Nonlinear dynamics of an aeroelastic airfoil with free-play in transonic flow

Nonlinear dynamic behaviors of an aeroelastic airfoil with free-play in transonic air flow are studied. The aeroelastic response is obtained by using time-marching approach with computational fluid dynamics (CFD) and reduced order model (ROM) techniques. Several standardized tests of transonic flutter are presented to validate numerical approaches. It is found that in time-marching approach with CFD technique, the time-step size has a significant effect on the calculated aeroelastic response, especially for cases considering both structural and aerodynamic nonlinearities. The nonlinear dynamic behavior for the present model in transonic air flow is greatly different from that in subsonic regime where only simple harmonic oscillations are observed. Major features of the responses in transonic air flow at different flow speeds can be summarized as follows. The aeroelastic responses with the amplitude near the free-play are dominated by single degree of freedom flutter mechanism, and snap-though phenomenon can be observed when the air speed is low. The bifurcation diagram can be captured by using ROM technique, and it is observed that the route to chaos for the present model is via period-doubling, which is essentially caused by the free-play nonlinearity. When the flow speed approaches the linear flutter speed, the aeroelastic system vibrates with large amplitude, which is dominated by the aerodynamic nonlinearity. Effects of boundary layer and airfoil profile on the nonlinear responses of the aeroelastic system are also discussed.     

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。     

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.     

多场耦合求解非线性气动弹性的研究综述

非线性气动弹性分析中,涉及到非线性流体动力学和非线性结构动力学的耦合问题.阐述了国内外应用计算流体动力学(computational fluid dynamics,CFD)/计算结构动力学(computational structural dynamics,CSD)耦合求解技术来处理非线性气动弹性问题的研究现状,全面分析了流体域和结构域的非线性特征模拟技术、高效网格运动策略、耦合界面相容性条件、耦合计算效率及降阶技术、气动弹性实验及算法验证、多学科耦合求解等关键技术,总结了相关最新研究的方法和成果, 对比分析了其优缺点并提出了展望.      

Comparison between computational fluid dynamics,fluid–structure interaction and computational structural dynamics predictions of flow-induced wall mechanics in an anatomically realistic cerebral aneurysm model

Haemodynamically induced stress plays an important role in the progression and rupture of cerebral aneurysms. The current work describes computational fluid dynamics (CFD), fluid–structure interaction (FSI) and computational structural dynamics (CSD) simulations in an anatomically realistic model of a carotid artery with two saccular cerebral aneurysms in the ophthalmic region. The model was obtained from three-dimensional (3D) rotational angiographic imaging data. CFD and FSI were studied under a physiologically representative waveform of inflow. The arterial wall was assumed elastic or hyperelastic, as a 3D solid or as a shell depending on the type of modelling used. The flow was assumed to be laminar, non-Newtonian and incompressible. The CFD, FSI and CSD models were solved with the finite elements package ADINA. Predictions of velocity field and wall shear stress (WSS) on the aneurysms made using CFD and FSI were compared. The CSD model of the aneurysms using complete geometry was compared with isolated aneurysm models. Additionally, the effects of hypertensive pressure on CSD aneurysm models are also reported. The vortex structure, WSS, effective stress, strain and displacement of the aneurysm walls showed differences, depending on the type of modelling used.     

Coupled fluid structure analysis for wing 445.6 flutter using a fast dynamic mesh technology

The flow around wing 445.6 was modelled using Navier–Stokes equations and S-A model. The wing vibration and flow mesh deformation were computed using a fast dynamic mesh technology proposed by our own group. Wing 445.6 flutter was analysed through a strong coupling between the wing vibration and flow. The reduced flutter velocity was predicted and results are in good agreement with the experimental data. It is found that the subsonic flutter is mainly induced by the flow separation and the transonic and supersonic flutter are mainly caused by the oscillating shock wave and its induced flow separation. The positive aerodynamic work increases due to the oscillating shock wave when the subsonic flow becomes transonic reducing the flutter velocity. While the positive aerodynamic work induced by the oscillating shock wave decreases when the transonic flow becomes supersonic increasing the flutter velocity. That is why the transonic dip exists.     

