In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
CO_(2)enhanced oil recovery plays an important role in carbon storage and utilization.However,the incomplete understanding of the underlying microscopic convection–diffusion mechanisms in complex pore structures has ...CO_(2)enhanced oil recovery plays an important role in carbon storage and utilization.However,the incomplete understanding of the underlying microscopic convection–diffusion mechanisms in complex pore structures has constrained the broader industrial application of CO_(2)geo-sequestration.This work develops a pore-scale numerical model considering molecular convection–diffusion to investigate CO_(2)-oil miscible displacement in two-and three-dimensional porous structures of conglomerate rocks.The effects of CO_(2)injection rates and pore structure properties on convection–diffusion are analyzed.By reconstructing the distribution of unexploited pores,the CO_(2)sweep efficiency is quantitatively evaluated.Furthermore,a sequestration factor is proposed to evaluate the CO_(2)storage capacity during miscible displacement.Convection significantly enhances the CO_(2)mass fraction in fractures with high flow rates.Subsequently,CO_(2)gradually diffuses into matrix pores without velocity distribution.Both convection and diffusion contribute to improving CO_(2)displacement efficiency.Diffusion facilitates the dissolution of CO_(2)into oil within small-diameter pores,and convection effectively mobilizes oil in large pore bodies.Developed and homogeneous pore structures enhance CO_(2)displacement efficiency,whereas CO_(2)flows along the main flow channels in heterogeneous pore structures,resulting in lower displacement efficiency.Diffusion plays a crucial role in CO_(2)storage within porous media.At low injection rates,dissolved CO_(2)is trapped in poorly connected and blind-end pores.The injection rate is negatively correlated with the sequestration factor.展开更多
Convection and diffusion are the main factors affecting radon migration.In this paper,a coupled diffusion-convection radon migration model is presented taking into account turbulence effects.In particular,the migratio...Convection and diffusion are the main factors affecting radon migration.In this paper,a coupled diffusion-convection radon migration model is presented taking into account turbulence effects.In particular,the migration of radon is simulated in the framework of the k-εturbulence model.The model equations are solved in a complex 3D domain by the finite element method(FEM).Special attention is paid to the case study about radon migration in an abandoned air defense shelter(AADS).The results show that air convection in a confined space has a great influence on the radon migration and the radon concentration is inversely proportional to the wind speed.展开更多
In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. ...In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O（ε1/2 ＋ h1/2）hk） convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain ...The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.展开更多
This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the op...This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.展开更多
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order...A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.展开更多
This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and t...This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.展开更多
In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of thi...In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.展开更多
In massive stars, convection in the interior is different from that of inter- mediate and small mass stars. In the main-sequence phase of small mass stars, there is a convective core and a radiative envelope, between ...In massive stars, convection in the interior is different from that of inter- mediate and small mass stars. In the main-sequence phase of small mass stars, there is a convective core and a radiative envelope, between which are the radiative inter- mediate layers with uneven chemical abundances. Semiconvection would occur in the intermediate layers between the convective core and the homogeneous envelope in massive stars. We treat core convective overshooting and semiconvection together as a process. We found that when decreasing overshooting, the semiconvection is more pronounced. In these two processes, we introduce one diffusive parameter D, which is different from other authors who have introduced different parameters for these two zones. The influences of the turbulent diffusion process on chemical evolution and other quantities of the stellar structure are shown in the present paper.展开更多
The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion conne...The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion connected with both barodiffusion and additional mechanism of pressure change in the pore volume due to the concentration gradient.Thus,the model is entirely coupled.The paper highlights the complexes composed of scales of physical quantities of different natures.The iteration algorithm for the numerical solution of the problem was developed for the coupled problem.The work involves numerical studies of the considered effects on the characteristics of the flow that can be convective or diffusive,depending on the relation between the dimensionless complexes.It is demonstrated that the distribution of velocity and concentration for different cylinder wall thicknesses is different.It is established that the barodiffusion has a considerable impact on the process in the convective mode or in the case of reduced cylinder wall thickness.展开更多
The mass migration velocity(absolute velocitv) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as we...The mass migration velocity(absolute velocitv) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow, the mass migration velocity of component i is( muss-weighted time average velocity). The diffusion velocity consists of turbulent diffusion velocity and molecular diffusion velocity is the simple lime average velocity of component i and a is a certain convection velocity). So, the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mdss conservation equation for component i, the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes. In turbulent flow, there could be no diffusion terms, or a turbulent diffusion term only or both the turbulent and molecular diffusion terms when or any velocity other than these two is taken as the convection velocity. The case, in which there could he molecular diffusion only without turbulent diffusion, occurs in laminar flow. The molecular diffusion term always depends on the adoption of convection velocitv.In two-phase flow, the value of the molecular diffusion term is often near or even exceeds that of the turbulent diffusion term, which is quite different from the case in gas mixture flow.展开更多
