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Keywords = isobaric expansion

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12 pages, 937 KiB  
Article
Heat Capacities and Thermal Coefficients of Sodium’s and Eutectic Sodium–Potassium’s Coolants for Nuclear Reactors
by Nikolay E. Dubinin
Appl. Sci. 2025, 15(13), 7566; https://doi.org/10.3390/app15137566 - 5 Jul 2025
Viewed by 306
Abstract
Temperature dependencies of the density, heat capacity at constant pressure, and isobaric thermal expansion coefficient are investigated for two liquid metal nuclear reactor coolants: pure sodium and sodium–potassium eutectic alloy (31.9 at. %Na). The variational method of the thermodynamic perturbation theory is used [...] Read more.
Temperature dependencies of the density, heat capacity at constant pressure, and isobaric thermal expansion coefficient are investigated for two liquid metal nuclear reactor coolants: pure sodium and sodium–potassium eutectic alloy (31.9 at. %Na). The variational method of the thermodynamic perturbation theory is used for the calculations. The calculations were carried out in temperature ranges of 373–1673 K for Na and 273–1573 K for 0.319Na-0.681K. The accuracy of two local pseudopotentials and three exchange–correlation functions is estimated. It is shown that two combinations between the pseudopotential and exchange–correlation function can be recommended for predicting the properties at high temperatures for which experimental information is absent. Full article
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15 pages, 6753 KiB  
Article
Thermodynamic Evaluation of Novel 1,2,4-Triazolium Alanine Ionic Liquids as Sustainable Heat-Transfer Media
by Kunhao Liang, Haiyun Yao, Jing Qiao, Shan Gao, Mingji Zong, Fengshou Liu, Qili Yang, Lanju Liang and Dawei Fang
Molecules 2024, 29(22), 5227; https://doi.org/10.3390/molecules29225227 - 5 Nov 2024
Cited by 3 | Viewed by 1166
Abstract
Ionic liquids, which are widely recognized as environmentally friendly solvents, stand out as promising alternatives to traditional heat-transfer fluids due to their outstanding heat-storage and heat-transfer capabilities. In the course of our ongoing research, we successfully synthesized ionic liquids 1-ethyl-4-alkyl-1,2,4-triazolium alanine [Taz(2,n [...] Read more.
Ionic liquids, which are widely recognized as environmentally friendly solvents, stand out as promising alternatives to traditional heat-transfer fluids due to their outstanding heat-storage and heat-transfer capabilities. In the course of our ongoing research, we successfully synthesized ionic liquids 1-ethyl-4-alkyl-1,2,4-triazolium alanine [Taz(2,n)][Ala], where (n = 4, 5); in this study, we present comprehensive data on their density, surface tension, isobaric molar heat capacity, and thermal conductivity for the first time. The key thermophysical parameters influencing the heat-transfer process, such as thermal expansibility, compressibility, isochoric heat capacity, and heat-storage density, were meticulously calculated from experimental data. Upon comparison with previously reported ionic liquids and commercially utilized heat-transfer fluids, [Taz(2,n)][Ala] demonstrated superior heat-storage and heat-transfer performance, particularly in terms of heat-storage density (~2.63 MJ·m−3·K−1), thermal conductivity (~0.190 W·m−1·K−1), and melting temperature (~226 K). Additionally, the presence of the alanine anion in [Taz(2,n)][Ala] provides more possibilities for its functional application. Full article
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14 pages, 4330 KiB  
Article
Determination of Compressed Liquid Densities for CO2 + n-Decane Using a Vibrating Tube Densimeter
by Tao Jia, Jinpeng Yang and Jia Yu
Appl. Sci. 2024, 14(20), 9232; https://doi.org/10.3390/app14209232 - 11 Oct 2024
Viewed by 914
Abstract
Understanding the density of CO2 + n-decane is crucial for designing and operating CO2 capture, transport, and storage. The safety and effectiveness of CO2 burial is directly affected by the density of CO2 + n-decane mixtures. The [...] Read more.
