圆环旋转黏性液体射流空间不稳定性研究

利用线性稳定性理论, 进行了液体黏性对不同旋转强度下圆环旋转液体射流 空间不稳定性影响的研究. 在推导出的三维扰动下具有固体涡核型旋转速度分布的圆环旋转 黏性液体射流色散方程的基础上, 针对中低速射流, 进行了类反对称模式与类对称模式下圆 环旋转黏性液体射流的空间不稳定性分析. 研究结果表明, 对于旋转强度较大的圆环旋转液 体射流, 液体黏性的增加, 不利于射流的破碎; 随着液体黏性的增加, 射流的特征频率和最 不稳定波数减小. 然而, 对于旋转强度较小的圆环旋转液体射流, 液体黏性的增加, 有利于 射流的破碎; 随着液体黏性的增加, 类反对称模式下射流特征频率先减小后增大, 类对称模 式下射流特征频率增大; 随着液体黏性的增加, 类反对称模式下射流最不稳定波数先减小后 增大, 类对称模式下射流最不稳定波数增大.     

混合流体分离比对摆动行波的影响

利用Simple算法对流体力学基本方程组进行了数值模拟,研究了摆动行波的特性。结果表明:在摆动行波存在的范围内,当相对瑞利数r较小时,腔体内沿着空间的平均波数是随着时间周期变化的;当r较大时,腔体内沿着空间的平均波数随着时间增大保持为常数。摆动行波的摆动周期随r的增大而减小;分离比负值越大,变化越平缓,摆动行波出现的范围越大。随着长高比增加,较小分离比时,摆动周期的上、下限明显提高;分离比较大时,摆动行波存在区间对应的r上、下限明显增加。     

摆动行波的时空结构

基于流体力学方程组,对长高比Γ=30腔体内混合流体对流中摆动行波的时空结构进行了数值模拟。结果发现:当分离比Ψ=-0.6,-0.4时,在摆动行波存在的下临界附近,摆动行波的对流滚动有消失也有产生,对流平均波数在周期内变化;在摆动行波存在的上临界附近,摆动行波的对流滚动既无消失也无产生,对流平均波数保持为常数。随着相对瑞利数r的增加,对流滚动的摆动幅度和摆动周期明显减小。当分离比Ψ=-0.6时,摆动行波是准周期的;当分离比Ψ=-0.4时,摆动行波是周期的;当分离比Ψ=-0.2时,在摆动行波存在的下临界附近,观察到了一种沿着行波的对称轴线两侧发生对称的摆动行波的新型对流结构。在摆动行波存在的上临界附近,摆动行波是无周期的。随着分离比负值减小,摆动行波存在的上、下限下移,摆动行波存在的稳定区间Δr减小。     

射线寻迹法分析旋转不等截面圆环结构的动态响应

用射线寻迹法分析了旋转不等截面圆环的自由响应和受迫响应问题。首先,建立了单元局域坐标系,用行波、快衰和近场波动表示波在单元结构内的振动位移;其次,将激励力视为一种特殊的不连续节点,激励点两端为两个不同单元,考虑不同单元之间通过转递系数和转换矩阵耦合,并引入反射矩阵和透射矩阵处理行波在单元间的传播;再次,将结构的稳态响应表达为波动所有迹的叠加,而将自由振动表达为波幅矢量初始迹为零的情况;最后,根据波传递规则将弹性波动的反射矩阵和透射矩阵进行集成,对独立波动单元进行总装,从所得的动力学模型得到旋转不等截面圆环的响应。在给出了行波在该动态模型中传播特性的基础上,由数值算例可以发现旋转状态下圆环的各阶响应频率都高于静止状态下的响应频率。研究内容有助于高速轴承保持架、MEMS转子等的动态特性的精确计算。     

质量周期分布对偏心旋转环状结构自由振动的影响

工程实际中,某些旋转对称设计结构由于存在制造安装误差常呈现偏心旋转状态,进而影响结构稳定性.针对该类环状周期结构,考虑其偏心运动,研究附加质量周期分布参数以及偏心率对系统固有频率与动力稳定性的影响.首先,在环状结构上建立随动坐标系,利用Hamilton原理建立动力学模型.其次,采用经典振动理论求解系统的特征值,分析不同参数组合下的模态特性和不稳定性.最后,利用数值法计算系统的动态响应,并与解析结果进行对比.结果表明,当附加质量个数与波数满足一定关系时,固有频率发生分裂;对于不同的偏心率和周期分布特征,系统在不同转速下动力性能差异较大,适当提高偏心率、选取合适的附加质量个数及大小可有效抑制不稳定性.此研究有助于分析工程实际中该类结构的动力学稳定性,为其振动控制提供借鉴.     

