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Journal of Applied Mechanics and Technical Physics

2019 year, number 6

On the Energy of a Hydroelastic System: Blood Flow in an Artery with Cerebral Aneurysm

M. Yu. Mamatyukov1,2, A. K. Khe1,2, D. V. Parshin1,2, P. I. Plotnikov1,2, A. P. Chupakhin1,2
1Lavrent'ev Institute for Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk National Research State University, Novosibirsk, 630090, Russia
Keywords: функционал Уиллмора, кривизна поверхности, церебральные аневризмы, гидроупругость, численный расчет, Willmore functional, surface curvature, cerebral aneurysms, hydroelasticity, numerical calculation

Abstract >>
An energy approach to the study of a hydroelastic system consisting of an elastic blood vessel, viscous fluid flow, and an aneurysm anomaly is developed to evaluate the various energy components of the system: viscous flow dissipation energy, tensile energy and bending energy of the aneurysm wall. To calculate the total energy of the system, we have developed a computing complex including commercial and free software and self-developed modules. The performance of the complex has been tested on model geometric configurations and configurations corresponding to blood vessels with cerebral aneurysms of real patients and those reconstructed by angiographic images. The calculated values of the Willmore functional characterizing the shell bending energy are consistent with theoretical data.

Effects of the Helmholtz Resonator on the Hartmann Whistle Operating at a High Nozzle Pressure Ratio

Y.-S. Jong1, Ch.-J. Kim2, Ch.-Y. Yun1
1Kim Chaek University of Technology, Pyongyang, Democratic People's Republic of Korea
2Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea
Keywords: генератор Гартмана, низкая частота, численное моделирование, резонатор Гельмгольца, Hartmann whistle, low frequency, numerical simulation, Helmholtz resonator

Abstract >>
A numerical simulation is carried out to investigate the effect of the Helmholtz resonator capacity on the Hartmann whistle operating at high values of the nozzle pressure ratio using the turbulence model. The results of the present numerical simulations are compared to experimental data. The simulation results show that the frequency and amplitude of the Hartmann whistle with the Helmholtz resonator are obviously lower as compared to the conventional Hartmann whistle. Moreover, the Mach number contours and streamlines indicate that the Helmholtz resonator does not affect the shock-cell structure between the nozzle and the cavity, and the Hartmann whistle with the Helmholtz resonator has a jet regurgitant mode that is different from the Hartmann whistle with a straight resonator. The diameter of the Helmholtz resonator is an important factor affecting the fundamental frequency.

Numerical Simulation of Viscous Dissipation in a Micropolar Fluid Flow Through a Porous Medium

S. Ahmad1, M. Ashraf1, K. Ali2
1Centre for Advanced Studies in Pure and AppliedMathematics, Bahauddin Zakariya University, Multan, 60800, Pakistan
2Department of Basic Sciences and Humanities, Muhammad Nawaz Sharif University of Engineering and Technology, Multan, 60000, Pakistan
Keywords: вязкая диссипация, микрополярная жидкость, пористая среда, квазилинеаризация, viscous dissipation, micropolar fluid, porous medium, quasi-linearization

Abstract >>
Taking into account the effect of viscous dissipation in the energy equation, we numerically explore the flow of an incompressible micropolar fluid with heat and mass transfer through a resistive porous medium between plane channel walls. By exploiting a similarity transformation, the governing partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations, which are solved numerically for various problem parameters by means of quasi-linearization. It is found that the effect of viscous dissipation is to increase the heat and mass transfer rate at both the lower and upper walls of the channel.

Barometric Gas Distribution SImulated by Solid Spheres

I. N. Cherepanov, P. V. Krauzin
Perm State University, Perm, 614990, Russia
Keywords: модель твердых сфер, седиментация, вириальное разложение, уравнение Карнагана-Старлинга, solid sphere model, sedimentation, virial decomposition, Carnahan - Starling equation

Abstract >>
Gas particle distribution simulated by solid spheres and located in a gravity field at a constant temperature is under study. A solid sphere model is poorly applicable to real gases, but it can be used to describe the distribution of nanoparticles in a colloidal solution. Various models of weakly nonideal gas are compared: virial expansion up to a second coefficient, a Wertheim - Thiel equation in a Percus - Yevick approximation, and a Carnahan - Starling approximation. In the case of virial expansion, an exact analytical solution for an equation of particle distribution by height is obtained. For more complex models, solutions are found using numerical methods. It is shown that accounting for a finite particle size leads to significant changes in the particle distribution as compared to the ideal gas distribution even at small volume fractions. The results obtained using virial decomposition are in good agreement with the results obtained using more complex models provided that the volume fraction of the impurity does not exceed 0.1.

