Modeling of permeability with the aid of 3D interdendritic flow simulation for equiaxed dendritic structures

Khajeh, Ehsan; Mirbagheri, S. M. H.; Davami, P.

doi:10.1016/j.msea.2007.04.076

Cited by 8 publications

(5 citation statements)

References 17 publications

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“…The main factor limiting the numerical determination of permeability is the lack of precise geometry. Numerical methods applied to determine the permeability of dendritic structures, use either simplified dendrite-like shapes 17 or images of actual dendrites. [18][19][20][21] A number of researchers have calculated the values of permeability on 2D dendritic structures obtained from sections of cast alloys.…”

Section: K~(mentioning

confidence: 99%

Numerical determination of permeability of Al–Cu alloys using 3D geometry from X-ray microtomography

Khajeh

Maijer

2010

Materials Science and Technology

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In the present study, the permeabilities of Al–15·5 wt-%Cu and Al–19·5 wt-%Cu have been determined numerically by solving the full Navier–Stokes equations on 3D geometries of interdendritic channels obtained by X-ray microtomography. The samples for X-ray microtomography imaging were sectioned from different heights in directionally solidified cylinders in order to obtain a variety of microstructures for each composition. The flow has been solved using a second order accurate finite volume method approach. The effect of employing uniform or unstructured mesh on the calculated permeability has been studied. The Marching–Cube triangulation method was used to extract accurate surfaces for unstructured volume meshing. Calculated values of permeability for this range of solid fractions show partial agreement with previous experiments. Observed deviations are analysed and ultimately attributed to experimental error associated with the difficulties of measuring permeability.

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Section: K~(mentioning

confidence: 99%

Numerical determination of permeability of Al–Cu alloys using 3D geometry from X-ray microtomography

Khajeh

Maijer

2010

Materials Science and Technology

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“…Finally, equation (6) was used for predicting microshrinkages in the casting samples. 25 Figure 12 shows the variation of the geometrical parameter (Pe) during the Assuming that the main cause of microshrinkage formation during the solidification is obstructing of interdendritic flow channels, the results of the present work can be linked with the solidification code. By reducing thermal variables, the permeability evolution can be obtained and by assuming a critical value of permeability for blocking the interdendritic channels, microshrinkage distribution is determined.…”

Section: Resultsmentioning

confidence: 75%

“…Finally, equation ( 6) was used for predicting microshrinkages in the casting samples. 25 Figure 12 shows the variation of the geometrical parameter (Pe) during the solidification progress, applying different cooling rates. This curve is obtained by solving the Fick's equation for solidification of the typical dendrite in an isothermal domain similar to the flow cell which is cooled with a constant cooling rate.…”

Section: Resultsmentioning

confidence: 99%

Modelling and simulation of equiaxed dendritic structures permeability for Pb–Sn alloys

Mirbagheri¹,

Khajeh²

2008

Materials Science and Technology

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In this investigation, the permeability of interdendritic liquid flow through the equiaxial mushy zone has been modelled for Pb-Sn alloys based on experimental measurements. In the present work by solving Navier-Stokes equation, the flow pattern around the equiaxed dendrite has been obtained and then permeability has been determined by applying Darcy's law. Numerical determined values of permeabilities have been analysed by the use of Statistical Package for the Social Sciences (SPSS) statistical software. Then an experimental method has been used to measure the permeability for flow through equiaxial mushy zone of Pb-Sn alloys. Results show that increasing the solid fraction and perturbation decreases the permeability, but unlike the solid fraction, perturbation has less effect on permeability. It seems that the empirical relationship presented in this article could be used to estimate permeability in the mushy Pb-Sn alloys.

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“…Several approaches have been used to directly measure the Darcy permeability of the mushy zone, e.g., by measuring the flow of eutectic melt in carefully temperaturecontrolled samples or by removing the melt during solidification and forcing water through the remaining porous microstructure [5,6].…”

Section: Related Workmentioning

confidence: 99%

Permeability Measurements of 3D Microstructures Generated by Phase Field Simulation of the Solidification of an Al-Si Alloy during Chill Casting

Berger

Apel

Laschet

et al. 2021

Metals

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The permeability of the semi-solid state is important for the compensation of volume shrinkage during solidification, since insufficient melt feeding can cause casting defects such as hot cracks or pores. Direct measurement of permeability during the dynamical evolution of solidification structures is almost impossible, and numerical simulations are the best way to obtain quantitative values. Equiaxed solidification of the Al-Si-Mg alloy A356 was simulated on the microscopic scale using the phase field method. Simulated 3D solidification structures for different stages along the solidification path were digitally processed and scaled up to generate 3D models by additive manufacturing via fused filament fabrication (FFF). The Darcy permeability of these models was determined by measuring the flow rate and the pressure drop using glycerol as a model fluid. The main focus of this work is a comparison of the measured permeability to results from computational fluid flow simulations in the phase field framework. In particular, the effect of the geometrical constraint due to isolated domain walls in a unit cell with a periodic microstructure is discussed. A novel method to minimize this effect is presented. For permeability values varying by more than two orders of magnitude, the largest deviation between measured and simulated permeabilities is less than a factor of two.

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Modeling of permeability with the aid of 3D interdendritic flow simulation for equiaxed dendritic structures

Cited by 8 publications

References 17 publications

Numerical determination of permeability of Al–Cu alloys using 3D geometry from X-ray microtomography

Numerical determination of permeability of Al–Cu alloys using 3D geometry from X-ray microtomography

Modelling and simulation of equiaxed dendritic structures permeability for Pb–Sn alloys

Permeability Measurements of 3D Microstructures Generated by Phase Field Simulation of the Solidification of an Al-Si Alloy during Chill Casting

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