The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Andrew M Mullis - One of the best experts on this subject based on the ideXlab platform.
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three dimensional thermal solute phase field simulation of binary Alloy Solidification
Journal of Computational Physics, 2015Co-Authors: P C Bollada, P K Jimack, Andrew M Mullis, C E Goodyer, Feng Wei YangAbstract:We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three scalar field variables. The mathematical model represents the non-isothermal Solidification of a metal Alloy into a melt substantially cooled below its freezing point at the microscale. Underlying physical molecular forces are captured at this scale by a specification of the energy field. The time rate of change of the temperature, Alloy concentration and an order parameter to govern the state of the material (liquid or solid) are controlled by the diffusion parameters and variational derivatives of the energy functional. The physical problem is important to material scientists for the development of solid metal Alloys and, hitherto, this fully coupled thermal problem has not been simulated in three dimensions, due to its computationally demanding nature. By bringing together state of the art numerical techniques this problem is now shown here to be tractable at appropriate resolution with relatively moderate computational resources.
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an adaptive fully implicit multigrid phase field model for the quantitative simulation of non isothermal binary Alloy Solidification
Acta Materialia, 2008Co-Authors: J Rosam, P K Jimack, Andrew M MullisAbstract:Abstract Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal Solidification of a dilute binary Alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ ∗ , was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant.
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a fully implicit fully adaptive time and space discretisation method for phase field simulation of binary Alloy Solidification
Journal of Computational Physics, 2007Co-Authors: J Rosam, P K Jimack, Andrew M MullisAbstract:A fully implicit numerical method based upon adaptively refined meshes for the simulation of binary Alloy Solidification in 2D is presented. In addition we combine a second-order fully implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method. The superiority of this method, compared to widely used fully explicit methods, with respect to CPU time and accuracy, is shown. Due to the high nonlinearity of the governing equations a robust and fast solver for systems of nonlinear algebraic equations is needed to solve the intermediate approximations per time step. We use a nonlinear multigrid solver which shows almost h-independent convergence behaviour.
Edyta Hetmaniok - One of the best experts on this subject based on the ideXlab platform.
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reconstruction of the boundary condition in the binary Alloy Solidification problem with the macrosegregation and the material shrinkage phenomena taken into account
Heat Transfer Engineering, 2019Co-Authors: Adam Zielonka, Edyta Hetmaniok, Damian SlotaAbstract:AbstractIn this paper we solve the inverse problem of the binary Alloy Solidification including two phenomena: macrosegregation and creation of the air gap between the cast and the mold in result o...
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inverse Alloy Solidification problem including the material shrinkage phenomenon solved by using the bee algorithm
International Communications in Heat and Mass Transfer, 2017Co-Authors: Adam Zielonka, Edyta Hetmaniok, Damian SlotaAbstract:Abstract In the paper we solve the one-phase inverse problem of Alloy solidifying within the casting mould, including the shrinkage of metal which results from the difference between densities of the liquid and solid phases. The process is modeled by means of the Solidification in the temperature interval basing on the heat conduction equation with the source element enclosed, whereas the shrinkage of metal is modeled by the proper application of the mass balance equation. The investigated inverse problem consists in reconstruction of the heat transfer coefficient on the boundary of the casting mould on the basis of measurements of temperature read from the sensor placed in the middle of the mould. Functional expressing the error of approximate solution is minimized with the aid of Artificial Bee Colony Optimization algorithm.
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identification of the heat transfer coefficient in the two dimensional model of binary Alloy Solidification
Heat and Mass Transfer, 2017Co-Authors: Edyta Hetmaniok, Damian Slota, Jordan Hristov, Adam ZielonkaAbstract:The paper presents the procedure for solving the inverse problem for the binary Alloy Solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the Alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the Alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.
