Natural Convection and Columnar-to-Equiaxed Transition Prediction in a Front-Tracking Model of Alloy Solidification

A meso-scale front-tracking model (FTM) of nonequilibrium binary alloy dendritic solidification has been extended to incorporate Kurz, Giovanola, and Trivedi (KGT) dendrite kinetics and a Scheil solidification path. Model validation via comparison with thermocouple measurements from a solidification experiment, in which natural convection is limited by design, is presented. Via solution of the flow field due to natural thermal buoyancy, it is shown that resultant liquid-phase convection creates conditions in which equiaxed solidification is favored. Comparison with simulations in which casting solidification is diffusion controlled show that natural convection has greatest effect at intermediate times, but that at early and late stages of columnar solidification, the differences are relatively small. It is, however, during the time of greatest divergence between the simulations that the authors’ predictive index for equiaxed zone formation is enhanced most by convection. Finally, the columnar-to-equiaxed transition is directly simulated, in directional solidification controlled by diffusion. This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: in Honor of Prof. John Hunt,” which occurred March 13–15, 2006 during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

Columnar-to-Equiaxed Transition During Directional Solidification Under Strong Magnetic Field

Effects of strong magnetic fields on the columnar-to-equiaxed transition(CET)have been investigated experimentally.Experimental results show that the application of a strong magnetic field causes a dendrite fragmentation and then the CET.The thermoelectric magnetic force acting on cells/dendrites and equiaxed grains in the mushy zone has been studied numerically.Numerical results reveal that a torque is created on cells/dendrites and equiaxed grains and the value of the thermoelectric magnetic force increases as the magnetic field intensity increase.This torque breaks cells/dendrites and drives the rotation of equiaxed grains.As a consequence,the CET will occur during directional solidification under a strong magnetic field.This may initiate a new method to induce the CET via an applied strong magnetic field during directional solidification.     

In-Situ and Real-Time Investigation of Columnar-to-Equiaxed Transition in Metallic Alloy

In this article, we present a review of observations during Al-3.5 wt pct Ni alloy solidi.cation experiments performed at the European Synchrotron Radiation Facility (ESRF) in Grenoble. These experiments provide direct access to dynamical phenomena during columnar growth (initial transient and breakdown of a planar solid-liquid interface), and for the first time to the transition from columnar-to-equiaxed microstructure (nucleation ahead of a columnar front and blocking of a columnar front by an equiaxed microstructure) and fully equiaxed growth (propagation of an effective front). Based on these experimental observations, critical parameters such as columnar growth velocity variation during the transition or equiaxed-grain diameter are measured and discussed. This article is based on a presentation made in the symposium entitled “Solidi.cation Modeling and Microstructure Formation: In Honor of Prof. John Hunt,” which occurred March 13–15, 2006, during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

Influence of Solidification Thermal Parameters on the Columnar-to-Equiaxed Transition of Aluminum-Zinc and Zinc-Aluminum Alloys

Understanding the interaction between the parameters involved in the columnar-to-equiaxed transition (CET) has gained considerable attention over the last two decades in the study of the structure of ingot castings. The present investigation was undertaken to investigate experimentally the directional solidification of Al-Zn and Zn-Al (ZA) alloys under different conditions of superheat and heat-transfer efficiencies at the metal/mold interface. The CET is observed; grain sizes are measured and the observations are related to the solidification thermal parameters: cooling rates, growth rates, thermal gradients, and recalescence determined from the temperature vs time curves. The temperature gradient in the melt, measured during the transition, is between –0.338 °C/mm and 0.167 °C/mm. In addition, there is an increase in the velocity of the liquidus front faster than the solidus front, which increases the size of the mushy zone. The size of the equiaxed grains increases with distance from the transition, an observation that was independent of alloy composition. The observations indicate that the transition is the result of a competition between coarse columnar dendrites and finer equiaxed dendrites. The results are compared with those previously obtained in lead-tin alloys. This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: in Honor of Prof. John Hunt,” which occurred March 13–15, 2006 during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

The Columnar-to-Equiaxed Transition in Melt Pools During Laser Powder Bed Fusion of M2 Steel

Metallurgical and Materials Transactions A - This work integrates experimental and numerical methods to determine the process conditions under which the columnar-to-equiaxed transition (CET)...     

Columnar-to-Equiaxed Transition and Equiaxed Grain Alignment in Directionally Solidified Ni3Al Alloy Under an Axial Magnetic Field

The effect of an axial magnetic field on the solidification structure in directionally solidified Ni-21.5Al-0.4Zr-0.1B (at. pct) alloy was investigated. The experimental results indicated that the application of a high magnetic field caused the deformation of dendrites and the occurrence of columnar-to-equiaxed transition (CET). The magnetic field tended to orient the 〈001〉 crystal direction of the equiaxed grains along the magnetic field direction. The bulk solidification experiment under a high magnetic field showed that the crystal exhibited magnetic crystalline anisotropy. Further, the thermoelectric (TE) magnetic force and TE magnetic convention were analyzed by three-dimensional (3-D) numerical simulations. The results showed that the maximum value of TE magnetic force localized in the vicinity of the secondary dendrite arm root, which should be responsible for the dendrite break and CET. Based on the high-temperature creep mechanism, a simple model was proposed to describe the magnetic field intensity needed for CET: \( B \ge kG^{ - 1.5} R^{1.25} \). The model is in good agreement with the experiment results. The experimental results should be attributed to the combined action of TE magnetic effects and the magnetic moment.

