Рамиль Рифгатович Сираев, Дмитрий Анатольевич Брацун
{"title":"Возбуждение релаксационных колебаний на искривленной межфазной границе в условиях внутренней задачи","authors":"Рамиль Рифгатович Сираев, Дмитрий Анатольевич Брацун","doi":"10.7242/1999-6691/2024.17.1.8","DOIUrl":"https://doi.org/10.7242/1999-6691/2024.17.1.8","url":null,"abstract":"The oscillatory mode of solutal Marangoni convection during the absorption of a surfactant from a homogeneous external solution into a water droplet is studied numerically. This is caused by the effect of gravity, which promotes the sedimentation of surfactant molecules in an aqueous medium. This version of oscillatory convection arising under the conditions of an internal problem was recently discovered experimentally. In the present paper, we consider the case of a chemically inert system, in which there are no reactions. The effects of interfacial deformation are assumed to be insignificant and thus they are neglected. The mathematical model includes the Navier—Stokes equations written in the Hele-Shaw and Boussinesq approximations, and the equations of surfactant transport in the system. We assume that the characteristic time of surfactant adsorption is shorter than the time of its diffusion in both solutions, which makes it possible to ignore the formation of a surface phase. The boundary value problem includes the equilibrium condition of the system, which takes into account different values of the chemical potential in the phases. It is shown that a water droplet is a surfactant accumulator that diffuses from the organic phase. The problem is solved in dimensional form using the COMSOL Multiphysics package and based on a set of physical constants for acetic acid which, like many other members of the carboxylic acid family, has the properties of surfactant in water. It was found that direct numerical simulation of the system is able to reproduce the relaxation oscillations observed in the experiment only under the additional phenomenological assumption of non-Newtonian rheology of the interface, which was previously proposed for the external problem. The physical mechanism which may be responsible for the delayed onset of Marangoni instability is discussed. We demonstrate that periodic oscillations are generated inside the drop due to the competition between the Marangoni effect and the gravity-dependent convective instability of the solution. Using direct numerical simulation, we identified the structures of convective motion at the interface and in its neighborhood, determined the flow intensity as a function of time, and obtained the range of change in the oscillation period.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"111 50","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140987015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling the piezoelectric effect in a composite polymer film filled with disperse piezoelectric","authors":"Олег Валерьевич Столбов, Юрий Львович Райхер","doi":"10.7242/1999-6691/2023.16.4.43","DOIUrl":"https://doi.org/10.7242/1999-6691/2023.16.4.43","url":null,"abstract":"Mesoscopic modelling of a composite material constituted by an electroneutral polymer (matrix) film filled with micropowder of piezoelectric ceramics (filler) is presented. The calculation scheme resembles that of the RVE (Representative Volume Element) method. The representative element (cell) is a right-angle prism with square cross-section, the height of which is equal to the film thickness. Around the midsection of the prism, there are a few (from 2 to 4) spherical piezoelectric particles positioned close to one another. The length of the base side of the prism is determined from the assumed solid phase content of the composite. To simulate the film, the cells are arranged in a continuous flat layer, inside which they are coupled by means of periodic boundary conditions imposed on their lateral surfaces. To reduce the artifacts of the model, the position of the center of each particle is chosen randomly within the area of the prism cross-section. In the framework of this approach, a low-density polyethylene film with embedded barium titanate particles is considered as an example. One of the surfaces of the film is fixed (no displacements), and the other one is left free. For the characteristics of the particles close to those used in the experiment and the typical matrix material parameters (elasticity moduli, Poisson coefficients, dielectric permittivity), the voltage output (piezoeffect) induced in the film in response to the uniform pressure applied to its free surface is evaluated. It is shown that the electric potential along the thickness of the film is nonuniform: it grows inside the particles and falls down in the interparticle gap. In order to present the results in the form applicative for comparison with the experimental data, for each variant of the system (number of the particles, weight fraction of the solid phase), the calculated values are averaged over a few tens of realizations of the particle positions inside the element.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"31 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Владимир Сергеевич Озерных, Геннадий Леонидович Лосев, Ефим Гольбрайх, Илья Владимирович Колесниченко
