Modern chromatography is increasingly focused on miniaturization and integration. Compared to conventional liquid chromatography, microfluidic chip liquid chromatography(microchip-LC) has the potential due to its zero...Modern chromatography is increasingly focused on miniaturization and integration. Compared to conventional liquid chromatography, microfluidic chip liquid chromatography(microchip-LC) has the potential due to its zero-dead volume connection and ease of integration. Nano-sized packings have the potential to significantly enhance separation performance in microchip-LC. However, their application has been hindered by packing difficulties. This study presents a method for packing nano-sized silica particles into a microchannel as the stationary phase. The microchip-LC packed column was prepared by combining the weir and the porous silica single-particle as frit to retain the packing particles. A surface tensionbased single-particle picking technique was established to insert porous single-particle frit into glass microchannels. Additionally, we developed a slurry packing method that utilizes air pressure to inject nano-sized packing into the microchannel. Pressure-driven chromatographic separation was performed using this nano-packed column integrated into a glass microchip. The mixture of four PAHs was successfully separated within just 8 min using a 5 mm separation channel length, achieving high theoretical plates(10~6plates/m). Overall, these findings demonstrate the potential of utilizing nano-sized packings for enhancing chromatographic performance in microchip systems.展开更多
Monodispersed potymeric microparticles were prepared by seed-poly- merization.High performance packings were obtained for anion chromatography by coating the surface-sutfonated partictes with quarternized latexes.
Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximatin...Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.展开更多
This paper presents the results of an experimental study carried out using large scale equipment to observe the effect of geometry on gas distribution properties of a high capacity corrugated sheet structured packing ...This paper presents the results of an experimental study carried out using large scale equipment to observe the effect of geometry on gas distribution properties of a high capacity corrugated sheet structured packing （Montz-pak B 1-250M） and to compare it with that of its conventional counterpart （Montz-pak B1-250）. Although the high capacity packing exhibits a significantly lower overall pressure drop, the gas distribution performance is similar to that of the conventional packing, and in both cases consistently good one.展开更多
Liquid-liquid equilibrium (LLE) data of water-caprolactam-benzene-(NH4)2SO4 system at 303 K were measured for extraction of caprolactam from aqueous ammonium sulfate solution. The influence of fluid flow rate, pulsati...Liquid-liquid equilibrium (LLE) data of water-caprolactam-benzene-(NH4)2SO4 system at 303 K were measured for extraction of caprolactam from aqueous ammonium sulfate solution. The influence of fluid flow rate, pulsation intensity on flooding velocity and mass transfer was studied for extraction of caprolactam from ammonium sulfate solution in a laboratory pulsed packed column. The flooding velocities and overall apparent height of a transfer unit were given under various operation conditions. An industrial column developed based on above study is operated well. The scale-up effect is discussed.展开更多
A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidati...A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidation degree of NOx and outlet acid concentration, liquid acid temperature are simulated and tested. The gas phase reactions and equilibria, gas phase mass transfer, interracial equilibria, and liquid phase reactions are considered in the model. Absorption of nitrogen oxides is studied in packed with Mellapak 250Y columns in series in an industrial process of 20000 t oxalic acid per year. Favorable agreement is shown between the model predictions and the on-site observations.展开更多
This paper studies the mass transfer performance of structured packings in the absorption of CO2 from air with aqueous Na OH solution. The Eight structured packings tested are sheet metal ones with corrugations of dif...This paper studies the mass transfer performance of structured packings in the absorption of CO2 from air with aqueous Na OH solution. The Eight structured packings tested are sheet metal ones with corrugations of different geometry parameters. Effective mass transfer area and overall gas phase mass transfer coefficient have been measured in an absorption column of 200 mm diameter under the conditions of gas F-factor in 0.38–1.52 Pa0.5and aqueous Na OH solution concentration of 0.10–0.15 kmol·m-3. The effects of gas/liquid phase flow rates and packing geometry parameters are also investigated. The results show that the effective mass transfer area changes not only with packing geometry parameters and liquid load, but also with gas F-factor. A new effective mass transfer area correlation on the gas F-factor and the liquid load was proposed, which is found to fit experiment data very well.展开更多
