飞行器跨声速气动弹性数值分析

将流体和结构运动方程分别构造为含子迭代的计算格式，发展了一种紧耦合气动弹性分析方法．其中流体计算的空间离散采用改进的HLLEW（Harten-Lax-van Leer-Einfeldt-Wada）格式．TFI（transfinite interpolation）方法用于生成随结构变形的自适应多块动网格．利用所发展的方法，对一翼-身-尾气动外形，数值预测了马赫数在0．3-1．3范围内的气动颤振边界．并详细研究了时间步长、子迭代步数、初始流场、耦合方法、疏密网格对颤振计算结果的影响．

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

A Pressure-Correction Method And Its Applications On An Unstructured Chimera Grid

In this paper, an unstructured Chimera mesh method is used to compute incompressible flow around a rotating body. To implement the pressure correction algorithm on unstructured overlapping sub-grids, a novel interpolation scheme for pressure correction is proposed. This indirect interpolation scheme can ensure a tight coupling of pressure between sub-domains. A moving-mesh finite volume approach is used to treat the rotating sub-domain and the governing equations are formulated in an inertial reference frame. Since the mesh that surrounds the rotating body undergoes only solid body rotation and the background mesh remains stationary, no mesh deformation is encountered in the computation. As a benefit from the utilization of an inertial frame, tensorial transformation for velocity is not needed. Three numerical simulations are successfully performed. They include flow over a fixed circular cylinder, flow over a rotating circular cylinder and flow over a rotating elliptic cylinder. These numerical examples demonstrate the capability of the current scheme in handling moving boundaries. The numerical results are in good agreement with experimental and computational data in literature. (C) 2007 Elsevier Ltd. All rights reserved.

Shallow Water Model On Cubed-Sphere By Multi-Moment Finite Volume Method

A global numerical model for shallow water flows on the cubed-sphere grid is proposed in this paper. The model is constructed by using the constrained interpolation profile/multi-moment finite volume method (CIP/MM FVM). Two kinds of moments, i.e. the point value (PV) and the volume-integrated average (VIA) are defined and independently updated in the present model by different numerical formulations. The Lax-Friedrichs upwind splitting is used to update the PV moment in terms of a derivative Riemann problem, and a finite volume formulation derived by integrating the governing equations over each mesh element is used to predict the VIA moment. The cubed-sphere grid is applied to get around the polar singularity and to obtain uniform grid spacing for a spherical geometry. Highly localized reconstruction in CIP/MM FVM is well suited for the cubed-sphere grid, especially in dealing with the discontinuity in the coordinates between different patches. The mass conservation is completely achieved over the whole globe. The numerical model has been verified by Williamson's standard test set for shallow water equation model on sphere. The results reveal that the present model is competitive to most existing ones. (C) 2008 Elsevier Inc. All rights reserved.

A Cip/Multi-Moment Finite Volume Method For Shallow Water Equations With Source Terms

A novel finite volume method has been presented to solve the shallow water equations. In addition to the volume-integrated average (VIA) for each mesh cell, the surface-integrated average (SIA) is also treated as the model variable and is independently predicted. The numerical reconstruction is conducted based on both the VIA and the SIA. Different approaches are used to update VIA and SIA separately. The SIA is updated by a semi-Lagrangian scheme in terms of the Riemann invariants of the shallow water equations, while the VIA is computed by a flux-based finite volume formulation and is thus exactly conserved. Numerical oscillation can be effectively avoided through the use of a non-oscillatory interpolation function. The numerical formulations for both SIA and VIA moments maintain exactly the balance between the fluxes and the source terms. 1D and 2D numerical formulations are validated with numerical experiments. Copyright (c) 2007 John Wiley & Sons, Ltd.