Numerical simulation of transonic limit cycle oscillations using high-order low-diffusion schemes

This paper simulates the NLR7301 airfoil limit cycle oscillation (LCO) caused by fluid–structure interaction (FSI) using Reynolds averaged Navier–Stokes equations (RANS) coupled with Spalart–Allmaras (S–A) one-equation turbulence model. A low diffusion E-CUSP (LDE) scheme with 5th order weighted essentially nonoscillatory scheme (WENO) is employed to calculate the inviscid fluxes. A fully conservative 4th order central differencing is used for the viscous terms. A fully coupled fluid–structural interaction model is employed. For the case computed in this paper, the predicted LCO frequency, amplitudes, averaged lift and moment, all agree excellently with the experiment performed by Schewe et al. The solutions appear to have bifurcation and are dependent on the initial fields or initial perturbation. The developed computational fluid dynamics (CFD)/computational structure dynamics (CSD) simulation is able to capture the LCO with very small amplitudes measured in the experiment. This is attributed to the high order low diffusion schemes, fully coupled FSI model, and the turbulence model used. This research appears to be the first time that a numerical simulation of LCO matches the experiment. The simulation confirms several observations of the experiment.     

基于POD和代理模型的静气动弹性分析方法

静气动弹性问题考虑弹性结构与定常气动力间的相互耦合作用,对飞行器的性能和安全具有显著的影响.在现代飞行器设计阶段,计算流体力学(CFD)/计算结构力学(CSD)直接耦合方法是精确考察静气动弹性影响的重要手段.然而,基于CFD技术的气动力仿真手段在耦合过程中计算量大且耗时长,难以满足设计阶段的需求.因此,为了兼顾计算精度与效率,文章采用本征正交分解(POD)和Kriging代理模型相结合的模型降阶方法,替代CFD求解过程并耦合有限元分析(FEA)方法,建立了高效、准确的静气动弹性分析框架.相较于传统的以模态法为主的静气动弹性分析方法,该方法能够解决更为复杂的静气动弹性问题以及提供静气动弹性变形过程中的气动分布载荷.针对典型三维跨声速HIRENASD机翼模型开展的马赫数、迎角变化的算例验证表明:由建立的静气动弹性分析方法与CFD/CSD直接耦合方法计算得到机翼翼梢处的静变形量间的相对误差在5%以内;同时该方法预测静平衡位置处的气动分布载荷的误差在5%以内,静气动弹性分析的计算效率至少提升了6倍.     

薄膜结构流固耦合的CFD数值模拟研究

基于弱耦合分区求解策略,在CompaqVisualFortran6．5环境下搭建了薄膜结构三维流固耦合效应的CFD数值模拟平台。程序采用模块化编程思想,主要包含几何建模、流体分析、结构分析和数据交换四个模块。其中几何建模模块采用自行编制的膜结构找形分析程序,流体分析模块采用经过二次开发的计算流体力学软件FLUENT6．0,结构分析模块采用自行编制的膜结构动力分析程序MDLFX;在数据交换模块中,编制了基于薄板样条法的插值计算程序,以实现流固交界面上不同区域网格间的数据传递问题,编制了基于代数法和迭代法的动网格变形程序,以实现流固耦合运算中的动网格更新。基于该软件平台,对单向柔性屋盖和鞍形膜结构屋盖进行了流固耦合数值模拟,验证了方法的有效性。     

一种几何大变形下的非线性气动弹性求解方法

非线性气动弹性的时域求解中, 涉及到非线性的流体动力学(CFD)和非线性的结构动力学(CSD)耦合问题. 基于Co-rotational理论, 推导了三维壳单元几何非线性下的切线刚阵和内力公式, 针对推进过程中的能量守恒, 引入预估-校正推进格式, 发展了一种近似能量守恒的非线性动态响应算法; 基于1/2时间步的交错耦合格式, 结合带有几何守恒律的双时间推进求解雷诺平均N-S方程的求解器, 发展了非线性气动弹性求解的高精度耦合格式. 通过结构几何大变形下的静力和动力分析验证了所发展的结构非线性求解器, 并通过AGARD445.6机翼的非线性气动弹性响应分析, 说明了所发展耦合求解方法的实用性.      