Far Fields of Internal Waves Excited by a Pulsing Source in a Stratified Medium with Shear Flows

V. V. Bulatov, Yu. V. Vladimirov
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526, Russia
Keywords: стратифицированная среда, внутренние гравитационные волны, частота плавучести, сдвиговые течения, stratified medium, internal gravitational waves, buoyancy frequency, shear flow

Abstract >>
A problem of the far field of internal gravitational waves excited by an oscillating point source of perturbations in a stratified medium with a shear flow is solved. A model distribution of the shear flow velocity by depth is considered and an analytical solution to this problem is obtained in the form of a characteristic Green's function, expressed in terms of the modified Bessel functions of the imaginary index. Expressions for dispersion relations are obtained and integral representations of solutions are constructed. The dependences of the wave characteristics of the excited fields on the main parameters of the used stratification models, flows, and generation regimes are investigated.

Asymptotic Study of Instability in a Three-Layer Stokes Flow with an Inhomogeneous Layer Thickness. Folding Process Simulation

V. V. Pak
V.I. Il'ichev Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041, Russia
Keywords: стоксово течение, многослойное течение, неустойчивость при нулевых числах Рейнольдса, тектонофизика, складкообразование, Stokes flow, multilayer flow, instability at zero Reynolds numbers, tectonophysics, folding

Abstract >>
Instability at zero Reynolds numbers in a three-layer Stokes flow of a viscous fluid with an inhomogeneous layer thickness in a two-dimensional region with a free boundary is investigated. The method of multiple scales to applied for constructing an asymptotic expansion of the solution of the boundary-value problem for the Stokes equations. The stability of the system of first-approximation equations is analyzed using the Fourier method, and it is concluded that the most significant increase in instability at zero Reynolds numbers occurs in the region of waves whose lengths are comparable with the thickness of the middle layer. In contrast to the case of a constant layer thickness, the instability parameters are variable. The mechanism of formation of geological folds is investigated.

Exact Solutions for the Layered Three-Dimensional Nonstationary Isobaric Flows of Viscous Incompressible Fluid

N. M. Zubarev1,2, E. Yu. Prosviryakov3
1Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016, Russia
2Lebedev Physical Institute, Russian Academy of Science, Moscow, 119991, Russia
3Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620016, Russia
Keywords: слоистые течения, изобарические течения, точные решения, переопределенная система уравнений, условия совместности, layered flows, isobaric flows, exact solutions, overdetermined system of equations, compatibility conditions

Abstract >>
This paper describes an overdetermined system of equations that describes three-dimensional layered unsteady flows of a viscous incompressible fluid at a constant pressure. Studying the compatibility of this system makes it possible to reduce it to coupled quasilinear parabolic equations for velocity components. The reduced equations allow constructing several classes of exact solutions. In particular, polynomial and spatially localized self-similar solutions of the motion equations are obtained. The passage to the limit of the case of an ideal fluid is investigated.

Numerical Study of the Hydrodynamics of the T-Graft in the Model Problem of Optimizing the Angle of Low-Flow Vascular Anastomosis

Yu. O. Kuyanova1,2, S. C. Presnyakov2, A. V. Dubovoi3, A. P. Chupakhin1,2, D. V. Parshin1,2
1Lavrent'ev Institute for Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk National Research State University, Novosibirsk, 630090, Russia
3Federal Neurosurgical Center, Novosibirsk, 630048, Russia
Keywords: гидродинамика тройника, гемодинамика, сосудистый анастомоз, угол установки анастомоза, численная задача оптимизации, T-graft hydrodynamics, hemodynamics, vascular anastomosis, anastomosis angle, numerical optimization problem

Abstract >>
The hydrodynamics of a T-graft is investigated as part of the problem of determining the optimal angle of vascular anastomosis during neurosurgery. Four possible angles corresponding to the most commonly used real configurations are considered: π/6, π/4, π/3, and π/2. The problem is solved numerically using the ANSYS code. The condition of minimum integral of the viscous dissipation energy is used as an optimality criterion. It is shown that the anastomosis angle π/3 is optimal and the angle π/4 is the least favorable.

