The effect of solutal undercooling on double‐diffusive convection and macrosegregation during binary alloy solidification: a numerical investigation

Chakraborty, Suman; Dutta, Pradip

doi:10.1002/fld.254

Cited by 23 publications

(11 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From Eqs. (14) and (15), an expression for the inverse of the latent heat function, corresponding to the case of multicomponent alloy solidification systems, can be obtained as…”

Section: Formulation Of Latent Heat Functionmentioning

confidence: 99%

“…Voller and Prakash [11] initially applied this formulation for modeling mushy-zone phase-change problems, in which a linear variation of temperature within the mushy zone was assumed. Subsequently, a number of advanced numerical studies were reported in the literature, which basically extended the earlier formulation to more complicated cases of alloy solidification problems [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Generalized Enthalpy-based Macro Model for Ternary Alloy Solidification Simulations

Ganguly

Chakraborty

2007

Numerical Heat Transfer, Part B: Fundamentals

Self Cite

View full text Add to dashboard Cite

In this article, a generalized macroscopic mathematical model is developed to simulate the transport phenomena occurring during the solidification of ternary alloy systems. The model is essentially based on a fixed-grid, enthalpy-based control-volume approach. Microscopic features pertaining to complex thermosolutal transport mechanisms are incorporated through a novel formulation of latent enthalpy evolution, consistent with the phase-change morphology of general multicomponent alloy systems. Numerical simulations are performed for two different ternary steel alloys of apparently contrasting thermosolutal transport characteristics, and the resulting convection and macrosegregation patterns are analyzed in detail. The mathematical model is also tested by comparing the present numerical results with benchmark analytical solutions and experimental data reported in the literature for ternary alloy solidification systems, and excellent agreement is found in this regard.

show abstract

“…From Eqs. (14) and (15), an expression for the inverse of the latent heat function, corresponding to the case of multicomponent alloy solidification systems, can be obtained as…”

Section: Formulation Of Latent Heat Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Generalized Enthalpy-based Macro Model for Ternary Alloy Solidification Simulations

Ganguly

Chakraborty

2007

Numerical Heat Transfer, Part B: Fundamentals

Self Cite

View full text Add to dashboard Cite

show abstract

“…This gives rise to a concentration gradient at the interface, which in turn, causes a local change in the liquidus temperature. This is commonly known as solutal undercooling, and is primarily governed by liquid species diffusivity, dendrite growth rate, thickness of the solutal boundary layer and the interface geometry (Rappaz 1989;Chakraborty et al 2002). In all the previous studies, solutal undercooling effect is essentially neglected while modelling solidification.…”

Section: Introductionmentioning

confidence: 99%

Numerical Modelling of Transport Phenomena and Macrosegregation during Ternary Alloy Solidification: Solutal Undercooling Effects

Ganguly

2019

JAFM

View full text Add to dashboard Cite

In this paper, a macroscopic mathematical model is developed for simulation of transport phenomena during ternary alloy solidification processes, taking into account non-equilibrium effects due to solutal undercooling. The model is based on a fixed-grid, enthalpy-based, control volume approach. Microscopic features pertaining to non-eFquilibrium effects on account of solutal undercooling are incorporated through a novel formulation of a modified partition coefficient. The effective partition coefficient is numerically modeled by means of macroscopic parameters related to the solidifying domain. Numerical simulations are performed for ternary steel alloy by employing the present model and the resulting convection and macrosegregation patterns are analyzed. It is observed that the consideration of non-equilibrium solidification in the present mathematical approach is able to capture the thermo-solutal convection and leads to prediction of accurate value of macrosegregation. The results from the present model matches well with the experimental observations published in the literature.

show abstract

“…This phenomenon is caused by the segregation of the alloy components at the front and is called solutal undercooling [1][2][3]. It leads to the formation of a region filled with the solid-liquid mixture called mushy zone.…”

Section: Introductionmentioning

confidence: 99%

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Skrzypczak

Węgrzyn-Skrzypczak

Winczek

2015

Archives of Metallurgy and Materials

View full text Add to dashboard Cite

The paper is focused on the modeling of the directional solidification process of pure metal. During the process the solidification front is sharp in the shape of the surface separating liquid from solid in three dimensional space or a curve in 2D. The position and shape of the solid-liquid interface change according to time. The local velocity of the interface depends on the values of heat fluxes on the solid and liquid sides. Sharp interface solidification belongs to the phase transition problems which occur due to temperature changes, pressure, etc. Transition from one state to another is discontinuous from the mathematical point of view. Such process can be identified during water freezing, evaporation, melting and solidification of metals and alloys, etc.The influence of natural convection on the temperature distribution and the solid-liquid interface motion during solidification of pure copper is studied. The mathematical model of the process is based on the differential equations of heat transfer with convection, Navier-Stokes equation and the motion of the interface. This system of equations is supplemented by the appropriate initial and boundary conditions. In addition the continuity conditions at the solidification interface must be properly formulated. The solution involves the determination of the temporary temperature and velocity fields and the position of the interface. Typically, it is impossible to obtain the exact solution of such problem. The numerical model of solidification of pure copper in a closed cavity is presented, the influence of the natural convection on the phase change is investigated. Mathematical formulation of the problem is based on the Stefan problem with moving internal boundaries. The equations are spatially discretized with the use of fixed grid by means of the Finite Element Method (FEM). Front advancing technique uses the Level Set Method (LSM). Chorin's projection method is used to solve Navier-Stokes equation. Such approach makes possible to uncouple velocities and pressure. The Petrov-Galerkin formulation is employed to stabilize numerical solutions of the equations. The results of numerical simulations in the 2D region are discussed and compared to the results obtained from the simulation where movement of the liquid phase was neglected.Keywords: Pure Metal, Solidification, Sharp Interface, Natural Convection, Finite Element Method, Level Set Method Praca porusza problematykę modelowania kierunkowego krzepnięcia czystego metalu. Podczas tego procesu obserwuje się formowanie ostrego frontu krzepnięcia w postaci powierzchni separującej ciecz i ciało stałe w przypadku trójwymiarowym lub krzywej w przypadku płaskim. Położenie oraz kształt interfejsu krzepnięcia zmieniają się w czasie a wartości prędkości lokalnych zależą od różnicy intensywności strumieni ciepła po stronie ciała stałego i cieczy. Krzepnięcie z ostrym frontem należy do grupy procesów z przemianami fazowymi, które warunkowane są zmianami temperatury, ciśnienia, itp. Przejście fazowe z jednego stanu w drugi...

show abstract

The effect of solutal undercooling on double‐diffusive convection and macrosegregation during binary alloy solidification: a numerical investigation

Cited by 23 publications

References 17 publications

A Generalized Enthalpy-based Macro Model for Ternary Alloy Solidification Simulations

A Generalized Enthalpy-based Macro Model for Ternary Alloy Solidification Simulations

Numerical Modelling of Transport Phenomena and Macrosegregation during Ternary Alloy Solidification: Solutal Undercooling Effects

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Contact Info

Product

Resources

About