三氧化二铝液滴对心碰撞直接数值模拟

为研究固体火箭发动机内三氧化二铝液滴碰撞的物理规律及结果预测模型,针对两个相同尺寸的三氧化二铝液滴对心碰撞,开展了直接数值模拟.首先进行了正十四烷液滴在氮气环境下的对心碰撞数值研究,数值与实验结果基本一致,验证了计算方法的可行性及准确性.针对三氧化二铝液滴开展了6 MPa压强下不同Weber数的对心碰撞数值研究,计算Weber数范围为10~200,Ohnesorge数为0.036 4;获得了反弹、大变形后聚合和自反分离3种结果类型,反弹与大变形后聚合的临界分离Weber数为26,大变形后聚合与自反分离的临界分离Weber数为44.根据临界Weber数对其他流体液滴碰撞模型进行修正,可以获得三氧化二铝液滴的碰撞模型.     

低Reynolds数下双层液膜的空间-时间不稳定性研究

分析了黏性分层双液体薄膜在空间-时间发展扰动下不稳定的触发状况．已有的研究结果给出了在零Reynolds数极限情况下,流动在时间发展模式下不稳定的论断,而这里的空间-时间发展理论却表明,在同一极限下,液膜的流动其实是中性稳定的．该文分析了这种差异及造成差异的原因．通过对能量方程的研究还找到了一种在时间发展模式下没有发现的新不稳定机制,并将这种机制与扰动对流现象的非Galilei不变性相关联．     

三维复Ginzburg-Landau方程的整体解的存在惟一性

在三维空间中研究带2σ次非线性项的复值Ginzburg—Landau方程(CGL) ut=ρu (1 iγ)△u-(1 iμ)|u|^2σu,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体解的存在性和惟一性．     

热毛细振荡对流的产生机理

本文用有限元方法定量分析讨论了液体桥中的温度分布。当液桥两端温差△T增大到一定值时,液桥中会出现温度梯度与重力方向平行且同向的流动区域。随着温差△T值的增大就可能产生浮力不稳定,形成热毛细振荡对流。根据地面实验所得发生振荡对流的临界Marangoni数,给出了微重力条件下临界Marangoni数的分布。分析表明,较小的典型尺度和较低的重力环境会延迟热毛细振荡对流的发生。     

具非局部源的非线性高阶抛物型方程解的全局存在性与非全局存在性（英文）

本文考虑一类具非局部源的高阶抛物型方程u_t=-(-Δ)^mu+(∫_Rⁿ|u|^1+σdy)⁽(p-1)/(1+σ))|u|^r的Cauchy问题.近年来,我们已给出这一方程的Fujita临界指标p_c=1+((2m-n(r-1))(1+σ))/(nσ),即当1 c时,对任意初值,解都在有限时刻发生爆破;当p> p_c时,存在非全局解也存在全局解,这取决于初值的大小.本文进一步确定了这一方程的第二临界指标a^*=(2m+(n(p-1))/(1+σ))/(p+r-2),用于在p>p_c这一全局解与非全局解的共存区域内鉴别初值的大小.我们发现:(1)与具局部源|u|^p的高阶抛物型方程的第二临界指标a^*=2/(p-m)不同的是,这里与空间维数n有关;(2)非局部源中参数σ的增大有...     

对流-扩散型问题Bubble-稳定有限元分析

本文针对形如σu α·u-kΔu=f对流—扩散型的模型问题,发展耦合局部bubble-函数的有限元方法,我们就α=0和σ=0两种情形证明了方法的与“影响因素”σ和pedlet-数无关稳定性及全局最佳收敛阶。     

基于正弦余弦算法的柯布-道格拉斯生产函数模型参数估计

研究了柯布-道格拉斯生产函数模型,建立了以误差为目标的最小二乘优化模型,采用正弦余弦算法确定了相关参数.算法在种群更新过程中分别使用了正弦和余弦函数,算法先进行全局探索再进行局部开发.最后通过一个算例,验证了正弦余弦算法的有效性.     

