Numerical Modeling of Growth Kinetics of Pro-eutectoid Ferrite Transformed from Austenite in Fe-C-∑X Alloys

In the present paper, a numerical modeling was developed to simulate the growth kinetics of ferrite transformed from austenite in Fe-C-∑X （X denotes substitution elements, such as Mn, Ni, Cr etc.） steels by solving the diffusion equation using finite difference method （FDM）. Coupled with the kinetic modeling, thermodynamic calculations were carried out to determine the γ/α phase equilibrium conditions using a para-equilibrium （PE） model. The dissipation of free energy for γ→α phase transformation due to the so-called solute drag effect （SDE） was taken into account in the thermodynamic modeling. With this modeling, simulations on the growth kinetics of ferrite in the steels containing austenite-stabilizing and ferrite-stabilizing elements （such as Ni, Mn and Si, Cr, respectively） were performed, which indicates that it deviates from the parabolic growth rate law after the initial stage of transformation. The results were compared with the experimental values given by Bradley and Aaronson, showing that this model has a reasonably good accuracy to predict the growth kinetics of ferrite.

Phase field simulation of liquid-solid-eutectoid multiple phase transformations of a Fe-C binary alloy

A new continuous multi-phase transformation field model was established for liquid-solid-eutectoid transformation. Taking Fe-C alloy as an example, the model was used to simulate the evolution of the micro-morphology of the liquid-solid phase transition, and the effects of temperature, solute and free energy on the nucleation of pearlite after the liquid-solid phase transition were analyzed. The micro-morphology of pearlite was simulated. The simulation results show that the austenite structure has hereditary effect on the pearlite, the morphology of pearlite structure was similar to that of the parent austenite. The eutectoid structure at the front of pearlite grows toward the interior of austenite grains in a bifurcation manner and in the spherical coronal shape. In addition, the growth rate of pearlite was related to the shape of concave-convex interface at the nucleation site, and the growth rate at the convex interface was faster than that at the concave interface.

一种新的gyrator变换的快速算法

为了研究gyrator变换在光学信息处理中的应用,提出了一种采用两次快速傅里叶变换实现快速计算gyrator变换的新算法。在量纲归一化条件下,研究了gyrator变换离散化过程,获得了空域、傅里叶变换域和gyrator变换域的采样间隔,形成了一种能避免尺度变换的算法。采用该算法进行了数值模拟实验,实验结果与相关文献中报道的计算结果一致。结果表明,该算法可以应用于gyrator变换的研究中。

基于Schwarz-Christoffel变换的平板电容器电场电荷分布仿真

本文利用施瓦兹-克里斯多菲(S-C)变换,得出并讨论了计及边缘效应的平行板电容器的电场、电荷分布函数.利用离散化与数值迭代的方法,通过Matlab数值仿真得出了其电场和电荷分布的较精确的可视化结果.

Towel型域到方形计算域全局同胚网格的数值生成方法

对任意维Towel型物理域 D到方形计算域Dc 的全局同胚映射数值实现方法进行研究 ,给出了任意维等参数正变换的数值迭代求解方法 ,并就迭代求解方法的误差进行分析 ,给出了数值网格点互不重合的一个充分性条件 .最后 ,根据该方法 ,给出了钱塘江口的二维不重叠数值网格生成算例 .

COUPLED NUMERICAL SIMULATION ON COLD ROLLER'S TEMPERATURE FIFLD-PHASE TRANSFORMATION - STRESS FIELD DURING ITS QUENCHING PSOCESS

Complicated changns occur inside the steel parts during quenching process. The abruptly changed boundary conditions make the temperature field,micro - structure and stress field change dramatically in very short time, and these variables take a contact interactions in the whole process. In this paper, a three dimensional non - linear mathematical model for queeching process has been founded and the numerical simulation on temperature field,microstructre and stress field has been realized.In the FEM analysis, the incremental iteration method is used to deal with such complicated nonlinear as boundary nonlinear, physical property nonlinear,transformation nonlinear etc.The effect of stress on transformation kinetics has been considered in the calculation of microstructure. In the stress field anal- ysis,a thermo- elasto - plastic model has been founded, which considers such factors as transforma- tion strain,transformation plastic strain, themal strain and the effect of temperature and transforma- tion on mechanical propertier etc. The transient temperature field, microstructure distribution and stress field of the roller on any time can be displayed vividly,and the cooling curve and the changes of stress on any position can also be given.

Progress in Modeling of Phase Transformation Kinetics

Several methods representing the evolution of microstructure were introduced, which include the Johnson-Mehl-Avrami-Kolmogorov （JMAK） equation, Internal State Variable （ISV） framework, Koistinen-Marburger （K-M） equation, modified Magee＇s rule and phase field model, etc. By combining calculation of martensite transformation kinetics, considering the selection of parameters with the effect of austenite grain size （AGS）, some suitable ways of obtaining better results have been proposed.

