弱粘性流体中垂直激励表面波的阻尼效应

在竖直振动的圆柱形容器中,将Navier-Stokes方程线性化,利用两时间尺度奇异摄动展开法研究了弱粘性流体的单一自由面驻波运动．整个流场被分为外部势流区和内部边界层区两部分,对两部分区域分别求解,得到包含阻尼项和外驱动影响的线性振幅方程．利用稳定性分析,得到形成稳定表面波的条件,给出了临界曲线．此外,还获得了阻尼系数的解析表达式．最后,将线性阻尼加到理想流体条件下所得到的色散关系中对其进行修正,理论结果证明修正后的驱动频率更加接近实验的结果．通过计算发现,当驱动的频率较低时,流体的粘性对表面波模式选择有重要影响,而表面张力的影响不明显;但当驱动频率较高时,流体的表面张力起主要作用,而流体的粘性影响甚小．     

Autoresonance in a dynamic system

Results on the asymptotic analysis of a model of autoresonance using a natural small parameter, the amplitude of forcing oscillations, are presented. The given forcing perturbation is rapidly oscillating oscillations with small amplitude and slow varying frequency. The goal of the paper is to reveal conditions under which the trajectory of the system goes away from the initial equilibrium point by a distance of order 1 under the influence of such a perturbation.Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 5, Asymptotic Methods, 2003.     

Numerical simulation of vortex induced vibrations and its control by suction and blowing

The vortex formation and shedding behind bluff structures is influenced by fluid flow parameters such as, Reynolds number, surface roughness, turbulence level, etc. and structural parameters such as, mass ratio, frequency ratio, damping ratio, etc. When a structure is flexibly mounted, the Kármán vortex street formed behind the structure gives rise to vortex induced oscillations. The control of these flow induced vibrations is of paramount practical importance for a wide range of designs. An analysis of flow patterns behind these structures would enable better understanding of wake properties and their control. In the present study, flow past a smooth circular cylinder is numerically simulated by coupling the mass, momentum conservation equations along with a dynamical evolution equation for the structure. An active flow control strategy based on zero net mass injection is designed and implemented to assess its efficacy. A three actuator system in the form of suction and blowing slots are positioned on the cylinder surface. A single blowing slot is located on the leeward side of the cylinder, while two suction slots are positioned at an angle α = 100°. This system is found to effectively annihilate the vortex induced oscillations, when the quantum of actuations is about three times the free stream velocity. The dynamic adaptability of the proposed control strategy and its ability to suppress vortex induced oscillations is verified. The exact quantum of actuation involved in wake control is achieved by integrating a control equation to decide the actuator response in the form of a closed loop feed back system. Simulations are extended to high Reynolds number flows by employing eddy viscosity based turbulence models. The three actuator system is found to effectively suppress vortex induced oscillations.     

Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes

A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A=0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f₀=1.5,2.5,3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discretization of the two-dimensional continuity and unsteady Navier-Stokes equations (when a solid body is present) on a fixed Cartesian grid. Two-fluid model based on improved volume-of-fluid method is used to discretize the free surface interface. The study focuses on the laminar asymmetric flow structure in the near wake region and lock-on phenomena at a Froude number of 0.2 and for the dimensionless cylinder submergence depths, h=0.25, 0.5 and 0.75. The equivorticity patterns and pressure distribution contours are used for the numerical flow visualization. The code validations in special cases show good comparisons with previous numerical results.     

On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations

We study the degrees of freedom of several conservative computational turbulence models that are derived via a non-dissipative regularizations of the Navier-Stokes equations. For the Navier-Stokes-α, the Leray-α and the Navier-Stokes-ω equations we prove that the longtime behavior of their respective solutions is completely determined by a finite set of grid values and by a finite set of Fourier modes. For each turbulence model the number of determining nodes and of determining modes is estimated in terms of flow parameters, such as viscosity, smoothing length, forcing and domain size. These estimates are global as they do not depend on an individual solution.     

Oscillatory reaction-diffusion equations with temporally varying parameters

Periodic wave trains are the generic one-dimensional solution form for reaction-diffusion equations with a limit cycle in the kinetics. Such systems are widely used as models for oscillatory phenomena in chemistry, ecology, and cell biology. In this paper, we study the way in which periodic wave solutions of such systems are modified by periodic forcing of kinetic parameters. Such forcing will occur in many ecological applications due to seasonal variations. We study temporal forcing in detail for systems of two reaction diffusion equations close to a supercritical Hopf bifurcation in the kinetics, with equal diffusion coefficients. In this case, the kinetics can be approximated by the Hopf normal form, giving reaction-diffusion equations of λ-ω type. Numerical simulations show that a temporal variation in the kinetic parameters causes the wave train amplitude to oscillate in time, whereas in the absence of any temporal forcing, this wave train amplitude is constant. Exploiting the mathematical simplicity of the λ-ω form, we derive analytically an approximation to the amplitude of the wave train oscillations with small forcing. We show that the amplitude of these oscillations depends crucially on the period of forcing.     

Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems

We consider small solutions of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibration.     

2D numerical simulation of submerged hydraulic jumps

Hydraulic jumps are usually used to dissipate energy in hydraulic engineering. In this paper, the turbulent submerged hydraulic jumps are simulated by solving the unsteady Reynolds averaged Navier–Stokes equations along with the continuity equation and the standard k–? equations for turbulence modeling. The Lagrangian moving grid method is employed for the simulation of the free surface. In the developed model, kinematic free-surface boundary condition is solved simultaneously with the momentum and continuity equations, so that the water elevation can be obtained along with velocity and pressure fields as part of the solution. Computational results are presented for Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. Comparisons with experimental measurements show that numerical model can simulate the velocity field, variation of free surface, maximum velocity, Reynolds shear and normal stresses at various stations with reasonable accuracy.     

