复杂约束环境下基于控制理论的透平叶栅气动优化

本文应用控制理论,基于网格节点位置坐标直接变分法建立了N-S方程的伴随系统.以叶栅通道内熵增最小为目标函数,并以流量为约束条件,详细推导了具有约束条件的二维N-S方程伴随系统的偏微分方程组及其相应的边界条件和敏感性导数的表达式。建立了基于黏性连续伴随方程和N-S方程的二维叶栅气动优化设计系统,并成功地应用于某一跨音速叶栅的优化设计。对计算结果的分析表明,该方法能够适用于透平叶栅气动优化设计。     

透平叶栅三维粘性气动反问题的控制理论方法

将基于控制理论的形状优化设计方法应用于粘性可压流动条件下的透平叶栅三维气动反设计,详细推导了三维N-S方程伴随系统的偏微分方程组及其各类边界条件.讨论了伴随系统的解的适定性条件,并由此给出应用N-S方程进行气动优化的目标函数的选取限制.研究了伴随方程的数值求解技术,给出敏感性导数的最终计算式,结合拟牛顿算法发展了三维透平叶栅粘性反问题的气动设计方法.     

透平叶栅三维形状反问题研究

随着CFD技术的发展,基于伴随方法的求解Euler和NS方程的气动优化设计已成为流体力学形状反问题研究中的热门领域.本文应用该方法对透平叶栅进行三维气动优化设计,详细推导了Euler方程伴随系统的偏微分方程组及其各类边界条件,首次给出了透平内流伴随方程边界条件的具体形式,并给出伴随变量的物理意义.结合拟牛顿算法发展了三维透平叶栅形状反问题气动优化算法,并给出了算法的流程.     

应用控制理论的叶栅气动反设计

基于控制理论的气动设计方法作为一种基于梯度的优化方法,通过引入伴随系统计算目标函数的敏感性导数,大大降低设计成本.本文将基于控制理论的气动设计方法应用到透平叶栅的气动反问题中,应用Euler方程研究了二维叶栅的压力反设计问题,并讨论了该方法具体实施中的关键问题,包括采用非均匀B样条进行二维叶栅造型;应用Thompson时间相关边界条件理论进行伴随方程特征分析;研究伴随方程的数值求解方法,构造伴随方程的耗散通量.通过算例证明了该气动设计方法适用性好,速度快,可以大大节约计算成本.     

二维不可压流函数N-S方程的多重网格方法

通过对二维不可压缩N-S方程的涡量-流函数方程组消去涡量而得到仅以流函数为求解变量的控制方程,从而 使不可压N-S方程的求解个数减到最少。求解方法采用本文提出的二阶精度的九节点紧致差分格式,因此无须对靠近边 界的网格点作特殊处理。为了加快迭代收敛速度,采用多重网格加速技术。数值实验结果验证了方法的精确性和可靠性。     

非定常动态演化伴随优化设计方法

研究了基于定常流动解和伴随方程定常解基础上的传统的伴随方法.在此基础上对定态飞行气动外形的优化设计提出了基于非定常流动控制方程瞬态解和非定常伴随方程瞬态解的新的优化方法,称之为动态演化伴随方法.这种新的优化方法保留了传统伴随方法适用于具有大数量设计变量的气动优化问题,而且比传统的伴随方法可节省大量的计算时间.大量算例计算结果表明,新方法与传统方法具有相同的精度.     

基于离散伴随方法的透平叶栅气动优化设计

本文研究并给出了基于离散伴随理论和自动微分技术构建离散伴随系统的方法、伴随系统的求解策略以及基于离散伴随方法的透平叶栅气动优化设计流程,建立了相应的优化设计系统。利用该优化系统在无黏环境下,以叶栅通道进出口的熵增率为目标函数、以叶栅通道内的质量流量为约束,对某二维跨音速透平叶栅进行了气动优化设计。与优化前相比,优化后透平叶栅进出口熵增率减少8.82%,质量流量变化幅度小于0.003%。优化结果表明,本文提出的优化系统能够有效改善透平叶栅的气动优化性能,验证了本文提出的基于离散伴随方法的透平叶栅气动优化设计方法的正确性与有效性。     

