Diffusive and phase change instabilities in a ternary mushy layer

2014 ◽  
Vol 760 ◽  
pp. 634-669 ◽  
Author(s):  
Peter Guba ◽  
Daniel M. Anderson
Keyword(s):  
Phase Change ◽  
Ternary Phase Diagram ◽  
Convective Transport ◽  
Solute Diffusion ◽  
Mushy Layer ◽  
Convective Instabilities ◽  
Stable Conditions ◽  
Thermodynamic Constraint ◽  
Small Growth ◽  
The Stability

AbstractWe analyse the stability of a mushy layer during the directional solidification of a ternary alloy. Our model includes diffusive and convective transport of heat and solutes, coupled by an equilibrium thermodynamic constraint of the ternary phase diagram. The model contains phase change effects due to latent-heat release, solute rejection and background solidification. We identify novel convective instabilities, both direct and oscillatory, which are present under statically stable conditions. We examine these instabilities asymptotically by simplifying to a thin mushy layer with small growth rates. We also discuss numerical results for the full problem, confirming the asymptotic predictions and providing the stability characteristics outside the small-growth-rate approximation. A physical explanation for these instabilities in terms of parcel arguments is proposed, indicating that the instability mechanisms generally involve different rates of solute diffusion, different rates of solute rejection and different background solute distributions induced by the initial alloy composition.

Convective Phenomena in Mushy Layers

2020 ◽  
Vol 52 (1) ◽  
pp. 93-119
Author(s):  
Daniel M. Anderson ◽  
Peter Guba
Keyword(s):  
Materials Science ◽  
Climate Modeling ◽  
Convective Transport ◽  
Transport Processes ◽  
Ternary Alloys ◽  
Annual Review ◽  
Mushy Layer ◽  
Polar Climate ◽  
Mushy Layers ◽  
Convective Instabilities

Since the Annual Review of Fluid Mechanics review of mushy layers by Worster (1997) , there have been significant advances in the understanding of convective processes in mushy layers. These advances have come in the areas of ( a) more detailed analysis, computation, and understanding of convective instabilities and chimney convection in binary alloys; ( b) investigations of diffusive and convective transport processes in ternary alloys; and ( c) applications of mushy layer theory in materials science, sea ice, and polar climate modeling, as well as other geophysical applications such as the convective dynamics of the Earth's core. Our objective for this review is to provide an updated account of the understanding of mushy layer convection and related applications and, in doing so, to provide a new resource to the fluid dynamics research community interested in these complex systems.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

scholarly journals High-Throughput Calculations on the Decomposition Reactions of Off-Stoichiometry GeSbTe Alloys for Embedded Memories

Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2382
Author(s):  
Omar Abou El Kheir ◽  
Marco Bernasconi
Keyword(s):  
Phase Separation ◽  
Phase Change ◽  
High Throughput ◽  
Crystallization Temperature ◽  
Density Functional ◽  
Phase Change Materials ◽  
Ternary Phase Diagram ◽  
Decomposition Reactions ◽  
Embedded Memories ◽  
Tie Line

Chalcogenide GeSbTe (GST) alloys are exploited as phase change materials in a variety of applications ranging from electronic non-volatile memories to neuromorphic and photonic devices. In most applications, the prototypical Ge2Sb2Te5 compound along the GeTe-Sb2Te3 pseudobinary line is used. Ge-rich GST alloys, off the pseudobinary tie-line with a crystallization temperature higher than that of Ge2Sb2Te5, are currently explored for embedded phase-change memories of interest for automotive applications. During crystallization, Ge-rich GST alloys undergo a phase separation into pure Ge and less Ge-rich alloys. The detailed mechanisms underlying this transformation are, however, largely unknown. In this work, we performed high-throughput calculations based on Density Functional Theory (DFT) to uncover the most favorable decomposition pathways of Ge-rich GST alloys. The knowledge of the DFT formation energy of all GST alloys in the central part of the Ge-Sb-Te ternary phase diagram allowed us to identify the cubic crystalline phases that are more likely to form during the crystallization of a generic GST alloy. This scheme is exemplified by drawing a decomposition map for alloys on the Ge-Ge1Sb2Te4 tie-line. A map of decomposition propensity is also constructed, which suggests a possible strategy to minimize phase separation by still keeping a high crystallization temperature.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Numerical Simulation of Coherent Structures in the Turbulent Boundary Layer under Different Stability Conditions

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1068
Author(s):  
Shujin Laima ◽  
Hehe Ren ◽  
Hui Li ◽  
Jinping Ou
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Correlation Coefficient ◽  
Wind Velocity ◽  
Coherent Structures ◽  
Stability Conditions ◽  
Velocity Spectrum ◽  
Turbulent Eddy ◽  
Stable Conditions ◽  
The Stability

