Map of regimes of pressure oscillations induced by absorption during gas jet injection through a submerged nozzle

Map of regimes of pressure oscillations induced by absorption during rapid injection of a soluble gas jet through a submerged nozzle into liquid, namely, oscillations during absorption, bubbling, internal chugging and small chugging, is suggested. Boundaries between various pressure oscillations regimes occurring when rapidly soluble gas is absorbed in water are investigated theoretically. It is showed that these boundaries are determined by four equations. It is showed that regime of high-frequency pressure oscillations during absorption occurs due to gas bubble oscillations, and other regimes of oscillations occur due to pressure oscillations in the whole system comprising the header, vent tubes and gas bubble. The conditions for excitation of high-frequency and low-frequency oscillations and boundaries between different regimes of pressure pulsations are determined. In a case when Henri's law for soluble gases is valid the developed model predicts that oscillations during absorption are not excited.     

Analysis of a class of undesired multimode oscillations

The behavior of a negative-resistance circuit in which the parameters permit self-sustained oscillations to occur is discussed. In such a circuit, undesired oscillations of higher frequency caused by parasitic elements can exist in addition to normal oscillations. Parasitic oscillations are described by second-order simultaneous non-linear differential equations, taking into account of existence of the shunt capacitance, lead inductance and resistance of a negative-resistance element. Assuming that the frequency of the parasitic oscillations is sufficiently high compared with that of the desired normal oscillations, the approximate periodic solutions are obtained by using a method of averaging. In addition, the theoretical results are compared with the observed behavior of an experimental oscillator having similar parameters.     

Studying the Complex Oscillations of a Star in the Field of a Galaxy

The oscillations of a star in the filed of a galaxy are studied. Initial energy conditions are established under which regular and complex oscillations occur. The latter are different from regular oscillations by the presence of saddle solutions in the trajectory. Unstable oscillations are due to only saddle solutions, with the trajectory tending to infinity     

Comparative Analysis of the Characteristics of the Vortex Wake behind a Flapping Wing Performing Oscillations of Different Types

The wake characteristics of a custom-designed airfoil performing pitching oscillations, heaving oscillations, and a combination of pitch and heave oscillations are compared in this study. The influence of flapping parameters are investigated at a constant Reynolds number Re\(_{c} = 2640\) and is presented for the Strouhal numbers based on the oscillation amplitude, St_A, varying in the \(0.1 \leqslant {\text{S}}{{{\text{t}}}_{A}} \leqslant 0.4\) range. The generation of vorticity above and below the airfoil depends on the airfoil’s initial direction of motion and remains the same for all types of flapping oscillations investigated. The evolution of the leading-edge and trailing-edge vortices is presented. The heaving oscillations of the airfoil are found to have a greater influence on the characteristics of the leading edge vortex. The wake behind the combined pitch-heave oscillations appears to be governed by pitching oscillations below \({\text{S}}{{{\text{t}}}_{A}} = 0.24\), whereas it is driven by heaving oscillations above \({\text{S}}{{{\text{t}}}_{A}} = 0.24\). The force computations indicate that the mere existence of the reverse von Kármán street is not sufficient to develop the thrust on the airfoil. The periodic component of velocity fluctuations significantly influences the wake characteristics. The anisotropic stress field developed around the airfoil due to the periodic fluctuations of the velocity is presented. The coherent structures developed in the wake are identified using the proper orthogonal decomposition and a qualitative comparison of the structures for different flapping oscillations is presented. The energy transfer from the flapping airfoil to the fluid for different flapping oscillations is highest for heaving oscillations followed by combined pitch-heave oscillations and pitching oscillations.

     

Model for the Formation of Acoustic Self-Oscillations in a Chamber with a Jet Flowing Through its Nozzle

This paper describes free acoustic oscillations of gas in a chamber with a jet flowing through its nozzle in the case of nonstationary intensity component of vortex sheet flowing down from the edge of the nozzle. There is established feedback between acoustic oscillations and oscillations induced by a corresponding vortex sheet component. It is shown that, in the presence of given feedback, there could be instability of acoustic oscillations, which would result in acoustic self-oscillations in the chamber. The boundaries of the domain in which instability is formed are determined by developing a mathematical model of stable acoustic oscillations in the chamber with account for the influence of the vortex sheet.     

