Solid-propellant rocket engines are simple in design, highly reliable, and able to store the propellant for a long time without its degradation. Their main feature is that the propellant is a mixture of a solid fuel and a solid oxidizer, thus ensuring a uniform combustion and a stable discharge of the combustion products. However, the combustion rate cannot be controlled, and the combustion cannot be stopped or restarted. This calls for efficient methods of thrust vector control. Gas-dynamic methods, such as a gas injection into the supersonic nozzle area, offer a required flight path control without complex high-power mechanical systems. The importance of this study lies in improving the accuracy and efficiency of rocket flight control, which is critical for today’s space and defense tasks. The numerical simulation of gas-dynamic control systems, in particular by an asymmetric gas injection, allows one to obtain detailed data on the flow behavior and optimize the design and operating conditions of the system. This study is concerned with a full-scale solid-propellant rocket engine with a gas-dynamic thrust vector control system based on the use of asymmetric forces that occur on the nozzle wall when the supersonic flow interacts with the injected transverse jets. To simulate the process in the Ansys Fluent software package, a geometric model of a nozzle with an asymmetric injection of the chamber gas into the supersonic area was developed. The injection flow rate was controlled by moving the valve flap. The simulation was carried out taking into account the temperature dependence of the main thermophysical gas parameters with consideration for dissociation processes by way of data approximation. The approximation was performed using piecewise polynomial functions. Nozzle flow patterns were obtained. The calculated results were compared with experimental test data and shown to be in satisfactory agreement with the lateral force measured during the fire bench tests of the prototype. From a practical point of view, the results obtained may be directly used to improve existing thrust vector control systems and develop new ones. This will improve rocket navigation accuracy, flight stability, and maneuverability, which is critical for complex space and defense tasks.
{"title":"Simulation of a gas injection into the supersonic nozzle area in gas-dynamic thrust vector control","authors":"O.D. Ihnatiev, H. Shevelova","doi":"10.15407/itm2024.02.013","DOIUrl":"https://doi.org/10.15407/itm2024.02.013","url":null,"abstract":"Solid-propellant rocket engines are simple in design, highly reliable, and able to store the propellant for a long time without its degradation. Their main feature is that the propellant is a mixture of a solid fuel and a solid oxidizer, thus ensuring a uniform combustion and a stable discharge of the combustion products. However, the combustion rate cannot be controlled, and the combustion cannot be stopped or restarted. This calls for efficient methods of thrust vector control. Gas-dynamic methods, such as a gas injection into the supersonic nozzle area, offer a required flight path control without complex high-power mechanical systems. The importance of this study lies in improving the accuracy and efficiency of rocket flight control, which is critical for today’s space and defense tasks. The numerical simulation of gas-dynamic control systems, in particular by an asymmetric gas injection, allows one to obtain detailed data on the flow behavior and optimize the design and operating conditions of the system. This study is concerned with a full-scale solid-propellant rocket engine with a gas-dynamic thrust vector control system based on the use of asymmetric forces that occur on the nozzle wall when the supersonic flow interacts with the injected transverse jets. To simulate the process in the Ansys Fluent software package, a geometric model of a nozzle with an asymmetric injection of the chamber gas into the supersonic area was developed. The injection flow rate was controlled by moving the valve flap. The simulation was carried out taking into account the temperature dependence of the main thermophysical gas parameters with consideration for dissociation processes by way of data approximation. The approximation was performed using piecewise polynomial functions. Nozzle flow patterns were obtained. The calculated results were compared with experimental test data and shown to be in satisfactory agreement with the lateral force measured during the fire bench tests of the prototype. From a practical point of view, the results obtained may be directly used to improve existing thrust vector control systems and develop new ones. This will improve rocket navigation accuracy, flight stability, and maneuverability, which is critical for complex space and defense tasks.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"20 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837555","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 current stage of space exploration is characterized by an increased interest in the development, deployment, and operation of low-orbit satellite constellations (LOSC) for Earth and near-Earth space remote sensing for military and civilian purposes and for global and regional satellite communications. Reusable space launch vehicles have significantly reduced the orbital injection cost. As a result, satellite operators are developing and deploying large-scale LOSCs of various orbital structures with a large number of spacecraft. According to current estimates, more than 70% of all the operating satellites operate in low-Earth orbits (LEOs) at altitudes between 160 km and 2,000 km. Since LEO satellites are generally much cheaper than satellites in geostationary orbits, the possibility of their on-orbit servicing (OOS) has not been the focus of research. However, the use of LEO OOS has prospects for growth. Techniques for ballistic planning of LEO OOS missions have been and are being developed. The disadvantages of approximate techniques include the use of simplified flight dynamics models. Most of the existing exact techniques are based on the use of full mathematical models of flight dynamics and the shooting method to solve the boundary value problem of an orbit transfer. Using the shooting method requires a sufficiently accurate initial guess, which is difficult to determine. To obtain a second approximation, use is mainly made of optimization methods, which do not always find a global minimum. In this regard, there is a need to develop new techniques that would be free from the above disadvantages. The goal of the article is to develop a ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems. The technique includes the identification of LEO areas promising for OOS, a mathematical model of the dynamics of perturbed OOS orbit transfers in modified equinoctial orbital elements, and a solution algorithm for the boundary value problem of determining the control parameters of perturbed OOS low-orbit transfers. The problem is solved using methods of statistical analysis, flight dynamics, shooting, genetic optimization, and mathematical simulation. The novelty lies in the identification of LEO areas promising for OOS and the development of a mathematical model of orbit transfer dynamics in modified equinoctial orbital elements and a solution algorithm for determining the control parameters of perturbed OOS low-orbit transfers. The results of the work may be used in the justification and planning of LEO OOS missions and the formulation of requirements for LEO OSS mission propulsion systems.