��������������������ƽ��߽��ķ����о�

对等离子体气动激励控制边界层进行了数值仿真。将等离子体气动激励对边界层的作用建模成动量和热量。通过由基于表面放电的二维流体体力模型得到的等离子体气动激励的体力分布函数,得到向边界层注入的动量和热量分布,将动量和热量以源项的形式引入N-S方程求解。研究了等离子体气动激励的强度、激励电极的数目、来流速度的大小以及热量项的大小对等离子体气动激励作用效果的影响,仿真结果与实验一致。     

切变入流风况下风力机尾流特性研究

致动线模型利用旋转的线表示叶片,利用二维翼型气动数据根据BEM理论计算叶素点作用力,同时通过求解N-S方程计算转子流场。本文首先基于商业CFD软件ANSYS FLUENT开发了致动线模型,并计算了切变入流风况下风力机的气动和尾流特性,发现由于地面阻碍和风切变效应导致风力机尾流存在明显的非对称特征。     

基于伴随方法的多级叶轮机三维叶片优化设计

伴随方法单次优化循环计算量与设计变量数目基本无关,多设计变量时计算成本低。本文采用伴随方法发展了多级叶轮机三维黏性气动形状优化方法,包括伴随方程及其边界条件、目标函数与设计变量的敏感性关系。结合基于Hicks-Henne函数的三维叶片参数化方法和最速下降法建立了气动形状优化设计系统。针对1.5级压气机第二排叶片的反设计验证了该优化系统的有效性;以进、出口熵增为目标函数改型设计某1.5级超音压气机,改型后气动性能明显提升。     

Energy flow analysis and design sensitivity of structural problems at high frequencies

The design sensitivity formulation of an energy finite element method is presented using the direct differentiation and adjoint variable methods. The continuum method is used to derive the design sensitivity equation of the energy flow equation, whereas the discrete method is used to calculate the variation of the coupling relation. For design variables, material property, panel thickness, and structural shape are taken into account, in addition to the structural damping factor. The design variable's effect on the power transfer coefficient is discussed in detail. Even if the system matrix equation is not symmetric, the adjoint problem is solved using the same factorized matrix from response analysis. Design sensitivity results calculated from the proposed method are compared to the finite difference sensitivity results with a good agreement.     

Vibro-acoustic design sensitivity analysis using the wave-based method

Conventional element-based methods, such as the finite element method (FEM) and boundary element method (BEM), require mesh refinements at higher frequencies in order to converge. Therefore, their applications are limited to low frequencies. Compared to element-based methods, the wave-based method (WBM) adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains. As such, the WBM does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency. In this paper, the design sensitivity formulation of a semi-coupled structural-acoustic problem is implemented using the WBM. Here, the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain, which consists of multiple wave-based subdomains. The cross-sectional area of each beam element is considered as a sizing design variable. Then, the adjoint variable method (AVM) is used to efficiently compute the sensitivity. The adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary. The proposed sensitivity formulation is subsequently applied to a two-dimensional (2D) vehicle model. Finally, the sensitivity results are compared to the finite difference sensitivity results, which show good agreement.     

Level set based structural topology optimization for minimizing frequency response

For the purpose of structure vibration reduction, a structural topology optimization for minimizing frequency response is proposed based on the level set method. The objective of the present study is to minimize the frequency response at the specified points or surfaces on the structure with an excitation frequency or a frequency range, subject to the given amount of the material over the admissible design domain. The sensitivity analysis with respect to the structural boundaries is carried out, while the Extended finite element method (X-FEM) is employed for solving the state equation and the adjoint equation. The optimal structure with smooth boundaries is obtained by the level set evolution with advection velocity, derived from the sensitivity analysis and the optimization algorithm. A number of numerical examples, in the frameworks of two-dimension (2D) and three-dimension (3D), are presented to demonstrate the feasibility and effectiveness of the proposed approach.     

