Rayleigh-Benard Convection During Directional Solidification of a Binary Solution Cooled From the Top

2002 ◽  
Author(s):  
P. Kumar ◽  
S. Chakraborty ◽  
K. Srinivasan ◽  
P. Dutta
Keyword(s):  
Directional Solidification ◽  
Ammonium Chloride ◽  
Binary Solution ◽  
Convective Transport ◽  
Mushy Region ◽  
Two Phase ◽  
Thermal Buoyancy ◽  
Neutrally Buoyant ◽  
Rayleigh Benard ◽  
Double Diffusive

In this paper, we investigate the effects of laminar double-diffusive natural convection on directional solidification of binary fluids when cooled and solidified from the top. The study is performed using aqueous ammonium chloride solution as the model fluid. The experiments are performed with an initial concentration of ammonium chloride is less than the eutectic composition, leading to an aiding double-diffusive convection. In this case, solidification leads to the formation of a diffused matrix of dendritic crystals (mushy region) separating the pure solid and liquid regions. Below the two-phase mushy region, Rayleigh-Benard type of cellular convective motions are observed. The cellular motions, which are caused by thermal buoyancy, die once the thickness of the liquid layer falls below a critical value. The features of convective transport are visualised using a sheet of laser light scattered through neutrally buoyant glass particles seeded in the solution. Numerical simulations are also performed, and the agreement with experimental results is found to be good.

Flow and Morphological Conditions Associated With Unidirectional Solidification of Aqueous Ammonium Chloride

1993 ◽  
Vol 115 (4) ◽  
pp. 1036-1043 ◽  
Author(s):  
C. S. Magirl ◽  
F. P. Incropera
Keyword(s):  
Ammonium Chloride ◽  
Unidirectional Solidification ◽  
Mushy Region ◽  
Bottom Surface ◽  
Double Diffusive Convection ◽  
Two Phase ◽  
Cold Surface ◽  
Diffusive Convection ◽  
Injection Techniques ◽  
Double Diffusive

Using a 27 percent aqueous ammonium chloride solution as a transparent analog, shadowgraph and dye injection techniques have been employed to observe flow and morphological conditions associated with unidirectional solidification (UDS) from below. Dendritic crystals, which initially form at the cold surface, reject lighter, solute deficient fluid, and the attendant instability is manifested by finger-type double-diffusive convection phenomena. As a two-phase (solid/liquid), or mushy, region grows from the bottom surface, vertical channels develop in the mushy region, and solutal plumes that emanate from the channels are characterized primarily by an ascending, oscillatory motion and secondarily by wisps of fluid, which detach and descend from bends in the plumes. In time, double-diffusive convection layers also form in the melt. From a numerical simulation of the process, it is concluded that the channels originate from perturbations at the liquid interface, which cause localized remelting and create conditions conducive to development of the channels.

Study of Freckles Formation During Directional Solidification Under the Influence of Single-Phase and Multiphase Convection

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Prodyut R. Chakraborty ◽  
Pradip Dutta
Keyword(s):  
Numerical Simulation ◽  
Directional Solidification ◽  
Ammonium Chloride ◽  
Solid Fraction ◽  
Single Phase ◽  
Solid Phase ◽  
Single Domain ◽  
Mushy Region ◽  
Convection Model ◽  
Coherency Point

Formation of freckles during directional solidification of hypereutectic aqueous ammonium-chloride in a bottom cooled cavity is studied numerically. The system studied is thermally stable but solutally unstable, which causes plume type convection and formation of channels in the growing solid mush. Solidification of hypereutectic solutions is usually characterized by detached and drifting solid crystals, thus resulting in multiphase convection. The numerical simulation is performed using a fixed grid single domain approach with single-phase and multiphase convection phenomena. For the multiphase convection modeling in the solidifying system under consideration, the mushy region is assumed to consist of an immobile coherent zone containing packed equiaxed crystals and a mobile noncoherent zone where the solid crystals are able to move. The two zones are demarcated by a critical solid fraction criterion, referred to as the coherency point. The overall effects of drifting solid phase on the freckles formation are compared with the results from conventional single-phase convection model.

scholarly journals Unsteady Finite Amplitude Convection of Water–Copper Nanoliquid in High-Porosity Enclosures

