Effect of the contact-line dynamics on the oscillations of a compressed droplet

This paper studies the natural and forced oscillations of a deformed droplet of an inviscid liquid surrounded by a different liquid and bounded in the axial direction by solid planes. In equilibrium, the droplet is a figure of revolution and the ratio of its radius to height is significant. The equilibrium contact angle between the side surface of the droplet and the solid surface is different from a right angle. The motion of the contact line is taken into account by setting an effective boundary condition. It is shown that three characteristic ranges of natural frequencies exist.     

Non-axisymmetric oscillations of a hemispherical drop

Natural oscillations of a hemispherical drop on a solid substrate are considered. The Hocking condition is used to take into account the contact angle dynamics. The natural oscillations attenuate due to dissipation on the contact line and the degeneracy in the azimuthal number is eliminated. Forced oscillations of the drop are studied for tangential vibrations of the substrate. For the case of a fixed contact line, the amplitude of the forced oscillations grows without bound near the fundamental requency. In other cases, the amplitude is finite.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 8–20. Original Russian Text Copyright © 2004 by Lyubimov, Lyubimova, Shklyaev.     

Experimental study of the influence of rectangular plates stiffening a cylindrical shell on its natural frequencies and modes

The results are presented of studying the influence of rectangular plates on the natural frequencies and modes of a fluid-filled cylindrical shell with different end conditions __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 93–95, February 2006.     

On the spectrum of natural frequencies of circular cylindrical shells completely filled with a fluid

The natural frequencies of cylindrical shells filled with a fluid and having the ends either simply supported or clamped are determined. Conditions are studied under which the natural frequencies of the shell are close or multiple __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 42–49, May 2006.     

Axisymmetric oscillations of a cylindrical droplet with a moving contact line

Forced oscillations of a cylindrical droplet of an inviscid liquid surrounded by another liquid and bounded in the axial direction by rigid planes are investigated. The system is affected by vibrations whose force is directed parallel to the axis of symmetry of the droplet. The velocity of motion of the contact line is proportional to the deviation of the contact angle from the value at which the droplet is in equilibrium. Linear and nonlinear oscillations are considered. The conditions of the occurrence of resonance are determined.     

Numerical and experimental investigation on droplet dynamics and dispersion of a jet engine injector

In the case of turbine combustors operating with liquid fuel the combustion process is governed by the liquid fuel atomization and its dispersion in the combustion chamber. By highly unsteady flow field conditions the transient interaction between the liquid and the gaseous phase is of interest, because it results in a temporal variation of air–fuel ratio which leads to a fluctuating temperature distribution. The objective of this research was the investigation of transient flow field phenomena (e.g. large coherent structures) on droplet dynamics and dispersion of an isothermal flow (of inert water droplets) as a necessary first step towards a full analysis of spray combustion in real-life devices. The advanced injector system for lean jet engine combustors PERM (Partial Evaporated Rapid Mixing) was applied, generating a dilute polydispersed spray in a swirled flow field. Experiments were performed using Phase Doppler Anemometry (PDA) and a patternator to determine the droplet polydispersity, concentration maps, and velocity profiles in the flow. An important finding is the effect of large-scale coherent structures due mainly to the precessing of the vortex core (PVC) of the swirling air jet on the particle dispersion patterns. The experimental results then serve as reference data to assess the accuracy of the Eulerian–Lagrangian computations using a Large Eddy Simulation (LES), a Unsteady Reynolds-Average Navier–Stokes Simulation (URANS) and two simplified (steady-state) simulations. There, a simplified droplet injection model was used and the required boundary conditions of injected droplet sizes were obtained from measurements. Important transient effects of deterministic droplet separation observed during experiments, could be perfectly replicated with this injection model. It is convincingly shown, through extensive computations, that the resolution of instantaneous vortical structures is indeed crucial; hence the LES, or a reasonably-well resolved URANS are preferred over the steady-state solutions with additional, stochastic-type, turbulent dispersion models.     

