A hybrid extended finite element/level set method for modeling phase transformations

A hybrid numerical method for modelling the evolution of sharp phase interfaces on fixed grids is presented. We focus attention on two‐dimensional solidification problems, where the temperature field evolves according to classical heat conduction in two subdomains separated by a moving freezing front. The enrichment strategies of the eXtended Finite Element Method (X‐FEM) are employed to represent the jump in the temperature gradient that governs the velocity of the phase boundary. A new approach with the X‐FEM is suggested for this class of problems whereby the partition of unity is constructed with C¹(Ω) polynomials and enriched with a C⁰(Ω) function. This approach leads to jumps in temperature gradient occurring only at the phase boundary, and is shown to significantly improve estimates for the front velocity. Temporal derivatives of the temperature field in the vicinity of the phase front are obtained with a projection that employs discontinuous enrichment. In conjunction with a finer finite difference grid, the Level Set method is used to represent the evolution of the phase interface. An iterative procedure is adopted to satisfy the constraints on the temperature field on the phase boundary. The robustness and utility of the method is demonstrated with several benchmark problems of phase transformation. Copyright © 2002 John Wiley & Sons, Ltd.     

Oxidation of porous nanocrystalline titanium nitride. II. Scale structure and composition

We have used x-ray phase analysis to study the composition of the products of reaction between oxygen and nanocrystalline powders with particle sizes 15, 40, 55, and 80 nm, and also specimens pressed (and sintered) from them. The powders were oxidized in air at 100°C (400 h) to 500°C (5 min), while the sintered specimens were oxidized at 600–900°C for 15, 120, and 240 min. In all cases, in the initial oxidation step the oxynitride Ti(O_xN_y) is formed, which over time is oxidized to TiO, Ti₂O₃, Ti₃O₅, TiO₂ (anatase) and TiO₂ (rutile). In the range 600–800°C, formation of a continuous oxide layer and conversion of anatase to rutile slows down diffusion of oxygen in the scale. We have established that at 900°C, the growth rate of the scale thickness increases and so the reflections from the oxynitride are barely noticeable on the diffraction patterns taken from the surface of the oxidized specimen. In these diffraction patterns, along with strong reflections from the rutile, we also observed weak reflections from lower oxides and anatase, which may be due to reaction between oxygen and the titanium ions diffused to the scale surface. We have concluded that at T > 850°C, the mechanism for oxidation of TiN changes. This is due to superposition of counterdiffusion of titanium ions on the diffusion of oxygen. __________ Translated from Poroshkovaya Metallurgiya, Nos. 3–4(448), pp. 72–78, March–April, 2006.     

同杆并架双回线基于电流突变量的综合选相

相电流差突变量选相元件在单回线故障中具有良好的选相性能，但在同杆双回线跨线故障中可能误选相。利用六序故障分量的分析方法，分析了相电流突变量在同杆双回线跨线故障中的幅值和相位特征，给出了其相位比相方程。在此基础上，提出了一种运用测量阻抗和方向元件相结合的综合选相方法，并给出了选相流程图。仿真结果表明，在双回线简单故障和跨线故障时，基于单回线单端电气量的同杆并架双回线综合选相方法具有较理想的选相性能。     

Phase equilibria in the system Al-Rh

Methods of differential thermal analysis, x-ray diffraction, microstructural analysis and electron probe microanalysis are used to study alloys of the Al-Rh system over the whole concentration range. It is established that the phase of equiatomic composition AlRh melts congruently at 2060°C and it has an extended range of homogeneity (45.1–54.2 at.% Rh). The solubility of aluminum in rhodium reaches 9 at.%, decreasing to 6 at.% at 850°C. Coordinates are determined for the eutectic point l ⇆ AlRh + 〈Rh〉 as 70 at.% Rh and 1715°C. The existence of intermediate phases, their crystal structure, and also the method of forming phases in the field of composition rich in aluminum given in publications are confirmed. __________ Translated from Poroshkovaya Metallurgiya, Nos. 5–6(449), pp. 48–56, May–June, 2006.     

