Predictions of the excess pressure drop of Boger fluids through a 2:1:2 contraction–expansion geometry using non-equilibrium molecular dynamics

Non-equilibrium molecular dynamics are used to generate the flow of polymer solutions, specifically of Boger fluids, through a planar 2:1:2 contraction–expansion geometry. The solvent molecules are represented by Lennard–Jones particles, while linear molecules are described by spring-monomers with a finite extensible non-linear elastic spring potential. The equations for Poiseuille flow are solved using a multiple time-scale algorithm extended to non-equilibrium situations. Simulations are performed at constant temperature using Nose–Hoover dynamics. At simulation conditions, changes in concentration show no significant effect on molecular conformation, velocity profiles, and stress fields, while variations in the Deborah number have a strong influence on fluid response. Increasing the magnitude of the Deborah number (De), larger deformation rates are developed in the flow region. For a Deborah number of one, the non-dimensional pressure drop presents values lower than the correspondent Newtonian case. However, for large Deborah numbers, the pressure drop increases above the Newtonian reference. An effective excess pressure drop above the Newtonian value is predicted for Boger fluids along this geometry.     

功能梯度圆锥扁壳的1:2内共振研究

对热载荷和机械载荷共同作用下的功能梯度圆锥扁壳进行了1:2内共振分析。假设材料属性与温度有关,材料组分沿厚度方向呈幂律梯度变化,基于一阶剪切变形理论和von-Karman几何非线性关系,运用Hamilton原理建立功能梯度圆锥扁壳的非线性动力学方程;采用Galerkin法将运动控制方程离散成一个两自由度非线性动力学系统,采用多尺度法对上述方程进行摄动分析,获得了系统的平均方程,进一步得到频率响应函数和力幅响应函数。研究了材料体积分数指数和面内载荷对幅-频响应特性的影响,结果表明:研究可以得出:改变材料体积分数指数会影响材料中金属的含量及分布,从而引起幅-频响应曲线刚度特性和共振峰带宽的变化;面内载荷的变化不会影响幅-频响应曲线的刚度特性,但是会改变共振峰的带宽。本文还研究了振幅跳跃现象,通过Runge-Kutta法对共振系统进行数值仿真,研究了面内载荷对系统非线性动力学行为的影响,得出:随着面内载荷的变化,系统的运动从周期运动经历概周期运动变成混沌运动。     

损伤效应对悬索2:1内共振响应影响分析

损伤是结构振动测试和运营维护中不可避免的问题，损伤效应会导致结构振动特性发生改变．本文以受损悬索为例，探究该非线性系统同时发生主共振和2:1内共振时，损伤效应对其面内耦合共振响应影响．首先基于哈密顿变分原理，引入与损伤程度、范围和位置相关的三个无量纲参数，建立受损悬索面内动力学模型，并推导其无穷维非线性运动微分方程．以2:1耦合共振为例，采用Galerkin法和多尺度法得到系统直角坐标形式的调谐方程．数值算例表明：损伤会导致悬索固有频率降低，使得频率间公倍关系发生改变，影响系统耦合共振响应；损伤会引发系统振动特性发生明显定量和定性改变，尤其是共振响应幅值及弹簧特性；损伤对直接激励模态响应幅值的影响比对内共振激发对响应幅值的影响要明显；损伤会导致霍普夫、鞍节点、叉形和倍周期分岔的位置发生偏移，从而影响分岔点附近系统的动力学行为；系统动态解和周期运动与损伤密切相关，损伤会导致系统展现出完全不同类型的吸引子．     

Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures

Detonation experiments in H₂–NO₂/N₂O₄–Ar mixtures (Equivalence ratio 1.2 and initial pressure lower than 0.1 MPa) confined in a tube of internal diameter 52 mm reveal two propagation regimes depending on initial pressure: (1) a quasi-CJ regime is observed along with a double cellular structure at high pressures; (2) at lower pressures, a low velocity detonation regime is observed with a single structure. Transition between this two regimes happens when the spinning detonation of the larger cell vanishes. Each detonation regime is characterized by velocity and pressure measurements and cellular structure records. Coherence between all experimental data for each experiment leads in assumption that losses are responsible for the transition between one regime to another. In a second part, we study such behaviour for a two-step mixture through numerical simulations using a global two-step chemical kinetics and a simple losses model. Numerical simulations qualitatively agree with experiments. Both detonation regimes with their own cellular structures are reproduced.     