Natural vibrations of a cylindrical shell reinforced with rectangular plates

This paper outlines a technique of determining the natural frequencies and modes of an elastic structure consisting of a cylindrical shell and noncrossing rectangular plates inserted into it. The influence of the position, number, and thickness of the plates on the natural frequencies and modes is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 89–96, March 2006.     

Tangential oscillations of a differentially rotating spherical fluid layer

The natural harmonic oscillations of a differentially rotating fluid layer under the action of a potential force are considered. The rise in the layer level is assumed to be negligible. The oscillations satisfy an ordinary second-order differential equation with singular coefficients that depend on the spatial coordinate. This equation is solved by the method of local separation of singularities based on the use of the properties of the Fuchs series for a bounded solution. Various laws for the latitude dependence of the angular rate of ocean rotation and the effect of these laws on the problem spectrum are considered. An equation is obtained for the streamlines of the oscillations investigated. Two cases in which the latitude dependence of the base flow velocity coincides with the real dependence for a celestial body are considered and the corresponding modes are found.     

不同壁面条件下液滴撞击铺展特性的模拟研究

液滴撞击不同润湿性壁面的传热流动问题在自然界和工业生产中广泛存在。研究采用CLSVOF方法,引入描述壁面润湿特性的动态接触角,并考虑液滴物性参数随温度的变化,建立液滴撞壁模型,模拟研究液滴撞击流动行为,通过与实验对比验证,确定模型有效性。在此基础上,对传热作用下考虑壁面润湿性的液滴撞击问题展开研究,探讨壁面传热作用对液滴撞击铺展特性的影响。研究表明,在撞击过程中,液滴先铺展后逐渐收缩,与静态接触角模型相比,采用动态接触角模型所得的液滴流动特性与实验结果更加吻合;随着接触角增大,液滴在撞壁初期不易铺展,随后则易于收缩;虽然固液传热作用会影响液滴铺展直径,但不改变液滴的运动趋势。     

Experimental analysis of the natural vibrations and stability of cylindrical shells reinforced with rectangular plates

The paper presents experimental results on the effect of reinforcing cylindrical shells with rectangular plates on the axial compressive critical loads and the natural frequencies and modes of two sets of shells __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 100–103, May 2008.     

Numerical prediction of droplet dynamics in turbulent flow,using the level set method

In the present article, the droplet dynamics in turbulent flow is numerically predicted. The modelling is based on an interfacial marker-level set (IMLS) method, coupled with the Reynolds-averaged Navier–Stokes (RANS) equations to predict the dynamics of turbulent two-phase flow. The governing equations for time-dependent, two-dimensional and incompressible two-phase flow are described in both phases and solved separately using a control volume approach on structured cell-centred collocated grids. The topological changes of the interface are predicted by applying the level set approach. The kinematic and dynamic conditions on the interface separating the two phases are satisfied. The numerical method proposed is validated against a well-known computational fluid dynamics problem. Further, the deformation and breakup of a single droplet either suddenly moved in air or exposed to turbulent stream are numerically investigated. In general, the developed numerical method demonstrates remarkable capability in predicting the characteristics of complex turbulent two-phase flows.     

Forced nonlinear oscillations of cylindrical shells interacting with fluid flow

The dynamic interaction of thin cylindrical shells with the fluid flow inside them under external periodic loads is studied. A technique is proposed to calculate the parameters of forced nonlinear oscillations of shells with a fluid moving with nearly critical velocities. The amplitude-frequency characteristics of the fluid-shell system under steady-state oscillation are plotted __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 91–99, April 2006.     

Effect of a precompressed spring on the discontinuity zone around a cylindrical cavity

This paper discusses the use of a cylindrical spring to increase the stability of a tunnel of circular cross section. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 141–148, May–June, 2005.     