Using the DEM-CFD method to predict Brownian particle deposition in a constricted tube

Modelling of the agglomeration and deposition on a constricted tube collector of colloidal size particles immersed in a liquid is investigated using the discrete element method (DEM). The ability of this method to represent surface interactions allows the simulation of agglomeration and deposition at the particle scale. The numerical model adopts a mechanistic approach to represent the forces involved in colloidal suspensions by including near-wall drag retardation, surface interaction and Brownian forces. The model is implemented using the commercially available DEM package EDEM 2.3^®, so that results can be replicated in a standard and user-friendly framework. The effects of various particle-to-collector size ratios, inlet fluid flow-rates and particle concentrations are examined and it is found that deposition efficiency is strongly dependent on the inter-relation of these parameters. Particle deposition and re-suspension mechanisms have been identified and analyzed thanks to EDEM's post processing capability. One-way coupling with computational fluid dynamics (CFD) is considered and results are compared with a two-way coupling between EDEM 2.3^® and FLUENT 12.1^®. It is found that two-way coupling requires circa 500% more time than one-way coupling for similar results.     

Experimental PIV/V3V measurements of vortex-induced fluid–structure interaction in turbulent flow—A new benchmark FSI-PfS-2a

The investigation of the bidirectional coupling between a fluid flow and a structure motion is a growing branch of research in science and industry. Applications of the so-called fluid–structure interactions (FSI) are widespread. To improve coupled numerical FSI simulations, generic experimental benchmark studies of the fluid and the structure are necessary. In this work, the coupling of a vortex-induced periodic deformation of a flexible structure mounted behind a rigid cylinder and a fully turbulent water flow performed at a Reynolds number of Re=30 470 is experimentally investigated with a planar particle image velocimetry (PIV) and a volumetric three-component velocimetry (V3V) system. To determine the structure displacements a multiple-point laser triangulation sensor is used. The three-dimensional fluid velocity results show shedding vortices behind the structure, which reaches the second swiveling mode with a frequency of about 11.2 Hz corresponding to a Strouhal number of St=0.177. Providing phase-averaged flow and structure measurements precise experimental data for coupled computational fluid dynamics (CFD) and computational structure dynamics (CSD) validations are available for this new benchmark case denoted FSI-PfS-2a. The test case possesses four main advantages: (i) the geometry is rather simple; (ii) kinematically, the rotation of the front cylinder is avoided; (iii) the boundary conditions are well defined; (iv) nevertheless, the resulting flow features and structure displacements are challenging from the computational point of view. In addition to the flow field and displacement data a PIV-based force calculation method is used to estimate the lift and drag coefficients of the moving structure.     

两种湍流模型时域颤振计算方法研究

采用时域计算分析方法进行了机翼跨音速颤振特性研究。在结构运动网格的基础上,采用格点格式有限体积方法进行空间离散和双时间全隐式方法进行时间推进求解雷诺平均N-S方程。针对流动粘性分别应用了SST湍流模型和SSG雷诺应力模型,通过对跨音速标模算例AGARD445.6机翼的计算结果与实验值的对比分析,其中应用SST湍流模型得到的颤振速度与实验值最为接近,特别是在跨音速段平均相对误差在3%以内;并且计算结果整体上反映了跨音速颤振"凹坑"物理特性,验证了方法的有效性。     

CFD／CSD紧耦合及新型动网格方法在气动弹性模拟中的应用

研发出一套基于紧耦合的CFD／CSD耦合方法和程序。非定常流场求解采用混合网格有限体积方法,时间离散采用基于LU-SGS隐式格式的双时间步长法。通过求解雷诺平均Navier—Stokes方程模拟了三维机翼的跨音速气动弹性现象。得到了其颤振边界,与风洞实验结果吻合较好,验证了方法和程序的有效性和实用意义。同时将Delau...     

