双参数曲面的泡泡网格化方法

为将双参数曲面离散成高质量的网格,首先在参数域内利用各向异性的非均匀泡泡布点方法优化布点,然后用各向异性Delaunay三角化方法将参数域网格化,最后用映射法得到双参数曲面的离散网格.参数域中的节点由二阶黎曼度量矩阵控制,该度量矩阵由三维曲面的网格度量矩阵和曲面参数方程的梯度计算得到.数值算例表明,泡泡布点法在参数域上能生成满足度量矩阵要求的节点集,将节点连接成网格并投影回曲面,所得曲面网格具有很高的质量.     

泡泡布点方法及其并行性

针对无网格和有限元方法中的布点需求,借鉴分子动力学方法和泡泡网格化方法的思想和处理技术,提出一种单纯的布点方法--泡泡布点方法.将区域内的点看作有相互作用力的泡泡,通过动态模拟得到高质量的点集,模拟中不需要网格连接.算例显示,生成的均匀点集和非均匀点集都具有很好的结构和渐进性,并对复杂区域具有很好的适应性.同时由于相互作用力的局部性,该布点方法类似于短程作用的分子动力学模拟,拥有潜在的并行性.通过初步的并行算例,验证了其并行化的可行性.     

自适应结构网格上扩散方程隐式时间积分算法及其应用

提出一种自适应结构网格(SAMR)上求解扩散方程的隐式时间积分算法.该算法从粗网格到细网格逐层进行时间积分,通过多层迭代同步校正保证粗细界面的流连续和计算区域的扩散平衡.分析算法复杂度,并给出评估算法低复杂度的准则.典型算例表明,相对于一致加密情形,本文算法能够在保持相同计算精度的前提下,大幅度降低网格规模和计算量,且具有低复杂度.将算法应用于辐射流体力学数值模拟中非线性扩散方程组求解,相对于一致加密网格,SAMR计算将计算量下降一个量级以上,计算效率提高33.2倍.     

温度体动网格模型中控制参数的研究

采用调整导热系数和源项分布的方式,对温度体动网格模型所生成的网格品质进行控制.温度体动网格模型将运动边界的位移虚拟为求解域的温度边界条件,以流体能量方程或固体导热方程作为控制方程,通过选取不同的导热系数或源项分布可以得到适合不同求解问题需要的温度分布,并将求解得到的网格节点的温度作为其动态位移量.采用温度体动网格模型计算平动、三维旋转运动、柔性体运动等流固耦合计算中可能涉及的动网格算例.结果表明,在计算效率和生成网格的品质方面,与已有的动态网格生成方法相比,具有较大的优势,可以有效解决流固耦合数值模拟中存在的动态网格生成难题.     

结合前沿推进的Delaunay三角化网格生成及应用

采用一种新的混合网格生成方法,生成复杂区域的非结构化网格.结合前沿推进法和Delaunay三角化两种非结构网格生成方法的特点,在边界处采用前沿推进法进行三角形初始网格的生成,在边界区域内部采用Delaunay三角化方法自动生成内部节点.分析表明,该算法简化网格生成过程,能够快速有效地生成非结构化网格.在计算时间以及网格的均匀性方面与其他方法相比具有一定的优势.最后,用混合网格生成方法生成方柱绕流的计算域网格,并运用基于特征线方程的分离算法进行流场计算.     

流动/运动松耦合与紧耦合计算方法及稳定性分析

为了更加精确地模拟流动/运动耦合问题, 建立了耦合动态混合网格生成非定常流场计算和六自由度运动方程求解的一体化计算方法, 并在统一框架内同时实现了松耦合与紧耦合方法.通过圆柱涡致自激振荡(vortex induced vibration, VIV)的模拟, 对不同时间精度的松耦合和紧耦合算法的优劣及适用范围进行了评估和分析; 通过引入附加质量的概念, 对耦合算法的稳定性进行了理论分析.研究表明:在流体的密度与物体的密度接近时, 松耦合方法是不稳定的, 必须采用紧耦合方法.最后利用耦合算法对二维鱼体的自主游动和钝锥三自由度自由飞过程进行了数值模拟, 证实了理论分析的结论.      

