Multiphase Systems最新文献

{"title":"Dispersed media: scattering of sound waves, stratification in swirling flows and sedimentation processes","authors":"S. Urmancheev","doi":"10.21662/mfs2022.1.008","DOIUrl":"https://doi.org/10.21662/mfs2022.1.008","url":null,"abstract":"A brief review on three problems from the multiphase media mechanics area related to the study of the dynamic behavior of disperse systems under various conditions and methods of interaction with external fields or the environment is presented. The problems are an integral part of the scientific project “Hydrodynamic effects in multiphase and thermoviscous media under wave and thermal effects”. The review is carried out in the context of the vector of development of modern research in the relevant areas. As a part of solving the problem of acoustic wave scattering by a set of spherical bubbles or drops, taking into account their sound permeability, the fast multipole method was developed to expand the possibilities of its application in the considered cases. On the basis of addition theorems for spherical wave functions, a new formula for the total scattering cross section for a set of interacting sound-permeable spheres arbitrarily located in space is obtained. An important aspect of the research was the estimation of the region in the parameter space of the problem, in which the effects of multiple scattering are significant. The second problem is related to mathematical modeling of a swirling turbulent flow containing particles of a dispersed phase. For numerical studies of temperature stratification in a vortex tube, an algorithm and a computer code were created using an orthogonalized finite-volume mesh with separation of the near-wall layer. A number of parametric studies have been carried out, in particular, the dependence of the temperature of the outgoing air in the cold diaphragm channel depending on the diameter of the diaphragm has been considered. In order to increase the efficiency of geological exploration in solving the third problem for describing the process of magmatic ore formation, a system of equations based on the methods of mechanics of multiphase media and thermohydrodynamics is proposed. The mathematical model provides for the heat exchange of the magmatic melt flow with the surrounding host rocks, as well as the release of heavy and light fractions from basaltic magma during its cooling. The results obtained in the course of the computational experiment indicate the possibility of a periodically inhomogeneous nature of the distribution of ore-forming fractions.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"5 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":"114878729","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 the spherical explosion attenuation process using aqueous foam","authors":"R. Bolotnova, E. F. Gainullina, E. A. Nurislamova","doi":"10.21662/mfs2019.2.015","DOIUrl":"https://doi.org/10.21662/mfs2019.2.015","url":null,"abstract":"The two-phase model of dry aqueous foam dynamic behavior under the strong shock wave influence is presented under assumption that the foam structure under shock loading is destroyed into a suspension of monodispersed microdrops with the formation of a gas-droplet mixture. The system of equations for the model of aqueous foam includes the laws of conservation of mass, momentum and energy for each phase in accordance with the single-pressure, two-speed, two-temperature approximations in a three-dimensional formulation, taking into account the Schiller–Naumann interfacial drag force and the Ranz–Marshall interfacial contact heat transfer. The thermodynamic properties of air and water forming a gas-droplet mixture are described by the Peng–Robinson and Mie–Grueneisen equations of state. The presence of non-uniform process in height of aqueous foam syneresis, which is due to gravitational forces, is taken into account by setting the distribution of the liquid volume fraction in the foam. An additional consideration of the syneresis process during calculating the intensity of interphase drag forces according to the Schiller–Naumann model was controlled by introducing the parameter depending on the spatial distribution of the initial liquid volume fraction of the foam. The spherical explosion is modeled in the form of the shock wave pulse whose energy coincided with the charge energy of the HE used in the experiments. The problem numerical solution is implemented using the OpenFOAM free software package based on the two-step PIMPLE computational algorithm. The numerical solution of the problem, obtained on the basis of the proposed gas-droplet mixture model, is in satisfactory agreement with the experimental data on a spherical explosion in aqueous foam. The analysis of the spherical shock wave dynamics while its propagation through aqueous foam is given. The causes of the significant decrease in the amplitude and velocity shock waves propagation in the medium under study are investigated.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"38 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":"114034496","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":"Survey of studies on degenerate boundary conditions and finite spectrum","authors":"A. M. Akhtyamov","doi":"10.21662/mfs2019.3.025","DOIUrl":"https://doi.org/10.21662/mfs2019.3.025","url":null,"abstract":"It is shown that for the asymmetric diffusion operator the case when the characteristic determinant is identically equal to zero is impossible and the only possible degenerate boundary conditions are the Cauchy conditions. In the case of a symmetric diffusion operator, the characteristic determinant is identically equal to zero if and only if the boundary conditions are false–periodic boundary conditions and is identically equal to a constant other than zero if and only if its boundary conditions are generalized Cauchy conditions. All degenerate boundary conditions for a spectral problem with a third–order differential equation y'''(x) = λy(x) are described. The general form of degenerate boundary conditions for the fourth–order differentiation operator D4 is found. 12 classes of boundary value eigenvalue problems are described for the operator D4, the spectrum of which fills the entire complex plane. It is known that spectral problems whose spectrum fills the entire complex plane exist for differential equations of any even order. John Locker posed the following problem (eleventh problem): are there similar problems for odd–order differential equations? A positive answer is given to this question. It is proved that spectral problems, the spectrum of which fills the entire complex plane, exist for differential equations of any odd order. Thus, the problem of John Locker is resolved. John Locker posed a problem (tenth problem): can a spectral boundary–value problem have a finite spectrum? Boundary value problems with a polynomial occurrence of a spectral parameter in a differential equation are considered. It is shown that the corresponding boundary–value problem can have a predetermined finite spectrum in the case when the roots of the characteristic equation are multiple. If the roots of the characteristic equation are not multiple, then there can be no finite spectrum. Thus, John Locker’s tenth problem is resolved.