Stability of an Isothermal Disk with Three-Dimensional Magnetic Fields and Radial Viscous Force

The stability of an isothermal thin disk with three-dimensional magnetic fields and radial viscous force is examined in this paper. We find that the radial viscous force has no influence on the stability of viscous modes. But there is more influence on the stability of magneto-acoustic modes, which is related to the perturbation wavelength and different parts of disk. Finally, we use our model to explain the long-term variability of Quasar 3C345.     

Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric. In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy, which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover, the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area. Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways, while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing the matrix viscosity. Received 15 April 2002 and Received in final form 3 October 2002 RID="a" ID="a"e-mail: alejandro.rey@mcgill.ca     

Modulation of Ion-Cyclotron Turbulence by Low-Frequency Perturbations in a Magnetized Plasma

We consider nonlinear coupling of ion-cyclotron turbulence with low-frequency fast magneto-acoustic perturbations across the external magnetic field in a magnetized plasma. It is found that such coupling leads to instability. The growth rate and the threshold of this instability are calculated.     

The Pulsational Instability of Non-Isothermal Magnetized Accretion Disk with Self-Gravity in the Transition Zone

By analyzing the fifth-order dispersion relation, the influence of coupled magnetic field and self-gravity on the pulsational instability of gas pressure dominated accretion disk is investigated. Our main results are that the viscous modes become more stable with the increase of self-gravity, magnetized field and viscosity, while they enhance the instabilities of acoustic modes. The effect of self-gravity to the instability is much greater than that of magnetic field in transition zone of the accretion disk. Especially, the self-gravity affects the thermal-modes and acoustic modes strongly. Finally, we discuss our results.     

To the theory of cyclotron instability of trapped alpha-particles in tokamak reactor

The authors analyse numerically the cyclotron thermonuclear instability accompanying the interaction of fast magneto-acoustic waves with trapped alpha-particles for a tokamak of circular cross-section. It is shown that the instability is caused mainly by the strongly trapped particles. The influence of the thermal spread of alpha-particles on the cyclotron instability of fast magneto-acoustic waves is investigated.     

Elastic connection disk subjected to periodically fluctuating transmitted torque and rotational speed

Involving the intrinsic power transmission torque/speed coupling characteristics of prime-movers, a rotating elastic connection disk subjected to periodically fluctuating transmitted torque and rotational speed generated by the fluctuation of external loads is investigated. Using Galerkin's method, the rotating elastic connection disk is modeled as a parametrically excited gyroscopic system. The effects of the torque/speed coupling, transmitted torque fluctuation amplitude and frequency, and constant parts of the transmitted torque and the rotational speed on the system dynamic stability are explored for the disk modes possessing different nodal diameters. The rotational speed, transmitted torque and their fluctuations can all result in system instability of the elastic connection disk. The instability can be suppressed or avoided by operating at small amplitude and low frequency of the transmitted torque fluctuation, and by operating in the weakly coupled torque/speed regime of the prime-movers. Low rotational speed avoids the instability in the case of a small transmitted torque, but medium rotational speed operation is valuable to suppress the instability induced by a large transmitted torque and its fluctuation. Instability parameter regions for the positive and negative torque/speed coupling coefficient are roughly similar in shape, but there are some differences in the value of the instability coefficient.     

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk, and it may be possible to access a turbulent regime in which many modes are unstable.     

Interaction of a Low Frequency Coherent Magneto-Acoustic Wave with a Turbulent Spectrum of Extra-Ordinary Waves

Starting from nonlinear evolution equations of a three-dimensional extra-ordinary wavepacket in a magnetized plasma and introducing a correlation function, equations are derived that describe interaction of a coherent low-frequency magneto-acoustic wave with a turbulent spectrum of high frequency extra-ordinary waves. These equations are used to derive the dispersion relation for a low frequency magnetoacoustic wave in the presence of a spectrum of turbulent high frequency extra-ordinary waves. In the narrow spectrum case, it is found that a small but finite spread in the spectrum of turbulence has a stabilizing influence on the instability which exists for vanishing spectral width. In the wide spectrum case, the effect of a weak turbulent spectrum of extra-ordinary waves is to produce a slight shift in frequency of the coherent low frequency magneto-acoustic wave and to damp or excite the wave.     

