AXIAL SEGREGATION IN UNSTEADY DIFFUSION-DOMINATED SOLIDIFICATION IN A FINITE AMPOULE

2006 ◽  
Vol 20 (18) ◽  
pp. 2551-2560
Author(s):  
ADRIAN NECULAE ◽  
AGNETA M. BALINT
Keyword(s):  
Numerical Simulations ◽  
Directional Solidification ◽  
Binary Alloy ◽  
Finite Length ◽  
Concentration Profile ◽  
Composition Profile ◽  
Microgravity Environment ◽  
Initial Transient ◽  
Axial Segregation ◽  
Infinite Crystal

The paper deals with axial segregation in unsteady diffusion dominated directional solidification from melt of a binary alloy in a finite cylindrical ampoule. The study focuses on the influence of the finite length of the ampoule on the concentration profile in a crystal obtained in a microgravity environment. The results are compared to those reported by Kim et al. [J. Crystal Growth183, 490 (1998)] for an infinite crystal. Numerical simulations are performed for two different situations: the initial transient solidification when the melt is uniform in composition, and the multipass solidification when the crystal is grown from the melt, formed by re-melting a crystal with an initial axial composition profile.

Morphological stability of a binary alloy during directional solidification: initial transient

1994 ◽  
Vol 140 (1-2) ◽  
pp. 139-147 ◽  
Author(s):  
S.R. Coriell ◽  
R.F. Boisvert ◽  
G.B. McFadden ◽  
L.N. Brush ◽  
J.J. Favier
Keyword(s):  
Directional Solidification ◽  
Binary Alloy ◽  
Morphological Stability ◽  
Initial Transient

Swirling flow states in finite-length diverging or contracting circular pipes

2017 ◽  
Vol 819 ◽  
pp. 678-712 ◽  
Author(s):  
Zvi Rusak ◽  
Yuxin Zhang ◽  
Harry Lee ◽  
Shixiao Wang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Finite Length ◽  
Vortex Breakdown ◽  
Steady States ◽  
Inviscid Limit ◽  
Circular Pipes ◽  
Outlet Flow ◽  
Separation Zones ◽  
Steady State Solutions

The dynamics of inviscid-limit, incompressible and axisymmetric swirling flows in finite-length, diverging or contracting, long circular pipes is studied through global analysis techniques and numerical simulations. The inlet flow is described by the profiles of the circumferential and axial velocity together with a fixed azimuthal vorticity while the outlet flow is characterized by a state with zero radial velocity. A mathematical model that is based on the Squire–Long equation (SLE) is formulated to identify steady-state solutions of the problem with special conditions to describe states with separation zones. The problem is then reduced to the columnar (axially-independent) SLE, with centreline and wall conditions for the solution of the outlet flow streamfunction. The solution of the columnar SLE problem gives rise to the existence of four types of solutions. The SLE problem is then solved numerically using a special procedure to capture states with vortex-breakdown or wall-separation zones. Numerical simulations based on the unsteady vorticity circulation equations are also conducted and show correlation between time-asymptotic states and steady states according to the SLE and the columnar SLE problems. The simulations also shed light on the stability of the various steady states. The uniqueness of steady-state solutions in a certain range of swirl is proven analytically and demonstrated numerically. The computed results provide the bifurcation diagrams of steady states in terms of the incoming swirl ratio and size of pipe divergence or contraction. Critical swirls for the first appearance of the various types of states are identified. The results show that pipe divergence promotes the appearance of vortex-breakdown states at lower levels of the incoming swirl while pipe contraction delays the appearance of vortex breakdown to higher levels of swirl and promotes the formation of wall-separation states.

scholarly journals Directional solidification of a binary alloy into a cellular convective flow: localized morphologies

1999 ◽  
Vol 395 ◽  
pp. 253-270 ◽  
Author(s):  
Y.-J. CHEN ◽  
S. H. DAVIS
Keyword(s):  
Directional Solidification ◽  
Binary Alloy ◽  
Temporal Dynamics ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Morphological Instability ◽  
Flow Strength ◽  
Weakly Nonlinear

A steady, two-dimensional cellular convection modifies the morphological instability of a binary alloy that undergoes directional solidification. When the convection wavelength is far longer than that of the morphological cells, the behaviour of the moving front is described by a slow, spatial–temporal dynamics obtained through a multiple-scale analysis. The resulting system has a parametric-excitation structure in space, with complex parameters characterizing the interactions between flow, solute diffusion, and rejection. The convection in general stabilizes two-dimensional disturbances, but destabilizes three-dimensional disturbances. When the flow is weak, the morphological instability is incommensurate with the flow wavelength, but as the flow gets stronger, the instability becomes quantized and forced to fit into the flow box. At large flow strength the instability is localized, confined in narrow envelopes. In this case the solutions are discrete eigenstates in an unbounded space. Their stability boundaries and asymptotics are obtained by a WKB analysis. The weakly nonlinear interaction is delivered through the Lyapunov–Schmidt method.

scholarly journals Phase-field simulation of competitive growth of grains in a binary alloy during directional solidification

China Foundry ◽  
2018 ◽  
Vol 15 (5) ◽  
pp. 333-342 ◽  
Author(s):  
Li Feng ◽  
Ya-long Gao ◽  
Ni-ni Lu ◽  
Chang-sheng Zhu ◽  
Guo-sheng An ◽  
...  
Keyword(s):  
Directional Solidification ◽  
Binary Alloy ◽  
Phase Field ◽  
Competitive Growth ◽  
Phase Field Simulation ◽  
Field Simulation
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