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2014 year, number 6

Flow of Micropolar and Viscoplastic Fluids in a Hele–Shaw Cell

V. V. Shelukhin1,2, V. V. Neverov1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: micropolar viscoplastic fluid, yield stress, HeleShaw cell, extension of Darcy's law

Abstract >>
A generalization of Darcy's law relating the velocity averaged over the transverse coordinate and the pressure gradient is obtained for flows in a thin layer. A nonlinear Darcy's law with a limiting gradient is derived taking into account microrotations and the yield stress. It is shown that the micropolarity of fluids manifests itself as an increase in the apparent viscosity and the limiting pressure gradient. A generalization of Darcy's law for the case of pseudo–plastic and dilatant Herschel—Bulkley fluids is obtained.

Traveling Waves in a One–Dimensional Model of Hemodynamics

A. M. Barlukova1, A. A. Cherevko1,2, A. P. Chupakhin1,2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University
Keywords: onedimensional equations of hemodynamics, viscoelastic tube, traveling wave solutions, singular point, oscillating solutions

Abstract >>
We consider a one–dimensional model of hemodynamicsblood flow in the blood vessels-which is based on the Navier—Stokes equations averaged over the cross section of the vessel, and conjugate with a linear or nonlinear model for the elastic wall of the vessel. The objective is to study traveling wave solutions using this model. For such solutions, the system of partial differential equations reduces to an ordinary differential equation of the fourth order. The only singular point of the corresponding system of differential equations is found. It is established that at the singular point, the linearization matrix of the system has real or complex roots for different values of the parameters of the problem. With a special choice of the parameters, it has four complex conjugate roots with a nonzero real part or purely imaginary roots. For this case, the effect of the model parameter corresponding to the viscoelastic response of the vessel wall on the solution is investigated. Numerical experiments are performed to verify and analyze the results, and various modes of blood movement are discussed.

Study of the Poloidal Beta and Internal Inductance by Solving the Simplest Grad-Shafranov Equation for a Tokamak with a Circular Cross Section

M. Asif1, A. Asif2
1COMSATS Institute of Information Technology, Lahore 54000, Pakistan
2The Interdisciplinary Research Centre in Biomedical Materials (IRCBM), Lahore 54000, Pakistan
Keywords: poloidal beta, internal inductance, magnetohydrodynamic instability, GradShafranov equation

Abstract >>
In this work, we present the poloidal beta βp and internal inductance li by solving the simplest Grad—Shafranov equation (GSE), using the Solov'ev assumption for an HT–7 tokamak with a circular cross section. The poloidal beta and internal inductance are measured by using diamagnetic and compensation loops, combined with poloidal magnetic probe array signals. In this paper, theoretical and experimental results of determining βp and li are presented. The calculated poloidal beta and internal inductance are demonstrated to depend on the kind of the discharge or plasma current.

Analysis of Flight Trajectories of a Ramjet—Powered Vehicle

V. M. Fomin1, S. M. Aulchenko1, V. I. Zvegintsev1, L. A. Ustinov2
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Tula State University, Tula, 300012 Russia
Keywords: ramjet, flight trajectory, optimization

Abstract >>
Based on numerical simulations of flight trajectories with ramjet–powered flying vehicles, it is found that all possible flight trajectories can be classified into three groups: ballistic trajectories, trajectories with a horizontal segment, and skipping trajectories. Trajectories of each group can be optimized, for instance, to ensure the maximum flight range under given initial conditions and constraints. Examples of optimal trajectories for a given amount of available fuel are presented as functions of the initial slope of the trajectory, angle of attack of the vehicle, instants of engine actuation, and engine operation time.

Approximate Modeling of the Flow Structure in a λ–Shaped Pseudoshock

A. E. Medvedev
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: pseudoshock, gas dynamics, shock waves, compression wave, expansion wave

Abstract >>
An approximate analytical model of the flow structure in a plane λ–shaped pseudoshock consisting of a viscous boundary layer and an inviscid core flow is proposed. It is assumed that the boundary layer edge is a streamline with a specified pressure distribution along the channel and that the flow in the pseudoshock consists of an input segment (Mach reflection of an oblique shock wave) and a sequence of internal segments with an identical structure (shock train). Comparisons with experimental data and results of numerical calculations are performed. It is shown that the model provides a sufficiently accurate description of the pseudoshock flow structure.