Rotating flexible disk under shaft temperature increment

A rotating flexible annular thin disk subjected to the temperature increment of the shaft clamping the disk was modeled in this paper. At disk top and bottom surfaces and free outer edge, the heat convection boundaries were assumed. Disk transverse deflection was considered as a function of both disk radial and circumferential coordinates, and temperature distribution was solved along disk thickness and radial directions simultaneously. As a result, the shaft temperature increment causes thermo-elastic instability of some disk modes. Effects of the shaft temperature increment, ratio of disk convective heat transfer coefficient to thermal conductivity, disk thickness, nodal circle and diameter numbers of disk mode on the natural frequencies, thermo-elastic instability and critical angular speed of the disk were discussed.     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

Temporal linear instability analysis of an electrified coaxial jet with inner driving liquid inside a coaxial electrode

In this paper, a temporal linear stability analysis is performed of a coaxial jet composed of two immiscible liquids inside a coaxial electrode. This analysis is carried out to investigate the case of an inner driving coaxial electrospray system. The assumption is made that the inner liquid has high electric conductivity, and the outer liquid is an insulating dielectric. The dimensionless dispersion equation for both the axisymmetric and non-axisymmetric modes is derived and solved numerically for the axisymmetric case. The effects of the relevant dimensionless parameters on the instability of the jet are discussed in detail. These parameters include the dimensionless electrostatic force E, the dielectric constant ratio ε, the diameter ratios a and b, the velocity ratio Λ, the density ratio S, the Weber number, and the interface tension ratio ζ. Two independent unstable modes, modes 1 and 2, are found and analyzed. Among the various parameters, the dimensionless electrostatic force and the dielectric constant have a similar and remarkable influence on modes 1 and 2, altering drastically the regime of the jet as they vary. The interface tension on the outer interface promotes the instability of both modes 1 and 2 in the region of long wavelengths while suppressing the growth rate in the region characterized by short wavelengths. The interface tension on the inner interface, however, promotes instability of only mode 2 in the same way. The diameter ratio a has a great effect on mode 2 while a negligible influence on mode 1. And the diameter ratio b has a slight effect on both the unstable modes.     

基于喷管节流的轴流转子非轴对称间隙布局研究

实际工作中的压气机转子叶尖间隙往往存在着非轴对称性,对压气机性能及稳定性产生影响.本文以上海交通大学LSRC压气机实验台的第一级转子为研究对象,开展了转子非轴对称间隙布局的数值模拟研究.在数值模拟中,通过在转子出口设置喷管的方式模拟节流过程,分析了喷管结构对压气机性能的影响,并对该方法与常规背压节流方法进行了对比验证....     

A numerical method for the study of nonlinear stability of axisymmetric flows based on the vector potential

We develop in this paper a numerical method to simulate three-dimensional incompressible flows based on a decomposition of the flow into an axisymmetric part, in terms of the stream function and the circulation, and a non-axisymmetric part in terms of a potential vector function. The method is specially suited for the study of nonlinear stability of axially symmetric flows because one may follow neatly the raising of the different non-axisymmetric modes, their nonlinear development, and their nonlinear interaction. The numerical technique combines finite differences on a non-uniform grid in the axial direction, a Chebyshev spectral collocation technique in the radial direction, and a Fourier spectral method in the azimuthal direction for the non-axisymmetric vector potential. As an example to check the efficiency and accuracy of the method we apply it to the flow inside a rotating circular pipe, and compare the resulting travelling waves with previous stability results for this problem, for different values of the Reynolds and the swirl numbers.     

The Radial-Azimuthal Instability of a Radiation-Pressure-Dominated Accretion Disk with Advection

A radial-azimuthal instability analysis of a radiation-pressure-dominated accretion disk with advection is presented. We find that the including of a very little advection has significant effect on two acoustic modes, which are no longer complex conjugates of each other. With the increase of azimuthal perturbations, the thermal mode becomes more unstable and the viscous mode more stable, but there has no effect on acoustic mode. For geometrically slim and advection-dominated disks, the azimuthal perturbation and increasing of advection do not affect the stability of all the modes.     

Calculation of natural frequencies and modes of tires in road contact by utilizing Eigenvalues of the axisymmetric non-contacting tire

Given the experimental or theoretical natural frequencies and modes of a tire mounted and inflated, but not in ground contact, an analytical method is presented that allows one to obtain the natural frequencies and modes when the tire is in ground contact. This is of practical advantage since measurements or calculations of the free axisymmetric tire are considerably simpler than directly measuring or analyzing the non-axisymmetric case of ground contact.     