DEVELOPMENT OF A THREE-DIMENSIONAL VISCOUS AEROELASTIC SOLVER FOR NONLINEAR PANEL FLUTTER

A new three-dimensional (3-D) viscous aeroelastic solver for nonlinear panel flutter is developed in this paper. A well-validated full Navier–Stokes code is coupled with a finite-difference procedure for the von Karman plate equations. A subiteration strategy is employed to eliminate lagging errors between the fluid and structural solvers. This approach eliminates the need for the development of a specialized, tightly coupled algorithm for the fluid/structure interaction problem. The new computational scheme is applied to the solution of inviscid two-dimensional panel flutter problems for subsonic and supersonic Mach numbers. Supersonic results are shown to be consistent with the work of previous researchers. Multiple solutions at subsonic Mach numbers are discussed. Viscous effects are shown to raise the flutter dynamic pressure for the supersonic case. For the subsonic viscous case, a different type of flutter behavior occurs for the downward deflected solution with oscillations occurring about a mean deflected position of the panel. This flutter phenomenon results from a true fluid/structure interaction between the flexible panel and the viscous flow above the surface. Initial computations have also been performed for inviscid, 3-D panel flutter for both supersonic and subsonic Mach numbers.     

Expectations for computational fluid dynamics

This article presents a sampling of the author's expectations for the field of computational fluid dynamics (CFD) in the areas of research, development and application. The primary focus of the discussion herein is related to the non-linear transonic flow regime, and more specifically, for calculations about commercial transport aircraft. However, many of these topics are pertinent to all flow field regimes and aircraft designs. The underlying goal is to enable the automation of multi-disciplinary design processes, which utilize state-of-the-art numerical simulation methods. These include issues pertaining to accuracy, robustness, efficiency, ease-of-use, uncertainty requirements and other challenges.     

HyperFLOW软件非结构网格亚跨声速湍流模拟的验证与确认

计算流体力学(computational fluid dynamics,CFD)数值模拟在航空航天等领域发挥越来越重要的作用,然而CFD数值模拟结果的可信度仍然需要通过不断地验证与确认来提高.本文给出了从制造解精度测试、简单到复杂外形湍流模拟网格收敛性研究等三个方面开展CFD软件验证与确认的方法,并对自主研发的CFD软件平台HyperFLOW在非结构网格上模拟亚跨声速湍流问题的能力进行了验证与确认.首先通过基于Euler方程和标量扩散方程的制造解精度测试,分别验证了HyperFLOW在非结构网格上对Euler方程和黏性项的求解精度,结果表明其能够在任意非结构网格上达到设计的二阶精度. 其次,通过NASATurbulence Modeling Resource中的湍流平板、二维翼型近尾迹流动、二维Bump等几个典型的亚声速湍流算例的网格收敛性研究,量化考察了数值结果的观测精度阶和网格收敛性指数,并与国外知名CFD解算器CFL3D,FUN3D的计算结果进行了对比,验证了HyperFLOW对简单湍流问题的模拟能力,且具有良好的网格收敛性和计算精度(阶). 最后,通过NASA CommonResearchModel标模定升力系数的网格收敛性研究和升阻极曲线预测,验证了软件在复杂外形亚跨声速湍流流动数值模拟中也具有良好的可信度.      

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.      

结合CFD和当地流活塞理论的全机组合体超声速颤振分析

针对翼．身组合体飞行器面对称布局的特点,利用模态振型的对称和反对称性,以分枝模态法建立结构的运动微分方程,结合CFD的当地流活塞理论计算飞行器的非定常气动力,建立飞行器全机组合体的气动弹性数学模型。对飞行器进行了来流为1．5～7马赫数下的颤振分析,结果与全CFD／CSD耦合时域仿真结果较好吻合,验证了本文方法在工程设计中的有效性和可行性。本文方法的效率在相同精度下比CFD／CSD耦合的时域方法高100倍。     

An embedded boundary framework for compressible turbulent flow and fluid–structure computations on structured and unstructured grids

The finite volume method with exact two‐phase Riemann problems (FIVER) is a two‐faceted computational method for compressible multi‐material (fluid–fluid, fluid–structure, and multi‐fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi‐phase flow problems, FIVER is a Godunov‐type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two‐phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi‐material computations on nonbody‐fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second‐order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)‐based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time‐dependent distance to the wall because it is required by many RANS‐based turbulence models. The second algorithm addresses the robust and accurate computation of the flow‐induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter‐rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A‐18 aircraft configuration and the comparison of the obtained numerical results with flight test data. Copyright © 2014 John Wiley & Sons, Ltd.