Profiles of salinity and temperature were measured in the strait of Hormuz（SH） during the winter of 2012, spring and summer of 2013. To investigate the double diffusion（DD） processes, Turner（TU） angle values are...Profiles of salinity and temperature were measured in the strait of Hormuz（SH） during the winter of 2012, spring and summer of 2013. To investigate the double diffusion（DD） processes, Turner（TU） angle values are calculated in all the stations in the SH. Different TU angle values correspond to salt fingering（SF）, diffusive convection（DC）and stable stratification. The distributions of the two forms of DD were plotted vertically along transects in the eastern, central and western part of the SH, and corresponding DD processes were described. The results show that both SF and DC occurred in most part of the study area. Two different water masses（the Indian Ocean surface water and the Persian Gulf water） were evident at the SH, and SF and DC were evident at the interface of two water masses. Due to evaporation, SF occurred in the surface layer of most Stations throughout the year. In the eastern part of the SH, occurrences of DC were more feasible in wintertime. SF was the main phenomenon at the end of hot season. For central part, SF occurred throughout the year in water column. In the western part,water column was stable in summer and DC happened in most part of water column in winter.展开更多
Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane ...Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane gap discharge tests were carried out under the gap distance of 5 m at the Qinghai Ultra High Voltage(UHV)test base at an altitude of 2200 m.The experiments measured the physical parameters such as the discharge current,electric field intensity and instantaneous optical power.The duration of the dark period and the critical charge of streamer-toleader transition were obtained at high altitude.Based on radial thermal expansion of the streamer stem,we established a modified streamer-to-leader transition model of the sphere-plane gap discharge at high altitude,and calculated the stem temperature,stem radii and the duration of streamer-to-leader transition.Compared with the measured duration of sphere-plane electrode discharge at an altitude of 2200 m,the error rate of the modified model was 0.94%,while the classical model was 6.97%,demonstrating the effectiveness of the modified model.From the comparisons and analysis,several suggestions are proposed to improve the numerical model for further quantitative investigations of the leader inception.展开更多
This work represents a 3 D numerical study of the effects of carbon nanotube(CNT)-water nanofluids on the double diffusive convection inside the triangular pyramid solar still.This numerical investigation is performed...This work represents a 3 D numerical study of the effects of carbon nanotube(CNT)-water nanofluids on the double diffusive convection inside the triangular pyramid solar still.This numerical investigation is performed for wide ranges of governing parameters such as buoyancy ratio(-10≤N≤0),volumetric fraction of nanoparticles(0≤Φ≤0.05) and Rayleigh number(10^(3)≤Ra≤10^(5)).The results are presented in terms of flow structure,temperature field,heat and mass transfer rates variations.It was found that the buoyancy ratio can be considered as an optimizing parameter for the heat and mass transfer,and the use of CNT has a positive effect on the solar still performances.展开更多
In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences o...In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences of the physical properties of two scalar components.We show that different scalar properties can affect the global transport behaviors.The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components.The scaling exponents of heat flux,however,depend mainly on the ratio of the diffusivities of two scalars.If one uses the local parameters of the finger layer in the bulk,the behaviors are very similar to those found in the fully periodic simulations.The horizontal width of the fingers is consistent with the wavelength of the fast growing mode.For one case we observe evidences of the thermohaline staircase,namely,the typical width of the flow structures changes significantly in different layers within the flow domain.展开更多
A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the m...A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the monomer concentration, the degree of polymerization, the polydispersity index （PDI）, etc. This model provides a more valid mathematical description by accounting for the monomer diffusion phenomena at two levels as multigrai model counts, and obtains results that are more applicable to the conditions existing in most polymerizations of industrial interest. Considering that some models on the mesoscale phenomena are so complex that some existingmodeling aspects have to be simplified or even neglected to make the model convenient for use in interesting engineering studies, it is very important to put some effort into determining what sort of numerical analysis works bestfor these problems. For this reason, special attentionis.paid to these studies to explorean efficient algorithm usingadaptive grid-point spacing in a tlnlte-ditterence technique to tlgure out more practical mass transport models andconvection-diffusion models efficiently. The reasonable outcomes, as well as the significant computation time saving, have been achieved, thereby displaying the advantage of this calculation method.展开更多
The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that t...The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.展开更多
文摘In this paper we make a close study of the finite analytic method by means of the maximum principles in differential equations and give the proof of the stability and convergence of the finite analytic method.
