Swirling flows of fluids and gases are an integral part of many complex flows which are widely encountered in nature and technology. The working process of numerous technical devices (cyclones, vortex combustion chambers, air separators, gas and steam turbines, electric machines and generators, etc.) is generally determined by the laws of hydrodynamics and heat exchange of rotating flows. The problem of deriving general laws for a turbulent flow in the field of centrifugal forces provokes considerable scientific interest since it belongs to an underdeveloped field of hydromechanics. Therefore, mathematical modeling of swirling turbulent flows is still an urgent problem. In this paper, a comparative analysis of the advanced turbulence models for the Taylor -Couette flow is carried out. For this purpose, the linear turbulence models (SARC and SST-RC), the Reynolds stress method SSG/LRR-RSM-w2012, and a two-fluid model are used. The results obtained using these models are compared with each other and with known experimental data and direct numerical simulation results. The numerical results calculated with the use of turbulence models for the Taylor-Couette flow confirm that almost all the models adequately describe velocity profiles. However, they yield different turbulent viscosity values and, as a result, different friction coefficients. A comparison of the numerical results shows that the friction coefficient calculated using a two-fluid turbulence model is the closest to that obtained experimentally.
{"title":"Comparison of advanced turbulence models for the Taylor-Couette flow","authors":"Z. Malikov, F. K. Nazarov, M. Madaliev","doi":"10.17223/19988621/78/10","DOIUrl":"https://doi.org/10.17223/19988621/78/10","url":null,"abstract":"Swirling flows of fluids and gases are an integral part of many complex flows which are widely encountered in nature and technology. The working process of numerous technical devices (cyclones, vortex combustion chambers, air separators, gas and steam turbines, electric machines and generators, etc.) is generally determined by the laws of hydrodynamics and heat exchange of rotating flows. The problem of deriving general laws for a turbulent flow in the field of centrifugal forces provokes considerable scientific interest since it belongs to an underdeveloped field of hydromechanics. Therefore, mathematical modeling of swirling turbulent flows is still an urgent problem. In this paper, a comparative analysis of the advanced turbulence models for the Taylor -Couette flow is carried out. For this purpose, the linear turbulence models (SARC and SST-RC), the Reynolds stress method SSG/LRR-RSM-w2012, and a two-fluid model are used. The results obtained using these models are compared with each other and with known experimental data and direct numerical simulation results. The numerical results calculated with the use of turbulence models for the Taylor-Couette flow confirm that almost all the models adequately describe velocity profiles. However, they yield different turbulent viscosity values and, as a result, different friction coefficients. A comparison of the numerical results shows that the friction coefficient calculated using a two-fluid turbulence model is the closest to that obtained experimentally.","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":"90866658","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}
Mikhail Selikhovkin, A. Akhmadieva, I. Zhukov, E. Marchenko, A. Khrustalyov
In this paper, the study of the effect of diamond nanoparticles on the structure and mechanical properties of the Mg-Ca-Zn magnesium alloy. The influence of diamond nanoparticles concentration amount of 0.1 wt. % in the structure of alloy Mg-Ca-Zn, the ultimate tensile strength increases from 294 up to 332 MPa, the elongation value increases from 22 % up to 27 % and the yield strength increases from 66 up to 75 MPa in the tested samples. Nanoparticles in magnesium alloy do not change the hardness of the alloy. The introduction of diamond nanoparticles into the magnesium alloy increased the Zn concentration from 4 % to 4.7 % and the Ca concentration from 1 % to 1.3 %. It is found that the introduction of the nanodiamond particles into a magnesium melt contributes to a decrease in the average grain size from ~ 100 to 64 pm in the obtained castings and, as a result, to an increase in the mechanical properties.