{"title":"Ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems","authors":"A. Alpatov, Yu.M. Holdshtein","doi":"10.15407/itm2024.02.003","DOIUrl":"https://doi.org/10.15407/itm2024.02.003","url":null,"abstract":"The current stage of space exploration is characterized by an increased interest in the development, deployment, and operation of low-orbit satellite constellations (LOSC) for Earth and near-Earth space remote sensing for military and civilian purposes and for global and regional satellite communications. Reusable space launch vehicles have significantly reduced the orbital injection cost. As a result, satellite operators are developing and deploying large-scale LOSCs of various orbital structures with a large number of spacecraft. According to current estimates, more than 70% of all the operating satellites operate in low-Earth orbits (LEOs) at altitudes between 160 km and 2,000 km. Since LEO satellites are generally much cheaper than satellites in geostationary orbits, the possibility of their on-orbit servicing (OOS) has not been the focus of research. However, the use of LEO OOS has prospects for growth. Techniques for ballistic planning of LEO OOS missions have been and are being developed. The disadvantages of approximate techniques include the use of simplified flight dynamics models. Most of the existing exact techniques are based on the use of full mathematical models of flight dynamics and the shooting method to solve the boundary value problem of an orbit transfer. Using the shooting method requires a sufficiently accurate initial guess, which is difficult to determine. To obtain a second approximation, use is mainly made of optimization methods, which do not always find a global minimum. In this regard, there is a need to develop new techniques that would be free from the above disadvantages. The goal of the article is to develop a ballistic planning technique for low-orbit servicing missions with low constant thrust propulsion systems. The technique includes the identification of LEO areas promising for OOS, a mathematical model of the dynamics of perturbed OOS orbit transfers in modified equinoctial orbital elements, and a solution algorithm for the boundary value problem of determining the control parameters of perturbed OOS low-orbit transfers. The problem is solved using methods of statistical analysis, flight dynamics, shooting, genetic optimization, and mathematical simulation. The novelty lies in the identification of LEO areas promising for OOS and the development of a mathematical model of orbit transfer dynamics in modified equinoctial orbital elements and a solution algorithm for determining the control parameters of perturbed OOS low-orbit transfers. The results of the work may be used in the justification and planning of LEO OOS missions and the formulation of requirements for LEO OSS mission propulsion systems.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"19 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837559","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 considers the effect of the solar radiation pressure on the motion of a satellite in an almostcircular low-Earth orbit. The formulation of the problem is due to the need to determine the effect of solar radiation pressure forces on the motion of light commercial Earth remote sensing (ERS) satellites with large surface areas (solar batteries and antennas). The goal is to determine the main regularities of this effect, construct reasonably simple and accurate estimates of changes in orbital parameters for the orbits under consideration, and clarify their physics (cause-and-effect relations) The novelty of this study also lies in the use of variables specially introduced to describe a motion in almost circular orbits. The study assumes that the solar radiation pressure force is constant throughout the entire orbit, and it is concerned with dawn-dusk orbits, which are often used for ERS satellites with radar observation systems. The paper presents simple analytical expressions that describe the main regularities of short-term (several days) changes in orbital parameters. It is shown that the change in the orientation of the orbital plane is determined by the action of the gyroscopic moment. This moment balances the effect of the moment of external forces aimed at changing the orientation and the change in the orientation perpendicular to the direction of the applied moment of the external forces. The main effect of the solar radiation pressure is the excitation of forced oscillations of the orbital radius, whose amplitude linearly increases with time. The maximums of these oscillations (apogee) are at the point where the light pressure forces maximally slow down the motion of the satellite (directed oppositely to the velocity), and the minimums (perigee) are at the point of the maximum motion acceleration. It is shown that the annual movement of the Sun can qualitatively change the picture of the evolution of orbital parameters. For sun-synchronous dawn-dusk orbits, compact analytical solutions for changes in orbital parameters are constructed, and it is shown that the annual movement of the Sun’s declination reverses the direction of evolution of the orbital shape. The calculations showed a reasonably high accuracy of the analytical solutions at the initial stage. The obtained numerical estimates make it possible to evaluate the effect of the solar pressure on changes in orbital parameters.