Development of the Algorithm for Simulating Stratified Flows with Obstacles and its Verification for a Flow with a Vertical Barrier

G. Yu. Evtushok, A. V. Boiko, S. N. Yakovenko
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: устойчивая стратификация, вертикальный барьер, внутренние волны, зоны рециркуляции, численное моделирование, stable stratification, vertical barrier, internal waves, recirculation zones, numerical simulation

Abstract >>
A numerical algorithm for solving CFD equations for the case of a stable stratified flow with a bluff body in the form of a thin vertical barrier generating internal waves is developed and verified with the use of the OpenFOAM software system. Numerical simulations of this flow are performed for different Froude numbers for steady and unsteady regimes of wave overturning; it is demonstrated that the results predicted by the proposed algorithm are qualitatively consistent with other available data. The reasons for the differences in the computed drag coefficient from the data obtained previously are discussed.

Problem of Studying the Acoustic and Hydrodynamic Properties of the Medium Occupying a Region Shaped as a Three-Dimensional Rectangular Wedge

V. A. Babeshko1, O. V. Evdokimova1, O. M. Babeshko2
1Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, 344006, Russia
2Kuban State University, Krasnodar, 350040, Russia
Keywords: метод блочного элемента, граничная задача, автоморфизм, псевдодифференциальные уравнения, клиновидная область, block element method, boundary-value problem, automorphism, pseudo-differential equations, wedge-shaped region

Abstract >>
A boundary-value problem for a three-dimensional Helmholtz equation in a region shaped as a rectangular wedge of infinite extent is under consideration. An exact solution to this boundary-value problem is constructed in the form of a packed block element necessary for investigating more complex and even mixed problems for block structures. The conjugation of packed blocks into a block structure is carried out by constructing quotient topologies of the topological spaces of blocks, and the equivalence relations are interblock boundary conditions.

Effects of Geometry Parameters on Cooling Performance and Conjugate Thermal-Elastic Property of Double-reverse-Jet Film Cooling

Z. Wang1,2, C. Zhang3, S.-J. Li2, J.-J. Liu1, H.-W. Zhang1
1Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China
2School of Energy and Power Engineering, Shandong University, Jinan, 250061, China
3Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin, 300384, China
Keywords: пленочное охлаждение парами разнонаправленных струй, геометрические параметры, почковидные "антивихри", связанные мультиполя, температурные напряжения, double-reverse-jet film cooling (DRJFC), geometric parameters, anti-kidney vortices, multi-field coupling, thermal stress

Abstract >>
In order to investigate the double-reverse-jet film cooling (DRJFC), the multi-field coupling calculating method is used to study the effect of geometric parameters on the resultant vortex structure and conjugate thermal-elastic property. The traditional streamwise film cooling is also investigated for comparison. The results indicate that the formation of effective anti-kidney vortices is the key to enhance the dimensionless temperature of DRJFC holes. At low blowing ratios, the streamwise or lateral distance between two DRJFC holes should be increased to widen the transverse shift of the jets, thus, to increase the cooling performance. At high blowing ratios, the lateral distance should be decreased to prevent two jets from separating apart so that the malfunction of the anti-kidney vortices could be avoided. The stress concentration resulting from the nonuniform temperature distribution is considered.

Film Cooling Performance for Cylindrical Holes Embedded in Contoured Craters: Effect of the Crater Depth

J.L. Fu1, L.C. Bai2,3, C. Zhang2,3, P.F. Ju2,3
1Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing, 100190, China
2Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, Tianjin, 300384, China
3National Demonstration Center for Experimental Mechanical and Electrical Engineering Education (Tianjin University of Technology), Tianjin. 300384, China
Keywords: пленочное охлаждение, профилированные кратеры, глубина кратера, параметр вдува, пара "антивихрей" почковидной формы, эффективность охлаждения адиабатической стенки, film cooling, contoured crater, crater depth, blowing ratio, anti-kidney-shaped vortex pair, adiabatic cooling effectiveness

Abstract >>
The present study deals with the flow field and cooling performance for flat-plate cylindrical film cooling holes embedded in contoured craters, especially considering the effect of the crater depth. A test matrix of the crater depth ranging from 0.25 to 1.25 times of the cylindrical hole diameter and the blowing ratio ranging from 0.5 to 2.0 is used in CFD computations. The numerical results show that the flow fields downstream from the hole exit can be altered significantly due to interaction between the ejected coolant and contoured crater. The cooling performance depends on both the specific crater depth and blowing ratio; however, the cratered hole is always superior to the cylindrical hole in terms of the area-averaged cooling effectiveness regardless of the crater depth and blowing ratio. The cratered hole with a crater depth equal to the hole diameter is recommended.