Coherent structures in the turbulent boundary layer were investigated under different stability conditions. Qualitative analyses of the flow field, spatial correlation coefficient field and pre-multiplied wind velocity spectrum showed that the dominant turbulent eddy structure changed from small-scale motions to large- and very-large-scale motions and then to thermal plumes as the stability changed from strong stable to neutral and then to strong unstable. A quantitative analysis of the size characteristics of the three-dimensional turbulent eddy structure based on the spatial correlation coefficient field showed that under near-neutral stability, the streamwise, wall-normal and spanwise extents remained constant at approximately 0.3 δ , 0.1 δ and 0.2 δ ( δ , boundary layer height), respectively, while for other conditions, the extent in each direction varied in a log-linear manner with stability; only the spanwise extent under stable conditions was also independent of stability. The peak wavenumber of the pre-multiplied wind velocity spectrum moves towards small values from stable conditions to neutral condition and then to unstable conditions; thus, for the wind velocity spectrum, another form is needed that takes account the effects of the stability condition.

scholarly journals Development of a CALPHAD Thermodynamic Database for Pu-U-Fe-Ga Alloys

2019 ◽  
Vol 9 (23) ◽  
pp. 5040 ◽  
Author(s):  
Emily E. Moore ◽  
Patrice E.A. Turchi ◽  
Alexander Landa ◽  
Per Söderlind ◽  
Benoit Oudot ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Density Functional ◽  
Ternary Phase Diagram ◽  
Thermodynamic Database ◽  
Impurity Effects ◽  
Functional Theory ◽  
Formation Enthalpies ◽  
Temperature Ranges ◽  
The Stability ◽  
First Time

The interaction of actinides and actinide alloys such as the δ-stabilized Pu-Ga alloy with iron is of interest to understand the impurity effects on phase stability. A newly developed and self-consistent CALPHAD thermodynamic database is presented which covers the elements: Pu, U, Fe, Ga across their whole composition and temperature ranges. The phase diagram and thermodynamic properties of plutonium-iron (Pu-Fe) and uranium-iron (U-Fe) systems are successfully reassessed, with emphasis on the actinide rich side. Density functional theory (DFT) calculations are performed to validate the stability of the stoichiometric (Pu,U)6Fe and (Pu,U)Fe2 compounds by computing their formation enthalpies. These data are combined to construct the Pu-U-Fe ternary phase diagram. The thermodynamic assessment of Fe-Ga is presented for the first time and application to the quaternary Pu-U-Fe-Ga system is discussed.

A Study of an Oscillating Corner Meniscus With Phase Change Using Image Analyzing Interferometry

Volume 4 ◽  
2004 ◽  
Author(s):  
Sashidhar S. Panchamgam ◽  
Shripad J. Gokhale ◽  
Joel L. Plawsky ◽  
Sunando DasGupta ◽  
Peter C. Wayner
Keyword(s):  
Fluid Flow ◽  
Phase Change ◽  
Contact Line ◽  
Quartz Substrate ◽  
Thin Liquid Film ◽  
Adsorbed Film ◽  
Line Region ◽  
The Stability ◽  
First Time

The thickness and curvature profiles in the contact line region of a moving evaporating thin liquid film of pentane on a quartz substrate were measured for the thickness region, δ < 2.5 microns. The critical region, δ < 0.1 microns, was emphasized. The profiles were obtained using image analyzing interferometry and an improved data analysis procedure. The precursor adsorbed film, the thickness, the curvature, and interfacial slope (variation of the local “apparent contact angle”) profiles were consistent with previous models based on interfacial concepts. Isothermal equilibrium conditions were used to evaluate the Hamaker constant in-situ and to verify the accuracy of the procedures. The profiles give fundamental insights into the phenomena of phase change, pressure gradient, fluid flow, spreading, and the physics of interfacial phenomena in the contact line region. The experimental results demonstrate explicitly for the first time, with microscopic detail, that the disjoining pressure controls fluid flow within an evaporating completely wetting thin curved film and the stability of the thin film. The change in the thickness of the adsorbed film with time is demonstrated for the first time.

Three-dimensional stability analysis for a salt-finger convecting layer

2018 ◽  
Vol 841 ◽  
pp. 636-653
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Grashof Number ◽  
Significant Difference ◽  
The Stability ◽  
Mode A

A three-dimensional linear stability analysis is carried out for a convecting layer in which both the temperature and solute distributions are linear in the horizontal direction. The three-dimensional results show that, for $Le=3$ and 100, the most unstable mode occurs invariably as the longitudinal mode, a vortex roll with its axis perpendicular to the longitudinal plane, suggesting that the two-dimensional results are sufficient to illustrate the stability characteristics of the convecting layer. Two-dimensional results show that the stability boundaries of the transverse mode (a vortex roll with its axis perpendicular to the transverse plane) and the longitudinal modes are virtually overlapped in the regime dominated by thermal diffusion and the regime dominated by solute diffusion, while these two modes hold a significant difference in the regime the salt-finger instability prevails. More precisely, the instability area in terms of thermal Grashof number $Gr$ and solute Grashof number $Gs$ is larger for the longitudinal mode than the transverse mode, implying that, under any circumstance, the longitudinal mode is always more unstable than the transverse mode.

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