Numerical Study of the Influence of Geometrical Characteristics of a Vertical Helical Coil on a Bubbly Flow

H. Saffari, R. Moosavi
Iran University of Science and Technology, Tehran, Iran
Keywords: twophase turbulent flow, EulerianEulerian model, CFD, helical coil

Abstract >>
In this article, turbulent single–phase and two-phase (airwater) bubbly fluid flows in a vertical helical coil are analyzed by using computational fluid dynamics (CFD). The effects of the pipe diameter, coil diameter, coil pitch, Reynolds number, and void fraction on the pressure loss, friction coefficient, and flow characteristics are investigated. The Eulerian—Eulerian model is used in this work to simulate the twophase fluid flow. Threedimensional governing equations of continuity, momentum, and energy are solved by using the finite volume method. The κε turbulence model is used to calculate turbulence fluctuations. The SIMPLE algorithm is employed to solve the velocity and pressure fields. Due to the effect of a secondary force in helical pipes, the friction coefficient is found to be higher in helical pipes than in straight pipes. The friction coefficient increases with an increase in the curvature, pipe diameter, and coil pitch and decreases with an increase in the coil diameter and void fraction. The close correlation between the numerical results obtained in this study and the numerical and empirical results of other researchers confirm the accuracy of the applied method. For void fractions up to 0.1, the numerical results indicate that the friction coefficient increases with increasing the pipe diameter and keeping the coil pitch and diameter constant and decreases with increasing the coil diameter. Finally, with an increase in the Reynolds number, the friction coefficient decreases, while the void fraction increases.

Method of Recovery of Gas Flow Pressure Based on the Results of Measurements in Short–Duration Wind Tunnels

V. A. Derevyanko1, S. V. Kukushkin1, A. F. Latypov2
1Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia
2Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: shortduration wind tunnel, pressure, Volterra integral equations of the first kind

Abstract >>
The paper presents a method of recovery of gas flow pressure from the results of measurements by a piezoelectric pressure sensor in short–duration wind tunnels. It is assumed that the measuring system is a linear dynamic object. A quasisolution of linear Volterra integral equation of the first kind is constructed based on the condition that the equation holds on average in successive intervals into which the time interval of the measurement is divided. An experimental technique for determining the normal response of the sensor (transfer function) is proposed, and an example of recovery of air flow pressure in a wind tunnel is given.

Simulation of Three–Dimensional Waves in a Liquid Film

S. P. Aktershev, S. V. Alekseenko
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: liquid film, threedimensional waves, numerical simulation, shear stresses, stability

Abstract >>
A model describing long–wave dimensional perturbations in a liquid film is developed that takes into account the presence of shear stress on the interfacial surface. This model is based on the decomposition of the liquid velocity vector components in a series in linearly independent basis functions (harmonics) and does not use the assumption of selfsimilarity of the velocity profile. A linear analysis of the stability of film flow with respect to threedimensional perturbations, and a numerical simulation of nonlinear waves were performed.

Migration of a Granule in a Rapidly Oscillating Inhomogeneous Velocity Field of a Viscous Fluid

I. V. Derevich
Bauman Moscow State Technical University, Moscow, 105005 Russia
Keywords: averaging over fast oscillations, migration, drift, granule inertia, frequency of oscillations

Abstract >>
A closed system of equations for calculating the drift of an inertial heavy granule in an inhomogeneous velocity field of the carrier fluid is derived by the Krylov—Bogolyubov method of averaging over fast oscillations of velocity. Exact analytical solutions are presented and compared with the results of the numerical solution of the equations of granule motion. The influence of the granule inertia, acceleration of mass forces, and frequency of oscillations on the granule dynamics in an inhomogeneous oscillating velocity field of the fluid is studied.