Modem packing technology is presented in terms of correlations and criteria for an extensive evaluation of up-to-date packing design used in current mass transfer operations. The corresponding basic information covers...Modem packing technology is presented in terms of correlations and criteria for an extensive evaluation of up-to-date packing design used in current mass transfer operations. The corresponding basic information covers the process engineering aspects, e.g. volumetric effectiveness and optimum geometry of the packing, and the techno-economic aspects, e.g. when selecting a packing adopted in practice for a certain application task. The correlations required for this investigation are derived and evaluated on the basis of a comprehensive experimental re- search by testing and comparison of modem packings, such as Raschig Super-Rings and reference packings. The results thus obtained are correlated and presented in graphic presentation of diagrams, figures and tables.展开更多
Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. ...Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.展开更多
Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ...Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ＋4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a （v, G, 1）-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening.展开更多
The objective of this work is to study a comprehensive performance of three types of structured parking in CO2 absorption application. One of them was developed in Mexican National Institute of Nuclear Research （ININ...The objective of this work is to study a comprehensive performance of three types of structured parking in CO2 absorption application. One of them was developed in Mexican National Institute of Nuclear Research （ININ abbreviation in Spanish of Instituto Nacional de lnvestigaciones Nucleates）, and the other two, Sulzer BX and Mellapak 250Y, by Sulzer Brothers Ltd. Aqueous solution of 30 weight % Monoethanolamine was employed as absorption solvent. The performance of the structured packing was evaluated in terms of the pressure drop, holds up, volumetric overall mass transfer coefficient and height of a global transfer unit of gas and liquid side as a function of the process operating parameters including gas and liquid load, by using hydrodynamic and mass transfer models. The pressure drop of ININ packing was higher than Sulzer BX and Mellapak 250Y, and volumetric overall mass transfer coefficient values are similar of Sulzer BX values and higher than Mellapak 250Y, although Sulzer BX and ININI 8 packing had less height of a global transfer unit of gas side values than Mellapak 250Y packing. The above-mentioned are consequences of the geometric characteristics and operational behavior for each packing.展开更多
A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs...A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.展开更多
Packed bed reactors of non-spherical particles are widely used in chemical industry with the aim to obtain a high active surface area and achieve a homogeneous flow.Despite this,little is known about the arrangement o...Packed bed reactors of non-spherical particles are widely used in chemical industry with the aim to obtain a high active surface area and achieve a homogeneous flow.Despite this,little is known about the arrangement of particles within the bed and the influence of this arrangement on the fluid flow distribution.Magnetic Resonance Imaging (MRI) is a non-invasive tomographic imaging technique that allows 3D visualisation of the packing and flow structure.However,the individual particle information is not obtained using MRI.In this work we investigate different particle detection methods to retrieve the particle position and orientation from MRI images.Results show the successful reconstruction of random packing structures of various non-spherical particle shapes: ellipsoid,spherocylinder,cylinder and cube.The applicability of each method in relation to the particle shape,as well as strengths and drawbacks of each particle detection method are discussed.This paper shows the ability to reconstruct real packed beds of non-spherical particle shapes from MRI images,which opens several research opportunities in the field of chemical engineering.展开更多
Metastability,disorder and jamming are the typical characteristics of amorphous systems,while the related structure changes remain unclear.Sphere packing is often used as a structure model for amorphous and crystallin...Metastability,disorder and jamming are the typical characteristics of amorphous systems,while the related structure changes remain unclear.Sphere packing is often used as a structure model for amorphous and crystalline states.In this article,sphere packing systems with packing densities ranging from 0.50 to 0.74 were simulated by using Discrete Element Method(DEM),and the obtained packing structures were assessed to investigate the densification process and jamming properties.An order parameter that can effectively distinguish the order and disorder of packing structures was proposed based on the distribution characteristics of jamming angles.Then the evolution of jamming characteristics during the transition from Random Loose Packing(RLP)to Random Close Packing(RCP)and the jamming-jamming relations of different packing structures were demonstrated.On this basis,a correlation between order-jamming-metastable states from the microscopic structural perspective was established,which is of valuable theoretical and practical implications for the characterization and synthesis of crystalline and amorphous materials.展开更多
