Axisymmetric longitudinal wave propagation in a finite prestretched compound circular cylinder made of incompressible materials

The propagation of an axisymmetric longitudinal wave in a finite prestrained compound (composite) cylinder is investigated using a piecewise-homogeneous body model and the three-dimensional linearized theory of wave propagation in prestressed body [13–15]. The inner and outer cylinders are assumed to be made of incompressible neo-Hookean materials. Numerical results on the influence of the prestrains in the inner and outer cylinders on wave dispersion are presented and discussed. These results are obtained for the case where the inner solid cylinder is stiffer than the outer hollow cylinder. In particular, it is established that the pretension of the cylinders increases the wave velocity     

Wave formation on the free surface of oil films

The origination of wave motion on the surface of a thin layer of oil is studied. This layer is considered as an incompressible pseudoplastic fluid, and surface tension is taken into account. It is shown analytically and numerically that these flows may be stable or unstable depending on the value of the Ostwald number. Profiles of the free surface are found for various values of the Ostwald and Weber numbers. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 139–147, July–August, 2000.     

Two-dimensional problem of a uniform flow of a two-layer fluid of finite depth past a circular cylinder

The linear steady problem of an irrotational uniform flow past a horizontal circular cylinder located in the upper or in the lower layer of a two-layer fluid is solved by the multipole-expansion method. The flow is perpendicular to the axis of the cylinder. The fluid is assumed to be inviscid and incompressible, and the flow in each layer is assumed to be potential. The upper layer can be bounded by a free surface or a solid lid, and the lower layer by a rigid horizontal bottom. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 91–101, November–December, 1998.     

Experimental study of variations in the thickness of a liquid film moving over the inner surface of a rotating cylinder

The behavior of a liquid layer moving in a mass-force field on the inner surface of a rotating vertical cylinder is studied experimentally. Free-surface profiles of the liquid moving under these conditions are constructed. An empirical dependence for the mean thickness of the film is obtained in criterial forms. The presence of a hydraulic jump in the lower part of the cylinder behind the entrance of the liquid onto the vertical surface is revealed. Tomsk, State Architectural-Building University, Tomsk 634003. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 65–71, November–December, 1998.     

Effect of convection on the stability of a liquid with a nonuniformly distributed heavy admixture

The effect of the transverse temperature gradient on the stability of steady motion of a viscous incompressible liquid in a plane vertical layer bounded by two infinite solid surfaces is studied. The motion of the liquid is caused by sedimentation of heavy solid spherical particles distributed nonuniformly across the layer and by the horizontal temperature gradient. Spectra of decrements of small normal perturbations are calculated for different particle sizes and different degrees of nonuniformity of the distribution of admixture particles. The stability of a steady flow of the liquid with an admixture decreases with increasing temperature gradient and increasing particle radius and increases with a tendency of the particles to a uniform distribution. Chelyabinsk State University, Chelyabinsk 454021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 180–187, September–October, 2000.     

Quasi-steady-state flows in a liquid film in a gas: Comparison of two methods of describing waves

The motion of thin films of a viscous incompressible liquid in a gas under the action of capillary forces is studied. The surface tension depends on the surfactant concentration, and the liquid is nonvolatile. The motion is described by the well-known model of quasi-steady-state viscous film flow. The linear-wave solutions are compared with the solution using the Navier-Stokes equations. Situations are studied where a solution close to the inviscid two-dimensional solutions exists and in the case of long wavelength, the occurrence of sound waves in the film due to the Gibbs surface elasticity is possible. The behavior of the exact solutions near the region of applicability of asymptotic equations is studied, and nonmonotonic dependences of the wave characteristics on wavenumber are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 103–111, May–June, 2007.     

Universal deformations of growing solids

A class of universal deformations of accreted hyperelastic incompressible bodies is studied. Accretion is realized by adding prestrained layers [1–4]. The deformations correspond layerwise to the transformation of a parallelepiped to a hollow circular cylinder. Discrete and continuous accretion modes are considered and classified. Solutions of the boundary-value problems for the elastic Mooney-Rivlin potential are constructed. The solutions of the discrete accretion problems are shown to converge to solutions of the corresponding problems of continuous accretion as the number of layers increases and the layer thickness decreases.     

