非定常可压等熵流非线性方程显式解析解的推导

本文对作者以前凭试凑、灵感、运气与经验得出的一系列非定常可压流动显式解析解,寻找线索,总结出其可能的推导途径,并以非定常可压等熵一维流为例,具体给出了四种新的求解方法。这些方法会对今后寻找工程热物理领域的非线性主控方程的解析解有所帮助。本文同时还给出了两个新的解析解。     

时间推进方法计算气液两相流动

１前言对气液、气固、液固两相或多相流体混合流动的研究在许多领域都显得十分重要,相对气固流动的研究来说,人们对气液两相流动的研究更为薄弱．而工程实际的需要（例如海底石油天然气混输问题）又要求我们对这种复杂流动有进一步的认识．在数值求解不可压单相或多相流动的方法中,应用较广的是压力－速度校正法。时间推进法是解可压问题的主要方法。如果能将它应用到不可压问题中去,在编程、计算兼容性方面都有较大优势。针对时间推进法在解不可压问题时遇到的困难,文献出提出一种所谓的人工可压缩性方法。本文用这种方法尝试计算了叶…     

可压涡卷空间演化的迎风紧致差分数值模拟

从数值算法的耗散和色散特征的时空全离散Fourier分析出发,通过直接求解二维非定常可压Navier Stokes方程,将发展的5阶迎风紧致差分格式用于无约束可压平面受迫剪切层中基频涡卷空间演化过程的数值模拟.采用被动守恒标量等方法显示了基频涡卷的饱和、一次对并、二次对并等现象,据此探讨了入口来流亚谐扰动引起的初值效应问题,表明可压大尺度涡结构空间演化形态与受迫扰动方式之间存在关联.     

可压剪切层线性稳定性特征直接数值模拟

基于伪随机数生成技术促白噪声扰动,以高精度迎风／对称紧致混合差分算法求解二维／三维非定常可压Navier－Stokes方程,揭示了可压自由剪切层初始剪切过程中扰动的线性演化特征,以及该过程对扰动波数和方向的内在选择性,验证了所用算法的有效性,表明线性理论同数值模拟相结合是可压剪切层研究的合理途径之一。     

环量控制翼型动态失速特性研究

本文用数值求解二维可压非定常Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的方法研究了环量控制翼型的动态失速特性．揭示了环量控制翼型在以不同吹气动量系数、不同频率做俯仰振荡时的动态失速特征．指出吹气动量系数对环量控制翼型动态失速的特性有很大影响,同时,振荡频率的影响与传统翼型相比也有不同．进一步分析了其失速的机理．     

透平级S_2流面内的反问题湍流计算

本文发展了应用湍流流函数方程计算湍流流场的方法。计算了扭曲叶片Ｓ２流面的湍流流场．在非正交曲线坐标可压湍流方程组中包含了以无量纲形式表示的能量方程，熵方程和Ｋ－ε湍流模型方程。固壁边界上采用了壁函数方程。通过计算得到了透平级内部的湍流流动合理的收敛解。此方法可以通过调节子午通道的形状及环量的大小分布来防止流动中负速度的出现，为高效透平级的设计提供了一种新的途径。     

微细光滑圆管内气体流动阻力特性的实验研究

本文采用内径为84．7μm及144．4μm的玻璃圆管作为实验管，对微细管内气体流动的阻力特性进行了实验研究．结果表明，层流状态下，微细圆管内气体流动的摩擦系数大于不可压、充分发展管内流动的数值．其物理机制为：微细圆管内气体流动的可压缩性导致速度抛面偏高抛物线分布，使得壁面处的速度梯度增加，摩擦阻力增大．     

光纤中变系数非线性Schr(o)dinger方程的孤子解及其应用

基于推广的立方非线性Klein—Gordon方程对一般形式的变系数非线性Schrodinger方程进行研究，讨论了无啁啾情形的孤子解，发现了包括亮、暗孤子解和类孤子解在内的一些新的精确解．同时对基本孤子的色散控制方法进行了简单讨论．作为特例，常系数非线性Schrodinger方程和两类特殊的变系数非线性Schrodinger方程的结果和已知的形式一致．此外，还研究了一个周期增益或损耗的光纤系统，得到了有意义的结果．     

一种新的流体力学预处理方法

本文介绍了一种新的流体力学预处理方法,它基于压力、速度与焓为原始变量,以时间推进方法为基础,能够有效地将可压与不可压流场的计算方法统一起来。它可以同时进行可压、不可压、高马赫数与低马赫数流场的计算。这种方法不但可以处理气体区或液体区的流场计算,还可以有效处理含有相变区域内的流场计算,为发生空化的流场仿真打下基础。     

用模拟法测绘二维流场和温度场

用模拟法测绘二维流场和温度场上海交通大学陈新雷，乔卫平在科学研究和工程设计中，常需要测定二维温度场，流体场的空间分布．对这些场参数的直接测量较难进行．如果应用计算机解微分方程，不但计算量大，且精度也欠佳．故我们在模拟法描绘静电场的基础上，依据物理上的...     