Application of wavelet transform in structural health monitoring

Structural health monitoring(SHM)is a process of implementing a damage detection strategy in existing structures to evaluate their condition to ensure safety.The changes in the material,geometric and/or structural properties affect structural responses,which can be captured and analyzed for condition assessment.Various vibration-based damage detection algorithms have been developed in the past few decades.Among them,wavelet transform(WT)gained popularity as an efficient method of signal processing to build a framework to identify modal properties and detect damage in structures.This article presents the state-of-the-art implementation of various WT tools in SHM with a focus on civil structures.The unique features and limitations of WT,and a comparison of WT and other signal processing methods,are further discussed.The comprehensive literature review in this study will help interested researchers to investigate the use of WT in SHM to meet their specific needs.

Interactions between the fluid and an isolation tool in a pipe:laboratory experiments and numerical simulation

A remote-control tether-less isolation tool is a mechanical device that is normally used in pipelines to block the flow at a given position by transforming a blocking module. In this study, the interactions between the fluid and the plug module of the isolation tool were investigated. Simulations of the plug process and particle image velocimetry measurements were performed to study the flow characteristics. Numerical solutions for the continuity, momentum, and energy equations were obtained by using commercial software based on finite-volume techniques. Box–Behnken design was applied, and response surface methodology（RSM）-based CFD simulation analysis was conducted. The dynamic model in the plug process was built by RSM and used to evaluate the influences of the main mechanical parameters on the pressure during the plug process. The diameter of the isolation tool and the diameter of the plug module have strong influences on the process, and the length of the isolation tool has only a little influence on the plug process.

Nonlinear Dispersion Relation in Wave Transformation

A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1< kh <1 5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.

Numerical and experimental study of phase transformation in resistance spot welding of 6082 aluminum alloy

Resistance spot welding（ RSW） is an efficient and convenient joining process for aluminum alloy sheet assembly. Because the RSW has the character of energy concentration and quick cooling rate, the microstructure transformation of the base metal can be confined in the least limit. The material properties and the welding parameters have significant effects on the quality of the nugget. To predict the microstracture evolution in the melted zone and the heat-affected zone, an electrical, thermal, metallurgical and mechanical coupled finite element model is described and applied to simulate the welding process of the 6082 aluminum alloy. Experimental tests are also carried out. The comparison between experimental and numerical results shows that the adopted model is effective enough to well interpret and predict some important phenomena in ierms of the phase transformation in spot welding of 6082 aluminum alloy.

Modelling Wave Transmission and Overtopping Based on Energy Balance Equation

Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters,which affects wave conditions and sediment transportation and becomes the focus of design in engineering.The objective of this paper is to present a simplified model to estimate these important wave parameters.This paper describes the incorporation of wave transmission and overtopping module into a wave model for multi-directional random wave transformation based on energy balance equation with the consideration of wave shoaling,refraction,diffraction,reflection and breaking.Wen's frequency spectrum and non-linear dispersion relation are also included in this model.The influence of wave parameters of transmitted waves through a smooth submerged breakwater has been considered in this model with an improved description of the transmitted wave spectrum of van der Meer et al.(2000) by Carevic et al.(2013).This improved wave model has been validated through available laboratory experiments.Then the verified model is applied to investigate the effect of wave transmission and overtopping on wave heights behind low-crested breakwaters in a project for nearshore area.Numerical calculations are carried out with and without consideration of the wave transmission and overtopping,and comparison of them indicates that there is a considerable difference in wave height and thus it is important to include wave transmission and overtopping in modelling nearshore wave field with the presence of low-crested breakwaters.Therefore,this model can provide a general estimate of the desired wave field parameters,which is adequate for engineers at the preliminary design stage of low-crested breakwaters.

Multi-phase field simulation of multi-grain peritectic transition in multiple phase transformation

Taking Fe-C binary alloy as an example,based on the multi-phase field model,the nucleation and growth ofδphase,peritectic reaction,peritectic transformation,and the growth of subsequent austenite are simulated.Effects of the nucleation site of austenite on the peritectic reaction rate and the starting time of the peritectic transformation were studied.The simulation results show that theγphase,as a shell,surrounds theδphase and grows rapidly when the peritectic reaction occurs between the dendriticδgrains,and a layer ofγphase shell is formed aroundδphase after the peritectic reaction.After theδphase is surrounded byγphase completely,the membrane shell separates the L phase from theδphase,so that the phase transfers from peritectic reaction to peritectic transformation.During the peritectic transformation,since the solute diffusion coefficient of the liquid phase is much greater than that of the solid phase,the average growth rate of austenite in the liquid phase is visibly higher than that of theδphase.The peritectic reaction rate is related to the curvature of the nucleation site of theγphase on theδphase grains.The peritectic reaction rate at the large curvatures is faster than that at small curvatures.