基金supported by National Natural Science Foundation of China(42172159,52404048)China Postdoctoral Science Foundation(2023M743870)+1 种基金Postdoctoral Fellowship Program of CPSF(GZB20230864)Frontier Interdisciplinary Exploration Research Program of China University of Petroleum,Beijing(2462024XKQY002).
文摘CO_(2)enhanced oil recovery plays an important role in carbon storage and utilization.However,the incomplete understanding of the underlying microscopic convection–diffusion mechanisms in complex pore structures has constrained the broader industrial application of CO_(2)geo-sequestration.This work develops a pore-scale numerical model considering molecular convection–diffusion to investigate CO_(2)-oil miscible displacement in two-and three-dimensional porous structures of conglomerate rocks.The effects of CO_(2)injection rates and pore structure properties on convection–diffusion are analyzed.By reconstructing the distribution of unexploited pores,the CO_(2)sweep efficiency is quantitatively evaluated.Furthermore,a sequestration factor is proposed to evaluate the CO_(2)storage capacity during miscible displacement.Convection significantly enhances the CO_(2)mass fraction in fractures with high flow rates.Subsequently,CO_(2)gradually diffuses into matrix pores without velocity distribution.Both convection and diffusion contribute to improving CO_(2)displacement efficiency.Diffusion facilitates the dissolution of CO_(2)into oil within small-diameter pores,and convection effectively mobilizes oil in large pore bodies.Developed and homogeneous pore structures enhance CO_(2)displacement efficiency,whereas CO_(2)flows along the main flow channels in heterogeneous pore structures,resulting in lower displacement efficiency.Diffusion plays a crucial role in CO_(2)storage within porous media.At low injection rates,dissolved CO_(2)is trapped in poorly connected and blind-end pores.The injection rate is negatively correlated with the sequestration factor.
基金supported by the National Natural Science Foundation of China[grant numbers 11705083]China Postdoctoral Science Foundation[grant number 2018M632975]+1 种基金National Natural Science Foundation of Hunan Province[grant number 2019JJ50488]Hunan Province Engineering Research Center of Radioactive Control Technology in Uranium Mining and Metallurgy&Hunan Province Engineering Technology Research Center of Uranium Tailings Treatment Technology,University of South China[grant number 2019YKZX1009].
文摘Convection and diffusion are the main factors affecting radon migration.In this paper,a coupled diffusion-convection radon migration model is presented taking into account turbulence effects.In particular,the migration of radon is simulated in the framework of the k-εturbulence model.The model equations are solved in a complex 3D domain by the finite element method(FEM).Special attention is paid to the case study about radon migration in an abandoned air defense shelter(AADS).The results show that air convection in a confined space has a great influence on the radon migration and the radon concentration is inversely proportional to the wind speed.
基金Supported by National Natural Science Foundation of China (10571046, 10571053, and 10871066)Program for New Century Excellent Talents in University (NCET-06-0712)+2 种基金Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal Universitythe Project of Scientific Research Fund of Hunan Provincial Education Department (09K025)the Key Scientific Research Topic of Jiaxing University (70110X05BL)
文摘In this article, we introduce a coupled approach of local discontinuous Calerkin and standard finite element method for solving convection diffusion problems. The whole domain is divided into two disjoint subdomains. The discontinuous Galerkin method is adopted in the subdomain where the solution varies rapidly, while the standard finite element method is used in the other subdomain due to its lower computational cost. The stability and a priori error estimate are established. We prove that the coupled method has O（ε1/2 ＋ h1/2）hk） convergence rate in an associated norm, where ε is the diffusion coefficient, h is the mesh size and k is the degree of polynomial. The numerical results verify our theoretical results. Moreover, 2k-order superconvergence of the numerical traces at the nodes, and the optimal convergence of the errors under L2 norm are observed numerically on the uniform mesh. The numerical results also indicate that the coupled method has the same convergence order and almost the same errors as the purely LDG method.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金the National Natural Science Foundation of China(No.10571017)supported in part by the National Natural Science Foundation of China(No.60533020)supported in part by NSF DMS 0712744
文摘The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.
文摘This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal Lp,1≤ p ≤ ＋∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.
基金supported by the National Natural Science Foundation of China (No. 10601022)NSF ofInner Mongolia Autonomous Region of China (No. 200607010106)513 and Science Fund of InnerMongolia University for Distinguished Young Scholars (No. ND0702)
文摘A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
文摘This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.
