基于边界元方法的气动弹性降阶模型及仿真

传统气动弹性的时域计算耗费了大量时间,为了提高计算效率,本文发展了基于边界元方法的降阶模型技术。首先基于边界元方法建立非定常流场的求解模型,结合特征值分析技术建立了非定常气动力的低阶模型;然后,利用边界元方法建立了气动网格和结构网格之间的信息转换矩阵;最后将非定常气动力降阶模型和结构动力学方程联合,建立了气动弹性系统的低阶状态空间模型。将所发展的降阶模型方法应用于NACA0012翼型的非定常气动力求解中,结果表明降阶模型可以在保证原系统计算精度的同时提高了计算效率;将降阶模型技术应用到三维机翼的气动弹性响应计算中,在系统阶数仅为12阶的情况下可以得到与原系统一致的极限环响应,说明降阶模型技术在求解气动弹性问题中的巨大优势。     

翼型、机翼非定常运动模式下动态数值模拟

基于RANS方程,通过刚性动网格技术实现对翼型和机翼典型运动模式的描述,采用双时间推进方法和Roe空间离散格式对流场求解,构建了一个非定常气动计算平台;以NACA0012翼型为算倒进行了动态数值模拟可信度验证。数值模拟结果与试验数据吻合较好,升力和俯仰力矩的最大计算误差分别为3％和10％,表明了该平台的可靠性。另外,还数值模拟了M6机翼的动态非定常流场,并分析了两种湍流模型对非定常流场激波的捕捉能力。结果表明非定常流动中S-A湍流模型对激波的捕捉较B-L模型更敏感。文中开发的非定常计算平台对进一步解决三维复杂流场的流动问题有很高的工程应用价值。     

基于特征正交分解的非定常气动力建模技术

采用特征正交分解(proper orthogonal decomposition, POD)方法, 建立了基于状态空间的非定常气动力降阶模型, 并耦合结构方程, 建立了降阶的气动弹性系统, 开展了颤振分析的初步研究, 计算效率提高了2~3个数量级. 具体过程是:首先获取全阶系统的频域快照构成关联矩阵, 通过对关联矩阵进行奇异值分解提取流场模态(或流场基), 对低能量模态截断形成降阶子空间, 并将其映射到全阶系统, 从而形成基于状态空间的降阶非定常气动力模型. 对气动弹性标模AGARD445.6进行算例验证, 证明了降阶方法正确, 可以提供高效、高精度的气动弹性分析.      

叶轮机械沿任意曲线的运动方程及其应用

本文推导了叶轮机械内理想气体沿任意曲线方向的运动方程,方程表示为流面上气体速度沿任意曲线方向变化率的一阶微分方程,适于求解。详细讨论了方程在S_1和S_2两类流面上的求解方法,包括电子计算机解和手算近似解。将计算实例与其它文献或实验结果作了比较,表明本文提供的方法适合在叶轮机械气动设计中应用。     

非粘滞阻尼系统时程响应分析的精细积分方法

考虑一个具有非粘滞阻尼特性的多自由度系统响应的时程分析问题.该非粘滞阻尼模型假设阻尼力与质点速度的时间历程相关,数学表达式体现为阻尼力等于质点速度与某一核函数的卷积.在利用状态空间方法将系统运动方程转换成一阶的状态方程的基础上,采用精细积分方法对状态方程进行数值求解,得到一种求解该阻尼系统时程响应的精确、高效的计算方法.通过两个数值算例表明,采用该方法得到几乎精确的数值计算结果,而且计算效率有成数量级的提高.     

非定常俯抑振荡下的横向喷流数值模拟

采用高精度格式数值求解RANS方程,研究了定常状态下横向喷流流场,压力分布计算结果与实验结果基本吻合,并捕捉到喷流干扰流场中多种流动结构.在非定常计算过程中,飞行器的振动引起了法向力和俯仰力矩系数的相位滞后,推力放大因子随俯仰角周期变化.飞行器振动过程中,喷流流场的动态气动特性与稳态喷流有明显的区别,因此在利用横向喷流对飞行器进行姿态控制时,应该考虑由于飞行器姿态的变化对横向喷流所产生的非定常影响问题.     