圆环旋转粘性液膜射流三维不稳定性研究

利用线性稳定性理论进行了射流液体粘性对圆环旋转液膜射流稳定性影响的研究,推导出了三维扰动下具有固体旋涡型速度分布的圆环旋转粘性液膜射流的色散方程;在此基础上进行了类反对称模式与类对称模式下的圆环旋转粘性液膜射流的三维不稳定性分析。研究结果表明,在类反对称模式下,液体粘性超过一定值后,射流最大扰动增长率随液体粘性的增加而迅速减小;轴对称模态的射流特征频率产生一个突降变化;随液体粘性增加,轴对称模态不稳定波数范围减小,非轴对称模态不稳定波数范围呈现出先减小后增大趋势。在类对称模式下,液体粘性对射流最大扰动增长率的影响主要体现在对非轴对称模态的影响上;液体粘性只在粘性较大时才会对非轴对称模态射流特征频率产生一定影响;液体粘性超过一定值后,轴对称模态与非轴对称模态的不稳定波数范围都会快速下降。     

旋转FGM圆环形截面柔性梁的振动特性

工程实际中直升机的旋翼和风力机的叶片等可简化为旋转柔性悬臂梁的动力学问题。针对旋转FGM圆环形截面柔性悬臂梁的横向振动问题,基于Euler-Bernoulli梁理论和Hamilton原理,建立了自由振动时的运动微分方程。对运动微分方程和边界条件进行量纲归一化处理,采用微分求积法对其进行离散化,得到了系统的广义特征方程。分析了旋转FGM圆环形截面柔性梁的前三阶量纲为一的固有频率随梯度指标和不同梯度指标、径长比下量纲为一的固有频率随轮毂量纲为一的角速度的变化关系。数值计算结果表明,在给定某些参数情况下,旋转FGM环形截面悬臂梁的前三阶量纲为一的固有频率随轮毂量纲为一的角速度的增大而增大,第二阶、第三阶量纲为一的固有频率随梯度指标的增大而增大的趋势较为明显。     

旋转载体驱动硅微机械陀螺幅频特性

介绍了一种安装在旋转体上,用于旋转体姿态控制的新型微机械陀螺.陀螺利用旋转载体的滚转获得角动量,当载体发生偏航或俯仰,敏感质量块受到周期性哥氏力的作用,从而敏感载体的偏航或俯仰角速度.飞行试验中舵机的舵偏打容易使陀螺发生共振,陀螺输出信号无法满足旋转载体姿态控制的要求.针对这一问题,需精确测量陀螺的固有频率.首先基于陀螺运动方程分析了其幅频特性和固有频率,并利用数值计算软件进行了仿真,最后提出了一种对该陀螺幅频特性的测量方法,得到了幅频特性曲线,确定了固有频率70 Hz.实际测量的幅频特性曲线和仿真曲线一致,测量的固有频率相对于舵偏打产生的共振频率点误差为2.1%,通过避开测得的70 Hz 固有频率,获得了符合姿态控制要求的陀螺输出信号.     

径向分布外压力作用下圆环失稳临界压力的突变理论解法

用突变理论方法验证了受均匀压缩圆环失稳的临界压力.从圆环突变模型的分叉集方程看到,圆环可以在高于各临界压力的情况下发生相应波数的失稳.文中给出在径向分布力作用下,圆环失稳前后其中层位移的近似表达式.     

径向分布外压力作用下圆环失稳临界压力的突变理论解法

用突变理论方法验证了受均匀压缩圆环失稳的临界压力.从圆环突变模型的分叉集方程看到,圆环可以在高于各临界压力的情况下发生相应波数的失稳.文中给出在径向分布力作用下,圆环失稳前后其中层位移的近似表达式.     

On the resonant nonlinear traveling waves in a thin rotating ring

Large amplitude, traveling wave motion of an inextensible, linearly elastic, rotating ring is analyzed. Equations governing the planar dynamics of a thin rod, curved in its undeformed state and moving in a horizontal reference frame which rotates about a fixed axis, are obtained via Hamilton's extended principle. The equations are specialized to study the behavior of a rotating circular ring and approximate solutions are obtained near resonance utilizing a perturbation analysis. Undamped free and viscously damped forced traveling wave motion is considered. The motion is found to consist of a forward and a backward traveling wave which may be coupled due to the non-linear terms present in the equations of motion     

Nonlinear vibrations of rotating thin circular cylindrical shell

Nonlinear vibrations of thin circular cylindrical shells are investigated in this paper. Based on Love thin shell theory, the governing partial differential equations of motion for the rotating circular cylindrical shell are formulated using Hamilton principle. Taking into account the clamped-free boundary conditions, the partial differential system is truncated by using the Galerkin method. Sequentially, the effects of temperature, geometric parameters, circumferential wave number, axial half wave number and rotating speed on the nature frequency of the rotating circular cylindrical shell are studied. The dynamic responses of the rotating circular cylindrical shell are also investigated in time domain and frequency domain. Then, the effects of nonlinearity, excitation and damping on frequency responses of steady solution are investigated.     

Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.     

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

Effect of Inertia of Elastic Waves in Elastic Systems with Axial Symmetry

We show that a standing wave excited in an elastic circular ring behaves like a material body: if the moment of external forces directed along the symmetry axis of the ring is applied to the ring, then not only the ring itself but also the initially standing wave excited in it will come to the accelerated rotation. In this motion, this “standing wave” does not change its shape and performs accelerated precession relative to the ring. In this case, the acceleration of the wave with respect to the ring constitutes a certain fraction of the acceleration of the ring relative to the inertial space. The moment of momentum of precessing and traveling waves is calculated.     

Free vibration analysis of thin rotating cylindrical shells using wave propagation approach

The wave propagation approach is extended to study the frequency characteristics of thin rotating cylindrical shells. Based on Sanders’ shell theory, the governing equations of motion, which take into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotation, are derived. And, the displacement field is expressed in the form of wave propagation associated with an axial wavenumber k _m and circumferential wavenumber n. Using the wavenumber of an equivalent beam with similar boundary conditions as the cylindrical shell, the axial wavenumber k _m is determined approximately. Then, the relation between the natural frequency with the axial wavenumber and circumferential wavenumber is established, and the traveling wave frequencies corresponding to a certain rotating speed are calculated numerically. To validate the results, comparisons are carried out with some available results of previous studies, and good agreements are observed. Finally, the relative errors induced by the approximation using the axial wavenumber of an equivalent beam are evaluated with respect to different circumferential wavenumbers, length-to-radius ratios as well as thickness-to-radius ratios, and the conditions under which the analysis presented in this paper will be accurate are discussed.     

Quasiperiodic and exponential transient phase waves and their bifurcations in a ring of unidirectionally coupled parametric oscillators

Phase waves rotating in a ring of unidirectionally coupled parametric oscillators are studied. The system has a pair of spatially uniform stable periodic solutions with a phase difference and an unstable quasiperiodic traveling phase wave solution. They are generated from the origin through a period doubling bifurcation and the Neimark?CSacker bifurcation, respectively. In transient states, phase waves rotating in a ring are generated, the duration of which increases exponentially with the number of oscillators (exponential transients). A power law distribution of the duration of randomly generated phase waves and the noise-sustained propagation of phase waves are also shown. These properties of transient phase waves are well described with a kinematical equation for the propagation of wave fronts. Further, the traveling phase wave is stabilized through a pitchfork bifurcation and changes into a standing wave through pinning. These bifurcations and exponential transient rotating waves are also shown in an autonomous system with averaging and a coupled map model, and they agree with each other.     

Vortex sound

Vortex motion is the only source of aerodynamic sound production in low Mach number flow: the unsteady part of the vorticity distribution contributes linearly to the sound field. The following fundamental model flows, which illustrate the vorticity as the predominant sound source in unsteady flows, are discussed: An initially planar elliptic vortex; two identical coaxial initially elliptic vortex rings, where a special case is the leap-frogging of two identical circular rings. For head-on collision of two identical circular vortex rings and for several cases of vortex-body interaction good agreement between theory and experiment exists. If the Mach number is not low, other mechanisms have also to be considered. Here the theory is not yet fully developed. Experimental results for a vortex-airfoil interaction in transonic flow show that local flow separation and boundary layer as well as compressibility effects play a basic role. However, if the motion of vorticity would be known in subsonic flow, essential parts of the sound field could be calculated by the theory. — In addition, it is shown that the general theory is well suited to provide a better understanding of the scattering of sound waves by vortex motion, at least for long wave lengths.     

Secondary flows in a rotating circular cylinder of incompressible conducting fluid as the result of the sudden turning-on of a transverse magnetic field

We study vortex flows in a rotating circular cylinder of incompressible fluid resulting from the sudden turning-on of a transverse magnetic field. The investigation is performed for the initial stage when secondary flow is determined mainly by Lorentz forces, and the effect of viscosity and the convective transport of vorticity by secondary flow is negligibly small. No restrictions are imposed on the magnetic Reynolds number R_m for the basic rotational motion; the number R_m' calculated from a typical secondary flow speed is assumed small.     

粘弹性夹芯层合旋转圆板的气动弹性动力稳定性分析

基于哈密尔顿原理,考虑作用于圆板上的空气动力载荷以及粘弹性复模量本构模型,本文建立了含有粘弹性夹芯层的旋转圆板的空气动力学模型,并给出了相应的稳定性的控制方程及边界条件。运用Galerkin方法,文中数值求解并给出了夹芯层合旋转圆板的动力学基本特征,以及结构几何参数、材料参数对于其前、后行波振动频率、阻尼和动力稳定性的影响。结果表明：通过优化合理选取粘弹性夹芯层合旋转圆板的几何参数和材料参数,可提高旋转圆板的临界转速和颤振速度,从而增强其稳定性。