考虑旋流的非定常几何一维流动解析解

对文献[1]给出的能反映管内非定常完全气体有旋流流动的一维计算模型,首次给出了其多套代数显式解析解,以便于在理论上了解此流动模型,尤其是有助于计算流体力学工作者验证与发展其计算方法与技巧。本文导出一些解析解时利用了作者以前推导普通(无旋流)非定常一维流所得的解与推导经验,也是一个特色。     

Hybrid power flow analysis using coupling loss factor of SEA for low-damping system—Part I: Formulation of 1-D and 2-D cases

This paper proposes a hybrid method for the prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the power flow analysis (PFA) algorithm and statistical energy analysis (SEA) coupling concepts. The main part of this method is the application of the coupling loss factor (CLF) of SEA to the boundary condition of PFA in reverberant system. First, for hybrid PFA, the hybrid boundary conditions on 1-D and 2-D cases were derived in the general form. To verify the derived boundary conditions, numerical analyses for each case were performed. The hybrid PFA solutions using derived boundary conditions were compared with the classical PFA solutions with various reverberance factors including the effects of the characteristic length, excitation frequency and group velocity besides damping loss factor of the subsystem. Additionally, the hybrid PFA on 3-D case and the hybrid power flow finite element method (PFFEM) for hybrid PFA of built-up structures are described in the other companion paper.     

一、二维弹塑性流体动力学数值计算的高精度新自由面格式

提出了适用于X射线或电子束辐照、爆炸和高速碰撞等问题的一、二维弹塑性流体动力学数值模拟计算的一种新自由面格式。对于X射线及电子束辐照材料与结构的热-力学效应的数值计算结果表明,该新自由面格式明显优于目前一直沿用的Richtmyer格式。从理论上证明了该新自由面格式具有三阶精度,而Richtmyer格式为一阶精度。     

基于积分方法的二维平行剪切层声远场预测

本文采用二维Ffowcs Williams＆Hawkings(FW-H)方程对平行剪切层远声场辐射特性进行了研究。近流场时间精确数据通过计算气动声学(Computational Aeroacoustics,CAA)技术数值模拟获得,声远场信息则通过FW-H方程对近流场内的可穿透积分面进行积分获得。该方法首先采用具有解析解的涡/尾缘干涉问题进行了校核,进一步采用CAA/FW-H匹配技术对二维平行剪切层声辐射问题进行了预测,计算结果表明,积分解与计算域内的CAA数值解吻合较好。     

用非结构网格与欧拉方程计算复杂区域的二维流动

提出用Delaunay三角化方法生成非结构网格的一种过程。所生成的网格可用于复杂多连通域内的可压流计算。采用Euler方程和格心有限体积法,研制出程序,给出了算例。     

二维翼型跨音速绕流的数值模拟

本文结合高精度TVD格式的数值通量和时间进展多步法给出了一种求解定常流问题的数值方法。同时给出一些特殊处理来加快数值解的收敛速度。本文用以上方法计算了翼型跨音速绕流问题,结果表明此方法具有分辨率高,收敛速度较快之性质。     

Two-dimensional models of expanding vacuum arc plasmas

Multifluid equations describing the plasma of vacuum arcs expanding anisotropically from a cathode spot are given and discussed. Some first and preliminary results from an approximate analytical integration of such a system of equations, based on the representation of all plasma parameters by asymptotic power series, are presented and evaluated. Though the dependence of the plasma parameters on the direction (angle ϑ) is weak, the inclusion of angular terms and angular equations changes some results significantly, compared with the experiences from usually 1-D models. While the basic radial dependence (r) of the terms ~r^-2k/5, k=0,1,2..., remains the same as in 1-D theories, we now get an angular dependence ~ϑ² of the parameters in a first approximation, with positive factors, i.e., a flattening of the whole plasma distribution. However, with analytical solutions of higher flexibility, cos-like distributions are possible as well. The final kinetic energy of the plasma ions in the case of Cu arc spots is caused by the electric field within the plasma (contributing approximately 27%), the ion pressure gradient (~24%), and the electron-ion friction (plasma resistivity, ~49%) in directions near to the discharge axis. Again, similar to the results from 1-D models. With an approach to the cathode surface (ϑ→π/2), the plasma flow becomes ambipolar. Finally, some further possibilities which are available with the help of this model are discussed     

Nonlinear evolution of periodic gas perturbations

A system of equations describing a 1-D nonsteady gas flow with a power law dependence of pressure on density is considered. General solutions of this system were obtained for several special cases. The problem of a periodic gas flow with respect to a spatial coordinate is solved. An analogy with an initial system of equations that describes the motion of quasi-gaseous media is presented.     

Sound transmission prediction by 3-D elasticity theory

The problem of sound transmission through layered panel structures is studied with the exact theory of three-dimensional (3-D) elasticity. The exact solution to the 3-D elasticity equations is obtained by the use of the Fourier spectral method. Based on this analytical solution, a transfer matrix is derived that relates the spectral displacements and stresses on the one surface of the panel to those on the opposite panel surface. The transfer matrix is then used to develop the analytical solutions for sound reflection and transmission coefficients. Explicit, concise expressions are obtained for the analytical solutions of the acoustic transmission and reflection coefficients under the general conditions of layered anisotropic panels. Examples are given for both single-layer and sandwich panels. Predictions on sound transmission from the 3-D elasticity theory are compared with available data from other methods, and the results are discussed.