壁板颤振的分析模型、数值求解方法和研究进展

研究壁板颤振问题需要计及大挠度变形下结构的几何非线性效应,不仅涉及气动弹性稳定性,而且关心结构的非线性颤振响应.该文回顾了飞行器壁板颤振问题的国内外研究情况,评述了在壁板颤振研究中采用的分析模型、数值求解方法以及在理论分析和试验方面的研究成果,并提出了今后壁板颤振问题的4个研究方向.      

激波主导流动下壁板的热气动弹性稳定性理论分析

针对激波主导流动下弹性壁板的热气动弹性稳定性分析问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性. 首先基于Hamilton原理和Von-Karman大变形理论,建立壁板的热气动弹性运动方程,其中假设壁板受热后温度均匀分布,激波前后区域的气动力模型采用当地一阶活塞流理论;利用Galerkin方法将具有连续参数系统的偏微分颤振方程离散为有限个自由度的常微分方程;基于李雅普诺夫间接法将非线性颤振方程组在平衡位置处进行线化,再用Routh-Hurwits判据来判断线性系统的稳定性,从而来推论出非线性颤振系统的气动弹性稳定性. 在时域中采用龙格--库塔法对非线性颤振方程进行数值积分,得到壁板非线性颤振响应的时间历程,与理论分析结果进行对比. 研究结果表明,壁板受到斜激波冲击时,更容易发生颤振失稳,并且激波强度越大,极限环幅值和频率越大;激波主导流场中的壁板失稳边界不同于传统单纯超声速气流中壁板颤振的失稳边界;只有在斜激波前后不同的动压值都满足颤振稳定性边界的条件下,壁板才可能保持其气动弹性稳定性.      

激波主导流动下壁板的热气动弹性稳定性理论分析

针对激波主导流动下弹性壁板的热气动弹性稳定性分析问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性.首先基于Hamilton原理和Von-Karman大变形理论,建立壁板的热气动弹性运动方程,其中假设壁板受热后温度均匀分布,激波前后区域的气动力模型采用当地一阶活塞流理论;利用Galerkin方法将具有连续参数系统的偏微分颤振方程离散为有限个自由度的常微分方程;基于李雅普诺夫间接法将非线性颤振方程组在平衡位置处进行线化,再用Routh-Hurwits判据来判断线性系统的稳定性,从而来推论出非线性颤振系统的气动弹性稳定性.在时域中采用龙格-库塔法对非线性颤振方程进行数值积分,得到壁板非线性颤振响应的时间历程,与理论分析结果进行对比.研究结果表明,壁板受到斜激波冲击时,更容易发生颤振失稳,并且激波强度越大,极限环幅值和频率越大;激波主导流场中的壁板失稳边界不同于传统单纯超声速气流中壁板颤振的失稳边界;只有在斜激波前后不同的动压值都满足颤振稳定性边界的条件下,壁板才可能保持其气动弹性稳定性.     

文章导读

正飞机结构气动弹性分析与控制研究(1–27,doi:10.6052/0459-1879-15-423)胡海岩,赵永辉,黄锐评述飞机结构气动弹性研究进展并重点介绍作者的如下研究成果:在亚音速气动弹性研究中,揭示多个控制面间隙、反馈时滞对颤振的影响机理,提出时滞最优控制方法,经风洞实验证明可在较大流速范围内抑制颤振;在跨音速气动弹性研究中,提出非线性气动力的降阶模型,进而有效提高了跨音速颤振分析和颤振主动抑制的效率.     

超声速复合材料层合壁板结构的颤振特性分析

对超声速复合材料壁板结构的气动弹性颠振特性进行了分析研究.采用Hamilton原理和假设模态法建立结构的运动方程,采用活塞理论模拟超声速非定常气动力,通过求解本征值问题,得到结构的固有频率和阻尼比等物理量.数值计算了结构无量纲固有频率随气动压力的变化曲线,确定颤振临界气动压力(或颤振速度),并计算了结构的受迫振动时间响应历程曲线,分析比较了不同纤维铺设方式和不同铺设角度对超声速复合材料壁板结构气动弹性稳定性的影响.本文研究结果对超声速飞行器壁板结构的气动弹性稳定性分析和设计具有理论参考价值.     