We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if ...We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.展开更多
The present paper presents an experimental and numerical investigation of the dispersion of the gaseous jet flow and co-flow for the simple unit cell(SUC)and body-centred cubic(BCC)configuration of particles in packed...The present paper presents an experimental and numerical investigation of the dispersion of the gaseous jet flow and co-flow for the simple unit cell(SUC)and body-centred cubic(BCC)configuration of particles in packed beds.The experimental setup is built in such a way that suitable and simplified boundary conditions are imposed for the corresponding numerical framework,so the simulations can be done under very similar conditions as the experiments.Accordingly,a porous plate is used for the co-flow to achieve the uniform velocity and the fully developed flow is ensured for the jet flow.The SUC and BCC particle beds consist of 3D-printed spheres,and the non-isotropy near the walls is mostly eliminated by placing half-spheres at the channel walls.The flow velocities are analysed directly at the exit of the particle bed for both beds over 36 pores for the SUC configuration and 60 pores for the BCC configuration,for particle Reynolds numbers of 200,300,and 400.Stereo particle image velocimetry is experimentally arranged in such a way that the velocities over the entire region at the exit of the packed bed are obtained instantaneously.The numerical method consists of a state-of-the-art immersed boundary method with adaptive mesh refinement.The paper presents the pore jet structure and velocity field exiting from each pore for the SUC and BCC packed particle beds.The numerical and experimental studies show a good agreement for the SUC configuration for all flow velocities.For the BCC configuration,some differences can be observed in the pore jet flow structure between the simulations and the experiments,but the general flow velocity distribution shows a good overall agreement.The axial velocity is generally higher for the pores located near the centre of the packed bed than for the pores near the wall.In addition,the axial velocities are observed to increase near the peripheral pores of the packed bed.This behaviour is predominant for the BCC configuration as compared to the SUC configuration.The velocities near the peripheral pores can become even higher than those at the central pores for the BCC configuration.It is shown that both the experiments as well as the simulations can be used to study the complex fluid structures inside a packed bed reactor.展开更多
The role of number of grain size fractions on structural and mechanical properties of uniaxially com- pressed granular packings with a uniform particle size distribution in terms of number of particles and with variou...The role of number of grain size fractions on structural and mechanical properties of uniaxially com- pressed granular packings with a uniform particle size distribution in terms of number of particles and with various particle size dispersities was studied using the discrete element method. The study addressed packing density, coordination number, contact forces, global stress, and energy dissipation in assemblies composed of frictional spheres. Packing density was found to change with increasing num- ber of granulometric fractions in mixtures with a small ratio of the diameters of the largest to smallest particles. Results indicated a certain value of particle size ratio below which the number of particle size fractions strongly affected packing density. The average coordination number decreased with increasing number of fractions. Detailed analysis of the effect of particle size dispersity on mechanical coordination number, including particles with no less than four contacts, revealed that, contrary to the average coordi- nation number, the mechanical coordination number increased with increasing ratio of the diameters of the largest to smallest particles in the sample. The composition of polydisperse samples strongly affected stress distribution and energy dissipation in granular packings.展开更多