Understanding the density of CO2 + n-decane is crucial for designing and operating CO2 capture, transport, and storage. The safety and effectiveness of CO2 burial is directly affected by the density of CO2 + n-decane mixtures. The liquid densities of CO2(1) + n-decane(2) mixtures with mole fractions of CO2 x1 = 0, 0.2032, 0.4434, 0.7589, and 0.8947 were measured using a vibrating tube densimeter. The combined expanded uncertainties of density with a level of confidence of 0.95 are estimated to be 0.6 kg·m−3. A total of 221 compressed liquid densities of CO2(1) + n-decane(2) mixtures along the five isotherms between T = (283 and 363) K with pressures up to 100 MPa were presented. The densities of mixtures were correlated by the modified Tait equation, resulting in absolute average deviations between the experimental and calculated values of 0.028%, 0.013%, 0.017%, 0.044%, and 0.042%. In addition, the isothermal compressibility, isobaric thermal expansivity, and excess molar volume were derived from the modified Tait equation. Full article
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32 pages, 770 KiB  
Review
On the Solute-Induced Structure-Making/Breaking Phenomena: Myths, Verities, and Misuses in Solvation Thermodynamics
by Ariel A. Chialvo
Liquids 2024, 4(3), 592-623; https://doi.org/10.3390/liquids4030033 - 3 Sep 2024
Cited by 3 | Viewed by 1640
Abstract
We review the statistical mechanic foundations of the fundamental structure-making/breaking functions, leading to the rigorous description of the solute-induced perturbation of the solvent environment for the understanding of the solvation process of any species regardless of the type and nature of the [...] Read more.
We review the statistical mechanic foundations of the fundamental structure-making/breaking functions, leading to the rigorous description of the solute-induced perturbation of the solvent environment for the understanding of the solvation process of any species regardless of the type and nature of the solute–solvent interactions. Then, we highlight how these functions are linked to unambiguous thermodynamic responses resulting from changes in state conditions, composition, and solute–solvent intermolecular interaction asymmetries. Finally, we identify and illustrate the pitfalls behind the use of surrogate approaches to structure-making/breaking markers, including those based on Jones–Dole’s B-coefficient and Hepler’s isobaric-thermal expansivity, while highlighting their ambiguities and lack of consistency and the sources of misinterpretations. Full article
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17 pages, 6508 KiB  
Article
Design and Characterisation of a 3D-Printed Pneumatic Rotary Actuator Exploiting Enhanced Elastic Properties of Auxetic Metamaterials
by Francesca Federica Donadio, Donatella Dragone, Anna Procopio, Francesco Amato, Carlo Cosentino and Alessio Merola
Actuators 2024, 13(9), 329; https://doi.org/10.3390/act13090329 - 30 Aug 2024
Viewed by 1937
Abstract
This paper describes the design and characterisation of a novel hybrid pneumatic rotational actuator that aims to overcome the limitations of both rigid and soft actuators while combining their advantages; indeed, the designed actuator consists of a soft air chamber having an auxetic [...] Read more.
This paper describes the design and characterisation of a novel hybrid pneumatic rotational actuator that aims to overcome the limitations of both rigid and soft actuators while combining their advantages; indeed, the designed actuator consists of a soft air chamber having an auxetic structure constrained between two rigid frames connected by a soft hinge joint inspired by the musculoskeletal structure of a lobster leg. The main goal is to integrate the advantages of soft actuation, such as inherent compliance and safe human–robot interaction, with those of rigid components, i.e., the robustness and structural stability limiting the ineffective expansion of the soft counterpart of the actuator. The air chamber and its auxetic structure are capable of leveraging the hyper-elastic properties of the soft fabrication material, thereby optimising the response and extending the operational range of the rotational actuator. Each component of the hybrid actuator is fabricated using a 3D-printing method based on Fused Deposition Modeling technology; the soft components are made of thermoplastic polyurethane, and the rigid components are made of polylactic acid. The design phases were followed by some experimental tests to characterise the hybrid actuation by reproducing the typical operating conditions of the actuator itself. In particular, the actuator response in unconstrained expansion and isometric and isobaric conditions has been evaluated. The experimental results show linearity, good repeatability, and sensitivity of the actuator response vs. pneumatic pressure input, other than a small percentage hysteresis, which is ten times less than that observed in commercial soft pneumatic actuators. Full article
(This article belongs to the Special Issue Advanced Technologies in Soft Pneumatic Actuators)
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19 pages, 6038 KiB  
Article
Numerical Study on the Fracturing of Deep Rock Masses by Blasting Based on the Material Point Method
by Hu Xiao, Meng Wang, Weiting Gao, Ming Zou, Yuntao Wang and Jinshan Sun
Processes 2024, 12(6), 1048; https://doi.org/10.3390/pr12061048 - 21 May 2024
Viewed by 1579
Abstract
Blasting is a prevalent technique in deep rock excavation, with the state of rock fragmentation under high in-situ stress conditions being distinct from that under low in-situ stress conditions. A new material point method framework utilizing the generalized interpolated material point and convective [...] Read more.
