Publishing House SB RAS:

Publishing House SB RAS:

Address of the Publishing House SB RAS:
Morskoy pr. 2, 630090 Novosibirsk, Russia

Advanced Search

Journal of Applied Mechanics and Technical Physics

2020 year, number 1

Three-Dimensional Model of the Human Bronchial Tree - Modeling of the Air Flow in Normal and Pathological Cases

A. E. Medvedev1,2, V. M. Fomin1,2, P. S. Gafurova1,2
1Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Novosibirsk State University, Novosibirsk, 630090, Russia
Keywords: бронхиальное дерево человека, бифуркация, математическая модель, ламинарное течение, сечение бронха, human bronchial tree, bifurcation, mathematical model, laminar flow, bronchus cross section

Abstract >>
The air flow in the human bronchial tree is simulated in the normal and pathological cases. Analytical formulas are derived to design the full bronchial tree. All surfaces of the bronchial tree are matched with the second order of smoothness (there are no acute angles or ribs). The geometric characteristics of the human bronchial tree in the pathological case are modeled by a “starry” shape of the inner structure of the bronchus; the pathology degree is defined by two parameters: bronchus constriction level and degree of distortion of the cylindrical shape of the bronchus. A numerical technique is proposed for stage-by-stage computing of the air motion in the human bronchial tree. A laminar air flow in the human bronchial tree is computed from the input bronchus to alveoli). It is demonstrated that the pressure decrease in the case of a laminar air flow in the bronchial tree is twice smaller than that in the turbulent case. Distortions of the cylindrical shape of the bronchi in the pathological case lead to a more significant pressure decrease in the bronchial tree.

Study of Hydrocephalus using Poroelastic Models

G. S. Yankova1,2, A. A. Cherevko1,2, A. K. Khe1,2, O. B. Bogomyakova3, A. A. Tulupov2,3
1Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk National Research State University, Novosibirsk, 630090 Russia
3International Tomographic Center, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090, Russia
Keywords: математическое моделирование, пороупругость, цереброспинальная жидкость, гидроцефалия, mathematical modeling, poroelasticity, cerebrospinal fluid, hydrocephalu

Abstract >>
The filtration of arterial, venous and capillary blood, and cerebrospinal fluid are investigated using a multiphase poroelastic model for the brain matter based on medical data. The model can be used to describe the healthy brain, the state of a brain with hydrocephalus, and the transition between them which occurs when changing model parameters.

Describing the Asymptotic Behavior of a Low-Viscosity Fluid in an Elliptical Plane with a Moving Boundary

Yu. V. Pivovarov
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: условие проскальзывания, пограничный слой, уравнение теплопроводности, завихренность, функция тока}, slip condition, boundary layer, heat equation, vorticity, current function

Abstract >>
A problem of plane-parallel steady motion of a low-viscosity incompressible fluid inside an elliptical cavity with a wall moving along its contour is under consideration. A slip condition with a constant or piecewise-constant slip function is set at the cavity boundary. This problem is solved using the method of merging asymptotic expansions. When the Reynolds number is of the order of Re=1500 and there are no corner points in the flow region, the calculation time decreases by hundreds of times compared with the case where the finite difference method is applied. The flow region is divided into an inviscid core in which vorticity is constant and a “weak” boundary layer. The equation of the “weak” boundary layer by changing variables is reduced to a heat equation whose solution is constructed in the form of a series.

Analysis of Modes in Rank Pipes with Round and Square Cross Sections of the Working Channel

I. K. Kabardin, V. I. Polyakova, M. Kh. Pravdina, N. I. Yavorskii, M. R. Gordienko
Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: вихревая труба, стабилизация, коэффициент скорости, коэффициент охлаждения, vortex tube, stabilization, velocity coefficient, cooling coefficient

Abstract >>
This study compares detailed mode maps during operation using air of two Rank pipes with round and square cross sections of the working channel in the case of identical guides at the inlet and identical outlets. The degree of air expansion and the fraction of flow rate through a cold outlet varies in ranges of 2-8 and 0.2-0.8, respectively. It is observed for both pipes that, as the degree of expansion increases, the dependences of the volumetric flow rate and the cooling coefficient on the fraction of cold flow rate become stable. It is revealed that the cooling coefficient in a round tube is 1.5-2.0 times greater than in a square channel, and the volumetric flow rate therein is approximately 10% lower.

