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.     

Numerical calculation of the motion of a gas from a surface explosion

The motion of a gas by the normal impact of a high-speed body at the interface between a dense half-space and a vacuum is investigated numerically. The motion of the shock wave and the shape and distribution of the parameters of the gas dispersing in the vacuum are obtained. The motion is studied during the formation of a region with high pressure at the boundary with the vacuum of a gas occupying the half-space z > 0. The assumption of cylindrical symmetry relative to the z axis enables this three-dimensional nonsteady-state problem in the general case to be solved as a two-dimensional problem. For the corresponding one-dimensional problem, the numerical solution and, for certain gases also, the analytic solutions are well known and are considered in detail in [1]. As a result of solving the two-dimensional problem, profiles of the gasdynamic quantities are obtained which are similar to the solutions in the one-dimensional case and the result of the solution by a self-similar method. The cup-shaped surface of the shock wave front with a pressure gradient on it “focusses” the dispersing gas so that its velocity component normal to the surface z = 0 is greater by an order of magnitude than the component parallel to the surface of separation of the medium, and only at individual points is their ratio close to 0.4. Therefore, the dispersing gas is formed into the shape of a “jet”, the pressure and density profiles on the axis of which have a shape similar to the one-dimensional problem of a brief shock, but in the plane z = 0 the pressure and density distributions are similar to the distributions of these quantities in the case of a powerful point explosion in an unbounded medium. The initial disturbance in the symmetrical problem being considered may be the result of either the normal impact of the body with a high velocity at the surface of the dense medium, or the consequence of the effect of a giant laser pulse, or some other process when a certain volume is formed with a high pressure at the interface between the dense medium and a vacuum, or with another low-density medium.     

Motions of a top on a smooth plane without separation

The problem on the motion of a heavy top (a dynamically and geometrically symmetric rigid body) without separation on a smooth horizontal plane is considered. In the case of a spherical top surface (the Thomson top), necessary and sufficient conditions on the parameters and the initial positions and velocities of the body under which the motion is all the time without separation are given. These conditions are represented by explicit analytic formulas that can be used in practice. Keywords: Thomson top, smooth surface, separation conditions.     

Oblique impact of an elongated three-dimensional body on a thin liquid layer

The problem of the impact of an elongated solid body with a blant bottom on a thin layer of an ideal incompressible liquid is considered in the case where the horizontal component of the body velocity is much greater than its vertical component. The initial stage of the impact, during which the contact area between the body and the liquid is rapidly expanding, is studied. The loads on the body are determined by strip theory. The method of matched asymptotic expansions is used to determine the position and size of the contact area in each section. The considered problem is coupled: the liquid flow due to the motion of the body and the body motion itself are determined simultaneously. A system of integrodifferential equations was derived and used for both numerical investigation of the body motion under the action of hydrodynamic loads and for determination of the hydrodynamic pressure distribution over the contact area.     

Cavitation deceleration of a circular cylinder in a liquid after impact

The formation of a cavity during vertical impact and subsequent deceleration of a circular cylinder semi-immersed in a liquid is investigated. The problem with unilateral constraints is formulated to determine the initial regions of separation and contact of liquid particles and the perturbations of the inner and outer free boundaries of the liquid at small times. The problem is solved using a direct asymptotic method which is effective at small times. Examples of numerical calculations of the formation of one or two cavities near the boundary of the body are given. It is shown that the acceleration of the cylinder has a significant effect on the liquid flow pattern near the body at small times.     

Unsteady weakly perturbed motion of a body of revolution in a liquid with jet separation

The unsteady weakly perturbed motion of a body in a liquid with jet separation has been investigated on various occasions in the twodimensional formulation [1–3]. The present paper gives a generalization of the formulation of this two-dimensional problem to the threedimensional case of flow past a body of revolution in accordance with Kirchhoff's scheme. A method is proposed for solving the obtained boundary-value problem using a Green's function. This function is constructed in a special system of curvilinear coordinates. To obtain an effective solution, a Laplace transformation is used. Expressions are given for the Laplace transforms of the vectors of the force and torque acting on the body in the unsteady motion.     

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.     

Formation of separation zones in an asymmetric motion of a body in an elastic medium

We obtain an analytical solution of the problem on the motion of a body with wedge-shaped nose in an elastic medium for the case in which a medium separation zone may occur near the nose owing to asymmetry. The character of the dependence of the separation region length on the body velocity, the nose opening angle, the motion asymmetry degree, and the friction coefficient is found. It is shown that if the body moves at a velocity greater than the transverse wave velocity, then there is a limit velocity at which the separation region near the nose of the body disappears.     