Blasting is a prevalent technique in deep rock excavation, with the state of rock fragmentation under high in-situ stress conditions being distinct from that under low in-situ stress conditions. A new material point method framework utilizing the generalized interpolated material point and convective particle domain interpolation functions was implemented to simulate the single-hole blasting process, analyze the stress distribution around the blasting hole, and elucidate the mechanism of how ground stress influences the expansion of blasting cracks through the interaction with the blasting load. In addition, the dynamic relaxation method realizes the stress’s initialization. It was concluded that the in-situ stress can increase the compressive stress induced by blasting load, whereas it decreases the caused tensile stress. With the increase in the ground stress, the scale of the cracks decreases. Under the non-isobaric condition, the blast-induced cracks preferentially expand along the high stress with the increase in the stress difference between the horizontal direction and the vertical direction, and the blast-induced cracks are suppressed to the greatest extent in the direction of the minimum ground stress. Full article
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15 pages, 2836 KiB  
Article
Isobaric Expansion Engines–Compressors: Thermodynamic Analysis of Multistage Vapor Driven Compressors
by Alexander Kronberg, Maxim Glushenkov, Sander Roosjen and Sascha Kersten
Energies 2023, 16(19), 6791; https://doi.org/10.3390/en16196791 - 24 Sep 2023
Cited by 2 | Viewed by 2134
Abstract
Isobaric expansion (IE) engines can directly convert heat into mechanical energy, making them particularly attractive for applications such as vapor-driven pumps and compressors. A recent initial assessment investigating the utilization of IE engines as vapor-driven reciprocating compressors has revealed that the vapor use [...] Read more.
Isobaric expansion (IE) engines can directly convert heat into mechanical energy, making them particularly attractive for applications such as vapor-driven pumps and compressors. A recent initial assessment investigating the utilization of IE engines as vapor-driven reciprocating compressors has revealed that the vapor use efficiency is inherently low in the case of the simplest direct-acting compressor designs. Based on this analysis, it was anticipated that multistage compression can offer significant advantages for vapor-driven compressors. Therefore, this paper aims to conduct a comprehensive analytical thermodynamic analysis of direct vapor-driven multistage reciprocating compressors. The analysis considers processes without intercooling and processes with intercooling of the compressed gas between stages. The findings demonstrate that, for vapor-driven compression, the benefits of multistage compression are superior to those known for conventional compression processes. Multistage vapor-driven compression not only reduces compression work and temperature elevation but, more importantly, mitigates the adverse effects on vapor compression of the driving vapor, thereby enabling a substantial improvement in vapor utilization efficiency. Furthermore, the total volume of the IE engine compressor experiences a significant decrease with an increasing number of stages. Consequently, under specific process parameters, the overall dimensions of the engine-compressor system may also decrease as the number of stages increases. The results offer significant opportunities for energy savings in energy-intensive compression processes by replacing electrical energy with readily available low-grade heat sources (<100 °C). Such processes include hydrogen, air, and ethylene compression at high pressure. Full article
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21 pages, 2910 KiB  
Article
Thermodynamic and Thermal Analyze of N,N-Dimethylformamide + 1-Butanol Mixture Properties Based on Density, Sound Velocity and Heat Capacity Data
by Magdalena Tyczyńska, Aleksandra Dentkiewicz and Małgorzata Jóźwiak
Molecules 2023, 28(12), 4698; https://doi.org/10.3390/molecules28124698 - 11 Jun 2023
Cited by 5 | Viewed by 2232
Abstract
The present paper contains data on the density (ρ), sound velocity (u), and specific heat capacity cp of the mixture of N,N-dimethylformamide + 1-butanol (DMF + BuOH) determined in the entire concentration range [...] Read more.
