A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics

This paper deals with the computation of Hopf bifurcation points in fluid mechanics. This computation is done by coupling a bifurcation indicator proposed recently (Cadou et al., 2006) [1] and a direct method (Jackson, 1987; Jepson, 1981) [2] and [3] which consists in solving an augmented system whose solutions are Hopf bifurcation points. The bifurcation indicator gives initial critical values (Reynolds number, Strouhal frequency) for the direct method iterations. Some classical numerical examples from fluid mechanics, in two dimensions, are studied to demonstrate the efficiency and the reliability of such an algorithm.     

Universal instability modes in internal and external flows

Two prototypical external and internal flows have been studied which display linear temporal instability followed by nonlinear saturation taking the flows to a new equilibrium state. Direct simulation results are obtained using a specific formulation and numerical methods with very high accuracy. These results are analyzed via proper orthogonal decomposition (POD), which reveal similar modes for flow past a circular cylinder and flow inside a lid-driven cavity, indicating universality of such modes. Unlike many other efforts on reduced order modeling via POD, here the emphasis has been on understanding the physical aspect of the flow instability which requires very high accuracy of the simulation. Then, the obtained POD modes are related to the instability modes (in the classical sense of defining the latter) and new generic types of instability modes are identified in the studied external and internal flows. These new modes have been reported for flow past a circular cylinder [Sengupta TK, Singh N, Suman VK. Dynamical system approach to instability of flow past a circular cylinder. J Fluid Mech 2010;656:82–115] which help one in understanding the instability sequence and the relative importance of these modes in the flow evolution starting from an impulsive start. Present comparative study, furthermore, reveals universality of such instability modes by showing their presence for the flow inside a lid-driven cavity as well. Despite seeming dissimilarities between these two flows, similarities between the instability portrait of these two flows suggest universality of such modes. From the equilibrium amplitude of vorticity time-series, we establish the presence of multiple modes and multiple bifurcation sequences for these flows in parameter space. Existing theory due to Landau and Stuart that considers only a single dominant mode and its self-interaction does not explain all these features. We invoke a multi-modal interaction model in the cited reference above, termed as Landau–Stuart–Eckhaus (LSE) equation in recognition of Eckhaus’ work in modifying the classical Stuart–Landau equation. We also show that the new instability modes do not follow either the classical Stuart–Landau or the newly proposed LSE model equations and for this reason we call these as anomalous modes. Two specific classes of anomalous modes are identified and classified in the present work. Empirical expressions for the evolution of these anomalous modes are presented and their unambiguous role during instabilities is discussed.     

Stability analysis in spanwise-periodic double-sided lid-driven cavity flows with complex cross-sectional profiles

Three-dimensional linear instability analyses are presented of steady two-dimensional laminar flows in the lid-driven cavity defined by [15] and further analyzed in the present volume [1], as well as in a derivative of the same geometry. It is shown that in both of the geometries considered three-dimensional BiGlobal instability leads to deviation of the flow from the two-dimensional solution; the analysis results are used to define low- and high-Reynolds number solutions by reference to the flow physics. Critical conditions for linear global instability and neutral loops are presented in both geometries.     

外腔半导体激光器在谐振式光学陀螺中的应用研究

陀螺是一种高精度的惯性传感器件,作为第二代陀螺的谐振式光纤陀螺,在理论上精度高于第一代干涉型光学陀螺。但是谐振式光学陀螺对光源有一个苛刻的要求,需要光源的调谐范围要宽,线宽要窄。一般达到要求的光源体积都很大,不利于谐振陀螺的小型化和成品化。基于谐振式陀螺的检测原理,提出了一种基于外腔半导体激光器的谐振陀螺控制方案,对光源的调制信号进行了分析,提出了温度恒定,控制电流的控制方案。并对外腔激光器电流特性和谐振陀螺入谷信号进行了分析。     

牙齿窝洞预备标准化数字教学评估研究

牙齿窝洞预备技术的训练是牙科临床教学中的一个重要环节.本文介绍了牙齿窝洞预备标准化数字教学评估的关键技术.通过对学生预备牙体进行非接触式三维扫描,获取牙体颌面的点云数据,以此实现了基于点云的牙体颌面窝洞形态的重建.通过比较标准形态与测试形态在窝洞轮廓线和窝洞深度上的不同,实现了牙齿窝洞预备结果的数字化评估.在此基础上研发了系统原型,该系统的快速评估过程大幅提高了教师的工作效率,同时提高了学生的口腔实践技能技术.     

柔性夹紧件的结构设计与有限元分析

为了实现微靶装配体的自动装配并保证装配精度,提出了一种通过弹性变形与半圆柱靶腔实现柔性夹持与自定心的装置.该装置的核心部件是柔性夹紧件,由橡胶材料加工而成,用于对内直径仅为800～1 000μm、壁厚约25～75μm的半圆柱靶腔的夹持.利用有限元软件对上述柔性夹紧件的结构设计是否合理进行分析和验证,通过反复的设计和修改以及软件分析和仿真验证,最终确定了一种较为合理的夹紧件结构设计方案.该设计方案不仅能满足对夹持半圆柱靶腔所提出的大部分要求,而且可以实现对其他类似形状的微小、薄壁的圆柱形物体的夹持.     

球形孔洞膨胀动态问题的弹性-损伤力学分析

研究了材料还没有出现塑性变形、仅含弹性区和损伤区的球形孔洞动态扩展问题．首先通过对弹性区的研究以及初始损伤分析获得弹性区的场量分布,并给出弹性／损伤区交界处的边界连续条件;然后在自相似假设条件下,推导出动态扩展时损伤区需满足的控制方程;最后通过打靶法进行数值求解．数值分析表明,许多材料参数如ν、n、m都对弹性区和损伤区的场量分布有影响．     

一种快速三角形电源地平面谐振腔模型

针对等腰直角三角形平面模型效率低和精度差的问题,在双频点近似算法的基础上,提出了一种快速的Spice兼容等腰直角三角形平面谐振腔模型.与电感近似的等腰直角三角形平面模型相比,提出的模型使用最少的谐振腔基本模式与单节的高阶修正电路,不仅提高了等腰直角三角形电源地平面的仿真效率,而且改善了模型精度.仿真结果表明,电感近似模型在分类关键因子为2时,最大误差约为10%;提出的模型在分类关键因子为1.3时,最大误差约为1%,其仿真时间仅为电感近似模型的26%,验证了该模型在提高等腰直角三角形电源地平面的仿真效率和改善模型精度上的有效性.     

基于光纤连接的腔系统实现两比特离散量子傅立叶变换

提出了在外加经典场驱动的情况下,利用光纤连接的2个腔系统执行两比特离散量子傅立叶变换的方案.该方案通过发送2个原子交替通过一系列经典场和腔场来实现,而且该两比特方案可推广至N比特离散量子傅立叶变换.     

共轨式喷油器容积腔压力波动仿真分析

电控喷油器是柴油机共轨系统的核心部件,喷油器容积腔内压力的波动直接影响燃油喷射系统稳定性.研究在对喷油器基本结构和工作原理分析的基础上,运用仿真软件研究容积腔不同容积下其内部压力波动曲线,探讨了喷油器容积腔大小对共轨喷油系统的影响,为共轨喷油器的设计和研发提供依据.