{"title":"Initial stage of formation of vortex flow in an inductor with counter-rotating magnetic fields","authors":"Владимир Сергеевич Озерных, Геннадий Леонидович Лосев, Ефим Гольбрайх, Илья Владимирович Колесниченко","doi":"10.7242/1999-6691/2023.16.4.41","DOIUrl":"https://doi.org/10.7242/1999-6691/2023.16.4.41","url":null,"abstract":"In this article, unsteady flows of electrically conductive fluid in a cylindrical cavity under the action of differently directed rotating magnetic fields are investigated. The relevance of the study is due to the presence of such a flow in the flow meter for liquid-metal heat carrier which is currently under development. The subject of study is the process of formation of the spin-up flow stage in a combined inductor of a rotating magnetic field. The acceleration or the spin-up stage is characterized by a significant change in the angular velocity of the liquid and begins with the formation of low pressure areas due to centrifugal forces. The alternation and movement of low and high pressure areas lead to velocity pulsations. For small values of the control parameter, which is the Taylor number, the flow energy gradually increases. In this case, the steady flow consists of two azimuthal and several poloidal vortices with clearly defined structures. When the Taylor number exceeds a critical value, strong pulsations occur in the flow, resulting in the decay of large-scale vortices. The intensity of the current is characterized by the Reynolds number. A power-law relationship with an exponent of 1.57 has been established between the Reynolds and Taylor numbers. It has been found that the time of formation of a steady flow varies from several seconds to tens of seconds, depending on the value of the Taylor number. The estimates of the control parameters have been obtained for a flowmeter operating in a typical mode. It has been shown that for the correct measurement of flow velocity in the flowmeter, it is necessary that that the Taylor numbers be higher than 108. The study is carried out using mathematical modeling and the obtained results are verified by experiment. The average calculated profiles are located within the confidence intervals of the experimental profiles.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"25 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Александр Ованесович Ватульян, Сергей Анатольевич Нестеров
{"title":"Об особенностях идентификации переменных термомеханических характеристик функционально-градиентного прямоугольника","authors":"Александр Ованесович Ватульян, Сергей Анатольевич Нестеров","doi":"10.7242/1999-6691/2023.16.4.42","DOIUrl":"https://doi.org/10.7242/1999-6691/2023.16.4.42","url":null,"abstract":"The inverse thermoelastic problem of identification of the variable properties of a functionally graded rectangle is studied. Unsteady vibrations are excited by applying mechanical and thermal loads to the upper side of the rectangle. To solve the direct problem in Laplace transforms, the method of separation of variables and the shooting method for harmonics are used. Transformants are inverted by expanding the origin in terms of shifted Legendre polynomials. The method proposed for solving the direct problem is verified by comparison with a finite element solution. The influence of the laws of change of variable characteristics on the boundary physical fields is analyzed. The displacement components give additional information on the mechanical loading, and the temperature measured on the upper side of the rectangle over a certain time interval – on the thermal loading. Assuming that the additional information admits expansion in Fourier series, the two-dimensional inverse problem is reduced to one-dimensional problems for various harmonics. The solution of the obtained nonlinear inverse problems is carried out on the basis of an iterative process, at each stage of which, in order to find corrections for thermomechanical characteristics, systems of Fredholm integral equations of the 1st kind are solved. The possibility of simultaneous reconstruction of several characteristics is investigated. The results of computational experiments on the phased reconstruction of thermomechanical characteristics are presented. The influence of the thermomechanical coupling parameter on the results of the thermal stress coefficient reconstruction was clarified.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"50 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139450796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Numerical investigation of fluid dynamics phenomena in external gear pump","authors":"R. A. Bilalov, O. Smetannikov","doi":"10.7242/1999-6691/2020.13.4.37","DOIUrl":"https://doi.org/10.7242/1999-6691/2020.13.4.37","url":null,"abstract":"A three-dimensional numerical model able to describe the performance of a gear pump taking into account turbulence and cavitation is presented. The computational model is implemented in the ANSYS CFX software package. As a method for modeling moving boundaries (taking into account the rotation of gears), the method of \"immersed solid\" is chosen. A homogeneous two-phase model is used to describe the flow of a viscous incompressible fluid with the formation of cavitation. The adequacy of the developed model is checked; the analysis of the numerical stability and convergence of the solution is carried out. With this model, a number of computational experiments were carried out at the experimental design stage to create a fuel system