This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fra...This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.展开更多
Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow pheno...Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.展开更多
A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing t...A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.展开更多
The modified QUICK scheme on unstructured grid was used to improve the advection flux approximation, and the depth-averaged κ-ε turbulence model with the scheme based on FVM by SIMPLE series algorithm was establishe...The modified QUICK scheme on unstructured grid was used to improve the advection flux approximation, and the depth-averaged κ-ε turbulence model with the scheme based on FVM by SIMPLE series algorithm was established and applied to spur-dike flow computation. In this model, the over-relaxed approach was adopted to estimate the diffusion flux in view of its advantages in reducing errors and sustaining numerical stability usually encountered in non-orthogonal meshes. Two spur-dike cases with different defection angles （90°and 135°） were analyzed to validate the model. Computed results show that the predicted velocities and recirculation lengths are in good agreement with the observed data. Moreover, the computations on structured and unstructured grids were compared in terms of the approximately equivalent grid numbers. It can be concluded that the precision with unstructured grids is higher than that with structured grids in spite that the CPU time required is slightly more with unstructured grids Thus, it is significant to apply the method to numerical simulation of practical hydraulic engineering.展开更多
To improve the corrosion resistance of steels for grounding grids, a low-carbon Cr micro-alloyed steel was developed （C 1 steel）, and corrosion behavior of Q235 steel and newly developed C1 steel in simulated acidic...To improve the corrosion resistance of steels for grounding grids, a low-carbon Cr micro-alloyed steel was developed （C 1 steel）, and corrosion behavior of Q235 steel and newly developed C1 steel in simulated acidic soil was investigated. The corrosion rate was evaluated with the mass loss measurements, while the corrosion morphology of surface and cross section of rust layer was observed by scanning electron microscopy. The corrosion products were analyzed by energy- dispersive X-ray spectrometry, X-ray diffraction and X-ray photoelectron spectroscopy, and the polarization curve was measured using potentiodynamic polarization method. Results indicated that C 1 steel displayed good corrosion resistance in the simulated acidic soil, of which the corrosion rate was only 30% of that of Q235 steel after corrosion for 360 h. The analysis of rust layer showed that lower carbon content in steel could reduce the tendency of micro cell corrosion and appropriate amount of chromium could improve the corrosion potential of metal matrix. Moreover, the analysis of X-ray photoelectron spectroscopy revealed that the chromium enriched in inner rust layer of C1 steel existed mainly in the form of Fe2CrO4, which facilitated the formation of Cr-goethite and improved the protection of corrosion products.展开更多
Regular grid of permanent sample plots (PSP) of ICP-Forests monitoring system was used for forest ecosystems biodiversity assessments and inventory. The supplementary features were added to the PSP structure to conduc...Regular grid of permanent sample plots (PSP) of ICP-Forests monitoring system was used for forest ecosystems biodiversity assessments and inventory. The supplementary features were added to the PSP structure to conduct biological diversity census: eight sample plots 1 × 1 m for geo-botanical description;two sample plots of 5 × 5 m each for description of the PSP’s undergrowth;one 25 × 25 m plot for coarse woody debris estimations;four soil inventory pits. The total number of PSP amounted to 248. Total data used are as following: 1) 1984 geo-botanical descriptions of vegetation belonging to ground cover layers made on 1 × 1 m sample plots;2) 496 descriptions of undergrowth on 5 × 5 m sample plots;3) 178 descriptions of woody debris on 25 × 25 m sample plots;4) 496 descriptions of soil inventory pits. General statistical indicators characterizing forest land cover diversity were calculated. Statistic indicators of α-diversity for the Karelian Isthmus forest vegetation cover have the following values: 1) m (mean number of species per PSP) = 26 species;2) σ (standard deviation) = 9.5 species;3) v (variation coefficient) = 36.5%;4) Р (deviation amplitude) = 60 – 7 = 53 species. β – diversity of forest ecosystems as well as γ – diversity also was studied on the base of information collected on the same regular grid of sample plots. It appears that sample plots distribution by species diversity gradation is well described by the standard curve of normal distribution for the entire Karelian Isthmus forest (determination coefficient of the curve being 95.2%) as well as for each type of forest. Hence, the criterion (standard) of biodiversity for forest ecosystems can be defined as the mean value of alpha diversity for each forest type group – m;and the standard deviation – σ, as a tool for assessing deviations from the standard. PSP locations are fixed using GPS technology, this allows biodiversity assessments at the same place in the next years for biodiversity trends estimations and consist the frame for systematic biodiversity inventory.展开更多
The Filtering Grid Scale （FGS） of sub-grid scale models does not match with the theoretical Proper FGS （PFGS） because of the improper mesh. Therefore, proper Large Eddy Simulation （LES） Mesh is very decisive for...The Filtering Grid Scale （FGS） of sub-grid scale models does not match with the theoretical Proper FGS （PFGS） because of the improper mesh. Therefore, proper Large Eddy Simulation （LES） Mesh is very decisive for better results and more economical cost. In this work, the purpose is to provide an adaptive control strategy for proper LES mesh with turbulence theory and CFD methods. A new expression of PFGS is proposed on the basis of -5/3 law of inertial sub-range and the proper mesh of LES can be built directly from the adjustment of RANS mesh. A benchmark of the backward facing step flow at Re = 5147 is provided for application and verification. There are three kinds of mesh sizes, including the RANS mesh, LAM （LES of adaptive-control mesh）, LFM （LES of fine mesh）, employed here. The grid number of LAM is smaller than those of LFM evidently, and the results of LAM are in a good agreement with those of DNS and experiments. It is revealed that the results of LAM are very close to those of LFM. The conclusions provide positive evidences for the novel strategy.展开更多
基金supported by the Natural Science Foundation of China (11061021)the Program of Higher-level talents of Inner Mongolia University (SPH-IMU,Z200901004)the Scientific Research Projection of Higher Schools of Inner Mongolia(NJ10016,NJ10006)
文摘This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.
