零攻角小钝头钝锥高超音速绕流边界层的稳定性分析和转捩预报

研究了零攻角小钝头圆锥高超音速边界层的稳定性及转捩预测问题．小钝头的球头半径为0.5 mm,锥的半锥角为5°,来流马赫数为6．采用直接数值模拟方法得到了钝锥的基本流场,利用线性稳定性理论分析了等温壁面和绝热壁面条件下的第一、第二模态不稳定波,并用“e-N”方法对转捩位置进行了预测．在没有实验给出N值的情况下,暂取N为10．研究发现,壁面温度条件对于转捩位置有较大影响．绝热边界层的转捩位置比等温边界层的靠后．且尽管高马赫数下第二模态波的最大增长率远大于第一模态波的最大增长率,但绝热边界层的转捩位置是由第一模态不稳定波决定的．研究方法应能推广到有攻角的三维边界层流动的转捩预测．     

高超音速零攻角尖锥边界层转捩的机理

先计算出高超音速零攻角尖锥边界层的定常层流流场．然后在计算域的入口引入两组有限幅值的T-S波扰动,对空间模式的转捩过程进行了直接数值模拟．分析了转捩过程的机理,发现平均流剖面稳定性的变化是其关键．并进一步讨论了不同模态初始扰动在高超音速尖锥边界层中的演化规律．     

PSE在边界层中预测转捩位置的应用

层流到湍流的转捩是自然界和各项工程实践中广泛存在的现象,层流和湍流的性质大不相同．因此,预测转捩位置是流体力学中的重要理论和实际问题．针对不可压缩边界层,入口加入展向等幅值型和展向波包型两类扰动,展向等幅值型扰动是由一个二维波(2-D)和两个三维波(3-D)组成,使用抛物化稳定性方程(PSE)的方法来研究扰动的演化和预测转捩位置,并且与数值模拟的结果相比较．结果表明,PSE可以研究扰动的演化和预测转捩位置,同时其计算比数值模拟快得多．     

后掠翼边界层定常横流涡的非线性演化

横流失稳是后掠翼边界层主要的失稳形式.实验和数值研究发现在后掠翼边界层转捩之前,有一段较长的非线性幅值饱和阶段,因此线性稳定性不能有效预测横流失稳转捩过程,所以研究横流涡的非线性演化过程就极为必要.以NLF(2)-0415翼型为研究模型,在来流Mach数为0.8、后掠角为45°、攻角为-4°的条件下,用扰动方程计算了定常横流涡非线性演化过程.结果显示非平行性起着更加不稳定的作用.当基本波的幅值到达0.1时,非线性作用开始明显.横流涡经历了非线性幅值饱和过程,涡的形状呈现半蘑菇状,涡的涡轴与边界层外缘无粘势流平行.饱和涡使得原有流场发生极大的扭曲,流向速度和展向剖面出现了拐点.     

超音速边界层中二维扰动的演化及小激波的产生

通过直接数值模拟的方法,对二维超音速边界层中扰动的演化进行了研究．以某一剖面作为入口,加入T-S波,研究小扰动波逐渐增长的演化过程．发现了扰动非线性演化的特征．探讨了二种判断激波存在的方法,证实了超音速边界层中当扰动达到一定的幅值时会有小激波出现．为建立可压缩流稳定性非线性理论提供一定的依据．     

脉冲波作用下的高超音速非定常流动模拟及影响研究

采用高阶精度有限差分方法模拟了快声波脉冲扰动作用下的高超音速非定常流场,分析了脉冲波与高超音速流场的相互干扰,并应用Fourier频谱分析研究扰动波在边界层的发展．结果表明:来流脉冲扰动波与激波及边界层强烈相互作用,弓形激波明显向内弯曲,激波后扰动波被显著放大;来流扰动波与弓形激波干扰形成的边界层外的扰动波和近壁面内形成的边界层扰动波存在明显分界．钝锥头部参数扰动幅值要远大于其他位置参数扰动幅值．在边界层内的发展阶段,一些扰动模态持续增长,一些扰动模态被过滤掉,不再增长,甚至衰减,而也有一些扰动模态先衰减再增长．总的来说,在钝锥头部低频扰动模态为主导模态,随着扰动从流场上游向下游发展,总扰动模态中的低频模态成份和高频模态成份所占的比例开始转变,高频模态成分显著地增大．     

计算可压缩边界层转捩及湍流的一种新方法——PSE＋DNS

提出了一种计算可压缩边界层转捩及湍流的新方法,它尤其适用于从小扰动开始的转捩及湍流计算.在层流阶段,直至转捩中的breakdown开始前,用抛物化稳定性方程(PSE)计算.然后用直接数值模拟(DNS)计算转捩过程和湍流,其入口条件是用PSE方法在该处得到的扰动.在两个测试算例中,包括亚音速和超音速边界层,此法得到的转捩位置和湍流都与只用DNS计算整个过程所得的一致.使用该方法的优点在于计算量比只用DNS方法小得多.     

