Computational fluid dynamics(CFD) has recently emerged as an effective tool for the investigation of the hydraulic parameters and efficiency of tray towers.The computation domain was established for two types of orien...Computational fluid dynamics(CFD) has recently emerged as an effective tool for the investigation of the hydraulic parameters and efficiency of tray towers.The computation domain was established for two types of oriented valves within a tray and meshed into two parts with different grid types and sizes.The volume fraction correlation concerning inter-phase momentum transfer source was fitted based on experimental data,and built in UDF for simulation.The flow pattern of oriented valve tray under different operating conditions was simulated under Eulerian-Eulerian framework with realizable k-ε model.The predicted liquid height from CFD simulation was in good agreement with the results of pressure drop and volume fraction correlations.Meanwhile,the velocity distribution and volume fraction of the two phases were demonstrated and analyzed,which are useful in design and analysis of the column trays.展开更多
As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion...As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.展开更多
Within today＇s product development process, various FE-simulations （finite element） for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simul...Within today＇s product development process, various FE-simulations （finite element） for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simulations are performed with great effort for discretization, use of simulations conditions, like taking different non-linearities （i.e., material behavior, etc.） into account, to create meaningful results. Despite knowing the effects of deformations occurring during the production processes, always the non-deformed design model of a CAD-system （computer aided design） is used for the FE-simulations. It seems rather doubtful that further refinement of simulation methods makes sense, if the real manufactured geometry of the component is not considered for in the simulation. For an efficient exploit of the potential of simulation methods, an approach has been developed which offers a geometry model for simulation based on the existing CAD-model but with integrated production deviations as soon as a first prototype is at hand by adapting the FE-mesh to the real, 3D surface detected geometry.展开更多
In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In ...In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.展开更多
文摘Computational fluid dynamics(CFD) has recently emerged as an effective tool for the investigation of the hydraulic parameters and efficiency of tray towers.The computation domain was established for two types of oriented valves within a tray and meshed into two parts with different grid types and sizes.The volume fraction correlation concerning inter-phase momentum transfer source was fitted based on experimental data,and built in UDF for simulation.The flow pattern of oriented valve tray under different operating conditions was simulated under Eulerian-Eulerian framework with realizable k-ε model.The predicted liquid height from CFD simulation was in good agreement with the results of pressure drop and volume fraction correlations.Meanwhile,the velocity distribution and volume fraction of the two phases were demonstrated and analyzed,which are useful in design and analysis of the column trays.
文摘As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.
文摘Within today＇s product development process, various FE-simulations （finite element） for the functional validation of the desired characteristics are made to avoid expensive testing with real components. Those simulations are performed with great effort for discretization, use of simulations conditions, like taking different non-linearities （i.e., material behavior, etc.） into account, to create meaningful results. Despite knowing the effects of deformations occurring during the production processes, always the non-deformed design model of a CAD-system （computer aided design） is used for the FE-simulations. It seems rather doubtful that further refinement of simulation methods makes sense, if the real manufactured geometry of the component is not considered for in the simulation. For an efficient exploit of the potential of simulation methods, an approach has been developed which offers a geometry model for simulation based on the existing CAD-model but with integrated production deviations as soon as a first prototype is at hand by adapting the FE-mesh to the real, 3D surface detected geometry.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2011CB013505&2014CB047100)the National Natural Science Foundation of China(Grant Nos.11572009&51538001)
文摘In order to reach the best numerical properties with the numerical manifold method(NMM),uniform finite element meshes are always favorite while constructing mathematical covers,where all the elements are congruent.In the presence of steep gradients or strong singularities,in principle,the locally-defined special functions can be added into the NMM space by means of the partition of unity,but they are not available to those complex problems with heterogeneity or nonlinearity,necessitating local refinement on uniform meshes.This is believed to be one of the most important open issues in NMM.In this study multilayer covers are proposed to solve this issue.In addition to the first layer cover which is the global cover and covers the whole problem domain,the second and higher layer covers with smaller elements,called local covers,are used to cover those local regions with steep gradients or strong singularities.The global cover and the local covers have their own partition of unity,and they all participate in the approximation to the solution.Being advantageous over the existing procedures,the proposed approach is easy to deal with any arbitrary-layer hanging nodes with no need to construct super-elements with variable number of edge nodes or introduce the Lagrange multipliers to enforce the continuity between small and big elements.With no limitation to cover layers,meanwhile,the creation of an even error distribution over the whole problem domain is significantly facilitated.Some typical examples with steep gradients or strong singularities are analyzed to demonstrate the capacity of the proposed approach.
