This paper is a follow-up to the first author’s series of works about shape modeling of orthotropic elastic material that takes the equilibrium form inside the area with the specified boundaries. M.S. Bukhtyak, in a number of his publications of 20162020, proposed an approach to the model building based on the application of surfaces with a constant ratio of principal curvatures. These surfaces are named pseudo-minimal surfaces. The theorem of existence has been demonstrated and the finitely-element model has been built. The condition distinguishing the class of pseudo-minimal surfaces, as applied to ruled surfaces, is either satisfied identically (trivial subclasses) or is satisfied along a family of lines. The corresponding classes of ruled surfaces have been comprehensively characterized geometrically. A partial differential equation that defines (in the local sense) the class of pseudo-minimal surfaces is very complex for analysis, which makes it relevant to consider approximate solutions. The current paper considers the pseudo-minimal surfaces of revolution. Generation of the approximate solutions is complicated by the tendency of the formal Taylor polynomial to diverge. However, the approximate solutions (of course, not ideal) have been generated. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
{"title":"Pseudo-minimal surfaces of revolution","authors":"M. S. Bukhtyak, Dmitrii E. Yesipov","doi":"10.17223/19988621/76/1","DOIUrl":"https://doi.org/10.17223/19988621/76/1","url":null,"abstract":"This paper is a follow-up to the first author’s series of works about shape modeling of orthotropic elastic material that takes the equilibrium form inside the area with the specified boundaries. M.S. Bukhtyak, in a number of his publications of 20162020, proposed an approach to the model building based on the application of surfaces with a constant ratio of principal curvatures. These surfaces are named pseudo-minimal surfaces. The theorem of existence has been demonstrated and the finitely-element model has been built. The condition distinguishing the class of pseudo-minimal surfaces, as applied to ruled surfaces, is either satisfied identically (trivial subclasses) or is satisfied along a family of lines. The corresponding classes of ruled surfaces have been comprehensively characterized geometrically. A partial differential equation that defines (in the local sense) the class of pseudo-minimal surfaces is very complex for analysis, which makes it relevant to consider approximate solutions. The current paper considers the pseudo-minimal surfaces of revolution. Generation of the approximate solutions is complicated by the tendency of the formal Taylor polynomial to diverge. However, the approximate solutions (of course, not ideal) have been generated. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84135988","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}
In this paper, the regions of orbital resonances 1:5, 1:7, 1:9, 1:10, and 1:11 at the Earth's rotation speed are considered. The motion of objects is simulated using the improved software package "Numerical Model of the Motion of AES Systems" on the SKIF Cyberia cluster of the National Research Tomsk State University. The modeling is performed with account for the effect of geopotential harmonics up to a degree and order of 10, as well as the attraction of the Moon and Sun. As a result, the maps of the distribution of orbital resonance multiplets and the MEGNO maps have been obtained for each region. All the regions are examined for the presence of real objects. The obtained data show that the chaotization of motion in the regions 1:5, 1:7, and 1:9 occurs due to the superposition of other different resonances on the second component of the orbital resonance. In the regions 1:10 and 1:11, the orbital resonance does not affect the chaotization of motion. All real objects located in the regions under consideration are not exposed to the effect of orbital resonances.