HIA: A Hybrid Integral Approach to model incompressible isotropic hyperelastic materials – Part 2: Finite element analysis

The present paper is devoted to the modeling of finite deformations of hyperelastic bodies by using the Hybrid Integral Approach (HIA) model introduced by the Authors. This model combines the affine behavior of chains included in the molecular 8-chains density, the interleaving constraint part and an original phenomenological integral density which allows to balance the mismatch between model and experimental data. A total Lagrangian formulation is adopted to describe the geometrical and material non-linearities and a finite element implementation is performed in the FER software. Four test examples, including homogeneous and non-homogeneous deformations, as well as complex computation involving dynamic contact and impact are proposed to show the applicability of the developed approach and the efficiency of the model.     

2:1 and 1:1 frequency-locking in fast excited van der Pol–Mathieu–Duffing oscillator

The frequency-locking area of 2:1 and 1:1 resonances in a fast harmonically excited van der Pol–Mathieu–Duffing oscillator is studied. An averaging technique over the fast excitation is used to derive an equation governing the slow dynamic of the oscillator. A perturbation technique is then performed on the slow dynamic near the 2:1 and 1:1 resonances, respectively, to obtain reduced autonomous slow flow equations governing the modulation of amplitude and phase of the corresponding slow dynamics. These equations are used to determine the steady state responses, bifurcations and frequency-response curves. Analysis of quasi-periodic vibrations is carried out by performing multiple scales expansion for each of the dependent variables of the slow flows. Results show that in the vicinity of both considered resonances, fast harmonic excitation can change the nonlinear characteristic spring behavior from softening to hardening and causes the entrainment regions to shift. It was also shown that entrained vibrations with moderate amplitude can be obtained in a small region near the 1:1 resonance. Numerical simulations are performed to confirm the analytical results.     

双频1:2激励下修正蔡氏振子两尺度耦合行为

不同尺度耦合系统存在的复杂振荡及其分岔机理一直是当前国内外研究的热点课题之一.目前相关工作大都是针对单频周期激励频域两尺度系统,而对于含有两个或两个以上周期激励系统尺度效应的研究则相对较少.为深入揭示多频激励系统的不同尺度效应,本文以修正的四维蔡氏电路为例,通过引入两个频率不同的周期电流源,建立了双频1:2周期激励两尺度动力学模型.当两激励频率之间存在严格共振关系,且周期激励频率远小于系统的固有频率时,可以将两周期激励项转换为单一周期激励项的函数形式.将该单一周期激励项视为慢变参数,给出了不同激励幅值下快子系统随慢变参数变化的平衡曲线及其分岔行为的演化过程,重点考察了3种较为典型的不同外激励幅值下系统的簇发振荡行为.结合转换相图,揭示了各种簇发振荡的产生机理.系统的轨线会随慢变参数的变化,沿相应的稳定平衡曲线运动,而fold分岔会导致轨迹在不同稳定平衡曲线上的跳跃,产生相应的激发态.激发态可以用从分岔点向相应稳定平衡曲线的暂态过程来近似,其振荡幅值的变化和振荡频率也可用相应平衡点特征值的实部和虚部来描述,并进一步指出随着外激励幅值的改变,导致系统参与簇发振荡的平衡曲线分岔点越多,其相应簇发振荡吸引子的结构也越复杂.     

