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Mathematical Modeling of Water Vapor Injection into a Saturated Porous Medium 水蒸气注入饱和多孔介质的数学建模
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602236
M. K. Khasanov, S. L. Borodin, M. V. Stolpovsky
{"title":"Mathematical Modeling of Water Vapor Injection into a Saturated Porous Medium","authors":"M. K. Khasanov, S. L. Borodin, M. V. Stolpovsky","doi":"10.1134/s1995080224602236","DOIUrl":"https://doi.org/10.1134/s1995080224602236","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A mathematical model of the process of water vapor injection into a porous reservoir containing methane is proposed, taking into account vapor condensation in the porous medium. A self-similar solution of this problem is constructed and an algorithm for its numerical solution is developed. Calculations were carried out, which showed good agreement between the self-similar and numerical solutions at a sufficiently low reservoir permeabilities. It is noted that for high-permeability reservoirs, in order to obtain adequate results, it is necessary to carry out longer-term calculations using the proposed numerical algorithm. Based on the analysis of the numerical experiment results, it is shown that when vapor is injected into a reservoir containing methane, five characteristic regions can be formed, namely: region with superheated vapor; with vapor and water in state of phase equilibrium; with methane, vapor and water in state of phase equilibrium; with methane and vapor; and region that contains only methane. Also the results of numerical experiments on the effect of vapor injection pressure and temperature on a reservoir heating are presented.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"65 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217083","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}
引用次数: 0
Application of the Wavelet Transform in the Analysis of Non-stationary Processes in Aerodynamic Experiments 小波变换在分析空气动力学实验中的非稳态过程中的应用
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602248
O. E. Kirillov
{"title":"Application of the Wavelet Transform in the Analysis of Non-stationary Processes in Aerodynamic Experiments","authors":"O. E. Kirillov","doi":"10.1134/s1995080224602248","DOIUrl":"https://doi.org/10.1134/s1995080224602248","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The article provides the technique and examples of using the wavelet transform to analyze time series with a non-stationary spectrum obtained in aerodynamic experiments. The peculiarity and novelty of this technique is the definition and use of the concept of wavelet energy as a simpler and more visual function of time, which allows analyzing the evolution of signal energy. As an example, the results of a study of the effect of anomalous passage of a high-frequency signal along a long pneumatic line are presented.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"9 6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217084","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}
引用次数: 0
Pressure Diffusion Waves in a Porous Medium Saturated by Three Phase Fluid 三相流体饱和多孔介质中的压力扩散波
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602339
R. V. Sadovnikov
{"title":"Pressure Diffusion Waves in a Porous Medium Saturated by Three Phase Fluid","authors":"R. V. Sadovnikov","doi":"10.1134/s1995080224602339","DOIUrl":"https://doi.org/10.1134/s1995080224602339","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Pressure diffusion waves in a porous medium saturated with three phase fluid are considered. The influence of frequency and saturations of phases are investigated on the governing relations for phase velocity, attenuation coefficient, wavelength, diffusion coefficient and penetration depth.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216937","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}
引用次数: 0
On Sums of Special Functions 论特殊函数之和
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602418
Yu. A. Brychkov
{"title":"On Sums of Special Functions","authors":"Yu. A. Brychkov","doi":"10.1134/s1995080224602418","DOIUrl":"https://doi.org/10.1134/s1995080224602418","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Sums of the form <span>(sum_{k=0}^{n}frac{prod_{i=1}^{p}left(a_{i}right)_{k}}{prod_{j=1}^{q}left(b_{j}right)_{k}}w^{k}{}F_{k}(z))</span> are considered<span>(,)</span> where <span>(F_{k}(z))</span> are special functions of hypergeometric type. Such sums involving Bessel, Struve, incomplete gamma functions, and Laguerre, Hermite, Jacobi, Legendre, and Chebyshev polynomials can be represented in terms of the Kampé de Fériet and generalized Horn hypergeometric functions of two variables.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216981","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}
引用次数: 0