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numerical procedure of solving some inverse problem in Solidification of the binary Alloy
Computer Assisted Mechanics and Engineering Sciences, 2017Co-Authors: Edyta Hetmaniok, Damian SlotaAbstract:The paper presents a solution of an inverse problem consisting in determination of boundary conditions in the process of binary Alloy Solidification when temperature measurements in selected points of the cast are known. In the investigated model the distribution of temperature is described using the Stefan model with the liquidus temperature varying in dependance on concentration of the Alloy component. For description of the concentration we apply the model in which the immediate equalization of chemical composition of the Alloy is assumed (lever arm model). Experimental verification of the developed algorithm is also presented.
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solution of the inverse problem in Solidification of binary Alloy by applying the aco algorithm
Inverse Problems in Science and Engineering, 2016Co-Authors: Edyta HetmaniokAbstract:The paper presents a solution of the inverse problem consisting in reconstruction of the heat flux and the distribution of temperature in the process of binary Alloy Solidification when the temperature measurements in the selected points of the Alloy are known. The considered task is mathematically modelled by means of the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependence on the concentration of the Alloy component, whereas for describing the concentration the lever arm model is applied. An important part of the procedure consists in minimization of some functional executed with the aid of ACO algorithm.
C Beckermann - One of the best experts on this subject based on the ideXlab platform.
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general evolution equation for the specific interface area of dendrites during Alloy Solidification
Acta Materialia, 2017Co-Authors: H Neumannheyme, Kerstin Eckert, C BeckermannAbstract:Abstract The specific area of the solid-liquid interface of an assembly of dendrites is an important integral measure of the morphology of the microstructure forming during Alloy Solidification. It represents the inverse of a characteristic length scale and is needed for the prediction of Solidification defects and material properties. In the present study, the evolution of the interfacial area of dendrites is analysed using 3D phase-field simulations. A general evolution equation is developed for the specific interface area as a function of time and solid volume fraction that accounts for the effects of growth, curvature-driven coarsening and interface coalescence. The relation is validated using data from previously performed synchrotron X-ray tomography and isothermal coarsening experiments. It is found to be valid for arbitrary and even varying cooling rates and for a wide range of binary Alloys. The rate constant in the evolution equation is successfully related to Alloy properties.
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phase field simulation of the columnar to equiaxed transition in Alloy Solidification
Acta Materialia, 2006Co-Authors: Arnoldo Badillo, C BeckermannAbstract:Abstract The columnar-to-equiaxed transition (CET) in directional Solidification of Alloys is simulated using the phase-field method. The method relies on the solution of a solute conservation equation and an equation for the propagation of the phase field on the scale of the developing microstructure. A parametric study is performed to investigate the effects of the applied temperature gradient and pulling speed, the seed spacing and nucleation undercooling for the equiaxed grains, and the crystalline anisotropy strength on the CET. The results qualitatively agree with a previously developed analytical model of the CET. At relatively high pulling speeds, a mixed columnar–equiaxed structure is found to be stable over a range of temperature gradients. Furthermore, the CET depends sensitively on the anisotropy strength. The simulations also reveal the presence of primary spacing adjustments during purely columnar growth due to nucleation of seeds, and deactivation of seeds by solutal interactions from nearby growing grains.
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phase field modeling of binary Alloy Solidification with coupled heat and solute diffusion
Physical Review E, 2004Co-Authors: Juan C Ramirez, Alain Karma, C Beckermann, H J DiepersAbstract:A phase-field model is developed for simulating quantitatively microstructural pattern formation in Solidification of dilute binary Alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i) the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii) kinetic effects are negligible. A recently derived antitrapping current [A. Karma, Phys. Rev. Lett. 87, 115701 (2001)] is used in the solute conservation equation to recover precisely local equilibrium at the interface and to eliminate interface stretching and surface diffusion effects that arise when the solutal diffusivities are unequal in the solid and liquid. Model results are first compared to analytical solutions for one-dimensional steady-state Solidification. Two-dimensional thermosolutal dendritic growth simulations with vanishing solutal diffusivity in the solid show that both the microstructural evolution and the solute profile in the solid are accurately modeled by the present approach. Results are then presented that illustrate the utility of the model for simulating dendritic Solidification for the large ratios of the liquid thermal to solutal diffusivities (Lewis numbers) typical of Alloys.