Subcritical flows from beneath a shield

The problem of a two-dimensional stationary flow of an ideal incompressible heavy vortex-free liquid that flows from beneath a shield is studied. The bottom is considered smooth and horizontal, and the flow is assumed to be subcritical. The existence of a solution that is different from a uniform flow is proved in an exact formulation. It is shown that the solution behaves like a Nekrasov wave at infinity. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 54–60, January–February, 1998.     

Pulsating liquid flow past a spherical body in an infinite cylinder

The problem of determination of the hydrodynamic characteristics of an ideal incompressible liquid moving with constant velocity past a spherical body in an infinite circular cylinder is considered. It is assumed that the cylinder axis passes through the mass center of the spherical body. The total liquid potential has been constructed both in spherical and cylindrical coordinate systems. The hydrodynamic characteristics of the flow in the cylinder were researched based upon comparison with the corresponding characteristics of the liquid flow of a spherical body in a boundless medium. S. P. Timoshenko Mechanics Institute, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 27–31, June, 1999.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Stability of the tubular layer of a deformed material in a rotating horizontal cylinder

The stability conditions for the steady-state motion of the tubular layer of a treated deformable material in a rotating horizontal cylinder are determined analytically. With allowance for the accepted similarity criteria, universal diagrams of the boundaries of transition of modes of motion of liquid and loose materials in the cylinder are obtained on the basis of experimental data. Analysis of the diagrams shows the identity of the stability conditions for a liquid layer and a loose medium, which can be regarded as a Newtonian liquid upon fast relative motions. It is shown also that the analytical stability conditions for the liquid layer correspond to the experimental data for large Reynolds numbers when the mode hysteresis occurs and do not correspond to these data for small Reynolds numbers when secondary circulating flows form. Rovno State Pedagogical Institute, Rovno 266000, Ukraine. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 120–127, January–February, 2000.     

Filtration convection in a high-frequency vibration field

The effect of high-frequency translational vibrations on the occurrence of filtration convection in a plane horizontal layer of a viscous incompressible liquid saturating a porous medium is studied. Constant temperature is maintained at the boundaries of the layer. It is established that for any vibration direction different from the vertical (transverse) direction, convection in gravity and thermal gravitational convection under both heating from above and heating from below can arise. In the case of reduced gravity, values of the vibration parameter that lead to transition to zero gravity are established. The results are obtained from an analysis of the averaged equations of filtration convection, derived for an arbitrary region. This work was presented at the joint X European and VI Russian Symposium on Physical Sciences in Microgravity (St. Petersburg, June 15–20, 1997). Rostov State university, Rostov-on-Don 344090. Rostov State Academy of Building, Rostov-on-Don 344022. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 22–29, May–June, 1999.     

Azimuthal wave motions on the surface of a rotating fluid cylinder

Wave motions in a fluid cylinder rotating about the axis are investigated within the framework of the linear theory. The cylinder is assumed to be fairly long. This makes it possible to restrict attention to the study of the plane oscillation pattern. The fluid is assumed to be ideal and incompressible. The models in which the fluid particles are confined by gravitational (body) or/and capillary forces (surface stress forces) are considered. A mode analysis is carried out and the dispersion relations are constructed. Traveling and steady-state waves on the surface of the fluid cylinder are investigated; qualitative effects ("wave inertia") are established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–133, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00221). An erratum to this article is available at .     

Plane strain wave in an isotropic layer of a viscoelastic material

The velocity and the rate of decay of a strain wave in a layer of a viscoelastic material rigidly fixed on a solid foundation are determined. The wave structure (ratio of the longitudinal to the transverse displacement) and the profiles of these displacements are analyzed. Attenuation of waves in the first mode is found to be more significant than that in an infinite space. The most intense decay is observed at resonance frequencies. A strong effect of compressibility of the medium on wave parameters is revealed. Conditions at which such a system operates as a waveguide are found. For a loss tangent higher than 0.13 (for an incompressible medium), the character of the dispersion dependence is observed to change drastically: the wave velocity decreases with decreasing frequency. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 104–111, May–June, 2006.     

Diffraction of internal waves by a circular cylinder near the pycnocline

Propagation of internal waves over a circular cylinder under the conditions of a continuous stratification characterized by the presence of a high-gradient density layer (the pycnocline) of finite thickness is studied. The dependences of the coefficent of wave propagation on the wavelength of the first-mode incident wave for various thicknesses of the pycnocline are obtained. In the diffraction of internal waves, substantial nonlinear effects are shown to occur, which result in the appearance of waves of double oscillation frequency compared to the frequency of the incident waves. The generation coefficient for these waves is found. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 79–85, March–April, 1999.     