Effect of gravity on nonlinear oscillations of a horizontal,immovable-end beam

A critical problem in designing large structures for space applications, such as space stations and parabolic antennas, is the limitation of testing these structures and their substructures on earth. These structures will exhibit very high flexibilities due to the small loads expected to be encountered in orbit. It has been reported in the literature that the gravitational sag effect under dead weight is of extreme importance during ground tests of space-station structural components [1–4]. An investigation of a horizontal, pinned-pinned beam with complete axial restraint and undergoing large-amplitude oscillations about the statically deflected position is presented here. This paper presents a solution for the frequency-amplitude relationship of the nonlinear free oscillations of a horizontal, immovable-end beam under the influence of gravity.The governing equation of motion used for the analysis is the Bernoulli-Euler type modified to include the effects of mid-plane stretching and gravity. Boundary conditions are simply supported such that at both ends there is no bending moment and no transverse and axial displacements. These boundary conditions give rise to an initial tension in the statically deflected shape. The displacement function consists of an assumed space mode using a simple sine function and unknown amplitude which is a function of time. This assumption provides for satisfaction of the boundary conditions and leads to an ordinary differential equation which is nonlinear, containing both quadratic and cubic functions of the amplitude. The perturbation method of multiple scales is used to provide an approximate solution for the fundamental frequency-amplitude relationship.Since the beam is initially deflected the small-amplitude fundamental natural frequency always increases relative to the free vibration situation provided in zero gravity. The nonlinear equation provides for interactions between frequency and amplitude in that both hardening and softening effects arise. The coefficient of the quadratic term in the nonlinear equation arises from the static (dead load) portion of the deflection. This quadratic term, depending upon its magnitude, introduces a softening effect that overcomes the hardening term (due to initial axial tension developed by deflection) for large slenderness ratios.For very large slender, immovable-end beams, the fundamental natural frequency is greater than that of beams without axial constraints undergoing small amplitude oscillations. This phenomenon is attributed to the stiffening effect of the statically-induced axial tension. However, the stiffening effect of axial tension in beams with slenderness ratios greater than approximately 392 undergoing large-amplitude symmetric-mode oscillations is overpowered by the presence of gravitational loading.Nomenclature A amplitude of the first harmonic - A ₁ cross-sectional area of beam - a(t) vibratory amplitude - E Young's modulus - g acceleration due to gravity - g ₁,g ₂,g ₃ constants defined in equations (8) - I area moment of inertia of cross-section - L length of beam - N axial tension force induced by gravitational loading     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Natural frequencies of rotating functionally graded cylindrical shells

Love’s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells.To verify the validity of the present method,the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results.Good agreement is obtained.The effects of the power law index,the wave numbers along the x-and θ-directions,and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples.It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed,the fundamental frequencies of the forward waves decrease with the increasing rotating speed,and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.     

基于FEM和RSM的深穴圆柱滚子优化设计

为消除圆柱滚子端部的应力集中现象,提高滚动轴承的疲劳寿命,对圆柱滚子内修形-深穴结构的形状控制参数(深穴开口度k、深穴长度l、深穴锥角α)进行了分析,建立了滚子接触有限元(FEM)模型。基于响应曲面法(RSM),建立了以滚子端部与中间接触应力差最小为优化目标,以k,l和α为设计变量的优化数学模型,并对响应面模型进行了求解,得到一组最优解,通过对比分析表明深穴滚子可以有效地降低滚子端部的应力集中现象,优化后深穴滚子应力分布更为均匀,避免了因局部应力过大而过早发生疲劳失效;采用FEM与RSM相结合的优化方法操作简单、效率高,可将其应用于其他机械零部件的优化设计。     

Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.     

Vibrations of a corrugated orthotropic cylindrical shell with free edges

The natural vibrations of a corrugated elastic orthotropic cylindrical shell with a directrix perpendicular to its edges that are free are examined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 97–114, December, 2006.