Motion of solid particles in an oscillating liquid

The problem of motion of two “free” solid particles in a uniformly oscillating liquid is formulated and solved. In particular, it is found that the particles are capable of performing (side by side with oscillations) an average, monotonous displacement in the liquid as a whole.     

Stability of a swarm of air bubbles in an oscillating liquid

The phenomenon of the formation of a swarm of air bubbles in a liquid executing vertical oscillations within a vertical tube is described. The explanation for the mechanism of air entry into the liquid and the behavior of the individual minute bubbles was given in [1], In the present paper we examine a swarm of bubbles—an air cushion; the stability of this swarm is studied. The results of experimental studies and theoretical calculations are compared.     

Waves in a heavy two-layer liquid excited by an oscillating sphere

An approximate solution of an initial-boundary-value problem appropriate for the semiaxist>0 (t is time) is constructed for a system of integrodifferential equations which describes the waves excited in an initially stationary unbounded heavy two-layer fluid by a vertically oscillating sphere located at a distance from the interface that is significantly greater than its radius. The shape of the steady-state wave is found by passing to the limit as time increases indefinitely. The wave resistance experienced by the sphere during the transient process and in the steady-state regime is studied as a function of frequency. Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 120–133, March–April, 1998.     

Heat transfer in an oscillating vertical annular liquid column open to atmosphere

The heat transfer from a surface heated with constant heat flux to an oscillating vertical annular liquid column having an interface with the atmosphere is investigated experimentally in the present paper. The analysis is carried out for the case of different oscillation frequencies while the displacement amplitude remains constant. Based on the experimental data a correlation equation is obtained for the cycle-averaged Nusselt number as a function of kinetic Reynolds number.     

The secondary flow induced around a sphere in an oscillating stream of elastico-viscous liquid

The present paper is devoted to the theoretical study of the secondary flow induced around a sphere in an oscillating stream of an elastico-viscous liquid. The boundary layer equations are derived following Wang's method and solved by the method of successive approximations. The effect of elasticity of the liquid is to produce a reverse flow in the region close to the surface of the sphere and to shift the entire flow pattern towards the main flow. The resistance on the surface of the sphere and the steady secondary inflow increase with the elasticity of the liquid.Nomenclature a radius of the sphere - b ^ik contravariant components of a tensor - e contravariant components of the rate of strain tensor - F() see (47) - G total nondimensional resistance on the surface of the sphere - g _ik covariant components of the metric tensor - f, g, h secondary flow components introduced in (34) - k ₀ measure of relaxation time minus retardation time (elastico-viscous parameter) - K =k ₀ ²/V ₀ ² , nondimensional parameter characterizing the elasticity of the liquid - n measure of the ratio of the boundary layer thickness and the oscillation amplitude - N, T defined in (44) - p arbitrary isotropic pressure - p _ik covariant components of the stress tensor - p ^ik contravariant components of the stress tensor associated with the change of shape of the material - R =V ₀ a/v, the Reynolds number - S =a/V ₀, the Strouhall number - r, , spherical polar coordinates - u, v, w r, , component of velocity - t time - V(, t) potential velocity distribution around the sphere - V ₀ characteristic velocity - u, v, t, y, P nondimensional quantities defined in (15) - reciprocal of s - density - defined in (32) - defined in (42) - ₀ limiting viscosity for very small changes in deformation velocity - complex conjugate of - oscillation frequency - = ₀/, the kinematic coefficient of viscosity - , defined in (52) - (, y) stream function defined in (45) - =(NT/2n)^1/2 y - /t convective time derivative (1) _ik      

Flow reversal of an elastico-viscous liquid between a stationary and a torsionally oscillating disc

The flow of an elastico-viscous liquid contained between two infinite discs, when one is held at rest and the other performs small-amplitude torsional oscillations about their common axis, is considered. The liquid is characterized by equations of state more general than, and containing as special cases, the equations of state used by previous authors who have considered this problem.The phenomenon of flow reversal is examined for large values of the Reynolds number, and the apparently different conclusions of previous authors are explained in terms of their particular choices of material parameters.It is also shown that in general the flow at high frequency is dominated by a particular combination of material parameters.     

