Numerical simulation of a short flexible pipe subject to forced motion and vortex-induced vibration

A series of numerical sinmlations about a small scale （aspect ratio： 63.2） flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration （VIV） have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction （FSI） problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method （Chen and Kim, 2008） was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test （Choi and Hong, 2000） via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn＇t only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.

Prediction Model for Vortex-Induced Vibration of Circular Cylinder with Data of Forced Vibration

A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions （VIV） of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson＇ s group are in rather good agreement.

Hydrodynamics of the Semi-Immersed Cylinder by Forced Oscillation Model Testing

In this paper, the hydrodynamic coefficients of a horizontal semi-immersed cylinder in steady current and oscillatory flow combining with constant current are obtained via forced oscillation experiments in a towing tank. Three nondimensional parameters(Re, KC and Fr) are introduced to investigate their effects on the hydrodynamic coefficients.The experimental results show that overtopping is evident and dominates when the Reynolds number exceeds 5×105 in the experiment. Under steady current condition, overtopping increases the drag coefficient significantly at high Reynolds numbers. Under oscillatory flow with constant current condition, the added mass coefficient can even reach a maximum value about 3.5 due to overtopping while the influence of overtopping on the drag coefficient is minor.

Is forced oscillation technique the next respiratory function test of choice in childhood asthma

Respiratory diseases, especially asthma, are common in children. While spirometry contributes to asthma diagnosis and management in older children, it has a limited role in younger children whom are often unable to perform forced expiratory manoeuvre. The development of novel diagnostic methods which require minimal effort, such as forced oscillation technique(FOT) is, therefore, a welcome and promising addition. FOT involves applying external, small amplitude oscillations to the respiratory system during tidal breathing. Therefore, it requires minimal effort and cooperation. The FOT has the potential to facilitate asthma diagnosis and management in preschool children by faciliting the objective measurement of baseline lung function and airway reactivity in children unable to successfully perform spirometry. Traditionally the use of FOT was limited to specialised centres. However, the availability of commercial equipment resulted in its use both in research and in clinical practice. In this article, we review the available literature on the use of FOT in childhood asthma. The technical aspects of FOT are described followed by a discussion of its practical aspects in the clinical field including the measurement of baseline lung function and associated reference ranges, bronchodilator responsiveness and bronchial hyperresponsiveness. We also highlight the difficulties and limitations that might be encountered and future research directions.

AVERAGING PRINCIPLE FOR QUASI-GEOSTROPHIC MOTIONUNDER RAPIDLY OSCILLATING FORCING

A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.

Side force control on slender body by self-excited oscillation flag

Strong asymmetrical vortices appear on the leeward of slender body at high angles of attack, which has very unfavorable effect on the stability and control of the aircraft. A method is developed to control the side force of slender body at high angles of attack, and is verified in wind tunnel. A thin-film triangular self-excited oscillation flag is fixed at the tip of the slender body model whose semi-apex angle is 10°. Side force is approximately linearly proportional to roll-setting angle of self-excited oscillation flag at high angles of attack, and the slop of fitting straight line obtained by the least square method is -0.158. The linear relationship between side force and roU-setting angle provides convenience for developing side force control law of slender body at high angles of attack. Experimental data shows that the side force coefficients vary linearly with roll-setting angles when a specific plastic self-excited oscillation flag is used as the control flag. The range of side force coefficient and roll-setting angle are, respectively, -3.2 to 3.0 and -20° to 20°. The device is simple, effective, and is of great potential in engineering application.

THE INFLUENCES OF FORCED OSCILLATIONS TOWARD VORTEX-BREAKDOWN

The experimental results on the influences of oscillating leading edge vortex-flaps of triangular wing toward the vortex breakdown are presented in this paper. The results reveal that forced oscillationscan delay the breakdown of concentrated vortices, and large reversed-flow-regions which originally appear at the upper surface of the fixed wing at high angles of attack would be suppressed to some extent, depending on the oscillation frequencies. As a consequence, the influences can be optimized by selecting proper oscillation frequencies.

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.

Quantization of the 1-D Forced Harmonic Oscillator in the Space (<i>x</i>, <i>v</i>)

The quantization of the forced harmonic oscillator is studied with the quantum variable (x, v∧), with the commutation relation , and using a Schrödinger’s like equation on these variable, and associating a linear operator to a constant of motion K (x, v, t) of the classical system, The comparison with the quantization in the space (x, p) is done with the usual Schrödinger’s equation for the Hamiltonian H(x, p, t), and with the commutation relation . It is found that for the non-resonant case, both forms of quantization bring about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the (x, v∧) quantization has fewer oscillations than the (x, p∧) quantization, the average energy of the system is higher in (x, p∧) quantization than on the (x, v∧) quantization, and the Boltzmann-Shannon entropy on the (x, p∧) quantization is higher than on the (x, v∧) quantization.

