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X. Bian - One of the best experts on this subject based on the ideXlab platform.
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undercooling and contact resistance in stagnation flow Solidification on a semi infinite substrate
International Journal of Heat and Mass Transfer, 1998Co-Authors: R H Rangel, X. BianAbstract:Abstract The inviscid stagnation-flow Solidification Problem in studied numerically including the effect of contact resistance and undercooling during Solidification. The effect of contact resistance at the initial liquid-solid contact plane is demonstrated by comparing the Solidification behavior for cases with different contact heat transfer coefficient. The effect of undercooling is examined by comparing model predictions including this effect with those obtained when equilibrium Solidification with interface temperature at the thermodynamic equilibrium temperature is used. The study shows that undercooling delays the start of Solidification but has a negligible effect on the long time behavior of the process. A sufficiently large contact resistance may prevent Solidification when undercooling is included in the model.
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The inviscid stagnation-flow Solidification Problem
International Journal of Heat and Mass Transfer, 1996Co-Authors: Roger H. Rangel, X. BianAbstract:The stagnation-flow Stefan Solidification Problem is defined and investigated. By applying the method of instantaneous similarity, the temperature field, the solid-liquid interface location and its growth rate, valid for the initial stages of Solidification, are obtained. Furthermore, with the use of the quasi-steady approximation, a solution of the Problem valid for the final stages of Solidification is obtained. The analysis reveals a fundamental difference between the stagnation-flow Solidification behavior and that in the classical Stefan Solidification Problem. Both methods of solution are used to show that the Solidification front grows asymptotically to a finite maximum value as time goes to infinity. For large values of time, both methods yield the same temperature distribution and the same value of the solid phase thickness, which are independent of the Stefan number.
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Analytical and numerical studies of the stagnation-flow Solidification Problem
1995Co-Authors: X. Bian, Roger H. RangelAbstract:The inviscid stagnation-flow Solidification Problem is defined and investigated by means of two analytical (quasi-steady and instantaneous-similarity) methods as well as the finite-difference method. The temperature distribution, solid-liquid interface location as well as its growth rate are obtained, and comparisons between the analytical and finite-difference methods are made. The finite-difference solution is started at a small time using the instantaneous-similarity solution as the initial field. The numerical solution confirms the existence of an asymptotic limit of the Solidification front predicted by both analytical methods.
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Numerical solution of the inviscid stagnation-flow Solidification Problem
Numerical Heat Transfer Part A: Applications, 1995Co-Authors: Roger H. Rangel, X. BianAbstract:The inviscid stagnation-flow Solidification Problem is investigated by applying the finite difference method after a coordinate transformation to a fixed domain. Numerical solutions of the temperature distribution and the solid-liquid interface location as well as its growth rate are obtained, and comparisons with the instantaneous-similarity solution and the quasi-steady solution are made. Since the transformed system of equations for this Solidification Problem has a singularity at t = 0, the finite difference solution is started at a small time using the instantaneous-similarity solution as the initial field. The numerical solution confirms the existence of an asymptotic limit of the Solidification front as previously demonstrated by means of both a quasi-steady and an instantaneous-similarity solution.
A. Hirata - One of the best experts on this subject based on the ideXlab platform.
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A numerical method for solving the two‐dimensional unsteady Solidification Problem with the motion of melt by using the boundary‐fitted co‐ordinate system
International Journal for Numerical Methods in Engineering, 1993Co-Authors: M. Saitou, A. HirataAbstract:A numerical method for solving the two-dimensional unsteady Solidification Problem with the motion of melt is proposed. The boundary-fitted co-ordinate system is applied to a treatment for the moving solid-liquid interface in cylindrical co-ordinates with a symmetry axis. An alternating-direction-implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.
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a numerical method for solving the two dimensional unsteady Solidification Problem with the motion of melt by using the boundary fitted co ordinate system
International Journal for Numerical Methods in Engineering, 1993Co-Authors: M. Saitou, A. HirataAbstract:A numerical method for solving the two-dimensional unsteady Solidification Problem with the motion of melt is proposed. The boundary-fitted co-ordinate system is applied to a treatment for the moving solid-liquid interface in cylindrical co-ordinates with a symmetry axis. An alternating-direction-implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.
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NUMERICAL SOLUTION OF THE UNSTEADY Solidification Problem WITH A SOLUTE ELEMENT BY USING THE BOUNDARY-FITTED COORDINATE SYSTEM
Numerical Heat Transfer Part B: Fundamentals, 1992Co-Authors: M. Saitou, A. HirataAbstract:A numerical method suitable for solving the unsteady Solidification Problem with a solute element is proposed. The schemes are based on a finite-difference solution of the equations of the transient heat and mass transfer on a boundary-fitted coordinate system, which is always adjusted to the current solid-liquid interface. The temperature and concentration on the moving solid-liquid interface are obtained from the conditions of the heat and solute balance on it. Several examples are displayed. The numerical results of the solid-liquid interface instability are in good agreement with the prediction of Mullins and Sekerka's theory.
