method for estimating heat transfer in a Bridgman furnace

Mooney

McFadden

Gabalcová

et al. 2014

Applied Thermal Engineering

View full text Add to dashboard Cite

Direct measurement of heat flux and heat transfer coefficients in a Bridgman furnace is not always possible using traditional methods. This study characterised a vertical tubular Bridgman furnace using experimental data so that the estimated heat flux and heat transfer coefficients may be used in simulations of future experiments using the same furnace. An experimental-numerical method is presented where a discrete proportional integral derivative controller manipulates the radial heat flux in a front tracking solidification model so that the output temperature profile matches experimental data. The method is applicable for other experimentalists and modellers and its usefulness is demonstrated by example. Highlights A combined experimental-numerical method to estimate heat flux and heat transfer coefficients in a Bridgman furnace is outlined in detail.  The inverse heat transfer problem is solved using a discrete proportional integral derivative controller in series with a front tracking solidification model.  The usefulness of the method is demonstrated by example.

show abstract

A Front Tracking Model for Transient Solidification of Al–7wt%Si in a Bridgman Furnace

Cited by 15 publications

References 10 publications

Order verification of a Bridgman furnace front tracking model in steady state

Order verification of a Bridgman furnace front tracking model in steady state

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

An experimental–numerical method for estimating heat transfer in a Bridgman furnace

Contact Info

Product

Resources

About