Pub Date : 2025-07-09DOI: 10.1134/S0869864324050068
V. E. Zhukov, N. N. Mezentseva
Passive intensification of heat transfer in a tube is achieved by using detachable intensifiers or changing the shape of the heat transfer surface. In this work, the intensification process was studied using spherical turbolizers located in a horizontal stainless steel channel. Experimental data were obtained during circulation of an alcohol-water mixture with a concentration of 30% wt. at a pressure in the vessel of 0.03–0.04 MPa. It is shown that the efficiency of spherical intensifiers is commensurate with the efficiency of spiral intensifiers at significantly lower pressure drops.
{"title":"Heat transfer in a channel with spherical intensifiers where a non-azeotropic alcohol-water mixture circulates","authors":"V. E. Zhukov, N. N. Mezentseva","doi":"10.1134/S0869864324050068","DOIUrl":"10.1134/S0869864324050068","url":null,"abstract":"<div><p>Passive intensification of heat transfer in a tube is achieved by using detachable intensifiers or changing the shape of the heat transfer surface. In this work, the intensification process was studied using spherical turbolizers located in a horizontal stainless steel channel. Experimental data were obtained during circulation of an alcohol-water mixture with a concentration of 30% wt. at a pressure in the vessel of 0.03–0.04 MPa. It is shown that the efficiency of spherical intensifiers is commensurate with the efficiency of spiral intensifiers at significantly lower pressure drops.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 5","pages":"963 - 966"},"PeriodicalIF":0.6,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-09DOI: 10.1134/S0869864324050172
D. A. Samoshkin, A. Sh. Agazhanov, S. V. Stankus
The thermal diffusivity and the thermal conductivity of solid erbium in the temperature interval of 295–1475 K have been measured using the laser flash method. Approximation equations and a table of reference values for the temperature dependence of heat transfer coefficients of the studied metal have been received. The obtained results have been compared with the known literature data. The temperature dependence of the erbium thermal conductivity is shown to be mainly determined by the electronic contribution.
{"title":"Thermal conductivity and thermal diffusivity of erbium in the temperature range of 295–1475 K","authors":"D. A. Samoshkin, A. Sh. Agazhanov, S. V. Stankus","doi":"10.1134/S0869864324050172","DOIUrl":"10.1134/S0869864324050172","url":null,"abstract":"<div><p>The thermal diffusivity and the thermal conductivity of solid erbium in the temperature interval of 295–1475 K have been measured using the laser flash method. Approximation equations and a table of reference values for the temperature dependence of heat transfer coefficients of the studied metal have been received. The obtained results have been compared with the known literature data. The temperature dependence of the erbium thermal conductivity is shown to be mainly determined by the electronic contribution.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 5","pages":"1089 - 1095"},"PeriodicalIF":0.6,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040073
M. M. Vasilev, V. V. Terekhov
Numerical simulations of droplet interaction dynamics with a biphilic surface are performed using the multi-relaxation-time lattice Boltzmann method (MRT-LBM). The biphilic surface is modeled as a superhydrophilic circular region imposed within a superhydrophobic plane. The study is aimed at considering key aspects of droplet spreading upon an impact at the center of the superhydrophilic spot, droplet rebound, and formation of a residual droplet as the size of the superhydrophilic region is varied. Three characteristic interaction regimes are identified: droplet detachment, transitional regime, and droplet adhesion. Additionally, the velocity fields inside the droplet are analyzed throughout the entire interaction process.