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"16 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":"131939899","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":"Application of free software to visualize the results of simulation of dynamic processes","authors":"I. Nasibullayev","doi":"10.21662/mfs2021.3.016","DOIUrl":"https://doi.org/10.21662/mfs2021.3.016","url":null,"abstract":"The paper presents an overview of modern free tools for dynamic visualization and gives recommendations for choosing tools depending on the research method, the form of presentation of the initial data, and the specifics of the phenomenon under study. For the convenience of using the materials of the work, the source codes are given both for the programs of computational experiments of classical problems, and for creating a graphical visualization of the simulation results. To animate the process described by analytical formulas, it is proposed to use the gif terminal of the gnuplot program or the Python visualization library. An example of applying this approach to solving the modified Verhulst-Pearl equation, which describes the change in the population under periodic external influence, is given. When studying non-stationary phenomena distributed in space, the results can be presented in video format. The problem of natural convection in a horizontal layer of fluid or gas was simulated in the program FreeFem++ for solving differential equations by the finite element method with the conversion of the results using the GhostScript and MEncoder programs into a video format. An example of using the finite difference method in modeling self-oscillating chemical reactions in the Qt environment with saving animation frames as graphic files is given. To display the results of modeling three-dimensional dynamic processes, it is proposed to use the Blender computer graphics program. Modeling and visualization of oscillations of an elastic pendulum using the built-in Blender Python API interpreter are presented. An approach is shown for dividing a computational experiment and visualizing its results, which makes it possible to increase the efficiency of the use of computational resources. A universal Python-script is proposed for constructing three-dimensional object motion trajectories based on external source data.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"66 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":"134256482","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":"Transformations of gas dynamics equations and basis operators of a admitted 11-dimensional Lie algebra","authors":"D. T. Siraeva, Y. Yulmukhametova","doi":"10.21662/mfs2020.3.133","DOIUrl":"https://doi.org/10.21662/mfs2020.3.133","url":null,"abstract":"In this paper, the gas dynamics equations are considered. The system is closed by a general equation of state. This equations describe a model of an inviscid non-heat-conducting gas motion in the absence of external force fields and external energy sources. The system is invariant under the 11-parameter group with the corresponding 11-dimensional Lie algebra. The gas dynamics equations, equations of motion, and basis operators of the Lie algebra are written in Cartesian, Cylindrical, and Spherical coordinate systems. The steps involved when changing the coordinate system are illustrated in detail.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"95 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":"114574488","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":"Using an ant algorithm to find a strategy for the behavior of a group of mobile robots on a work field with obstacles","authors":"O. Darintsev, A. Migranov","doi":"10.21662/mfs2022.3.016","DOIUrl":"https://doi.org/10.21662/mfs2022.3.016","url":null,"abstract":"A more complex solution to the problem of the distribution of tasks in a group of mobile robots, in the presence of obstacles in the workspace, is considered. The work is a continuation of a cycle of research in which the basic algorithm for solving the tasks was one of the types of ant algorithm — the multicolonial ant system method in combination with the trajectory planning algorithm implemented using the principle of dynamic programming. The task statement, the workspace model, the goals of the robots functioning and the parameters characterizing their work have been adjusted. The choice of free parameters of the ant algorithm for performing multi-criteria optimization and tuning of the solution is carried out: the number of iterations, the number of intercolonial groups of ants, the weight of the concentration of the pheromone of arcs, the weight of the heuristic attractiveness of arcs and the pheromone evaporation coefficient. The results of computational experiments conducted in the presence of static (known in advance) and dynamic (other robots) obstacles in the workspace are presented. The proposed algorithm was tested using the example of a group consisting of three robots performing 10 tasks. As shown in the results of computational experiments, robot trajectories are built on a subset of free cells of the workspace and do not intersect cells with obstacles. At the same time, the configuration of the work field affects not only the actual routes of robots, but also the redistribution of tasks between them, and the number of robots involved. Additionally, a series of computational experiments with different combinations of values of free parameters was carried out to determine the optimal ratios and implement a more efficient ant algorithm. Optimization was carried out by a single adjustment method, which allowed us to find the required values of free parameters. It is shown that the adjustment of the parameters made it possible to reduce the relative error in the synthesis of the optimal route of movement of a group of robots by 3–6 %.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"26 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":"114723466","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":"Longitudinal oscillation of a rod with a variable cross section","authors":"I. Utyashev","doi":"10.21662/mfs2019.2.019","DOIUrl":"https://doi.org/10.21662/mfs2019.2.019","url":null,"abstract":"Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"1 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":"130561025","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":"On the distortion of transmitted and reflected shock waves when interacting with a layer of a granular medium","authors":"K. Bashirova","doi":"10.21662/mfs2020.3.134","DOIUrl":"https://doi.org/10.21662/mfs2020.3.134","url":null,"abstract":"A model of a shock tube has been prepared to study the behavior of a shock wave in a curved layer of light elastic granular particles located in the center of the tube. For the given problem, a standard mathematical model is written for a two-phase system, consisting of equations of continuity, state and energy, as well as an equation for the force of interphase interaction. Computational experiments were made using the OpenFOAM package. The prepared model allowed to carry out simulations for pressure between 3×10^5 Pa and 10^5 Pa and concentration of particles 20%, which creates a shock wave. Pressure distributions were obtained at different times in different sections before and after passing through the curved layer, as well as velocity profiles in similar sections. Numerical experiments have shown that the curvature of the layer of granular particles leads to significant scattering of the wave. In addition, significant changes in the wave front were revealed in the near-wall regions after the passage of a layer of granular medium. The redistribution of the fluid flow in the near-wall region is caused by the curvature of the lower boundary of the particle layer.","PeriodicalId":309215,"journal":{"name":"Multiphase Systems","volume":"73 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":"124698358","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}