Impact of a body with a plane bottom on a thin liquid layer at a small angle

The problem of the impact of a body with a plane bottom (of the type of a box) on a thin liquid layer at a small angle is solved in the two-dimensional formulation. The nonlinear shallow water equations are used, together with the method of matched asymptotic expansions. It is found that at certain values of the input parameters of the problem the liquid pressure diminishes near the lower end of the body and becomes smaller than the atmospheric pressure, which results in liquid separation from the box bottom. The numerical results show that all input parameters of the problem have a considerable effect on the nature of body motion. The liquid separation effect on body motion is analyzed.     

Formation of a cavity in the initial stage of motion of a circular cylinder in a fluid with a constant acceleration

This paper considers the joint motion of an ideal fluid and a circular cylinder completely immersed in it at small times. It is assumed that the cylinder, which was initially at rest, moves in a horizontal direction with a constant acceleration. The dynamics of the internal and external free boundaries of the fluid at small times is studied. An asymptotic analysis of the form of the internal free surface near the separation points is performed. It is shown that at high acceleration of the circular cylinder, a large cavity is formed behind, with a strong perturbation of the external free surface of the fluid over the surface of the cylinder.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Falling of a body with a flat elastic bottom on a thin liquid layer at a small angle

Nonlinear shallow water equations and the method of matched asymptotic expansions are used to solve the problem of the impact of a box-type body with a flat bottom on a thin elastic liquid layer at a small angle in the plane formulation. It is established that, at certain values of the input parameters of the problem, the liquid pressure near the body edges becomes less than atmospheric pressure, and the liquid separates from the bottom of the box. Calculations demonstrating the influence of elastic bottom and liquid separation on the body motion are performed. It is shown that the presence of an elastic bottom significantly changes the hydrodynamic pressure distribution and can cause loads higher than in the case of a rigid body.     

Wave Motions in a Two-Layer Fluid Driven by Small Oscillations of a Cylinder Intersecting the Interface

The plane problem of steady-state small oscillations of a horizontal cylinder located at the interface between two fluids of different densities and indefinite depth is considered in the linear formulation. Boundary integral equations for the surface source distribution are derived. The behavior of the distributed singularities at points of intersection of the body contour and the interface is investigated. The problem of oscillations of a circular cylinder is solved by the multipole expansion method. The apparent mass and damping coefficients of the radiation problem and the reflection coefficient of the problem of scattering of an impinging wave by a floating body are calculated.     

The Flow and Heat Transfer at Start-Up of an Arbitrarily Shaped Body in a Viscous Heat-Conducting Gas

The flow corresponding to the start-up of an arbitrarily shaped body in a viscous heat-conducting gas is analyzed. The established fact of fluid incompressibility at short times is used. In the first approximation, in the neighborhood of each point on the body surface the flow and heat transfer are proved to be the same as for an infinite plate coinciding with the tangential plane at this point. The corrections for the curvature of the body surface are found. For determining the flows near a cylinder of arbitrary shape and near a spherical bluntness, the start-up problems for a circular cylinder and a sphere are considered. The possibility of extending the results to the case of reacting gases is discussed.     

Non-Newtonian end effects in falling ball viscometry of concentrated suspensions

In a Newtonian fluid contained in a cylinder, a small ball initially at rest released just below the surface would accelerate to achieve a steady-state velocity within one cylinder diameter. After traversing the center section of the cylinder, the ball would begin slowing down within one cylinder diameter of the bottom. This behavior is also observed in suspensions where the size of the suspended particles is small relative to the containing cylinder. However, in concentrated suspensions of larger suspended particles, balls released near the upper surface travel faster than the steady state velocity. In addition, the length of the upper surface end effect, where the falling ball decelerates to the steady state velocity, and the lower end effect zone, where the ball decelerates to rest at the bottom, is many times longer than in a Newtonian single-phase liquid. These non-Newtonian end effects are reduced if the suspended particles are polydisperse in their size distribution.     

