奇妙的“波浪云”——浅谈开尔文-亥姆霍兹不稳定性现象

开尔文-亥姆霍兹不稳定性是两种流体作平行于水平界面的相对运动时的流动稳定性问题之一. 文章从自然现象\"波浪云\" 谈起,介绍了开尔文-亥姆霍兹不稳定性的理论定义、该不稳定性现象形成发展的过程及其流动可视化;并简单阐述了实验室和自然界中其他\"类开尔文-亥姆霍兹不稳定\" 现象,重点介绍了梵高名画《星月夜》和笔者在从事沟槽壁面湍流场可视化实验中观察到的一种展向\"类开尔文-亥姆霍兹涡棍\" 结构,指出它们的形成及发展演化是沟槽湍流减阻达到最优之后,减阻效应趋弱直至增阻的原因.     

纵向沟槽壁面湍流边界层内类开尔文-亥姆霍兹涡结构的流动显示

纵向沟槽壁面的湍流边界层,当沟槽的脊-脊内尺度无量纲展向间距s⁺ 在一定范围内,与光滑壁面湍流边界层相比,具有减阻效应;并在s⁺ 约为17 个黏性长度单位时减阻效果达到最优,之后其减阻趋弱,直至增阻;其原因可能是沟槽壁面湍流边界层由于“开尔文-亥姆霍兹” 不稳定性而产生的一种“类开尔文-亥姆霍兹”展向涡结构. 实验采用烟雾流动显示技术,首次在风洞中显示了这种“类开尔文-亥姆霍兹” 展向涡结构,确认了其存在性,并在概念上简单勾勒了其结构模型.     

比例边界等几何分析方法Ⅰ:波导本征问题

提出比例边界等几何方法 (scaled boundary isogeometric analysis, SBIGA), 并用以求解波导本征值问题. 在比例边界等几何坐标变换的基础上, 利用加权余量法将控制偏微分方程进行离散处理, 半弱化为关于边界控制点变量的二阶常微分方程, 即 TE 波或 TM 波波导的比例边界等几何分析的频域方程以及波导动刚度方程, 同时利用连分式求解波导动刚度矩阵. 通过引入辅助变量进一步得出波导本征方程. 该方法只需在求解域的边界上进行等几何离散, 使问题降低一维, 计算工作量大为节约, 并且由于边界的等几何离散, 使得解的精度更高, 进一步节省求解自由度. 以矩形和 L 形波导的本征问题分析为例, 通过与解析解和其他数值方法比较, 结果表明该方法具有精度高、计算工作量小的优点.     

带冷却气流的亥姆霍兹共振器的声类比模型

亥姆霍兹共振器(HR)作为典型的被动消声装置,常被安装于航空发动机和燃气轮机的燃烧室上用以吸收噪声进而抑制燃烧热声振荡.在实际应用中,为防止燃烧室内高温气体损坏HR,常引入冷却气流从HR的背部空腔通过其颈部流入燃烧室,以保护HR.该冷却气流的温度一般显著低于燃烧室内的燃气温度.将这样的HR安装到燃烧室上时,该温差可能影...     

提琴声中的摩擦原理

介绍了提琴的音乐声中有关摩擦的学问,内容涉及琴弦振动中的亥姆霍兹运动与提琴音质的关系,引发琴弦振动的摩擦粘滑现象、以及粘滑的发生机理等. 想要说明在日常生活乃至音乐艺术中的许多现象背后都有着科学的规律,而对这些现象的科学研究将会影响和改变我们的生活.     

能量守恒定律的发现------力学史杂谈之二十

能量守恒定律的定型,是经过一个漫长的过程的. 简述了从活力的提出、活力死力的论战、热量和温度概念的区分、到能量概念的形成,最后简述了迈尔、焦耳和亥姆霍兹对能量守恒定律的最终表述和确立的过程.     

