The Mathematical Model Applied to Solidify and Segregation of Ledeburite Tool Steel Ingots

2017 ◽  
Vol 15 (12) ◽  
pp. 28-31
Author(s):  
Vasile Bratu ◽  
Ileana Nicoleta Popescu
Keyword(s):  
Ingot Mold ◽  
Solidification Process ◽  
Height Ratio ◽  
Fluid Equation ◽  
Steel Type ◽  
Solid Diffusion ◽  
Steel Ingots ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
The Mathematical Model

Abstract In order to determine the optimum geometry of the ingot mold format (the format of ingot mold with a diameter per height ratio H / D <3 and the conicity of minimum 7%) was analyzed by mathematical modeling of solidification and segregation of the carbon and sulfur in it.It was considered 205Cr115 steel type (according with , STAS 3611 - Romanian stardandization) and known also as X210Cr12 steel type (according with European standard). It has been considered an element of volume of coordinates x, y, z in the solidifying ingot and have made the following assumptions: (i) the equilibrium distribution ratio K, is applied to the solid-liquid interface; (ii) solid diffusion is negligible during solidification; and (iii) the solid density is constant during solidification. In carrying out the simulation of segregation mechanisms are resolved heat transfer equation, that simulating the solidification process and are are solved the interdendritic fluid equation of motion.

Effect of Twin/Tilt on the Growth of Graphite

1984 ◽  
Vol 34 ◽  
Author(s):  
Zhu Peiyue ◽  
Sha Rozeng ◽  
Li Yanxiang
Keyword(s):  
Solidification Process ◽  
Twin Plane ◽  
Liquid Interface ◽  
Tilt Boundary ◽  
Twin Defects ◽  
Solid Liquid Interface ◽  
Graphite Growth ◽  
Solid Liquid

ABSTRACTThe effect of twin/tilt initiated in the process of graphite growth making the graphite curling and change from flake to vermicular and spheroidal is discussed. With the developing of the solidification process,the modifying elements enrich in the front of solid-liquid interface, the amount of twin defects in the graphite increases,its tilt fashion changes and the graphite formed varies from flake to vermicular and spheroidal. The modifying elements promote the formation of twin/tilt. When the modifying elements are insufficient for spheroidizing,the tilt orientation of twins is changeable,and the graphite formed is twisted. When the modifying elements are sufficient enough, the tilt orientation of twins becomes singular, and the graphite formed tends to be round. According to the energy and kinetics consideration of the formation of twin/tilt boundary, it is predicted that the twin plane would firstly adopt (10Tm), especially the (10T2) plane. This result coincides well with the experimental observations. It is proposed that the formation of SG can be divided into two steps: growth of graphite nucleus into spherulite by twin/tilt mechanism and brancing on it in a spiral mode.

Solidification of a Liquid Metal with Natural Convection in a Thick-Walled Container

1999 ◽  
Vol 15 (2) ◽  
pp. 47-55
Author(s):  
H. C. Tien ◽  
C.C. Wang
Keyword(s):  
Natural Convection ◽  
Weighting Function ◽  
Solidification Rate ◽  
Thermal Contact ◽  
Solidification Process ◽  
External Cooling ◽  
Implicit Solver ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Change Material

ABSTRACTThe solidification of a phase change material (PCM), exemplified by a molten metal, in a thick-walled container is analyzed in this paper. The effects of natural convection and several important controlling parameters are investigated extensively. These parameters include the initial temperature of the PCM, external cooling conditions, thickness and thermal properties of the wall, and the thermal contact resistance at the PCM/wall interface. Two representative configurations are examined in this study. A modified version of the enthalpy formulation in which the sensible heat is separated from the latent heat, is employed to construct the energy equation for the PCM. Vorticity-stream-function approach is adopted for solving the flow field. The governing equations pertinent to the problem are discretized by the weighting function scheme and finally solved by the SIS (Strongly Implicit Solver) algorithm. It is demonstrated that for both configurations natural convection has prominent effect on the temperature distribution of the liquid phase of the PCM; however, the effect of natural convection on the shape of the solid/liquid interface and the overall solid fraction is case dependent. It is also shown that the above-mentioned controlling parameters have a direct impact on the solidification process. Specifically, an increase in the Biot number (from 1 to infinity) and the thermal diffusivity of the mold (from 0.8 to 5) enhances the solidification rate. Reverse effect was found for the other controlling parameters.