单柱单锥型液—液旋流分离管内流场的LDV诊断

应用二维激光多普勒仪（ＬＤＶ）对一种单柱单锥型液－液旋流分离管内流场进行了测量,考察了流量、溢流比、压力比和气芯等参数对流场的影响。测量结果表明：切向速度分布呈典型的Ｒａｎｋｉｎｅ涡结构,沿轴向衰减很少,表明所用锥角是合适的;因该旋流管的水力直径较大,切向速度的总体水平较低,由于对了离特性带来了不利影响。此外,没有观察到切向速度分布的的双峰分布现象。轴向速度的总体水平较低,尤其是在锥形管的上游更为     

HYDRODYNAMIC RESISTANCE EFFECT OF FLUID LAYER BETWEEN TWO IMMERSED APPROACHING PARTICLES

1. Introduction The mechanisms of impact and rebound of solid parti- cles in particulate flow systems are of interest over a wide range of application areas such as fluidized beds, pneu- matic transport, filtration processes, erosion and pollution control of suspended particles. In many cases, the colli- sions of particles against themselves and against walls may affect the properties of the mixture. Efforts have been made to describe the fundamental mechanics of particle collisions. The conta…     

Separation efficiency of liquid–solid undergoing vibration based on breakage of liquid bridge

Vibrating separation is a significant method for liquid–solid separation. A typical example is the vibrating screen to dewater wet granular matter. The properties of granular matter and the vibrating parameters significantly affect the separation efficiency. This study investigates the effect of vibration parameters in separation based on the breakage of large-scale liquid bridge numerically by using a calibrated simulation model. Through analysing the simulation results, the liquid bridge shape and the volume between two sphere particles for various particle sizes and particle distances were studied in the static condition under the effect of gravity. The results show a general reducing trend of liquid bridge volume when the radius ratio of two particles increases, particularly when the ratio increases to 5. Additionally, a set of vibrating motion was applied to the liquid bridge in the simulation model. A group of experiments were also performed to validate the simulation model with vibration. Then, the effect of vibrating peak acceleration, distance between spheres and radius on the separation efficiency which was reflected by the residual water were investigated. It is found that separation efficiency increased obviously with the peak acceleration and the increase slowed down after the peak acceleration over 1 m/s².     

Motion of a slender body made of magnetizable composite in a traveling magnetic field

The motion of a slender body made of magnetizable composite in a channel, along which coils producing a heterogeneous “traveling” magnetic field are mounted, is investigated. The coil axes are vertical and lie in the same plane. A mathematical model of a slender body made of viscoelastic magnetizable material is proposed. The magnetic force is calculated from a formula used in ferrohydrodynamics of magnetic fluids with equilibrium magnetization. The problem of the motion of this body in a channel in a vertical plane under the action of the magnetic field produced in an experimental setup is numerically solved. The dependence of the body velocity on the coil switching frequency is calculated and the effect of different problem parameters on the form of this dependence is studied. The theoretical results are compared with the experimental data.     

Boundary-layer separation on a cooled body and interaction with a hypersonic flow

In previous papers, e.g., [1, 2], boundary-layer separation was investigated by analyzing solutions of the boundary-layer equations with a given external pressure distribution. In general, this kind of solution cannot be continued after the separation point. Study of the asymptotic behavior of solutions of the Navier-Stokes equations [3–5] shows that, in boundarylayer separation in supersonic flow over a smooth surface, the main effect on the flow in the immediate vicinity of the separation point is a large local pressure gradient induced by interaction with the external flow. The solution can be continued beyond the separation point and linked to the solutions in the other regions, located downstream [5]. Similar results for incompressible flow were recently obtained in [6]. We can assume that in general there is always a small region near the separation point in which separation is self-induced, and where the limiting solution of the Navier-Stokes equations does not contain unattainable singular points. However, this limiting slope picture can be more complex and can contain more regions where the behavior of the functions differed from that found in [3–6]. The present paper investigates separation on a body moving at hypersonic speed, where the ratio of the stagnation temperature to the body temperature is large. It is shown that both. for hypersonic and supersonic speeds the flow near the separation point is appreciably affected by the distribution of parameters over the entire unperturbed boundary layer, and not only in a narrow layer near the body, as was true in the flows studied earlier [3–6]. Regions may appear with appreciable transverse pressure drops within the zone occupied by layers of the unperturbed boundary layer. Similarity parameters are given, the boundary problems are formulated, and the results of computer calculation are presented. The concept of subcritical and supercritical boundary layers is refined, and the dependence of pressure coefficients responsible for separation on the temperature factor is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 99–109, November–December 1973.     

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.     