SPH后处理研究

提出一套相对完整的光滑粒子流体动力学(SPH)后处理方法.凸区域和严重变形的非凸区域上的SPH计算结果都可用该方法处理.首先,对SPH粒子集进行Delaunay三角化,可得到由粒子作为节点的三角单元集;根据每个单元中三个节点是否彼此为粒子作用对,决定是否将该单元从单元集中删除.将保留下的单元作为有限单元并利用它们节点上的函数值,根据有限元插值方法即可得单元内部任何一点的函数值.根据该方法,可提取介质的自由表面.数值算例表明方法可行.对含固体壁面、严重粒子飞溅、多重介质互相作用的情况,提出相应对策;为SPH以至其它无网格方法形成较通用的后处理软件提供可行的途径.     

一种含运动固壁超声速流动的Descartes网格算法

提出一种Descartes网格算法,用于数值求解含任意复杂及运动固壁的超声速流动问题.采用位标集函数确定和跟踪流-固界面.引入虚网格技术处理流-固边界条件,并沿法向和切向分别进行计算.该算法简单、稳健,可与高阶有限差分格式并用.选取一组一维/二维静止或运动物体绕流算例,验证其有效性.     

RKDG有限元法求解一维拉格朗日形式的Euler方程

描述一种新的求解Euler方程的拉格朗日格式,该格式用Runge-Kutta Discontinuous Galerkin(RKDG)方法在拉格朗日坐标系求解Euler方程,剖分网格随流体运动.新格式不仅保证流体的质量、动量和能量守恒,而且能够在时间和空间上同时达到二阶精度.数值算例表明在一维情况,随着拉氏网格的移动和改变,格式在时间和空间上仍保持二阶精度,并且没有数值震荡.     

一类非线性偏微分方程初边值问题的逐层优化算法

针对非线性偏微分方程初边值问题,基于差分法和动态设计变量优化算法原理,以时间计算层上离散节点的未知函数值为设计变量,以离散节点的差分方程组构造程式化的目标函数,提出了离散节点处未知函数值的逐层高精度优化算法.编制通用程序求解具体典型算例.并通过与解析解对比,表明了求解方法的正确性和有效性,为广泛的工程应用提供条件.     

Interaction of a bubble and a bubble cluster in an ultrasonic field

Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.     

Spatial-temporal dynamics of cavitation bubble clouds in 1.2 MHz focused ultrasound field

Cavitation bubbles have been recognized as being essential to many applications of ultrasound. Temporal evolution and spatial distribution of cavitation bubble clouds induced by a focused ultrasound transducer of 1.2 MHz center frequency are investigated by high-speed photography. It is revealed that at a total acoustic power of 72 W the cavitation bubble cloud first emerges in the focal region where cavitation bubbles are observed to generate, grow, merge and collapse during the initial 600 μs. The bubble cloud then grows upward to the post-focal region, and finally becomes visible in the pre-focal region. The structure of the final bubble cloud is characterized by regional distribution of cavitation bubbles in the ultrasound field. The cavitation bubble cloud structure remains stable when the acoustic power is increased from 25 W to 107 W, but it changes to a more violent form when the acoustic power is further increased to 175 W.     

Flow of an electrically conducting bubble liquid in the field of an electromagnetic force

Physical processes accompanying the flow of a conducting bubble liquid in crossed electric and magnetic fields are considered. Based on the general equations of mechanics of multiphase media, we develop a one-dimensional model of the flow of and heat exchange in a compressible bubble liquid when the phases are not in thermal and velocity equilibrium. The model is numerically investigated. It is demonstrated that, when the bubble liquid flows along the electromagnetic force vector, the bubbles lag behind the carrying flow and are compressed and warmed up. This causes oscillations of the bubble volume, as well as oscillations of the parameters of both the disperse and carrying phase. In particular, the compression of the bubbles reduces the volumetric gas content, as well as increases the effective conductivity of the flow and the electromagnetic force in the downstream direction. This sets conditions for crisis of the bubble flow when the electromagnetic force expels the bubbles against the main stream. On the basis of the solutions obtained, the efficiency of a gas compressor is calculated.     