超音速尖锥边界层中扰动演化特征的数值研究

采用高精度紧致格式, 对超音速尖锥边界层中二维扰动的空间演化, 进行了直接数值模拟．结果表明,虽然尖锥边界层流动存在一定的锥面法向速度,但小扰动的幅值及相位的演化都与由平行流假设得到的线性理论结果吻合．还研究了有限幅值扰动的演化,给出了其演化规律．并在扰动幅值增长到一定值时,发现了小激波．     

PSE在超音速边界层二次失稳问题中的应用

用抛物化稳定性方程（PSE）研究超音速边界层中的二次失稳问题．结果显示无论二维基本扰动是第一模态还是第二模态的T-S波,二次失稳机制都起作用．三维亚谐波的放大率随其展向波数和二维基本波幅值的变化关系与不可压缩边界层中所得类似．但是,即使二维波的幅值大到2％的量级,三维亚谐波的最大放大率仍远小于最不稳定的第二模态二维T-S波的放大率．因此,二次失稳应该不是导致超音速边界层转捩的主要因素．     

二维平板可压缩边界层的二次稳定性分析

本文在二维可压缩边界层中应用Floquet分析,建立了控制次谐波稳定性的方程组,研究在二维可压缩边界层转捩过程中二维有限振幅的T-S波对三维线性小扰动的作用,并计算了来流马赫数对次谐波的产生和发展情况的影响,从中可以看出二维和三维扰动波相互作用对二维可压缩流动边界层的发展过程所产生的影响.     

抛物化稳定性方程在可压缩边界层中应用的检验

用抛物化稳定性方程（PSE）,研究了可压缩边界层中扰动的演化,并与由直接数值模拟（DNS）所得进行比较．目的在检验PSE方法用于研究可压缩边界层中扰动演化的可靠性．结果显示,无论是亚音速还是超音速边界层,由PSE方法和由DNS方法所得结果都基本一致,而温度比速度吻合得更好．对超音速边界层,还计算了小扰动的中性曲线．与线性稳定性理论（LST）的结果相比,二者的关系和不可压边界层的情况相似．     

Transition to turbulence, small disturbances, and sensitivity analysis II: The Navier-Stokes equations

Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one-dimensional Burgers' equation. In this paper, we extend the analysis to study the effects of small disturbances on transition to turbulence in the three-dimensional Navier-Stokes equations. We show that the change in a laminar flow with respect to small variations in the initial flow or small forcing acting on the system is large when the linearized operator is stable yet nonnormal. In this case, the solution of the disturbed problem can be very large (and potentially turbulent) even if the disturbances are extremely small. We also give bounds on the disturbed flow in terms of certain constants associated with the linearized operator.     

Effect of surface elasticity on the transformation of acoustic disturbances into Tollmien-Schlichting waves in a boundary layer at transonic free-stream velocities

Within the framework of the triple deck theory, the effect of an elastic surface on the characteristics of a wave packet generated by acoustic disturbances in a boundary layer at transonic free-stream velocities is investigated.     

4度Cayley图的Hamilton圈分解的新方法与理论证明

给出了＂Hamilton圈侧枝循环＂等四个定理.它揭示了Abel群上4度Cayley图的Hamilton圈分解的特点及规律.同时,提出了Hamilton圈上＂单向通道＂的＂离合＂理论.在此基础上给出了Abel群上4度Cayley图的Hamilton圈分解的新方法-＂离合法＂,此方法具有简明、快捷、分解方案多的特点.另外,Hamilton圈＂单向通道＂的＂离合＂理论还为解决6度Cayley图的Hamilton圈分解奠定了理论基础.     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

Robust state estimation and fault diagnosis for uncertain hybrid nonlinear systems

Robust state estimation and fault diagnosis are challenging problems in the research of hybrid systems. In this paper, a novel robust hybrid observer is proposed for a class of uncertain hybrid nonlinear systems with unknown mode transition functions, model uncertainties and unknown disturbances. The observer consists of a mode observer for discrete mode estimation and a continuous observer for continuous state estimation. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to unknown transition functions, model uncertainties and disturbances can be guaranteed by disturbance decoupling and selecting proper thresholds. The transition detectability and mode identifiability conditions are rigorously analyzed. Based on the robust hybrid observer, a robust fault diagnosis scheme is presented for faults modeled as discrete modes with unknown transition functions, and the analytical properties are investigated. Simulations of a hybrid three-tank system demonstrate that the proposed approach is effective.     

二级传递性与二级传递模糊矩阵

推广传递性概念,给出二级传递性的定义;研究二级传递模糊矩阵的性质,给出其若干等价刻画;证明二级传递模糊矩阵或者收敛或者周期为2,指数不大于n 1;讨论二级传递与强传递、k-传递和泛传递等概念之间的关系,指出二级传递是传递性概念的一种新的推广形式。