Properties of a solution to a nonstationary flow of a viscous weakly compressible gas

We study the dependence of integral norms of an exact solution to a nonstationary flow of a viscous weakly compressible gas on a parameter characterizing the compressibility and viscosity in the case of two spatial variables.     

Non-isothermal,compressible gas flow for the simulation of an enhanced gas recovery application

In this work, we present a framework for numerical modeling of CO₂ injection into porous media for enhanced gas recovery (EGR) from depleted reservoirs. Physically, we have to deal with non-isothermal, compressible gas flows resulting in a system of coupled non-linear PDEs. We describe the mathematical framework for the underlying balance equations as well as the equations of state for mixing gases. We use an object-oriented finite element method implemented in C++. The numerical model has been tested against an analytical solution for a simplified problem and then applied to CO₂ injection into a real reservoir. Numerical modeling allows to investigate physical phenomena and to predict reservoir pressures as well as temperatures depending on injection scenarios and is therefore a useful tool for applied numerical analysis.     

Formulation of the problem of the flutter of a shell of revolution and a shallow shell in a high-velocity supersonic gas flow

Aero-elastic vibration is investigated in the case of a shallow shell of revolution or a cylindrical panel, which respectively occupy a part of a thin cylindrical body or a thin profile, in a high-velocity supersonic gas flow at zero angle of attack. Particular attention is paid to finding the pressure interaction and this problem is solved within the framework of the law of plane sections in boundary-layer theory. An expression is obtained which refines and supplements the well-known formula of “piston” theory. A linearized formulation of the problem of the panel flutter of a shallow shell is presented. Using the example of a plate located on one of the sides of a wedge, it is shown that the formula of “piston” theory is complemented with a term which has the meaning of a compressive force in the plane of the plate. It is shown that, when account is taken of this term, there is a reduction in the critical flow velocity.     

Forced vibrations of a shell immersed in a viscous compressible fluid

Institute for Mechanics Problems, Academy of Sciences of the USSR. Moscow Physico-Technological Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 4, pp. 93–95, October–December, 1991.     

Interstructural filling and its effect on the properties of polymers

The existence of interstructural filling is demonstrated on the basis of an analysis of the author's own data and the results of others. An attempt is made to use this concept to explain the specific behavior of the physicomechanical properties of the polymer in the filled system formed by introducing small amounts of highly dispersed solids into a polymer matrix. The theory also provides a basis for an explanation of certain aspects of the enhanced stability of the properties in question under various conditions.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 1, pp. 162–166, January–February, 1976.     

CAUCHY PROBLEM FOR LINEARIZED SYSTEM OF TWO-DIMENSIONAL ISENTROPIC FLOW WITH AXISYMMETRICAL INITIAL DATA IN GAS DYNAMICS

§1IntroductionIn the present paper,we are interested in solving the Cauchy problem for linearizedsystem of two-dimensional isentropic flow with initial data in gas dynamicsρt+ρ0xu+yv=0,ut+p′(ρρ00)xρ=0,vt+p′(ρ0ρ0)yρ=0,(1.1)t=0:(ρ,u,v)=(ρ0(r),u0(r),v0(r)),(1.2)whereρis the density,(u,v)is the velocity,ρ0is a positive constant,p=p(ρ)is theequation of state satisfying p′(ρ0)>0,(r,θ)is the polar coordinate such thatx=rcosθ,y=rsinθ,0≤r<+∞,0≤θ≤2π…     

The influence of anisotropy on the stress concentration near a hole in a conical shell

On the basis of the variational method we discuss an approach to the computation of the stress-strain state of a conical shell made of a composite material and weakened by a hole. For a glass-plastic shell with a round unreinforced hole we study the influence of the variation of an interlayer shear and orthotropy on the stress concentration. Two tables. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 63–67, 1991.     

The large deformation of nonlinearly elastic rings in a two-dimensional compressible flow

The nonlinear nonlocal system of the equilibrium equations ofan elastic ring under the action of an external two-dimensionaluniformly subsonic potential barotropic steady-state gas flowis considered. The configurations of the elastic ring are identifiedby a pair of functions (, ). The simple curve represents theshape of the ring and the real-valued function identifies theorientation of the material sections of the ring. The pressurefield on the ring depends nonlocally on , and on two parametersU and P which represent the pressure and the velocity at infinity.The system is shown to be equivalent to a fixed-point problem,which is then treated with continuation methods. It is shownthat the solution branch ensuing from certain equilibrium states((₀, ₀), 0, P₀) in the solution-parameter space of ((₀, ₀),0, P₀) either approaches the boundary of the admissible ((,), U,p)'s in a well-defined sense, or is unbounded, or is homotopicallynontrivial in the sense that there exists a continuous map from the branch to a two-dimensional sphere which is not homotopicin the sphere to a constant, while restricted to the branchminus ((₀, ₀), 0, P₀) is homotopic to a constant in the sphere.Furthermore, by fixing the pressure parameter at P₀ and by consideringthe one-parameter problem in ((, ), U), the following holds.Every hyperplane in the solution-parameter space of the ((,), U)'s which contains the equilibrium state ((₀, ₀), 0) anddoes not include a welldetermined one-dimensional subspace intersectsthe solution branch above at a point different from ((₀, ₀),0).     