（Ba1-xSrx）（Zn1/3Nb2/3）O3微波介质陶瓷温度系数的异常

研究了（Ba1-xSrx）（Zn1/3Nb2/3）O3微波介质陶瓷温度系数的非线性变化以及异常的原因。根据CM公式，随着系统中Sr（Zn1/3Nb2/3）O3的增多，τc的异常是由于氧八面体的畸变导致的相转变（对称性降低）所造成的（晶体结构由无序立方相向有序赝立方相的连续变化）。相转变的发生相应影响了极化以及极化模式，这是造成τc异常的根本原因。     

An investigation of the relation between the temperature dependences of the initial unbalance and the output signal of resistance strain sensor bridge circuits

The relation between the initial unbalance and the output signal of bridge circuits when acted upon simultaneously by the physical factor being measured and the temperature of the surroundings when the bridge is supplied from a voltage or current source is investigated. Analytic relations are obtained which explain the temperature dependence of the useful output voltage under external physical action. __________ Translated from Izmeritel’naya Tekhnika, No. 1, pp. 48–49, 2007.     

Structure modification of rapidly solidified Al-11 wt% Si alloy by the addition of 2 wt% Fe

An investigation of the structure formation of as-cast Al-11 wt% Si (AlSi11) and Al-11 wt% Si-2 wt% Fe (AlSi11Fe2) rapidly solidified (RS) ribbons is performed. Ribbon samples are examined in detail using Auger electron spectroscopy (AES) and transmission electron microscopy (TEM). A nanoscale thickness layer of Si-precipitations, at both Al-grains boundary and oxide/Al-matrix interface, is found to be characteristic for “pure” AlSi11 ribbons. For Fe-doped ribbons, this layer comprises Fe-containing phase also, which appears to possess amorphous nature and is situated between the Si-grains and Al-matrix. A possible mechanism of altering the thermally activated volume diffusion of elements, due to the effect of Fe on the structure modification, is speculated based on the obtained results.     

Imaging the domain pattern of the canted magnetization state in Co/Pt multilayer films

The exact magnetization pattern of magnetic films close to a spin-reorientation transition is difficult to analyze due to the intrinsically three-dimensional (3d) variation of the orientation of the local magnetization. We present a technique how this can be performed, based on the analysis of high quality 2d polarization maps from a single scanning electron microscope with polarization analysis (SEMPA) measurement with tilted sample. The key tool is the statistical distribution of all occurring polarization doublets, visualized in a 2d histogram plot. From the shape of the distribution the type of transition—canted-phase, or coexisting phases—can be inferred. For the canted-phase state, the canting angle can be accurately determined from geometrical considerations. With help of the histogram the image data can be analyzed and the three components of the magnetization can be calculated for most points of the image. For a Co/Pt multilayer film we found a cone state. The magnetization forms a complex pattern consisting of out-of-plane domains while the in-plane magnetization shows a maze pattern.     

A general formula for the evaluation of thermodynamic and aerodynamic losses in nucleating steam flow

Near saturation steam undergoing rapid expansion, with homogeneous nucleation of water droplets, is numerically studied in a series of converging/diverging nozzles with and without shocks. To understand loss mechanisms in such flows a numerical model is presented to calculate thermodynamic losses, which is further used to quantify associated total aerodynamic losses. For the converging/diverging nozzle configuration, the model shows that the overall thermodynamic loss is only mildly influenced by increasing shock strength, while the aerodynamic losses follow that of the single phase flow, and are of the same magnitude as the thermodynamic loss only in the case of very weak shocks. The thermodynamic losses can be attributed to two influences, the homogeneous nucleation event, and the post-shock thermal oscillations in the two-phase system. The calculations rely on a new two-phase CFD model, previously reported, for non-equilibrium phase change with droplet nucleation applicable to general 3D flow configurations.     

A Finite Element Computational Method for Gas Hydrate. Part I: Theory

A finite element scheme is presented to model the dissociation of gas hydrates in porous media by hot water injection. We show a complete derivation of the finite element formulation, including the associated mass and energy conservation equations capable of performing transient analysis of both conductive and convective heat transfer for gas and liquid flow in porous media. The scheme also includes the latent heat effect to accommodate the change of phase due to melting of hydrate. In the companion paper, Part II, this method is successfully applied to hydrate reservoirs.