THE LOSS OF STABILITY OF LAMINAR FLOW IN OPEN CHANNEL AND THE MECHANISM OF SAND RIPPLE FORMATION

In the flow on a mobile bed in an open channel, sand ripple often appears after the sediment begins to move. Different scholars have different views on the formation of sand ripples. This paper holds that as the ripple in general is very small, its formation is due to the instability of the laminar flow or the evolution of the small-scale coherent structures in the sublayer adjacent to the wall of the open channel. When the shear stresses caused by the disturbing waves or the coherent structure near the bed surface boundary and the water flow itself are greater than the shields stresses, responses on the bed surface appear and the sand ripple forms. If the frequency of the shear stress caused by the disturbance is close to the natural frequency of the sand grains that produced resonance, such a phenomenon is called the 'detection property' of the sediment. It is at this point that the maximum resonance appears and the sand ripple develops rapidly.

Reynolds and Mass-Damping Effect on Prediction of the Peak Amplitude of A Freely Vibrating Cylinder

The Reynolds effect and mass-damping effect on the peak amplitude of a freely vibrating cylinder is studied by using forced oscillating data from Gopalkrishnan＇ s research in 1993, in which all experimental cases were carried out at a fixed Reynolds and the tested cylinder was recognized as a body that had no mass and damping. However, the Reynolds and roass-damping are the very important parameters for the peak amplitude of a freely vibrating cylinder. In the present study, a function F is introduced to connect the forced oscillation and free vibration. Firstly the peak amplitude AG^＊ can be obtained from the function F using forced oscillation data of Gopalkrishnan＇ s experimental at Re = 10^4, and then the Reynolds effect is taken into account in the function f（Re）, while the mass-damping effect is considered in the function K（ α ）, where a is the mass-damping ratio. So the peak amplitude of a freely vibrating cylinder can be predicted by the expression： A ^＊ = K（ α ）f（ Re ）AG^＊ . It is found that the peak transverse amplitudes predicted by the above equation agree very well with many recent experimental data under both high and low Reynolds conditions while roass-damping varies. Furthermore, it is seen that the Reynolds number does have a great effect on the peak amplitude of a freely vibrating cylinder. The present idea in this paper can be applied as an update in the empirical models that also use forced oscillation data to predict the vortex induced vibration （VIV） response of a long riser in the frequency domain.

Study on Viscoelastic Property of Nanometer SiO_2 Doped Rare Earth Carboxylate Grafting Poly-Silicone Liquid ERF

Nano-SiOdoped with rare earth carboxylate grafting continuous component of functional poly-silicone liquid, a kind of subsidence high-resistance. Electrorheological fluid (ERF) was synthesized. And its viscoelastic properties were investigated experimentally. The special polarization effect of rare earth in the ERF was also discussed. The forced oscillating behavior was obtained using a rheometer. The variation of the shear modulus of ERF subjected to various stress amplitude and frequency were investigated. The complex shear modulus and storage modulus of ERF were also given at different electric field intensities. Meanwhile, the creep and recovery characteristics of ERF were also measured. The equilibrium compliance Jc and the steady state recoverable compliance JR were investigated as a function of electric field strength and ratio of reactant, and the effect of ERF′s structure was analyzed. With increasing in electric field strength at fixed ratio of reactant, the plastic response diminishes, and the elastic behavior rose.

Large Eddy Simulation on Interaction Between in-Line and Cross-Flow Oscillation of A Circular Cylinder

This paper discusses numerical results from three-dimensional large eddy simulations of an oscillating cylinder under prescribed movements in uniform flow. Six cases, namely pure in-line, pure cross-flow and two groups of ＇Figure of Eight＇ oscillation patterns are under investigation at Reynolds number Re = 24000. The ＇ Figure of Eight＇ pattern in each group is with identical shape but oppusite orbital directions. The numerical results on hydrodynamic forces, higher order force components, and vortex shedding modes are extensively studied and compared with the measured experimental data. It is found that the fluid force in phase with the velocity, which represents the energy transfer between the fluid and the cylinder, has opposite sign and different magnitude due to the opposite orbital direction. Higher order force components in cross-flow direction are found to occur at odd nmnber times of the oscillating frequency, while even nmbers dominate the higher order force components in in-llne direction. The 2C and 2T vortex shedding modes are well reproduced due to the opposite orbital direction effect. Comparisons between numerical and experimental results indicate that the present numerical model could be a rational tool for the identification of hydrodynamic coefficients which are normally applied in empirical models to predict the vortex-induced vibrations of slender marine structures.

NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER

In the cylindrical coordinate system,a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subject to a vertical oscillation.It is assumed that the fluid in the circular cylindrical vessel is inviscid,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubic and vertically excited terms of the vessel was derived by expansion of two-time scales without considering the effect of surface tension.It is shown by numerical computation that different free surface standing wave patterns will be formed in different excited frequencies and amplitudes.The contours of free surface waves are agreed well with the experimental results which were carried out several years ago.

Analytical approximations to a generalized forced damped complex Duffing oscillator:multiple scales method and KBM approach

In this investigation,some different approaches are implemented for analyzing a generalized forced damped complex Duffing oscillator,including the hybrid homotopy perturbation method(H-HPM),which is sometimes called the Krylov-Bogoliubov-Mitropolsky(KBM)method and the multiple scales method(MSM).All mentioned methods are applied to obtain some accurate and stable approximations to the proposed problem without decoupling the original problem.All obtained approximations are discussed graphically using different numerical values to the relevant parameters.Moreover,all obtained approximate solutions are compared with the 4thorder Runge-Kutta(RK4)numerical approximation.The maximum residual distance error(MRDE)is also estimated,in order to verify the high accuracy of the obtained analytic approximations.

CAPILLARY EFFECT ON VERTICALLY EXCITED SURFACE WAVE IN CIRCULAR CYLINDRICAL VESSEL

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension. A nonlinear slowly varying amplitude equation, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from potential flow equation. The results show that, when forced frequency is lower, the effect of surface ten- sion on mode selection of surface wave is not important. However, when forced frequency is higher, the surface tension can not be neglected. This proved that the surface tension causes free surface returning to equilibrium location. In addition, due to considering the effect of surface tension, the theoretical result approaches to experimental results much more than that of no surface tension.

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Contrastive Analysis of General and Special Forced Oscillations of Power Systems

With the continuous incorporation of renewable energy and new loads into the electric power grid,random factors that induce general forced oscillations(GFOs)gradually become risks that affect the power system's security and stability.T his research conducts a comparative analysis of the generation mechanisms of GFOs versus the traditional special forced oscillations(SFOs),specifically,from the perspective of frequency domain.Similarities and differences in en-oscillating conditions,occurrence probabilities,and the influencing factors of GFO and SFO are compared to better understand and recognize the GFO theory and the response characteristics of the power system under random excitations.A series of simulations in the lO-generator,39-bus New England Test System is carried out to verify the analysis.

FORCED OSCILLATIONS OF A CLASS OF NONLINEAR DISPERSIVE WAVE EQUATIONS AND THEIR STABILITY

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries （KdV） equation and the damped Benjamin-Bona-Mahony （BBM） equation. In this paper we intend to show the same results hold for the pure KdV equation （without the damping terms） posed on a finite domain. Consideration is given to the initial-boundary-value problem {ut＋ux＋uux＋uxxx=0, u（x,0）=φ（x）, 0〈x〈1, t〉0,u（0,t）=h（t）, u（1,t） = 0, ux（1,t） = 0, t〉0.It is shown that if the boundary forcing h is periodic with small ampitude, then the small amplitude solution u of （＊） becomes eventually time-periodic. Viewing （＊） （without the initial condition） as an infinite-dimensional dynamical system in the Hilbert space L^2（0, 1）, we also demonstrate that for a given periodic boundary forcing with small amplitude, the system （＊） admits a （locally） unique limit cycle, or forced oscillation, which is locally exponentially stable. A list of open problems are included for the interested readers to conduct further investigations.

NUMERICAL STUDY OF THE SHORT-TERM CLIMATIC OSCILLATION FORCED BY EL NINO DURING NORTHERN WINTER

Using a nine-layer global spectral model, numerical schemes with two different SST distributions in January (control case and abnormal case) have been tested to study the climatic effect, propagation charateris- tics and the maintenance mechanism of the short-term climatic oscillation caused by El Nino during northern winter. The main results are as follows: (1) During northern winter, there exist two wave trains because of the influence of El Nino. One is similar to PNA pattern, and the other is similar to EUP pattern. (2) The PNA-like wave train caused by the anomalous SST forcing in central and eastern equatorial Pacific Ocean is due to the response of ultralong wave and long wave components of Rossby mode, and the EUP-like wave train crossing Eurasia is mainly due to the wave component of Rossby mode. (3) During northern winter, the warm water region in central equatorial Pacific Ocean is the source of forced wave trains. (4) In northern winter, the energy source for maintaining the short-term climatic oscillation is from the interaction between eddies, and between eddy and zonal flow.