磁声参量振荡的理论

在本文中,我们从磁-弹性耦合的宏观表达式,通过经典场论的方法,求得弹性振动和磁振璗的耦合方程,用来分析了伴随波长约等于铁氧体样品的线度的声振动而存在的磁振璗(磁声模)。文中指出,Spencer和LeCraw所发现的磁声效应是磁声模和静磁模在注入场的激发下产生的参量振璗现象(也可以说是热声子的电磁讯号的放大)。我们引用Berk等人在讨论一种半静磁操作放大器的文章中给出的公式,算出Spencer-LeCraw实验所需要的功率,其结果与记录的数据相接近。我们提出了使任一静磁模配合磁声模产生振璗的调谐条件以及降低激发功率和观测几十到几百兆赫的声频的办法。通过磁声模和静磁模的交变场向量的空间对称性的分析,我们推导出磁声参量振璗的选择定则:对于球体三个主要弹性振动模(旋转模、向径模和椭球模),(1)静磁模(n,m,r)的Walker指标n是偶数者不产生磁声效应;(2)指标m是奇数者不与旋转模产生磁声效应,m是偶数者不与向径模或椭球模产生磁声效应。我们也举出第一类本征振动中有只可能和n是偶数、m是奇数的静磁模产生参量振璗的例子。Spencer-LeCraw局限于使静磁场调谐在(110)模上,所观察到的现象仅仅是本文所给出理论预见的一个特殊情况。他们发现了椭球模和向径模的频率显著地出现,但并无旋转模的频率,这是上述的选择定则的具体验证。最后,我们指出,热声子的参量放大可形成铁氧体微波放大器的噪声的来源。     

Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder

Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder is studied by using the normal mode expansion method (NME). Different sources such as angle beam, tube end excitation with normal beam, and comb transducer possibilities are discussed based on the derivations of the NME method. Numerical calculations are focused on the case of angle beam partial loading. Based on the NME method, the amplitude coefficients for all of the harmonic modes are obtained. Due to the difference of phase velocities for different modes, the superimposed total field varies with propagating distances and hence makes particle displacement distribution patterns (angular profile) change with distance. This varying non-axisymmetric angular profile of guided waves represents a nonuniform energy distribution around the hollow cylinder and thus has an impact on the inspection ability of guided waves. The angular profiles of an angle beam source are predicted by theory and then verified by experiments. The predicted angular profiles also provide information for determining the transducer location to find defects in a certain position on the hollow cylinder.     

Rotordynamical simulations of a fibre refiner during production

A key component in panel board production is the refiner, whose task is to break raw cellulose wood chips into slender fibres, done by a relative angular motion between stator and rotor. The main problem in predicting the dynamics of these machines is to model the complicated fibre breaking process, since the refining process leads to a three-phase flow (solid wood, water and steam) between the stator and rotor. By modelling the rotor as a rigid body, the process can only contribute by a resulting force and a resulting moment. Through this approach and axial force measurements, it has been shown that the refining process can be treated as a time dependent stiffness matrix and external load. The objective for this paper is to predict and explain dynamical characteristics of fibre refiners during production in such a way that the results can be used already at early stages of the product development process. Two different pressure distribution cases are studied, i.e. one axisymmetric with only radial variations and one non-axisymmetric. It is found that the axisymmetric case only excited forward modes, while the non-axisymmetric case excited all modes. The time dependent stiffness matrix resulted in unstable domains, but also in stable domains with intermittent high amplitudes.     

Dispersion and attenuation by transmission,reflection, and mode conversion in welded pipes

Torsional wave dispersion and attenuation in an open empty welded pipe are determined from a multi-receiver position reflection experiment. The fundamental torsional wave is dominantly reflected at the free end and the converted non-axisymmetric flexural modes are naturally attenuated. The resulting phase velocity contours are in agreement with theoretical predictions. The transmission losses are quantified and compared to those reflective elements associated with end and weld reflection. At any reflective node, the incident wave is split between back and forward preserved mode scattering (“reflection/transmission”), conversion to other modes plus energy lost by absorption. The ratios for each element are quantified.     

Plasmonic split disk resonator based on graphene

In this paper, we designed and simulated an ultra-compact plasmonic filter consisting of a graphene ribbon laterally coupled to a graphene split disk resonator. Introducing a split inside the disk leads to split of the resonance modes symmetrically and asymmetrically. The spacing between the symmetric and asymmetric modes can be controlled through changing length of the split in the disk and the simulation results reveal that all modes identically shift as a result of changing the Fermi level of the disk. finite-difference time-domain method is used to investigate the device performance.