{"title":"Investigation of the effect of diamond nanoparticles on the structure and mechanical behavior of Mg-Ca-Zn alloy","authors":"Mikhail Selikhovkin, A. Akhmadieva, I. Zhukov, E. Marchenko, A. Khrustalyov","doi":"10.17223/19988621/79/13","DOIUrl":"https://doi.org/10.17223/19988621/79/13","url":null,"abstract":"In this paper, the study of the effect of diamond nanoparticles on the structure and mechanical properties of the Mg-Ca-Zn magnesium alloy. The influence of diamond nanoparticles concentration amount of 0.1 wt. % in the structure of alloy Mg-Ca-Zn, the ultimate tensile strength increases from 294 up to 332 MPa, the elongation value increases from 22 % up to 27 % and the yield strength increases from 66 up to 75 MPa in the tested samples. Nanoparticles in magnesium alloy do not change the hardness of the alloy. The introduction of diamond nanoparticles into the magnesium alloy increased the Zn concentration from 4 % to 4.7 % and the Ca concentration from 1 % to 1.3 %. It is found that the introduction of the nanodiamond particles into a magnesium melt contributes to a decrease in the average grain size from ~ 100 to 64 pm in the obtained castings and, as a result, to an increase in the mechanical properties.","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":"81755647","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 Reynolds equations are solved with account for inertial forces in a plane wedge-shaped layer using the Slezkin-Targ method. The analytical expressions determining the dimensionless longitudinal velocity, hydrodynamic pressure, and total pressure force as functions of the lubricating Reynolds number and dimensionless parameter of the problem are obtained. A new method for solving the Reynolds equations is proposed accounting for inertial forces and avoiding averaging the inertial terms with respect to the gap height. The numerical analysis of the proposed method shows that in the first and second approximations, the deviations for the total hydrodynamic pressure force in a plane wedge-shaped layer differ little from each other in the considered range of the lubricating Reynolds number for varying dimensionless parameter of the problem, but exceed the deviation obtained using the Slezkin-Targ method. The coincidence of the first approximation with the second one gives ground to believe that the proposed method is more accurate for calculating the total hydrodynamic pressure force in the fluid flow occurring in a plane wedge-shaped layer.
{"title":"Pressure calculation for a fluid flowing in a plane wedge-shaped layer with account for inertial forces","authors":"P. V. Kaurov","doi":"10.17223/19988621/79/6","DOIUrl":"https://doi.org/10.17223/19988621/79/6","url":null,"abstract":"The Reynolds equations are solved with account for inertial forces in a plane wedge-shaped layer using the Slezkin-Targ method. The analytical expressions determining the dimensionless longitudinal velocity, hydrodynamic pressure, and total pressure force as functions of the lubricating Reynolds number and dimensionless parameter of the problem are obtained. A new method for solving the Reynolds equations is proposed accounting for inertial forces and avoiding averaging the inertial terms with respect to the gap height. The numerical analysis of the proposed method shows that in the first and second approximations, the deviations for the total hydrodynamic pressure force in a plane wedge-shaped layer differ little from each other in the considered range of the lubricating Reynolds number for varying dimensionless parameter of the problem, but exceed the deviation obtained using the Slezkin-Targ method. The coincidence of the first approximation with the second one gives ground to believe that the proposed method is more accurate for calculating the total hydrodynamic pressure force in the fluid flow occurring in a plane wedge-shaped layer.","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":"78333418","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}
This paper presents a theoretical study of quick methods for determining the aerodynamic characteristics of fixed-wing unmanned aerial vehicles (UAVs). The purpose of the research is to create tools for aircraft shape optimization problems. The developed analytical techniques allow one to determine aerodynamic lift and drag coefficients as well as the efficiency characteristics based on the aircraft general characteristics. Other properties that can be derived are the wing shape parameters, the take-off mass, the structural mass, and the required characteristics of the propulsion and power supply system according to the specified flight performance characteristics. The use of these techniques for discrete points with aerodynamic characteristics obtained numerically or experimentally allows one to extrapolate the results to the entire range of operating angles of attack. As a result, the stages of conceptual and preliminary design of UAVs can be passed in a shorter span of time. Two UAVs have been designed in Tomsk State University with the use of the proposed techniques. The first is the preliminary designed UAV Prototype-2E; the second is the Prototype-2T UAV, which has been fully designed and then manufactured. The data calculated with these techniques on a SKIF Cyberia supercomputer in Tomsk State University are compared with the results of numerical simulations implemented in OpenFOAM and ANSYS Fluent. Good agreement of the results is revealed.