{"title":"Modeling the dynamics of incident droplet interaction with a biphilic surface","authors":"M. M. Vasilev, V. V. Terekhov","doi":"10.1134/S0869864324040073","DOIUrl":"10.1134/S0869864324040073","url":null,"abstract":"<div><p>Numerical simulations of droplet interaction dynamics with a biphilic surface are performed using the multi-relaxation-time lattice Boltzmann method (MRT-LBM). The biphilic surface is modeled as a superhydrophilic circular region imposed within a superhydrophobic plane. The study is aimed at considering key aspects of droplet spreading upon an impact at the center of the superhydrophilic spot, droplet rebound, and formation of a residual droplet as the size of the superhydrophilic region is varied. Three characteristic interaction regimes are identified: droplet detachment, transitional regime, and droplet adhesion. Additionally, the velocity fields inside the droplet are analyzed throughout the entire interaction process.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"699 - 709"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040231
S. Benattalah
From the literature, there is few experimental data on the Dumitrescu–Taylor bubble wall shear stress in stagnant and flowing liquid in vertical tube Thus, in this study, experimental results are presented on the wall shear stress recorded around an individual Dumitrescu–Taylor bubble. The experiments were carried out in a counter-current laminar downward flow in vertical tube with an inner diameter of 0.0102 m. With the experimental device, the bubble can have two extreme travel velocities; from a low bubble velocity in counter-current flow to a maximum velocity in stagnant flow. The real picture recording signals of wall shear stress are presented over a wide range of an axial position below the nose of the bubble and for the two extreme bubble velocity. The results show clearly the sensitivity of the velocity effect on the wall shear stress profiles. The wall shear stress appears to decrease as the bubble velocity increases in counter-current flow. According to the shear stress profiles results, valuable information on the liquid film flow regime is provided with a reverse flow behind the bubble’s bottom. The change of the flow direction, the length of the parietal vortices and the distance of the flow stabilization behind the bottom of the bubble has been characterized.
{"title":"Experimental study of Dumitrescu–Taylor bubble wall shear stress in stagnant and counter-current vertical flow","authors":"S. Benattalah","doi":"10.1134/S0869864324040231","DOIUrl":"10.1134/S0869864324040231","url":null,"abstract":"<div><p>From the literature, there is few experimental data on the Dumitrescu–Taylor bubble wall shear stress in stagnant and flowing liquid in vertical tube Thus, in this study, experimental results are presented on the wall shear stress recorded around an individual Dumitrescu–Taylor bubble. The experiments were carried out in a counter-current laminar downward flow in vertical tube with an inner diameter of 0.0102 m. With the experimental device, the bubble can have two extreme travel velocities; from a low bubble velocity in counter-current flow to a maximum velocity in stagnant flow. The real picture recording signals of wall shear stress are presented over a wide range of an axial position below the nose of the bubble and for the two extreme bubble velocity. The results show clearly the sensitivity of the velocity effect on the wall shear stress profiles. The wall shear stress appears to decrease as the bubble velocity increases in counter-current flow. According to the shear stress profiles results, valuable information on the liquid film flow regime is provided with a reverse flow behind the bubble’s bottom. The change of the flow direction, the length of the parietal vortices and the distance of the flow stabilization behind the bottom of the bubble has been characterized.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"865 - 877"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S086986432404022X
Yi Gao, Juanmian Lei, Jintao Yin
In this paper, computational fluid dynamics simulation was conducted for a lateral-jet-controlled spinning missile under supersonic conditions to investigate the influence of jet interference on the aerodynamic characteristics of the spinning missile. For numerical simulation, the Menter shear-stress transport turbulence model was used to solve the three-dimensional unsteady compressible Navier–Stokes equations, and the sliding mesh method was utilized to simulate the flow field numerically. The methodology and mesh were validated by comparing the numerical results with the realistic wind tunnel data. The lateral jet interference characteristics of a spinning missile were studied, in which the various characteristics of the interference flow field structure, interference amplification factors and the lateral force were analysed and compared with those without the effects of spinning. Moreover, the effects of different pressure ratios on the flow field and aerodynamic characteristics were also studied. The results show that the missile spinning motion changes the shape of the separation region before the jet nozzle, and the jet wake deflects circumferentially. The deflection angle of the low-pressure region behind the jet is larger than the one of the high-pressure region ahead of the jet, therefore a jet-induced lateral force is generated on the spinning missile. The magnitude of lateral force increases with the increase of spin rate, and the direction of lateral force may change with the increase of angles of attack. The directions of jet interference force and jet control force will deflect when spinning missile adopting lateral jet control, and the deflection angles increases with the increase of spin rate. When spin rate is same, lateral force coefficient increases with the increase of pressure ratios and the deflection angles of jet interference force and jet control force decrease with the increase of pressure ratios.
