Response of an annular cylindrical liquid column to various axial excitations in zero-gravity

An annular liquid layer is subjected in a zero-gravity environment to different harmonic axial excitations. The liquid is treated as frictionless and is held together by free surface tension, which acts as the restoring force. The response of the system has been determined for the free surface elevation and the velocity distribution. It was found, that the first resonance response is sharply tuned and could easily be missed in a sweeping experiment. Damping was introduced in the resonance terms.     

Response of a spinning liquid column to axial excitation

Summary The response of a solidly rotating finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀).Notation a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - P liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _02n –1 natural frequency of harmonic axial response With 8 Figures     

Response of a spinning liquid column to pitch excitation

Summary The response of a solidly rotating liquid bridge consisting of inviscid liquid is determined for pitch excitation about its undisturbed center of mass. Free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic (<2₀) excitation frequency range.List of symbols a radius of liquid column - h length of column - I ₁ modified Besselfunction of first kind and first order - J ₁ Besselfunction of first kind and first order - r, ,z cylindrical coordinates - t time - u, v, w velocity distribution in radial-, circumferential-and axial direction resp. - mass density of liquid - free surface displacement - velocity potential - ₀ rotational excitation angle - ₀ velocity of spin - forcing frequency - _1n natural frequency - surface tension - acceleration potential - for elliptic range >2₀ - for hyperbolic range >2₀     

Natural frequencies and response of spinning liquid column with apparently sliding contact line

Summary The contact line of a liquid with a solid does in many cases—depending on the smoothness of the solid, the viscosity, the surface tension and the excitation force—apparently flow along the solid during oscillations. The influence of this effect upon the natural frequencies, the stability and the response of the system has been investigated at an oscillating and spinning cylindrical liquid column.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - axial excitation amplitude - elliptic case ( > 2 ₀) - hyperbolic case ( > 2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _on natural frequency of harmonic axial response     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Natural damped frequencies and axial response of a rotating finite viscous liquid column

Summary For a finite solidly rotating cylindrical liquid column the damped natural axisymmetric frequencies have been determined. The liquid was considered incompressible and viscous. The cases of freely slipping edges and that of anchored edges have been treated. It was found that instability appears in a purely aperiodic root for the spinning liquid bridge. This is in contrast to the instability appearing in the damped oscillatory natural frequency of a nonspinning liquid column at . The spinning viscous liquid column exhibits the same instability as the frictionless liquid. It appears at for axisymmetric oscillations.List of symbols a radius of liquid column - I _m modified Bessel function of first kind and orderm - s complex frequency ( ) - r, ,z polar cylindrical coordinates - p pressure - t time - u, v, w radial-, azimuthal- and axial velocities of liquid, respectively - Weber number - h height of liquid column - dynamic viscosity of liquid - v kinematic viscosity of liquid (v=/) - density of liquid - surface tension of liquid - _r , _rz shear stress - (r, z, t) circulation - (r, z, t) streamfunction - ₀ angular velocity of liquid column about the axis of symmetry - (,t) free surface displacement     

Anchored edge pitching response of a spinning frictionless liquid column due to bottom and/or top excitation

The response of an anchored spinning frictionless liquid bridge to different pitching top and/or bottom excitation has been determined. The free surface displacement is obtained for synchronous, counter-excited and one-sided pitching excitation as a function of the dimensionless forcing frequency . The contactlines at the rim of the upper and lower discs are considered to be anchored. In synchronous pitching excitation only the even resonances show response peaks, while in a counter-excited system only odd resonances appear, which is in contrast to axial excitation modes. For one-sided excitation, all reasonances appear. Because of the different natural frequencies in direction of spin and opposite to it double peaks are present in the responses.     

Response of a liquid column to one-sided axial excitation in zero gravity

A finite cylindrical liquid column consisting of incompressible and frictionless liquid is subjected at the upper end to axial harmonic excitation. The liquid system is in a zero-gravity environment and is held together by surface tension, which acts as restoringforce. The response of the system has been determined for the free surface elevation and the velocity distribution. In addition the transient behavior was investigated. Damping has been introduced in the resonance terms. It was found, that the first resonance response is sharply tuned and could easily be missed by a sweeping experiment. The investigation was performed for the preparation of the German-D-2 Spacelab-Mission “LICORE”.     

Natural frequencies and axial response of a liquid layer under the influence of an axial steady micro-gravity field

Under the action of a steady axial gravity field a liquid layer experiences a change of natural frequencies in comparison to the annular layer. The natural frequencies exhibit a decrease with increasing axial Bond number and liquid height. This is particularly pronounced in the range of the lower modes. In addition the response of the liquid layer to axial excitation has been investigated and shows resonance peaks for all modes in contrast to those of the circular cylindrical layer. Increase of axial Bond number yields an increase of response magnitude.     