for a promising gas turbine engine. The technical characteristics of the pump, such as the flow rate, presence and degree of cavitation, were checked. Simulation results for different pump operating modes are analyzed. Comparison of the numerical results for single-phase and two-phase flow is performed. The places of cavitation formation and its level are shown and justified. The localization and volume of cavitation areas, cavitation concentration, and the level of its possible influence on the consumable-technical and strength characteristics of the product are examined in relation to the rotational speed of gears. It has been found that cavitation areas are formed, especially, at high gear speeds. The simulation results are presented in the form of graphical functional dependencies and contour plots. The developed numerical model of the gear pump makes it possible to carry out computational experiments instead of expensive full-scale ones, and to give recommendations for preventive improvement of the design, even before the manufacture of prototypes of the product.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114434418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Sukhinov, I. Y. Kuznetsova, A. Chistyakov, E. Protsenko, Y. Belova
{"title":"Study of the accuracy and applicability of the difference scheme for solving the diffusion-convection problem at large grid Péclet numbers","authors":"A. Sukhinov, I. Y. Kuznetsova, A. Chistyakov, E. Protsenko, Y. Belova","doi":"10.7242/1999-6691/2020.13.4.34","DOIUrl":"https://doi.org/10.7242/1999-6691/2020.13.4.34","url":null,"abstract":"The work is devoted to the study of a difference scheme for solving the diffusion-convection problem at large grid Peclet numbers. The suspension transport problem numerical solving is carried out using the improved Upwind Leapfrog difference scheme. Its difference operator is a linear combination of the operators of Upwind and Standard Leapfrog difference schemes, while the modified scheme is obtained from schemes with optimal weighting coefficients. At certain values of the weighting coefficients, this combination leads to mutual compensation of approximation errors, and the resulting scheme gets better properties than the original schemes. In addition, it includes a cell filling function that allows simulating problems in areas with complex geometry. Computational experiments were carried out to solve the suspension transport problem, which arises, for example, during the propagation of suspended matter plumes in an aquatic environment and changes in the bottom topography due to the deposition of suspended soil particles into the sediment during soil unloading into a reservoir (dumping). The results of modeling the suspension transport problem at various values of the grid Peclet number are presented. The algorithm implementation was carried out using the software and hardware architecture of parallel computing: on a central processing unit (Central Processing Unit - CPU) and on a graphics accelerator (Graphics Processing Unit - GPU). The solution to the applied problem has shown its efficiency on the CPU with small computational grids and, if it is necessary to decrease the space steps, then the GPU solution is preferable. It was found that, when using the modified Upwind Leapfrog scheme, an increase in the speed of the water flow does not lead to a loss of solution accuracy due to dissipative sources and is accompanied by an insignificant increase in computational labor costs.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131971137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability of the interface between two thin liquid layers under tangential high frequency vibrations","authors":"G. Khilko","doi":"10.7242/1999-6691/2019.12.4.31","DOIUrl":"https://doi.org/10.7242/1999-6691/2019.12.4.31","url":null,"abstract":"In this paper, a system of two equally thin layers of immiscible incompressible isothermal ideal liquids under high frequency horizontal harmonic vibrations is considered theoretically. The vessel containing the liquids is assumed to be closed, of rectangular form with weakly-deformable side borders and infinitely long in horizontal direction. Previous studies showed that, for significantly thin layers, the main instability in the system, oscillatory Kelvin-Helmholtz instability, should be the long-wave instability. Therefore, the problem was solved analytically using “shallow water” approximation. For all equations, a formal expansion with respect to two small parameters was used: one associated with a small ratio of the vertical to horizontal scale and another with small perturbations of the flat interface. Evolutionary equations were derived for the interface in the main order of expansion for vibration intensity less than a threshold value for oscillatory Kelvin-Helmholtz instability (subcritical area). The solutions found for these evolutionary equations correspond to traveling waves with soliton or cnoidal interfacial surface. The soliton profile is a limiting case of the cnoidal profile. The maximum speed of these waves was determined. It was demonstrated that the obtained solutions exist only in the subcritical area of parameters and from the critical level subcritical bifurcation emerges. For special case of traveling waves in a quasi-stationary mode (i.e. with static interface) also referred to as a “frozen wave”, a numerical analysis of linear stability was performed using a Fourier series expansion in a horizontal coordinate. The instability of quasi-stationary modes to small disturbances was demonstrated.