浮筏系统中的碰撞动力学离散模型(2):随机模型

本文建立了浮筏系统在部分冲击受损后形成的碰撞振动系统的离散动力学随机模型.在此随机模型中,浮筏系统的运动满足高斯分布,零部件的运动方程中的非线性是由于空隙单元产生,可以采用非高斯截断技术导出随机系统的平均碰撞庞加莱映射.实例分析指出,随机模型中由于增加了噪声的摄动,表现出的动力学特性比确定性模型更丰富,噪声的影响有时会增加零部件与设备之间的碰撞次数,也会抑制零部件与筏体之间的碰撞次数,噪声将增加系统动力学特性的复杂性.     

A Feature-Based Stochastic Permeability of Shale: Part 2–Predicting Field-Scale Permeability

Transport in Porous Media - In a recent numerical study, it was demonstrated that characterizing reservoir permeability in terms of rock’s quality, as observed in lab and field, is the most...     

双频1:2激励下修正蔡氏振子两尺度耦合行为

不同尺度耦合系统存在的复杂振荡及其分岔机理一直是当前国内外研究的热点课题之一. 目前相关工作大都是针对单频周期激励频域两尺度系统,而对于含有两个或两个以上周期激励系统尺度效应的研究则相对较少. 为深入揭示多频激励系统的不同尺度效应,本文以修正的四维蔡氏电路为例,通过引入两个频率不同的周期电流源,建立了双频1:2周期激励两尺度动力学模型. 当两激励频率之间存在严格共振关系,且周期激励频率远小于系统的固有频率时,可以将两周期激励项转换为单一周期激励项的函数形式. 将该单一周期激励项视为慢变参数,给出了不同激励幅值下快子系统随慢变参数变化的平衡曲线及其分岔行为的演化过程,重点考察了3种较为典型的不同外激励幅值下系统的簇发振荡行为. 结合转换相图,揭示了各种簇发振荡的产生机理. 系统的轨线会随慢变参数的变化,沿相应的稳定平衡曲线运动,而fold分岔会导致轨迹在不同稳定平衡曲线上的跳跃,产生相应的激发态. 激发态可以用从分岔点向相应稳定平衡曲线的暂态过程来近似,其振荡幅值的变化和振荡频率也可用相应平衡点特征值的实部和虚部来描述,并进一步指出随着外激励幅值的改变,导致系统参与簇发振荡的平衡曲线分岔点越多,其相应簇发振荡吸引子的结构也越复杂.      

Forced convective heat transfer from premixed flames —Part 2: Impingement heat transfer

A study of convective heat transfer from impinging flames is completed with the presentation of heat transfer rates measured in premixed methane-air flames. Unburnt gas equivalence ratios from 0.8 to 1.2 have been examined, with burner exit Reynolds numbers ranging from 2000 to 12 000. Heat fluxes measured at the stagnation point of a body of revolution and a circular cylinder demonstrate that the trends observed in measured heat flux profiles are mainly determined by variations in the mean velocity and temperature within a flame, with peak heat transfer rates occuring within or close to the flame reaction zone. Increases in Reynolds number lead to an increase in the peak heat flux attained within a flame and to a decrease in the axial extent of the flame equilibrium region. Variations in equivalence ratio away from approximately stoichiometric conditions lead to a decrease in the maximum rate of heat transfer from a flame and to a shifting of the position of maximum flux downstream. Theoretical predictions applicable to the equilibrium region of the flames are in reasonable accord with experimental data.     

RLC串联电路与微梁耦合系统1:2内共振分析

研究电阻电感电容串联电路与微梁耦合系统的非线性振动,应用拉格朗日-麦克斯韦方程,建立受静电激励RLC串联电路与微梁耦合系统的数学模型。根据非线性振动的多尺度法,得到了在内共振ω2≈2ω1的情况下的近似解,并进行数值计算,得到用椭圆函数表示的解析解。计算结果表明,在无阻尼情况下,振动和能量在两个态间相互转换,没有能量损失。     