Response of an anchored frictionless liquid bridge to pitching bottom and/or top excitation

The natural frequencies and response of a circular cylindrical liquid bridge consisting of incompressible and non-viscous liquid has been determined. Three cases of pitching excitations have been treated: synchronous- and counter-excitation of the end discs, as well as the pitching excitation of only one end disc. The contact lines were considered to be anchored at the end discs.     

Response of an annual cylindrical liquid column in zero-gravity

An annular liquid layer is subjected in a zero-gravity environment to harmonic axial- and pitching excitation. The liquid is treated as frictionless and is held together by free surface tension, which acts as the restoring force. The response of the system has been determined for the free surface elevation and the velocity distribution. It was found, that the first resonance response is sharply tuned and could easily be missed in a sweeping experiment. Damping was introduced in the resonance terms.     

一起上塔液悬故障的处理

简介了6000m^3／h空分设备上塔液悬故障的现象及原因，从减少上升蒸汽和回流液体两方面详细分析了消除液悬的措施。     

一起上塔液悬故障的处理

简介了6000m~3/h空分设备上塔液悬故障的现象及原因,从减少上升蒸汽和回流液体两方面详细分析了消除液悬的措施。     

Stochastic response of flexible rotor-bearing system to seismic excitations

Random vibration analysis of flexible rotor-bearing systems subjected to six-component nonstationary earthquake ground accelerations is carried out. The rotor system consists of several rigid disks and a flexible shaft that is modelled as a Timoshenko beam. The governing equations of motion involve both inhomogeneous random excitations and random parametric excitations. Analytically, the Markov vector approach using the Ito equation and Stratonovich averaging procedures is employed to determine the response statistics. Unfortunately, the second moments of the response quantities thus obtained involve a great discrepancy when compared with the results of Monte Carlo simulation. The difficulty involved in analytically solving such a complicated problem is pointed out. Currently, the method of Monte Carlo simulation appears to be the only practical approach for such a problem. The significant influence of the seismic base rotations and the flexibility of the rotor-bearing system on the overall dynamic structural response is demonstrated by a numerical example.     

The hydrodynamic theory of a positive discharge column in an axial magnetic field

The influence of an axial magnetic field on the performance of a low-pressure cylindrical positive discharge column is studied from the hydrodynamic point of view. It is shown that the magnetic field affects the distribution of the plasma density, its speed, and the energy of electrons. The energy of electrons, the concentration and the speed of plasma, and the azimuth speed of electrons and ions as functions of the radius have been found for a helium atom in a magnetic field of varying intensity. It has been noticed that the electron and ion azimuth movement equations should account for inertia. The obtained hydrodynamic results significantly deviate from the ones obtained in the wide-spread diffusion model of a positive column. It is shown that the distribution of plasma concentration and the radial speed in the positive column are generally close to the results using the diffusion approach, if the axial inductance of the magnetic field and the gas density are increased. However, major differences are found near the walls.     

Viscous flow of liquid glycerin-polyethylene glycol-water mixtures

The viscous flow of liquid water-glycerin mixtures is analyzed within the framework of free volume theory and thermodynamic reaction-rate theory.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 4, pp. 651–655, October, 1981.     

基于Lyapunov特征指数的钢制储液罐动力失稳概率分析

为有效量化储液罐在地震激励下的失稳概率,参考震害报告选取536组三维地震波记录,由压力-位移格式的流固耦合模型建立等效动力扰动方程,然后通过计算动态Lyapunov特征指数确定储液罐的动力失稳概率。选取某10万m3钢制储油罐作为分析对象,结果表明：水平向地震比竖向地震更易引起动力失稳,多维地震比单维地震更加危险;动力失稳概率随抗风圈的增加而减小;地震动方位、维数及抗风圈设置对“失稳概率-持时”曲线的影响较小。上述方法大幅降低了直接基于流固耦合模型确定储液罐动力失稳概率的计算成本,并能同时考虑地震动峰值与持时变化,从而全面直观反映地震动三要素的影响。     

Response of differently axially excited spinning liquid columns

Summary A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (>2₀) and hyperbolic range (<2₀). Differences of the various cases are presented.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - axial excitation amplitude - elliptic case (>2₀) - hyperbolic case (<2₀) - liquid density - surface tension - liquid surface displacement - _n damping factor - phase angle - acceleration potential - ₀ rotational speed - , ₁,₂ axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response