基金supported by the National Natural Science Foundation of China(Nos.11701253,11971259,11801216)Natural Science Foundation of Shandong Province(No.ZR2017BA010)。
文摘In this paper,we investigate a stochastic meshfree finite volume element method for an optimal control problem governed by the convection diffusion equations with random coefficients.There are two contributions of this paper.Firstly,we establish a scheme to approximate the optimality system by using the finite volume element method in the physical space and the meshfree method in the probability space,which is competitive for high-dimensional random inputs.Secondly,the a priori error estimates are derived for the state,the co-state and the control variables.Some numerical tests are carried out to confirm the theoretical results and demonstrate the efficiency of the proposed method.
基金co-sponsored by the National Natural Science Foundation of China (Grant Nos.11333006 and 10973035)the Chinese Academy of Sciences (Grant No.KJCX2-YW-T24)
文摘In massive stars, convection in the interior is different from that of inter- mediate and small mass stars. In the main-sequence phase of small mass stars, there is a convective core and a radiative envelope, between which are the radiative inter- mediate layers with uneven chemical abundances. Semiconvection would occur in the intermediate layers between the convective core and the homogeneous envelope in massive stars. We treat core convective overshooting and semiconvection together as a process. We found that when decreasing overshooting, the semiconvection is more pronounced. In these two processes, we introduce one diffusive parameter D, which is different from other authors who have introduced different parameters for these two zones. The influences of the turbulent diffusion process on chemical evolution and other quantities of the stellar structure are shown in the present paper.
基金the Government Research Assignment for ISPMS SB RAS,project FWRW-2021-0007.Author information。
文摘The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion connected with both barodiffusion and additional mechanism of pressure change in the pore volume due to the concentration gradient.Thus,the model is entirely coupled.The paper highlights the complexes composed of scales of physical quantities of different natures.The iteration algorithm for the numerical solution of the problem was developed for the coupled problem.The work involves numerical studies of the considered effects on the characteristics of the flow that can be convective or diffusive,depending on the relation between the dimensionless complexes.It is demonstrated that the distribution of velocity and concentration for different cylinder wall thicknesses is different.It is established that the barodiffusion has a considerable impact on the process in the convective mode or in the case of reduced cylinder wall thickness.
基金Project supported by the National Natural Science Foundation of China
文摘The mass migration velocity(absolute velocitv) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow, the mass migration velocity of component i is( muss-weighted time average velocity). The diffusion velocity consists of turbulent diffusion velocity and molecular diffusion velocity is the simple lime average velocity of component i and a is a certain convection velocity). So, the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mdss conservation equation for component i, the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes. In turbulent flow, there could be no diffusion terms, or a turbulent diffusion term only or both the turbulent and molecular diffusion terms when or any velocity other than these two is taken as the convection velocity. The case, in which there could he molecular diffusion only without turbulent diffusion, occurs in laminar flow. The molecular diffusion term always depends on the adoption of convection velocitv.In two-phase flow, the value of the molecular diffusion term is often near or even exceeds that of the turbulent diffusion term, which is quite different from the case in gas mixture flow.
基金The proieect of Iranian National Institute for Oceanography and Atmospheric Science(INIOAS)in the framework of PG-GOOS cruise under contract No.391-021-01
文摘Profiles of salinity and temperature were measured in the strait of Hormuz（SH） during the winter of 2012, spring and summer of 2013. To investigate the double diffusion（DD） processes, Turner（TU） angle values are calculated in all the stations in the SH. Different TU angle values correspond to salt fingering（SF）, diffusive convection（DC）and stable stratification. The distributions of the two forms of DD were plotted vertically along transects in the eastern, central and western part of the SH, and corresponding DD processes were described. The results show that both SF and DC occurred in most part of the study area. Two different water masses（the Indian Ocean surface water and the Persian Gulf water） were evident at the SH, and SF and DC were evident at the interface of two water masses. Due to evaporation, SF occurred in the surface layer of most Stations throughout the year. In the eastern part of the SH, occurrences of DC were more feasible in wintertime. SF was the main phenomenon at the end of hot season. For central part, SF occurred throughout the year in water column. In the western part,water column was stable in summer and DC happened in most part of water column in winter.