Research of Thermal Explosion Conditions in Nonlinear Heat Conduction Problems with a Nonlinear Heat Source 带非线性热源的非线性热传导问题中的热爆炸条件研究
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602443
V. A. Kudinov, K. V. Trubitsyn, K. V. Kolotilkina, S. V. Zaytsev, T. E. Gavrilova
{"title":"Research of Thermal Explosion Conditions in Nonlinear Heat Conduction Problems with a Nonlinear Heat Source","authors":"V. A. Kudinov, K. V. Trubitsyn, K. V. Kolotilkina, S. V. Zaytsev, T. E. Gavrilova","doi":"10.1134/s1995080224602443","DOIUrl":"https://doi.org/10.1134/s1995080224602443","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Using an additional sought function (ASF) and additional boundary conditions (ABCs), an analytical solution of the nonlinear heat conduction problem for a symmetric plate with a nonlinear heat source has been obtained. ASF characterizes the temperature change over time at the center of the plate. Its usage enables the solution reduction of the original partial differential equation to the integration of a temporal ordinary differential equation (ODE). From its solution, exact eigenvalues are found, determined by classical methods from solving the Sturm–Liouville boundary value problem specified in the spatial coordinate domain. Hence, this study considers another direction of their determination, based on solving the temporal ODE with respect to ASF. ABCs are formulated in such a way that their fulfillment by the sought solution is equivalent to satisfying the original differential equation at the boundary points. It leads to its fulfillment within the considered domain, bypassing the direct integration process over the spatial variable and confining it only to the execution of the heat balance integral—the averaged original differential equation.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"132 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217031","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}
引用次数: 0
Acoustic Streaming and Heat Transfer in a Rectangular Channel with Differently Heated Horizontal Walls 带有不同加热水平壁的矩形通道中的声流和热传递
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602157
A. A. Gubaidullin, A. V. Pyatkova
{"title":"Acoustic Streaming and Heat Transfer in a Rectangular Channel with Differently Heated Horizontal Walls","authors":"A. A. Gubaidullin, A. V. Pyatkova","doi":"10.1134/s1995080224602157","DOIUrl":"https://doi.org/10.1134/s1995080224602157","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Acoustic streaming and heat transfer in a vibrating rectangular two-dimensional channel filled with gas, the vertical walls of which are thermally insulated and the horizontal walls are maintained at different temperatures, are numerically investigated. The features of the wave motion of the gas are studied. The influence of the temperature difference of the walls, amplitude and frequency of vibration on acoustic streaming and the period average temperature is determined.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"45 22 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217074","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}
引用次数: 0
Acoustics of a Viscoelastic Liquid with Perfluorocarbon Droplets in the Presence of Phase Transitions 带有全氟碳化物液滴的粘弹性液体在相变情况下的声学特性
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602169
D. A. Gubaidullin, D. D. Gubaidullina, Yu. V. Fedorov
{"title":"Acoustics of a Viscoelastic Liquid with Perfluorocarbon Droplets in the Presence of Phase Transitions","authors":"D. A. Gubaidullin, D. D. Gubaidullina, Yu. V. Fedorov","doi":"10.1134/s1995080224602169","DOIUrl":"https://doi.org/10.1134/s1995080224602169","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this work, a modified Rayleigh–Lamb equation which takes into account the radial oscillations of a perfluorocarbon droplet with a vapor bubble in the center in a viscoelastic liquid has been derived. The viscoelasticity of the carrier medium has been taken into account based on the Zener rheological model. For small inclusion oscillations, the problem of heat and mass transfer between vapor, liquid phase and carrier liquid has been solved. The energy equation has been found. Based on the obtained equations of radial oscillations of the inclusion, energy and the well-known wave equation for a bubbly liquid, the dispersion relation has been determined. For a mixture of polydimethylsiloxane with droplets of octafluoropropane C<span>({}_{3})</span>F<span>({}_{8})</span> and vapor bubbles in the center, the dependencies of the phase velocity and attenuation coefficient on the perturbation frequency have been plotted. The influence of the shear modulus and relaxation time of the elastic carrier liquid on the dynamics of acoustic waves has been illustrated.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217088","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}