Nonlinear Internal Waves in Multilayer Shallow Water

V. Yu. Lyapidevskii1,2, M. V. Turbin2, F. F. Khrapchenkov2,3, V. F. Kukarin4
1Lavrentyer Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Voronezh State University, Voronezh, 394018, Russia
3V.I. Il'ichev Pacific Oceanological Institute, Far Eastern Branch Russian Academy of Science, Vladivostok, 690041, Russia
4Nikolaev Institute of Inorganic Chemistry Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: многослойная мелкая вода, внутренние волны, волновой бор, натурный эксперимент, multilayer shallow water, internal waves, wave bore, field experiment

Abstract >>
Within the framework of the second approximation of the shallow water theory, the flow of a multilayer fluid stratified in density is under study. A mathematical model for the propagation of near-bottom and near-surface large-amplitude internal waves is constructed, taking into account the influence of the fine structure of thermocline (pycnocline). Using the resulting solutions describing the propagation of solitary waves and wave bores, field data are interpreted.

Suppression of the Detonation Wave with the Aid of a Multi-Component Particle Cloud

A. M. Tahsini
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Keywords: юдетонационная волна, соударение, многокомпонентное облако частиц, численное моделирование, подавление, detonation wave, impact, multi-component cloud of particles, numerical simulation, suppression

Abstract >>
The aim of this study is to investigate the effect of diversity of particles in the downstream cloud on detonation wave suppression. The multi-component two-phase model for a reacting compressible flow field including clouds of chemically inert solid particles is utilized here. The detonation wave is simulated in a stoichiometric hydrogen and oxygen mixture using a detailed full chemistry model. The finite volume scheme is used in the developed numerical program, where the advection upstream splitting method is used in addition to the Saurel method for the multi-particle cloud in order to compute the particle-phase and gas-phase fluxes. The impact of the detonation wave on the rigid wall is investigated, and the magnitude of the resulting pressure rise is accurately predicted in the case of a head-on collision of two similar waves instead of direct simulation of the wall reflection. The results demonstrate that the impact pressure rise is rather strong and destructive, and using a multi-component particle cloud may have better attenuating features for both short and long action times and require a shorter required propagation length for detonation wave suppression than using a single-component particle cloud.

Spray Interface Drag Modeling Based on the Power-Law Droplet Velocity using the Moment Theory

A. A. Majhool1, N. H. Hamza1, N. M. Jasim2
1Mechanical Engineering Department, University of Al-Qadisiyah, Ad'Diwaniya, 58001, Iraq
2Mechanical engineering department, University Of Al-Kufa, Al-Najaf, 54003, Iraq
Keywords: моменты распыления, распределение капель по размерам, распределение скоростей капель, межфазная модель сопротивления, моделирование сопротивления, spray moments, droplet size distribution, droplet velocity distribution, interfacial drag model, drag modeling

Abstract >>
Interphase momentum exchange of a polydispersed two-phase flow is numerically studied by using a model based on interfacial drag effects of a bulk liquid, ligaments, and droplets entrained in the air flow. A power-law relation is proposed between the droplet velocity and its diameter. The dispersed phase is modeled using the methodology of spray moments of the drop size distribution. All the equations are solved in a Eulerian framework using the finite volume approach, and the phases are coupled with the source terms. The proposed dependence accurately simulates the droplet behavior because droplets with larger diameters experience a higher drag and generally have higher velocities than smaller droplets. The model shows reasonable agreement with experimental and numerical data on the spray tip penetration and Sauter mean radius.

Numerical Investigation on the Effects of the Deposit Height and Position on the Film Cooling Efficiency

A. Guelailia1,2, A. Khorsi2, S. A. Slimane1,2, M. M. Bencherif2,3, K. Gourssma2
1Centre of Satellite Development (CDS), Space Mechanical Research Department, BP 4065 Ibn Rochd USTO, Oran, Algeria
2Laboratory of Applied Mechanics, Faculty of Mechanical Engineering, University of Sciences and Technology Mohamed Boudiaf, BP 1505, El M'Nouar, 31001 Oran, Algeria
3Ecole Nationale Polytechnique d'Oran Maurice Audin, Route d'Es-Senia, B.P. 1523 El M'Naouer 31000, Oran, Algerie
Keywords: вычислительная гидродинамика, тепломассообмен, турбулентность, тепловая защита, сопло ракеты, пленочное охлаждение, отложение, computational fluid dynamics, heat and mass transfer, turbulence, thermal protection, rocket nozzle, film cooling, deposit

Abstract >>
The main objective of this study is to analyze the effect of the solid deposits downstream of the injection hole on the film cooling efficiency by highlighting the impact of several geometrical and physical parameters, such as the blowing ratio, deposit position, and deposit height, by using the ANSYS CFX software. Several configurations are tested by changing the deposit position and deposit height. The turbulence is approximated by the shear stress transport (SST) model. The film cooling effectiveness distributions are presented for different blowing ratios. The numerical results are compared with available experimental data, and good agreement is noted.