{"title":"Effect of the solar radiation pressure on the motion of satellites in almost circular Earth orbits","authors":"A. I. Maslova, A. Pirozhenko, O.O. Pirozhenko","doi":"10.15407/itm2024.02.041","DOIUrl":"https://doi.org/10.15407/itm2024.02.041","url":null,"abstract":"This paper considers the effect of the solar radiation pressure on the motion of a satellite in an almostcircular low-Earth orbit. The formulation of the problem is due to the need to determine the effect of solar radiation pressure forces on the motion of light commercial Earth remote sensing (ERS) satellites with large surface areas (solar batteries and antennas). The goal is to determine the main regularities of this effect, construct reasonably simple and accurate estimates of changes in orbital parameters for the orbits under consideration, and clarify their physics (cause-and-effect relations) The novelty of this study also lies in the use of variables specially introduced to describe a motion in almost circular orbits. The study assumes that the solar radiation pressure force is constant throughout the entire orbit, and it is concerned with dawn-dusk orbits, which are often used for ERS satellites with radar observation systems. The paper presents simple analytical expressions that describe the main regularities of short-term (several days) changes in orbital parameters. It is shown that the change in the orientation of the orbital plane is determined by the action of the gyroscopic moment. This moment balances the effect of the moment of external forces aimed at changing the orientation and the change in the orientation perpendicular to the direction of the applied moment of the external forces. The main effect of the solar radiation pressure is the excitation of forced oscillations of the orbital radius, whose amplitude linearly increases with time. The maximums of these oscillations (apogee) are at the point where the light pressure forces maximally slow down the motion of the satellite (directed oppositely to the velocity), and the minimums (perigee) are at the point of the maximum motion acceleration. It is shown that the annual movement of the Sun can qualitatively change the picture of the evolution of orbital parameters. For sun-synchronous dawn-dusk orbits, compact analytical solutions for changes in orbital parameters are constructed, and it is shown that the annual movement of the Sun’s declination reverses the direction of evolution of the orbital shape. The calculations showed a reasonably high accuracy of the analytical solutions at the initial stage. The obtained numerical estimates make it possible to evaluate the effect of the solar pressure on changes in orbital parameters.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"66 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837748","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}
Present-day small satellites for Earth remote sensing have found wide practical application in solving different problems in the socio-economic and defense areas. The use of small satellites is justified as a basis for the formation both of large constellations and constellations of several spacecraft or single spacecraft with the aim to reduce the cost of Earth remote sensing information. The miniaturization of electron components and the latest technological advances have made radar systems compatible with small satellites. The goal of this paper is to present, based on small satellites, expressions for calculating the key parameters of radar systems and their analysis and to calculate possible values of the parameters considered. Possibilities in principle of using synthetic aperture radars (SARs) are considered. The paper presents an overview of Internet sources that give broad information on the recent trends, technologies, and use SAR-equipped satellites. Particular attention is paid to the development of mini- and microspacecraft with X-band SARs operating, in particular, in the stripmap and spotlight modes. The key parameters that have an effect on the SAR possibility of producing high-quality images are presented. By the example of the ICEYE constellation of small satellites, important technical characteristics and parameters of modern radar systems equipped with an active phased array antenna are presented. A model of SAR imaging in the stripmap mode is considered. In the approximation of a rectangular antenna aperture, expressions are given to estimate the slant and the horizontal range resolution and the azimuthal resolution. The available range of the small-satellite SAR pulse repetition frequency is estimated. Relationships between the maximum swath width and the minimum SAR pulse repetition frequency are presented. Expressions are given to estimate the antenna dimensions, the SAR sensitivity, and the signal-to-noise ratio. The presented expressions allow one to analyze the effect of the main technical characteristics and parameters of minisatellite SARs on the design and power characteristics of small satellites and the orbit parameters. The obtained results make it possible to develop recommendations on the design of imaging equipment for home low-orbit satellites and their constellations.
