scholarly journals Optimizing the Conditions of Metal Solidification with Vibration

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 366 ◽  
Author(s):  
Olga Kudryashova ◽  
Marina Khmeleva ◽  
Pavel Danilov ◽  
Vladislav Dammer ◽  
Alexander Vorozhtsov ◽  
...  
Keyword(s):  
Stefan Problem ◽  
Vibration Frequency ◽  
Solidification Process ◽  
Optimal Conditions ◽  
Efficiency Criterion ◽  
Metal Solidification ◽  
Vibration Treatment ◽  
Practical Challenge ◽  
Metal Processing ◽  
Liquid Metal Processing

Vibration treatment of solidifying metals results in improvement in the ingot structure. There is a need to study this process not only because of the practical potential of vibration treatment but also due to the lack of understanding the process. An important practical challenge is to find optimal conditions for liquid metal processing. In this paper, the authors consider a solidification process in the particular case of a cylindrical chill mold with vibration as a solution of the Stefan problem. An integral value of mechanical stresses in the melt during solidification is considered as an efficiency criterion of vibration treatment. A dependence of this value on the vibration frequency and amplitude is obtained through solving the Stefan problem numerically. The solution allows one to find the optimal vibration frequency and amplitude. We verified the numerical solution with experimental data obtained upon vibration treatment of aluminum melt under different conditions. The experimentally found optimal conditions for metal processing were similar to those proposed in theory, i.e., a vibration frequency of about 60 Hz and an amplitude of about 0.5 mm.

scholarly journals Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Ying Qin ◽  
Yue-Xing Duan ◽  
Mao-Ren Yin
Keyword(s):  
Stefan Problem ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Solidification Process ◽  
Analytic Solutions ◽  
Unknown Boundary ◽  
Two Phase ◽  
Metal Solidification ◽  
Adomian Decomposition

An Adomian decomposition method (ADM) is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

Extended Stefan problem for the solidification of binary alloys in a sphere

2020 ◽  
pp. 1-38
Author(s):  
FERRAN BROSA PLANELLA ◽  
COLIN P. PLEASE ◽  
ROBERT A. VAN GORDER
Keyword(s):  
Boundary Layer ◽  
Stefan Problem ◽  
Layer Structure ◽  
Binary Alloys ◽  
Lewis Number ◽  
Solidification Process ◽  
Constitutional Supercooling ◽  
Asymptotic Solutions ◽  
Spherical Domain ◽  
Boundary Layer Structure

We study the extended Stefan problem which includes constitutional supercooling for the solidification of a binary alloy in a finite spherical domain. We perform an asymptotic analysis in the limits of large Lewis number and small Stefan number which allows us to identify a number of spatio-temporal regimes signifying distinct behaviours in the solidification process, resulting in an intricate boundary layer structure. Our results generalise those present in the literature by considering all time regimes for the Stefan problem while also accounting for impurities and constitutional supercooling. These results also generalise recent work on the extended Stefan problem for finite planar domains to spherical domains, and we shall highlight key differences in the asymptotic solutions and the underlying boundary layer structure which result from this change in geometry. We compare our asymptotic solutions with both numerical simulations and real experimental data arising from the casting of molten metallurgical grade silicon through the water granulation process, with our analysis highlighting the role played by supercooling in the solidification of binary alloys appearing in such applications.

scholarly journals Ultrasonic liquid metal processing: The essential role of cavitation bubbles in controlling acoustic streaming

2019 ◽  
Vol 55 ◽  
pp. 243-255 ◽  
Author(s):  
G.S. Bruno Lebon ◽  
Iakovos Tzanakis ◽  
Koulis Pericleous ◽  
Dmitry Eskin ◽  
Patrick S. Grant
Keyword(s):  
Liquid Metal ◽  
Essential Role ◽  
Acoustic Streaming ◽  
Cavitation Bubbles ◽  
Metal Processing ◽  
Liquid Metal Processing

Numerical Modeling of Inclusion Behavior in Liquid Metal Processing

JOM ◽  
2013 ◽  
Vol 65 (9) ◽  
pp. 1164-1172 ◽  
Author(s):  
Jean-Pierre Bellot ◽  
Vincent Descotes ◽  
Alain Jardy
Keyword(s):  
Numerical Modeling ◽  
Liquid Metal ◽  
Metal Processing ◽  
Liquid Metal Processing

Paths of progress in liquid metal processing

JOM ◽  
1995 ◽  
Vol 47 (4) ◽  
pp. 67-72 ◽  
Author(s):  
A. McLean ◽  
H. Soda ◽  
I. D. Sommerville
Keyword(s):  
Liquid Metal ◽  
Metal Processing ◽  
Liquid Metal Processing

scholarly journals Evaluation of Shearing Time Sufficient for Effective Liquid Metal Processing

JOM ◽  
2017 ◽  
Vol 69 (4) ◽  
pp. 720-724 ◽  
Author(s):  
Agnieszka Dybalska ◽  
Dmitry Eskin ◽  
Jayesh B. Patel
Keyword(s):  
Liquid Metal ◽  
Metal Processing ◽  
Liquid Metal Processing

A New Approach to the Numerical Modeling of Pure Metal Solidification

2019 ◽  
Vol 22 ◽  
pp. 1-8
Author(s):  
Mariusz Ciesielski ◽  
Bohdan Mochnacki
Keyword(s):  
Source Function ◽  
Control Volume ◽  
Type Equation ◽  
Additional Term ◽  
Solidification Process ◽  
Pure Metal ◽  
Metal Solidification ◽  
New Approach ◽  
Fourier Type ◽  
Volume Method

Solidification and cooling processes proceeding in the metal domain can be described in different ways. One of them consists in the application of the Fourier-type equation in which the additional term (source function) controlling the solidification process is introduced. In this paper this type of energy equation is used, but for the phase change modeling the equation discussed is in some way transformed. Such a modification is possible if one considers the pure metal for which the solidification point is a constant value. The numerical model used at the stage of computations is based on the Control Volume Method. In the final part of the paper, examples of computations are shown.

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