橡胶复合靶板抗射流侵彻的理论和实验研究

根据射流侵彻橡胶复合靶板后射流变形情况,将橡胶复合靶板抗射流侵彻过程分为4个阶段。基于应力波传播理论和开尔文-亥姆霍兹不稳定性对橡胶复合靶板抗射流侵彻过程进行了理论分析,得到射流失稳时射流的速度区间及橡胶复合靶板对射流的干扰频率,并分析了射流侵彻橡胶复合靶板后的剩余侵彻能力。分析了橡胶夹层厚度变化和橡胶复合靶板倾角对橡胶复合靶板抗射流干扰的影响,得到最佳橡胶夹层厚度和倾角,并通过实验对理论结果进行了验证。结果表明,开尔文-亥姆霍兹不稳定性能很好地分析橡胶复合靶板对射流的干扰作用。橡胶复合靶板在倾角为60、橡胶夹层厚度为3~3.5mm 时具有最佳防护性能。     

Applications of active acoustics in particle technology

Earlier work by the authors in which active sound pressure signals and impulsive pressure disturbances were used to measure flow rates in gas solid systems was briefly reviewed. Work in progress with an emerging technology in which Helmholtz resonance is applied to the measurement of volume is outlined.     

Constraint-induced restriction and extension operators with applications

The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.     

A novel twice-interpolation finite element method for solid mechanics problems

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.     

A NEW HYBRID QUADRILATERAL FINITE ELEMENT FOR MINDLIN PLATE

ＡＮＥＷＨＹＢＲＩＤＱＵＡＤＲＩＬＡＴＥＲＡＬＦＩＮＩＴＥＥＬＥＭＥＮＴＦＯＲＭＩＮＤＬＩＮＰＬＡＴＥＣｈｉｎＹｉ（秦奕）（ＴｉａｎｊｉｎＡｒｃｈｉｔｅｃｔｕｒａｌＤｅｓｉｇｎＩｎｓｔｉｔｕｔｅ,Ｔｉａｎｊｉｎ）ＺｈａｎｇＪｉｎｇ－ｙｕ（张敬宇）（Ｉ...     

薄板弯曲问题的P型杂交解析有限元方法

本文采用两套变量构造有限元试函数空间，在单元内部要求试函数精确满足平衡微分方程，在单元边界上对位移和转角分别用Ｐｅａｎｏ升阶函数插值，然后利用广义变分原理建立了一种薄板弯曲问题的Ｐ型杂交解析有限方法，与常规有限元法相比，该方法不心进行过细的网格剖分，通过增加单元插值多项式的阶数Ｐ来提高精度，此外，该方法还具有积分计算只需在单元边界上进行、单元钢度矩阵和载荷向量具有嵌入结构、协调程度可以自动控制等优     

COARSE-MESH-ACCURACY IMPROVEMENT OF BILINEAR Q4-PLANE ELEMENT BY THE COMBINED HYBRID FINITE ELEMENT METHOD

IntroductionByadding‘nodeless’incompatiblebubblemodesandpreservinggeometriccharacteristicofthevariationalprincipleinmechanics,thecombinedhybridmethod[1～4 ]remarkablelyenhancedcoarse_mesh_accuracyofconventionalquadrilateralelementsoflowerorder.ThequadrilateralplaneelasticelementCH(0_1 )proposedinRef.[3 ]isasuccessfulexample.Followingthegeometricpointofviewinmechanicscombinedwithmathematicalanalysis,anovelexpressionofthecombinedhybridvariationalprincipleisintroducedtoclarifyitsintrinsicmecha…     

APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARAMETRIC HYBRID FINITE ELEMENT ANALYSIS

By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method in three-dimensional isoparametric hybrid finite element was discussed.The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented. The penalty balance method can effectively refrain the parasitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the presented element not only is effective in improving greatly the numeric calculation precision of distorted grids but also has the universality.     