基于流形切空间插值的折叠翼参数化气动弹性建模

变体飞行器的气动弹性力学建模是当前先进飞行器设计的研究热点和难点. 然而传统的气动弹性动力学建模方法对于具有结构参变特性的变体飞行器气动弹性力学研究存在建模效率低、计算复杂等问题. 本研究提出了一种基于流形切空间插值的可折叠式变体机翼参数化气动弹性建模方法. 首先, 该方法建立若干个典型折叠角下的折叠翼结构有限元模型, 通过流形切空间插值方法建立折叠翼参数化结构动力学模型. 其次, 采用偶极子网格法得到参数化非定常气动力模型, 进而建立气动和结构相互耦合的折叠翼参数化气动弹性模型. 为了验证该参数化建模方法在折叠翼气动弹性分析中的准确性, 本文以一小展弦比折叠翼为研究对象, 从折叠翼自由振动时的参变模态特性、颤振边界预测两方面进行了算例验证, 并与直接计算方法进行了对比, 进一步验证了参数化气动弹性模型的有效性. 研究结果表明, 该参数化气动弹性模型对上述两类问题的计算精度与直接计算方法一致, 并且有着计算效率更高的优势.      

采用压电材料提高超声速飞行器壁板结构的颤振特性

采用压电材料对结构进行振动主动控制已经进行了广泛研究,论文进一步采用压电材料改进超声速壁板结构的气动弹性颤振特性,研究中考虑压电材料力电耦合效应的影响.采用Hamilton原理和Rayleigh-Ritz方法建立壁板及压电材料整体结构的运动方程,采用超声速活塞理论模拟气动力,利用加速度反馈控制策略对压电材料施加外电压,获得结构的主动质量.求解运动方程的特征值问题获得固有频率,进而确定气动弹性颤振边界,分析了反馈控制增益对超声速飞行器壁板结构主动颤振特性的影响,研究表明,采用压电材料可以提高超声速壁板结构的气动弹性颤振特性.     

浅谈飞行器与桥梁的颤振问题

颤振属于气动弹性动不稳定现象，常见于飞行器机翼和尾翼、桥梁等弹性结构，一旦发生，可能会引发结构的毁灭性破坏。本文首先介绍颤振的基本概念和特征，以及工程领域中常用的颤振研究方法，以展弦比为16的NACA0012弹性平直机翼为例介绍颤振速度和颤振频率；然后对结构发生颤振的原因进行讨论，并详细阐述基于流动降阶模型的稳定性分析方法在层流分离颤振诱发机理研究中的应用；最后对防止和规避颤振的控制措施进行介绍。     

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法. 首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识. 其次,引入状态和控制输入的非线性函数, 采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比, 进一步说明本文所提出方法的有效性.研究结果表明, 该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.      

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法.首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识.其次,引入状态和控制输入的非线性函数,采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比,进一步说明本文所提出方法的有效性.研究结果表明,该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.     

CONTROL OF BLADE FLUTTER USING CASING WITH ACOUSTIC TREATMENT

Control of blade flutter by use of a nonrigid wall may have several advantages compared with the existing method of suppressing blade flutter; but it indeed leads to numerous theoretical problems which have never been clearly elucidated by the existing theories. In the present investigation a new lifting surface model has been suggested based on the application of generalized Green's function theory and double Fourier transformation technique, which is expressed as various upwash integral equations and the corresponding kernel function. In particular, it is found that the change of wall boundary condition not only affects the eigenvalues of the system but also the eigenfunction normalizing factor in comparison with a rigid boundary condition, and it is these variations that finally affect the flow and acoustic field. In addition, the numerical results show that whether a nonrigid wall has positive or negative effect on suppressing blade flutter will mainly depend on what admittance value the wall possesses. It is clear that this conclusion has two implications. One is that there is indeed some possibility for designing a liner for suppressing blade flutter. The second is that modern jet engines using a nonrigid wall or liner to suppress the noise can introduce a detrimental effect on blade flutter stability.     

Quasi-steady prediction of coupled bending–torsion flutter under rotating stall

A method is presented in this paper to predict cascade flutter under subsonic stalled flow condition in a quasi-steady manner. The ability to predict the occurrence of aeroelastic flutter is highly important from the compressor design point of view. In the present work, the well known Moore–Greitzer compression system model is used to evaluate the flow under rotating stall and the linearized aerodynamic theory of Whitehead is used to estimate the blade loading. The cascade stability is then predicted by solving the structural model, which is posed as a complex eigenvalue problem. The possibility of occurrence of flutter in both bending and torsional modes is considered and the latter is found to be the dominant one, under subsonic stalled flow, for a large range of frequency ratios examined. It is also shown that the design of compressor blades at frequency ratios close to unity may result in rapid initiation of torsional flutter in the presence of stalled flow. A frequency ratio of 0.9 is primarily emphasized for most part of the study as many interesting features are revealed and the results are physically interpreted. Roughly a pitchfork pattern of energy distribution appears to occur between bending mode and torsional mode which ensures that only one flutter mode is possible at any instant in time. A bifurcation from bending flutter to torsional flutter is shown to occur during which the frequency of the two vibrating modes appear to coalesce for a very short period of time.     