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Two-dimensional unsteady Solidification Problem calculated by using the boundary-fitted coordinate system
Journal of Computational Physics, 1992Co-Authors: M. Saitou, A. HirataAbstract:Abstract Using the boundary-fitted coordinate system, we calculate the unsteady Solidification Problem. The model for calculation is constructed of cylindrical coordinates with a symmetrical axis. The Gauss-Seidel scheme with second-order accuracy of time and space is used as a solution method for the governing equations and the boundary-fitted coordinate system enables us to calculate the moving interface easily. The numerical results are compared with the analysis of a one-dimensional unsteady Solidification Problem and are in good agreement with it. From the calculations, we find a simple form of the crystal growth rate.
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Numerical calculation of two-dimensional unsteady Solidification Problem
Journal of Crystal Growth, 1991Co-Authors: M. Saitou, A. HirataAbstract:Abstract We calculate the variation of the solid-liquid interface in time to simulate crystal growth by the vertical Bridgman technique. The boundary-fitted coordinate system as a calculation method is used to treat the moving interface easily. It is found that the crystal growth rate is described by the moving velocity of the temperature profile and the delay time. After the delay time, the solid-liquid interface shape becomes independent of time. We find the relationships between the delay time and the growth conditions through the calculations. The results of our calculation are in good agreement with the experiments of Bridgman crystal growth.
M. Saitou - One of the best experts on this subject based on the ideXlab platform.
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A numerical method for solving the two‐dimensional unsteady Solidification Problem with the motion of melt by using the boundary‐fitted co‐ordinate system
International Journal for Numerical Methods in Engineering, 1993Co-Authors: M. Saitou, A. HirataAbstract:A numerical method for solving the two-dimensional unsteady Solidification Problem with the motion of melt is proposed. The boundary-fitted co-ordinate system is applied to a treatment for the moving solid-liquid interface in cylindrical co-ordinates with a symmetry axis. An alternating-direction-implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.
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a numerical method for solving the two dimensional unsteady Solidification Problem with the motion of melt by using the boundary fitted co ordinate system
International Journal for Numerical Methods in Engineering, 1993Co-Authors: M. Saitou, A. HirataAbstract:A numerical method for solving the two-dimensional unsteady Solidification Problem with the motion of melt is proposed. The boundary-fitted co-ordinate system is applied to a treatment for the moving solid-liquid interface in cylindrical co-ordinates with a symmetry axis. An alternating-direction-implicit (ADI) method is used to solve the transformed equations of motion and energy, which are expressed in terms of the vorticity and stream function. Several examples are displayed.
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NUMERICAL SOLUTION OF THE UNSTEADY Solidification Problem WITH A SOLUTE ELEMENT BY USING THE BOUNDARY-FITTED COORDINATE SYSTEM
Numerical Heat Transfer Part B: Fundamentals, 1992Co-Authors: M. Saitou, A. HirataAbstract:A numerical method suitable for solving the unsteady Solidification Problem with a solute element is proposed. The schemes are based on a finite-difference solution of the equations of the transient heat and mass transfer on a boundary-fitted coordinate system, which is always adjusted to the current solid-liquid interface. The temperature and concentration on the moving solid-liquid interface are obtained from the conditions of the heat and solute balance on it. Several examples are displayed. The numerical results of the solid-liquid interface instability are in good agreement with the prediction of Mullins and Sekerka's theory.
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Two-dimensional unsteady Solidification Problem calculated by using the boundary-fitted coordinate system
Journal of Computational Physics, 1992Co-Authors: M. Saitou, A. HirataAbstract:Abstract Using the boundary-fitted coordinate system, we calculate the unsteady Solidification Problem. The model for calculation is constructed of cylindrical coordinates with a symmetrical axis. The Gauss-Seidel scheme with second-order accuracy of time and space is used as a solution method for the governing equations and the boundary-fitted coordinate system enables us to calculate the moving interface easily. The numerical results are compared with the analysis of a one-dimensional unsteady Solidification Problem and are in good agreement with it. From the calculations, we find a simple form of the crystal growth rate.
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A numerical solution of the steady Solidification Problem in two dimensions by boundary-fitted coordinate systems
Journal of Computational Physics, 1991Co-Authors: M. Saitou, Eizaburo Kanda, Mitsuo KawashimaAbstract:Abstract A simple numerical scheme is proposed to solve the Problem of determining the interface shape under the thermal equilibrium condition. The procedure is based on a finite difference method using boundary-fitted coordinate systems. Several examples are given. This simple numerical solution method can be easily applied to any arbitrary shape and the unsteady Solidification Problem.
R H Rangel - One of the best experts on this subject based on the ideXlab platform.