{"title":"Investigation of dynamics of a region with high-order orbital resonances","authors":"Evgeniya V. Blinkova, T. Bordovitsyna","doi":"10.17223/19988621/79/5","DOIUrl":"https://doi.org/10.17223/19988621/79/5","url":null,"abstract":"In this paper, the regions of orbital resonances 1:5, 1:7, 1:9, 1:10, and 1:11 at the Earth's rotation speed are considered. The motion of objects is simulated using the improved software package \"Numerical Model of the Motion of AES Systems\" on the SKIF Cyberia cluster of the National Research Tomsk State University. The modeling is performed with account for the effect of geopotential harmonics up to a degree and order of 10, as well as the attraction of the Moon and Sun. As a result, the maps of the distribution of orbital resonance multiplets and the MEGNO maps have been obtained for each region. All the regions are examined for the presence of real objects. The obtained data show that the chaotization of motion in the regions 1:5, 1:7, and 1:9 occurs due to the superposition of other different resonances on the second component of the orbital resonance. In the regions 1:10 and 1:11, the orbital resonance does not affect the chaotization of motion. All real objects located in the regions under consideration are not exposed to the effect of orbital resonances.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81536795","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}
The problem of an unsteady temperature field during two-dimensional fluid filtration in a multilayer reservoir is investigated taking into account the barothermal effect, radial and vertical permeability inhomogeneities. The results of comparing the analytical and numerical calculations of the temperature changes of the fluid flowing from the reservoir for two various models of reservoir heterogeneity are presented. From the obtained results it follows that 1. The presence of radial inhomogeneity of permeability in the near-well zone of the layered formation leads to fluid flows between the layers, which affects the temperature change rate of the liquid flowing from individual layers. 2. Non-stationary temperature profiles over the thickness of the layered formation at low inflow times contain information about the flows between the layers due to radial inhomogeneity in the near-well zone of the formation. 3. Flows between layers lead to large errors in solving the inverse problem of estimating the distribution of permeability in the reservoir based on non-stationary temperature data. 4. The presence of flows between the layers does not exclude the possibility of estimating the radius of the contamination zone. 5. To correctly account for the influence of flows between layers when calculating the nonstationary temperature in a layered formation with a disturbed near-well zone, it is necessary either to use a two-dimensional numerical model of non-isothermal filtration or to change the algorithm for correcting the layer’s flow rate for short and long inflow times in the onedimensional analytical model.
{"title":"Investigation of nonisothermal two-dimensional filtration in multylayer reservoir","authors":"D. Islamov, A. Ramazanov","doi":"10.17223/19988621/75/9","DOIUrl":"https://doi.org/10.17223/19988621/75/9","url":null,"abstract":"The problem of an unsteady temperature field during two-dimensional fluid filtration in a multilayer reservoir is investigated taking into account the barothermal effect, radial and vertical permeability inhomogeneities. The results of comparing the analytical and numerical calculations of the temperature changes of the fluid flowing from the reservoir for two various models of reservoir heterogeneity are presented. From the obtained results it follows that 1. The presence of radial inhomogeneity of permeability in the near-well zone of the layered formation leads to fluid flows between the layers, which affects the temperature change rate of the liquid flowing from individual layers. 2. Non-stationary temperature profiles over the thickness of the layered formation at low inflow times contain information about the flows between the layers due to radial inhomogeneity in the near-well zone of the formation. 3. Flows between layers lead to large errors in solving the inverse problem of estimating the distribution of permeability in the reservoir based on non-stationary temperature data. 4. The presence of flows between the layers does not exclude the possibility of estimating the radius of the contamination zone. 5. To correctly account for the influence of flows between layers when calculating the nonstationary temperature in a layered formation with a disturbed near-well zone, it is necessary either to use a two-dimensional numerical model of non-isothermal filtration or to change the algorithm for correcting the layer’s flow rate for short and long inflow times in the onedimensional analytical model.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74592270","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}
One of the most important problems in the design of modern aircrafts is the study of the force effects of high-energy flows on the elements of their structures and on the aircraft as a whole. Aeroballistic installations are widely used as a research tool. Determination of the drag force coefficient is the main task of experimental ballistics from which aerodynamic studies begin. The studies are designed to determine the drag coefficient of missiles having different aerodynamic shapes, which can be used in rocket science, artillery, and other areas of technology involved in the study of the movement of bodies in gaseous and liquid media. A feature of the aeroballistic method for determining the coefficient of drag force is that, in order to obtain values of CXO of a given accuracy, experiments can be carried out only with bodies that are stable during the whole time of movement in the studied section of the trajectory. The research is aimed at solving the problem of calculating the drag coefficient of bodies using trajectory data on their coaxial movement. During the ballistic test, the body is sequentially photographed relative to a fixed coordinate system, coordinates of its characteristic points and the time between the moments of photographing are recorded, and the displacements of the characteristic points of the body relative to the moving coordinate system associated with the base body performing a rectilinear motion with a zero angle of attack, are simultaneously measured. In this case, the base body is axially and movably connected to the body under study. It is shown that the applied group motion effect allows, within the framework of the accepted assumptions, to increase the accuracy and simplify the determination of the drag force coefficient of bodies of a complex geometric shape.