基于气动力降阶模型的跨音速气动弹性稳定性分析

基于离散型输入输出差分模型,运用非定常CFD方法训练信号,然后运用最小二乘方法进行参数辨识,得到降阶的非定常气动力模型,再将该离散差分模型转换为连续时间域内的状态方程。耦合气动状态方程和结构状态方程,得到耦合系统的气动弹性状态方程。求解不同动压下状态矩阵的特征值,根据根轨迹图分析系统的稳定性特性。分析结果与直接耦合CFD/CSD方法结果相吻合,可以计算跨音速非线性气动弹性问题。其计算效率比直接耦合CFD/CSD方法提高1~2个数量级。针对Isogai wing在跨音速出现的S型颤振边界进行了较为细致的分析,阐述了该现象是由于系统诱发颤振的分支随着速度(来流动压)的提高而发生转移所导致的。     

横向荷载作用下弹性地基上梁的主共振分析

基于Winkler地基模型及Euler-Bernoulli梁理论,建立了弹性地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,并利用多尺度法求得该系统主共振的一阶近似解.分析了长细比、地基刚度、外激励幅值和阻尼系数等参数对系统主共振幅频响应的影响,然后通过与非共振硬激励情况对比分析主共振对其动力响应的影响.结果表明:主共振幅频响应存在跳跃和滞后现象;阻尼对主共振响应有抑制作用;主共振显著增大系统稳态动力响应位移.     

大长细比导弹的气动弹性降阶模型

对于大长细比导弹,需要在设计阶段准确计算气动弹性/气动伺服弹性,但其复杂的气动力给计算带来困难,因此气动力降阶模型是突破大长细比导弹跨音速气动弹性分析与控制瓶颈的关键技术.虽然气动力模型降阶方法已在预测二维机翼结构的气动弹性方面取得重要进展,但几乎未见关于全机模型的气动力降阶模型研究报道.本文基于递归Wiener模型的气动力降阶方法,利用CFD计算的气动力作为模型辨识数据,用鲁棒子空间和Levenberg-Marquardt算法辨识降阶模型参数,建立了大长细比导弹气动力降阶模型.在此基础上与大长细比导弹有限元模型相结合,构造出气动弹性降阶模型,并在数值仿真中测试气动弹性降阶模型在不同马赫数下的适用性.数值仿真结果表明,该气动弹性降阶模型能够精确预测导弹模型在不同飞行条件下的非定常气动力和导弹模型的气动弹性频率响应特性.     

考虑气动热对粘性系数μt影响的压气机流场计算

根据气动热影响叶片壁面附面层粘性系数tμ的理论,把考虑气动热对粘性系数tμ影响的粘性体积力计算方法运用于压气机叶栅三维粘性流场计算。计算时使用有限体积显式时间推进法解算Navier-Stokes方程,用Baldwin-Lomax模型模拟湍流流动。所得结果比不考虑气动热影响的三维计算结果更接近实验结果,能更真实地反映压气机叶栅流场的流动。     

基于随机森林算法的非定常气动力建模研究

针对现有的非定常气动力建模方法对气动弹性预测的准确性和效率问题,将随机森林算法引入非定常气动力建模研究领域,构建了基于随机森林算法的非定常气动力降阶模型。将所得模型用于预测气动弹性,选择二维NACA0012翼型进行颤振边界的预测,选用NACA64A010翼型预测LCO特性,并说明了该降阶模型建模的详细过程,将其计算结果与CFD/CSD耦合计算结果及试验结果进行了对比。研究结果表明,该模型可行、高效且精确,可以快速准确地预测飞行器气动弹性特性。     

