A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

Zabaras, Nicholas; Samanta, Deep

doi:10.1002/nme.998

Cited by 45 publications

(58 citation statements)

References 39 publications

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“…Since solidification occurs in a diffused-interface, following a volume-averaging approach as in [19], we can write the energy equation (applicable in the whole domain Ω) as follows:…”

Section: Assumptionmentioning

confidence: 99%

“…where ρ ≡ ρ l Φ + ρ s (1 − Φ), e g is the unit vector in the direction of gravity, g is the gravity constant and v from now on denotes the volume-averaged velocity equal to Φv l [19]. For simplicity of the model, we assume that the solid/liquid densities and specific heats are the same but we allow for different conductivities.…”

Section: Assumptionmentioning

confidence: 99%

“…The velocity in the solid region is set to zero, so that no-slip condition is applied at the solid/liquid interface. The formulation is briefly summarized below with more details provided in [19]. The flow equations are first re-cast in dimensionless form as follows:…”

Section: Incorporating Melt Convectionmentioning

confidence: 99%

“…The interface conditions are accurately enforced on an implicit manner while maintaining energy conservation for the overall system. The melt flow is modelled using equal-order velocity-pressure interpolation that has been shown to lead to better convergence rates and accuracy [19] than the fractional step method commonly used in dendritic solidification models. The present methodology will be shown to be computationally efficient and accurate for both two-and three-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

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A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods

Tan

Zabaras

2006

Journal of Computational Physics

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116

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A method combining features of front tracking methods and fixed domain methods is presented to model dendritic solidification of pure materials. To explicitly track the interface growth and shape of the solidifying crystals, a front tracking approach based on the level set method is implemented. To easily model the heat and momentum transport, a fixed domain method is implemented assuming a diffused freezing front where the liquid fraction is defined in terms of the level set function. The fixed domain approach, by avoiding the explicit application of essential boundary conditions on the freezing front, leads to an energy conserving methodology that is not sensitive to the mesh size. To compute the freezing front morphology, an extended Stefan condition is considered. Applications to several classical Stefan problems and two-and three-dimensional crystal growth of pure materials in an undercooled melt including the effects of melt flow are considered. The computed results agree very well with available analytical solutions as well as with results obtained using front-tracking techniques and the phase field method.

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“…Since solidification occurs in a diffused-interface, following a volume-averaging approach as in [19], we can write the energy equation (applicable in the whole domain Ω) as follows:…”

Section: Assumptionmentioning

confidence: 99%

Section: Assumptionmentioning

confidence: 99%

Section: Incorporating Melt Convectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods

Tan

Zabaras

2006

Journal of Computational Physics

Self Cite

116

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“…With the above assumptions, the volumeaveraged form of the macroscopic transport equations for momentum and energy are [9,10] …”

Section: Mold Solid Shellmentioning

confidence: 99%

A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys

Tan

Zabaras

2005

Materials Science and Engineering: A

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A thermomechanical study of the effects of mold topography on the solidification of aluminum alloys at early times is provided. The various coupling mechanisms between the solid-shell and mold deformation and heat transfer at the mold/solid-shell interface during the early stages of aluminum solidification on molds with uneven topographies are investigated. The air-gap nucleation time, the stress evolution and the solid-shell growth pattern are examined for different mold topographies to illustrate the potential control of aluminum cast surface morphologies during the early stages of solidification using proper design of mold topographies. The unstable shell growth pattern in the early solidification stages results mainly from the unevenness of the heat flux between the solid-shell and the mold surface. This heat flux is determined by the size of the air-gaps formed between the solidifying shell and mold surface or from the value of the contact pressure. Simulation results show that a sinusoidal mold surface with a smaller wavelength leads to nucleation of air-gaps at earlier times. In addition, the unevenness in the solid-shell growth pattern decreases faster for a smaller wavelength. Such studies can be used to tune mold surfaces for the control of cast surface morphologies.

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Projection method for flows with large local density gradients: Application to dendritic solidification

Heinrich

Sajja

Felicelli

et al. 2008

Numerical Methods in Fluids

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SUMMARYNumerical models of solidification including a mushy zone are notoriously inefficient; most of them are based on formulations that require the coupled solution to the velocity components in the momentum equation greatly restricting the range of applicability of the models. Initial attempts at modeling directional solidification in the presence of a developing mushy zone using a projection formulation encountered difficulties once solidification starts, which were traced to the inability of the method to deal with large local density differences in the vicinity of the fluid-mush interface. A modified formulation of the projection method has been developed that maintains the coupling between the body force and the pressure gradient and is presented in this work. This formulation is shown to be robust and extremely efficient; reducing very significantly the necessary storage and the computational time required for the simulation of problems involving very large meshes when compared with previously published data. This is illustrated in this work through its application to simulations involving a Pb-Sn alloy.

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A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

Cited by 45 publications

References 39 publications

A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods

A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods

A thermomechanical study of the effects of mold topography on the solidification of Aluminum alloys

Projection method for flows with large local density gradients: Application to dendritic solidification

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