Numerical modeling of the process of emplying a tank with a cryogenic liquid

Results of calculation of temperature and velocity fields in a cylindrical vessel with a cryogenic liquid (liquid hydrogen) upon its emptying are discussed. A problem is formulated for a viscous incompressible fluid at thermal boundary conditions of the first kind. Streamlines and isotherms for a variable fluid column are presented. Solutions are obtained for Rayleigh Ra = 10 ⁷ … 10 ¹⁰ and Reynolds Re = 10 ³ … 10 ⁴ numbers. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 409–412, May–June, 1997.     

On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction

Partitioned Newton type solution strategies for the strongly coupled system of equations arising in the computational modelling of fluid–solid interaction require the evaluation of various coupling terms. An essential part of all ALE type solution strategies is the fluid mesh motion. In this paper, we investigate the effect of the terms which couple the fluid flow with the fluid mesh motion on the convergence behaviour of the overall solution procedure. We show that the computational efficiency of the simulation of many fluid–solid interaction processes, including fluid flow through flexible pipes, can be increased significantly if some of these coupling terms are calculated exactly.     

Mechanism of initiation of acoustic emission in crystallization and melting of a substance. II

In[Inzh.-Fiz. Zh.,73,No. 5, 1064–1072 (2000)], the authors investigated one of the possible mechanisms of initiation of the acoustic effect of crystallization (melting) of substances, which was based on the assumption of a stepwise character of motion of the crystal-melt interface. In the present work, consideration is given to another mechanism of initiation of the acoustic effect of crystallization, which is based on the concept of possible enhancement of waves propagating in the liquid and in the crystal during the motion of their interface. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 1073–1079, September–October, 2000.     

The evolution of homogeneous turbulence in a density-stratified medium. 3. Analysis of the near region

Development of a turbulent perturbation in a homogeneous flow moving within a medium that is linearly density-stratified across the direction of flow motion is described. The initial region of the evolution of turbulence with a large turbulent Reynolds numberR _λ is considered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 393–403, May–June, 1997.     

Synthesis, Ion Mobility, and Superionic Conductivity of (1 ? x)PbF2 ? xMFn(M = Li, Na, K, Rb, Cs, Zr) Solid Solutions

Ionic motion and conduction in (1 − x)PbF₂ ⋅ xZrF4 and (1 − x)PbF₂ ⋅ xMF (M = alkali-metal cation) solid solutions are studied by ¹⁹F and ²⁰⁷Pb NMR and impedance spectroscopy. The factors determining ionic motion in the solid solutions and their structure and energetics in the range 170–550 K are analyzed. The ionic conductivity of (1 − x)PbF₂ ⋅ xZrF₄ with x ≤ 0.4 and 0.93PbF₂ ⋅ 0.07MF is shown to be 10⁻⁴ to 10⁻² S/cm at temperatures above 425 K, which places these materials among superionics. __________ Translated from Neorganicheskie Materialy, Vol. 41, No. 11, 2005, pp. 1388–1396. Original Russian Text Copyright ? 2005 by Kavun, Slobodyuk, Tararako, Mikhteeva, Goncharuk, Uvarov, Sergienko.     

Long-wavelength stability of an unsupported multilayer liquid film falling under gravity

The long-wavelength stability of an unsupported multilayer liquid film falling under the effects of gravity and surface tension is investigated. By considering the Navier–Stokes equations for two fluid layers in the high-Reynolds-number and small-aspect-ratio limits the steady-state solutions are obtained. The stability criterion found by Lin (J Fluid Mech 104:111–118, 1981) for a one-layer fluid curtain is generalised to the two-layer case and the criterion for an n-layer curtain is established.     

Corrosion behavior in SBF for titania coatings on Mg–Ca alloy

TiO₂ coating was obtained by sol–gel method to improve the corrosion resistance of Mg–Ca alloy in human body environment. The corrosion behavior of Mg–1.0 Ca alloy with TiO₂ coating was investigated by electrochemical tests and immersion tests in simulated body fluid (SBF). Bare Mg–1.0 Ca alloy suffered serious attack after immersed in simulated body fluid only for 48 h. While for the Mg–1.0 Ca alloy with TiO₂ coating, the surface almost maintained intact with only several collapses after immersed in SBF for 168 h. The electrochemical test results showed that the free corrosion current (i _corr) of Mg–1.0 Ca alloy substrate was 3.3275e−2A/cm², while the i _corr of TiO₂ coating was only 1.58549e−5A/cm². Therefore, TiO₂ coating significantly improved the corrosion resistance of Mg–1.0 Ca alloy in SBF. This enhances the potential of Mg–Ca alloy used as biodegradable orthopedic material.     

