Growth of a new phase in a substance in a metastable state

A model of kinetics of phase transitions in a substance in a metastable state is proposed, where the probability of extensive nucleation owing to homogeneous mechanisms is rather large; the model is an alternative to Kolmogorov’s model. The use of this model is demonstrated to offer analytical solutions that describe both the crystallization processes with similar densities of the liquid and solid phases and, for instance, the kinetics of nucleation and growth of bubbles in surface boiling. Solutions obtained by Kolmogorov’s model and by the present model coincide at the initial stage of the process where the volume fraction of the new phase is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 75–80, March–April, 2007.     

On a Paradox in the Motion of a Rigid Particle along a Wall in a Fluid

The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure.     

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.     

Lateral migration of a capsule in a plane Poiseuille flow in a channel

Three-dimensional numerical simulation is presented on the motion of a deformable capsule undergoing large deformation in a plane Poiseuille flow in a channel at small inertia. The capsule is modeled as a liquid drop surrounded by an elastic membrane which follows neo-Hookean law. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for the deformable interface. The methodology can address large deformation of a capsule over a wide range of capsule-to-medium viscosity ratio. An extensive validation of the methodology is presented on capsule deformation in linear shear flow and compared with the boundary-element/integral simulations. Motion of a capsule in wall-bounded parabolic flow is simulated over an extended period of time to consider both transient and steady-state motion. Lateral migration of the capsule towards the centerline of the channel is observed. Results are presented over a range of capillary number, viscosity ratio, capsule-to-channel size ratio, and lateral location. After an initial transient phase during which the capsule deforms very quickly, the flow of the capsule is observed to be a quasi-steady process irrespective of capillary number (Ca)$(\mathit{Ca})$, capsule-to-channel size ratio (a/H)$(a/H)$, and viscosity ratio (λ)$(\lambda )$. Migration velocity and capsule deformation are observed to increase with increasing Ca$\mathit{Ca}$ and a/H$a/H$, but decrease with increasing λ$\lambda$, and increasing distance from the wall. Numerical results on the capsule migration are compared with the analytical results for liquid drops, and capsules with Hookean membrane which are valid in the limit of small deformation. Unlike the prediction for liquid drops, capsules are observed to migrate toward the centerline for 0.2?λ?5$0.2?\lambda ?5$ range considered here. The migration velocity is observed to depend linearly on (a/H)³$(a/H{)}^3$, in agreement with the small-deformation theory, but non-linearly on Ca$\mathit{Ca}$ and the distance from the wall, in violation of the theory. Using the present numerical results and the analytical results, we present a correlation that can reasonably predict migration velocity of a capsule for moderate values of a/H$a/H$ and Ca$\mathit{Ca}$.     

Transients in a two-phase medium flowing in a pipeline

The paper examines a water hammer in an elastic pipeline through which a liquid containing solid particles flows. The effect of the particle phase on the pressure jump in the liquid-particle mixture is studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 80–86, October, 1999.     

Pressure waves in a separated gas-liquid layer in a horizontal duct with a step

Pressure wave propagation into a separated gas-liquid layer in a horizontal duct with a step is investigated analytically. The linear solution is derived assuming a large density ratio of liquid to gas. The solution can be found first for the gas layer and then for the liquid layer. The linear wave in a liquid layer is valid even for fairly large initial pressure ratios, and clearly exhibits the dispersive characteristics of the pressure wave in a liquid layer. As the initial pressure ratio is increased, the pressure wave in the gas layer becomes a shock wave. Thus, its effect on the wave in a liquid layer can be found analytically by modifying the boundary condition in part. The wave in a liquid layer consists of a main wave, which propagates with the shock speed in gas, and a precursor wave, whose front propagates with the speed of sound in liquid. The precursor wave has an oscillatory structure; its amplitude increases with increasing shock strength and also with liquid layer thickness.     

Motion of a sphere in a vibrating liquid in the presence of a wall

A solution is obtained for the problem of the motion of a sphere in an ideal liquid bounded from outside by a wall which performs specified vibrations far from the sphere. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090, Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 125–132, July–August. 1999.     

Natural convection from a cylinder in a narrow gap and in a porous medium

The problem of natural convection from a horizontal cylinder in a narrow gap and in a porous medium is solved both theoretically and experimentally. An integral method for calculating heat transfer from the cylinder for constant flux on its surface was suggested. Numerical analysis clarified the role of regime and geometrical factors. It is shown that natural convection from a cylinder in a porous medium can be modeled by a Hele Shaw cell. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 140–150. January–February, 1999.     