Forced oscillations of a gas bubble in a spherical volume of a compressible liquid

A spherically symmetric problem of oscillations of a single gas bubble at the center of a spherical flask filled with a compressible liquid under the action of pressure oscillations on the flask wall is considered. A system of differential-difference equations is obtained that extends the Rayleigh-Plesset equation to the case of a compressible liquid and takes into account the pressure-wave reflection from the bubble and the flask wall. A linear analysis of solutions of this system of equations is performed for the case of harmonic oscillations of the bubble. Nonlinear resonance oscillations and nearly resonance nonharmonic oscillations of the bubble caused by harmonic pressure oscillations on the flask wall are analyzed. Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 111–118, March–April, 1999.     

Ellipsoidal Oscillations of a Gas Bubble with Periodic Variation of the Surrounding Fluid Pressure

Ellipsoidal linear and nonlinear oscillations of a gas bubble under harmonic variation of the surrounding fluid pressure are studied. The system is considered under conditions in which periodic sonoluminescence of the individual bubble in a standing acoustic wave is observable. A mathematical model of the bubble dynamics is suggested; in this model, the variation of the gas/fluid interface shape is described correct to the square of the amplitude of the deformation of the spherical shape of the bubble. The character of the air bubble oscillations in water is investigated in relation to the initial bubble radius and the fluid pressure variation amplitude. It is shown that nonspherical oscillations of limited amplitude can occur outside the range of linearly stable spherical oscillations. In this case, both oscillations with a period equal to one or two periods of the fluid pressure variation and aperiodic oscillations can be observed.     

Oscillations of conservative systems with complex trajectories

The principles of formation of closed and quasiperiodic orbitally stable trajectories of conservative systems are formulated. It is revealed that irregular oscillations are due to the orbital instability of quasiperiodic oscillations. A bistable oscillator with periodic forcing is considered. The existence of random oscillations at low level of energy and the conditions for orbitally stable oscillations are established To the Beginning of the Third Millennium __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 3–25, July 2008.     

Oscillations of a viscous fluid in a thin layer between two coaxial disks rotating together

A study is made of the problem of the motion of an incompressible viscous fluid in the space between two coaxial disks rotating together with constant angular velocity under the assumption that the pressure changes in time in accordance with a harmonic law. The problem is solved using the equations of unsteady motion of an incompressible viscous fluid in a thin layer. It is shown that the velocity field in this case is a superposition on a steady field of damped oscillations with cyclic frequency equal to twice the angular velocity of the disks and forced oscillations with cyclic frequency equal to the cyclic frequency of the oscillations of the pressure field. It is shown that the amplitude of the forced oscillations of the velocity field depends strongly on the ratio of the cyclic frequency of the oscillations of the pressure field to the angular velocity of the disks. It is shown that there is a certain value of the ratio at which the amplitude of the forced oscillations has a maximal value (resonance). It is shown that even for very small amplitudes of the pressure oscillations the amplitude of the oscillations of the relative velocity at resonance may reach values comparable with the mean velocity of the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–169, January–February, 1984.     

Convective heat transfer in single-phase flow in a vertical tube subjected to axial low frequency oscillations

The effect of oscillations on the heat transfer in a vertical tube has been studied experimentally. A vertical tube was mounted on a plate and the whole plate was subjected to oscillations in the vertical plane using a mechanical oscillator to provide low frequency oscillations. A section of the tube in the middle is subjected to a constant heat flux. The effect of the oscillations on the heat transfer coefficient has been examined. It was found that the heat transfer coefficient increased with oscillations in the laminar regime. In turbulent flow regime (Re > 2,100) it is found that the effect of oscillations did not show any change. A correlation has been developed for enhancement of the local Nusselt number in terms of the effective acceleration and Reynolds number. Using this, an expression has been proposed to calculate the mean Nusselt number as a function of the tube length.     