基金King Mongkut’s University of Technology North Bangkok (KMUTNB)the Office of the Higher Education Commission (OHEC)the National Metal and Materials Technology Center (MTEC) for supporting this research work
文摘Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.
基金financially supported by the Science and Technology Project of the Ministry of Transport (Grant No. 2011329224170)
文摘A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.
基金the National Nature Science Foundation of China (Grant Nos. 50679019 and 50009001)the National Basic Research Program of China (973 Program, Grant No. 2008CB418202)the Social Technology Development Foundation of Jiangsu Province (Grant No.BS2006095)
文摘The modified QUICK scheme on unstructured grid was used to improve the advection flux approximation, and the depth-averaged κ-ε turbulence model with the scheme based on FVM by SIMPLE series algorithm was established and applied to spur-dike flow computation. In this model, the over-relaxed approach was adopted to estimate the diffusion flux in view of its advantages in reducing errors and sustaining numerical stability usually encountered in non-orthogonal meshes. Two spur-dike cases with different defection angles （90°and 135°） were analyzed to validate the model. Computed results show that the predicted velocities and recirculation lengths are in good agreement with the observed data. Moreover, the computations on structured and unstructured grids were compared in terms of the approximately equivalent grid numbers. It can be concluded that the precision with unstructured grids is higher than that with structured grids in spite that the CPU time required is slightly more with unstructured grids Thus, it is significant to apply the method to numerical simulation of practical hydraulic engineering.
文摘To improve the corrosion resistance of steels for grounding grids, a low-carbon Cr micro-alloyed steel was developed （C 1 steel）, and corrosion behavior of Q235 steel and newly developed C1 steel in simulated acidic soil was investigated. The corrosion rate was evaluated with the mass loss measurements, while the corrosion morphology of surface and cross section of rust layer was observed by scanning electron microscopy. The corrosion products were analyzed by energy- dispersive X-ray spectrometry, X-ray diffraction and X-ray photoelectron spectroscopy, and the polarization curve was measured using potentiodynamic polarization method. Results indicated that C 1 steel displayed good corrosion resistance in the simulated acidic soil, of which the corrosion rate was only 30% of that of Q235 steel after corrosion for 360 h. The analysis of rust layer showed that lower carbon content in steel could reduce the tendency of micro cell corrosion and appropriate amount of chromium could improve the corrosion potential of metal matrix. Moreover, the analysis of X-ray photoelectron spectroscopy revealed that the chromium enriched in inner rust layer of C1 steel existed mainly in the form of Fe2CrO4, which facilitated the formation of Cr-goethite and improved the protection of corrosion products.
文摘Regular grid of permanent sample plots (PSP) of ICP-Forests monitoring system was used for forest ecosystems biodiversity assessments and inventory. The supplementary features were added to the PSP structure to conduct biological diversity census: eight sample plots 1 × 1 m for geo-botanical description;two sample plots of 5 × 5 m each for description of the PSP’s undergrowth;one 25 × 25 m plot for coarse woody debris estimations;four soil inventory pits. The total number of PSP amounted to 248. Total data used are as following: 1) 1984 geo-botanical descriptions of vegetation belonging to ground cover layers made on 1 × 1 m sample plots;2) 496 descriptions of undergrowth on 5 × 5 m sample plots;3) 178 descriptions of woody debris on 25 × 25 m sample plots;4) 496 descriptions of soil inventory pits. General statistical indicators characterizing forest land cover diversity were calculated. Statistic indicators of α-diversity for the Karelian Isthmus forest vegetation cover have the following values: 1) m (mean number of species per PSP) = 26 species;2) σ (standard deviation) = 9.5 species;3) v (variation coefficient) = 36.5%;4) Р (deviation amplitude) = 60 – 7 = 53 species. β – diversity of forest ecosystems as well as γ – diversity also was studied on the base of information collected on the same regular grid of sample plots. It appears that sample plots distribution by species diversity gradation is well described by the standard curve of normal distribution for the entire Karelian Isthmus forest (determination coefficient of the curve being 95.2%) as well as for each type of forest. Hence, the criterion (standard) of biodiversity for forest ecosystems can be defined as the mean value of alpha diversity for each forest type group – m;and the standard deviation – σ, as a tool for assessing deviations from the standard. PSP locations are fixed using GPS technology, this allows biodiversity assessments at the same place in the next years for biodiversity trends estimations and consist the frame for systematic biodiversity inventory.
基金Project supported by the National Natural Science Foundation of china (Grant No. 50776056)the National High Technology Research and Development of China (863 Program,Grant No. 2009AA05Z201)
文摘The Filtering Grid Scale （FGS） of sub-grid scale models does not match with the theoretical Proper FGS （PFGS） because of the improper mesh. Therefore, proper Large Eddy Simulation （LES） Mesh is very decisive for better results and more economical cost. In this work, the purpose is to provide an adaptive control strategy for proper LES mesh with turbulence theory and CFD methods. A new expression of PFGS is proposed on the basis of -5/3 law of inertial sub-range and the proper mesh of LES can be built directly from the adjustment of RANS mesh. A benchmark of the backward facing step flow at Re = 5147 is provided for application and verification. There are three kinds of mesh sizes, including the RANS mesh, LAM （LES of adaptive-control mesh）, LFM （LES of fine mesh）, employed here. The grid number of LAM is smaller than those of LFM evidently, and the results of LAM are in a good agreement with those of DNS and experiments. It is revealed that the results of LAM are very close to those of LFM. The conclusions provide positive evidences for the novel strategy.