Hydromagnetic flow at an oscillating plate

Uniformly valid solutions are obtained for the hydromagnetic flow at a moving plate and at an oscillating plate. In each case, two different representations for the solution are presented. On one representation a half order fractional operator is used, whereas the other representation did not rely on fractional operator. Solutions for special cases of the oscillating plate are calculated for finite times. Furthermore, the effects of the nondimensional numbers M (the magnetic parameter), Re (the suction Reynolds number) on the flow are compared with the existing results and are discussed.     

Convection in an oscillating force field and microgravity

Convective flows in a plane layer of viscous fluid in the presence of an oscillating external force are investigated numerically [1 – 8]. The layer is assumed to be placed in a gravitational field. The cases in which the external field oscillations are generated by rotation about the horizontal axis or by vibration in the longitudinal direction are considered. The Navier-Stokes equations and the Boussinesq approximation are used for describing the fluid motion. The flows developing in the layer in the presence of a transverse temperature gradient are determined, the stability boundaries of these flows are found, and the supercritical motion regimes are studied. These investigations are carried out using the averaging method (in order to find the stability limits for high rotation velocities and vibration frequencies) and the Galerkin method.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–106, September–October, 1994.     

Strain localization in an oscillating Maxwell viscoelastic cylinder

The transient rotation responses of simple, axisymmetric, viscoelastic structures are of interest for interpretation of experiments designed to characterize materials and closed structures such as the brain using magnetic resonance techniques. Here, we studied the response of a Maxwell viscoelastic cylinder to small, sinusoidal displacement of its outer boundary. The transient strain field can be calculated in closed form using any of several conventional approaches. The solution is surprising: the strain field develops a singularity that appears when the wavefront leaves the center of the cylinder, and persists as the wavefront reflects to the outer boundary and back to the center of the cylinder. The singularity is alternately annihilated and re-initiated upon subsequent departures of the wavefront from the center of the cylinder until it disappears in the limit of steady state oscillations. We present the solution for this strain field, characterize the nature of this singularity, and discuss its potential role in the mechanical response and evolved morphology of the brain.     

Interaction of wave disturbances in an oscillating boundary layer

A theoretical analysis is made of the interaction of wave disturbances of small finite amplitude in a boundary layer in the case when the velocity distribution contains a periodic component that oscillates in time in accordance with a harmonic law. It is shown that it is in principle possible for there to be a four-wave synchronous (resonance) interaction in a cubic nonlinearity; equations are obtained for the amplitudes. Calculations made to test the effectiveness of the resonance phenomena have shown that the coupling coefficients are not sufficiently large for the superimposed oscillations to change significantly the nature of the interaction of the waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–158, September–October, 1980.We thank A. G. Volodin for assistance in the calculations.     

Laminar boundary layer on an oscillating wedge

A study is made of the nonstationary laminar boundary layer on a sharp wedge over which a compressible perfect gas flows; the wedge executes slow harmonic oscillations about its front point. It is assumed that the perturbations due to the oscillations are small, and the problem is solved in the linear approximation. It is also assumed that the thickness of the boundary layer is small compared with the thickness of the complete perturbed region. Then in a first approximation the influence of the boundary layer on the exterior inviscid flow can be ignored, and the parameters on the outer boundary of the boundary layer can be taken equal to their values on the body for the case of inviscid flow over the wedge. They are determined from the solution to the inviscid problem that is exact in the framework of the linear formulation. The wall is assumed to be isothermal. The dependence of the viscosity on the temperature is linear. Under these assumptions, the problem of calculating the nonstationary perturbations in the boundary layer on the wedge is a self-similar problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 146–151, July–August, 1980.     

