Limit Cycle Oscillations of a Wing Section with a Tip Mass

This paper presents an investigation into the limit cycleoscillation phenomenon for a nonlinear aeroelasticsystem under unsteady aerodynamics. The system consists of a sweptbackwing section carrying a tip mass with one degree of freedom. Thejunction stiffness considered between the wing and the tip mass istrilinear. The method of harmonic balance, which can be very practicalin the study of nonlinear flutter, is used for the theoretical analysisof limit cycle oscillations. Stable, unstable and semi-stable limitcycles are predicted in the system for both cases of hardening andsoftening springs. Results found by numerical simulation provide theamplitudes of limit cycles. The experimental results in wind tunneltests agree well with the predictions obtained both theoretically andnumerically.     

多维非定常中子迁移方程Galerkin有限元法近似解的收敛性和广义解的存在性

使用Galerkin有限元法研究了多维非定常中子迁移方程，证明了Galerkin有限元法近似解的收敛性和广义解的存在性．     

广义二阶流体涡流速度的衰减和温度扩散

将分数阶微积分运算引入到二阶流体的本构关系中,建立了带分数阶导数的广义二阶流体模型．研究了广义二阶流体涡流速度的衰减和温度扩散,利用分数阶导数的Laplace变换和广义Mittag-Leffler函数,得到了涡流速度场和温度场的精确解,分析了分数阶指数对涡流速度的衰减和温度扩散的影响．     

Low‐order stabilized finite element methods for the unsteady Stokes/Navier‐Stokes equations with friction boundary conditions

In this paper, we consider low‐order stabilized finite element methods for the unsteady Stokes/Navier‐Stokes equations with friction boundary conditions. The time discretization is based on the Euler implicit scheme, and the spatial discretization is based on the low‐order element (P₁−P₁ or P₁−P₀) for the approximation of the velocity and pressure. Moreover, some error estimates for the numerical solution of fully discrete stabilized finite element scheme are obtained. Finally, numerical experiments are performed to confirm our theoretical results.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

高超音速湍流分离表面热流率的脉动特性

本文给出高超音速湍流分离不稳定特性的实验研究结果。试验条件是:自由流马赫数为 7.8,单位长度雷诺数为 3.5×10~7/米。分离流场由有限展长前向台阶产生,并用有高空间分辨率和快速响应的一列平齐安装的铂膜电阻温度计和多通道系统测量其表面热流率脉动。信号的条件采样分析结果表明:分离激波的根部由一束压缩波构成,流向展长约二分之一来流边界层厚度,在边界层外汇聚成单一主激波。这种激波结构极其不稳定,出现大尺度运动,流向运动的尺度约为分离激波上游影响区域长度的22％。激波振荡频率为一宽频带,主要集中在 1～3 千赫。在分离激波运动区域,热流脉动呈间歇性,在无扰动和激波扰动间跳跃。可以认为这种间歇性是分离激波系统大尺度振荡的结果。在激波运动区域的下游为分离区,流体继续压缩,热流脉动无间歇。     

A third‐order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time‐accurate solution of the compressible Navier–Stokes equations

A space and time third‐order discontinuous Galerkin method based on a Hermite weighted essentially non‐oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower‐upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third‐order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third‐order discontinous Galerkin methods, and less computing time than the lower‐order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Reducing memory requirements of unsteady adjoint by synergistically using check-pointing and compression

The unsteady adjoint method used in gradient-based optimization in 2D and, particularly, 3D industrial problems modeled by unsteady PDEs may have significant storage requirements and/or computational cost. The reason for this is that the backward in time integration of the adjoint equations requires the previously computed instantaneous flow fields to be available at each time-step. This article proposes remedies to this problem, by extending/upgrading relevant techniques proposed by the group of authors as well as other researchers. Their applicability is wide, even if these remedies are herein demonstrated in shape optimization problems in unsteady fluid mechanics. Check-pointing is in widespread use as it reduces the memory footprint and CPU cost of the optimization with a controllable computational overhead. Alternatively, flow field time-series can be stored in a lossless or lossly compressed form. The novelty of this article is the development of a Compressed Coarse-grained Check-Pointing strategy for second-order accurate schemes in time, by optimally combining check-pointing and lossy compression. The latter includes (a) the incremental Proper Generalized Decomposition (iPGD) algorithm and (b) a hybridization of the iPGD with the ZFP and Zlib algorithms. This is implemented within OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization, and assessed in 2D/3D aerodynamic shape optimization problems on unstructured grids. Effectiveness in data reduction, computational cost, and reconstruction accuracy are compared, vis-à-vis also to the “standard” binomial check-pointing technique after adjusting it to second-order accurate schemes in time.     

飞行器变后掠过程非定常气动特性形成机理

可变体飞行器变后掠过程中的时变气动力与力矩特性对于飞行安全具有重要意义,是亟待深入研究的基础问题.通过风洞实验对其开展了研究,揭示了可变体飞行器变后掠引起的气动特性动态迟滞现象及滞回环大小与方向的影响因素.基于风洞实验结果和力学中一些重要概念,提出了3种物理效应:流场迟滞效应、附加运动效应、固壁牵连效应,以此定性与定量论证了可变体飞行器变后掠过程中非定常气动特性的形成机理.除了能解释实验现象,这一机理研究亦可用于后续可变体飞行器变后掠过程中的气动特性建模.