FAST SOLUTION FOR LARGE SCALE LINEAR ALGEBRAIC EQUATIONS IN FINITE ELEMENT ANALYSIS

The computational efficiency of numerical solution of linear algebraic equations in finite elements can be improved in two ways. One is to decrease the fill-in numbers, which are new non-zero numbers in the matrix of global stiffness generated during the process of elimination. The other is to reduce the computational operation of multiplying a real number by zero. Based on the fact that the order of elimination can determine how many fill-in numbers should be generated, we present a new method for optimization of numbering nodes. This method is quite different from bandwidth optimization. Fill-in numbers can be decreased in a large scale by the use of this method. The bi-factorization method is adopted to avoid multipying real numbers by zero. For large scale finite element analysis, the method presented in this paper is more efficient than the tradiational LDLT method. Project supported by the Foundation for University Key Teachers under the Ministry of Education of China. Received 18 October 2000.     

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media,a general Gurtin variational principle for theinitial boundary value problem of dynamical response of fluid-saturated elastic porous media isdeveloped by assuming infinitesimal deformation and incompressible constituents of the solid andfluid phase.The finite element formulation based on this variational principle is also derived.Asthe functional of the variational principle is a spatial integral of the convolution formulation,thegeneral finite element discretization in space results in symmetrical differential-integral equationsin the time domain.In some situations,the differential-integral equations can be reduced to sym-metrical differential equations and,as a numerical example,it is employed to analyze the reflectionof one-dimensional longitudinal wave in a fluid-saturated porous solid.The numerical results canprovide further understanding of the wave propagation in porous media.     

间断Galerkin有限元和有限体积混合计算方法研究

通过局部坐标变换而建立的非正交单元间断Galerkin(DG)有限元计算方法计算精度高， 但计算量大、内存需求大；而非结构网格有限体积方法虽然准确计算热流的问题目 前还没有完全解决，但其具有计算速度快和内存需求小的优点. 该研究是将有 限元和有限体积方法的优点结合，发展有限元和有限体积的混合方法. 在物面 附近黏性占主导作用的区域内采用有限元方法进行计算，在远离物面的区域采用快速的有限 体积方法进行计算，在有限元和有限体积方法结合处要保证通量守恒. 通过算例说明有 限元和有限体积混合方法既能保证黏性区域的热流计算精度和流场结构的分辨率，又能 降低内存需求和提高计算效率，使有限元方法应用于复杂外形(实际工程问题)的计 算成为可能.     

构造满足特征值要求的杂交元应力子空间

通过引进适当参数给出了杂交元应力空间特征值与参数之间的关系,从而可以通过调节参数来构造满足特征值即模态刚度要求的杂交元应力子空间。本在位移元本征应力模式基础上引进调节参数,同时,利用矩阵H对角化方法计算杂交元应力子空间的本征应力模式,然后由此方便有效地计算特征值,从而大大提高了计算效率。本通过建立Q4杂交应力元特征值与参数之间关系说明了这一方法是确定可行的。     

一种三维体罚平衡应力杂交元

主要研究三维体罚平衡杂交元理论并建立相应的单元模型，采用罚平衡方法可以在不增中自由度的前提下，有效地扼制寄生应力，从而大幅度提高畸变网格下的计算精度，所给算例对８节点空间六面体单元（ＤＭ８）、优化杂交元和该文得出的单元进行了比较，证明了这一点，文中还尝试将该文 于方板和不可压缩问题的计算，得出了令人满意的结果。     

A NEW HYBRID ELEMENT ANALYSIS FOR EXPONENTIALLY VARYING FGM BASED ON AN ASYMPTOTIC STRESS FIELD

A hybrid finite element for exponentially varying Fhnctionally Graded Material （FGM） is established based on a derived stress field for an intact plate. Elements with both single layer and two layers of gradient are presented. The general stress field is obtained through an asymptotic analysis coupled with Westergaard＇s stress function approach. With the aid of boundary collocation technique, convergence of the derived stress field is verified. Effectiveness and efficiency of the element is investigated through calculation and comparison. Based on that element, stress field of FGM plate under different loading cases is studied briefly.