{"title":"Technique for the experimental determination of the force coefficient of the frontal co-resistance of unstable in flight bodies","authors":"V. Bimatov, V. Kudentsov, V. I. Trushlyakov","doi":"10.17223/19988621/75/6","DOIUrl":"https://doi.org/10.17223/19988621/75/6","url":null,"abstract":"One of the most important problems in the design of modern aircrafts is the study of the force effects of high-energy flows on the elements of their structures and on the aircraft as a whole. Aeroballistic installations are widely used as a research tool. Determination of the drag force coefficient is the main task of experimental ballistics from which aerodynamic studies begin. The studies are designed to determine the drag coefficient of missiles having different aerodynamic shapes, which can be used in rocket science, artillery, and other areas of technology involved in the study of the movement of bodies in gaseous and liquid media. A feature of the aeroballistic method for determining the coefficient of drag force is that, in order to obtain values of CXO of a given accuracy, experiments can be carried out only with bodies that are stable during the whole time of movement in the studied section of the trajectory. The research is aimed at solving the problem of calculating the drag coefficient of bodies using trajectory data on their coaxial movement. During the ballistic test, the body is sequentially photographed relative to a fixed coordinate system, coordinates of its characteristic points and the time between the moments of photographing are recorded, and the displacements of the characteristic points of the body relative to the moving coordinate system associated with the base body performing a rectilinear motion with a zero angle of attack, are simultaneously measured. In this case, the base body is axially and movably connected to the body under study. It is shown that the applied group motion effect allows, within the framework of the accepted assumptions, to increase the accuracy and simplify the determination of the drag force coefficient of bodies of a complex geometric shape.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76404923","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}
Victor S. Dmitriev, L. Minkov, T. Kostyuchenko, V. V. Derdiyashchenko, Dmitry S. Panfilov, Dmitrij V. Ermakov
Reducing the vibration activity of low-noise fans is becoming the most important direction in the creation of their new modifications. It is analytically shown that the efficiency of vibration damping of a mechanical system depends not only on the ratio of natural frequencies, vibration frequencies and damping coefficient, but also on technical solutions for installing dampers, for example, on an elastic or rigid foundation. The article proposes an algorithm for minimizing the vibration activity of a mechanical system which is an axial low-noise fan. To solve the problem of minimizing noise in the operating mode of the fan, an innovative technical solution for the construction of the case is being considered - the walls are made in the form of a "sandwich" consisting of layers of structural materials that provide strength characteristics, as well as noise and vibration protection. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
{"title":"Minimizing vibration of low-noise fans","authors":"Victor S. Dmitriev, L. Minkov, T. Kostyuchenko, V. V. Derdiyashchenko, Dmitry S. Panfilov, Dmitrij V. Ermakov","doi":"10.17223/19988621/76/8","DOIUrl":"https://doi.org/10.17223/19988621/76/8","url":null,"abstract":"Reducing the vibration activity of low-noise fans is becoming the most important direction in the creation of their new modifications. It is analytically shown that the efficiency of vibration damping of a mechanical system depends not only on the ratio of natural frequencies, vibration frequencies and damping coefficient, but also on technical solutions for installing dampers, for example, on an elastic or rigid foundation. The article proposes an algorithm for minimizing the vibration activity of a mechanical system which is an axial low-noise fan. To solve the problem of minimizing noise in the operating mode of the fan, an innovative technical solution for the construction of the case is being considered - the walls are made in the form of a \"sandwich\" consisting of layers of structural materials that provide strength characteristics, as well as noise and vibration protection. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85403917","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 numerical approach is proposed to solve the linear sloshing problem of an incompressible inviscid liquid with account for surface tension effects, which are predominant in the low-gravity environment. A variational formulation is derived by the linearization of motion equations for the liquid near its initial equilibrium state with consideration of a pressure drop on the free surface and a free-end boundary condition on the contact line. The continuous problem domain is discretized by the finite element method. After discretization, the classical generalized eigenvalue problem is obtained, whose solutions are the natural frequencies and mode shapes. Several examples show the effect of the Bond number and the fluid-filled volume on the liquid behavior in toroidal tanks. A comparison of numerical results with experimental measurements under ground conditions reveals that under microgravity condition, the surface tension force and the boundary condition on the contact line play an important role when determining the natural frequencies and mode shapes of the liquid sloshing. Each fluid-filled volume has its own characteristic Bond number, above which the natural frequencies approximate to the experimental values obtained under ground conditions. The presented results can be used in the coupling dynamic analysis of a spacecraft with propellant tanks. The author is grateful to the supervisor associate professor A.N. Tem-nov for help in formulating the problem and discussion of the results of the work.