Drop and Bubble Deformation in an Electric Field

A steady problem of drop (bubble) shape in a uniform electric field is considered when the drop and the surrounding medium are immiscible. The electric-charge transport includes both the ohmic current across the interphase boundary and convective transport over the interface. If there is no convective transport, the drop (bubble) may be transformed into either an elongated or a flattened spheroid. Under these conditions, the sign of the deformation remains unchanged for arbitrary values of the problem parameters. Convective charge transport along the surface initiates additional motion in both the drop and the surrounding medium. However, with increase in the convective-transport intensity the deformed drops display different behavior. The compression of a flattened drop slows and, under certain conditions, compression is replaced by extension. However, an elongated spheroid cannot be transformed into a flattened spheroid. The calculations were performed under the assumption that the drop is convex. It was found that, for both an elongated and a flattened drop, the maximum ratio of the major and minor spheroid axes is 2:1. In experiments with oils, the possibility of both a decrease in the drop compression rate and deformation sign reversal was demonstrated.     

Free-molecular gas flow through an oscillating membrane

Free-molecular gas flow through a membrane oscillating in its own plane is investigated. The probability of the passage through the membrane by gas molecules is calculated as a function of dimensionless parameters characterizing the channel geometry, themolecularmass, the gas temperature, and the membrane oscillation frequency and amplitude. It is shown that the membrane permeability for one or another gas can be controlled by means of changing the forced oscillation parameters.     

Fluid excitation of an oscillating circular cylinder in cross-flow

This paper presents an experimental technique developed to identify the fluid excitation force of a circular cylinder during Vortex-Induced Vibrations (VIV). To this end, an actuator is used to provide controlled damping and a Van der Pol model is proposed to describe the fluid excitation force, where the associated parameters are identified from experiments by a least square fitting. The Reynolds number was in the range 1650–4950, and the technique is validated with experimental free vibration data of an elastically supported circular cylinder. Also, comparison with free vibration measurements from other experiments carried out with similar Reynolds numbers is presented.     

Performance of an oscillating subsoiler in breaking a hardpan

A single shank tractor mounted oscillating subsoiler was developed to break hardpan, common in sugarcane (Saccharum officinarum) farms especially after harvest when heavy trucks transport the cut canes from the field to the sugar factory. Field experiments were conducted to determine the optimum combination of performance parameters of the subsoiler. Field tests were conducted at frequencies of oscillation of 3.7, 5.67, 7.85, 9.48 and 11.45 Hz; amplitudes of 18, 21, 23.5, 34 and 36.5 mm; and forward speeds of 1.85, 2.20 and 3.42 km h⁻¹ at moisture contents close to the lower plastic limit of the clay soil. A reduction in draft but an increase in total power requirement was found for oscillating compared to non-oscillating subsoiler. The draft and power ratios were significantly affected by the forward speed, frequency and amplitude. Their combined interaction, expressed in terms of the velocity ratio (the ratio of peak tool velocity to forward speed), however, had the strongest influence. At the same velocity ratio, the draft reduction and power increase were less at higher amplitude of oscillation. For the field conditions tested, the optimum operation for least energy expenditure was obtained at an amplitude of 36.5 mm, frequency of 9.48 Hz and speed of 2.20 km h⁻¹ with a draft ratio of 0.33 and power ratio of only 1.24. It could be concluded that the oscillating subsoiler reduces draft for breaking hardpan, reduces soil compaction and promotes the use of lighter tractors by utilizing tractor power-take-off (p.t.o.) power to achieve higher efficiency of power transmission. ©     

Self-consistent bunches of oscillating heavy particles in an accelerator

The possibility of the existence of self-consistent spheroidal bunches having a constant density which consists of heavy particles or bodies is demonstrated. In a projection onto the transverse plane the particles describe circles or ellipses, while along the spheroid axis the particles oscillate sinusoidally. It is possible for an infinite set of particle distributions to appear with respect to the half-axes of the transverse ellipses and with respect to the amplitudes of the longitudinal oscillations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 140–142, July–August, 1970.