计及Hall和离子滑移电流的旋转流体在与时间相关初值条件下的MHDCouette流动

考虑Hall和离子滑移电流的影响,在旋转系统中研究导电流体非稳定的MHD Couette流动．在小数值磁场Reynolds数假定下,推导出基本的控制方程,使用著名的Laplace变换技术,数值地求解该基本方程．分两种情况:磁场相对于流体或者移动平板固定时,得到速度和表面摩擦力统一的闭式表达式．用图形讨论了问题的不同参数,对速度和表面摩擦力的影响．所得结果显示,主流速度u和次生速度v随着Hall电流而增大．离子滑移电流的增大,也会导致主流速度u的增大,但会使次生速度v减小．还给出了旋转、Hall和离子滑移参数的综合影响,确定了次生运动对流体流动的贡献．     

E1οEd型距离正则图及 Q-多项式的性质

设Г是一个直径d ≥ 3的非二部距离正则图,其特征值θ0＞θ1＞…＞θ<,d.设θ1 ∈{θ1,θd),θd,是θ1在{θ1,θd}中的余.又设Г是具有性质E1οEd=|X|-1＞(qd-11dEd-1 qd1dEd)的E1○Ed型距离正则图,σ0,σ1,…,σd,ρ0,ρ1,…,ρd和β0,β1,…,βd分别是关于θ1',θd和θd-1'的余弦序列.利用上述余弦序列,给出了Г关于θ1或θd是 Q-多项式的充要条件.     

可渗透收缩薄膜引起的三维不稳定边界层流动

研究可渗透收缩薄膜上的不稳定粘性流动．通过相似变换得到相似方程．在不同的不稳定参数、质量吸入参数、收缩参数、Prandtl数下,数值地求解相似方程,得到速度和温度的分布,以及表面摩擦因数和Nusselt数等．结果发现,与不稳定的伸展薄膜不同,在质量吸入参数和不稳定参数的某一范围内,可渗透收缩薄膜上的不稳定流动存在双重解．     

Asymptotic Analysis and Stability of Inviscid Liquid Sheets

Asymptotic methods are employed to determine the leading-order equations that govern the fluid dynamics of slender, and thin and slender, inviscid, irrotational, planar liquid sheets subject to pressure differences and gravity. Two flow regimes have been identified depending on the Weber number, and analytical solutions to the steady state equations are provided. Linear stability studies indicate that the sinuous mode corresponds to Weber numbers on the order of unity, while the varicose mode is associated with small Weber numbers. For small Weber numbers, the nonlinear stability of liquid sheets is determined analytically in terms of elliptic integrals of the first and second kinds. It is also shown that the sinuous mode of thin and slender liquid sheets is identical to the same mode for slender sheets.     

Linear response of a viscous liquid sheet to external pressure perturbation. Long wave approximations

This paper is concerned with the linear signal response analysis of a thin viscous liquid sheet which is at rest in an appropriate frame of reference and in contact with passive external media, and on which localized external pressures act from the passive media as sources of perturbation.The frame of the analysis is provided by general formulae for the response signals of the sheet in the two excitation modes, sinuous and varicose, which result as the solution of the appropriate fluid dynamic initial-boundary value problems by the Fourier-Laplace transform technique. These formulae display how the signals depend on the nature of the perturbation and on the spectrum of the (linear) eigenmodes of the sheet.     

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a “torpedo” shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour.     

热传导对气-液射流界面不稳定性的作用机理研究

研究了平面分层气-液射流在非线性温度分布条件下的界面不稳定性性质.考虑了气体的可压缩性、液体的粘性、以及气体热导率和密度随温度变化等事实.并应用正则模态方法将问题转化为四阶变系数常微分方程,用数值积分和多重打靶法对模型的空间模式进行了计算,研究了不稳定模态随各物理参量的变化趋势.计算表明模型所体现的不稳定性特征与其它模型的计算结果是一致的.同时计算还得出气体和液体的温差越小、雷诺数越大、热导率变大均将有利于液体射流有效雾化的结果.该结论与HJE.Co.Inc(Glens Falls,NY,USA)的实验数据是定性吻合的.     

Temporal analysis of a power-law liquid sheet in the presence of acoustic oscillations

The instability of a non-Newtonian liquid sheet in the presence of acoustic oscillations is investigated theoretically. The power-law model is used to describe the viscosity of the non-Newtonian liquid. The corresponding dispersion relation is obtained by linear analysis. The effects of the mean velocity of the gas, the oscillation amplitude, the oscillation frequency, and the gas density on the instability of the power-law liquid sheet are studied. The results show that the shear-thickening liquid sheet is more unstable than Newtonian and shear-thinning liquid sheets when the effects of acoustic oscillations are considered. In particular, a second unstable region appears on the shear-thickening liquid sheet at a low oscillation frequency. Especially, for the shear-thinning liquid sheet, there is a second unstable region in the dispersion curve at a high mean gas velocity. A third unstable region appears on the shear-thinning liquid sheet at a high gas density in the presence of acoustic oscillations. The unstable range of the Newtonian liquid is always the widest among these liquids.     