Ice-going ships play a crucial role in polar transportation and resource extraction.Different from the existing modeling approach which assumes that ships remain stationary,dynamic overset grid technology and DFBI(Dyn...Ice-going ships play a crucial role in polar transportation and resource extraction.Different from the existing modeling approach which assumes that ships remain stationary,dynamic overset grid technology and DFBI(Dynamic Fluid-Body Interaction)method are employed in this paper to enable the free-running motion of the ship in modeling.A numerical model capable of simulating a ship navigating through pack ice area is proposed,which uses Computational Fluid Dynamics(CFD)method to solve the flow field and applies the Discrete Element Method(DEM)to simulate ship-ice and ice-ice interactions.Besides,the proposed high-precision method for generating pack ice area can be used in conjunction with the proposed numerical model.By comparing the numerical results with the available model test data and experimental observations,the effectiveness of the numerical model is validated,demonstrating its strong capability of predicting resistance and simulating ship navigation in pack ice,as well as its significant potential and applicability for further studies.展开更多
To improve the high-temperature oxidation resistance of TiAlNb9 alloy,a Cr-Al-Y co-deposition coating was prepared on the alloy surface by the pack cementation method.The microstructure of the coating was analyzed by ...To improve the high-temperature oxidation resistance of TiAlNb9 alloy,a Cr-Al-Y co-deposition coating was prepared on the alloy surface by the pack cementation method.The microstructure of the coating was analyzed by scanning electron microscope,energy dispersive spectrometer,and X-ray diffractometer,and the high-temperature oxidation properties of the substrate and coating at 1273 K were compared and studied.The results show that the Cr-Al-Y coating is about 30μm in thickness,and it has a dense structure and good film-substrate bonding.The coating includes an outer layer composed of TiCr_(2),TiCr,Ti4Cr,and(Ti,Nb)Cr4 phases as well as an inner layer composed of Ti_(2)Al,and Nb-richγ-TiAl interdiffusion zone.The TiAlNb9 substrate forms an oxide layer composed of TiO2 and Al_(2)O_(3) at 1273 K.Due to its loose and porous structure,TiO2 oxide film cannot effectively isolate the internal diffusion of element O,resulting in continuous oxidation damage to the substrate.The Cr-Al-Y co-deposition coating forms a dense Cr2O3 and Al_(2)O_(3) oxide layer during oxidation,effectively preventing the internal diffusion of element O and significantly improving the high-temperature oxidation resistance of the substrate alloy.展开更多
Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition d...Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.展开更多
基金supported by the National Natural Science Foundation of China (No.21936001)the Beijing Outstanding Young Scientist Program (No.BJJWZYJH01201910005017)。
文摘Modern chromatography is increasingly focused on miniaturization and integration. Compared to conventional liquid chromatography, microfluidic chip liquid chromatography(microchip-LC) has the potential due to its zero-dead volume connection and ease of integration. Nano-sized packings have the potential to significantly enhance separation performance in microchip-LC. However, their application has been hindered by packing difficulties. This study presents a method for packing nano-sized silica particles into a microchannel as the stationary phase. The microchip-LC packed column was prepared by combining the weir and the porous silica single-particle as frit to retain the packing particles. A surface tensionbased single-particle picking technique was established to insert porous single-particle frit into glass microchannels. Additionally, we developed a slurry packing method that utilizes air pressure to inject nano-sized packing into the microchannel. Pressure-driven chromatographic separation was performed using this nano-packed column integrated into a glass microchip. The mixture of four PAHs was successfully separated within just 8 min using a 5 mm separation channel length, achieving high theoretical plates(10~6plates/m). Overall, these findings demonstrate the potential of utilizing nano-sized packings for enhancing chromatographic performance in microchip systems.
文摘Monodispersed potymeric microparticles were prepared by seed-poly- merization.High performance packings were obtained for anion chromatography by coating the surface-sutfonated partictes with quarternized latexes.
基金This project is supported in part by NSF of China(60575004, 10231040)NSF of GuangDong, Grants from the Ministry of Education of China(NCET-04-0791)Grants from Sun Yat-Sen University
文摘Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed.
文摘This paper presents the results of an experimental study carried out using large scale equipment to observe the effect of geometry on gas distribution properties of a high capacity corrugated sheet structured packing （Montz-pak B 1-250M） and to compare it with that of its conventional counterpart （Montz-pak B1-250）. Although the high capacity packing exhibits a significantly lower overall pressure drop, the gas distribution performance is similar to that of the conventional packing, and in both cases consistently good one.