Gas Jet Deposition of Diamond on a Steel Surface Covered by a Layer of WC-Co or Mo

A. K. Rebrov1, I. S. Batraev2, T. T. B'yadovskii1, E. V. Gladkikh3, A. S. Useinov3, M. N. Khomyakov4
1Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
3Technological Institute for Superhard and Novel Carbon Materials, Troitsk, 142190, Russia
4Institute of Laser Physics SB RAS, Novosibirsk, 630090, Russia
Keywords: химическое газофазное осаждение, алмазное покрытие, детонационное напыление, промежуточные слои, механические измерения, chemical vapor deposition, diamond coating, detonation sputtering, intermediate layers, mechanical measurements

Abstract >>
Results of studying the growth of diamond structures on steel samples with the use of intermediate layers of molybdenum or tungsten carbide cemented by cobalt are reported. The intermediate layers are deposited by means of detonation sputtering. Subsequent deposition of diamond films onto the clad steel samples is formed by the gas jet method and a special thermocatalytic reactor with extended activating surfaces. The nucleation process on the intermediate layer surfaces is intensified by preliminary seeding of the samples in a colloid solution containing nanodiamonds. Information about the phase and structural composition of the resultant samples and about the film surface morphology is obtained by scanning electron microscopy, Raman spectroscopy, and X-ray diffraction analysis. The tribology of the samples is studied with the use of hardness nano-sensor and by Rockwell hardness identation.

Contact Problems for Hollow Cylinders Made of a Nonhomogeneous Material

D. A. Pozharskii1, N. B. Zolotov2
1Don State Technical University, Rostov-on-Don, 344000, Russia
2Southern Federal University, Rostov-on-Don, 344090, Russia
Keywords: цилиндр из упругого неоднородного материала, контакт, асимптотика, cylinder made of an elastic nonhomogeneous material, contact, asymptotic

Abstract >>
Contact problems for elastic hollow cylinders made of a nonhomogeneous materia are considered. The cylinders are subjected to uniformly distributed internal or external pressure and interact with a stiff shroud or finite-length insert. Poisson's ratio (Young's modulus) of the elastic material varies along the radial coordinate. The problem equations are reduced to integral equations with respect to contact pressures. A singular asymptotic method, which is fairly effective for contact regions of sufficiently large length, is applied to solve the problem.

On the Choice of Forming Modes and Estimation of Residual Service Life by Kinetic Equations with the Scalar Damage Parameter

I. A. Banshchikova
Lavrent'ev Institute for Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: конструкционные сплавы, разупрочнение, упрочнение, повреждаемость, рациональные режимы ползучести, растяжение, structural alloys, softening, hardening, damage, rational creep, tension

Abstract >>
The kinetic equations of creep are used to compare damage accumulation in rods under tension in two forming modes: at constant stresses and at constant strain rates corresponding to strain rates in steady-state creep for the same stresses. It is found that from the point of view of increasing the residual service life at the production stage, forming to the required strain value with given kinematics is preferable to forming under the action of constant stresses for materials on whose strain-time charts for = const, the fracture strain decreases monotonically with increasing stress. Forming at constant stress is preferred for materials on whose strain-time charts for = const, the fracture strain increases monotonically with increasing stress. Calculation results for several alloys are presented.