钝体分离旋涡流动的区域分解、杂交数值模拟——Ⅰ.理论方法及其应用

为克服涡旋法不能精确预计物体附近小尺度流动结构的理论缺陷,减少高Reynolds数流动N-S方程差分解的困难,本文提出一种区域分解、杂交耦合N-S方程有限差分解及涡旋法的新的数值模型和理论方法.将流场分解为内外两区,在靠近物体表面、范围为O(R)的内区进行N-S方程有限差分解,外区作Lagrange-Euler涡旋法解,建立了分区流动的联结、耦合条件,给出了杂交耦合求解的数值计算方法.用本方法作了Re=10~2,10~3的圆柱绕流计算,考察了区域交界面位置变化时解的稳定性.与全场N-S方程解及实验结果的比较表明本文方法能精确预计流动分离及近场流动的详细结构,并可有效地计算流动的总体特性,且比全场N-S方程解显著节省机时和计算量.

非线性弹塑性问题的数学分析和有限元公式

本文将国际上流行的两点张量法及 Lagrange 描写方法统一起来。运用虚功原理及张量变换得到了 Lagrangian 坐标系及 Euler 坐标系中的应力率平衡方程以及与之等价的变分方程;同时推导出塑性大变形三维有限元公式。作为特例又导出二维平面应变及平面应力的有限元公式。

材料在高速变形时的动力松弛性质和一维杆中的塑性波

材料在高速变形时,它的整个变形过程能不能只用一个状态方程来描写是值得讨论的。本文认为,状态方程只在x-t Lagrange平面的部分区域内才反映高速变形过程的力学规律。 本文讨论了函数g(σ,ε)在高速变形时的性质,并建议采用如下的形式:g(σ,ε)=A[1-e~-B(1-ε)(σ-f(ε))]. 本文认为横向惯性的存在是状态方程中应力提高项出现的原因或原因之一. 本文用应变率相关理论解释了等应变区的存在. 在每秒几十米的撞击速度范围内,撞击端面间的摩擦力对塑性波的形成和传播具有不可忽视的影响.但在速度高到100米/秒以上时,这种影响又可能予以忽略. 以上五点看法是给合了铬钢短试件和2S铝杆的高速变形分析得到的.

柔性弦中弹塑性波的传播

本文用Lagrange方法研究了弦中弹塑性枞波和横波的传播,对不论是强间断或弱间断建立了一般微分关系式.着重讨论了相似问题.对于无滑动冲击的情况,问题是容易求解的;对于滑动冲击的情况,在补充考察了摩擦条件后,问题也可以求解.此外,论证了能量守恒条件;讨论了理想塑性弦的特殊情况.文中指出了文献[1]和[2]的某些错误.

Domain decomposition hybrid method for numerical simulation of bluff body flows:theoretical model and application

The discrete vortex method is not capable of precisely predicting the bluff body flow separation and the fine structure of flow field in the vicinity of the body surface. In order to make a theoretical improvement over the method and to reduce the difficulty in finite-difference solution of N-S equations at high Reynolds number, in the present paper, we suggest a new numerical simulation model and a theoretical method for domain decomposition hybrid combination of finite-difference method and vortex method. Specifically, the full flow. field is decomposed into two domains. In the region of O(R) near the body surface (R is the characteristic dimension of body), we use the finite-difference method to solve the N-S equations and in the exterior domain, we take the Lagrange-Euler vortex method. The connection and coupling conditions for flow in the two domains are established. The specific numerical scheme of this theoretical model is given. As a preliminary application, some numerical simulations for flows at Re=100 and Re-1000 about a circular cylinder are made, and compared with the finite-difference solution of N-S equations for full flow field and experimental results, and the stability of the solution against the change of the interface between the two domains is examined. The results show that the method of the present paper has the advantage of finite-difference solution for N-S equations in precisely predicting the fine structure of flow field, as well as the advantage of vortex method in efficiently computing the global characteristics of the separated flow. It saves computer time and reduces the amount of computation, as compared with pure N-S equation solution. The present method can be used for numerical simulation of bluff body flow at high Reynolds number and would exhibit even greater merit in that case.

层合板自由振动和强迫振动的三维精确解

主要基于三维弹性力学和状态空间法给出了四边简支各向同性矩形层合板自由振动和强迫振动问题的精确解.首先基于三维弹性力学建立了层合板的基本方程,利用状态空间法解决了层合板的自由振动问题,然后根据Lagrange动力学方程求解了层合板受到横向冲击时的强迫振动响应.