超临界CO_2-水两相流与CO_2毛细捕获:微观孔隙模型实验与数值模拟研究

CO_2毛细捕获机制是CO_2地质封存中的关键科学问题,然而有关孔隙尺度下(微米极)超临界CO_2毛细捕获的研究较少.采用高压流体-显微镜-微观模型实验装置,开展超临界CO_2条件(8.5 MPa,45?C)下CO_2驱替水(排水)和水驱替CO_2(吸湿)实验,采用高分辨率照相机采集CO_2水两相流运动图像,并借助光学显微镜直接观测孔隙尺度下CO_2毛细捕获特征.同时,采用计算流体动力学方法对实验过程进行三维数值模拟.数值模拟不仅反映了实验过程中两相流驱替锋面的推进过程,还刻画了孔隙尺度下被捕获的CO_2液滴/团簇三维空间形态特征.最后,基于数值模拟给出了CO_2初始饱和度与残余饱和度曲线,即毛细捕获曲线,并对比分析了3种毛细捕获曲线预测模型(即Jurauld模型、Land模型和Spiteri模型)的优劣.分析表明,Jurauld模型的描述能力稍优于Land模型,Spiteri模型的描述能力较弱.由于Land模型只需单个参数,且参数具有明确的物理意义,因此在实际工程中,建议优先采用Land模型.     

C2H2-O2-Ar和C2H2-N2O-Ar直接起爆形成爆轰的临界能量

采用高压电点火进行直接起爆形成爆轰,起爆能量通过放电过程中电流的输出信号确定。首先通 过实验测定并对比C2H2-O2-Ar和C2H2-N2O-Ar等2种混合物在各种初始状态下直接起爆形成爆轰的临界 起爆能量。实验结果表明,在相同状态下C2H2-N2O-Ar混合物的临界起爆能量显著高于C2H2-O2-Ar混合 物的。进一步基于各物质爆炸特征长度和爆轰临界管径的参量关系对临界起爆能量差异性进行分析,得到了 C2H2-N2O-Ar混合气体的爆轰临界管径预测曲线,并在此基础上得出C2H2-N2O-Ar混合物爆炸特征长度 与临界管径的关系为r0=2.5dc,而C2H2-O2-Ar两者关系为r0=2dc。结果清晰地表明,使用N2O 作为氧化 剂,爆炸特征长度与爆轰临界管径之间的比例因数增大,表明该物质直接起爆形成爆轰所需的起爆源单位能 量增大,因而直接形成爆轰的临界能量相应提高。     

C2H2/Ar流量比对a-C:H涂层结构及摩擦学性能的影响

a-C:H涂层因具有高硬度、低摩擦系数及良好的化学惰性等性能,使其作为表面防护材料具有广泛的应用前景,而涂层中的H含量和sp2C/sp3C比值是影响其力学及摩擦学性能的重要因素. 本研究中采用非平衡磁控溅射技术在9Cr18钢表面制备了a-C:H涂层,对比研究了前驱体组成对不同结构含H碳膜的氢含量、微观结构、力学性能和摩擦学性能的影响. 结果表明:增大C₂H₂/Ar流量比,涂层的生长率及H含量逐渐增大,但致密性降低. 由于涂层中C-H键及致密性的变化,a-C:H涂层的硬度和弹性模量随C₂H₂/Ar流量比的增大而逐渐减小,但结合强度却先增大后降低. 当C₂H₂/Ar流量比低于4:3时,涂层表现出良好的减摩耐磨性能,当C₂H₂/Ar流量比高于4:3时,涂层的摩擦系数和磨损率出现了急增的现象. 总体而言,a-C:H涂层的摩擦系数和磨损率随C₂H₂/Ar流量比的增加呈现先增大后降低的趋势. 由于H原子的钝化作用及涂层力学性能的变化,使a-C:H涂层的磨损机制由磨粒磨损和黏着磨损变为磨粒磨损. 当C₂H₂/Ar流量比为1:1时,a-C:H涂层具有最低的摩擦系数(约为0.1)和磨损率[8.0×10?8 mm3/(N·m)],表现出最佳的力学及摩擦学性能,这种性能的变化与涂层中的H含量和sp2C/sp3C比密切相关.      