引用次数: 0
The Temperature Effect on the Stress-strain State of Inelastic Torispherical Heads under Internal Pressure 温度对内压下非弹性球形封头应力应变状态的影响
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602273
V. E. Moiseeva, Z. V. Skvortsova
{"title":"The Temperature Effect on the Stress-strain State of Inelastic Torispherical Heads under Internal Pressure","authors":"V. E. Moiseeva, Z. V. Skvortsova","doi":"10.1134/s1995080224602273","DOIUrl":"https://doi.org/10.1134/s1995080224602273","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The effect of a temperature change on nonlinear axisymmetric straining of the clamped torispherical shell under internal pressure is investigated. The solution is based on the Kirchhoff–Love hypothesis, taking into account geometric and material nonlinearities. The stress-strain state is examined at cryogenic or elevated temperatures with the temperature-dependent material’s characteristics. The analysis has been performed numerically using a combination of linearization and S.K. Godunov’s orthogonal sweep methods. Shells made of alloys with various mechanical and thermophysical properties are considered. The effect of the alloy’s properties on the nature of the stress-strain state dependence of the torispherical heads on temperature is discussed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"181 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217089","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}
引用次数: 0
Evolution of Acoustic Streaming Inside and Around the Open Tube Resonator 开放管谐振器内部和周围声流的演变
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602327
P. P. Osipov, D. A. Gubaidullin, A. A. Abdyushev
{"title":"Evolution of Acoustic Streaming Inside and Around the Open Tube Resonator","authors":"P. P. Osipov, D. A. Gubaidullin, A. A. Abdyushev","doi":"10.1134/s1995080224602327","DOIUrl":"https://doi.org/10.1134/s1995080224602327","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Using the numerical integration of the equations of ideal gas dynamics, written in a conservative form in a cylindrical coordinate system, the velocity and pressure fields inside and around the tube of an open resonator are investigated at the first resonant frequency. The patterns of streamlines of instantaneous and cycle-averaged velocities, as well as the evolution of intense secondary streaming near the open end of the tube are analyzed. An intense secondary streaming inside and around the tube resonator is developed, forming toroidal vortex inside and strong jet outside the tube along the axis. Comparison of simulation results with experimental data of other authors shows good agreement.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217094","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}
引用次数: 0
Stress-strain State Analysis of Porous Elasto-plastic Size-dependent Plates Subjected to Hygro-Mechanical Loads Using the Variational Iterations Method 使用变量迭代法分析受水文机械荷载作用的多孔弹塑性尺寸相关板的应力应变状态
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224600948
A. D. Tebyakin, T. V. Yakovleva, A. V. Krysko
{"title":"Stress-strain State Analysis of Porous Elasto-plastic Size-dependent Plates Subjected to Hygro-Mechanical Loads Using the Variational Iterations Method","authors":"A. D. Tebyakin, T. V. Yakovleva, A. V. Krysko","doi":"10.1134/s1995080224600948","DOIUrl":"https://doi.org/10.1134/s1995080224600948","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this study, for the first time, a mathematical model of the stress-strain state of porous elasto-plastic size-dependent plates is constructed, taking into account hygro-mechanical loads. An original algorithm is proposed and developed. It uses the highly accurate Variational Iteration Method (VIM) or the Extended Kantorovich Method (EKM). This algorithm is applied to study stress-strain state of porous metallic Kirchhoff’s plates, taking into account elasto-plastic deformations, medium moisture and porosity. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The developed algorithm includes two nested one-to-one iteration procedures: the Variational Iteration Method and Birger’s method of variable elasticity parameter (MVEP). For each of these iterative methods there are theorems proving their convergence. Elasto-plastic deformations are considered using the deformation theory of plasticity. The proposed mathematical model and the developed algorithm provide high accuracy and computational speed in comparison to the results obtained by grid, variational and finite element methods. The effect of three porosity patterns and moisture accounting on the stress-strain state depending on the value of the size-dependent parameter is analysed.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217096","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}
引用次数: 0
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