Numerical simulations of acoustic cavitation noise with the temporal fluctuation in the number of bubbles

Numerical simulations of cavitation noise have been performed under the experimental conditions reported by Ashokkumar et al. (2007) [26]. The results of numerical simulations have indicated that the temporal fluctuation in the number of bubbles results in the broad-band noise. “Transient” cavitation bubbles, which disintegrate into daughter bubbles mostly in a few acoustic cycles, generate the broad-band noise as their short lifetimes cause the temporal fluctuation in the number of bubbles. Not only active bubbles in light emission (sonoluminescence) and chemical reactions but also inactive bubbles generate the broad-band noise. On the other hand, “stable” cavitation bubbles do not generate the broad-band noise. The weaker broad-band noise from a low-concentration surfactant solution compared to that from pure water observed experimentally by Ashokkumar et al. is caused by the fact that most bubbles are shape stable in a low-concentration surfactant solution due to the smaller ambient radii than those in pure water. For a relatively high number density of bubbles, the bubble–bubble interaction intensifies the broad-band noise. Harmonics in cavitation noise are generated by both “stable” and “transient” cavitation bubbles which pulsate nonlinearly with the period of ultrasound.     

氦离子低温预辐照对不锈钢中氦泡生长抑制作用的Monte Carlo模拟研究

实验中已发现氦离子低温预辐照不锈钢材料能有效抑制高温辐照阶段的氦泡生长,但这一结果一直缺少理论解释.基于持续注入粒子的三维格子气模型,采用Monte Carlo模拟方法研究了不同温度模式对氦泡生长行为的影响.研究发现,计算结果能很好地再现氦离子低温预注入抑制高温氦泡生长的实验现象,其原理为低温预注入时材料中形成了较高数密度的小氦泡,由于氦泡数量较多从而限制了氦泡平均尺寸的增大.     

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.     

The effects of coupling and bubble size on the dynamical-systems behaviour of a small cluster of microbubbles

This study endeavours to apply a theoretical model for predicting the dynamics of a bubble cluster of various sizes, within which each bubble may assume different initial conditions from other bubbles in the cluster. The resulting system of coupled Keller-Miksis-Parlitz equations are solved numerically, and the effects of coupling and bubble size on bubble cluster dynamics are examined for a given set of ultrasound parameters. It has been found that the effects of coupling are significant, and a bubble cluster's bifurcation characteristics and route to chaos can be altered by inter-bubble interactions. This gives rise to the possibility of suppressing the chaotic oscillations of microbubbles by varying bubble cluster size. Small equilibrium radii bubbles have little influence on the dynamics of neighbouring bubbles in a cluster via coupling. Furthermore, a bubble system consisting of smaller-sized bubbles transitions from order to chaos at lower driving pressure amplitudes.     

无阀微泵腔内气泡对周期驱动压力的影响

气泡的存在使无阀微泵的工作性能和使用寿命大大降低, 甚至无法正常工作. 为了合理地预测无阀微泵腔内气泡对周期驱动压力的影响, 给出了用来描述收缩管/扩张管型无阀压电微泵的数学模型, 包括泵腔体积变化、连续性方程、流体有效体积弹性模量以及锥管阻力系数的计算. 同时, 分析了腔内不同气泡体积对无阀微泵周期驱动压力的影响, 并对两个气泡进入无阀微泵泵腔时压力脉动过程进行了仿真和试验研究. 通过仿真结果与试验数据的比较表明, 所提出的存在气泡时无阀微泵数学模型及仿真方法是合理的. 关键词： 无阀微泵 气泡 压力脉动