文摘Liquid-liquid equilibrium (LLE) data of water-caprolactam-benzene-(NH4)2SO4 system at 303 K were measured for extraction of caprolactam from aqueous ammonium sulfate solution. The influence of fluid flow rate, pulsation intensity on flooding velocity and mass transfer was studied for extraction of caprolactam from ammonium sulfate solution in a laboratory pulsed packed column. The flooding velocities and overall apparent height of a transfer unit were given under various operation conditions. An industrial column developed based on above study is operated well. The scale-up effect is discussed.
文摘A mathematical model of nitrogen oxide （NOx） absorption is adopted and solved for adiabatic operation of a column with structured packings on the basis of the film theory. Removal rate, outlet concentration, oxidation degree of NOx and outlet acid concentration, liquid acid temperature are simulated and tested. The gas phase reactions and equilibria, gas phase mass transfer, interracial equilibria, and liquid phase reactions are considered in the model. Absorption of nitrogen oxides is studied in packed with Mellapak 250Y columns in series in an industrial process of 20000 t oxalic acid per year. Favorable agreement is shown between the model predictions and the on-site observations.
基金Supported by the National Natural Science Foundation of China(51134017)and Petro China(2011E-24-09)
文摘This paper studies the mass transfer performance of structured packings in the absorption of CO2 from air with aqueous Na OH solution. The Eight structured packings tested are sheet metal ones with corrugations of different geometry parameters. Effective mass transfer area and overall gas phase mass transfer coefficient have been measured in an absorption column of 200 mm diameter under the conditions of gas F-factor in 0.38–1.52 Pa0.5and aqueous Na OH solution concentration of 0.10–0.15 kmol·m-3. The effects of gas/liquid phase flow rates and packing geometry parameters are also investigated. The results show that the effective mass transfer area changes not only with packing geometry parameters and liquid load, but also with gas F-factor. A new effective mass transfer area correlation on the gas F-factor and the liquid load was proposed, which is found to fit experiment data very well.
文摘Modem packing technology is presented in terms of correlations and criteria for an extensive evaluation of up-to-date packing design used in current mass transfer operations. The corresponding basic information covers the process engineering aspects, e.g. volumetric effectiveness and optimum geometry of the packing, and the techno-economic aspects, e.g. when selecting a packing adopted in practice for a certain application task. The correlations required for this investigation are derived and evaluated on the basis of a comprehensive experimental re- search by testing and comparison of modem packings, such as Raschig Super-Rings and reference packings. The results thus obtained are correlated and presented in graphic presentation of diagrams, figures and tables.
基金supported by the National Natural Science Foundation of China(10701084)Chongqing Natural Science Foundation (2008BB0151)
文摘Rodin and Sullivan （1987） proved Thurston＇s conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞.
文摘Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ＋4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a （v, G, 1）-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening.
文摘The objective of this work is to study a comprehensive performance of three types of structured parking in CO2 absorption application. One of them was developed in Mexican National Institute of Nuclear Research （ININ abbreviation in Spanish of Instituto Nacional de lnvestigaciones Nucleates）, and the other two, Sulzer BX and Mellapak 250Y, by Sulzer Brothers Ltd. Aqueous solution of 30 weight % Monoethanolamine was employed as absorption solvent. The performance of the structured packing was evaluated in terms of the pressure drop, holds up, volumetric overall mass transfer coefficient and height of a global transfer unit of gas and liquid side as a function of the process operating parameters including gas and liquid load, by using hydrodynamic and mass transfer models. The pressure drop of ININ packing was higher than Sulzer BX and Mellapak 250Y, and volumetric overall mass transfer coefficient values are similar of Sulzer BX values and higher than Mellapak 250Y, although Sulzer BX and ININI 8 packing had less height of a global transfer unit of gas side values than Mellapak 250Y packing. The above-mentioned are consequences of the geometric characteristics and operational behavior for each packing.
文摘A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.