Comparison of Theory and Experiment in Simulation of Dam Break in a Rectangular Channel with a Sudden Change in Cross–Sectional Area

V. V. Degtyarev1, V. V. Ostapenko2, O. A. Kovyrkina2, A. V. Zolotykh1
1Novosibirsk State Architecture and Civil Engineering University (Sibstrin), Novosibirsk, 630008 Russia
2Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: shallowwater theory, sudden change in crosssectional area, dambreak problem, selfsimilar solutions, laboratory experiment

Abstract >>
This paper, presents the results of comparison of theory and laboratory experiment for simulation of the wavy flows resulting from dam break on a sudden change in the rectangular cross–sectional area of a channel whose width is greater upstream than downstream. Exact selfsimilar solutions containing an heuristic parameter dependent on the total energy of the flow lost on the sudden change in crosssectional area were obtained using the first approximation of the spatially onedimensional theory of shallow water. It is shown that theoretical solutions agree quite well with the results laboratory experiments on the possible types of waves, the their propagation velocity, and asymptotic depth values behind their fronts.

Causes of Bed Instability

A. G. Petrov1, I. I. Potapov2
1Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia
2Computing Centre, East Branch, Russian Academy of Sciences, Khabarovsk, 680000 Russia
Keywords: channel processes, transported sediments, bed layer, bottom waves, bed instability

Abstract >>
The causes of bed instability in a sandy bed channel are analyzed using a formula of sediment transport rate containing no phenomenological parameters. The sediment transport rate is uniquely determined by the normal and shear stresses on the bed and the slope of the bed surface. Using a linear model, it is shown that the only factor responsible for bed instability is perturbations of the normal bed pressure regardless of their nature.

Propulsive Device of the Flapping Wing Type

D. N. Gorelov
Omsk Department of the Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, 644043 Russia
Keywords: flapping wing, unsteady flow around the wing, thrust force, propulsive device of the flapping wing type

Abstract >>
Problems associated with the development of a propulsive device of the flapping wing type are discussed. Specific features of an unsteady flow around such a wing and the influence of its geometric parameters and the law of wing flapping on the thrust force and hydrodynamic efficiency are analyzed. Formulas for calculating the thrust force at high Strouhal numbers are derived. Some configurations of propulsive devices and possible applications are considered.

Mathematical Modeling of Moisture Extraction from Rice Grains

A. V. Fedorov, A. A. Zhilin
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: acoustoconvective drying of unhusked Korean rice, moisture extraction, coefficients of diffusion and moisture extraction

Abstract >>
The process of moisture extraction from unhusked Korean rice is modeled with the use of a diffusion model. The diffusion coefficient is determined, which makes it possible to reconstruct the dynamics of the moisture distribution in a cylindrical sack filled by rice. It is demonstrated that the results of calculations performed for different values of the initial humidity are in reasonable agreement with experimental data obtained in the case of drying of unhusked rice in an acousto–convective drier. Results testifying to significant intensification of acoustoconvective drying as compared to natural drying are obtained.

Description of Creep and Fracture of Modern Construction Materials using Kinetic Equations in Energy Form

B. V. Gorev1, I. V. Lyubashevskaya1, V. A. Panamarev2, S. V. Iyavoynen3
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Siberian State Industrial University, Novokuznetsk, 654007 Russia
3Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: kinetic theory of creep, fracture, scalar damage parameter, equivalent stresses, normalized specific energy dissipation

Abstract >>
It has been shown experimentally and theoretically that the equations of the Rabotnov kinetic theory of creep with a scalar damage parameter can be used to describe the deformation (up to fracture) of metallic materials in creep without restrictions on the creep strain and energy dissipation at the moment of fracture. In finding the functional dependences in the equations of creep and damage, the damage parameter is determined by the amount of normalized specific energy dissipation in the process of material creep under the necessary condition of similarity of the initial creep curves for constant stresses and temperatures in the normalized variables.

Forced Vibrations of a Layer of a Viscoelastic Material under the Action of a Convective Wave of Shear Stresses

V. M. Kulik
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: forced vibration, friction oscillation, dynamic compliance, elasticity modulus, loss factor, Poisson ratio

Abstract >>
A two-dimensional problem of deformation of a layer of a viscoelastic material glued to a solid base by a traveling wave of shear stress is solved. Analytical expressions for two shear compliance components corresponding to two surface displacement components are obtained. It is shown that the dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wavelength to the layer thickness λ / H, and the ratio of the wave velocity to the propagation rate of shear vibrations V/Ct0. Data on the dynamic compliance in the ranges 0.2 < λ / H < 60.0 and 0.2 < V/Ct0 <5.0 are given. It is established that, in the range 1.5 < λ / H < 5.0, the normal component of the shear compliance decreases sharply. Diagrams of the phase shift of the displacement components relative to the phases of the applied oscillatory shear stresses and diagrams of displacements and shifts of their phases over the thickness of the viscoelastic layer are presented.