{"title":"Determination of aerodynamic characterisitcs of fixed-wing unmanned aerial vehicle by analytical techniques","authors":"Kuatbay Ismailov","doi":"10.17223/19988621/78/9","DOIUrl":"https://doi.org/10.17223/19988621/78/9","url":null,"abstract":"This paper presents a theoretical study of quick methods for determining the aerodynamic characteristics of fixed-wing unmanned aerial vehicles (UAVs). The purpose of the research is to create tools for aircraft shape optimization problems. The developed analytical techniques allow one to determine aerodynamic lift and drag coefficients as well as the efficiency characteristics based on the aircraft general characteristics. Other properties that can be derived are the wing shape parameters, the take-off mass, the structural mass, and the required characteristics of the propulsion and power supply system according to the specified flight performance characteristics. The use of these techniques for discrete points with aerodynamic characteristics obtained numerically or experimentally allows one to extrapolate the results to the entire range of operating angles of attack. As a result, the stages of conceptual and preliminary design of UAVs can be passed in a shorter span of time. Two UAVs have been designed in Tomsk State University with the use of the proposed techniques. The first is the preliminary designed UAV Prototype-2E; the second is the Prototype-2T UAV, which has been fully designed and then manufactured. The data calculated with these techniques on a SKIF Cyberia supercomputer in Tomsk State University are compared with the results of numerical simulations implemented in OpenFOAM and ANSYS Fluent. Good agreement of the results is revealed.","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":"77778107","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}
Classical mechanics of deformable bodies is based on the continuity hypothesis. However, many structural elements are made of porous materials. Porous natural materials (soil, rocks) have invariable porosity. Porous synthetic materials (ceramics, concrete, graphite, and pressed powder metals) have controlled porosity. To calculate the strength and hardness of the structure, the material is assumed to be conditionally continuous with the adjusted porosity. Nowadays, there are many available works presenting mechanical characteristics of materials with different porosities. This paper proposes a new class of problems in mechanics of deformable solids. Considering a low arch stability problem, which is important in construction practice, the problem of optimal arch design is solved by controlling the properties of the material. The solution to the problem of stability of the low arch made of porous material is presented. The flat arch with a rectangular crosssection is exposed to equally distributed loading. The near-rational law of the porosity distribution over the cross-section is used. The load is considered as a random variable. The solution to the problem is obtained using the theory of stationary random processes. A comparative analysis of the reliability and material consumption is carried out for the arch with continuous and porous sections. The calculation shows that the porous structure of the arch reduces the material consumption by 13.3% without stability and reliability losses.
{"title":"A stability problem for a low-height curvilinear porous arch under random loading","authors":"S. Shlyakhov, Elvira F. Krivulina","doi":"10.17223/19988621/79/14","DOIUrl":"https://doi.org/10.17223/19988621/79/14","url":null,"abstract":"Classical mechanics of deformable bodies is based on the continuity hypothesis. However, many structural elements are made of porous materials. Porous natural materials (soil, rocks) have invariable porosity. Porous synthetic materials (ceramics, concrete, graphite, and pressed powder metals) have controlled porosity. To calculate the strength and hardness of the structure, the material is assumed to be conditionally continuous with the adjusted porosity. Nowadays, there are many available works presenting mechanical characteristics of materials with different porosities. This paper proposes a new class of problems in mechanics of deformable solids. Considering a low arch stability problem, which is important in construction practice, the problem of optimal arch design is solved by controlling the properties of the material. The solution to the problem of stability of the low arch made of porous material is presented. The flat arch with a rectangular crosssection is exposed to equally distributed loading. The near-rational law of the porosity distribution over the cross-section is used. The load is considered as a random variable. The solution to the problem is obtained using the theory of stationary random processes. A comparative analysis of the reliability and material consumption is carried out for the arch with continuous and porous sections. The calculation shows that the porous structure of the arch reduces the material consumption by 13.3% without stability and reliability losses.","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":"79520655","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. Afonin, V. G. Butov, Victor A. Solonenko, A. A. Yashchuk, Andrey A. Yakushev
This paper presents the results of numerical simulation of the processes in a two-chamber plasma generator of the pulsed MHD generator running on combustion products of a combined pyrotechnic fuel with afterburning in air oxygen. A mixture of Mg powder (a fuel) and KNO3 powder (an oxidizer and a source of the easily ionized additive) is chosen as a pyrotechnic fuel. The considered plasma generator includes a gas generator and an afterburner. Multicomponent combustion products of the selected pyrotechnic fuel contain solid particles of MgO and gaseous Mg. Within the afterburner, the unburnt Mg is burned up in the presence of air oxygen, forming MgO liquid particles. The proposed mathematical model allows one to numerically investigate all the processes occurring in a plasma generator of an MHD generator with an afterburner and to obtain the required data for determining the shape of the accelerating nozzle and the relevant parameters for calculations in the MHD channel.