基金supported by National Natural Science Foundation of China(Scientific Funds for Young Scientists)(No.52007064)。
文摘Historically,streamer-to-leader transition studies mainly focused on the rod-plane gap and low altitude analysis,with limited attention paid to the sphere-plane gap at high altitude analysis.In this work,sphere-plane gap discharge tests were carried out under the gap distance of 5 m at the Qinghai Ultra High Voltage(UHV)test base at an altitude of 2200 m.The experiments measured the physical parameters such as the discharge current,electric field intensity and instantaneous optical power.The duration of the dark period and the critical charge of streamer-toleader transition were obtained at high altitude.Based on radial thermal expansion of the streamer stem,we established a modified streamer-to-leader transition model of the sphere-plane gap discharge at high altitude,and calculated the stem temperature,stem radii and the duration of streamer-to-leader transition.Compared with the measured duration of sphere-plane electrode discharge at an altitude of 2200 m,the error rate of the modified model was 0.94%,while the classical model was 6.97%,demonstrating the effectiveness of the modified model.From the comparisons and analysis,several suggestions are proposed to improve the numerical model for further quantitative investigations of the leader inception.
基金funded by the Deanship of Scientific Research, Princess Nourah bint Abdulrahman University, through the Program of Research Project Funding After Publication, grant No (41- PRFA-P-23)。
文摘This work represents a 3 D numerical study of the effects of carbon nanotube(CNT)-water nanofluids on the double diffusive convection inside the triangular pyramid solar still.This numerical investigation is performed for wide ranges of governing parameters such as buoyancy ratio(-10≤N≤0),volumetric fraction of nanoparticles(0≤Φ≤0.05) and Rayleigh number(10^(3)≤Ra≤10^(5)).The results are presented in terms of flow structure,temperature field,heat and mass transfer rates variations.It was found that the buoyancy ratio can be considered as an optimizing parameter for the heat and mass transfer,and the use of CNT has a positive effect on the solar still performances.
基金supported by the Major Research Plan of National Natural and Science Foundation of China for Turbulent Structures(Grants 91852107 and 91752202).
文摘In this work fingering double diffusive convection,i.e.the buoyancy-driven flow with fluid density being affected by two different scalar components,is investigated numerically with special efforts on the influences of the physical properties of two scalar components.We show that different scalar properties can affect the global transport behaviors.The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components.The scaling exponents of heat flux,however,depend mainly on the ratio of the diffusivities of two scalars.If one uses the local parameters of the finger layer in the bulk,the behaviors are very similar to those found in the fully periodic simulations.The horizontal width of the fingers is consistent with the wavelength of the fast growing mode.For one case we observe evidences of the thermohaline staircase,namely,the typical width of the flow structures changes significantly in different layers within the flow domain.
基金Supported by the National High Technology Development Program of China （No.2006AA05Z226）, Natural Science Foundation of Zhejiang Province （No.Y105370）, National HI-TECH Industrialization Program of China （No.2004-2080）, and Science Fund for Distinguished Young Scholars of Zhejiang University （No. 111000-581645）.
文摘A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the monomer concentration, the degree of polymerization, the polydispersity index （PDI）, etc. This model provides a more valid mathematical description by accounting for the monomer diffusion phenomena at two levels as multigrai model counts, and obtains results that are more applicable to the conditions existing in most polymerizations of industrial interest. Considering that some models on the mesoscale phenomena are so complex that some existingmodeling aspects have to be simplified or even neglected to make the model convenient for use in interesting engineering studies, it is very important to put some effort into determining what sort of numerical analysis works bestfor these problems. For this reason, special attentionis.paid to these studies to explorean efficient algorithm usingadaptive grid-point spacing in a tlnlte-ditterence technique to tlgure out more practical mass transport models andconvection-diffusion models efficiently. The reasonable outcomes, as well as the significant computation time saving, have been achieved, thereby displaying the advantage of this calculation method.
基金the Department of Science and Technology, New Delhi for granting him a fellowship under the Innovation in Science Pursuit for the Inspired Research (INSPIRE) Program (No. DST/INSPIRE Fellowship/[IF 150253])
文摘The weakly nonlinear stability of the triple diffusive convection in a Maxwell fluid saturated porous layer is investigated. In some cases, disconnected oscillatory neutral curves ave found to exist, indicating that three critical thermal Darcy-Rayleigh numbers are required to specify the linear instability criteria. However, another distinguishing feature predicted from that of Newtonian fluids is the impossibility of quasi-periodic bifurcation from the rest state. Besides, the co-dimensional two bifurcation points are located in the Darcy-Prandtl number and the stress relaxation parameter plane. It is observed that the value of the stress relaxation parameter defining the crossover between stationary and oscillatory bifurcations decreases when the Darcy-Prandtl number increases. A cubic Landau equation is derived based on the weakly nonlinear stability analysis. It is found that the bifurcating oscillatory solution is either supercritical or subcritical, depending on the choice of the physical parameters. Heat and mass transfers are estimated in terms of time and area-averaged Nusselt numbers.