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A solutal interaction mechanism for the columnar-to-equiaxed transition in Alloy Solidification
Metallurgical and Materials Transactions A, 2003Co-Authors: M. A. Martorano, C Beckermann, C. -a. GandinAbstract:A multiphase/multiscale model is used to predict the columnar-to-equiaxed transition (CET) during Solidification of binary Alloys. The model consists of averaged energy and species conservation equations, coupled with nucleation and growth laws for dendritic structures. A new mechanism for the CET is proposed based on solutal interactions between the equiaxed grains and the advancing columnar front—as opposed to the commonly used mechanical blocking criterion. The resulting differences in the CET prediction are demonstrated for cases where a steady state can be assumed, and a revised isotherm velocity ( V _ T ) vs temperature gradient ( G ) map for the CET is presented. The model is validated by predicting the CET in previously performed unsteady, unidirectional Solidification experiments involving Al-Si Alloys of three different compositions. Good agreement is obtained between measured and predicted cooling curves. A parametric study is performed to investigate the dependence of the CET position on the nucleation undercooling and the density of nuclei in the equiaxed zone. Nucleation undercoolings are determined that provide the best agreement between measured and calculated CET positions. It is found that for all three Alloy compositions, the nucleation undercoolings are very close to the maximum columnar dendrite tip undercoolings, indicating that the origin of the equiaxed grains may not be heterogeneous nucleation, but rather a breakdown or fragmentation of the columnar dendrites.
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a multiphase solute diffusion model for dendritic Alloy Solidification
Metallurgical and Materials Transactions A-physical Metallurgy and Materials Science, 1993Co-Authors: Chaoyang Wang, C BeckermannAbstract:A solute diffusion model, aimed at predicting microstructure formation in metal castings, is proposed for dendritic Solidification of Alloys. The model accounts for the different length scales existing in a dendritic structure. This is accomplished by utilizing a multiphase approach, in which not only the various physical phases but also phases associated with different length scales are considered separately. The macroscopic conservation equations are derived for each phase using the volume averaging technique, with constitutive relations developed for the interfacial transfer terms. It is shown that the multiphase model can rigorously incorporate the growth of dendrite tips and coarsening of dendrite arms. In addition, the distinction of different length scales enables the inclusion of realistic descriptions of the dendrite topology and relations to key metallurgical parameters. Another novel aspect of the model is that a single set of conservation equations for solute diffusion is developed for both equiaxed and columnar dendritic Solidification. Finally, illustrative calculations for equiaxed, columnar, and mixed columnar-equiaxed Solidification are carried out to provide quantitative comparisons with previous studies, and a variety of fundamental phenomena such as recalescence, dendrite tip undercooling, and columnar-to-equiaxed transition (CET) are predicted.
P K Jimack - One of the best experts on this subject based on the ideXlab platform.
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three dimensional thermal solute phase field simulation of binary Alloy Solidification
Journal of Computational Physics, 2015Co-Authors: P C Bollada, P K Jimack, Andrew M Mullis, C E Goodyer, Feng Wei YangAbstract:We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three scalar field variables. The mathematical model represents the non-isothermal Solidification of a metal Alloy into a melt substantially cooled below its freezing point at the microscale. Underlying physical molecular forces are captured at this scale by a specification of the energy field. The time rate of change of the temperature, Alloy concentration and an order parameter to govern the state of the material (liquid or solid) are controlled by the diffusion parameters and variational derivatives of the energy functional. The physical problem is important to material scientists for the development of solid metal Alloys and, hitherto, this fully coupled thermal problem has not been simulated in three dimensions, due to its computationally demanding nature. By bringing together state of the art numerical techniques this problem is now shown here to be tractable at appropriate resolution with relatively moderate computational resources.