Influence of Thermal Treatment on the Destruction of a Weld of an Al-Cu-Li Aircraft Alloy at Different Temperatures

E. V. Karpov1, A. G. Malikov2, A. M. Orishich2, B. D. Annin1
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
2Khristianovich Institute of Theoretical and Applied Mechanics, Novosibirsk, 630090, Russia
Keywords: лазерная сварка, алюминиево-литиевый сплав, термообработка, локализация пластических деформаций, влияние температуры, laser welding, aluminum-lithium alloy, thermal treatment, plastic strain localization, temperature effect

Abstract >>
Results of an experimental study of how temperature affects the destruction of laser welds of an Al-Cu-Li aircraft aluminum alloy are presented. A comparison is made of the deformation and fracture of welds in the initial state and after two-stage thermal treatment. It is shown that the mechanical characteristics of welded samples have values close to those of the initial alloy.

On the Construction of Constitutive Equations for Orthotropic Materials with Different Properties under Tension and Compression in Creep

I. A. Banshchikova
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: конструкционные сплавы, ортотропия, разносопротивляемость растяжению и сжатию, ползучесть, плоское напряженное состояние, сдвиг, кручение стержней с кольцевым сечением, минимум дополнительного рассеяния, structural alloys, orthotropy, different resistance in tensile and compression, creep, plane stress state, shear, torsion of annular cross-section rods, additional dissipation power

Abstract >>
Constitutive steady-state creep equations are proposed for orthotropic materials with different tensile and compressive resistance properties. Power functions with different exponents for tension and compression are used to describe the resistance. The equations of the problems of tension and shear and the equations of the plane stress problem are given. The model is used to solve the problem of torsion of annular cross-section rods cut from a plate of AK4-1 transversally isotropic alloy in the normal and longitudinal directions by a constant moment at a temperature T = 200oC. Constitutive equations for torsion are obtained. Values of model parameters were obtained in experiments on uniaxial tension and compression of solid round samples cut in various directions. An analytical solution for the rate of torsion angle of an annular cross section rod cut in the normal direction of the plate was obtained for the same exponent index under tension and compression. For a rod cut in the longitudinal direction of the plate, an upper bound of the rate of torsion angle was obtained. The calculation results are in satisfactory agreement with the experimental data.

Viscoelastic-Plastic Deformation of Plates with Spatial Reinforcement Structures

A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: пластины, пространственное армирование, плоское армирование, динамический изгиб, теория Редди, вязкоупругопластическое деформирование, тело Максвелла - Больцмана, схема типа "крест", plates, spatial reinforcement, flat reinforcement, dynamic bending, Reddy theory, viscoelastic-plastic deformation, Maxwell-Boltzmann body, "cross" type scheme

Abstract >>
A mathematical model of viscoelastic-plastic flexural deformation of spatially reinforced plates was developed based on the method of time steps. The viscoelastic behavior of the components of the composition is described by the Maxwell-Boltzmann equations, and plastic behavior by flow theory with isotropic hardening. The low resistance of composite plates to transverse shear is taken into account within the framework of Reddy's theory, and the geometric nonlinearity of the problem is considered in the Karman approximation. The corresponding initial-boundary-value problem is solved using a numerical scheme of the “cross” type. The dynamic viscoelastic plastic bending of spatially reinforced fiberglass rectangular plates under the influence of an air blast wave was investigated. It is shown that for relatively thick plates, replacing a flat reinforcement structure by spatial leads to a significant decrease in the maximum and residual deflections and strain intensities of the binding material, while for relatively thin plates, this replacement is ineffective. It is found that in the initial stage of deformation, the amplitude of oscillation of the composite plate significantly exceeds the residual deflection.