Shape design sensitivity analysis for the radiated noise from the thin-body

Many industrial applications generally use thin-body structures in their design. To calculate the radiated noise from vibrated structure including thin bodies, the conventional boundary element method (BEM) using the Helmholtz integral equation is not an effective resolution. Thus, many researchers have studied to resolve the thin-body problem in various physical fields. No major study in the design sensitivity analysis (DSA) fields for thin-body acoustics, however, has been reported.A continuum-based shape DSA method is presented for the radiated noise from the thin-body. The normal derivative integral equation is employed as an analysis formulation. And, for the acoustic shape design sensitivity formulation, the equation is differentiated directly by using material derivative concept. To solve the normal derivative integral equation, the normal velocities on the surface should be calculated. In the acoustic shape sensitivity formulation, not only the normal velocities on the surface are required but also derivative coefficients of the normal velocities (structural shape design sensitivity) are also required as the input. Hence, the shape design sensitivity of structural velocities on the surface, with respect to the shape change, should be calculated. In this research, the structural shape design sensitivities are also obtained by using a continuum approach. And both a modified interpolation function and the Cauchy principle value are used to regularize the singularities generated from the acoustic shape design sensitivity formulation.A simple annular disk is considered as a numerical example to validate the accuracy and efficiency of the shape design sensitivity equations derived in this research. The commercial BEM code, SYSNOISE, is utilized to confirm the results of the developed in-house code based on a normal derivative integral equation. To validate the calculated design sensitivity results, central finite difference method (FDM) is employed. The error between FDM and the analytical result are less than 3%. This comparison demonstrates that the proposed design sensitivities of the radiated pressure are very accurate.     

Neutron and Proton Diffusion in Fusion Reactions for the Synthesis of Superheavy Nuclei

The restriction of the one dimensional （1D） master equation （ME） with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional （2D） master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out.     

基于Riccati方程和LMI算法的H∞控制器的设计与实现

H∞控制是一种重要的鲁棒控制方法,它以H∞范数作为控制性能指标,是一种最优控制方法,目的是求出系统内部稳定的控制器,使闭环传递函数的无穷范数极小,达到控制的目的。以固高公司的直线一级倒立摆为控制对象,实现基于Riccati方程和LMI算法的H∞控制器设计,采用M文件及simulink实现系统建模、控制器的设计,完成系统算法的验证,实验表明,控制器的输出、倒立摆系统的状态变量变化平稳,系统具有较强的鲁棒性,系统表现出良好的动态品质,验证了H∞控制器的有效性。     

夹层式光纤激光水听器探头优化设计

为改善分布反馈式(DFB)光纤激光器水声探测性能,利用有限元软件ANSYS,以相对加速度灵敏度为目标函数,结构尺寸参数为设计变量,结构第一阶固有频率和探头声压灵敏度为状态变量,对夹层式封装结构进行了优化设计,对其声压探测及抗加速度机理进行了分析。分析表明,基于优化结果设计的探头在采用100m非平衡干涉仪时,其声压灵敏度约为-135.1dB,相对加速度灵敏度可达到-19.6dB。结果表明,基于封装结构敏感部分分别承受声压激励和加速度激励时的不同响应机理,对夹层式封装结构关键部位尺寸进行优化设计后,通过合理选择承压梁与中间变形梁的厚度以及上下连接点的位置,封装制得的光纤激光水听器具有较高的声压灵敏度和良好的抗加速度性能。     

Shape and topology optimization based on the phase field method and sensitivity analysis

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.     

Stabilization of an axially moving web via regulation of axial velocity

In this paper, a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented. The principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly. The optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations (ODEs). For control design purposes, these ODEs are rewritten into state-space equations. The vibration energy of the axially moving beam is represented by the quadratic form of the state variables. In the optimal control problem, the cost function modified from the vibration energy function is subjected to the constraints on the state variables, and the axial transport velocity is considered as a control input. Numerical simulations are performed to confirm the effectiveness of the proposed control algorithm.