{"title":"A Study of processes in a plasma generator of the pulsed MHD generator running on a combined pyrotechnic fuel","authors":"A. Afonin, V. G. Butov, Victor A. Solonenko, A. A. Yashchuk, Andrey A. Yakushev","doi":"10.17223/19988621/78/5","DOIUrl":"https://doi.org/10.17223/19988621/78/5","url":null,"abstract":"This paper presents the results of numerical simulation of the processes in a two-chamber plasma generator of the pulsed MHD generator running on combustion products of a combined pyrotechnic fuel with afterburning in air oxygen. A mixture of Mg powder (a fuel) and KNO3 powder (an oxidizer and a source of the easily ionized additive) is chosen as a pyrotechnic fuel. The considered plasma generator includes a gas generator and an afterburner. Multicomponent combustion products of the selected pyrotechnic fuel contain solid particles of MgO and gaseous Mg. Within the afterburner, the unburnt Mg is burned up in the presence of air oxygen, forming MgO liquid particles. The proposed mathematical model allows one to numerically investigate all the processes occurring in a plasma generator of an MHD generator with an afterburner and to obtain the required data for determining the shape of the accelerating nozzle and the relevant parameters for calculations in the MHD channel.","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":"80226411","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}
K. Imomnazarov, Abdulhamid E. Kholmurodov, A. Omonov
In applied problems related to propagation of elastic waves, it is often necessary to take into account porosity, fluid saturation of the media, and the hydrodynamic background. Real geological media are multiphase, electrically conductive, fractured, porous, etc. When propagating, seismic waves dissipate due to the absorption of energy. In this paper, the wave propagation process occurs in terms of partial densities of phases, stress tensor, pore pressure, and velocities of the corresponding phases. In the first section, for completeness, the presentation presents a quasilinear system of equations of the poroelasticity theory [1-3]. In the second section, the corresponding linear system of equations of the poroelasticity theory for a homogeneous medium is obtained. In the third section, we construct a fundamental solution for the system of equations of the poroelasticity theory obtained in the second section. In the final section, the inverse poroelasticity problem of determining the distributed source in a half-space using additional information about the free surface mode is considered.
{"title":"Direct and inverse dynamic problems of poroelasticity","authors":"K. Imomnazarov, Abdulhamid E. Kholmurodov, A. Omonov","doi":"10.17223/19988621/75/8","DOIUrl":"https://doi.org/10.17223/19988621/75/8","url":null,"abstract":"In applied problems related to propagation of elastic waves, it is often necessary to take into account porosity, fluid saturation of the media, and the hydrodynamic background. Real geological media are multiphase, electrically conductive, fractured, porous, etc. When propagating, seismic waves dissipate due to the absorption of energy. In this paper, the wave propagation process occurs in terms of partial densities of phases, stress tensor, pore pressure, and velocities of the corresponding phases. In the first section, for completeness, the presentation presents a quasilinear system of equations of the poroelasticity theory [1-3]. In the second section, the corresponding linear system of equations of the poroelasticity theory for a homogeneous medium is obtained. In the third section, we construct a fundamental solution for the system of equations of the poroelasticity theory obtained in the second section. In the final section, the inverse poroelasticity problem of determining the distributed source in a half-space using additional information about the free surface mode is considered.","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":"82196058","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 aim of this work is to develop the method of boundary states for the class of torsion problems as applied to transversely isotropic elastic bodies of revolution. Efforts, displacements, or a combination of both are used as twisting conditions at the border. Proceeding from the general solution to the problem of cross section warping, the basis of the space of internal states is formed. The search for an internal state is reduced to the study of the boundary state isomorphic to it. The solution is a Fourier series. The proposed technique is implemented in solving the first main problem for a body in the form of a truncated cone; the second main problem for a circular cylinder; and the main mixed problem for a non-canonical body of revolution. The solution was verified and the calculation accuracy was assessed. The obtained characteristics of the elastic field have a polynomial form. The elastic field in each problem satisfies the specified boundary conditions in the form of their distribution over the surface and does not satisfy them only in the integral sense.
{"title":"Boundary state method in solving torsion problems for transversely isotropic bodies of revolution","authors":"D. A. Ivanychev","doi":"10.17223/19988621/75/7","DOIUrl":"https://doi.org/10.17223/19988621/75/7","url":null,"abstract":"The aim of this work is to develop the method of boundary states for the class of torsion problems as applied to transversely isotropic elastic bodies of revolution. Efforts, displacements, or a combination of both are used as twisting conditions at the border. Proceeding from the general solution to the problem of cross section warping, the basis of the space of internal states is formed. The search for an internal state is reduced to the study of the boundary state isomorphic to it. The solution is a Fourier series. The proposed technique is implemented in solving the first main problem for a body in the form of a truncated cone; the second main problem for a circular cylinder; and the main mixed problem for a non-canonical body of revolution. The solution was verified and the calculation accuracy was assessed. The obtained characteristics of the elastic field have a polynomial form. The elastic field in each problem satisfies the specified boundary conditions in the form of their distribution over the surface and does not satisfy them only in the integral sense.","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":"84336598","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 subject under analysis is construction of differential equations of equilibrium in displacements for plane deformation of physically and geometrically nonlinear continuous media when the closing equations are biquadratically approximated in a Cartesian rectangular coordinate system. Proceeding from the assumption that, generally speaking, the diagrams of volume and shear deformation are independent from each other, six main cases of physical dependences are considered, depending on the relative position of the break points of biquadratic diagrams of volume and shear deformation. Construction of physical dependencies is based on the calculation of the secant module of volume and shear deformation. When approximating the graphs of volume and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations; the secant modulus of volume expansion-contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volume and shear deformation, the secant shear modulus is a fractional (rational) function of the intensity of shear deformations; the secant modulus of volume expansion-contraction is a fractional (rational) function of the first invariant of the strain tensor. The obtained differential equations of equilibrium in displacements can be applied in determining the stress-strain state of physically and geometrically nonlinear continuous media under plane deformation the closing equations of physical relations for which are approximated by biquadratic functions.