Numerical identification of mechanisms triggering 2D choke flutter in transonic fan

Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery choke flutter appears when a strong shock-wave chokes the blade passage. The aim of this study is to identify mechanisms responsible for the instability. An innovative methodology relying on the splitting of the emitter and receiver role of the blade is presented. It is successfully applied to 2D linearized RANS computations of choke flutter. The emission splitting shows that the vibration of the blades downstream of the shock-wave generates a backward traveling pressure wave triggering the aeroelastic instability. The reception splitting demonstrates the destabilising contribution of the shock-wave / separated boundary layer interaction. The source of flutter is finally a combination of inviscid (regressive waves) and viscous (unsteady separation) mechanisms.     

Eigenvalue problem for integro-differential equation of supersonic panel,flutter

The dynamic stability of a thin plate in supersonic flow based on 2-dimensional linear theory leads to the study of a new problem in mathematical physics: complex eigenvalue prob-lem for a non-self-adjoint fourth-order integro-differential equation of Volterra’s type.Exact solutions of the aeroelastic system is obtained. In contrast to various approximate analyses, our critical curve agrees satisfactorily with experimental data, being free from divergence in the low supe’rsonic region. Moreover, we observe some notable physical behaviors: (1) mutual separation of flutter and vacuum frequency spectrums, (2) degeneracy of critical Mach number. The present method may be generalized in solving the supersonic flutter for 3-dimensional airfoil model as well as blade cascade in turbo-generator.     

A check on the energy method of predicting blade transonic stall flutter

An improved structural dynamic model of an oscillating blade in two degrees of freedom is combined with an unsteady aerodynamic model for the transonic flow about a cascade with separation, which results in a coupled system. The system is solved in an iterative way between the two models. As a check on the current energy methods, the stall flutter boundaries for two real rotors are predicted by using the present method and the results are compared with the experiments and those predicted by using an energy method.     

Investigation of flow separation in a transonic-fan linear cascade using visualization methods

An extensive experimental study into the nature of the separated flows on the blade suction surface of modern transonic fans is described in this paper. The study was a subtask of a larger experimental effort focused on blade flutter excited by flow separation in the blade tip region. The tip sections of airfoils on transonic fan blades are designed for precompression and consequently they differ from sections on the rest of the blade. The blade tip section was modeled by a low aspect ratio blade and therefore most of the blade tested was exposed to the secondary flow effects. The aim of this work was to supply reliable data on flow separation on transonic fan blades for validation of future analytical studies. The experimental study focused on two visualization techniques: surface flow visualization using dye oils and schlieren (and shadowgraph) flow visualization. The following key observations were made during the study. For subsonic inlet flow, the flow on the suction surface of the blade was separated over a large portion of the blade, and the separated area increased with increasing inlet Mach number. For the supersonic inlet flow condition, the flow was attached from the leading edge up to the point where a bow shock from the upper neighboring blade imposed on the blade surface. Downstream, there was a separated flow region in which air flowed in the direction opposite the inlet flow. Finally, past the separated flow region, the flow reattached to the blade surface. For subsonic inlet flow, the low cascade solidity resulted in an increased area of separated flow. For supersonic flow conditions, the low solidity resulted in an improvement in flow over the suction surface.     

Numerical modeling of gas flow around oscillating compressor blades

The problem of gas flow around a plane cascade of oscillating blades is numerically solved using the ANSYS CFX package. The blade surface displacement is taken into account using a movable grid generated before the beginning of the calculations at each time step. The calculated and experimental data are compared. The calculated results are used for determining the blade stability against flutter.     

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。     

Mathematical model of aeroelastic vibrations of cascades of axial turbomachine blades,caused by circumferential nonuniformity of the flow

A system of linear differential equations with time-dependent coefficients, which describes aeroelastic vibrations of blade cascades in a nonuniform flow, is derived. With the use of the model of an ideal incompressible fluid and the hypothesis of cylindrical sections, determination of aerodynamic forces acting on the blades is reduced to solving problems by methods fairly well developed in the theory of cascades in unsteady flow. The possibility of the emergence of a parametric resonance is analyzed. It is demonstrated that circumferential nonuniformity of the flow in the turbomachine duct can substantially reduce the critical velocity of the cascade flutter.