谐波齿轮系统的快慢振荡机制研究

谐波齿轮减速器是一种新型的传动装置, 因其具有诸多的优点, 因而得到了广泛应用. 谐波齿轮减速器涉及不同振荡尺度之间的耦合作用, 这通常会诱发复杂的快慢振荡, 严重影响了谐波齿轮系统的正常工作. 本文考虑涉及扭转刚度非线性因素的谐波齿轮系统, 旨在研究系统的快慢动力学, 揭示新型的快慢振荡机制. 首先, 构建了非线性扭转刚度下的谐波齿轮系统的快慢动力学模型. 然后, 通过改变扭转刚度系数, 得到了系统从常规振荡向快慢振荡的转迁过程. 接着, 简要地论述了有关快慢系统的基础理论. 在此基础上, 采用快慢分析法研究了快子系统的动力学特性, 揭示了快慢振荡的产生机制. 研究表明, 当系统参数改变时, 快子系统的平衡点曲线并未发生失稳或分岔; 然而, 在某一点附近, 平衡点曲线能够产生急剧量变, 其特征是平衡点在局部小范围内可以在正坐标值与负坐标值之间快速转迁. 在此基础上, 揭示了一种诱发快慢振荡的新型动力学机制, 比较了这种诱发机制与其他相关机制之间的区别. 本文丰富了系统通向快慢振荡的路径, 为实际谐波齿轮传动系统中的快慢振荡机理与控制研究提供参考.      

Nonstationary one-dimensional gas flows in channels in the presence of periodic perturbations of the boundary conditions

A study is made of the propagation in channels of forced oscillations generated by harmonic variation of the boundary conditions at the entrance and exit sections. Linear theory is used to find classes of boundary conditions and frequencies of the forced oscillations corresponding to the greatest gain or attenuation of high-frequency oscillations in a channel of variable section and of oscillations of arbitrary frequency in a channel of constant section. The resonance phenomenon that arises in channels when the frequencies of the forced oscillations and the fundamental oscillations are equal is studied. The wave process in a channel of variable section is investigated numerically, its characteristics found, and a comparison made with the linear theory. It is shown that the results of the calculations and the data of the linear analysis agree well.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 127–135, September–October, 1980.We thank A. B. Vatazhin for helpful discussions.     

Nonsmall liquid oscillations in a right circular cylinder

In this study we consider certain nonlinear effects which occur during oscillations of a liquid partially filling a right circular cylinder. The problem of nonlinear oscillations of a liquid in a circular cylinder has been considered in [1, 2]. The same problem has been solved in [3, 4] for arbitrary cavities by a somewhat different method.In the present paper we investigate the stability of forced oscillations of a liquid in a cylinder when the latter performs small harmonic oscillations in a plane passing through its axis.     

Oscillations of liquid in a vessel in the form of a rectangular parallelepiped

We consider the forced and the free oscillations of a liquid partially filling a cavity in the form of a rectangular parallelepiped. The characteristics of these oscillations are studied for small deformations of the free surface. It is shown that for definite frequencies and amplitudes of two-dimensional translational motions of the parallelepiped the fundamental of the liquid oscillations is excited in the plane perpendicular to the plane of motion of the vessel. The effect of small linear damping of the liquid oscillations on the shape of the boundaries of the principal region of instability of the liquid oscillations is evaluated. Fairly large oscillations of a liquid in a cylinder were considered in [1]. The same problem for a cavity of arbitrary configuration was studied in [2]. We note also that the conclusions of the study presented here are in qualitative agreement with the basic results obtained by a somewhat different method in [3] for a cavity in the form of a right circular cylinder.     

Seiche oscillations in a rectangular channel with an abrupt expansion of the cross section

The natural frequencies and modes of seiche oscillations in a closed water reservoir consisting of a long narrow channel connected to a wide basin were investigated theoretically and experimentally. Calculations were made using linear shallow-water theory in two-dimensional and one-dimensional formulations. The spectral properties of free-surface oscillations at points lying on the nodal lines of the first four modes of seiche oscillations were studied experimentally. The one-dimensional model adequately predicts lower-mode frequencies, but the data on the positions of the nodal points of seiche oscillations obtained using this model are somewhat different from those obtained experimentally and using the two-dimensional model.     