Special characteristics of the breakup of liquid drops with a high gas pressure

In a majority of power plants, the conversion of a liquid fuel into combustion products takes place at high pressure and with a high velocity of the motion of the gas. It is natural that in the choice of the working scheme of the process account must be taken of the effect of possible changes in the characteristics of the atomization process of a liquid fuel, connected with a change in the density of the gas. Of particular importance is the effect of perturbations of the pressure and the velocity on the behavior of liquid drops in a high-density gas flow. The number of communications in which such questions are discussed is very limited, since an overwhelming number of experiments were made at atmospheric pressure [1–7]. Only articles [8, 9] give qualitative concepts with respect to the effect of perturbations of the pressure on the breakup of drops with a gas pressure up to 30 atm. From the information given in [8, 9] it is difficult to form a judgment with respect to the change in the critical conditions and the time parameters of the process of the breakup of drops with a rise in the initial pressure (density) of the gas.     

Attenuation of forced weak plane pressure waves in a gas with radiative heat transfer

This paper considers the effect of radiative heat transfer on the propagation of forced plane harmonic pressure waves of small amplitude in an infinite emitting-absorbing inviscid nonconducting gas. The radiative pressure and radiative energy are neglected. The purpose of this paper is: a) to construct a theory based on the exact directional distribution of the total (frequency-integrated) specific intensity and to use this theory to calculate the parameters of the wave motion, b) to compare the exact theory with results obtained on the basis of the direction-averaged equation of radiative transfer [1] so as to estimate the errors introduced by various directional approximations and to demonstrate the importance of the anisotropy of radiation in radiation gasdynamics.In the linear theories of Stokes, Rayleigh, Kirchhoff, and Langevin the problem of wave attenuation is separated into special cases, in each of which only one single process is considered. This separation is admissible when to the first approximation the effects of the different dissipation mechanisms (viscosity, thermal conductivity, radiation, etc.) are additive. When only one factor is considered the problem becomes much simpler and the results are more amenable to physical interpretation, and these results can then be used in the solution of the complete problem.     

Problems of Hydrodynamics for a Triaxial Ellipsoid

Problems of motion of a triaxial ellipsoid in an ideal liquid and in a viscous liquid in the Stokes approximation and also equilibrium shapes of the rotating gravitating liquid mass are considered. Solutions of these problems expressed via four quadratures depending on four parameters are significantly simplified because they are expressed via the only function of two arguments. The efficiency of the proposed approach is demonstrated by means of analyzing the velocity and pressure fields in an ideal liquid, calculating the added mass of the ellipsoid, determining the viscous friction, and studying the equilibrium shapes and stability of the rotating gravitating capillary liquid. The pressure on the triaxial ellipsoid surface is expressed via the projection of the normal to the impinging flow velocity. The shape of an ellipsoid that ensures the minimum viscous drag at a constant volume is determined analytically. A simple equation in elementary functions is derived for determining the boundary of the domains of the secular stability of the Maclaurin ellipsoids. An approximate solution of the problem of equilibrium and stability of a rotating droplet is presented in elementary functions. A bifurcation point with non-axisymmetric equilibrium shapes branching from this point is found.     

Laminar boundary layer on the moving surface of a rankine oval

A numerical investigation has been made of the laminar boundary layer that arises on the moving surface of a cylindrical body (Rankine oval with relative elongation 4) that moves with constant velocity in an incompressible fluid. The distributions of the frictional stress on the surface of the cylinder for different velocities of the wall motion are found. Numerical integration was employed to determine the work needed to overcome the frictional drag, the pressure, and also the work expended on the motion of the moving surface of the body in the case of constant velocity. In the presence of a separation region the drag forces are calculated under the assumption that in the separation region the pressure and the frictional stress on the wall are constant and equal to the corresponding values at the singular point of the solution of the boundary layer equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 3, pp. 171–174, May–June, 1984.I thank G. G. Chernyi for constant interest in the work and discussing the results.     

Impact of a long thin body on a cylindrical cavity in liquid: A plane problem

An approach is developed to the investigation of the shock interaction between a long thin cylindrical body and a cylindrical cavity in an infinite compressible perfect liquid. This process accompanies the supercavitation of the body. Three typical cases of cross-sectional dimensions of the body and the cavity are examined. For each case, a mixed nonstationary boundary-value problem with an unknown moving boundary is formulated. The unknown quantities are expanded into Fourier series. An auxiliary problem is solved using the Laplace transform to establish the relationship between the pressure and the velocity on the cavity surface. As a result, the problem is reduced to an infinite system of Volterra equations of the second kind solved simultaneously with the equation of transverse motion and the equation of the contact boundary. An asymptotic solution valid at the initial stage of interaction is obtained for all the three cases, and a numerical solution is found for the most typical case __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 32–53, June 2006.