目前用于地球遥感的小型卫星在解决社会经济和国防领域的各种问题方面得到了广泛的实际应用。为了降低地球遥感信息的成本，有理由使用小型卫星作为组建大型星群和由多个航天器或单个航天器组成的星群的基础。电子元件的微型化和最新的技术进步使雷达系统与小型卫星兼容。本文的目的是以小型卫星为基础，介绍雷达系统关键参数的计算表达式及其分析，并计算所考虑的参数的可能值。原则上考虑了使用合成孔径雷达（SAR）的可能性。本文概述了互联网资料来源，这些资料来源提供了有关最新趋势、技术和使用配备合成孔径雷达的卫星的广泛信息。特别关注了配备 X 波段合成孔径雷达的小型和微型航天器的发展情况，尤其是在条带图和聚光灯模式下的运行情况。介绍了影响合成孔径雷达能否产生高质量图像的关键参数。以 ICEYE 小卫星星座为例，介绍了配备有源相控阵天线的现代雷达系统的重要技术特征和参数。考虑了条带图模式下的合成孔径雷达成像模型。在近似矩形天线孔径的情况下，给出了估算倾斜和水平测距分辨率以及方位角分辨率的表达式。估算了小卫星合成孔径雷达脉冲重复频率的可用范围。提出了最大扫描带宽度和最小合成孔径雷达脉冲重复频率之间的关系。给出了估算天线尺寸、合成孔径雷达灵敏度和信噪比的表达式。利用所给出的表达式可以分析微型卫星合成孔径雷达的主要技术特征和参数对小型卫星的设计和功率特征以及轨道参数的影响。所获得的结果使我们有可能就家用低轨道卫星及其星座的成像设备设计提出建议。
{"title":"Requirements for the parameters of synthetic aperture radars onboard small satellites for Earth remote sensing","authors":"O. Volosheniuk, O.O. Pyrozhenko","doi":"10.15407/itm2024.02.055","DOIUrl":"https://doi.org/10.15407/itm2024.02.055","url":null,"abstract":"Present-day small satellites for Earth remote sensing have found wide practical application in solving different problems in the socio-economic and defense areas. The use of small satellites is justified as a basis for the formation both of large constellations and constellations of several spacecraft or single spacecraft with the aim to reduce the cost of Earth remote sensing information. The miniaturization of electron components and the latest technological advances have made radar systems compatible with small satellites. The goal of this paper is to present, based on small satellites, expressions for calculating the key parameters of radar systems and their analysis and to calculate possible values of the parameters considered. Possibilities in principle of using synthetic aperture radars (SARs) are considered. The paper presents an overview of Internet sources that give broad information on the recent trends, technologies, and use SAR-equipped satellites. Particular attention is paid to the development of mini- and microspacecraft with X-band SARs operating, in particular, in the stripmap and spotlight modes. The key parameters that have an effect on the SAR possibility of producing high-quality images are presented. By the example of the ICEYE constellation of small satellites, important technical characteristics and parameters of modern radar systems equipped with an active phased array antenna are presented. A model of SAR imaging in the stripmap mode is considered. In the approximation of a rectangular antenna aperture, expressions are given to estimate the slant and the horizontal range resolution and the azimuthal resolution. The available range of the small-satellite SAR pulse repetition frequency is estimated. Relationships between the maximum swath width and the minimum SAR pulse repetition frequency are presented. Expressions are given to estimate the antenna dimensions, the SAR sensitivity, and the signal-to-noise ratio. The presented expressions allow one to analyze the effect of the main technical characteristics and parameters of minisatellite SARs on the design and power characteristics of small satellites and the orbit parameters. The obtained results make it possible to develop recommendations on the design of imaging equipment for home low-orbit satellites and their constellations.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"22 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837456","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 goal of this work is to theoretically substantiate the possibility of determining the charged particle density in the ionospheric plasma by separately measuring the electric currents of an insulated probe system in the electron saturation region. The ionospheric plasma composition is modeled by two ion species with significantly different masses and electrons to keep the plasma quasi-neutrality. The probe system, which is electrically insulated from the spacecraft structure, consists of cylindrical electrodes: a probe and a reference electrode. The reference electrode to probe current-collecting area ratio can be significantly less than required by the single cylindrical probe theory. The electrodes are oriented transversely to a supersonic flow of a collisionless plasma. In addition to the main plasma with two ion species, a model plasma with a single ion species is considered. The mass of the model ions is such that the ion saturation current to the cylinder is the same for both plasma models. Based on a previously obtained asymptotic solution for the electron saturation current in a plasma with a single ion species, computational formulas are found for determining the ion mass composition and the electron density by probe current measurements. The errors of the formulas are estimated numerically and analytically as a function of the probe system geometry, the bias potential of the probe relative to the reference electrode, and the accuracy of potential and current measurements. It is shown that a proper choice of the probe system settings and the accuracy of probe measurements assures a reliable determination of the charged particle densities in a plasma with two ion species. A priori estimates are presented for the effect of the current bias potential measurement errors on the reliability of determining the ion mass composition and the electron density of the ionospheric plasma.