Averaged systems of equations of the theory of elasticity in a medium with weakly compressible inclusions

Translated from Matematicheskie Zametki, Vol. 51, No. 1, pp. 126–133, January, 1992.     

Effect of steady-state flow of a polyisobutylene solution on its dynamic characteristics measured in the direction of flow

The effect of steady-state flow on the linear dynamic characteristics of a 10% solution of polyisobutylene in cetane, measured in the direction of flow, is investigated. The material characteristics in steady-state flow quantitatively describe the dynamic viscosity and elasticity at deformation frequencies small as compared with the steady-state shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 913–919, September–October, 1970.     

Stability of a cylindrical shell in a stratified flow

Analysis of the Kelvin stability of a horizontal plane flow of two fluid layers of different densities and one moving relative to the other is extended to the case of longitudinal coaxial flow of a two-layered fluid within a circular cylindrical shell. It is shown that the loss of stability of the whole system sets in for low velocities of the layer motion, one relative to the other. A comparison is made with classical flutter for which the flow is not stratified.     

Interaction of infinite thin elastic cylindrical shell and pulsating spherical inclusion in potential subsonic flow of ideal compressible liquid

In the present paper a method is proposed to investigate behaviour of the axis symmetric system consisting of an infinite thin elastic cylindrical shell, filled by potential flow of ideal compressible liquid and containing pulsating spherical inclusion. This coupled problem is considered in the framework of classical mechanics models: linear potential flow theory and thin elastic shells theory based on the Kirchhoff - Love hypotheses. The approach suggested consists in possibility of rewriting general solution of the corresponding mathematical physics equations from one to the other coordinate system. It enables to satisfy boundary conditions on both the spherical and the cylindrical surfaces and to get an exact analytical solution (as a Fourier series) of the coupled interaction problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of secondary flow on an infinite yawed cylinder in a compressible stream

In this paper a study of the secondary flow on an infinite yawed cylinder in a compressible stream is made at stagnation for unit Prandtl number and for a given Mach number. The secondary flow profiles are calculated for different edge inclination angles. The chordwise and spanwise velocity profiles given by Crabtree¹ are used here in the calculation. It is found that the secondary flow profiles are the same for complementary edge inclination angles and they are maximum for the edge inclination angle of 45°. A comparison with the incompressible flow profiles² is made. It is found that the magnitude of the secondary flow profiles in a compressible stream is less than that in an incompressible stream for the same edge inclination angle.     

The influence of wall properties on the MHD peristaltic flow of a Maxwell fluid with heat and mass transfer

This article describes the effects of heat and mass transfer on the magnetohydrodynamic (MHD) peristaltic flow in a planar channel with compliant walls. An incompressible Maxwell fluid occupies a porous space. The mathematical formulation is based upon the modified Darcy’s law. The analytic treatment of the solution is given by choosing a small wave number. The expressions of stream function, temperature distribution, concentration field and heat coefficient are constructed. The variations of several interesting parameters are discussed by sketching plots.     

Weak oscillations of a gas bubble in a spherical volume of compressible liquid

The following spherically symmetric problem is considered: a single gas bubble at the centre of a spherical flask filled with a compressible liquid is oscillating in response to forced radial excitation of the flask walls. In the long-wave approximation at low Mach numbers, one obtains a system of differential-difference equations generalizing the Rayleigh-Lamb-Plesseth equation. This system takes into account the compressibility of the liquid and is suitable for describing both free and forced oscillations of the bubble. It includes an ordinary differential equation analogous to the Herring-Flinn-Gilmore equation describing the evolution of the bubble radius, and a delay equation relating the pressure at the flask walls to the variation of the bubble radius. The solutions of this system of differential-difference equations are analysed in the linear approximation and numerical analysis is used to study various modes of weak but non-linear oscillations of the bubble, for different laws governing the variation of the pressure or velocity of the liquid at the flask wall. These solutions are compared with numerical solutions of the complete system of partial differential equations for the radial motion of the compressible liquid around the bubble.     

Existence of shocklets in a two-dimensional supersonic mixing layer and its influence on the flow structure

The spatial evolution of a T-S wave and its subharmonic wave, introduced at the inlet in a 2-D supersonic mixing layer, was investigated by using DNS. The relationship between the amplitude of the disturbance wave and the strength of the shocklet caused by the disturbance was investigated. We analyzed the shape of the disturbance velocity profile on both sides of the shocklet, and found that the existence of shocklet affected appreciably the disturbance velocity. The effects on the high speed side and low speed side of the mixing layer were found to be different