Eigenoscillations near a plate in a channel

Acoustic eigenoscillations of a gas near a plate in a rectangular channel, i.e., the eigenfrequency of oscillations as a function of the chord length and the position of the plate in the channel, and the form of the eigenfunctions are studied in a two-dimensional formulation. A mathematical model of eigenoscillations near a plate in a channel has been proposed and substantiated, and the dependence of the eigenfrequency of oscillations on the geometric parameters is studied numerically with the use of this model. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 78–90, March–April, 1998.     

Stresses in a plate kept in equilibrium by a pin

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 144–148, January–February, 1990.     

Convection in a Horizontal Layer in a Rotating Heat Field

An asymptotic laminar-convection pattern in a plane horizontal liquid layer with a radially nonuniform temperature gradient on its boundaries is investigated. The problem arises in applications connected with modified Czochralski crystal growth technology using the heat field rotation method. An analytical model of the flow is compared with the results of experiments, specially carried out using model fluids and a technological melt. The conditions of adequacy of the model are analyzed and the restrictions on the parameter values and fluid thermophysical properties that ensure the validity of the model are found. The range of variation of the heat field rotation velocity for which the mixing of the melt in the crucible is maximum is determined.     

Relations between the forces on a body moving in a rarefied gas in a light flux and in a hypersonic newtonian stream

For three-dimensional axisymmetric and two-dimensional bodies we derive relations, valid in an arbitrary coordinate system, between the aerodynamic forces for motion of the body when the locality law is valid (i.e., the momentum flux at the surface of the body depends on the local angle between the velocity and the normal to the surface) and we determine the total forces and moments by integration over that part of the surface of the body facing the flow. We obtain equations defining the change in the lift (and, consequently, the frontal drag and lift-drag ratio), depending on the angle of attack, as a function of the area of projection of the surface of the body on the plane perpendicular to the direction of flight. Particular cases of the relations we obtain are, for example, the Newtonian motion of a body at hypersonic velocities, the motion of a body in a rarefied gas, and the effect of light pressure on a body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 89–95, July–August, 1973.     

Flow of a conductive gas in a circular tube in a strong axiosymmetric magnetic field

The flow of a conductive gas along a channel in an external axiosymmetric magnetic field with a finite value of the magnetogasodynamic parameter N is examined. Numerical flow calculations are performed for a circular tube in such a field. Gas dynamic parameter fields, total pressure losses, and electric current intensities with the presence of transsonic zones and highly compressed regions are determined. Through comparison of the results obtained with linear theory data, the range of applicability of the latter is determined. Of the works dedicated to study of flow in external magnetic fields with N1, we should take note of [1], in which the process of entry of the gas into a transverse magnetic field was examined; [2], which studied one-dimensional transient motion with shock waves; and [3], where mixed flow in a Laval nozzle with an axiosymmetric homogeneous magnetic field was studied. Flow in a circular tube was examined in [4]; but the analysis performed by the characteristic method permitted calculation of only the initial supersonic flow zone. Motion in circular tubes in the presence of an axiosymmetric, magnetic field was studied in the linear formulation in [4, 5].Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–155, September–October, 1972.     

Vibrations of a cylinder in a uniform flow in the presence of a no-slip side-wall

A circular cylinder placed in a uniform flow, and that spans the entire length between two side walls, may experience either parallel or oblique vortex shedding depending on the end conditions. It was shown by Mittal and Sidharth (2014) that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by the cylinder. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. The free vibrations of a circular cylinder, in the presence of a wall, are investigated. For comparison, computations with end walls, where a slip condition on velocity is specified, are also carried out. The Reynolds number, based on the diameter of the cylinder and free-stream speed of the flow, is Re=100. The initial condition for the free vibrations is the fully developed unsteady flow past a stationary cylinder with oblique shedding. It is found that as the amplitude of vibration of the cylinder builds up, the vortices shed from the cylinder align with its axis leading to parallel shedding. The response of the cylinder is associated with two branches: initial and lower. On the lower branch, the response of the cylinder is virtually identical from two- and three-dimensional computations. The flow as well as the response is different on the initial branch and outside the synchronization regime. Forced vibrations confirm the phenomena.     

Transition process in a fluid layer in a rotating paraboloid in response to a sudden change in its angular velocity

The process of establishment of the rigid-body rotation state in a liquid layer in a rotating paraboloid upon a sudden increase in its angular velocity is studied theoretically and experimentally. The theoretical study is performed within the framework of linear shallow-water theory with account for the bottom Ekman friction. Analytical solutions describing the transition process are obtained and the dependence of the establishment time on the liquid depth and the radius of curvature of the paraboloid is investigated. It is shown that the effect of free surface deformation may lead to a significant increase in the establishment time. Good agreement with the results of special laboratory experiments is found.