Studies on two-phase cross flow. Part I: Flow characteristics around a cylinder

A two-phase flow around a body has scarcely been studied until now, though the flow is used in many industrial components. The cross flows around a spacer in a fuel assembly of light water reactors (LWR) and tube supports in a steam generator are closely related to the long-term reliability and the safety. The present study has been planned to clarify the two-phase flow and heat transfer characteristics around a body including the unknown complicated flow behavior. In the first report, the flow characteristics near and behind a cylinder which was located in a vertical upward air-water bubbly flow were investigated. From the observation of the flow patterns and the measurements of the distributions of void fraction, liquid velocity and static pressure, it is revealed that the vortex flow and the change of the static pressure and liquid velocity distribution around the cylinder resulted in the large distortion of the void fraction distribution around the cylinder. The most noticeable phenomena in the wake were that the peaks of the local void fraction appeared in the vicinity of the cylinder surface near the separation point and in the wake behind the cylinder.     

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.     

Mixed Convection Adjacent to a Suddenly Heated Horizontal Circular Cylinder Embedded in a Porous Medium

The mixed convection caused when a horizontal circular cylinder is suddenly heated is investigated in the situation when the initial flow past the cylinder is uniform and its direction either upwards or downwards. An analytical series solution, which is valid at small times, is obtained using the matched asymptotic expansions technique. A numerical solution, which is valid at all times and for any values of the Rayleigh and Péclet numbers, is also obtained using a fully implicit finite-difference method. Three different regimes, when either the free or forced convection is dominant or when they have the same order of magnitude, are considered. In the free convection dominated regime, two vortices develop near the sides of the cylinder in both situations of an upward or downward external flow. Comparisons between the analytical and numerical results at small times, as well as a detailed discussion of the evolution of the numerical solution are presented. The numerical results obtained for large Rayleigh, Ra, and Péclet Pe, numbers show that a thermal boundary-layer forms adjacent to the cylinder for any value of the ratio Ra/e. The steady state boundary-layer analysis, similar to that performed by Cheng and Merkin, is analysed in comparison to the numerical solution obtained for large values of Ra and Pe at very large times.     

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.     

Example of motion of a cylindrical solid in a viscous liquid

The problem of motion of a pulsating solid (an infinitely long circular cylinder) in an oscillating viscous liquid in the presence (or absence) of an external stationary force is considered. The perturbation method is applied. It is found that the solution of the time-average motion of a body exists if and only if body pulsations, liquid vibrations, and external forces satisfy a certain relation. The presence of a plane analog of the phenomenon of predominantly unidirectional motion of a compressible solid in an oscillating liquid is established.     

Dynamics of a rigid cylinder near a plane boundary in the radiation field of an acoustic wave

An approach is described for investigation of the interaction between a rigid body and a viscous fluid boundary under acoustic wave propagation. The influence of the liquid on the rigid body is determined as a mean force, which is a constant in the time component of the hydrodynamic force. This enables the use of a previously developed technique for calculation of pressure in a compressible viscous liquid. The technique takes into account the second-order terms with respect to the wave field parameters and is based on investigation of a system of initially nonlinear hydromechanics equations that can be simplified with respect to the wave motion parameters of the liquid. It has proven possible to retain the second-order terms for determination of stresses in the liquid without having to solve the system of nonlinear equations. The stresses can be expressed in terms of parameters found in the solution of the linearized equations of the compressible viscous liquid. In this way, the solution of linearized equations is expressed in terms of a scalar and vector potentials. The problem statement is derived for a rigid cylinder located near a rigid flat wall under the effects of a wave propagating perpendicular to the wall. The solution for this particular example is obtained.     