{"title":"Mathematical simulation of ionospheric plasma diagnostics by electric current measurements using an insulated probe system","authors":"D. Lazuchenkov, N. Lazuchenkov","doi":"10.15407/itm2024.02.112","DOIUrl":"https://doi.org/10.15407/itm2024.02.112","url":null,"abstract":"The goal of this work is to theoretically substantiate the possibility of determining the charged particle density in the ionospheric plasma by separately measuring the electric currents of an insulated probe system in the electron saturation region. The ionospheric plasma composition is modeled by two ion species with significantly different masses and electrons to keep the plasma quasi-neutrality. The probe system, which is electrically insulated from the spacecraft structure, consists of cylindrical electrodes: a probe and a reference electrode. The reference electrode to probe current-collecting area ratio can be significantly less than required by the single cylindrical probe theory. The electrodes are oriented transversely to a supersonic flow of a collisionless plasma. In addition to the main plasma with two ion species, a model plasma with a single ion species is considered. The mass of the model ions is such that the ion saturation current to the cylinder is the same for both plasma models. Based on a previously obtained asymptotic solution for the electron saturation current in a plasma with a single ion species, computational formulas are found for determining the ion mass composition and the electron density by probe current measurements. The errors of the formulas are estimated numerically and analytically as a function of the probe system geometry, the bias potential of the probe relative to the reference electrode, and the accuracy of potential and current measurements. It is shown that a proper choice of the probe system settings and the accuracy of probe measurements assures a reliable determination of the charged particle densities in a plasma with two ion species. A priori estimates are presented for the effect of the current bias potential measurement errors on the reliability of determining the ion mass composition and the electron density of the ionospheric plasma.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"69 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837640","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}
With the ever-increasing prices of and demand for traditional fuels and the decreasing availability thereof, renewable energy sources, such as wind energy, are gaining enormous popularity. First of all, this branch of "green" energy is environmentally friendly. A significant increase in the use of wind power plants (WPPs) is observed all over the world. Modern WPPs are of two types: vertical- and horizontal-axis ones. Vertical-axis WPPs, in contrast to horizontal-axis ones, have a number of specific design advantages, such as, for example, insensitivity to the wind direction, which significantly simplify their design and increase their reliability. The operation of vertical-axis WPPs involves the need to stabilize their operating regimes, the main objective of which is to stabilize electricity production in conditions of a variable wind speed using appropriate stabilization systems (SSs). In SS development, use is made of various control algorithms, which make a basis for harnessing physical principles of SS construction. Recently, SSs based on blade swept area variation have become widespread. Such systems, unlike systems based on, for example, generator load variation, actually use the adaptation of WPPs to a variable wind speed, and they dispense with the need for mechanical dissipation of excess energy by resistance forces and, to some extent, with the need to transfer it to the support. The last point significantly reduces the load on the rotor-to-generator transmission systems and alleviates the requirements for anchor systems in the case of WPPs installed on floating platforms. In terms of design, the stabilization of vertical-axis WPPs by swept area variation can be performed in three ways: by varying the blade length, varying the length of the traverses whereby the blades are attached to the rotor shaft, and by simultaneously varying the length of the blades and the traverses, i.e., by varying WPP rotor configuration. The elaboration of approaches to the development of algorithms for the stabilization of vertical-axis WPPs controlled by rotor configuration variation is an important and promising task. The goal of this paper is to develop efficient algorithms for stabilizing the variable-configuration WPP rotor speed providing the stability and operability of the channels of blade and traverse length variation in their simultaneous operation. The problem is solved using methods of the classical theory of automatic control and mathematical simulation. The novelty lies in extending the concept of control by swept area variation to Darrieus vertical-axis WPPs, synthesizing efficient algorithms for stabilizing the rotor speed of Darrieus vertical-axis WPPs controlled by rotor configuration variation, and determining conditions for their stability and operability. The algorithms and approach developed may be used in substantiating design solutions for Darrieus vertical-axis WPPs.
{"title":"Darrieus rotor speed stabilization by joint variation of the blade and the traverse length","authors":"S.V. Tarasov, O.N. Molotkov","doi":"10.15407/itm2024.02.092","DOIUrl":"https://doi.org/10.15407/itm2024.02.092","url":null,"abstract":"With the ever-increasing prices of and demand for traditional fuels and the decreasing availability thereof, renewable energy sources, such as wind energy, are gaining enormous popularity. First of all, this branch of \"green\" energy is environmentally friendly. A significant increase in the use of wind power plants (WPPs) is observed all over the world. Modern WPPs are of two types: vertical- and horizontal-axis ones. Vertical-axis WPPs, in contrast to horizontal-axis ones, have a number of specific design advantages, such as, for example, insensitivity to the wind direction, which significantly simplify their design and increase their reliability. The operation of vertical-axis WPPs involves the need to stabilize their operating regimes, the main objective of which is to stabilize electricity production in conditions of a variable wind speed using appropriate stabilization systems (SSs). In SS development, use is made of various control algorithms, which make a basis for harnessing physical principles of SS construction. Recently, SSs based on blade swept area variation have become widespread. Such systems, unlike systems based on, for example, generator load variation, actually use the adaptation of WPPs to a variable wind speed, and they dispense with the need for mechanical dissipation of excess energy by resistance forces and, to some extent, with the need to transfer it to the support. The last point significantly reduces the load on the rotor-to-generator transmission systems and alleviates the requirements for anchor systems in the case of WPPs installed on floating platforms. In terms of design, the stabilization of vertical-axis WPPs by swept area variation can be performed in three ways: by varying the blade length, varying the length of the traverses whereby the blades are attached to the rotor shaft, and by simultaneously varying the length of the blades and the traverses, i.e., by varying WPP rotor configuration. The elaboration of approaches to the development of algorithms for the stabilization of vertical-axis WPPs controlled by rotor configuration variation is an important and promising task. The goal of this paper is to develop efficient algorithms for stabilizing the variable-configuration WPP rotor speed providing the stability and operability of the channels of blade and traverse length variation in their simultaneous operation. The problem is solved using methods of the classical theory of automatic control and mathematical simulation. The novelty lies in extending the concept of control by swept area variation to Darrieus vertical-axis WPPs, synthesizing efficient algorithms for stabilizing the rotor speed of Darrieus vertical-axis WPPs controlled by rotor configuration variation, and determining conditions for their stability and operability. The algorithms and approach developed may be used in substantiating design solutions for Darrieus vertical-axis WPPs.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"76 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837653","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}