Experimental Investigation of Fluid Flow and Phase Moving Interface During the Solidification of Binary Mixture in Trapezoidal Cavity

Volume 3 ◽  
2004 ◽  
Author(s):  
C. Ghenai ◽  
R. K. Duggirala ◽  
C. X. Lin ◽  
M. A. Ebadian
Keyword(s):  
Ammonium Chloride ◽  
Binary Solution ◽  
Solidification Process ◽  
Convection Flow ◽  
Initial Concentration ◽  
Moving Interface ◽  
Image Velocimetry ◽  
Convection Patterns ◽  
Solid Liquid Interface ◽  
Solid Liquid

This experimental study focuses on the solidification of a ammonium chloride-water (NH4Cl-H2O) solution in a trapezoidal cavity with one and two vertical cooling walls. The effect of the initial concentration of ammonium chloride (sub-eutectic: f < 19.8% and eutectic f = 19.8%, where f is the percentage in weight) and boundary temperatures (Tcold = −30°C to −10°C) on the solidification process is examined. Particle Image Velocimetry (PIV) is used in this study to measure the velocity fields in the melt during the solidification process. The temperatures distributions at discrete locations in the solution and the boundary walls were measured by 32 thermocouples. The convection flow patterns; the ice shape and thickness; the velocity of the moving liquid/solid interface; and the temperature distribution were obtained. The convection patterns obtained for different initial concentrations showed significant differences. The results showed that the process of solidification is slower with an increase in the initial concentration levels of the binary solution. The growth rate of the frozen layer, the velocity of the moving solid-liquid interface and the temperature in the melt was significantly reduced when increasing the initial concentration of ammonium chloride.

Numerical Simulation of the Effect of the Size of Nanoparticles on the Solidification Process of Nanoparticle-Enhanced Phase Change Materials

2012 ◽  
Author(s):  
Yousef M. F. El Hasadi ◽  
J. M. Khodadadi
Keyword(s):  
Particle Size ◽  
Phase Change ◽  
Phase Change Materials ◽  
Concentration Field ◽  
Solidification Process ◽  
Liquid Interface ◽  
Constitutional Supercooling ◽  
Fluid Mixture ◽  
Solid Liquid Interface ◽  
Solid Liquid

Nanoparticle-enhanced phase change materials (NEPCM) were proposed recently as alternatives to conventional phase change materials due to their enhanced thermophysical properties. In this study, the effect of the size of the nanoparticles on the morphology of the solid-liquid interface and evolving concentration field, during solidification had been reported. The numerical method that was used is based on the one-fluid-mixture model. The model takes into account the thermal as well as the solutal convection effects. A square cavity model was used in the simulation. The NEPCM that was composed of a suspension of copper nanoparticles in water was solidified from the bottom. The nanoparticles size used were 5 nm and 2 nm. The temperature difference between the hot and cold sides was 5 degrees centigrade and the loading of the nanoparticles that have been used in the simulation was 10% by mass. The results obtained from the model were compared with those existing in the literature, and the comparison was satisfactory. The solid-liquid interface for the case of NEPCM with 5 nm particle size was almost planar throughout the solidification process. However, for the case of the NEPCM with particle size of 2 nm, the solid-liquid interface evolved from a planar stable shape to an unstable dendritic shape, as the solidification process proceeded with time. This was attributed to the constitutional supercooling effect. It has been observed that the constitutional supercooling effect is more pronounced as the particle size decreases. Furthermore, the freezing time increases as the particle size decreases.