Resonance interactions of waves in an ice channel

The properties of low-amplitude surface waves propagating in an ice channel are investigated in the shallow-water approximation. The ice cover is modelled either by a rigid cap or by a thin elastic plate floating on a liquid surface. It is shown that an ice channel is a waveguide for surface waves. The dispersive properties of the natural oscillations of the liquid in the channel are investigated. The resonance velocities of the motion of the load on the channel surface, at which the amplitude of the forced oscillations of the liquid increases without limit in time, are determined. The decay instability of the natural oscillations of high harmonics with respect to waves of the first mode is demonstrated. The process is described by the standard equations for non-linear three-wave interaction. The investigations lead to the conclusion that critical modes of motion of a boat are realizable in an ice channel.     

有线性阻尼和变长度的单摆

应用多尺度法和势能逼近法研究有线性阻尼和变长度的单摆．通过摩擦因数与摆长慢变参数阶的比较,详细讨论了3种不同的情况并得到振幅、频率和解的渐近分析表达式．势能逼近法的应用使结果对大幅振动也有效．当摩擦因数不是很小时,修正的多尺度法用于得到更精确的首次近似解．与数值结果的比较表明本文的方法是有效的．     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．     

Statistical modeling of compressible turbulent channel flow

Several questions that are relevant to turbulence modeling are addressed on the basis of recently obtained direct numerical simulation results of turbulent supersonic channel flow. In particular, this concerns the turbulence frequency production mechanism, wall damping effects on turbulence model parameters, and the relevance of compressibility effects. Limited support is found for usually applied models for the turbulence frequency production and wall damping effects. In contrast to that it is shown that turbulence frequency production mechanisms and wall damping effects may be explained very well on the basis of a frequency scaling that characterizes mean flow changes. The influence of compressibility is found to be relevant. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulent diffusion: Direct numerical simulation

Direct numerical simulations (DNS) of a vibrating grid turbulence at two different Reynolds numbers (based on an amplitude and frequency of the grid) Re = 500, 1000 are presented. The evolution of a turbulent/non-turbulent interface was detected and compared to the theoretical results obtained in the paper [1] using Lie group analysis of the governing equations. Good agreement was found between DNS and theory. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Subharmonic and bursting oscillations of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet

This paper considers the dynamics of an electromechanical system consisting of a ferromagnetic mass fixed on a spring and subjected to an AC electromagnet. Subharmonic and bursting oscillations are found and their shape analyzed when one varies the viscous damping coefficient, the number of turns of the coil, the frequency and amplitude of the AC voltage. Pulse packages patterns and sharp burstings are observed in the motion of the mechanical part.     

An energy-based computational method in the analysis of the transmission of energy in a chain of coupled oscillators

In this paper we study the phenomenon of nonlinear supratransmission in a semi-infinite discrete chain of coupled oscillators described by modified sine-Gordon equations with constant external and internal damping, and subject to harmonic external driving at the end. We develop a consistent and conditionally stable finite-difference scheme in order to analyze the effect of damping in the amount of energy injected in the chain of oscillators; numerical bifurcation analyses to determine the dependence of the amplitude at which supratransmission first occurs with respect to the frequency of the driving oscillator are carried out in order to show the consequences of damping on harmonic phonon quenching and the delay of appearance of critical amplitude.     

Numerical Investigation of the Interaction of Turbulent Wind Flow and Elastic Structures

The Interaction between wind flow and structures plays an important role in the computation of civil engineering application. In case of gravity prestressed membrane roofs, the wind lifting forces may exceed the dead load leading to high amplitude structural oscillations, which interact with the flow field. To investigate the interaction a consistent discretization method based on stabilized space‐time finite elements is applied. The flow field is modeled with the incompressible Reynolds Averaged Navier‐Stokes (RANS) equations with an anisotropic eddy‐viscosity turbulence model. The structural motion is described with the theory for geometrically nonlinear elastic deformation behavior, a strong coupling algorithm for the time‐dependent fluid‐structure interaction is implemented. Two applications show the capability of the turbulence model in representing the anisotropic turbulence structure, the differences in the flow field over a bluff body between two configurations representing a rigid and an elastic membrane roof, discusses the structural responses of the roof at a high Reynolds number. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamics regularization with tree-like structures

The dynamics of a fully nonlinear, tree-structured resonator and its response to a broadband forcing of the branches is examined. It is shown that the broadband forcing yields a transfer of energy between the parts of the spectrum so that the spectrum becomes progressively more narrow-band for each level of the tree-like structure in the direction of the stem. We show that this behavior is in contrast to the response of a linear oscillator, which simply filters out the harmonics away from the resonance. We term such behavior “regularization” and examine its significance for two- and three-dimensional motion using a Lagrangian framework. Key to our analysis is to investigate the dependence of the spectrum of motion, and its narrowing, on the parameters of the tree-like structure, for instance the lengths of different branches. Model predictions are obtained for idealized wind forcing characterized by an airflow that is interrupted at random time intervals. Our numerically-derived results are then compared against the data collected from select analogue laboratory experiments, which confirm the robust nature of the vibration regularization.