{"title":"Differential equations of continuum equilibrium for plane deformation in cartesian axials at biquadratic approximation of closing equations","authors":"S. V. Bakushev","doi":"10.17223/19988621/76/6","DOIUrl":"https://doi.org/10.17223/19988621/76/6","url":null,"abstract":"The subject under analysis is construction of differential equations of equilibrium in displacements for plane deformation of physically and geometrically nonlinear continuous media when the closing equations are biquadratically approximated in a Cartesian rectangular coordinate system. Proceeding from the assumption that, generally speaking, the diagrams of volume and shear deformation are independent from each other, six main cases of physical dependences are considered, depending on the relative position of the break points of biquadratic diagrams of volume and shear deformation. Construction of physical dependencies is based on the calculation of the secant module of volume and shear deformation. When approximating the graphs of volume and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations; the secant modulus of volume expansion-contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volume and shear deformation, the secant shear modulus is a fractional (rational) function of the intensity of shear deformations; the secant modulus of volume expansion-contraction is a fractional (rational) function of the first invariant of the strain tensor. The obtained differential equations of equilibrium in displacements can be applied in determining the stress-strain state of physically and geometrically nonlinear continuous media under plane deformation the closing equations of physical relations for which are approximated by biquadratic functions.","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":"74297487","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 acoustic characteristics of a single supersonic jet flowing from a nozzle of a rocket engine into a flooded space at different pressure ratios are studied. A system of the Favre-averaged Navier-Stokes equations is used to describe the unsteady flow of a viscous compressible heat-conducting gas in a supersonic Laval nozzle and an outflowing jet. The system is enclosed by the ideal gas law. The implementation of the physical and mathematical model and the numerical studies are carried out using the OpenFOAM Extended open platform based on the modified dbnsTurbFoam solver. A conical nozzle with an opening angle of 45° at the Mach number of 3 at the nozzle exit is considered in this study. Air is used as the working gas. Amplitude-frequency spectra of acoustic radiation at the point located at a distance from the nozzle outlet are obtained at different pressure ratios of the outflowing supersonic jet. Analysis of the amplitude-frequency characteristics of the jet under study shows that the maxima occur mainly at low frequencies. The maximum oscillation amplitude for the considered jet configurations is revealed at a pressure ratio of 1 on a frequency of 787 Hz. The maximum sound pressure level is 149 dB.
{"title":"Investigation of acoustic characteristics of a single supersonic jet flowing into a flooded space","authors":"Adil A. Askerov, A. V. Chervakova, K. Kostyushin","doi":"10.17223/19988621/78/4","DOIUrl":"https://doi.org/10.17223/19988621/78/4","url":null,"abstract":"In this paper, the acoustic characteristics of a single supersonic jet flowing from a nozzle of a rocket engine into a flooded space at different pressure ratios are studied. A system of the Favre-averaged Navier-Stokes equations is used to describe the unsteady flow of a viscous compressible heat-conducting gas in a supersonic Laval nozzle and an outflowing jet. The system is enclosed by the ideal gas law. The implementation of the physical and mathematical model and the numerical studies are carried out using the OpenFOAM Extended open platform based on the modified dbnsTurbFoam solver. A conical nozzle with an opening angle of 45° at the Mach number of 3 at the nozzle exit is considered in this study. Air is used as the working gas. Amplitude-frequency spectra of acoustic radiation at the point located at a distance from the nozzle outlet are obtained at different pressure ratios of the outflowing supersonic jet. Analysis of the amplitude-frequency characteristics of the jet under study shows that the maxima occur mainly at low frequencies. The maximum oscillation amplitude for the considered jet configurations is revealed at a pressure ratio of 1 on a frequency of 787 Hz. The maximum sound pressure level is 149 dB.","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":"89333075","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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