Mathematical modeling of macrosegregation of iron carbon binary alloy: Role of double diffusive convection
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INTRODUCTION
SEGREGATION of solute during alloy solidification is one of the major casting defects. The fluid flow in the mushy and liquid regions causes transport of solute from inter dendritic space to other parts of the casting and consequently causes macrosegregation. Since macrosegregation in cast products results in chemical inhomogeneity and cannot be eliminated completely by subsequent treatments, such as homogenization, it results in products o f nonuniform quality. Therefore, a thorough understanding of the role of fluid flow in the final solutal field is important, and researchers recently have studied this aspect extensively by carrying out simulation studies on various alloy systems/~-~41 Flemings and coworkersp,2,31 first theoretically analyzed macrosegregation based on conservation of solute along with known velocity distribution in the liquid [1,2~ and, subsequently, by consideration of coupled solute and interdendritic fluid flow.t3] However, experimental studiest4] have clearly shown that the fluid flow during alloy solidification is induced by both thermal and concentration gradients in the liquid phase and mushy region. Temperature gradients are the outcome of externally imposed boundary conditions as well as latent heat evolution within the mushy zone. Concentration gradients, on the other hand, are caused by the preferential rejection of solute at the solid liquid interface and are due to transportation by convective flow in the liquid region. These two gradients lead to fluid flow due to thermal and solutal buoyancy in both mushy and liquid regions. The resulting flow is known as double diffusive convection. Recently, there have been a large number of publications t5-14] in which the role of fluid flow on thermal and
A.K. S1NGH and B. BASU, Scientists, are with the Tata Research Development and Design Centre, Pune 411 001, India. Manuscript submitted August 16, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS B
solutal fields during solidification has been studied using numerical models based on continuum formulation. Several studies employing this formulation deal with solidification of ammonium chloride water, iS-10] Pb_Sn,[ 11] and A1-Cu. p2~ Bennon and IncroperaE6,7~proposed a model based on conservation of energy, solute, mass, and momentum to investigate solidification of a binary, aqueous ammonium chloride solution in a rectangular cavity. Later, Beckermann and Viskanta t81 and Voller e t al.m~ carried out numerical and experimental studies on the same system. The most important finding of these studies t6-9] is that double diffusive convection plays an important role in the long range transport of solute and thereby controls the final macrosegregation pattern. More recently, Neilson and Incropera t~~ and Felliceli et aL[~] studied numerically the role of double diffusive convection on solute transport and freckle formation during unidirectional solidification of NH4C1-H20 and Pb-Sn systems, respectively. Similarly, Diao and Tsaitl2] studied the role o f double diffusive convectio
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