{"title":"Numerical investigation of lateral jet interaction effects on a spinning missile","authors":"Yi Gao, Juanmian Lei, Jintao Yin","doi":"10.1134/S086986432404022X","DOIUrl":"10.1134/S086986432404022X","url":null,"abstract":"<div><p>In this paper, computational fluid dynamics simulation was conducted for a lateral-jet-controlled spinning missile under supersonic conditions to investigate the influence of jet interference on the aerodynamic characteristics of the spinning missile. For numerical simulation, the Menter shear-stress transport turbulence model was used to solve the three-dimensional unsteady compressible Navier–Stokes equations, and the sliding mesh method was utilized to simulate the flow field numerically. The methodology and mesh were validated by comparing the numerical results with the realistic wind tunnel data. The lateral jet interference characteristics of a spinning missile were studied, in which the various characteristics of the interference flow field structure, interference amplification factors and the lateral force were analysed and compared with those without the effects of spinning. Moreover, the effects of different pressure ratios on the flow field and aerodynamic characteristics were also studied. The results show that the missile spinning motion changes the shape of the separation region before the jet nozzle, and the jet wake deflects circumferentially. The deflection angle of the low-pressure region behind the jet is larger than the one of the high-pressure region ahead of the jet, therefore a jet-induced lateral force is generated on the spinning missile. The magnitude of lateral force increases with the increase of spin rate, and the direction of lateral force may change with the increase of angles of attack. The directions of jet interference force and jet control force will deflect when spinning missile adopting lateral jet control, and the deflection angles increases with the increase of spin rate. When spin rate is same, lateral force coefficient increases with the increase of pressure ratios and the deflection angles of jet interference force and jet control force decrease with the increase of pressure ratios.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"841 - 863"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040206
D. A. Suslov, S. G. Skripkin, M. A. Tsoy, E. Yu. Gorelikov, S. I. Shtork
This paper presents the development of active control methods for vortex phenomena in hydro turbines. The flow pattern downstream of a simplified turbine runner was studied under conditions typical of a hydro turbine operating at partial load, which are prone to generating large-scale vortex structures and inducing powerful pressure pulsations. Active control was achieved through the injection of additional air jets into the center of the runner cone. The results of experiments covering velocity distributions, velocity pulsations, and pressure pulsations following the injection of jets are presented. Control jets, regardless of their orientation, successfully suppress pressure pulsations. However, jets oriented radially provide the most effective suppression of vortices and reduce the total flow swirl in the draft tube. The pattern of jet supply directly affects the formation of a recirculation zone downstream of the runner. Experimental data on optimal injection align with previous theoretical estimates based on flow linear stability analysis.
{"title":"Active vortex control downstream the turbine runner in the Francis hydro turbine model","authors":"D. A. Suslov, S. G. Skripkin, M. A. Tsoy, E. Yu. Gorelikov, S. I. Shtork","doi":"10.1134/S0869864324040206","DOIUrl":"10.1134/S0869864324040206","url":null,"abstract":"<div><p>This paper presents the development of active control methods for vortex phenomena in hydro turbines. The flow pattern downstream of a simplified turbine runner was studied under conditions typical of a hydro turbine operating at partial load, which are prone to generating large-scale vortex structures and inducing powerful pressure pulsations. Active control was achieved through the injection of additional air jets into the center of the runner cone. The results of experiments covering velocity distributions, velocity pulsations, and pressure pulsations following the injection of jets are presented. Control jets, regardless of their orientation, successfully suppress pressure pulsations. However, jets oriented radially provide the most effective suppression of vortices and reduce the total flow swirl in the draft tube. The pattern of jet supply directly affects the formation of a recirculation zone downstream of the runner. Experimental data on optimal injection align with previous theoretical estimates based on flow linear stability analysis.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"819 - 830"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040127
I. V. Vladyko, A. S. Surtaev, N. B. Miskiv, A. V. Mikhailov, A. D. Nazarov, A. N. Pavlenko
The results of an experimental investigation on heat transfer and critical heat flux during surface cooling with a dispersed flow of deeply subcooled liquid are presented. The study was carried out using a pressure nozzle with a mass flow rate of water of 24.2 g/s. A record critical heat flux of 13.2 MW/m2 was achieved in these experiments. The findings indicate that the onset of boiling within the liquid film formed on the impact surface during spraying leads to a notable reduction in the temperature non-uniformity across the heater.
