Design and control of interfacial temperature gradients in solidification

Hale, Stephanie; Keyhani, M.; Frankel, J. I.

doi:10.1016/s0017-9310(00)00011-9

Cited by 14 publications

(6 citation statements)

References 15 publications

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“…Nobuaki ITO 1,2) and Koichi ANZAI 2) microstructure arrangement. 10) Meanwhile, Sakaguchi disclosed the method to predict the thickness of the chill layer with simulated CR and surface temperature gradient.…”

Section: Design Methods For Solidification Structures In Micro Continmentioning

confidence: 97%

“…In fact, microstructure prediction has already been used in actual design for less convective castings for well-studied composition, e.g., directional solidification of multi-crystalline highly pure silicon. In some microstructure predictions, local microscopic field properties, such as the solidification rate v m , are used as a controlled parameter that can decide the microstructure 1,2) from the intuitively from the semi-empirical microstructure arrangements of Kurz and Fisher,3) although their concern is mainly placed on the methodology of predicting accurate v m . Thus, little attention has been paid to directly indexing microstructures with specific v m , even in these relatively simple castings.…”

Section: Introductionmentioning

confidence: 99%

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Design Methods for Solidification Structures in Micro Continuous Casting

Ito¹,

Anzai²

2010

ISIJ Int.

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Micro continuous casting, which includes, for example, single-roll casting, twin-roll casting, and EFG, is a comprehensive casting method concept for high-performance material produced with rapid solidification. When a new material functionalized through micro continuous casting is industrially developed, the caster type generally differs between design (experimental) phases because of the discrepancy of the purpose in each design phase. In the present design method, experimental data is arranged as 'solidification structure map' with local field properties, solidification rates, and temperature gradients, as the dominant general parameters is assisted with the casting simulation of temperature and flow field without microstructure prediction. The present method could reduce the design steps necessary for conventional design, in which the fully empirical method has been adopted, because no solidification microstructure model can determine the structure for industrial accuracy for untested material composition or casting conditions.The present design method requires high accuracy for solidification models because the shape of the 'solidification structure map' changes significantly by the model accuracy in a casting simulation.

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Section: Design Methods For Solidification Structures In Micro Continmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Design Methods for Solidification Structures in Micro Continuous Casting

Ito¹,

Anzai²

2010

ISIJ Int.

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“…Therefore, an enthalpy method [23][24][25] with a fixed grid is applied to obtain the numerical solution to Eqs. (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). At the freezing front, the jump in heat flux is proportional to the latent heat, which corresponds to an isothermal change in the enthalpy for water at its freezing point.…”

Section: B Numerical Methods To Solve the Conduction Modelmentioning

confidence: 99%

“…Demirci et al [10] applied a control method over heat fluxes and velocity of a freezing front to achieve specified casting properties and structures in materials processing. Hale et al [11] proposed a general methodology to achieve independent management of the solidifying speed and the liquid-side interfacial temperature gradient. Stelian et al [12] conducted a numerical study of a temperature oscillation effect on the freezing front speed in the vertical Bridgman growth process using the finite element analysis software FIDAP.…”

