scholarly journals МОДЕЛЮВАННЯ ЕНЕРГОПЕРЕНОСУ В ФАЗОПЕРЕХІДНОМУ ТЕПЛОАКУМУЛЯТОРІ СОНЯЧНОЇ ТЕРМОДИНАМІЧНОЇ УСТАНОВКИ

2020 ◽  
Vol 2 (32) ◽  
pp. 5-14
Author(s):  
I. V. Harkavskyi, ◽  
L. I. Knysh
Keyword(s):  
Mushy Layer

Проведено числове дослідження процесів фазового переходу «тверде тіло – рідина» в тепловому акумуляторі сонячної термодинамічної установки. В основі математичної моделі та числового алгоритму покладено метод “Mushy Layer”, який відображає фізичну суть явища. Комп’ютерне моделювання задачі Стефана дозволило виявити особливості процесу фазового переходу, визначити розподіл температур в рідкій та твердий фазі, товщину твердої та рідкої фаз теплоакумулюючого матеріалу, швидкість руху границі розподілу фаз.

Unidirectional solidification with a mushy layer. The influence of weak convection

2006 ◽  
Vol 54 (9) ◽  
pp. 2401-2406 ◽  
Author(s):  
D.L. Aseev ◽  
D.V. Alexandrov
Keyword(s):  
Unidirectional Solidification ◽  
Mushy Layer

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.

Finite bandwidth, nonlinear convective flow in a mushy layer

2017 ◽  
Vol 49 (2) ◽  
pp. 025513
Author(s):  
D N Riahi
Keyword(s):  
Convective Flow ◽  
Mushy Layer ◽  
Finite Bandwidth

Mathematical modeling of a mushy layer at the inner core boundary of the Earth. Part 2. Theoretical description

2015 ◽  
Author(s):  
D. V. Alexandrov ◽  
A. P. Malygin ◽  
I. V. Alexandrova
Keyword(s):  
Mathematical Modeling ◽  
Inner Core ◽  
Theoretical Description ◽  
Mushy Layer ◽  
The Earth ◽  
Core Boundary

On weakly nonlinear evolution of convective flow in a passive mushy layer

2010 ◽  
Vol 11 (5) ◽  
pp. 4010-4020 ◽  
Author(s):  
Dambaru Bhatta ◽  
Mallikarjunaiah S. Muddamallappa ◽  
Daniel N. Riahi
Keyword(s):  
Convective Flow ◽  
Nonlinear Evolution ◽  
Mushy Layer ◽  
Weakly Nonlinear

On nonlinear evolution of convective flow in an active mushy layer

2011 ◽  
Vol 74 (1) ◽  
pp. 73-89 ◽  
Author(s):  
Dambaru Bhatta ◽  
Daniel N. Riahi ◽  
M. S. Muddamallappa
Keyword(s):  
Convective Flow ◽  
Nonlinear Evolution ◽  
Mushy Layer

A new oscillatory instability in a mushy layer during the solidification of binary alloys

1996 ◽  
Vol 307 ◽  
pp. 245-267 ◽  
Author(s):  
D. M. Anderson ◽  
M. Grae Worster
Keyword(s):  
Classical Case ◽  
Oscillatory Instability ◽  
Mushy Layer ◽  
Quiescent State ◽  
Specific Interest ◽  
Small Deviations ◽  
Stefan Number ◽  
Field Temperature ◽  
Diffusive Effects ◽  
Double Diffusive

We consider the solidification of a binary alloy in a mushy layer and analyse the linear stability of a quiescent state with specific interest in identifying an oscillatory convective instability. We employ a near-eutectic approximation and consider the limit of large far-field temperature. These asymptotic limits allow us to examine the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of uniform permeability. We consider also the limit of large Stefan number, which incorporates a key balance necessary for the existence of the oscillatory instability. The model we consider here contains no double-diffusive effects and no region in which a statically stable density gradient exists. The mechanism underlying the oscillatory instability we discover is instead associated with a complex interaction between heat transfer, convection and solidification.

Experimental study of directional solidification of aqueous ammonium chloride solution

1991 ◽  
Vol 227 ◽  
pp. 567-586 ◽  
Author(s):  
C. F. Chen ◽  
Falin Chen
Keyword(s):  
Directional Solidification ◽  
Liquidus Temperature ◽  
Chloride Solution ◽  
Mean Value ◽  
Mushy Layer ◽  
Bottom Temperature ◽  
Casting System ◽  
All Solutions ◽  
The Mean ◽  
Temperature Surface

Directional solidification experiments have been carried out using the analogue casting system of NH4Cl-H2O solution by cooling it from below with a constant-temperature surface ranging from - 31.5°C to + 11.9 °C. The NH4Cl concentration was 26% in all solutions, with a liquidus temperature of 15 °C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as + 11.0 °C. However, when the bottom temperature was raised to + 11.9 °C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250.

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