Adiabatic Heating of Material in Elastoplastic Torsion with Finite Deformations

G. M. Sevast'yanov, A. A. Burenin
Institute of Engineering and Metallurgy, Far East Branch, Russian Academy of Sciences, Komsomolsk-on-Amur, 681005, Russia
Keywords: кручение цилиндрических стержней, конечные деформации, упругопластическая задача, связанная термопластичность, температурное разупрочнение, адиабатические условия, несжимаемый материал Муни - Ривлина, условие Треска, эффект Пойнтинга, torsion of cylindrical rods, finite deformations, elastoplastic problem, related thermoplasticity, temperature softening, adiabatic conditions, Mooney-Rivlin incompressible material, Tresca condition, Poynting effect

Abstract >>
In this paper, we study the torsion of an incompressible circular cylinder with fixed ends made of polymer material relative to the axis of symmetry taking into account adiabatic heating. The conservative deformation mechanism is determined by the elastic Mooney-Rivlin potential, and the dissipative deformation mechanism by the Tresca-Saint-Venant plastic potential. The problem is solved using multiplicative division of the total Almansi strain measure into elastic and plastic components. It is assumed that the local change in material temperature is due only to plastic dissipation. The thermal deformation of the material and hardening are neglected. The exact solution of the problem is obtained for an arbitrary dependence of the mechanical characteristics of the material on temperature. In particular, the axial force, the torque, and the temperature distribution in the sample as a function of increasing loading parameter are determined. The obtained solution is compared with the available experimental data.

Fracture of Quasi-Brittle Geomaterial with a Circular Hole under Non-Uniformly Distributed Compression

S. V. Suknev
Chersky Institute of Mining of the North, Siberian Branch, Russian Academy of Sciences, Yakutsk, 677980, Russia
Keywords: хрупкое разрушение, квазихрупкое разрушение, геоматериалы, масштабный эффект, концентрация напряжений, отверстие, нелокальные критерии разрушения, brittle fracture, quasi-brittle fracture, geomaterials, size effect, stress concentration, hole, nonlocal fracture criteria

Abstract >>
The influence of hole diameter on the fracture of quasi-brittle geomaterial in the stress concentration zone under non-uniformly distributed compression has been studied theoretically and experimentally taking into account the size effect. The failure load is determined using modified nonlocal criteria which are the development of the average stress criterion, the point stress criterion, and the fictitious crack criterion, and which contain a complex parameter that characterizes the size of the fracture process zone and takes into account not only the material structure, but also the plastic properties of the material, the geometry of the sample, and its loading conditions. The calculation results are compared with experimental data.

Micromechanical Model of Polycrystalline Ferroelectrelastic Material Defects

A. S. Semenov
St. Petersburg Polytechnic University of Peter the Great, St. Petersburg, 195251, Russia
Keywords: поликристаллическая пьезокерамика, точечные дефекты, диссипация, гистерезис, поверхность переключения, непропорциональное нагружение, гомогенизация, моделирование, polycrystalline piezoceramics, point defects, dissipation, hysteresis, switching surface, nonproportional loading, homogenization, modeling

Abstract >>
Constitutive equations are proposed that describe the nonlinear behavior of a polycrystalline ferroelectroelastic material and taking into account the dissipative nature of the movement of domain walls, the presence of point defects, and their effect on switching processes in the temperature range not accompanied by phase transitions. The method of two-level homogenization is used to describe the behavior of a polycrystalline ferroelectroelastic material at the macro level. Accounting for defects in the micromechanical model of ferroelectroelastic materials has significantly improved the predictive ability of the model under multiaxial loading. Comparison of the results of computations with experimental data on dielectric hysteresis curves and switching surfaces under nonproportional loading of polycrystalline piezoelectric ceramics PZT-4D, PZT-5H and BaTiO3 shows that the proposed model has good prediction accuracy.

Finite Deformation of a Panel in the Cases of Ideal Plasticity and Superplasticity

V. V. Glagolev, L. V. Glagolev, A. A. Markin
Tula State University, Tula, 300600, Russia
Keywords: конечные деформации, сверхпластичность, идеальная пластичность, режим устойчивого деформирования, логарифмический модуль скоростного упрочнения, finite deformations, superplasticity, ideal plasticity, stable deformation, logarithmic module of fast hardening

Abstract >>
Finite deformation of the panel under the influence of pressure is considered. The statement of the problem in displacements with equilibrium conditions represented via true stresses in Lagrangian coordinates is proposed. It is proven that the initial equations are satisfied when the panel is uniformly curved during deformation. The use of the previously proposed defining relation make it possible to determine a differential relationship between the laws of pressure and curvature with time at an arbitrary strain rate. Ideally plastic and superplastic deformations are considered. The dependences of pressure on the curvature and strain time are obtained at which superplasticity occurs. It is revealed that in this case that the range of stable changes in the curvature does not depend on the strain rate, and the threshold stress does not affect the time it takes to reach a given curvature of the panel.