Propagation of cylindrical blast waves in a multicomponent,viscoplastic medium having variable viscosity

Institute of Fluid Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 10, pp. 29–35, October, 1992.     

On transient flow of a reactive variable viscosity third-grade fluid through a cylindrical pipe with convective cooling

This paper studies the transient flow of a reactive variable viscosity third grade fluid in a cylindrical pipe with convective heat exchange at the pipe surface. It is assumed that exothermic chemical reactions take place in the flow system. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using an unconditionally stable and convergent semi-implicit finite difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system.     

Shrink fit of an elastic layer having a cylindrical cavity

Summary This paper deals with the problem of determining the stress distribution in an elastic layer with a cylindrical cavity when the mixed boundary conditions are prescribed on the curved surface of the cylinder. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. These dual integral equations are subsequently reduced to a singular integral equation. The solution of this integral equation is obtained numerically, and the quantities of physical interest are calculated.     

The viscosity of a polar fluid with suspensions

Summary The apparent viscosity of a polar fluid with suspensions of rigid spherical particles undergoing a prescribed bulk motion is calculated. It is shown that the increased rate of dissipation in a polar fluid with suspensions is greater than that of a Newtonian fluid. It is found that the relationship between the viscosity and the concentration has a same form with that of a Newtonian fluid suspension of which ambient fluid has a shear viscosity multiplied by a factor which is greater than unity.

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Zusammenfassung Die scheinbare Viskosität einer polaren Flüssigkeit mit suspendierten steifen, kugelförmigen Teilchen, die eine vorgeschriebene Bewegung ausführen, wird berechnet. Es wird gezeigt, daß die anwachsende Dissipationsgeschwindigkeit in einer polaren Flüssigkeit mit suspendierten Teilchen größer ist als die einerNewtonschen Flüssigkeit. Es zeigt sich, daß die Beziehung zwischen der Viskosität und der Konzentration die gleiche Form hat wie die einerNewtonschen Flüssigkeitssuspension, bei der die umgebende Flüssigkeit eine Scherviskosität besitzt, multipliziert mit einem Faktor größer als 1.

     

Convection within a cylindrical cell containing a freezing fluid

The effects of convection upon freezing/melting processes within a cylindrical cell are studied numerically over a wide range of the Rayleigh number (Ra). Establishment of the steady state and the heat transfer across the cell are analyzed. A self-sustained oscillatory process characterized by the emergence and decay of vortices near the interface of the frozen and thawed zones is identified. At large Rayleigh numbers the solution is unstable.Tyumen'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 125–129, September–October, 1995.     

Sloshing behavior of a magnetic fluid in a cylindrical container

 Sloshing of a magnetic fluid in a laterally vibrated cylindrical container subject to a non-uniform vertical magnetic field was examined. Internal velocity profiles were measured using ultrasound Doppler velocimetry. The effect of the magnetic field on the resonant frequency of the fluid–container system was examined and the results were compared with theoretical results. The second and third peaks of the power spectra of velocity shifted to lower frequencies as the magnetic field was increased. It was observed that these derived frequency peaks were connected with swirling in the cylindrical container. Received: 9 May 2000 / Accepted: 29 May 2001 Published online: 29 November 2001     

Motion of a flexible finite-length filament in a flow of a viscous fluid

The two-dimensional problem of the configuration of a flexible filament of finite length in a deformable viscous fluid is solved. The flexuural stresses in the filament and the inertial and gravitational forces are not taken into account. The equilibrium equations are obtained. The friction force that acts on the filament surface from the side of the viscous fluid is proportional to the flow rate. The specific features of the evolution of a bent filament under the conditions of pure and simple shear of a fluid are studied numerically. Analytical solutions are obtained for the evolution of a rectilinear filament; in particular, the stretching force in the filament is found. For the indicated types of flow, the stability of a rectilinear filament against small perturbations is investigated. Volzhskii Polytechnical Institute at the Volgograd State Technical University, Volgograd 404121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 144–153, March–April, 2000.     

Formation of differential rotation in a cylindrical fluid layer

The formation of differential rotation in a rotating cylindrical layer heated locally is investigated numerically. In the simulations performed, geometric parameters (the layer height and radius and the heating area), the kinematic viscosity, the heat flux, and the angular velocity of the cylinder were varied. Integral characteristics of differential rotation are obtained. The dependence of the relative angular momentum of the layer on various parameters is investigated.     

Effects of temperature-dependent viscosity variation on entropy generation,heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].     

A model for the bulk viscosity of a non-Newtonian fluid

A model for the bulk viscosity of a non-Newtonian fluid is presented. An elementary two-phase cell containing an incompressible non-Newtonian fluid and a gas bubble is compared with a one-phase cell consisting of a corresponding compressible non-Newtonian fluid. The rates of work of both cells are set equal to one another. The deformation histories of both cells are represented by the density history. From the extra stress an expression for the bulk viscosity of the compressible non-Newtonian fluid is derived. The material data are expressed in terms of the known properties of the two-phase flow.     

Collapse of a cylindrical cavity in a fluid layer under impact

The case of impact on a thin annular fluid layer with a gas-filled cavity is considered. The solution of the problem reduces to integrating a system of two first-order ordinary differential equations. The equations are analyzed qualitatively, and some exact solutions are found. Cases are noted of pulsation of the cavity, and the influence of counter-pressure and viscosity is investigated. The experimental results obtained are in agreement with the numerical computations carried out herein.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 98–106, November–December, 1970.The authors are grateful to A. M. Kogan and L. V. Mostovaya for performing the computations.     

Quasisteady pulsed flow of a thixotropic fluid in a cylindrical pipe

An approximate solution is obtained to the problem of inertialess periodic flow of fluid with a variable structure in a pipe of circular cross section. A study is made of the effect of the parameters which define the kinetics of the variations in the structure and the fluctuations in the pressure gradient on the effective viscosity and the other mean hydrodynamic characteristics. A comparison is made between the solutions to the problems of the flow of a thixotropic and a nonlinearly viscous fluid. The results are discussed in connection with their application to the circulation of the blood.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–9, January–February, 1987.