Axial-radial acoustic eigenoscillations near a thin-walled obstacle in a cylindrical channel with stepped narrowings

The dependencies are investigated of eigenfrequencies and eigenfunctions of acoustic axial-radial oscillations near a thin-walled obstacle in a channel with stepped narrowings on the geometric parameters of the oscillation region. It is discovered that, near the thin-walled cylindrical obstacles in an inhomogeneous cylindrical channel with the stepped two-sided cylindrical narrowing, the number of eigenfrequencies of the acoustic axial-radial oscillations of a gas may increase. The dependencies are obtained of eigenfrequencies on the geometric parameters of obstacles and the inhomogeneities of the channel.     

Roll waves in an annular channel

The goal of this study is to analytically construct periodic wind perturbations in an annular channel that are numerically produced by a regularized model. R. Dressler’s technique in the shallow water approximation is used to prove the nonexistence of smooth periodic solutions, and discontinuous solutions related to roll waves on inclined surfaces are constructed. The constraints on the accelerating and dissipating forces are obtained under which periodic solutions can exist. A numerical analysis of the problem is carried out, and a qualitative comparison of the numerical and theoretical results is presented.     

Pulsating magnetohydrodynamic flow in an annular channel

Pulsating laminar flow of a viscous incompressible electrically conducting fluid in an annular channel between two infinitely long circular cylinders under a radial impressed magnetic field is considered. The solutions of magnetohydrodynamic equations have been obtained on the assumption that the space between two cylinders is small compared to their mean radius. The solutions were also obtained on the assumption of small magnetic Reynolds number with special consideration of those for low and high frequencies.     

Stress distribution in an annular retarded-elastic plate with cylindrical anisotropy

Formulas for the stresses and displacements in an annular plate with cylindrical anisotropy are obtained with allowance for the time factor. Different cases of loading of the inside and outside edges of the plate are examined.Mekhanika Polimerov, Vol. 2, No. 3, pp. 403–412, 1966     

Stability of the cylindrical flame front in an annular combustion chamber

Using small perturbations, within the framework of phenomenological theory of mixture combustion we study stability of the cylindrical front of deflagration combustion in an annular combustion chamber. The flame front is described as a discontinuity of gasdynamic parameters. It is discovered that the flame front is unstable for some types of small perturbations of the mainstream flow of the fuel mixture and the flame front. The mechanics of instability is examined using both numerical and analytical methods. The cases are presented of evolution of the instabilities rotating in the annular channel.     

Motion of a non-Newtonian liquid in the annular channel of an insulation-coating tool

The axisymmetric flow of a non-Newtonian liquid with an exponential rheological law between two coaxial cylinders is considered for the case when the outer cylinder is fixed and the inner cylinder moves freely together with the liquid. At the outer cylinder the liquid moves either with or without slip. The individual theoretical conclusions are confirmed by the experimental results.Mekhanika Polimerov, Vol. 3, No. 1, pp. 151–155, 1967     

A numerical algorithm for modeling laminar flows in an annular channel with eccentricity

We propose a numerical algorithm for simulating steady laminar flows of an incompressible fluid in annular channels with eccentricity and rotation of the inner cylinder. This algorithm enables us to describe this class of flows for wide ranges of the annular channel and flow parameters. We present the implementation details and the results of testing this numerical method. For a series of flows in an annular clearance, we compare the numerical results to available analytic solutions and experimental data. In all cases under consideration the simulated data agree well with the available experimental, analytical, and numerical solutions.     

Axisymmetric instability of pressure-driven flow in an annular channel at high Reynolds numbers

For the pressure-driven flow in an annular channel, its linear instability with respect to axisymmetric perturbations at high Reynolds numbers is investigated within the framework of the triple-deck theory. It is shown that the problem is reduced to that of the two-dimensional linear instability of the Poiseuille flow in a plane channel. The ratio of the inner to outer radii of the channel is found at which the instability is minimal.     

Inverse boundary value problem of aerohydrodynamics for an axisymmetric body with blowing from an annular channel

A numerical-analytical method is developed for determining the shape of a streamlined with jet blowing axisymmetric body from a given velocity distribution along its meridional section. Numerical result examples are given. Forces, which are influence on axisymmetric body, are calculated. Comparisons of aerodynamic characteristics for bodies with different location of annular channel are carried out.     

Hydrodynamic analysis of the flow of a liquid with an exponential rheological equation in the cylindrical channel of an extruder screw

Equations are obtained for the angular velocity profile and flow rate in the case of integral and nonintegral exponents n when a non-Newtonian liquid with an exponential rheological equation moves between two rotating cylinders in the presence of a tangential pressure gradient.Branch Institute of Chemical Physics, AS USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1094–1102, November–December, 1968.     