文摘Packed bed reactors of non-spherical particles are widely used in chemical industry with the aim to obtain a high active surface area and achieve a homogeneous flow.Despite this,little is known about the arrangement of particles within the bed and the influence of this arrangement on the fluid flow distribution.Magnetic Resonance Imaging (MRI) is a non-invasive tomographic imaging technique that allows 3D visualisation of the packing and flow structure.However,the individual particle information is not obtained using MRI.In this work we investigate different particle detection methods to retrieve the particle position and orientation from MRI images.Results show the successful reconstruction of random packing structures of various non-spherical particle shapes: ellipsoid,spherocylinder,cylinder and cube.The applicability of each method in relation to the particle shape,as well as strengths and drawbacks of each particle detection method are discussed.This paper shows the ability to reconstruct real packed beds of non-spherical particle shapes from MRI images,which opens several research opportunities in the field of chemical engineering.
基金the National Natural Science Foundation of China(grant No.51374070)Liaoning Revitalization Talents Program(grant No.XLYC1805007)of ChinaNatural Science Foundation of Jiangsu Province(grant No.BK20200269)for the financial support to this work.
文摘Metastability,disorder and jamming are the typical characteristics of amorphous systems,while the related structure changes remain unclear.Sphere packing is often used as a structure model for amorphous and crystalline states.In this article,sphere packing systems with packing densities ranging from 0.50 to 0.74 were simulated by using Discrete Element Method(DEM),and the obtained packing structures were assessed to investigate the densification process and jamming properties.An order parameter that can effectively distinguish the order and disorder of packing structures was proposed based on the distribution characteristics of jamming angles.Then the evolution of jamming characteristics during the transition from Random Loose Packing(RLP)to Random Close Packing(RCP)and the jamming-jamming relations of different packing structures were demonstrated.On this basis,a correlation between order-jamming-metastable states from the microscopic structural perspective was established,which is of valuable theoretical and practical implications for the characterization and synthesis of crystalline and amorphous materials.
基金supported by National Natural Science Foundation of China (Grant Nos. 11871094 and 12122119)supported by National Natural Science Foundation of China (Grant No. 12171480)+1 种基金Hunan Provincial Natural Science Foundation of China (Grant Nos. 2020JJ4658 and 2022JJ10059)Scientific Research Program Funds of National University of Defense Technology (Grant No. 22-ZZCX-016)。
文摘We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.
基金funded by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)-Project-ID 422037413-TRR 287Gefördert durch die Deutsche Forschungsgemeinschaft(DFG)-Projektnummer 422037413-TRR 287.
文摘The present paper presents an experimental and numerical investigation of the dispersion of the gaseous jet flow and co-flow for the simple unit cell(SUC)and body-centred cubic(BCC)configuration of particles in packed beds.The experimental setup is built in such a way that suitable and simplified boundary conditions are imposed for the corresponding numerical framework,so the simulations can be done under very similar conditions as the experiments.Accordingly,a porous plate is used for the co-flow to achieve the uniform velocity and the fully developed flow is ensured for the jet flow.The SUC and BCC particle beds consist of 3D-printed spheres,and the non-isotropy near the walls is mostly eliminated by placing half-spheres at the channel walls.The flow velocities are analysed directly at the exit of the particle bed for both beds over 36 pores for the SUC configuration and 60 pores for the BCC configuration,for particle Reynolds numbers of 200,300,and 400.Stereo particle image velocimetry is experimentally arranged in such a way that the velocities over the entire region at the exit of the packed bed are obtained instantaneously.The numerical method consists of a state-of-the-art immersed boundary method with adaptive mesh refinement.The paper presents the pore jet structure and velocity field exiting from each pore for the SUC and BCC packed particle beds.The numerical and experimental studies show a good agreement for the SUC configuration for all flow velocities.For the BCC configuration,some differences can be observed in the pore jet flow structure between the simulations and the experiments,but the general flow velocity distribution shows a good overall agreement.The axial velocity is generally higher for the pores located near the centre of the packed bed than for the pores near the wall.In addition,the axial velocities are observed to increase near the peripheral pores of the packed bed.This behaviour is predominant for the BCC configuration as compared to the SUC configuration.The velocities near the peripheral pores can become even higher than those at the central pores for the BCC configuration.It is shown that both the experiments as well as the simulations can be used to study the complex fluid structures inside a packed bed reactor.