{"title":"Sloshing of a liquid fuel in toroidal tanks with account for capillary effect","authors":"Zhaohu Yu","doi":"10.17223/19988621/78/12","DOIUrl":"https://doi.org/10.17223/19988621/78/12","url":null,"abstract":"A numerical approach is proposed to solve the linear sloshing problem of an incompressible inviscid liquid with account for surface tension effects, which are predominant in the low-gravity environment. A variational formulation is derived by the linearization of motion equations for the liquid near its initial equilibrium state with consideration of a pressure drop on the free surface and a free-end boundary condition on the contact line. The continuous problem domain is discretized by the finite element method. After discretization, the classical generalized eigenvalue problem is obtained, whose solutions are the natural frequencies and mode shapes. Several examples show the effect of the Bond number and the fluid-filled volume on the liquid behavior in toroidal tanks. A comparison of numerical results with experimental measurements under ground conditions reveals that under microgravity condition, the surface tension force and the boundary condition on the contact line play an important role when determining the natural frequencies and mode shapes of the liquid sloshing. Each fluid-filled volume has its own characteristic Bond number, above which the natural frequencies approximate to the experimental values obtained under ground conditions. The presented results can be used in the coupling dynamic analysis of a spacecraft with propellant tanks. The author is grateful to the supervisor associate professor A.N. Tem-nov for help in formulating the problem and discussion of the results of the work.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78640771","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}
Manzur Kh. Ziatdinov, A. Zhukov, N. Evseev, M. A. Markov, V. Bobyr, D. A. Tkachev, P. Nikitin
This work presents a study of the preparation of additive materials based on a nickel-chromium alloy of the Ni-Cr-CrN system by direct metal laser sintering (DMLS). The additive materials were produced on the EOS M270 setup (with the option of open editing modes). The research range: laser radiation from 100 to 200 W, the speed of the laser beam from 600 to 1100 mm/s. The chemical composition of the obtained materials is investigated. The composition indicates a high final content of nitrogen in the alloy (0.5%). The structure of the obtained samples and their mechanical characteristics, namely, the bending strength (1500 MPa) and Vickers microhardness (450 HV), have been investigated. The morphology, microstructure, and elemental analysis of the initial powder and the resulting additive materials were studied by scanning electron microscopy and X-ray spectral microanalysis on the TESCAN Vega research complex. Analysis of the structure shows that the elements Ni, Cr and Fe are distributed evenly over the entire area of the samples, which indicates a uniform Ni-Cr-CrN melt. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
{"title":"Study of the structure and properties of products made of heat-resistant alloys based on Ni-Cr-CrN with a high nitrogen content by direct metal laser sintering","authors":"Manzur Kh. Ziatdinov, A. Zhukov, N. Evseev, M. A. Markov, V. Bobyr, D. A. Tkachev, P. Nikitin","doi":"10.17223/19988621/76/9","DOIUrl":"https://doi.org/10.17223/19988621/76/9","url":null,"abstract":"This work presents a study of the preparation of additive materials based on a nickel-chromium alloy of the Ni-Cr-CrN system by direct metal laser sintering (DMLS). The additive materials were produced on the EOS M270 setup (with the option of open editing modes). The research range: laser radiation from 100 to 200 W, the speed of the laser beam from 600 to 1100 mm/s. The chemical composition of the obtained materials is investigated. The composition indicates a high final content of nitrogen in the alloy (0.5%). The structure of the obtained samples and their mechanical characteristics, namely, the bending strength (1500 MPa) and Vickers microhardness (450 HV), have been investigated. The morphology, microstructure, and elemental analysis of the initial powder and the resulting additive materials were studied by scanning electron microscopy and X-ray spectral microanalysis on the TESCAN Vega research complex. Analysis of the structure shows that the elements Ni, Cr and Fe are distributed evenly over the entire area of the samples, which indicates a uniform Ni-Cr-CrN melt. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78867443","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}
V. Arkhipov, S. Basalaev, Ksenia G. Perfllieva, S. Polenchuk, A. Usanina