A note on the effect of submerged obstacles on water waves in a channel

Summary By combining the results due to Jeffrey and Mvungi [1], with the work of Jeffrey and Saw Tin [2, 3], the transmission and reflection properties of an acceleration wave propagating on the surface of water at rest in a vertical walled channel of arbitrary continuously varying width and piecewise continuously varying depth are determined. An explicit expression derived for the amplitude of the transmitted wave as a function of position by Jeffrey and Mvungi is used to find the effect of a discontinuous change of depth on the wave amplitude and to derive a criterion for the breaking of the wave.

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Zusammenfassung Durch Kombination der Resultate von Jeffrey und Mvungi [1] mit denen von Jeffrey and Saw Tin [2, 3] wird die Transmission und die Reflexion einer Beschleunigungswelle an der Oberfläche von ruhendem Wasser berechnet, in einem Kanal mit vertikalen Wänden, dessen Weite beliebig kontinuierlich und dessen Tiefe abschnittsweise kontinuierlich variiert. Ein expliziter Ausdruck für die Amplitude der durchgelassenen Welle in Funktion der Lage nach Jeffrey und Mvungi wird dazu benützt, um den Effekt einer Diskontinuität in der Tiefe zu finden und ein Kriterium für das Brechen der Welle herzuleiten.

     

Reflection of acoustic waves in a cylindrical channel from the perforated part

The reflection and transmission of harmonic waves and waves of finite duration through the boundary of the perforated part of a cylindrical channel (a lined borehole), filled with a fluid and surrounded by a permeable porous medium, is investigated. A model of the plane time-varying fluid flow in the cylindrical channel in a quasi-one-dimensional approximation and of the seepage absorption of the fluid in the porous medium surrounding the channel is presented. The effect of the collector characteristics of the porous medium surrounding the channel and the quality of the perforation (the length of the perforation channels) on the evolution of the waves when they are reflected from the boundary of the perforated part of the wall are investigated.     

Steady-state thermal stresses in an infinite elastic medium containing an annular crack

An axisymmetric steady-state thermoelastic problem of an infinite isotropic medium containing an annular crack is considered. The faces of the crack are exposed to prescribed temperature distribution. The normal components of stress and displacement on the crack plane and the stress-intensity factors at the boundaries of the crack are expressed in power series in terms of the ratio between the radii of the inner and outer boundaries. These are illustrated graphically.     

An equivalent mechanical model for fluid sloshing in a rigid cylindrical tank equipped with a rigid annular baffle

A mass-spring mechanical model for linear sloshing of fluid in a rigid cylindrical tank with a rigid annual baffle is developed. By means of the subdomain method, the complicated fluid domain is divided into several subdomains with pure boundary conditions and interface conditions. Combined with the continuity conditions of velocity and pressure on interfaces, the velocity potential of fluid in each subdomain is analytically solved. The mass-spring model for fluid sloshing is established by generating the same hydrodynamic shear force and overturning moment as those from the exact solutions when the tank is subjected to horizontal excitations. The present model gives all the mechanical parameters including the convective mass-spring oscillators and the impulsive mass as well as their positions. Comparative studies between the present solutions and the available results verify the correctness of the mechanical model. Based on the normalized equivalent masses and spring stiffnesses, the dynamic responses of fluid in tanks are discussed with respect to the fluid height, the baffle position and the inner radius of the baffle, respectively. The present model is especially suitable for dealing with complicated liquid-structure systems. The motivation and novelty of this study are confirmed by an application of the present model to a multi-tank system.     

Axisymmetric flow over a backward-facing step in an annular pipe

The incompressible flow of a Newtonian fluid over a backward-facing step is investigated numerically. The geometry is an annular pipe in which the radius of the inner cylinder decreases suddenly. Keeping the radial expansion ratio fixed axisymmetric flows are computed for outlet radius ratios from 0.1 to 1 (ratio of the inner to the outer outlet radius). The Reynolds number at which the flow separates from the outer cylinder decreases as the outlet radius ratio decreases for constant inlet geometry. The growth with Reynolds number of the recirculation zone on the inner outlet cylinder just behind the step is strongly reduced when the recirculation zone on the outer cylinder is established. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical model of an internal crack in an elastoplastic cylindrical shell

We propose a mathematical model that makes it possible to reduce the problem of the stressed state and limit equilibrium of a cylindrical anisotropic elastoplastic shell with internal crack to a system of nonlinear singular integral equations with discontinuous functions on the right-hand sides. We construct an algorithm for numerical solution of such systems together with the conditions of plasticity and boundedness of stresses near the crack. For a transversally isotropic shell, we carry out a numerical analysis of the dependence of the opening of the internal crack front on the load and geometric and mechanical parameters. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 111–116, April–June, 1998