文摘The role of number of grain size fractions on structural and mechanical properties of uniaxially com- pressed granular packings with a uniform particle size distribution in terms of number of particles and with various particle size dispersities was studied using the discrete element method. The study addressed packing density, coordination number, contact forces, global stress, and energy dissipation in assemblies composed of frictional spheres. Packing density was found to change with increasing num- ber of granulometric fractions in mixtures with a small ratio of the diameters of the largest to smallest particles. Results indicated a certain value of particle size ratio below which the number of particle size fractions strongly affected packing density. The average coordination number decreased with increasing number of fractions. Detailed analysis of the effect of particle size dispersity on mechanical coordination number, including particles with no less than four contacts, revealed that, contrary to the average coordi- nation number, the mechanical coordination number increased with increasing ratio of the diameters of the largest to smallest particles in the sample. The composition of polydisperse samples strongly affected stress distribution and energy dissipation in granular packings.
文摘Ice-going ships play a crucial role in polar transportation and resource extraction.Different from the existing modeling approach which assumes that ships remain stationary,dynamic overset grid technology and DFBI(Dynamic Fluid-Body Interaction)method are employed in this paper to enable the free-running motion of the ship in modeling.A numerical model capable of simulating a ship navigating through pack ice area is proposed,which uses Computational Fluid Dynamics(CFD)method to solve the flow field and applies the Discrete Element Method(DEM)to simulate ship-ice and ice-ice interactions.Besides,the proposed high-precision method for generating pack ice area can be used in conjunction with the proposed numerical model.By comparing the numerical results with the available model test data and experimental observations,the effectiveness of the numerical model is validated,demonstrating its strong capability of predicting resistance and simulating ship navigation in pack ice,as well as its significant potential and applicability for further studies.
基金National Natural Science Foundation of China(52161009)Innovation Project of Postgraduate Students in North Minzu University(YCX24104)。
文摘To improve the high-temperature oxidation resistance of TiAlNb9 alloy,a Cr-Al-Y co-deposition coating was prepared on the alloy surface by the pack cementation method.The microstructure of the coating was analyzed by scanning electron microscope,energy dispersive spectrometer,and X-ray diffractometer,and the high-temperature oxidation properties of the substrate and coating at 1273 K were compared and studied.The results show that the Cr-Al-Y coating is about 30μm in thickness,and it has a dense structure and good film-substrate bonding.The coating includes an outer layer composed of TiCr_(2),TiCr,Ti4Cr,and(Ti,Nb)Cr4 phases as well as an inner layer composed of Ti_(2)Al,and Nb-richγ-TiAl interdiffusion zone.The TiAlNb9 substrate forms an oxide layer composed of TiO2 and Al_(2)O_(3) at 1273 K.Due to its loose and porous structure,TiO2 oxide film cannot effectively isolate the internal diffusion of element O,resulting in continuous oxidation damage to the substrate.The Cr-Al-Y co-deposition coating forms a dense Cr2O3 and Al_(2)O_(3) oxide layer during oxidation,effectively preventing the internal diffusion of element O and significantly improving the high-temperature oxidation resistance of the substrate alloy.
基金Supported in part by the National Key R&D Program of China(No.2020YFA0712300)NSFC(No.61872353)。
文摘Fraction repetition(FR)codes are integral in distributed storage systems(DSS)with exact repair-by-transfer,while pliable fraction repetition codes are vital for DSSs in which both the per-node storage and repetition degree can easily be adjusted simultaneously.This paper introduces a new type of pliable FR codes,called absolute balanced pliable FR(ABPFR)codes,in which the access balancing in DSS is considered.Additionally,the equivalence between pliable FR codes and resolvable transversal packings in combinatorial design theory is presented.Then constructions of pliable FR codes and ABPFR codes based on resolvable transversal packings are presented.