Study of forced convection in the presence of a liquid-porous-medium interface

Exact solutions of the problem of forced convection of an incompressible fluid (gas) are obtained for a number of geometries with the presence of an interface between an "ideal" fluid and a saturated porous medium. A generalization of the Darcy law allowing for viscous effects that are substantial at the boundaries of a porous body is used to model flow in a porous layer. The flow velocity as a function of the Darcy number is studied. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 895–901, November–December, 1997.     

The Effect of Axial Concentration Gradient on Electrophoretic Motion of a Charged Spherical Particle in a Nanopore

The electrophoretic motion of a charged spherical nanoparticle along the axis of a nanopore connecting two fluid reservoirs, subjected to an axial electric field and electrolyte concentration gradient, has been investigated using a continuum model. The model consists of the Poisson and Nernst–Planck equations for the electric potential and ionic concentrations and the Stokes equations for the hydrodynamic field with zero gravity. In addition to the electrophoresis generated by the externally imposed electric field, the particle also experiences diffusiophoresis arising from the externally imposed concentration gradient. The effects of the diffusiophoresis on the axial electrophoretic motion are examined with changes in the ratio of the particle size to the thickness of the electric double layer (EDL), and the imposed concentration gradient. Since the EDL thickness, the particle size, and the nanopore size are of the same order of magnitude, the diffusiophoresis is dominated by the induced electrophoresis driven by the generated electric field arising from the double-layer polarization (DLP). For a relatively small κa _p , the ratio of the particle size to the EDL thickness, the diffusiophoresis is dominated by the induced electrophoresis from the type II DLP, which propels the particle toward regions with lower salt concentration. Depending on the magnitude and direction of the externally imposed concentration gradient, the electrophoretic motion can be accelerated, decelerated, and even reversed by the diffusiophoresis.     

Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations–of–motion approach for time–dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known “correlated” random–phase approximation (CRPA), our approach has the following properties: (i) The CRPA is reproduced when pair fluctuations are neglected. (ii) The first two energy–weighted sumrules are fulfilled implying a correct static structure. (iii) No ad–hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the zero sound mode in ³He. (iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.     

Resistance reduction and stability improvement for helicopter-shipped loads when a leading separation zone is organized

Based on flight tests in shipment by helicopters and numerical modeling of flow along parallelepiped-like loads the authors analyze the resistance reduction and stability improvement for the motion of a blunt body with vertical stabilizers when a leading separation zone is organized. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 990–995, November–December, 1997.     

Forced oscillations of three-layered rod with a liquid interlayer

The problem of damping of three-layered rod oscillations by a in compressible Newtonian fluid which forms an interlayer between two ideally rectangular rods is considered Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 493–499 May–June, 1997.     

Oscillating two-phase flow in a prestressed thick elastic tube

Summary The pulsating flow of a fluid with dusty particles in a prestressed thick walled elastic tube has been studied. The tube, subjected to a static inner pressure P_i and an axial stretch λ, is taken to be an incompressible, isotropic, elastic material. The fluid with particles is treated as incompressible Newtonian. Employing the theory of small deformation superimposed on large initial deformations, for an axially symmetric perturbed motion the governing equations are obtained in cylindrical polar coordinates. The analytical solutions of the equations of motion for the dust and the fluid have been obtained. Because of the variable character of the coefficients of the resulting equations for the solid body they are solved numerically. The dispersion relation is obtained as a function of the stretch, the thickness ratio and the parameters for dusty particles.     

Mathematical simulation of the azimuthal-radial distribution of temperature in a well in the presence of heat sources

The results of theoretical investigations of radial and azimuthal distributions of temperature in a well-rock system in the presence of heat sources are presented. The problem considered is connected with determination of the intervals of fluid motion outside the column by thermal methods. It is shown that in the case of long existence of the channel of fluid overflow outside the column, useful information can be obtained by creating a “contrast” temperature, for example, by heating the fluid inside the casing and subsequently measuring the azimuthal distribution of temperature in the process of its recovery on disconnection of a heater. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 5, pp. 80–82, September–October, 2006.     

Oscillations of a rotary fluid flowing out of a closed vessel

Consideration is given to the problem of the proper motion of a rotary fluid that fills the entire cylindrical tank in the presence of outflow through a rigid bottom. The problem is solved in a quasistationary formulation within the framework of the ideal-fluid model with allowance for hydraulic losses in the flow of the fluid through the bottom of the vessel. The spectrum of eigenvalues is investigated and the characteristics of wave motions of the fluid are revealed; the results of calculating the wave numbers and the complex attenuation factor are given. Translated from Inzhenerno Fizicheskii Zhurnal, Vol. 73, No. 1, pp. 165–173, January–February, 2000.     