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undercooling and contact resistance in stagnation flow Solidification on a semi infinite substrate
International Journal of Heat and Mass Transfer, 1998Co-Authors: R H Rangel, X. BianAbstract:Abstract The inviscid stagnation-flow Solidification Problem in studied numerically including the effect of contact resistance and undercooling during Solidification. The effect of contact resistance at the initial liquid-solid contact plane is demonstrated by comparing the Solidification behavior for cases with different contact heat transfer coefficient. The effect of undercooling is examined by comparing model predictions including this effect with those obtained when equilibrium Solidification with interface temperature at the thermodynamic equilibrium temperature is used. The study shows that undercooling delays the start of Solidification but has a negligible effect on the long time behavior of the process. A sufficiently large contact resistance may prevent Solidification when undercooling is included in the model.
Nicholas Zabaras - One of the best experts on this subject based on the ideXlab platform.
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numerical study of convection in the directional Solidification of a binary alloy driven by the combined action of buoyancy surface tension and electromagnetic forces
Journal of Computational Physics, 2001Co-Authors: Rajiv Sampath, Nicholas ZabarasAbstract:Abstract Directional Solidification of a dilute electrically conducting binary alloy driven by the combined action of buoyancy, surface-tension, and electromagnetic forces is considered. A numerical methodology using a moving finite element technique is proposed for the simulation of the above phase change process. The melt is modeled as a Boussinesq fluid and the transient Navier–Stokes equations are solved simultaneously with the transient heat and solute transport equations. The location of the advancing solid–liquid interface is numerically determined using an energy preserving weak form of the Stefan condition. The standard SUPG/PSPG method for the simulation of incompressible fluid flow is here extended to flows driven by the combination of buoyancy, surface tension, and electromagnetic forces. A reference Problem of directional Solidification of a dilute germanium alloy in a horizontal open-boat configuration is considered. The relative influence of thermocapillary convection and buoyancy-driven convection on the Solidification process is investigated by varying the Bond number. Thermocapillary convection is shown to have a significant influence on various Solidification parameters, such as the shape of the solid–liquid interface and the solute segregation, especially under low gravity conditions. The influence of an external magnetic field on the reference Solidification Problem is investigated both in a normal and a reduced gravity environment. It is demonstrated that the application of an appropriate strong magnetic field significantly damps the melt flow and improves the solute segregation pattern. The relative influence of an external magnetic field on the Solidification process is also studied by independently varying the orientation and magnitude of the applied magnetic field.
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On the solution of an ill‐posed design Solidification Problem using minimization techniques in finite‐ and infinite‐dimensional function spaces
International Journal for Numerical Methods in Engineering, 1993Co-Authors: Nicholas Zabaras, Shinill KangAbstract:This paper provides a comparative study of two alternative methodologies for the solution of an inverse design Solidification Problem. It is the one-dimensional Solidification Problem of calculating the boundary heat flux history that achieves a desired freezing front velocity and desired heat fluxes at the freezing front. The front velocity h(t) and flux history qmS(t) on the solid side of the front control the obtained cast structure. As such, the potential applications of the proposed methods to the control of casting processes are enormous. The first technique utilizes a finite-dimensional approximation of the unknown boundary heat flux function q0(t). The second technique uses the adjoint method to calculate in L2 the derivative of the cost functional, ‖Tm – T(h(t), t;q0)‖, that expresses the square error between the calculated T(h(t), t; q0) and the given freezing front temperature Tm. Both steepest descent (SDM) and conjugate gradient methods (CGM) are examined. A front tracking FEM technique is used for the discretization of the state space. A detailed numerical analysis of the space and time discretization of the ‘parameter’ and state spaces, of the effect of the end condition of the adjoint Problem and of other parameters in the solution are examined.
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on the solution of an ill posed design Solidification Problem using minimization techniques in finite and infinite dimensional function spaces
International Journal for Numerical Methods in Engineering, 1993Co-Authors: Nicholas Zabaras, Shinill KangAbstract:This paper provides a comparative study of two alternative methodologies for the solution of an inverse design Solidification Problem. It is the one-dimensional Solidification Problem of calculating the boundary heat flux history that achieves a desired freezing front velocity and desired heat fluxes at the freezing front. The front velocity h(t) and flux history qmS(t) on the solid side of the front control the obtained cast structure. As such, the potential applications of the proposed methods to the control of casting processes are enormous. The first technique utilizes a finite-dimensional approximation of the unknown boundary heat flux function q0(t). The second technique uses the adjoint method to calculate in L2 the derivative of the cost functional, ‖Tm – T(h(t), t;q0)‖, that expresses the square error between the calculated T(h(t), t; q0) and the given freezing front temperature Tm. Both steepest descent (SDM) and conjugate gradient methods (CGM) are examined. A front tracking FEM technique is used for the discretization of the state space. A detailed numerical analysis of the space and time discretization of the ‘parameter’ and state spaces, of the effect of the end condition of the adjoint Problem and of other parameters in the solution are examined.