Exact solution of the problem of convective heat exchange for a circular cylinder at small Prandtl numbers

The problem of the heat exchange of a circular cylinder in an incompressible flow at small Prandtl numbers Pr ≪ 1 is solved. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 43–48, January–February, 1994.     

Stability of flow between two rotating cylinders in the presence of a constant heat flux at the outer cylinder and radial temperature gradient – wide gap problem

The stability of Couette flow of a viscous incompressible fluid between two concentric rotating cylinders in the presence of a radial temperature gradient due to a constant heat flux at the outer cylinder is studied. The critical values of `a' (the wave number) and Ta (the Taylor number) are listed in a table and some critical Taylor numbers are shown graphically. It is shown that as the heat flux is increased the flow becomes more unstable for all values of μ calculated, where μ is the ratio of the angular velocity of the outer cylinder to that of the inner cylinder. Received on 04 March 1997     

波浪与新型双排开孔圆筒防波堤相互作用三维数值模拟

双排开孔圆筒防波堤是基于圆筒、板式结构的一种复合式新型结构型式;基于不可压缩两相流模型建立三维数值波浪水槽,通过RNG k-ε湍流模型进行湍流封闭,并采用TruVOF方法捕捉自由液面,开展波浪与双排开孔圆筒防波堤相互作用数值模拟,探究相对排间距、开孔率对新型双排开孔圆筒防波堤消浪性能的影响,分析了后排开孔圆筒防波堤附近的复杂水动力现象和流动特性.结果表明,在本文研究工况范围内,沿程平均波高随相对排间距的增大先增大后减小,随开孔率的增大而增大,周期对沿程平均波高的影响没有明显规律;当B/D=9, e=23.11%时,新型双排开孔圆筒防波堤消浪效果最优,反射系数在0.4～0.46之间,透射系数在0.3～0.35之间,耗散系数在0.8～0.85之间;自由液面破碎、水气掺混、环状涡运动演化是新型双排开孔圆筒防波堤紊动耗能消波的主要原因;相对排间距会引起后排防波堤附近涡量分布以及剪切层形态的变化,从而导致不同的紊动特性,影响双排开孔圆筒防波堤消浪特性.研究结果可以为新型双排开孔圆筒防波堤工程设计与消浪机理研究提供理论支撑.     

Two-dimensional problem of the impact of a vertical wall on a layer of a partially aerated liquid

The two-dimensional unsteady problem of the impact of a vertical wall on a layer of a liquid which is mixed with air near the wall and does not contain air bubbles away from the wall is solved in a linear approximation. The gas-liquid mixture is modeled by a homogeneous, ideal, and weakly compressible medium with a reduced sound velocity dependent on the air concentration in the gas-liquid mixture. Outside the gas-liquid layer, the liquid is considered ideal and incompressible. During the initial stage of the impact, the liquid flow and the hydrodynamic pressure are determined using the linear theory of the potential motion of an inhomogeneous liquid. The dependence of the amplitude of the impact pressure along the wall on the air concentration in the gas-liquid layer and on the thickness of this layer is investigated. For a small relative thickness of the layer, the thin-layer approximation is used. It is shown that the solution of the original problem tends to the approximate solution as the thickness of the layer decreases. It is shown that the presence of the gas-liquid layer leads to wall pressure oscillations. Estimates are obtained for the pressure amplitude and the oscillation period. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 34–46, September–October, 2006.     

Ligament formation in sheared liquid–gas layers

We perform numerical simulations of two-phase liquid–gas sheared layers, with the objective of studying atomization. The Navier–Stokes equations for two-dimensional incompressible flow are solved in a periodic domain. A volume-of-fluid method is used to track the interface. The density ratio is kept around 10. The calculations show good agreement with a fully viscous Orr–Sommerfeld linear theory over several orders of magnitude of interface growth. The nonlinear development shows the growth of finger-like structures, or ligaments, and the detachment of droplets. The effect of the Weber and Reynolds numbers, the boundary layer width and the initial perturbation amplitude are discussed through a number of typical cases. Inversion of the liquid boundary layer is shown to yield more readily ligaments bending upwards and is thus more likely to produce droplets.