Many practical problems call for constructing the maximum interpoint distance distribution for random pints in a plane. In the literature, the case of a great number of points is considered, for which an asymptotic distribution is determined. This paper addresses the problem of constructing the maximum interpoint distance distribution for a small number of random points in a plane whose coordinates are independent random quantities that obey the standard normal distribution. The special case of three random points in a plane is considered as the basic one, for which three ways to construct the maximum interpoint distance distribution are studied. The first way is to construct the distribution function from geometrical considerations. To do this, the loci of three points are considered from the condition that the maximum distance between them shall not exceed a certain value. The position of the third point in the plane is determined relative to the two other points: the leftmost and the lowermost one. In this case, the construction of the distribution function involves the successive evaluation of several integrals using numerical methods. The obtained results are in good agreement with those of statistical simulation. The second way is based on studying the distance between pairs of random normal points in a plane. Taken separately, the distances between each pair of random normal points obey one-dimensional Rayleigh distributions, but in the aggregate they prove to be correlated because they are determined from the same pint coordinates. A joint distribution of the squared distances between three points is constructed using the three-dimensional Moran-Downton distribution. Using it, a distribution function of the squared maximum distance between three random normal points, which is identical with the maximum interpoint distance distribution, is obtained. It is found that for small values it underestimates the actual probability of the maximum distance not exceeding a certain value. For great distance values, the above probabilities coincide. The third way uses the Rice distribution (a generalization of the Rayleigh distribution) to approximate the unknown maximum interpoint distance distribution for three random normal points in a plane. The Rice distribution parameters found by the least-squares method are in good agreement with those obtained by statistical simulation. The results for three random normal points are generalized to a greater number of points (up to 30). It is shown that in this case the third way is most efficient.
{"title":"Ways to construct the maximum interpoint distance distribution for random normal points in a plane","authors":"E. Hladkyi, V.I. Perlyk","doi":"10.15407/itm2024.02.076","DOIUrl":"https://doi.org/10.15407/itm2024.02.076","url":null,"abstract":"Many practical problems call for constructing the maximum interpoint distance distribution for random pints in a plane. In the literature, the case of a great number of points is considered, for which an asymptotic distribution is determined. This paper addresses the problem of constructing the maximum interpoint distance distribution for a small number of random points in a plane whose coordinates are independent random quantities that obey the standard normal distribution. The special case of three random points in a plane is considered as the basic one, for which three ways to construct the maximum interpoint distance distribution are studied. The first way is to construct the distribution function from geometrical considerations. To do this, the loci of three points are considered from the condition that the maximum distance between them shall not exceed a certain value. The position of the third point in the plane is determined relative to the two other points: the leftmost and the lowermost one. In this case, the construction of the distribution function involves the successive evaluation of several integrals using numerical methods. The obtained results are in good agreement with those of statistical simulation. The second way is based on studying the distance between pairs of random normal points in a plane. Taken separately, the distances between each pair of random normal points obey one-dimensional Rayleigh distributions, but in the aggregate they prove to be correlated because they are determined from the same pint coordinates. A joint distribution of the squared distances between three points is constructed using the three-dimensional Moran-Downton distribution. Using it, a distribution function of the squared maximum distance between three random normal points, which is identical with the maximum interpoint distance distribution, is obtained. It is found that for small values it underestimates the actual probability of the maximum distance not exceeding a certain value. For great distance values, the above probabilities coincide. The third way uses the Rice distribution (a generalization of the Rayleigh distribution) to approximate the unknown maximum interpoint distance distribution for three random normal points in a plane. The Rice distribution parameters found by the least-squares method are in good agreement with those obtained by statistical simulation. The results for three random normal points are generalized to a greater number of points (up to 30). It is shown that in this case the third way is most efficient.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"31 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837594","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 goal of this paper is to develop a method for determining the values of system failure rates optimal in terms of net profit maximization with account for spacecraft mass limitations. It is adopted that the spacecraft systems are independent in terms of reliability, each of them can be only in two states (a functioning state or a failure state), and each equipment type of the special complex makes an independent contribution to the overall effect. The paper considers the case where the spacecraft system failure time obeys the exponential law. Use is made of the Lagrange multiplier method and numerical optimization methods. The problem is solved using the mass ? failure rate and cost ? failure rate relationships of the spacecraft systems. For the supporting complex, the dimension of the mathematical simulation problem is reduced to two: a formula is derived to find the optimal failure rates of all the systems of the supporting complex using the optimal failure rates of two systems of it. The variables for the special complex and the supporting complex are separated. Due to the fact that each special complex system makes an independent contribution to the overall effect, the problem for the whole spacecraft is reduced to a system of two equations for the special complex and the supporting complex and ncn equations in one variable for the special complex with two coupling variables between the supporting complex and the special complex where ncn is the number of the special complex systems. The paper presents a numerical-and-analytical method for spacecraft system failure rate optimization where the initial guess is specified indirectly: by specifying the supporting complex mass and probability of no-failure operation. The method may be used in the development of a space hardware design methodology accounting for economic factors. From the optimal values of the spacecraft system failure rates found using the mass ? failure rate and cost ? failure rate relationships, one can find the masses and costs of the spacecraft systems to be used in optimizing the parameters and development cost of the systems. The method is expected to increase the profitability and competitiveness of spacecraft under development.