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126462458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling of grain-boundary diffusion under nonstationary heating conditions","authors":"M. V. Chepak-Gizbrekht, A. Knyazeva","doi":"10.7242/1999-6691/2019.12.1.6","DOIUrl":"https://doi.org/10.7242/1999-6691/2019.12.1.6","url":null,"abstract":"Grain boundary diffusion appreciably affects the physicomechanical and chemical properties of constructional materials. Experimental studies show that transfer processes run more intensively in materials with a larger area of internal boundaries. For these materials, the temperature required for diffusion activation is reduced. Much attention is paid to grain-boundary diffusion in such areas as materials science, physics and chemistry of metals, and metal science. However, there are practically no published works where the diffusion along the grain boundaries and phases under non-isothermal conditions has been studied. This work presents a two-dimensional model of alloying element redistribution from the amorphous coating into the substrate. The substrate is represented by alternating grains with a clear selection of the triple junction. The areas adjacent to the grain boundaries are clearly selected in the model and have a finite thickness. Different ratios between the grain sizes and the boundaries widths relate to diffusion in micro- and nanocrystalline materials. The redistribution of the alloying element is initiated by one or several thermal pulses associated with the action of the electron beam. It is taken into account when the heat part of the problem has been formulated that the typical scales of the heat and diffusion processes are essentially different. The diffusion problem takes into account the temperature dependence of the diffusion coefficients in the volume of grains and along the boundaries between them. The problem was solved numerically. Varying the parameters of the model, it was found by that the ratio of activation energies in the phases has the greatest influence on the diffusant distribution. Pulsed treatment compared to treatment with constant heating results in slower leads to a slow down of diffusion along the grain boundaries. The simulation results are qualitatively consistent with the data found in the literature.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123829175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-isothermal mechanodiffusion model of the initial stage of penetration of particle flow in a target surface","authors":"E. Parfenova, A. Knyazeva","doi":"10.7242/1999-6691/2019.12.1.4","DOIUrl":"https://doi.org/10.7242/1999-6691/2019.12.1.4","url":null,"abstract":"Представлена в неизотермическом приближении связанная математическая модель начальной стадии процесса внедрения частиц в поверхность металла. Предполагается, что имплантируемые частицы в момент столкновения с мишенью обладают энергией, достаточной для генерации упругих механических возмущений, которые влияют на перераспределение имплантируемого материала. В общем случае модель включает уравнения неразрывности, теплопроводности, баланса для внедряемого компонента и уравнение движения. Определяющие соотношения соответствуют теории обобщенной термоупругой диффузии. В модели учитываются конечность времен релаксации к термодинамическому равновесию потоков тепла и массы и взаимодействие волн разной физической природы (волн концентрации примеси, волн напряжений (деформаций) и температуры). Подробно описаны упрощающие приближения, процесс обезразмеривания уравнений модели и метод их решения. Задача реализована численно с использованием метода прогонки. Приведены примеры решения связанной задачи для системы материалов Mo(Ni). Детально процессы внедрения и перераспределения примеси в поверхностном слое мишени рассмотрены в моменты времени, меньшие и большие значений относительных времен релаксации потоков тепла и массы. Установлено, что с течением времени взаимодействие процессов проявляется по-разному. Показано, что взаимовлияние волн различной физической природы приводит к распределениям температуры и концентрации, которые не отвечают классическим представлениям, следующим из моделей с законами Фурье и Фика. В работе продемонстрированы искажения волн деформации и температуры, которые и свидетельствуют о взаимодействии исследуемых процессов. Выявлено, что чем ближе текущий момент времени к относительному времени релаксации потока массы и времени действия внешнего импульса, тем заметнее меняются профили волн.","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124409390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Sokovikov, M. Simonov, V. Oborin, V. Chudinov, S. Uvarov, O. Naimark
{"title":"Study of localized shear failure of AMg6 alloy specimens under static and dynamic loading","authors":"M. Sokovikov, M. Simonov, V. Oborin, V. Chudinov, S. Uvarov, O. Naimark","doi":"10.7242/1999-6691/2021.14.3.25","DOIUrl":"https://doi.org/10.7242/1999-6691/2021.14.3.25","url":null,"abstract":"","PeriodicalId":273064,"journal":{"name":"Computational Continuum Mechanics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114648357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}