Dynamics of Drop Coalescence on a Surface: The Role of Initial Conditions and Surface Properties

An investigation of the coalescence of two water drops on a surface is presented and compared with drop spreading. The associated capillary numbers are very low (< 10⁻⁵). The drops relax exponentially towards equilibrium. The typical relaxation time t_c decreases with contact angle. t_c is proportional to the drop size R, thus defining a characteristic velocity U^* = R/t_c. The corresponding U* values are smaller by many orders of magnitude than the bulk hydrodynamic velocity (U = σ /η, with σ the gas–liquid surface tension and η the viscosity). The dynamics of receding (coalescence) and spreading motion is found to be of the same order when coalescence or spreading is induced by a syringe. The dynamics of coalescence induced with the syringe deposition is systematically faster by an order of magnitude than condensation-induced coalescence. This disparity is explained by the coupling of the contact line motion with the oscillation of the drop observed for syringe deposition but absent for condensation-induced coalescence. Paper presented at the Fifteenth Symposium on Thermophysical Properties, June 22–27, 2003, Boulder, Colorado, U.S.A.     

Power-series solution for the two-dimensional inviscid flow with a vortex and multiple cylinders

The problem of a point vortex and N fixed cylinders in a two-dimensional inviscid fluid is studied and an analytical-numerical solution in the form of an infinite power series for the velocity field is obtained using complex analysis. The velocity distribution for the case of two cylinders is compared with the existing results of the problem of a vortex in an annular region which is conformally mapped onto the exterior of two cylinders. Limiting cases of N cylinders and the vortex, being far away from each other are studied. In these cases, “the dipole approximation” or “the point-island approximation” is derived, and its region of validity is established by numerical tests. The velocity distribution for a geometry of four cylinders placed at the vertices of a square and a vortex is presented. The problem of vortex motion with N cylinders addressed in the paper attracted attention recently owing to its importance in many applications. However, existing solutions using Abelian function theory are sophisticated and the theory is not one of the standard techniques used by applied mathematicians and engineers. Moreover, in the N ≥ 3 cylinder problem, the infinite product involved in the presentation of the Schottky–Klein prime function must also be truncated. So, the approach used in the paper is simple and an alternative to existing methods. This is the main motivation for this study.     

Motion and force equilibrium of a local process (a soliton) in a continuous fluid medium

Consideration is given to the motion and force equilibrium of a local process (a soliton) in a continuous fluid medium. Integral characteristics of a soliton are introduced. An equation of motion, a global equation of force equilibrium, and equations of force equilibrium along individual axes are obtained that include the integral characteristics of a soliton. These equations are shown to permit direct evaluation of the interrelationship of the most important parameters of a local process based on generalized information on its structure. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 358–369, March–April, 2000.     

Broadening of the particle resonance drift trajectory and tritium injection into a fusion reactor with an I=3 helical winding

Two fusion reactor problems, removal of helium ash and fuel (tritium) injection, can be solved using the concept of “drift island motion.” The motion of a drift island is an indicator of the broadening of the resonant trajectory of a charged particle guiding center. This trajectory broadening occurs if two conditions are satisfied. First, the drift pitch angle of the particle is equal to the resonance values i*=n/m, where n and m are the “wave numbers” of the perturbing magnetic field. Second, the drift pitch angle i*=n/m “moves” over the plasma cross section as the particle moves. This displacement is caused by a slow change in the helical magnetic field with time as the particle moves. It is shown that this effect may occur in a fusion reactor with an l=3 helical winding and may be used for tritium ion injection. Pis’ma Zh. Tekh. Fiz. 25, 5–13 (January 26, 1999)     

Modelling with viscous and viscoplastic materials under combining and separating flow configurations

Combining and separating incompressible flow of Newtonian and inelastic Herschel–Bulkley fluids is studied numerically employing a semi-implicit Taylor–Galerkin pressure-correction algorithm, where steady solutions are obtained through a transient finite element procedure. The influence of inertia and fluid rheology is analysed on flow patterns, velocity fields and pressure drops for various flow configurations, with fixed geometric gap width that stimulates the merging and splitting in the flow. For Newtonian fluids and at larger levels of inertia, the appearance of vortices was observed, with an increase in velocity differences and pressure drops across the channel. In this case, the numerical procedure was verified with good agreement against previous numerical and experimental observations. To extend the consideration to non-Newtonian inelastic materials, the material rheological characteristics were approximated with the use of the Herschel–Bulkley fluid model, incorporating the Ostwald–de Waele power-law model and viscoplastic yield stress. Findings for unyielded power-law fluids reveal slight increase in the size of the vortices as power index (m) was decreased. Variation of the consistency index (k) shows strong influence on the streamline patterns with a rapid increase in the vortex formation as k was decreased. For Bingham model solutions, devoid of shear-thinning and increasing yield stress, a higher value of Reynolds number is required for equivalent levels of vortex formation; also one observes the appearance of yielded and unyielded regions. Under Herschel–Bulkley modelling, there was little change noted in the kinematics, but some was apparent in rheological response. Once more, observations reveal the tendency to eliminate vortices at larger yield stress levels, with the appearance of unyielded regions.