Influence of Periodic Change in the Yield Strength in a Plate on the Development of Plastic Zones Near a Crack Tip

V. D. Kurguzov1, V. M. Kornev1, V. V. Moskvichev2, A. A. Kozlov2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Nauka Special Design and Technological Bureau, Krasnoyarsk, 660049 Russia
Keywords: plastic zone, crack tip, finite element method

Abstract >>
An experimental study of plastic deformation zones in the vicinity of stress concentrators found a deviation of the shapes of plastic zones at the crack tip from the shapes obtained using conventional models. Moreover, the systems of bands of slip lines observed in the experiment and predicted by linear fracture mechanics are significantly different. Mathematical modeling of the propagation of plastic zones based on a finite element numerical solution of the equations of deformable solid mechanics was performed with the framework of the theory of large elastoplastic deformations. The basis of the mathematical model is the hypothesis that the structural heterogeneity of the material has a substantial effect throughout the volume of the test sample on the formation of plastic bands. Nonuniformity of the yield strength of the material is specified as a checkerboard distribution and as a system of horizontal and vertical bands. The results of the numerical calculations are compared with the experimental data, and it is shown that they are in qualitative agreement.

Stress–Strain State and Stress Intensity Factor in the Vicinity of CrackLike Defects under Biaxial Tension of a Plate

A. A. Ostsemin1, P. B. Utkin2
1Russian Presidential Academy of National Economy and Public Administration, Chelyabinsk, 454077 Russia
2South Ural State University, Chelyabinsk, 454080 Russia
Keywords: fracture mechanics, stress intensity factors, stress state, the Kolosov—Muskhelishvili method, a plate with an elliptic hole, holographic interferometry method

Abstract >>
The problem of determining a stress-strain state described by singular and regular terms and a stress intensity factor in the vicinity of the top of a crack–like defect in a plate under biaxial loading is considered. The Kolosov—Muskhelishvili method was used to obtain expressions for the stress tensor near the top of the ellipse, which yield the formulas for stresses in the case of blunt cracks. Maximum shear stress, principal stresses, and stress intensity are determined. Formulas for the stress intensity factor under biaxial loading of a plate with a cracklike defect are obtained and can be used in the holographic interferometry method.

Fracture Model for Structured Quasibrittle Materials

V. D. Kurguzov1, N. S. Astapov1, I. S. Astapov2
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Research Institute of Mechanics, Moscow, 119192 Russia
Keywords: fracture criteria, prefracture zone, characteristic size of structural element, quasi–ductile fracture diagram

Abstract >>
We analyze the applicability of a modified Leonov—PanasyukDugdale model to the description of the propagation of a mode I crack in structured materials under plane stress conditions. For quasi-brittle materials, refined formulas of the critical length of the prefracture zone and the critical load containing a structural parameter are proposed. The Kornev model is extended to the case of quasi-ductile materials. Numerical simulation of plastic zones in square plates of a bimetal and a homogeneous material under quasi–static loading is performed. In the numerical model, the equations of deformable solid mechanics are expressed in the Lagrangian formulation, which is the most preferred for large-strain deformations of elastoplastic materials. The results of the numerical experiments are consistent with the results of calculations using the analytical model for the fracture of structured materials.

Accurate Investigation of Lateral Vibrations of a Quintic Nonlinear Beam on an Elastic Foundation: using an Exact Formulation of the Beam Curvature

H. M. Sedighi, K. H. Shirazi
Shahid Chamran University, PO box 61357-43337, Ahvaz, Iran
Keywords: quintic nonlinearity, parameter expansion method, elastic foundation, nonlinear vibrations of the beam

Abstract >>
This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above–mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.