mentioning

confidence: 99%

Freezing Front Propagation on Microgrooved Substrates

Zhong

Jacobi

Georgiadis

2010

Journal of Thermophysics and Heat Transfer

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An experimental and numerical study of a planar freezing front propagating in a water layer above microgrooved substrates is presented. Classical photolithographic technology is employed to fabricate the microgrooves, and the morphological effect on the front propagation speed is quantified and compared with that predicted by the numerical simulation. The simulation is performed using enthalpy method and the finite element analysis package FIDAP in order to understand the physical mechanisms. The experimental results show that the speed of a freezing front oscillates when the front moves across the adjacent crests and troughs of microgrooves. The propagation speed on crests is about two to eight times that in troughs. The simulation results agree well with experiments and demonstrate that the silicon crests change the heat transfer direction into vertical as the latent heat is released from the freezing front, leading to a fast propagation on crests. The shape of the freezing front, the impact of the sample geometry, and the cooling rate of the system are also reported and discussed. The findings provide insight into how the speed and shape of a freezing front can be manipulated and might find broad application in systems with solidification. Nomenclature A= temperature at the cold end of a unit cell under the initial condition B = temperature at the hot end of a unit cell under the initial condition C p = specific heat d = depth of the trough d s = thickness of the substrate d w = water thickness above the substrate H = enthalpy K = cooling rate derived from the curve fit of the experimental data k = thermal conductivity L = latent heat of water, 333:6 kJ=kg for water n 1 = normal direction of the freezing front (solid-liquid interface) in the water layer n 2 = normal direction of the silicon-water interface T= temperature T f = melting temperature of ice, 0 C (273.2 K) t = time V = volume of water w = width of the microgrooves x = horizontal direction, i.e., the direction of the freezing front propagation z = vertical direction = volumetric ratio of the water above a trough to the water above a crest T=x = temperature gradient in the horizontal direction t = time period calculated from the simulation = time period measured in the experiments = Dirac delta function = density v = speed vñ 1 = freezing front propagation speed, i.e., solidification rate v 0 = speed of the water freezing point (T 0 C) calculated from the simulation = angle of the wedgelike front from the horizontal direction Subscripts c = cold end of the test specimen, or the crest of the microgrooves f = freezing front, i.e., solid-liquid interface h = hot end of the test specimen s = silicon t = trough of the microgrooves w = water, including its liquid phase and solid phase 0 = water freezing point (T 0 C) Superscripts l = liquid phase of water s = solid phase of water (ice)

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“…For example, the processes can be controlled by utilizing measurements, such as thermocoupletemperature measurements, during a process and then adjusting the external boundary conditions at a ow inlet in a real-time mode to give improved and desired results during solidi cation. Furthermore, Hale et al 2 present an inverse methodology that permits independent control of the interfacial temperature gradient during a solidi cation process. These developmentsprovide important progressin the development of advanced materials with improved mechanical properties.…”

mentioning

confidence: 99%

Controlling Phase Interface Motion in Inverse Heat Transfer Problems with Solidification

Naterer

2003

Journal of Thermophysics and Heat Transfer

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In this paper, an inverse numerical model is presented for solidi cation problems. It is used to predict the transient boundary conditions, which produce a prescribed interfacial surface motion and heat transfer. The formulation calculates the required boundary temperature to provide a speci ed velocity of the phase interface during solidliquid phase transition. A control-volume-based nite element method is employed for the numerical solution of the energy conservation equation. The nite element framework provides a novel alternative to other inverse techniques based on structured grids. The effects of Stefan number and interface velocity on the solidi cation processes will be investigated. Numerical examples are presented and discussed for one-dimensional and twodimensionalsolidi cation problems. The accuracy and performance of the formulationare assessed by comparisons with analytical solutions. Based on the model's capability of ef ciently providing stable and accurate results, it is viewed to be a worthy design tool in practical engineering applications such as thermal energy storage and materials processing, such as casting and extrusion processes. Nomenclature c = speci c heat e = internal energy k = thermal conductivity L = latent heat N = shape function R = sensitivity coef cient in temperature calculation S = source term Ste = Stefan number T = temperature t = time V = interface velocity X 0 = reference length x; y = spatial coordinates ® = thermal diffusivity 0 = thermophysical property 1t = time step » ,´= local coordinates ½ = density 8 = general scalar variable Subscripts l = liquid p = nodal point r; 0; w = reference s = solid Superscript m = iterative counter

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Design and control of interfacial temperature gradients in solidification

Cited by 14 publications

References 15 publications

Design Methods for Solidification Structures in Micro Continuous Casting

Design Methods for Solidification Structures in Micro Continuous Casting

Freezing Front Propagation on Microgrooved Substrates

Controlling Phase Interface Motion in Inverse Heat Transfer Problems with Solidification

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