{"title":"Heat transfer regimes and critical heat flux during spray cooling with subcooled water","authors":"I. V. Vladyko, A. S. Surtaev, N. B. Miskiv, A. V. Mikhailov, A. D. Nazarov, A. N. Pavlenko","doi":"10.1134/S0869864324040127","DOIUrl":"10.1134/S0869864324040127","url":null,"abstract":"<div><p>The results of an experimental investigation on heat transfer and critical heat flux during surface cooling with a dispersed flow of deeply subcooled liquid are presented. The study was carried out using a pressure nozzle with a mass flow rate of water of 24.2 g/s. A record critical heat flux of 13.2 MW/m<sup>2</sup> was achieved in these experiments. The findings indicate that the onset of boiling within the liquid film formed on the impact surface during spraying leads to a notable reduction in the temperature non-uniformity across the heater.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"749 - 753"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040024
E. V. Usov, P. D. Lobanov, V. I. Chukhno, I. A. Klimonov, N. A. Mosunova, S. I. Lezhnin, N. A. Pribaturin
Models of the severe-accident SAFR module used to calculate the cladding melt relocation along the fuel pin surface during its melting are presented in relation to severe accidents in fast-neutron reactors cooled by liquid metal. The choice of the basic system of equations and closing relations is presented. The models are validated based on experiments on melting and flow of cladding simulator melts. The error of calculating the cladding mass loss due to its melting and flowing along the fuel pin surface is estimated.
{"title":"Physical models of the severe-accident SAFR module of the integral EVKLID/V2 code for calculating the cladding melt relocation over the fuel pin surface","authors":"E. V. Usov, P. D. Lobanov, V. I. Chukhno, I. A. Klimonov, N. A. Mosunova, S. I. Lezhnin, N. A. Pribaturin","doi":"10.1134/S0869864324040024","DOIUrl":"10.1134/S0869864324040024","url":null,"abstract":"<div><p>Models of the severe-accident SAFR module used to calculate the cladding melt relocation along the fuel pin surface during its melting are presented in relation to severe accidents in fast-neutron reactors cooled by liquid metal. The choice of the basic system of equations and closing relations is presented. The models are validated based on experiments on melting and flow of cladding simulator melts. The error of calculating the cladding mass loss due to its melting and flowing along the fuel pin surface is estimated.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"645 - 652"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040036
A. Sh. Agazhanov, R. A. Khairulin, R. N. Abdullaev, S. V. Stankus
A density and a volumetric thermal expansion coefficient of the LiK3Pb4 ternary alloy (12.5 at. % Li, 37.5 at. % K, and 50.0 at. % Pb) in the liquid state are measured for the first time. Volumetric properties are studied using a gamma-ray attenuation technique in the range from the liquidus temperature TL = 812 K to 990 K. The LiK3Pb4 solid alloy is known to be an intermetallic compound. Its thermal analysis at cooling from the liquid state carried out in this work has shown that the compound is likely formed by a peritectic reaction at 789 K. Based on the experimental results obtained, a table of recommended values for the volumetric properties of the LiK3Pb4 melt has been developed in the studied temperature range.
{"title":"Density and thermal expansion of LiK3Pb4 liquid alloy","authors":"A. Sh. Agazhanov, R. A. Khairulin, R. N. Abdullaev, S. V. Stankus","doi":"10.1134/S0869864324040036","DOIUrl":"10.1134/S0869864324040036","url":null,"abstract":"<div><p>A density and a volumetric thermal expansion coefficient of the LiK<sub>3</sub>Pb<sub>4</sub> ternary alloy (12.5 at. % Li, 37.5 at. % K, and 50.0 at. % Pb) in the liquid state are measured for the first time. Volumetric properties are studied using a gamma-ray attenuation technique in the range from the liquidus temperature <i>T</i><sub>L</sub> = 812 K to 990 K. The LiK<sub>3</sub>Pb<sub>4</sub> solid alloy is known to be an intermetallic compound. Its thermal analysis at cooling from the liquid state carried out in this work has shown that the compound is likely formed by a peritectic reaction at 789 K. Based on the experimental results obtained, a table of recommended values for the volumetric properties of the LiK<sub>3</sub>Pb<sub>4</sub> melt has been developed in the studied temperature range.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"653 - 658"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1134/S0869864324040061
