The modelling of heat, mass and solute transport in solidification systems

Voller, V. R.; Brent, A. D.; Prakash, C.

doi:10.1016/0017-9310(89)90054-9

Cited by 446 publications

(218 citation statements)

References 22 publications

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“…For details of the volume-averaging procedure and the form of the macroscopic volume-averaged formulations, see Beckermann and Viskanata. 57) Further exploration of aspects of the volume-averaging procedure and assumptions were made by Ganesan, Poirier, and Voller et al 49,58) Following the pioneering works highlighted above, many studies used similar or modified versions of the same continuum equations to examine a number of different solidification phenomena, including channel formation in directionally-solidified alloys, [59][60][61][62][63][64] the effect of solidification shrinkage and pore formation, [63][64][65][66][67][68][69][70][71][72][73][74] and the effect of transformation-induced strains. [75][76][77] Many authors have also examined the particular formulations and assumptions of the original models.…”

Section: Continuum Modelsmentioning

confidence: 99%

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

Pickering

2013

ISIJ Int.

143

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The macro-scale segregation of alloying elements during the casting continues to afflict the manufacturers of steel ingots, despite many decades of research into its prediction and elimination. Defects such as A-segregates are still commonplace, and components are regularly scrapped due to their presence, leading to increased economic and environmental costs. With the growth of the nuclear power industry, and the increased demands placed on new pressure vessels, it is now more important than ever that today's steel ingots are as chemically homogeneous as possible.This article briefly reviews the development of our current understanding of macrosegregation phenomena during the 20 th century, before going on to assess the latest developments in the field of macrosegregation modelling. The aim of the text is to highlight the shortcomings of applying contemporary macromodels to steel-ingot casting, and to suggest practical alternatives. In addition, the experimental characterisation of macrosegregation is explored, and a review of the various techniques currently available is presented.

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Section: Continuum Modelsmentioning

confidence: 99%

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

Pickering

2013

ISIJ Int.

143

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“…Supplementary relationships are required to update the liquid fraction f l during the melting/solidification process. A method developed by Voller et al 19 was implemented to solve for f l in each time step with the assumption of local composition equilibrium at the S/L interface. The relation of a mixture concentration c and the corresponding liquidus temperature can be derived from the equilibrium phase diagram in Fig.…”

Section: E Heat Transfermentioning

confidence: 99%

Numerical simulation of heat transfer and fluid flow in coaxial laser cladding process for direct metal deposition

Mazumder

2006

Journal of Applied Physics

289

105

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Articles you may be interested inThe coaxial laser cladding process is the heart of direct metal deposition ͑DMD͒. Rapid materials processing, such as DMD, is steadily becoming a tool for synthesis of materials, as well as rapid manufacturing. Mathematical models to develop the fundamental understanding of the physical phenomena associated with the coaxial laser cladding process are essential to further develop the science base. A three-dimensional transient model was developed for a coaxial powder injection laser cladding process. Physical phenomena including heat transfer, melting and solidification phase changes, mass addition, and fluid flow in the melt pool, were modeled in a self-consistent manner. Interactions between the laser beam and the coaxial powder flow, including the attenuation of beam intensity and temperature rise of powder particles before reaching the melt pool were modeled with a simple heat balance equation. The level-set method was implemented to track the free surface movement of the melt pool, in a continuous laser cladding process. The governing equations were discretized using the finite volume approach. Temperature and fluid velocity were solved for in a coupled manner. Simulation results such as the melt pool width and length, and the height of solidified cladding track were compared with experimental results and found to be reasonably matched.

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“…A single domain fixed-grid enthalpy-porosity approach (Brent et al, 1988) in conjunction with an appropriate enthalpy updating closure scheme (Voller et al, 1989) is utilized for modeling the phase change phenomena in presence of a continuously evolving solid-liquid interface. In this method, the morphology of the phase change domain can be treated as an equivalent porous medium that offers a frictional resistance toward fluid flow in that region.…”

Section: Physical Problem and Mathematical Modelsmentioning

confidence: 99%

A Comparison of Numerical Strategies for Modeling the Transport Phenomena in High-Energy Laser Surface Alloying Process

Chatterjee

2017

Front. Mech. Eng.

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A comparative assessment is done on the effectiveness of some developed and reported macroscopic and mesoscopic models deployed for addressing the three-dimensional thermo-fluidic transport during high-power laser surface alloying process. The macroscopic models include the most celebrated k-ε turbulence model and the large eddy simulation (LES) model, whereas a kinetic theory-based lattice Boltzmann (LB) approach is invoked under the mesoscopic paradigm. The time-dependent Navier-Stokes equations are transformed into the k-ε turbulence model by performing the Reynolds averaging technique, whereas a spatial filtering operation is used to produce the LES model. The models are suitably modified to address the turbulent melt-pool convection by using a modified eddy viscosity expression including a damping factor in the form of square root of the liquid fraction. The LB scheme utilizes three separate distribution functions to monitor the underlying hydrodynamic, thermal and compositional fields. Accordingly, the kinematic viscosity, thermal and mass diffusivities are adjusted independently. A single domain fixed-grid enthalpy-porosity approach is utilized to model the phase change phenomena in conjunction with an appropriate enthalpy updating closure scheme. The performance of these models is recorded by capturing the characteristic nature of the thermo-fluidic transport during the laser material processing. The maximum values of the pertinent parameters in the computational domain obtained from several modeling efforts are compared to assess their capabilities. The comparison shows that the prediction from the k-ε turbulence model is higher than the LES and LB models. In addition, the results from all three models are compared with the available experimental results in the form of dimensionless composition of the alloyed layer along the dimensionless depth of the pool. The comparison reveals that the LB and the LES approaches are better than the k-ε turbulence approach in reproducing the experimental results.

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The modelling of heat, mass and solute transport in solidification systems

Cited by 446 publications

References 22 publications

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

Macrosegregation in Steel Ingots: The Applicability of Modelling and Characterisation Techniques

Numerical simulation of heat transfer and fluid flow in coaxial laser cladding process for direct metal deposition

A Comparison of Numerical Strategies for Modeling the Transport Phenomena in High-Energy Laser Surface Alloying Process

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