Zigzag and Breakup Instabilities of Stripes and Rings in the Two-Dimensional Gray–Scott Model

Two different types of instabilities of equilibrium stripe and ring solutions are studied for the singularly perturbed two‐component Gray–Scott (GS) model in a two‐dimensional domain. The analysis is performed in the semi‐strong interaction limit where the ratio O(?^?2) of the two diffusion coefficients is asymptotically large. For ?→ 0 , an equilibrium stripe solution is constructed where the singularly perturbed component concentrates along the mid‐line of a rectangular domain. An equilibrium ring solution occurs when this component concentrates on some circle that lies concentrically within a circular cylindrical domain. For both the stripe and the ring, the spectrum of the linearized problem is studied with respect to transverse (zigzag) and varicose (breakup) instabilities. Zigzag instabilities are associated with eigenvalues that are asymptotically small as ?→ 0 . Breakup instabilities, associated with eigenvalues that are O(1) as ?→ 0 , are shown to lead to the disintegration of a stripe or a ring into spots. For both the stripe and the ring, a combination of asymptotic and numerical methods are used to determine precise instability bands of wavenumbers for both types of instabilities. The instability bands depend on the relative magnitude, with respect to ?, of a nondimensional feed‐rate parameter A of the GS model. Both the high feed‐rate regime A=O(1) , where self‐replication phenomena occurs, and the intermediate regime O(?^1/2) ?A?O(1) are studied. In both regimes, it is shown that the instability bands for zigzag and breakup instabilities overlap, but that a zigzag instability is always accompanied by a breakup instability. The stability results are confirmed by full numerical simulations. Finally, in the weak interaction regime, where both components of the GS model are singularly perturbed, it is shown from a numerical computation of an eigenvalue problem that there is a parameter set where a zigzag instability can occur with no breakup instability. From full‐scale numerical computations of the GS, it is shown that this instability leads to a large‐scale labyrinthine pattern.     

Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk

The dynamics of a circular cylindrical shell carrying a rigid disk on the top and clamped at the base is investigated. The Sanders–Koiter theory is considered to develop a nonlinear analytical model for moderately large shell vibration. A reduced order dynamical system is obtained using Lagrange equations: radial and in-plane displacement fields are expanded by using trial functions that respect the geometric boundary conditions.The theoretical model is compared with experiments and with a finite element model developed with commercial software: comparisons are carried out on linear dynamics.The dynamic stability of the system is studied, when a periodic vertical motion of the base is imposed. Both a perturbation approach and a direct numerical technique are used. The perturbation method allows to obtain instability boundaries by means of elementary formulae; the numerical approach allows to perform a complete analysis of the linear and nonlinear response.     

Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer

For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation that adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet is given here. Spatial evolution is considered for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through a nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.     

Nonlinear simulations of vesicle wrinkling

In this paper, we study nonlinear wrinkling dynamics of a vesicle in an extensional flow. Motivated by the recent experiments and linear theory on wrinkles of a quasi‐spherical membrane, we are interested in examining the linear theory and exploring wrinkling dynamics in a nonlinear regime. We focus on a quasi‐circular vesicle in two dimensions and show that the linear analytical results are qualitatively independent of the number of dimensions. Hence, the two‐dimensional studies can provide insights into the full three‐dimensional problem. We develop a spectral accurate boundary integral method to simulate the nonlinear evolution of surface tension and the nonlinear interactions between flow and membrane morphology. We demonstrate that for a quasi‐circular vesicle, the linear theory well predicts the characteristic wavenumber during the wrinkling dynamics. Nonlinear results of an elongated vesicle show that there exist dumbbell‐like stationary shapes in weak flows. For strong flows, wrinkles with pronounced amplitudes will form during the evolution. As far as the shape transition is concerned, our simulations are able to capture the main features of wrinkles observed in the experiments. Interestingly, numerical results reveal that, in addition to wrinkling, asymmetric rotation can occur for slightly tilted vesicles. The mathematical theory and numerical results are expected to lead to a better understanding of related problems in biology such as cell wrinkling. Copyright © 2013 John Wiley & Sons, Ltd.     

弹性地基上正交各向异性变厚度圆薄板的大挠度问题

本文推出了均布载荷下弹性基地上的正交各向异性变厚度圆薄板大挠度问题的基本方程。利用修正迭代法获得了该问题的二阶近似解。