{"title":"Determination of optimal spacecraft reliability norms with account for economic indexes","authors":"O.M. Savonik","doi":"10.15407/itm2024.02.066","DOIUrl":"https://doi.org/10.15407/itm2024.02.066","url":null,"abstract":"The goal of this paper is to develop a method for determining the values of system failure rates optimal in terms of net profit maximization with account for spacecraft mass limitations. It is adopted that the spacecraft systems are independent in terms of reliability, each of them can be only in two states (a functioning state or a failure state), and each equipment type of the special complex makes an independent contribution to the overall effect. The paper considers the case where the spacecraft system failure time obeys the exponential law. Use is made of the Lagrange multiplier method and numerical optimization methods. The problem is solved using the mass ? failure rate and cost ? failure rate relationships of the spacecraft systems. For the supporting complex, the dimension of the mathematical simulation problem is reduced to two: a formula is derived to find the optimal failure rates of all the systems of the supporting complex using the optimal failure rates of two systems of it. The variables for the special complex and the supporting complex are separated. Due to the fact that each special complex system makes an independent contribution to the overall effect, the problem for the whole spacecraft is reduced to a system of two equations for the special complex and the supporting complex and ncn equations in one variable for the special complex with two coupling variables between the supporting complex and the special complex where ncn is the number of the special complex systems. The paper presents a numerical-and-analytical method for spacecraft system failure rate optimization where the initial guess is specified indirectly: by specifying the supporting complex mass and probability of no-failure operation. The method may be used in the development of a space hardware design methodology accounting for economic factors. From the optimal values of the spacecraft system failure rates found using the mass ? failure rate and cost ? failure rate relationships, one can find the masses and costs of the spacecraft systems to be used in optimizing the parameters and development cost of the systems. The method is expected to increase the profitability and competitiveness of spacecraft under development.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"19 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837561","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 gives a general overview of components and layouts used in supersonic rockets of different purposes. The rocket layout is specified as a structure and a set of components (a wing, a rudder, a stabilizer, a destabilizer, and a superstructure) arranged along the rocket structure. The goal of this work is to develop a unified approach to specifying the shape parameters of rocket layouts regardless of the rocket type. For complex-shape rocket layouts, the paper proposes an approach in which the shapes of the rocket structure and the additional components installed thereon are specified independently. The additional components of the rocket layout are bound to the rocket structure using operation parameters. The use of the operation parameters binds each additional component of the rocket layout to the rocket structure, thus offering a unified method for specifying the geometrical parameters of variously shaped rocket layouts. This approach is developed towards more complex shapes of rocket layout elements arbitrarily placed on rocket structures. The outside shape of each rocket component is specified in a Cartesian system of coordinates rigidly bound thereto. A unified approach to specifying the outside shape of various rocket components is presented. According to the general scheme of specifying the geometrical parameters of rocket layout components, they are specified by three methods: analytically, by plan shape, and by plan shape with board and end chord profiles. To describe the outside shape of a component, the specification method and the number and the values of its key parameters are specified. To specify rocket layout input data, one has to fix the number of additional components to be installed on the rocket structure. For each layout component, the parameters that define its shape, location on the rocket structure, and deflection angle are specified. To each layout component there corresponds an input data set of its own. The set consists of parameters that define the shape of the component and parameters of its operation as a part of the layout. A standard input data file for specifying rocket layout shapes is configured.