A Pressure Field in an Acoustic Medium Containing a Cylindrical Solid and a Sphere Oscillating in a Predetermined Manner

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered     

An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged body

An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave–body interaction problem into body and free‐surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free‐surface problem satisfies modified nonlinear free‐surface boundary conditions. It is then shown that the nonlinear free‐surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free‐surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo‐spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite Oscillations of a Cylinder in a Coaxial Duct Subjected to Annular Compressible Flow

As a generalization considering small fluid-structural vibrations, the present paper examines the finite magnitude oscillatory motion of an elastically supported rigid cylinder in a cylindrical rigid duct conveying a compressible flow. The fluid is assumed to be inviscid and irrotational and free purely transverse vibrations of the body are dealt with. The governing equations of motion are the fully nonlinear Euler equations together with the continuity equation and a state equation (here for an ideal gas), the ordinary differential equation for the vibrating cylinder, and the kinematical transition and boundary conditions at the moving contact interface between fluid and body and the outside fluid border, respectively. A pertubation analysis is performed to calculate not only the dynamic characteristics for small coupled oscillations but also the corrections due to the inherent nonlinearities of the vibroacoustic problem. To make the calculation steps more transparent, the simpler problem of a two-dimensional channel flow between a rigid wall and an elastically supported rigid plate is also included in the present study. As an outlook, the influence of flexibility of the cylinder (or the plate) is addressed and the problem of forced vibrations is touched. This revised version was published online in July 2006 with corrections to the Cover Date.     

章动角对旋转章动充液腔体运动稳定性的影响

旋转章动充液腔体的运动稳定性，主要分两大类。当Ｒｅｙｎｏｌｄｓ数很小时，出现转速衰减不稳定性，Ｒｅｙｎｏｌｄｓ数增大到一定程度，又出现共振不稳定性。本文考虑Ｒｅｙｎｏｌｄｓ数较大时的情况，此时腔内液体的惯性波振动与腔体的章动频率耦合即可发生共振不稳定性。当章动角增大时，共振频带又发生转移。采用变形参数法讨论章动角增大时弱非线影响，很简明地得出特征值修正公式，并计算了液体力矩的变化曲线。     

Liquid flow in a gap between a cylinder and a wall in motion

The results of an experimental investigation and calculations of the location of the minimum pressure point are presented for the case, when a cylindrical body moves along a wall in the presence of a small gap. The pressure on the cylindrical body surface is measured in the confusor and diffuser regions. It is shown that with decrease in the gap the minimum pressure point is displaced toward the minimum gap line, with increase in the pressure drop. An increase in the velocity of the motion at a constant gap leads only to a pressure increase in the diffuser region, while the location of the minimum pressure point remains the same. It is established that an increase in the inner cylinder radius moves the minimum pressure location away from the minimum gap line. The formation of two return flow regions in the confusor and diffuser regions near the cylindrical surface is detected. It is shown that the return flow in the pressure drop region reaches the stage of incipient cavitation bubbles. The results obtained can be useful in lubrication theory, as well as in medicine and biology.     

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.     

Fluid–structure interaction during the impact of a cylindrical shell on a thin layer of water

A two-dimensional unsteady analysis of an elastic circular cylindrical shell that enters a thin layer of an ideal incompressible liquid is considered. The cylinder initially touches the liquid free surface at a single point and then penetrates the liquid layer at a constant vertical velocity. The problem is coupled because the liquid flow, the shape of the elastic shell and the geometry of the contact region between the body and the liquid must be determined simultaneously. The flow region is subdivided into four complementary regions that exhibit different properties: the region beneath the entering body surface, the jet root, the spray jet, and the outer region. A complete solution is obtained by matching the solutions within these four subdomains. The structural analysis is based on the normal-mode method. Strain-time histories of the inner surface of the cylinder are of particular interest. In the case of a very flexible shell three distinct regimes of the impact process were found. For a high impact velocity the lower part of the shell flattens and the shell does not enter the water. For a moderate impact velocity the shell reaches the bottom and an effect of “fluid capture” may occur. For a low impact velocity the shell penetrates the liquid, but the size of the contact region decreases before the shell reaches the bottom. This behaviour corresponds to exit or “reflection” of the shell from the water layer.