The present paper contains data on the density (ρ), sound velocity (u), and specific heat capacity cp of the mixture of N,N-dimethylformamide + 1-butanol (DMF + BuOH) determined in the entire concentration range of solution and in the temperature range (293.15–318.15) K. The analysis of thermodynamic functions such as isobaric molar expansion, isentropic and isothermal molar compression, isobaric and isochoric molar heat capacity, as well as their excess functions (Ep,mE,KS,mE,KT,mE,Cp, mE,CV, mE) and also VmE was undertaken. The analysis of changes in the physicochemical quantities was based on consideration of the system in terms of intermolecular interactions and resulting changes in the mixture structure. The results available in the literature were confusing during the analysis and became the reason for our decision to thoroughly examine the system. What is more, for a system whose components are widely used, there is very scarce information in the literature regarding the heat capacity of the tested mixture, which was also achieved and presented in this publication. The conclusions drawn from so many data points allow us to approximate and understand the changes that occur in the structure of the system due to the repeatability and consistency of the obtained results. Full article
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10 pages, 3495 KiB  
Article
Isobaric Thermal Expansivity and Isothermal Compressibility of Liquid Metals
by Yuri N. Starodubtsev and Vladimir S. Tsepelev
Materials 2023, 16(10), 3801; https://doi.org/10.3390/ma16103801 - 17 May 2023
Cited by 1 | Viewed by 1822
Abstract
The relationship between the volumetric thermodynamic coefficients of liquid metals at the melting point and interatomic bond energy was studied. Using dimensional analysis, we obtained equations that connect cohesive energy with thermodynamic coefficients. The relationships were confirmed by experimental data for alkali, alkaline [...] Read more.
The relationship between the volumetric thermodynamic coefficients of liquid metals at the melting point and interatomic bond energy was studied. Using dimensional analysis, we obtained equations that connect cohesive energy with thermodynamic coefficients. The relationships were confirmed by experimental data for alkali, alkaline earth, rare earth, and transition metals. Cohesive energy is proportional to the square root of the ratio of melting point Tm divided by thermal expansivity αp. Thermal expansivity does not depend on the atomic size and atomic vibration amplitude. Bulk compressibility βT and internal pressure pi are related to the atomic vibration amplitude by an exponential dependence. Thermal pressure pth decreases with an increasing atomic size. Fcc and hcp metals with high packing density, as well as alkali metals, have the relationships with the highest coefficient of determination. The contribution of electrons and atomic vibrations to the Grüneisen parameter can be calculated for liquid metals at their melting point. Full article
(This article belongs to the Special Issue Advances in Alloys - Microstructure, Manufacturing and Analysis)
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23 pages, 3437 KiB  
Article
The Group Contribution to the Function Derived from Density and Speed-of-Sound Measurements for Glymes in N,N-Dimethylformamide + Water Mixtures
by Małgorzata Jóźwiak, Marlena Komudzińska and Magdalena Tyczyńska
Molecules 2023, 28(4), 1519; https://doi.org/10.3390/molecules28041519 - 4 Feb 2023
Viewed by 1417
Abstract
The density and speed of sound of pentaglyme and hexaglyme in the N,N-dimethylformamide + water mixture at four temperatures are presented. The limiting apparent molar volumes (VΦ,m0=Vm0), the isobaric molar [...] Read more.