Unsteady aerodynamic reduced-order modeling of an aeroelastic wing using arbitrary mode shapes

Computational fluid dynamics (CFD) based unsteady aerodynamic reduced-order model (ROM) can offer significant improvements to the efficiency of transonic aeroelastic analysis. To construct a ROM based on mode shapes, one run of CFD solver is needed to compute aerodynamic responses corresponding to mode excitations. When mode shapes change with structure, another run of the CFD solver is required to construct the new ROM. The typically large computational cost associated with repeated runs of the CFD solver impedes the application of existing unsteady aerodynamic reduced-order modeling methods to transonic aeroelastic design optimization and aeroelastic uncertainty analysis. This paper demonstrates a method that can replace the CFD solver used in the process of existing unsteady aerodynamic reduced-order modeling. It can produce aerodynamic responses corresponding to mode excitations for arbitrary mode shapes within a few seconds. Computational cost can be reduced by two orders of magnitude using the mode excitations and the corresponding aerodynamic responses computed by the method to construct the ROMs used for flutter analyses in aeroelastic design optimization or aeroelastic uncertainty analysis in transonic regime compared with the existing unsteady aerodynamic reduced-order modeling methods. Results show that the method can accurately produce the aerodynamic responses corresponding to the mode excitations and predict the flutter characteristics of AGARD 445.6 wings root-attached in three different ways.     

Methods of fluid–structure coupling in frequency and time domains using linearized aerodynamics for turbomachinery

Two methods of fluid–structure coupling for turbomachinery are presented, the first one in the frequency domain and the second in both frequency and time domains. In both methods, the structure and the fluid are assumed to have circumferential cyclic symmetric properties and the unsteady aerodynamic forces are assumed to be linear in terms of the structural displacements. The motion equation of the reference sector in the travelling wave coordinates is projected on the complex eigenmodes for each phase number. The generalized unsteady aerodynamic forces are computed by solving the Euler equations and by assuming the structural motion to be harmonic with a constant phase angle between two adjacent sectors. In the frequency domain, the complex, nonlinear eigenvalue problem for the aeroelastic stability analysis is solved iteratively either by the double scanning method or by using Karpel's minimum state smoothing of the aerodynamic coefficient matrix. In the time domain, Karpel's smoothing method is used to obtain an approximation of the generalized unsteady aerodynamic forces by means of auxiliary state variables. These coupling methods are tested on a compressor blade row and the good agreement obtained between their results and those of the direct coupling method shows that the proposed numerical methods, already used in aircraft applications, are adapted to turbomachinery.     

跨音速极限环型颤振的高效数值分析方法

事先建立一个低阶的非线性、非定常气动力模型是开展非线性流场中气动弹性问题研究的一个捷径. 基于CFD方法, 通过计算结构在流场中自激振动的响应来获得系统的训练数据. 采用带输出反馈的循环RBF神经网络, 建立时域非线性气动力降阶模型.耦合结构运动方程和非线性气动力降阶模型, 采用杂交的线性多步方法计算结构在不同速度(动压)下的响应历程, 从而获得模型极限环随速度(动压)变化的特性. 两个典型的跨音速极限环型颤振算例表明, 基于气动力降阶模型方法的计算结果与直接CFD仿真结果吻合很好, 与后者相比其将计算效率提高了1~2个数量级.      

The effect of aerodynamic asymmetries on turbomachinery flutter

In this paper, the effect of aerodynamic asymmetries on the flutter characteristics of turbomachinery blades is investigated. Specifically, the present method is used to study the effect of leading edge blending in loaded and unloaded rotors. The unsteady aerodynamic response of the blades to self-excited vibrations is modeled using a harmonic balance method, which allows one to model the entire wheel using complex periodic boundary conditions and a computational grid spanning a single sector (symmetry group). This reduces the computational and memory requirements dramatically compared to similar time-accurate analyses. It is shown that alternate blending degrades the stability of a loaded rotor whereas it improves the stability of an unloaded rotor. On the other hand, when blends are spaced five blades apart their effect is less pronounced.     