S. V. Rykov, I. V. Kudryavtseva, V. A. Rykov
A new model of the phase equilibrium line (PEL) of methane has been developed on the basis of the Clapeyron–Clasius equation and the relations of the renormalization group (RG) theory. In contrast to the known PEL, when describing the density of a saturated liquid ρ+, density ρ−, and pressure ps of saturated methane vapor, a system of mutually consistent equations (CE) including those describing the saturation density line and saturation vapor line is used. These equations have a number of common parameters: critical indices, critical pressure, critical temperature Tc, critical density, as well as a series of coefficients of the average diameter model, df, coefficient D2β, complexes D2β/D1−α and D2β/Dτ, calculated within the framework of modern RG theory for asymmetric systems. Based on the proposed approach, a methane saturation line has been developed; its average diameter in a wide vicinity of the critical point is described in accordance with the RG theory by the dependence: df = D2βτ2β + D1−ατ1−α + Dττ, where τ = (1 − T/Tc). It has been established that df = df(T) within the framework of the proposed approach is a strictly decreasing function of temperature in the range from the triple point to the critical point. It has also been found that the derivative of the vaporization heat with respect to temperature, in accordance with the principles of thermodynamics, has a minimum in the vicinity of the triple point. Within the framework of the proposed PEL model, experimental data on ρ+, ρ−, and ps published by R. Kleinrahm and W. Wagner in 1986 are provided with standard deviation 0.0011 %, 0.0072 %, and 0.0012 %, respectively, that is, with greater accuracy than the international equations of U. Setzmann and W. Wagner derived in 1991.
{"title":"Saturation line of methane in the renormalization group theory in the range from the triple to the critical point","authors":"S. V. Rykov, I. V. Kudryavtseva, V. A. Rykov","doi":"10.1134/S0869864324040061","DOIUrl":"10.1134/S0869864324040061","url":null,"abstract":"<div><p>A new model of the phase equilibrium line (PEL) of methane has been developed on the basis of the Clapeyron–Clasius equation and the relations of the renormalization group (RG) theory. In contrast to the known PEL, when describing the density of a saturated liquid <i>ρ</i><sup>+</sup>, density <i>ρ</i><sup>−</sup>, and pressure <i>p</i><sub>s</sub> of saturated methane vapor, a system of mutually consistent equations (CE) including those describing the saturation density line and saturation vapor line is used. These equations have a number of common parameters: critical indices, critical pressure, critical temperature <i>T</i><sub>c</sub>, critical density, as well as a series of coefficients of the average diameter model, <i>d</i><sub><i>f</i></sub>, coefficient <i>D</i><sub>2<i>β</i></sub>, complexes <i>D</i><sub>2<i>β</i></sub>/<i>D</i><sub>1−<i>α</i></sub> and <i>D</i><sub>2<i>β</i></sub>/<i>D</i><sub><i>τ</i></sub>, calculated within the framework of modern RG theory for asymmetric systems. Based on the proposed approach, a methane saturation line has been developed; its average diameter in a wide vicinity of the critical point is described in accordance with the RG theory by the dependence: <i>d</i><sub><i>f</i></sub> = <i>D</i><sub>2<i>β</i></sub><i>τ</i><sup>2<i>β</i></sup> + <i>D</i><sub>1−<i>α</i></sub><i>τ</i><sup>1−<i>α</i></sup> + <i>D</i><sub><i>τ</i></sub><i>τ</i>, where <i>τ</i> = (1 − <i>T/T</i><sub>c</sub>). It has been established that <i>d</i><sub><i>f</i></sub> = <i>d</i><sub><i>f</i></sub>(<i>T</i>) within the framework of the proposed approach is a strictly decreasing function of temperature in the range from the triple point to the critical point. It has also been found that the derivative of the vaporization heat with respect to temperature, in accordance with the principles of thermodynamics, has a minimum in the vicinity of the triple point. Within the framework of the proposed PEL model, experimental data on <i>ρ</i><sup>+</sup>, <i>ρ</i><sup>−</sup>, and <i>p</i><sub>s</sub> published by R. Kleinrahm and W. Wagner in 1986 are provided with standard deviation 0.0011 %, 0.0072 %, and 0.0012 %, respectively, that is, with greater accuracy than the international equations of U. Setzmann and W. Wagner derived in 1991.</p></div>","PeriodicalId":800,"journal":{"name":"Thermophysics and Aeromechanics","volume":"31 4","pages":"685 - 698"},"PeriodicalIF":0.5,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}