The density and speed of sound of pentaglyme and hexaglyme in the N,N-dimethylformamide + water mixture at four temperatures are presented. The limiting apparent molar volumes (VΦ,m0=Vm0), the isobaric molar thermal expansion (Ep,m0), the isentropic compressibility (κS), and the limiting partial molar isentropic compression (KS,Φ,m0 = KS,m0) were calculated. Changes in the values obtained from the physicochemical parameters, as functions of composition and temperature, were analyzed in terms of the molecular interactions and structural differentiation of the investigated systems. The hydrophobic hydration process of the studied glymes was visible in the area of high water content in the mixture. The hydration number of glymes in water at four temperatures was calculated and analyzed. The contribution of the –CH2– and –O– group to the functions describing the volume and acoustic properties of the investigated system was calculated. The calculated values of the functions analyzed using the group contribution are in agreement with the values obtained from the experimental data. Thus, such contributions are valuable for wide ranges of data, which can be used to analyze the hydrophobic hydration and preferential solvation processes, as well as to calculate the values of these functions for other similar compounds. Full article
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14 pages, 3400 KiB  
Article
Waste Heat Recovery Systems with Isobaric Expansion Technology Using Pure and Mixed Working Fluids
by Sander Roosjen, Maxim Glushenkov, Alexander Kronberg and Sascha Kersten
Energies 2022, 15(14), 5265; https://doi.org/10.3390/en15145265 - 20 Jul 2022
Cited by 6 | Viewed by 2602
Abstract
Economic expedience of waste heat recovery systems (WHRS), especially for low temperature difference applications, is often questionable due to high capital investments and long pay-back periods. With a simple design, isobaric expansion (IE) machines could provide a viable pathway to utilizing otherwise unprofitable [...] Read more.
Economic expedience of waste heat recovery systems (WHRS), especially for low temperature difference applications, is often questionable due to high capital investments and long pay-back periods. With a simple design, isobaric expansion (IE) machines could provide a viable pathway to utilizing otherwise unprofitable waste heat streams for power generation and particularly for pumping liquids and compression of gases. Different engine configurations are presented and discussed. A new method of modeling and calculation of the IE process and efficiency is used on IE cycles with various pure and mixed working fluids. Some interesting cases are presented. It is shown in this paper that the simplest non-regenerative IE engines are efficient at low temperature differences between a heat source and heat sink. The efficiency of the non-regenerative IE process with pure working fluid can be very high, approaching Carnot efficiency at low pressure and heat source/heat sink temperature differences. Regeneration can increase efficiency of the IE cycle to some extent. Application of mixed working fluids in combination with regeneration can significantly increase the range of high efficiencies to much larger temperature and pressure differences. Full article
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20 pages, 2499 KiB  
Article
Isobaric Expansion Engine Compressors: Thermodynamic Analysis of the Simplest Direct Vapor-Driven Compressors
by Alexander Kronberg, Maxim Glushenkov, Sander Roosjen and Sascha Kersten
Energies 2022, 15(14), 5028; https://doi.org/10.3390/en15145028 - 9 Jul 2022
Cited by 4 | Viewed by 2135
Abstract
Isobaric expansion (IE) technology is a promising solution for mini- and medium-scale low-grade heat utilization. IE engines directly convert heat to mechanical energy and are particularly interesting as direct-acting, vapor-driven pumps and compressors. The elimination of multiple energy transformations, technical simplicity and the [...] Read more.
Isobaric expansion (IE) technology is a promising solution for mini- and medium-scale low-grade heat utilization. IE engines directly convert heat to mechanical energy and are particularly interesting as direct-acting, vapor-driven pumps and compressors. The elimination of multiple energy transformations, technical simplicity and the ability to use widely available low-grade heat (<100 °C) instead of fossil fuels are attractive features of this technology. The purpose of this paper was to present a new compression technology based on IE Worthington type engines, analyze the process analytically and numerically, and provide a first assessment of its potential. The simplest single- and double-acting schemes were considered for arbitrary low and high pressures of the compressed gas/vapor and driving vapor. In these schemes, the compressor piston was rigidly connected to that of an engine/driver. The vapor use efficiency of the driver process was characterized by the ratio of the network carried out in the cycle to the consumed mass of the driving vapor. The performed thermodynamic analysis showed how the vapor use efficiency depends on the process parameters. It was found that the efficiency of vapor use in the simplest schemes was low in comparison with the efficiency in pumps if the compressor work was much less than the pump work at the same pressure ratio. This occurred because the energy of the driving vapor was spent on the compression of the vapor itself. As a result, the thermal efficiency of the IE engine compressors was lower than that of the IE engine pumps. The difference was very large if the work of the engine feed pump was significant and no heat regeneration is applied. The results obtained are very useful for achieving improvements in this interesting technology, which will be reported in subsequent publications. Full article
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17 pages, 2377 KiB  
Article
Synthesis and Characterization of Fluorinated Phosphonium Ionic Liquids to Use as New Engineering Solvents
by María C. Naranjo, Andres E. Redondo, Jacqueline C. Acuña, Nicole S. M. Vieira, João M. M. Araújo and Ana B. Pereiro
ChemEngineering 2022, 6(3), 38; https://doi.org/10.3390/chemengineering6030038 - 24 May 2022
Cited by 3 | Viewed by 3107
Abstract
In this work, a set of novel fluorinated ionic liquids (FILs), based on different tetra-alkyl-phosphonium cations with perfluorobutanesulfonate and perfluoropentanoate anions, were synthesized and characterized in order to check their suitability to apply as engineering solvents. Thermophysical and thermal properties were both determined [...] Read more.