On the detachment of step-tapered doublers: Part 2—evolution of pressure loaded structures

One-dimensional edge debonding of layerwise step-tapered patches from both flat and cylindrical structures subjected to applied pressure is studied in the context of the general formulation presented in Part 1. Numerical simulations based on analytical solutions of the problems of interest are performed and intricate results presented in the form of threshold curves/delamination paths for various taper angles and support conditions. Configurations corresponding to full contact of the debonded segments, edge contact of the debonded segments and no contact of the debonded segments of the evolving composite structure are included in the model and found to significantly affect the predicted behavior of the debonding structure as does the manner of support. The degree of taper is generally found to influence the onset and characteristics of debonding in a nontrivial manner. It is seen that in many instances, the introduction of edge taper within a wide range of angles often enhances the structures propensity for debonding, rather than diminishing it, both with regard to the critical load level and with regard to the stability and extent of debond propagation.     

Fracture mechanics analysis on Smart-Cut~ technology.Part 2:Effect of bonding flaws

In Part 2 of the paper on the Smart-Cut process,the effects of bonding flaws characterized by the size andinternal pressure before and after splitting are studied byusing fracture mechanics models.It is found that the bon-ding flaws with large size are prone to cause severe devia-tion of defect growth,leading to a non-transferred area ofthin layer when splitting.In a practical Smart-Cut processwhere the internal pressure of bonding flaws is very small,large interfacial defects always promote defect grow...     

The G2 constant displacement discontinuity method – Part I: Solution of plane crack problems

A new constant displacement discontinuity element was presented in a previous paper applied initially for the numerical solution of either isolated straight cracks or for co-linear cracks of the three fundamental deformation modes I, II and III due to the special form of the solution. It was based on the strain-gradient elasticity theory in its simplest possible Grade-2 variant. The assumption of the G2 expression for the stresses has resulted to a better average stress value at the mid-point of the straight displacement discontinuity compared to the classical elasticity solution. This new element gave considerably better predictions of the stress intensity factors compared to the constant displacement discontinuity element and the linear displacement discontinuity element. Moreover, it preserved the simplicity and hence the high speed of computations. In this Part I, the solution for this element is extended for the analysis of cracks of arbitrary shape in an infinite plane isotropic elastic body and it is validated against three known analytical solutions.     

2:1内共振条件下变转速预变形叶片的非线性动力学响应

在工程实际中,涡轮机叶片的转速在很多应用场景下不是一个定常值,比如发动机在启动、变速、停机等工况下,转子输入与输出功率失衡,伴随产生扭振,产生速度脉冲. 另外,由于服役环境、安装误差等因素会引起叶片在所难免的预变形. 本文主要研究预变形叶片,在变转速条件下的非线性动力学行为. 考虑叶片转速由一定常转速和一简谐变化的微小扰动叠加而成. 应用拉格朗日原理得到变转速叶片的动力学控制方程,并采用假设模态法将偏微分方程转为常微分方程,通过引入无量纲,使方程更具有一般性. 运用多尺度方法求解了该参激振动系统,得到了在 2:1 内共振情形下的平均方程,进而获得系统的稳态响应. 详细研究温度梯度、阻尼以及转速扰动幅值等系统参数对叶片动力学响应的影响规律,同时考察了立方项在 2:1 内共振下对方程的影响. 对原动力方程进行正向、反向扫频积分来观察其跳跃现象,并对解析解进行验证. 结果发现参数的变化对叶片均有不同程度影响,在 2:1 内共振下立方项对系统响应的影响很小,解析解与数值解吻合很好.      

The G2 constant displacement discontinuity method – Part II: Solution of half-plane crack problems

In the previous Part I, the G2 constant displacement discontinuity element was presented that is dedicated for the fast (only one collocation point per element), stable and accurate numerical solution of modes I, II and III cracks of arbitrary shape in an infinite plane isotropic elastic body. Herein, another G2 constant displacement discontinuity element is constructed for the case of cracks in the half-plane. It is successfully validated against existing semi-analytical and numerical solutions of crack problems in the half-plane.