Delamination of a Coating Lying on an Elastic Base

A. O. Vatul'yan, K. L. Morozov
Southern Federal University, Rostov-on-Don, 344006, Russia
Keywords: покрытие на упругом основании, отслоение, трансцендентное уравнение, закритическое поведение, метод Ритца, elastic coating, delamination, transcendental equation, supercritical behavior, Ritz method

Abstract >>
Known models were used to investigate the delamination of a pre-compressed coating from an elastic base, to study in detail the corresponding transcendental equation, prove the existence of a solution in a certain range of parameter values, and obtain simple formulas for the critical value. The supercritical behavior of the coating was studied using the linearization procedure and the Ritz method. It was proposed to simplify the problem by solving the problem for a beam with Winkler type boundary conditions in the delamination area, and an assessment of this simplification was made.

Investigation of Mechanical Properties and Mode I Cohesive Failure of the Adhesive Layer in Sandwich Beams with a Cellular Core

M. Shishesaz, M. Dehghani, M. Hasanvand
Shahid Chamran University of Ahvaz, Ahvaz, Iran
Keywords: ячеистый заполнитель, трещина нормального отрыва, связующий слой, метод конечных элементов, cellular core, mode I fracture, cohesive crack, finite element method

Abstract >>
The effect of the cellular core on the stress intensity factor at the tip of a crack in the adhesive layer of a five-layer sandwich composite beam is investigated. A Nomex sheet is used to model the cellular core with honeycomb, square, and triangular cells. The mechanical properties of these cells are obtained by the finite element analysis supported by theoretical two- and three-dimensional equations. Based on the deduced properties, the load-displacement curve is generated for a sandwich beam under mode I fracture. The numerical findings are validated against available experimental data. It is shown that the lowest values of the stress intensity factor are observed for a core with a honeycomb structure as compared to the other two cell shapes used in this study, which are composed of equilateral triangles or squares. An increase in the wall thickness of the cells leads to an increase in the stress intensity factor.

Numerical Method for Determining a Stress Intensity Factor in the Case of Solids of Homogeneous and Heterogeneous Materials with a Crack

V. M. Tikhomirov
Siberian State University of Railway Engineering, Novosibirsk, 630049 Russia
Keywords: коэффициент интенсивности напряжений, трещина на границе раздела двух сред, асимптотическое решение, метод конечных элементов, stress intensity factor, crack at the interface between two media, asymptotic solution, finite element method

Abstract >>
Algorithms for determining the stress intensity factor are developed on the basis of the results of the analysis of asymptotic solutions to the problems of deformation of a homogeneous solid with a cut and a plate with a crack located at an interface between two media,. The proposed algorithms are used to calculate stress intensity coefficients using the results of a numerical solution of the problems of loading various flat and spatial homogeneous cracked solids, as well as a plate with a crack located at the interface between two elastic media. It is shown that the calculation results are in good agreement with the data obtained by other methods.

Extension of the GГјnter Derivatives to the Lipschitz Domains and Application to the Boundary Potentials of Elastic Waves

A. Bendali1, S. Tordeux2, Yu. M. Volchkov3,4
1UniversitГ©de Toulouse, Institut MathГ©matique de Toulouse, Toulouse, France
2UniversitГ© de Pau et des Pays de l'Adour, Pau, France
3Lavrent'ev Institute for Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
4Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: граничные интегральные операторы, производные Гюнтера, упругие волны, поверхностные потенциалы, липшицевы области, boundary integral operators, GГјnter derivatives, elastic waves, layer potentials, Lipschitz domains

Abstract >>
Regularization techniques for the trace and the traction of elastic waves potentials previously built for domains of the class C2 are extended to the Lipschitz case. In particular, this yields an elementary way to establish the mapping properties of elastic wave potentials from those of the scalar Helmholtz equation without resorting to the more advanced theory for elliptic systems in the Lipschitz domains. Scalar Günter derivatives of a function defined on the boundary of a three-dimensional domain are expressed as components (or their opposites) of the tangential vector rotational Δ δ Ωu × n of this function in the canonical orthonormal basis of the ambient space. This, in particular, implies that these derivatives define bounded operators from Hs to Hs-1 (0 ≤ s ≤ 1) on the boundary of the Lipschitz domain and can easily be implemented in boundary element codes. Representations of the Günter operator and potentials of single and double layers of elastic waves in the two-dimensional case are provided.