Efficient unsteady aerodynamic loads prediction based on nonlinear system identification and proper orthogonal decomposition

In the present work, an efficient surrogate-based framework is developed for the prediction of motion-induced surface pressure fluctuations and integral force and moment coefficients. The model construction is realized by performing forced-motion computational fluid dynamics (CFD) simulations, while the result is processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, a nonlinear system identification is carried out with respect to the applied excitation and the resulting POD coefficients. For the input/output model identification task, a recurrent local linear neuro-fuzzy approach is employed in order to capture the linear and nonlinear characteristics of the dynamic system. Once the reduced-order model (ROM) is trained, it can substitute the flow solver within unsteady aerodynamic or aeroelastic simulation frameworks for a given configuration at fixed freestream conditions. For demonstration purposes, the ROM approach is applied to the LANN wing in high subsonic and transonic flow. Due to the characteristic lambda-shock system, the unsteady aerodynamic surface pressure distribution is dominated by nonlinear effects. Numerical investigations show a good correlation between the results obtained by the ROM methodology in comparison to the full-order CFD solution. In addition, the surrogate approach yields a significant speed-up regarding unsteady aerodynamic calculations, which is beneficial for multidisciplinary computations.     

尾流激励的叶片气动力降阶模型

气动力降阶模型是研究叶片气动弹性振动快速高效的新方法。现有气动力降阶模型的研究主要集中在叶片颤振方面,没有涉及更为常见的上游尾流激励的叶片振动问题。本文提出基于Volterra级数的尾流激励叶片气动力降阶模型,为尾流激励下叶片振动和动静叶干涉振动研究提供了新的思路。采用行波法简化尾流的参数个数,用阶跃信号法识别降阶模型的核函数。二维叶片的算例结果表明,本文方法可以较准确地描述尾流激励引起的叶片气动力振荡,而且计算效率极高。     

用扰动涡方法模拟叶轮机内动静叶的相互作用

发展了一种研究叶轮机内动、静叶间的相互作用的新方法———扰动涡方法，它利用全三维的定常解为基础解，并由此给出非定常扰动场的初始解．为计算叶片对扰动场的响应过程，采用拉格朗日方法追踪扰动涡团的对流流动过程，用确定性涡方法来描述流体的粘性扩散过程．发展了代数湍流模型（Ｂａｌｄｗｉｎ Ｌｏｍａｘ湍流模型）在尾迹中的应用方法，克服了其它数值方法中无法准确捕捉尾迹中心线的运动轨迹，以及计算出的边界层外的湍流涡粘性系数偏大的缺陷．利用该方法计算轴流叶轮机内由于动、静叶间的相互作用而引起的非定常流动过程，与实验的对照表明，模拟结果与实验数据吻合得相当好，从而说明本文发展的方法是可信的，为更直观地描述尾迹等非定常因素的流动及叶轮机内的掺混问题提供依据．     

International journal of computational fluid dynamics real-time prediction of unsteady flow based on POD reduced-order model and particle filter

An integrated method consisting of a proper orthogonal decomposition (POD)-based reduced-order model (ROM) and a particle filter (PF) is proposed for real-time prediction of an unsteady flow field. The proposed method is validated using identical twin experiments of an unsteady flow field around a circular cylinder for Reynolds numbers of 100 and 1000. In this study, a PF is employed (ROM-PF) to modify the temporal coefficient of the ROM based on observation data because the prediction capability of the ROM alone is limited due to the stability issue. The proposed method reproduces the unsteady flow field several orders faster than a reference numerical simulation based on Navier–Stokes equations. Furthermore, the effects of parameters, related to observation and simulation, on the prediction accuracy are studied. Most of the energy modes of the unsteady flow field are captured, and it is possible to stably predict the long-term evolution with ROM-PF.