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
P. G. Siddheshwar ◽  
K. M. Lakshmi
Keyword(s):  
Porous Medium ◽  
Heat Transport ◽  
Heat Storage ◽  
Finite Amplitude ◽  
High Porosity ◽  
Two Phase ◽  
Onset Of Convection ◽  
Maximum Heat ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Unicellular Rayleigh–Bénard convection of water–copper nanoliquid confined in a high-porosity enclosure is studied analytically. The modified-Buongiorno–Brinkman two-phase model is used for nanoliquid description to include the effects of Brownian motion, thermophoresis, porous medium friction, and thermophysical properties. Free–free and rigid–rigid boundaries are considered for investigation of onset of convection and heat transport. Boundary effects on onset of convection are shown to be classical in nature. Stability boundaries in the R1*–R2 plane are drawn to specify the regions in which various instabilities appear. Specifically, subcritical instabilities' region of appearance is highlighted. Square, shallow, and tall porous enclosures are considered for study, and it is found that the maximum heat transport occurs in the case of a tall enclosure and minimum in the case of a shallow enclosure. The analysis also reveals that the addition of a dilute concentration of nanoparticles in a liquid-saturated porous enclosure advances onset and thereby enhances the heat transport irrespective of the type of boundaries. The presence of porous medium serves the purpose of heat storage in the system because of its low thermal conductivity.

Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation

2011 ◽  
Vol 172-174 ◽  
pp. 608-617 ◽  
Author(s):  
William A. Soffa ◽  
David E. Laughlin ◽  
Nitin Singh
Keyword(s):  
Nearest Neighbor ◽  
Binary Solution ◽  
Mean Field ◽  
Lattice Relaxation ◽  
Two Phase ◽  
First Order ◽  
Tetragonal Lattice ◽  
Wide Range ◽  
Third Law Of Thermodynamics ◽  
The Mean

The tetragonal lattice relaxation has been included in the thermodynamics of the fcc→L10ordering to produce a first-order character of the transition within the mean field description of the binary solution energetics. In view of growing interest in such systems e.g. Fe-Pd and Co-Pt alloys, which display a wide range of applications relevant to current and futuristic technologies, the fcc→L10two-phase field is re-examined utilizing a generalized Bragg-Williams approach including first and second nearest neighbor interactions. The thermodynamic behavior is examined in the limit of T→0K and discussed in terms of the implications of the Third Law of Thermodynamics.

scholarly journals Directional Solidification of Sn-Cu6Sn5 In Situ Composites

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Osvaldo Fornaro
Keyword(s):  
Directional Solidification ◽  
Eutectic Reaction ◽  
Secondary Phase ◽  
Phase Region ◽  
Primary Phase ◽  
Point Of View ◽  
System Stability ◽  
Two Phase ◽  
Directional Growth ◽  
Free Solder

The Sn-Cu system presents an important interest from academic and technological point of view because it is part of the family of alloys proposed as lead-free solder alloys for electronic components and also due to the mechanisms involved during the growth of the different phases. Sn-Cu system has two intermetallic phases, i.e., ε-Cu3Sn and η-Cu6Sn5, and η can be used as the negative (anode) electrode in Li-ion batteries, alone or as part of (Co,Ni)xCu6−xSn5-type composites. Obtaining this η phase from liquid with the appropriate chemical composition is a very difficult task because it has a formation temperature lower than liquidus for such a composition. In this way, the η phase appears as a consequence of a solid-solid transformation from the ε phase However, it is possible to find the η phase as the primary or secondary phase after a eutectic reaction for lower concentrations of Cu. On the other side, the Cu6Sn5 phase shows a hexagonal to monoclinic solid-solid transformation around 187°C, which could affect the mechanical system stability when it is used as solder. In this work, directional solidification at different growth velocities of hypereutectic Sn-Cu samples was performed. The resultant microstructure varies with the growth velocity, but it is formed for a fibber-like primary phase Cu6Sn5 which is projected towards the liquid phase. Behind this region, these fibbers are rounded by a two-phase Sn-Cu6Sn5 structure. In this way, three zones could to be defined in the sample during the directional growth: (i) an entirely solid two-phase region, formed by η rounded by β(Sn) + η eutectic-like structure, (ii) a two-phase solid (η) + liquid, and (iii) the remnant liquid in front of the interface.

Randomly forced Rayleigh-Bénard convection

1980 ◽  
Vol 98 (2) ◽  
pp. 329-348 ◽  
Author(s):  
Bharat Jhaveri ◽  
G. M. Homsy
Keyword(s):  
Convective Transport ◽  
Time Intervals ◽  
Onset Of Convection ◽  
Nonlinear Convection ◽  
Bénard Convection ◽  
Benard Convection ◽  
Random Fluctuations ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We consider the onset of Rayleigh–Bénard convection from random fluctuations arising within a fluid. In the specific case in which the fluctuations are thermodynamically determined, we reduce the problem to a random initial value problem for the Fourier modes. For the case of weak nonlinear convection, it is possible to truncate the number of modes and this truncated set is solved both by a Monte Carlo technique and by moment methods for various Rayleigh numbers. We find three stages in the evolution of ordered convection from random fluctuations which correspond to time intervals in which the fluctuations and the nonlinearity have different degrees of importance. It is shown that no simple moment truncation method will succeed and that the time for onset of convection is a mean over a distribution of times for which members of an ensemble exhibit appreciable convective transport.

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