The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential char...The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential characteristics of mesoscale eddies ascertained through each approach,and attempting to identify factors influencing eddy lifetime.The findings suggest that eddies identified via the sea surface height(SSH)method in the Eulerian framework typically have larger spatial extents compared to those identified using the Lagrangian Average Vorticity Deviation(LAVD)method.The latter is characterized by a greater number of vortices with smaller average values of characteristic parameters.SSH eddies exhibited more remarked seasonal variations than LAVD vortices,and the seasonal variations of their respective cyclonic and anticyclonic eddies showed opposite trends.Analysis in both frameworks indicates that eddy lifetime is positively correlated with various eddy characteristic parameters,including radius,vorticity,kinetic energy,amplitude,EKE/MKE(ratio of boundary to spatial mean kinetic energy),and U/c(max rotation speed to mean propagation speed ratio).A subsequent comparison between SSH eddies with LAVD cores(SSH eddy with LAVD vortex inside)and those without reveals a greater likelihood of extended lifetime in the former.Compared to the characteristic parameters of eddies,the presence of LAVD cores emerges as a critical factor in determining the lifetime of SSH eddies.展开更多
This numerical simulation investigates the two⁃phase flow under the condition of supercooled large droplets impinging on the aircraft surface.Based on Eulerian framework,a method for calculating supercooled water drop...This numerical simulation investigates the two⁃phase flow under the condition of supercooled large droplets impinging on the aircraft surface.Based on Eulerian framework,a method for calculating supercooled water droplet impingement characteristics is established.Then,considering the deformation and breaking effects during the movement,this method is extended to calculate the impingement characteristics of supercooled large droplets,as well as the bouncing and splashing effects during impingement.The impingement characteristics of supercooled large droplets is then investigated by this method.The results demonstrate that the deformation and breaking effects of supercooled large droplets have negligible influence on the impingement characteristics under the experimental conditions of this paper.In addition,the results of the impingement range and collection efficiency decrease when considering the bouncing and splashing effects.The bouncing effect mainly affects the mass loss near the impingement limits,while the splashing effect influences the result around the stagnation point.This investigation is beneficial for the analysis of aircraft icing and the design of anti⁃icing system with supercooled large droplet conditions.展开更多
This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with...This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.展开更多
A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）...A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）, then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying λ（D） ≥α（D）, then D is supereulerian.展开更多
A vertex cycle cover of a digraph H is a collection C = {C<sub>1</sub>, C<sub>2</sub>, …, C<sub>k</sub>} of directed cycles in H such that these directed cycles together cover all ...A vertex cycle cover of a digraph H is a collection C = {C<sub>1</sub>, C<sub>2</sub>, …, C<sub>k</sub>} of directed cycles in H such that these directed cycles together cover all vertices in H and such that the arc sets of these directed cycles induce a connected subdigraph of H. A subdigraph F of a digraph D is a circulation if for every vertex in F, the indegree of v equals its out degree, and a spanning circulation if F is a cycle factor. Define f (D) to be the smallest cardinality of a vertex cycle cover of the digraph obtained from D by contracting all arcs in F, among all circulations F of D. Adigraph D is supereulerian if D has a spanning connected circulation. In [International Journal of Engineering Science Invention, 8 (2019) 12-19], it is proved that if D<sub>1</sub> and D<sub>2</sub> are nontrivial strong digraphs such that D<sub>1</sub> is supereulerian and D<sub>2</sub> has a cycle vertex cover C’ with |C’| ≤ |V (D<sub>1</sub>)|, then the Cartesian product D<sub>1</sub> and D<sub>2</sub> is also supereulerian. In this paper, we prove that for strong digraphs D<sub>1</sub> and D<sub>2</sub>, if for some cycle factor F<sub>1</sub> of D<sub>1</sub>, the digraph formed from D<sub>1</sub> by contracting arcs in F1 is hamiltonian with f (D<sub>2</sub>) not bigger than |V (D<sub>1</sub>)|, then the strong product D<sub>1</sub> and D<sub>2</sub> is supereulerian.展开更多
A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian...A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Suis eulerian(or subeulerian,or eulerian and|E-(S)|is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′such that S′is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges e_(i)and e_(j)of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S′are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S∈S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S∈S′.展开更多
This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open pro...This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.展开更多