火箭剩余推进剂排放过程的分析与模拟

为了减少空间碎片的产生，星箭分离后，需要在轨排放火箭末级贮箱内的剩余推进剂．分析表明，排放条件下的推进剂射流进入太空后，立即失稳破碎为大量液滴；液滴在高真空环境下扩散，它们的表面不断有气体分子蒸发，逐渐在箭体周围形成了一个由液滴和蒸气分子组成的羽流场．采取Lagrange方法追踪该流场中每个液滴的运动轨迹以及表面蒸发冷凝过程，利用直接模拟Monte Carlo方法计算蒸气分子的运动和碰撞，然后通过微观量的统计平均获得感兴趣的宏观流场、箭体表面的压力和剪应力分布等．为了检验稀薄蒸气算法、模型和程序，模拟了真空水射流周围水蒸气羽流场，获得的径向Pitot压力分布与Fuchs和Legge的实验数据的符合．在此基础上，分别模拟了CZ-4B火箭末级剩余燃料偏二甲肼在不同排放方式下的三维稀薄蒸气与液滴羽流场．计算表明：原排放方式的扰动力矩相当大，超出了火箭姿控范围，新排放方式的扰动力矩很小，处于火箭姿控范围之内．这些预测得到了飞行遥测数据的支持．

基于插值函数的海底管道多点提升分析

建立海管点提升的力学模型，用多项式插值得到各种提升状态下的变形和内力.和现有方法相比，该法编程简单，易于实现，能满足工程的计算精度.

Numerical Analyses of Transonic Fluid/Structure interaction in Aircraft Engineering

Through the coupling between aerodynamic and structural governing equations, a fully implicit multiblock aeroelastic solver was developed for transonic fluid/stricture interaction. The Navier-Stokes fluid equations are solved based on LU-SGS (lower-upper symmetric Gauss-Seidel) Time-marching subiteration scheme and HLLEW (Harten-Lax-van Leer-Einfeldt-Wada) spacing discretization scheme and the same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Transfinite interpolation (TFI) is used for the grid deformation of blocks neighboring the flexible surfaces. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between fluid and structure. The developed code was fort validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. In the subsonic and transonic range, the calculated flutter speeds and frequencies agree well with experimental data, however, in the supersonic range, the present calculation overpredicts the experimental flutter points similar to other computations. Then the flutter character of a complete aircraft configuration is analyzed through the calculation of the change of structural stiffness. Finally, the phenomenon of aileron buzz is simulated for the weakened model of a supersonic transport wing/body model at Mach numbers of 0.98 and l.05. The calculated unsteady flow shows, on the upper surface, the shock wave becomes stronger as the aileron deflects downward, and the flow behaves just contrary on the lower surface of the wing. Corresponding to general theoretical analysis, the flow instability referred to as aileron buzz is induced by a stronger shock alternately moving on the upper and lower surfaces of wing. For the rigid structural model, the flow is stable at all calculated Mach numbers as observed in experiment

Transonic Aeroelastic Numerical Simulation in Aeronautical Engineering

A lower-upper symmetric Gauss-Seidel (LU-SGS) subiteration scheme is constructed for time-marching of the fluid equations. The Harten-Lax-van Leer-Einfeldt-Wada (HLLEW) scheme is used for the spatial discretization. The same subiteration formulation is applied directly to the structural equations of motion in generalized coordinates. Through subiteration between the fluid and structural equations, a fully implicit aeroelastic solver is obtained for the numerical simulation of fluid/structure interaction. To improve the ability for application to complex configurations, a multiblock grid is used for the flow field calculation and transfinite interpolation (TFI) is employed for the adaptive moving grid deformation. The infinite plate spline (IPS) and the principal of virtual work are utilized for the data transformation between the fluid and structure. The developed code was first validated through the comparison of experimental and computational results for the AGARD 445.6 standard aeroelastic wing. Then, the flutter character of a tail wing with control surface was analyzed. Finally, flutter boundaries of a complex aircraft configuration were predicted.