Analysis and design of mechanical crack arrestors for gas pipeline

Mechanical arrestors are frequently used in gas transmission pipelines to prevent the possibility of long running cracks. These arrestors have the effect of reducing the pipe from opening as the crack passes. This decreases the available crack driving force and, as a result, crack arrest may take place. This essentially is a second line of defence against catastrophic failure in the event crack initiation cannot always be prevented. A novel analyzing method presented in this paper has been developed to investigate the suitability of these crack arrestors. This is based on a fluid/structure/fracture interaction package, PFRAC. A dynamic finite element approach has been developed for a three dimension curved beam with initial plane curvature, which has been implemented in PFRAC to simulate the behaviour of the arrestor. The contact conditions between the pipe wall and the arrestor, along with the various computational procedures, are described. Several numerical results for a cracked pipe with arrestors are presented and compared with those for pipes without arrestors.     

Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.     

Shock-induced ignition of thermally sensitive explosives

The process of planar detonation ignition, induced by a constant-velocitypiston or equivalently by a shock reflected from a stationarywall, is investigated using high-resolution one-dimensionalnumerical simulations. The standard one-step model with Arrheniuskinetics, which models thermally sensitive explosives, is employed.Emphasis is on comparing and contrasting the results of thefinite activation temperature simulations with high activationtemperature asymptotic predictions and previous simulations.During the induction phase, it is shown that the asymptoticresults give qualitatively good predictions. However, for parametersrepresentative of gaseous explosives, subsequent to thermalrunaway at the piston and the formation of a reaction wave,the high activation temperature asymptotic theory is qualitativelyincorrect for moderately high activation temperatures. It isshown that the results are very sensitive to the value of theactivation temperature, especially the distance from the pistonat which a secondary shock forms and the degree of unsteadinessin the reaction wave which moves away from the piston. The dependenceof the ignition evolution on the other parameters (initial shockMach number, heat of reaction and polytropic index) is alsoinvestigated. It is shown that qualitative predictions regardingthe dependence of the ignition evolution on each of the parameterscan be elucidated from finite activation temperature homogeneousexplosion calculations together with the high activation temperatureasymptotic shock ignition results. It is found that for sufficientlystrong initiating shocks the ignition evolution is qualitativelydifferent from cases studied previously in that no secondaryshock forms. For a high polytropic index, corresponding to asimple equation of state model for condensed phase explosives,the results are in much better qualitative agreement with theasymptotic theory.     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise charac-     

Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock     

寿命服从对数正态分布、有置信度时概率疲劳S-N曲线的合理重构

当概率疲劳S-N曲线以特定存活概率(P)和置信度(C)的方式给出并无法重做试验时,除特定P-C外无法做其它概率水平的可靠性分析.因此,需要广泛适用的曲线模型.建立了疲劳寿命服从对数正态分布时疲劳试验S-N数据及广义曲线的Monte Carlo模拟重构方法.为了避免现有人为放大样本到数千给出偏危险评价,从实际试验情况出发,采用了材料小试样每组样本7至20、结构试样每组样本至多10个、还原统计参量误差小于5%的模拟策略.然后,依据模拟数据利用回归法重建了可实现任意P-C水平可靠性分析的P-C-S-N曲线.铁路60Si2Mn高强度弹簧钢概率曲线的重构实践说明了方法的有效性与适用性.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007     

多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真

建立了针对多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真模型，导出了多分散 系统的有效自由程分布函数. 给出了半径为50nm与550nm及其三种不同体积浓度比混合的聚 苯乙烯微球作为散射粒子的高浓度介质的仿真结果. 定性地分析了多分散介质偏振光后向扩 散散射的光强空间分布特征与粒子的体积浓度比的关系. 关键词： 后向扩散散射 偏振光 多分散高浓度介质 Monte Carlo仿真     

Mathematical modelling and computational analysis of enzymatic degradation of xenobiotic polymers

We study the enzymatic degradation of xenobiotic polymers mathematically. As a mathematical model, we derive a linear second-order hyperbolic partial differential equation which governs the evolution of the weight distribution with respect to the molecular weight. Given an initial weight distribution and a final weight distribution, we formulate a problem to determine a degradation rate. We establish a necessary and sufficient condition for which the problem has a local solution. We also introduce a numerical technique based on our analysis, and present a numerical result that we obtained applying weight distributions before and after enzymatic degradation of polyvinyl alcohol.     

The effect of three-body interactions on thermal desorption spectra

Thermal desorption spectra are calculated for a one-dimensional chain and for a two-dimensional square lattice using the transfer-matrix technique and Monte Carlo simulations. Lateral interactions of adsorbed particles cause a splitting of spectra. The repulsive three-body interactions are shown to lead to an inequality of the integral intensities of the thermal desorption peaks.