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an adaptive fully implicit multigrid phase field model for the quantitative simulation of non isothermal binary Alloy Solidification
Acta Materialia, 2008Co-Authors: J Rosam, P K Jimack, Andrew M MullisAbstract:Abstract Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal Solidification of a dilute binary Alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ ∗ , was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant.
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a fully implicit fully adaptive time and space discretisation method for phase field simulation of binary Alloy Solidification
Journal of Computational Physics, 2007Co-Authors: J Rosam, P K Jimack, Andrew M MullisAbstract:A fully implicit numerical method based upon adaptively refined meshes for the simulation of binary Alloy Solidification in 2D is presented. In addition we combine a second-order fully implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method. The superiority of this method, compared to widely used fully explicit methods, with respect to CPU time and accuracy, is shown. Due to the high nonlinearity of the governing equations a robust and fast solver for systems of nonlinear algebraic equations is needed to solve the intermediate approximations per time step. We use a nonlinear multigrid solver which shows almost h-independent convergence behaviour.
Damian Slota - One of the best experts on this subject based on the ideXlab platform.
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reconstruction of the boundary condition in the binary Alloy Solidification problem with the macrosegregation and the material shrinkage phenomena taken into account
Heat Transfer Engineering, 2019Co-Authors: Adam Zielonka, Edyta Hetmaniok, Damian SlotaAbstract:AbstractIn this paper we solve the inverse problem of the binary Alloy Solidification including two phenomena: macrosegregation and creation of the air gap between the cast and the mold in result o...
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inverse Alloy Solidification problem including the material shrinkage phenomenon solved by using the bee algorithm
International Communications in Heat and Mass Transfer, 2017Co-Authors: Adam Zielonka, Edyta Hetmaniok, Damian SlotaAbstract:Abstract In the paper we solve the one-phase inverse problem of Alloy solidifying within the casting mould, including the shrinkage of metal which results from the difference between densities of the liquid and solid phases. The process is modeled by means of the Solidification in the temperature interval basing on the heat conduction equation with the source element enclosed, whereas the shrinkage of metal is modeled by the proper application of the mass balance equation. The investigated inverse problem consists in reconstruction of the heat transfer coefficient on the boundary of the casting mould on the basis of measurements of temperature read from the sensor placed in the middle of the mould. Functional expressing the error of approximate solution is minimized with the aid of Artificial Bee Colony Optimization algorithm.
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identification of the heat transfer coefficient in the two dimensional model of binary Alloy Solidification
Heat and Mass Transfer, 2017Co-Authors: Edyta Hetmaniok, Damian Slota, Jordan Hristov, Adam ZielonkaAbstract:The paper presents the procedure for solving the inverse problem for the binary Alloy Solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the Alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the Alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.
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numerical procedure of solving some inverse problem in Solidification of the binary Alloy
Computer Assisted Mechanics and Engineering Sciences, 2017Co-Authors: Edyta Hetmaniok, Damian SlotaAbstract:The paper presents a solution of an inverse problem consisting in determination of boundary conditions in the process of binary Alloy Solidification when temperature measurements in selected points of the cast are known. In the investigated model the distribution of temperature is described using the Stefan model with the liquidus temperature varying in dependance on concentration of the Alloy component. For description of the concentration we apply the model in which the immediate equalization of chemical composition of the Alloy is assumed (lever arm model). Experimental verification of the developed algorithm is also presented.
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parallel procedure based on the swarm intelligence for solving the two dimensional inverse problem of binary Alloy Solidification
PPAM (2), 2016Co-Authors: Edyta Hetmaniok, Damian Slota, Adam ZielonkaAbstract:In the paper an application of Ant Colony Optimization algorithm for solving the two-dimensional inverse Solidification problem of binary Alloy is presented. Aim of the considered problem lies in reconstruction of the boundary condition on the basis of temperature values measured in selected points of the cast. Presented approach is grounded on two procedures: the finite difference method with application of the generalized alternating phase truncation method and the parallelized Ant Colony Optimization algorithm serving for minimization of a functional representing the important part of the procedure.