New methods for studying the effect of gas injection from the surface of a solid spherical particle on its drag coefficient in the transient and self-similar regimes of flow around the particle have been presented. An advantage of the proposed methods is the ability to isolate in a pure form the effect of the mass flux from the particle surface (without the effect of other factors, for example, particle acceleration) on the drag coefficient. New results of an experimental study of the effect of air flow blowing on the drag coefficient of a solid perforated sphere in the Reynolds number range Re = 133÷9900 have been presented. It has been shown that the drag coefficient decreases when air is blown from the particle surface. As the Reynolds number Re increases, the drag coefficient CD upon gas injection in the transient flow regime decreases to a certain critical value corresponding to the onset of the self-similar regime. At the onset of the selfsimilar regime (reaching the critical value of CD), the drag coefficient increases with an increase in the Reynolds number and asymptotically tends to a constant value CD = 0.44. However, the opposite effect has been found for a small diameter of the particle (D = 1 cm) at a blowing velocity ue ≥ 1.3 m/s: an increase in the drag coefficient of the particle CD at air efflux from the particle surface in comparison with the drag coefficient value in the absence of gas flow injection (ue = 0 m/s). This is apparently associated with a change in the characteristics of the boundary layer of the particle due to the rearrangement of the flow profile near the spherical particle surface caused by a decrease in its size. An empirical dependence of the drag coefficient of a solid sphere on the ratio of the velocity of injection from the surface of the particle to the velocity of blowing CD = 0.15 + (0.44 - 0.15)/ (1 + 9ū/53.8) (with the coefficient of determination R2 = 0.89) has been obtained for a self-similar particle regime flow. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
{"title":"Methods for determining the drag coefficient at gas injection from the surface of spherical particle","authors":"V. Arkhipov, S. Basalaev, Ksenia G. Perfllieva, S. Polenchuk, A. Usanina","doi":"10.17223/19988621/76/5","DOIUrl":"https://doi.org/10.17223/19988621/76/5","url":null,"abstract":"New methods for studying the effect of gas injection from the surface of a solid spherical particle on its drag coefficient in the transient and self-similar regimes of flow around the particle have been presented. An advantage of the proposed methods is the ability to isolate in a pure form the effect of the mass flux from the particle surface (without the effect of other factors, for example, particle acceleration) on the drag coefficient. New results of an experimental study of the effect of air flow blowing on the drag coefficient of a solid perforated sphere in the Reynolds number range Re = 133÷9900 have been presented. It has been shown that the drag coefficient decreases when air is blown from the particle surface. As the Reynolds number Re increases, the drag coefficient CD upon gas injection in the transient flow regime decreases to a certain critical value corresponding to the onset of the self-similar regime. At the onset of the selfsimilar regime (reaching the critical value of CD), the drag coefficient increases with an increase in the Reynolds number and asymptotically tends to a constant value CD = 0.44. However, the opposite effect has been found for a small diameter of the particle (D = 1 cm) at a blowing velocity ue ≥ 1.3 m/s: an increase in the drag coefficient of the particle CD at air efflux from the particle surface in comparison with the drag coefficient value in the absence of gas flow injection (ue = 0 m/s). This is apparently associated with a change in the characteristics of the boundary layer of the particle due to the rearrangement of the flow profile near the spherical particle surface caused by a decrease in its size. An empirical dependence of the drag coefficient of a solid sphere on the ratio of the velocity of injection from the surface of the particle to the velocity of blowing CD = 0.15 + (0.44 - 0.15)/ (1 + 9ū/53.8) (with the coefficient of determination R2 = 0.89) has been obtained for a self-similar particle regime flow. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78880005","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 model operator hμ(k), k∈(-π,π], corresponding to the Hamiltonian of a system of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function is considered. The function describes the transfer of a particle from site to sites interacting using a short-range attraction potential νμ, μ = (μ0,μ1,μ2,μ3) ∈ ℝ+4. The detailed descriptions of changes in the number of eigenvalues of the energy operator hμ(k), k∈(-π,π], relative to values of the particle interaction vector and the total quasi-momentum k ∈ Т of the system of two particles is presented.