Finite amplitude oscillations of a hyperelastic spherical cavity

We present numerical results for the finite oscillations of a hyperelastic spherical cavity by employing the governing equations for finite amplitude oscillations of hyperelastic spherical shells and simplifying it for a spherical cavity in an infinite medium and then applying a fourth-order Runge-Kutta numerical technique to the resulting non-linear first-order differential equation.The results are plotted for Mooney-Rivlin type materials for free and forced oscillations under Heaviside type step loading. The results for Neo-Hookean materials are also discussed. Dependence of the amplitudes and frequencies of oscillations on different parameters of the problem is also discussed in length.     

Confinement of dynamical chaos expansion in rotifer populations inhabiting heterogeneous environments: an effect of attractor size invariance

We study the impact of inter-habitat interactions in rotifer populations with intrinsically different types of dynamics: chaotic and regular. For this purpose we use a modified version of the Consensus model. The Consensus model has been shown to be realistic enough to reproduce distinguishing features of the rotifer species dynamics. Being uncoupled, a habitat with chaotic dynamics and habitats with regular oscillations of the rotifer density do not affect each other. Migration of the rotifers between the habitats leads to the invasion of chaos into neighboring habitats, that is chaotic rotifer oscillations replace regular oscillations of the rotifer density in neighboring habitats. The invasion of chaos distorts spatial borders of the rotifer oscillations synchronization clusters. We show that the invasion of chaos is spatially confined. Invariance of the attractor size under transformation of regular oscillations into chaotic ones is demonstrated to be responsible for the chaos confinement.     

Impact of Atmospheric Front Parameters on Free and Forced Oscillations of Level and Current in the Sea of Azov

Level and current oscillations in the basin of the Sea of Azov have been studied by hydrodynamic modeling using the Princeton ocean model (POM). The hypothesis on the role of the resonance mechanism in the occurrence of extremely large amplitudes of storm surge and seiche oscillations depending on the velocity and time of motion of atmospheric fronts of the Sea of Azov has been tested. It is found that at the same wind, pressure perturbations moving over the Sea of Azov induce forced oscillations, and after the perturbations cease, free oscillations with amplitudes that are 14% higher than those obtained at constant atmospheric pressure. It is shown that the motion of the atmospheric front (whose velocity and time are selected under the assumption that waves with maximum amplitudes are generated) plays an important but not decisive role in the formation of the structure of currents and level oscillations in the Sea of Azov.     

Skin temperature oscillation model for assessing vasomotion of microcirculation

It has been proved that there exists a certain correlation between fingertip temperature oscillations and blood flow oscillations. In this work, a porous media model of human hand is presented to investigate how the blood flow oscillation in the endothelial frequency band influences fingertip skin temperature oscillations. The porosity which represents the density of micro vessels is assumed to vary periodically and is a function of the skin temperature. Finite element analysis of skin temperature for a contra lateral hand under a cooling test was conducted. Subsequently, wavelet analysis was carried out to extract the temperature oscillations of the data through the numerical analysis and experimental measurements. Furthermore, the oscillations extracted from both numerical analyses and experiments were statistically analyzed to compare the amplitude. The simulation and experimental results show that for the subjects in cardiovascular health, the skin temperature fluctuations in endothelial frequency decrease during the cooling test and increase gradually after cooling, implying that the assumed porosity variation can represent the vasomotion in the endothelial frequency band.     

Calculation of the decay rate of oscillations of a low-viscosity fluid rotating in a cylindrical vessel

A study is made of the problem of small oscillations of a low-viscosity fluid rotating under conditions of weightlessness in a cylindrical vessel. For fixed volume of the fluid and different values of the angular velocity and the wetting angle the decay rate and frequency of the characteristic oscillations are calculated. For an ideal fluid, the shapes of the characteristic oscillations of the free surface of the fluid are also calculated.