A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles...A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.展开更多
In this paper,the Eulerian Stochastic Field(ESF)model in the Transported Probability Density Function(TPDF)class model is combined with the Flamelet Generated Manifolds(FGM)model.This method solves the joint probabili...In this paper,the Eulerian Stochastic Field(ESF)model in the Transported Probability Density Function(TPDF)class model is combined with the Flamelet Generated Manifolds(FGM)model.This method solves the joint probability density function transport equation by ESF method that considers the interaction mechanism between flame and turbulence with high precision.At the same time,by making use of the advantage of the FGM model,this model is able to incorporate the detailed chemical reaction mechanism(GRI 3.0)with acceptable computational cost.The new model has been implemented in the open source CFD suite-Open FOAM.Validation of the model has been carried out by simulating the Sandia flame series(three turbulent piloted methane jet flames)issued by the National Laboratory of the United States.The accuracy and advancement of the ESF/FGM turbulent combustion model are verified by comparing the LES results of the new model with the rich experimental data as well as the RANS results.The results demonstrate that the model has a strong ability in capturing combustion phenomena such as extinction and re-ignition in turbulent flame,which is essential in the accurate prediction of the combustion process in real combustion devices,for example,aircraft engines.展开更多
Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which ...Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which the wet steam is regarded as mixture comprisingtwo coupled systems: the vapor phase and the liquid phase. These two systems are both described byconservation equations. High resolution TVD scheme is employed to capture condensing phenomena inwet steam flow. This model has been validated by numerical simulations of condensing flows in 1D and2D nozzles. Compared with experimental data, a good agreement is observed. This Eulerian/Eulerianmodel can be extended to 3D calculation of condensing flow.展开更多
基金Supported by the National Natural Science Foundation of China(No.41906021)the Guangdong Ocean University Scientific Research Start-up Fund(No.060302112312)。
文摘The study of mesoscale eddies is generally categorized in Eulerian or Lagrangian frameworks.We employed the eddy identification techniques in both frameworks in the South China Sea(SCS),examining the differential characteristics of mesoscale eddies ascertained through each approach,and attempting to identify factors influencing eddy lifetime.The findings suggest that eddies identified via the sea surface height(SSH)method in the Eulerian framework typically have larger spatial extents compared to those identified using the Lagrangian Average Vorticity Deviation(LAVD)method.The latter is characterized by a greater number of vortices with smaller average values of characteristic parameters.SSH eddies exhibited more remarked seasonal variations than LAVD vortices,and the seasonal variations of their respective cyclonic and anticyclonic eddies showed opposite trends.Analysis in both frameworks indicates that eddy lifetime is positively correlated with various eddy characteristic parameters,including radius,vorticity,kinetic energy,amplitude,EKE/MKE(ratio of boundary to spatial mean kinetic energy),and U/c(max rotation speed to mean propagation speed ratio).A subsequent comparison between SSH eddies with LAVD cores(SSH eddy with LAVD vortex inside)and those without reveals a greater likelihood of extended lifetime in the former.Compared to the characteristic parameters of eddies,the presence of LAVD cores emerges as a critical factor in determining the lifetime of SSH eddies.
基金supported in part by the National Natural Science Foundation of China(No.51806008)the Open Fund of Key Laboratory of Rotor Aerodynamics Key Laboratory(No.RAL202104-2)。
文摘This numerical simulation investigates the two⁃phase flow under the condition of supercooled large droplets impinging on the aircraft surface.Based on Eulerian framework,a method for calculating supercooled water droplet impingement characteristics is established.Then,considering the deformation and breaking effects during the movement,this method is extended to calculate the impingement characteristics of supercooled large droplets,as well as the bouncing and splashing effects during impingement.The impingement characteristics of supercooled large droplets is then investigated by this method.The results demonstrate that the deformation and breaking effects of supercooled large droplets have negligible influence on the impingement characteristics under the experimental conditions of this paper.In addition,the results of the impingement range and collection efficiency decrease when considering the bouncing and splashing effects.The bouncing effect mainly affects the mass loss near the impingement limits,while the splashing effect influences the result around the stagnation point.This investigation is beneficial for the analysis of aircraft icing and the design of anti⁃icing system with supercooled large droplet conditions.