In this work, a set of novel fluorinated ionic liquids (FILs), based on different tetra-alkyl-phosphonium cations with perfluorobutanesulfonate and perfluoropentanoate anions, were synthesized and characterized in order to check their suitability to apply as engineering solvents. Thermophysical and thermal properties were both determined between 293.15 and 353.15 K, and the molecular volumes and free volumes and the coefficients of isobaric thermal expansion were determined from experimental values of refractive index and density. Lastly, the Walden plot was used to evaluate the ionicity of the novel FILs. The cytotoxicity of these compounds was also determined using the human hepatocellular carcinoma cells (HepG2) and the human colon carcinoma cells (Caco-2). Finally, the results were all discussed with the aim of understanding the behaviour of these compounds, considering the influence of the anion and the hydrogenated alkyl chain length. In summary, the new FILs synthesized in this work present adequate properties for their application in different industrial processes. Most of these compounds are liquid at room temperature with high decomposition temperatures. All phosphonium-based FILs have lower densities than conventional ionic liquids and common organic solvents, and the viscosity depends directly on the selected anion. Furthermore, the ionicity of FILs based on the sulfonate anion is higher than those based on the carboxylate anion. Finally, the phosphonium-based FILs have no significant effect on cellular viability at lower concentrations. Full article
(This article belongs to the Special Issue Ionic Liquids as New Alternative Engineering Solvents)
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20 pages, 2779 KiB  
Article
Thermodynamic Conditions for Consolidation of Dissimilar Materials in Bimetal and Functional Graded Structures
by Alexander Khaimovich, Yaroslav Erisov and Igor Shishkovsky
Materials 2022, 15(3), 825; https://doi.org/10.3390/ma15030825 - 21 Jan 2022
Cited by 3 | Viewed by 1970
Abstract
Functional Graded Structures and Functional Graded parts, made using dissimilar materials, are designed to provide specific properties to the final product. One of the most promising methods for manufacturing 3D Functional Graded objects is 3D laser cladding and/or direct energy deposition. However, the [...] Read more.
Functional Graded Structures and Functional Graded parts, made using dissimilar materials, are designed to provide specific properties to the final product. One of the most promising methods for manufacturing 3D Functional Graded objects is 3D laser cladding and/or direct energy deposition. However, the construction of graded and especially layered graded structures in the process of joining materials with different thermophysical properties under certain conditions is accompanied by the formation of cracks along the phase boundaries, which are a consequence of residual stresses and/or chemical segregations. The conditions for phase consolidation are macroscopic balancing of residual stresses in the region of the interface. In a broader sense, in the field of the interface, it is necessary to consider the thermodynamic equilibrium of the phases in connection with mechanical equilibrium. In this regard, the article proposed criteria for the thermodynamic affinity of phases in the area of the Functional Graded Structures interface, including the coefficients of thermal expansion and isobaric and isochoric heat capacities of the phases. Examples of cracking and the use of the obtained criteria are provided. Full article
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20 pages, 1079 KiB  
Article
New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations
by Renata Nikonorova, Dilara Siraeva and Yulia Yulmukhametova
Mathematics 2022, 10(1), 123; https://doi.org/10.3390/math10010123 - 1 Jan 2022
Cited by 3 | Viewed by 2029
Abstract
In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the [...] Read more.
In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras. Full article
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