On controlled solidification studies of some TiO2 binary alloys

1992 ◽  
Vol 7 (4) ◽  
pp. 980-991 ◽  
Author(s):  
C.T. Yen ◽  
D.O. Nason ◽  
W.A. Tiller
Keyword(s):  
Solubility Limit ◽  
Solid Solubility Limit ◽  
Solid Diffusion ◽  
Melting Technique ◽  
Eutectic Concentration ◽  
Crystal Fibers ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Laser Heated ◽  
Controlled Precipitation

TiO2 single crystal fibers in the 1 mm diameter range were pulled from different alloy melts using the laser heated pedestal melting technique. The alloying elements studied were CaO, MnO, MgO, SiO2, FeO, and Al2O3. Phase diagram solute partition coefficient, k0, maximum solid solubility limit, CS(max), eutectic concentration, CE, and eutectic temperature, TE, were determined for each of these alloys. Solute redistribution effects in the solid, controlled precipitation in the solid, smooth solid-liquid interfaces in the presence of high melt concentrations and substantial crystal broadening by fluid migration up the solid from the melt all indicated the existence of a very strong thermodynamic field and a large solid diffusion coefficient operating in the solid behind the solid/liquid interface.

The Cooling Time of Gas Assisted Injection Molding

2011 ◽  
Vol 221 ◽  
pp. 422-428
Author(s):  
Qiu Xiang Bu ◽  
Xiao Zhang ◽  
Hai Ying Chen ◽  
Qing Zhen Yin
Keyword(s):  
Mathematical Model ◽  
Injection Molding ◽  
Wall Thickness ◽  
Cooling Time ◽  
Cooling Process ◽  
Liquid Phases ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
The Mathematical Model ◽  
Plastic Products

The mathematical model of solid-liquid interface is obtained by making an idealized hypothesis for parameters of the cooling process in gas-assisted injection molding, and simplifying the mathematical model. And then the cooling time of plastic products in the process is obtained by using two ways of solving the solid and liquid phases. And verified by example the conclusions that some plastic products of gas-assisted injection molding, when the materials and workmanship conditions are constant, cooling time of the airway is proportional to the square of the wall thickness is obtained.

scholarly journals Effect of Fe Content on the As-Cast Microstructures of Ti–6Al–4V–xFe Alloys

Metals ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 989
Author(s):  
Ling Ding ◽  
Rui Hu ◽  
Yulei Gu ◽  
Danying Zhou ◽  
Fuwen Chen ◽  
...  
Keyword(s):  
Grain Size ◽  
Solidification Process ◽  
Experimental Methods ◽  
Composition Distribution ◽  
Local Composition ◽  
Levitation Melting ◽  
Fe Content ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Solidification Microstructures

In this work, the evolution of the solidification microstructures of Ti–6Al–4V–xFe (x = 0.1, 0.3, 0.5, 0.7, 0.9) alloys fabricated by levitation melting was studied by combined simulative and experimental methods. The growth of grains as well as the composition distribution mechanisms during the solidification process of the alloy are discussed. The segregation of the Fe element at the grain boundaries promotes the formation of a local composition supercooling zone, thus inhibiting the mobility of the solid–liquid interface and making it easier for the grains to grow into dendrites. With the increase in Fe content, the grain size of the alloy decreased gradually, while the overall decreasing trend was mitigated. The segregation of Fe was more obvious than that of Al and V, and the increase in Fe content had less effect on the segregation of Al and V.

Oscillatory Instabilities in Cellular Solidification

1990 ◽  
Vol 43 (5S) ◽  
pp. S56-S58 ◽  
Author(s):  
K. Brattkus
Keyword(s):  
Directional Solidification ◽  
Absolute Stability ◽  
Symmetric Model ◽  
Solid Diffusion ◽  
Long Wave ◽  
Spatially Periodic ◽  
The Stability ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Oscillatory Instabilities

We adapt the recent derivation of a long-wave evolution equation for a solid-liquid interface undergoing directional solidification near the limit of absolute stability to the case of a symmetric model that includes solid diffusion. The stability of steady and spatially periodic solutions are investigated and it is found that these cellular solutions are subject to an oscillatory instability with twice the wavenumber of the underlying pattern. We discuss this instability in the context of experiments on the directional solidification of nematic liquid crystals.

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