{"title":"On the number of eigenvalues of a model operator on a one-dimensional lattice","authors":"A. Imomov, I. Bozorov, A. Khurramov","doi":"10.17223/19988621/78/2","DOIUrl":"https://doi.org/10.17223/19988621/78/2","url":null,"abstract":"A model operator hμ(k), k∈(-π,π], corresponding to the Hamiltonian of a system of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function is considered. The function describes the transfer of a particle from site to sites interacting using a short-range attraction potential νμ, μ = (μ0,μ1,μ2,μ3) ∈ ℝ+4. The detailed descriptions of changes in the number of eigenvalues of the energy operator hμ(k), k∈(-π,π], relative to values of the particle interaction vector and the total quasi-momentum k ∈ Т of the system of two particles is presented.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73460374","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}
In this work, mathematical modeling of relative dynamics of a bifullerene complex is carried out on the assumption that the inner shell does not form covalent bonds with an outer carbon skeleton. This fact enables free angular movements of the inner shell. In particular, the directed rotation of the inner fullerene can be provided. This, in turn, allows for accumulating of a significant fraction of kinetic energy at internal degrees of freedom of the complex under consideration. In this case, the direction of rotations is not related to temperature; the outer shell of the complex restrains the transfer of the stored energy into thermal vibrations. Therefore, calculations are performed to estimate the stability of the rotational motion of an encapsulated fullerene relative to translational displacements of the outer shell. The calculations are carried out using a separate description of the dynamics of closed carbon molecules in terms of translational and rotational displacements. Translational displacements are determined using the equations of motion for the centers of mass of molecules. Rotational displacements are found on the basis of the dynamic Euler equations. The power centers in the considered framework structures of the molecules are carbon atoms. Therefore, the strength characteristics of intermolecular interactions are obtained in accordance with an atom-atom approach. In this case, the interaction parameters of individual atoms correspond to the case when these atoms are located in a structure of the surface carbon crystal.
{"title":"Relative dynamics of shells of a bifullerene complex","authors":"M. Bubenchikov, D. Mamontov, A. S. Chelnokova","doi":"10.17223/19988621/77/5","DOIUrl":"https://doi.org/10.17223/19988621/77/5","url":null,"abstract":"In this work, mathematical modeling of relative dynamics of a bifullerene complex is carried out on the assumption that the inner shell does not form covalent bonds with an outer carbon skeleton. This fact enables free angular movements of the inner shell. In particular, the directed rotation of the inner fullerene can be provided. This, in turn, allows for accumulating of a significant fraction of kinetic energy at internal degrees of freedom of the complex under consideration. In this case, the direction of rotations is not related to temperature; the outer shell of the complex restrains the transfer of the stored energy into thermal vibrations. Therefore, calculations are performed to estimate the stability of the rotational motion of an encapsulated fullerene relative to translational displacements of the outer shell. The calculations are carried out using a separate description of the dynamics of closed carbon molecules in terms of translational and rotational displacements. Translational displacements are determined using the equations of motion for the centers of mass of molecules. Rotational displacements are found on the basis of the dynamic Euler equations. The power centers in the considered framework structures of the molecules are carbon atoms. Therefore, the strength characteristics of intermolecular interactions are obtained in accordance with an atom-atom approach. In this case, the interaction parameters of individual atoms correspond to the case when these atoms are located in a structure of the surface carbon crystal.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76215209","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}
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