     

Deterministic Advection-Diffusion Model Based on Markov Processes

A new deterministic numerical formulation named DisPar-k based on particle displacement probability distribution for Markov processes was developed to solve advection-diffusion problems in a one-dimensional discrete spatial grid. DisPar-k is an extension of DisPar, and the major difference is the possibility of establishing a number of consecutive particle destination nodes. This was achieved by solving an algebraic linear system where the particle displacement distribution moments are known parameters taken from the Gaussian distribution. The average was evaluated by an analogy between the Fokker-Planck and the transport equations, being the variance Fickian. The particle displacement distribution is used to predict deterministic mass transfers between domain nodes. Mass conservation was guaranteed by the distribution concept. It was shown that, for linear conditions, the accuracy order is proportional to the number of particle destination nodes. DisPar-k showed to be very sensible to physical discontinuities in the transport parameters (water depth, dispersion, and velocity), showing that this type of problem can only be disguised by introducing numerical dispersion (i.e., changing the Fickian variance).     

Optimal Layout of Sewer Systems: A Deterministic versus a Stochastic Model

The optimization of a new or partially existing urban drainage system may be modeled as a subproblems sequence of layout and optimal design within the discrete search space. The design optimization, incorporating the optimal selection of the pumping stations, intermediate manholes, pipe sections, and installation depths, for a general system fixed layout in plan, is a high level sequential decision problem which may be efficiently solved deterministically through a multilevel dynamic programming model. The optimal general layout may be selected in a deterministic way by means of a simple economical comparison of all plan solutions having optimized designs, for small to medium sized systems (if the specific restrictions of the applications are appropriately exploited) in practicable computer time. For larger dimension networks, where it is clearly impossible to achieve plan optimization with full enumeration (which is a NP complete), stochastic search models can be used. For the subproblem layout, an effective enumeration model is presented; the results of a stochastic model proposed previously, using simulated annealing for an application example, are compared and discussed in detail.     

三相整流变压器有载调压开关过渡电阻烧毁原因与解决方法

通过详细的分析计算，找出了三相整流变压器有载调压开关切换过波电阻烧毁的主要原因，并提出了相应的解决办法。     

A Simplified Three-Phase Model of Equiaxed Solidification for the Prediction of Microstructure and Macrosegregation in Castings

Macrosegregation is a result of the interplay of various transport mechanisms, including natural convection, solidification shrinkage, and grain motion. Experimental observations also indicate the impact of grain morphology, ranging from dendritic to globular, on macrosegregation formation. To avoid the complexity arising due to modeling of an equiaxed dendritic grain, we present the development of a simplified three-phase, multiscale equiaxed dendritic solidification model based on the volume-averaging method, which accounts for the above-mentioned transport phenomena. The validity of the model is assessed by comparing it with the full three-phase model without simplifications. It is then applied to qualitatively analyze the impact of grain morphology on macrosegregation formation in an industrial scale direct chill cast aluminum alloy ingot.     

Computer-Aided Model Generation for Nonlinear Structural Analysis Using a Structural Component Model Database

This paper presents an approach for efficiently building analytical models for nonlinear analysis. The objective has been achieved by establishing structural component model database by collecting various structural component models addressing various structural details. A common data structure and a relational database schema for storing structural component models were proposed in this study. The proposed structural component model database can serve as a decision supporting system for building nonlinear analytical models manually. In addition, the modeling information stored in this database can be presented in XML document format to be parsed and manipulated by computer system for generating nonlinear analytical model in file automatically. A school building database is used as a case study to show the feasibility of automatic modeling for nonlinear analysis using the proposed structural component database. A semiautomatic model generation system was developed to provide an efficient modeling process, which is in the manner of form filling and option selecting on web-based user interfaces, so that the model builder can focus on making engineering decisions. The modeling details are handled automatically by the proposed system based on user selection and setting.     

粉末烧结钢温压粘结剂玻璃化温度调整的预测方程

推导出了作为润滑剂载体的粘结剂的玻璃化温度的预测方程，并讨论了方程用于烧结钢温压工艺的合理性。     

A Model for Calculating Hydrogen Solubility in Liquid Transition Metals

The documented experimental results of hydrogen solubility in different liquid metals were summarized according to the periodic table. It is found that the hydrogen solubility in liquid transition metals is much higher than in others and it changes regularly with the atomic number to form a V-shaped curve. It is supposed that the electron interaction between the hydrogen and metal atoms of the liquid is the major factor in determining hydrogen solubility in the liquid metal. Based on this consideration, a model was proposed for characterizing electron interaction and calculating the hydrogen solubility in various liquid metals according to the nearly free-electron theory. The calculated hydrogen solubility in liquid transition metals agrees well with the documented experimental results, and some undocumented results could be predicted.     