基于Schwarz-Christoffel变换的非圆截面血管流场分布研究

应用Schwarz-Christoffel(S-C)变换方法,实现从复平面单位圆到多边形区域的共形映射,结合圆形管道下完全发展脉动流的Womersley算法理论,建立了基于S-C映射的非圆入口截面下的Womersley速度边界模型.在边界模型建立的基础上,应用计算流体力学方法,对基于生理真实的人体肺动脉二级分支血管在一个心动周期内的血流流动情况进行了数值模拟,并与通过外接圆管法设定入口速度边界条件得到的流场模拟结果进行了对比分析.分析结果表明,两者的模拟结果高度一致,但考虑到模拟效率和数值模拟结果的确定性,基于S-C映射的Womersley速度边界模型优于外接圆管方法,对于血管血流动力学的模拟研究更具有现实意义.

SIMPLIFIED SCALING TRANSFORMATION FOR THE NUMERICAL SIMULATION OF MEMS DEVICES WITH THIN FILM STRUCTURES

Thin film is a widely used structure in the present microelectromechanical systems （MEMS） and plays a vital role in many functional devices. However, the great size difference between the film＇s thickness and its planar dimensions makes it difficult to study the thin film performance numerically. In this work, a scaling transformation was presented to make the different dimensional sizes equivalent, and thereby, to improve the grid quality considerably. Two numerical experiments were studied to validate the present scaling transformation method. The numerical results indicated that the largest grid size difference can be decreased to one to two orders of magnitude by using the present scaling transformation, and the memory required by the numerical simulation, i.e., the total grid number, could be reduced by about two to three orders of magnitude, while the numerical accuracies with and without this scaling transformation were nearly the same.

基于矢量分解和相位截取Gyrator变换的图像加密

为了提高光学图像加密系统的安全性,采用了矢量分解和相位截取Gyrator变换进行图像加密。原始图像和随机相位函数叠加后做Gyrator变换,矢量分解将Gyrator变换域信息分解为一个随机相位函数和一个复函数。随机相位函数和复函数分别做不同变换角度的Gyrator变换后截取相位得到一个公钥和加密图像,截取振幅得到两个非对称相位密钥。进行了理论分析和数值验证,同时,设计了解密光学装置。结果表示:两个非对称相位密钥做为私钥,三个Gyrator变换角度做为额外密钥,这对增强系统的安全性是有帮助的。

A VERTICAL COORDINATE TRANSFORMATION FOR 3-D NUMERICAL MODELLING OF OCEAN CIRCULATION

A so called sine-sigma vertical coordinate transformation is proposed. A vertical implicit scheme is de-rived by using cubic-spline representation of vertical current profiles. The derived 3-D nurmericalmodel has been applied to simulate the water leved field and the vertical structures of wind-induced cur-rents in an enclosed rectangular region, and the tides in the Bohai Sea. The model is believed to besatisfactory after comparing its results with an analytical soclution and observed data from tidal staions.

PGOPO Approach to Design Linear Servomechanism of Time-Varying Systems with Time-Delay

Based on a new linear, continuous and bounded operator (PGOPO), a more effective approach and optimal control algorithm than by the block-pulse functions and Walsh functions to design the linear servomechanism of time-varying systems with time-delay is proposed in the paper. By means of the operator, the differential equation is transferred to a more explicit algebraic form which is much easier than the numerical integration of nonlinear TPBVP derived from Pantryagin's maximum principle method. Furthermore, the method is established strictly based on the theory of convergence in the mean square and it is convenient and simple in computation. So the method can be applied to industry control and aeronautics and astronautics field which is frequently mixed with time varying and time delay. Some illustrative numerical examples are interpreted to support the technique.

Numerical Simulation of Nonlinear Surface Gravity Waves Transformation under Shallow-Water Conditions

This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are resulted boundary and initial conditions. The method of splitting into physical processes receives system from three equations. Then we define the approximation order and investigate stability conditions of the discrete model. The sweep method was used to calculate the system of equations. This work presents surface gravity wave profiles for different propagation phases.

Spatio-spectral dynamics of soliton pulsation with breathing behavior in the anomalous dispersion fiber laser

We have numerically and experimentally observed the soliton pulsation with obvious breathing behavior in the anomalous fiber laser mode-locked by a nonlinear polarization rotation technique.The numerical study of the soliton pulsation with breathing behavior was analyzed through the split-step Fourier method at first,and it was found that the phase difference caused by the polarization controller would affect the breathing characteristics.Then,taking advantage of the dispersive Fourier transform technique,we confirmed the breathing characteristic of soliton pulsation in the same fiber laser as the simulation model experimentally.These results complement the research on the breathing characteristic of soliton pulsation.