{"title":"Input data generation for marching calculation of supersonic flow past various rocket layouts","authors":"V. Halynskyi","doi":"10.15407/itm2024.02.026","DOIUrl":"https://doi.org/10.15407/itm2024.02.026","url":null,"abstract":"This paper gives a general overview of components and layouts used in supersonic rockets of different purposes. The rocket layout is specified as a structure and a set of components (a wing, a rudder, a stabilizer, a destabilizer, and a superstructure) arranged along the rocket structure. The goal of this work is to develop a unified approach to specifying the shape parameters of rocket layouts regardless of the rocket type. For complex-shape rocket layouts, the paper proposes an approach in which the shapes of the rocket structure and the additional components installed thereon are specified independently. The additional components of the rocket layout are bound to the rocket structure using operation parameters. The use of the operation parameters binds each additional component of the rocket layout to the rocket structure, thus offering a unified method for specifying the geometrical parameters of variously shaped rocket layouts. This approach is developed towards more complex shapes of rocket layout elements arbitrarily placed on rocket structures. The outside shape of each rocket component is specified in a Cartesian system of coordinates rigidly bound thereto. A unified approach to specifying the outside shape of various rocket components is presented. According to the general scheme of specifying the geometrical parameters of rocket layout components, they are specified by three methods: analytically, by plan shape, and by plan shape with board and end chord profiles. To describe the outside shape of a component, the specification method and the number and the values of its key parameters are specified. To specify rocket layout input data, one has to fix the number of additional components to be installed on the rocket structure. For each layout component, the parameters that define its shape, location on the rocket structure, and deflection angle are specified. To each layout component there corresponds an input data set of its own. The set consists of parameters that define the shape of the component and parameters of its operation as a part of the layout. A standard input data file for specifying rocket layout shapes is configured.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"12 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837499","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}
At present, the study of diffusion-controlled processes with volume and heterogeneous chemical reactions plays an important role in various systems, in particular engineering ones, which include electric current sources. Based on familiar equations, this work considers ion exchange processes in the porous spaces of the electrodes of a lead-acid battery during its discharge. Allowance is made for electrochemical processes between the solid electrodes and the electrolyte that fills the porous space. As distinct from the majority of works, allowance is also made for the two-dimensionality of the process, which is due to the geometry of the apparatus and its physical characteristics. An important feature of the work is that in the open zone between the electrodes, the mass transfer is assumed to be convective, whose intensity is much higher than that of the diffusive one in the pores of the electrodes. This allows one to ignore, at least as a first approximation, the resistance of the central zone of the electric cell in the process of ion transfer. This, as one might say, limiting scheme, greatly simplifies the problem of charge transfer through the central zone of the electrochemical cell. It is shown that the electrical conductivity of the solid part of the electrodes plays an important role in the distribution of potentials both in the electrodes themselves and in the porous space. Due to the high electrical conductivity, the negative electrode relative to the positive one operates practically in a one-dimensional mode. It should also be noted that the additional resistance of the separator has a noticeable effect on the operation of the positive electrode, which manifests itself at relatively high currents, when the lack of the charging component becomes noticeable. Another important aspect of the calculation is the determination of the distribution of poorly soluble and poorly conductive lead sulfate (PbSO4), which affects the mass transfer process to a large extent, up to the termination of the discharge. It is shown that at relatively high currents, the formation of the passivating product is concentrated on the outer sides of the electrodes.
{"title":"Mass transfer in the porous electrodes of a lead-acid battery during its discharge","authors":"V.I. Yeliseyev, Y. Sovit, M.O. Katrenko","doi":"10.15407/itm2024.02.124","DOIUrl":"https://doi.org/10.15407/itm2024.02.124","url":null,"abstract":"At present, the study of diffusion-controlled processes with volume and heterogeneous chemical reactions plays an important role in various systems, in particular engineering ones, which include electric current sources. Based on familiar equations, this work considers ion exchange processes in the porous spaces of the electrodes of a lead-acid battery during its discharge. Allowance is made for electrochemical processes between the solid electrodes and the electrolyte that fills the porous space. As distinct from the majority of works, allowance is also made for the two-dimensionality of the process, which is due to the geometry of the apparatus and its physical characteristics. An important feature of the work is that in the open zone between the electrodes, the mass transfer is assumed to be convective, whose intensity is much higher than that of the diffusive one in the pores of the electrodes. This allows one to ignore, at least as a first approximation, the resistance of the central zone of the electric cell in the process of ion transfer. This, as one might say, limiting scheme, greatly simplifies the problem of charge transfer through the central zone of the electrochemical cell. It is shown that the electrical conductivity of the solid part of the electrodes plays an important role in the distribution of potentials both in the electrodes themselves and in the porous space. Due to the high electrical conductivity, the negative electrode relative to the positive one operates practically in a one-dimensional mode. It should also be noted that the additional resistance of the separator has a noticeable effect on the operation of the positive electrode, which manifests itself at relatively high currents, when the lack of the charging component becomes noticeable. Another important aspect of the calculation is the determination of the distribution of poorly soluble and poorly conductive lead sulfate (PbSO4), which affects the mass transfer process to a large extent, up to the termination of the discharge. It is shown that at relatively high currents, the formation of the passivating product is concentrated on the outer sides of the electrodes.","PeriodicalId":507620,"journal":{"name":"Technical mechanics","volume":"29 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837459","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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