Random Composites Characterization Using a Classifier Model

A new method is introduced for characterizing and analyzing materials with random heterogeneous microstructure. The method begins with classifiers which process information from high-fidelity analyses of small-sized simulated microstructures. These classifiers are subsequently used in a multipass moving window to identify subregions of potentially critical microscale behavior such as strain concentrations. In the derivation of the method, it is shown how information theory-based concepts can be formulated in a Bayesian decision theory framework that addresses microstructural issues. Furthermore, it is shown how a sequence of classifiers can be constructed to refine the analysis of microstructure. While the method presented herein is general, a relatively simple example of a two-dimensional, two-phase composite is used to illustrate the analysis steps.     

Random Uncertainties Model in Dynamic Substructuring Using a Nonparametric Probabilistic Model

This paper presents a new approach, called a nonparametric approach, for constructing a model of random uncertainties in dynamic substructuring in order to predict the matrix-valued frequency response functions of complex structures. Such an approach allows nonhomogeneous uncertainties to be modeled with the nonparametric approach. The Craig–Bampton dynamic substructuring method is used. For each substructure, a nonparametric model of random uncertainties is introduced. This nonparametric model does not require identifying uncertain parameters in the reduced matrix model of each substructure as is usually done for the parametric approach. This nonparametric model of random uncertainties is based on the use of a probability model for symmetric positive-definite real random matrices using the entropy optimization principle. The theory and a numerical example are presented in the context of the finite-element method. The numerical results obtained show the efficiency of the model proposed.     

Uncertainty Assessment of a Water-Quality Model for Ephemeral Rivers Using GLUE Analysis

Every model is, by definition, a simplification of the system under investigation. Although it would be desirable to reduce the gap between the simulated and the observed behaviors of the system to zero, this reduction is generally impossible owing to the unavoidable uncertainties inherent in any modeling procedure. Uncertainty analyses can provide useful insights into the best model approach to be used for obtaining results with a high level of significance and reliability. The evaluation of parameter uncertainties is necessary for calibration and for estimating the impact of these uncertainties on model performance. In this context, the uncertainty of a river water-quality model developed in previous studies is presented. The main goal is to gain insights into the modeling approaches concerning small rivers. Previous works generally focused on modeling the large river while neglecting the small one. Following a model calibration, the model uncertainty has been assessed by means of the generalized likelihood uncertainty estimation (GLUE). The results showed that the biological process related to the biological oxygen demand (BOD) removal influenced mainly by the parameters characterizing deoxygenation and nitrogen removal. On the other hand, the biological processes related to nitrogen removal were influenced not only by the parameters related to the nitrogen removal but also to oxygen concentration. The application of the GLUE methodology shows that the river quality model considered is suitable for simulating the important processes involved. Uncertainty bounds showed different amplitudes with respect to the pollutant species considered. In particular, the oxygen uncertainty bounds were narrower with respect to the other model components suggesting much attention must be paid to both model algorithms and quality data to be gathered. The study confirmed the suitability of the GLUE methodology as a powerful tool as a simplified screening methodology to assess uncertainty.     

灰色预测模型在冷轧动态张力控制中的应用

针对PID控制器参数保持不变时很难保证轧机架间张力稳定在裕量范围内的问题.在分析轧机辊缝与速度动态张力控制原理的基础上,推导出机架间张力控制对象的数学模型,并利用灰色预测PID控制方法,实现了机架间张力稳定控制.从仿真数据和实际应用结果数据可以得出,此方法对比其他传统PID控制方法,能够有效地保证张力系统较高的动静态控制性能和干扰抑制性能要求,且控制精度更高.     

Parameter Estimation for the Nonlinear Muskingum Model Using the BFGS Technique

In the past, various methods have been used to estimate the parameters in the nonlinear three-parameter Muskingum model to allow the model to more closely approximate a nonlinear relation compared to the original two-parameter Muskingum model. In this study, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) technique, which searches the solution area based on mathematical gradients, is introduced. The technique found the best parameter values compared to previous results in terms of the sum of the square deviation between the observed and routed outflows, using the smallest number of computational iterations. A sensitivity analysis showed that the initial values of certain parameters were critical when finding the optimal solution. Although this gradient-based technique makes use of initial value assumptions and involves complicated calculus, different initial values reach the same optimal or near-optimal solution within less time. Moreover, this mathematical technique does not require the algorithm parameters that are essential factors in meta-heuristics such as genetic algorithm or harmony search. The technique also considers the hydrologic parameters to be continuous rather than discrete variables for pure structures.