基金Project supported by the National Natural Sciences Foundation of China(No.11272175)the Specialized Research Found for Doctoral Program of Higher Education(No.20130002110044)
文摘This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1176107161363020)+1 种基金Science and Technology Innovation Project of Xinjiang Normal University(Grant No.XSY201602013)the"13th Five-Year"Plan for Key Discipline Mathematics of Xinjiang Normal University(Grant No.17SDKD1107)
文摘A digraph D is supereulerian if D has a spanning eulerian subdigraph. Bang- Jensen and Thomasse conjectured that if the arc-strong connectivity ）,（D） of α digraph D is not less than the independence number α（D）, then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfying λ（D） ≥α（D）, then D is supereulerian.
文摘A vertex cycle cover of a digraph H is a collection C = {C<sub>1</sub>, C<sub>2</sub>, …, C<sub>k</sub>} of directed cycles in H such that these directed cycles together cover all vertices in H and such that the arc sets of these directed cycles induce a connected subdigraph of H. A subdigraph F of a digraph D is a circulation if for every vertex in F, the indegree of v equals its out degree, and a spanning circulation if F is a cycle factor. Define f (D) to be the smallest cardinality of a vertex cycle cover of the digraph obtained from D by contracting all arcs in F, among all circulations F of D. Adigraph D is supereulerian if D has a spanning connected circulation. In [International Journal of Engineering Science Invention, 8 (2019) 12-19], it is proved that if D<sub>1</sub> and D<sub>2</sub> are nontrivial strong digraphs such that D<sub>1</sub> is supereulerian and D<sub>2</sub> has a cycle vertex cover C’ with |C’| ≤ |V (D<sub>1</sub>)|, then the Cartesian product D<sub>1</sub> and D<sub>2</sub> is also supereulerian. In this paper, we prove that for strong digraphs D<sub>1</sub> and D<sub>2</sub>, if for some cycle factor F<sub>1</sub> of D<sub>1</sub>, the digraph formed from D<sub>1</sub> by contracting arcs in F1 is hamiltonian with f (D<sub>2</sub>) not bigger than |V (D<sub>1</sub>)|, then the strong product D<sub>1</sub> and D<sub>2</sub> is supereulerian.
基金Supported by the National Natural Science Foundation of China(Grant No.12261016)。
文摘A signed graph S=(S^(u),σ)has an underlying graph Suand a functionσ:E(S^(u))-→{+,-}.Let E^(-)(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Suis eulerian(or subeulerian,or eulerian and|E-(S)|is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′such that S′is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges e_(i)and e_(j)of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S′are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S∈S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S∈S′.
文摘This paper provides the number of combinatorially distinct general rooted Eulerian planar maps with the number of edges and the valency of rooted vertex of the maps as. two parameters. It is also an answer to open problem 7.1 in [1]. Meanwhile, the case of three variables can be derived by using Lagrangian inversion.
文摘A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.
基金supported by the National Natural Science Foundation of China(No.51706241).
文摘In this paper,the Eulerian Stochastic Field(ESF)model in the Transported Probability Density Function(TPDF)class model is combined with the Flamelet Generated Manifolds(FGM)model.This method solves the joint probability density function transport equation by ESF method that considers the interaction mechanism between flame and turbulence with high precision.At the same time,by making use of the advantage of the FGM model,this model is able to incorporate the detailed chemical reaction mechanism(GRI 3.0)with acceptable computational cost.The new model has been implemented in the open source CFD suite-Open FOAM.Validation of the model has been carried out by simulating the Sandia flame series(three turbulent piloted methane jet flames)issued by the National Laboratory of the United States.The accuracy and advancement of the ESF/FGM turbulent combustion model are verified by comparing the LES results of the new model with the rich experimental data as well as the RANS results.The results demonstrate that the model has a strong ability in capturing combustion phenomena such as extinction and re-ignition in turbulent flame,which is essential in the accurate prediction of the combustion process in real combustion devices,for example,aircraft engines.
基金This project is supported by National Natural Science Foundation of China (No.50176035)Doctorate Foundation of Xi'an Jiaotong University,China (No.DFXJU2000-18)
文摘Wet steam condensing flow in low-pressure steam turbine leads to efficiencylosses and blade erosions. In order to investigate this problem by numerical approach, anEulerian/Eulerian model has been developed, in which the wet steam is regarded as mixture comprisingtwo coupled systems: the vapor phase and the liquid phase. These two systems are both described byconservation equations. High resolution TVD scheme is employed to capture condensing phenomena inwet steam flow. This model has been validated by numerical simulations of condensing flows in 1D and2D nozzles. Compared with experimental data, a good agreement is observed. This Eulerian/Eulerianmodel can be extended to 3D calculation of condensing flow.
