A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） met...A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） method in the frame of two incompressible and immiscible viscous fluids under the action of gravity, taking into consideration of surface tension effects. A comparison of the numerical results by this method with those by other works indicates the validity of the method. In the frame of inviseid and incompressible fluids without taking into consideration of surface tension effects, the mechanisms of the generation of the liquid jet and the transition from spherical shape to toroidal shape during the bubble or drop deformation, the increase of the ring diameter of the toroidal bubble or drop and the decrease of its cross-section area during its motion, and the effects of the density ratio of the two fluids on the deformation of the bubble or drop are analysed both theoretically and numerically.展开更多
In the inviscid and incompressible fluid flow regime, surface tension effects on the behavior of two initially spherical bubbles with same size rising axisymmetrically in an infinite and initially stationary liquid ar...In the inviscid and incompressible fluid flow regime, surface tension effects on the behavior of two initially spherical bubbles with same size rising axisymmetrically in an infinite and initially stationary liquid are investigated numerically with the VOF method. The numerical experiments are performed for two bubbles with two different bubble distances. The ratio of gas density to liquid density is 0.001, which is close to the case of air bubbles rising in water. In the case of Dis = 2.5, where Dis is defined as the ratio of the distance between the bubble centroids to the radius of the bubble, it is found from numerical experiments that there exist four critical Weber numbers We1 , We2 , We3 and We4 , which are in between 10 and 100, 3 and 4, 1.5 and 1.8, and 0.2 and 0.3, respectively. In the case of Dis = 2.3, similar phenomena also appear but the corresponding four critical Weber numbers are lower than those in the case of Dis = 2.5. The mechanism of the above phenomena is analyzed theoretically and numerically.展开更多
Density and porosity are fundamental and important physical properties of rocks in various geological problems, and affect the other physical properties. Therefore, measurements of density and porosity of rock samples...Density and porosity are fundamental and important physical properties of rocks in various geological problems, and affect the other physical properties. Therefore, measurements of density and porosity of rock samples are important investigation items in both geo-science and geo-engineering areas. Several measurement techniques of the density and porosity are available and being applied currently. To ensure the data quality and to conduct its quality assessment, comparison of measurement results by different measurement techniques is necessary since the techniques are based on different principles and test procedures. In this study, we collected eight types of rock samples including a gabbro, a granite, four sandstones, a welded tuff and a mudstone as study materials, and also prepared several metal specimens for the experimental comparison. The porosities of the eight rocks covered a very wide range from 0.3% to 50% approximately. We employed three methods (caliper, buoyancy and helium-displacement pycnometer) to measure volumes of regularly-shaped specimens and to determine their bulk densities and porosities. As a result, the three techniques yielded almost same bulk densities and porosities for all the specimens. In addition, we also applied mercury intrusion porosimetry to measure density and porosity as well as to determine pore size distribution of the rock samples. Porosity values obtained by the porosimetry method were underestimated in the case of high-porosity (soft) rock samples and overestimated for the very low-porosity rock samples. Ability to determine pore size distribution, however, is a very important advantage of the porosimetry method.展开更多
Free convection of a viscous electrically conducting liquid past a vertical stretching surface is investigated in the presence of a transverse magnetic field.Natural convection is driven by both thermal and solutal bu...Free convection of a viscous electrically conducting liquid past a vertical stretching surface is investigated in the presence of a transverse magnetic field.Natural convection is driven by both thermal and solutal buoyancy.The original partial differential equations governing the problem are turned into a set of ordinary differential equations through a similar variables transformation.This alternate set of equations is solved through a Differential Transform Method(DTM)and the Pade approximation.The response of the considered physical system to the non-dimensional parameters accounting for the relative importance of different effects is assessed considering different situations.展开更多
A novel amplitude factorization method is applied to solve a discrete buoyancy wave equation with arbitrary wind and temperature height distribution.The solution is given in the form of a cumulative product of complex...A novel amplitude factorization method is applied to solve a discrete buoyancy wave equation with arbitrary wind and temperature height distribution.The solution is given in the form of a cumulative product of complex factors,which are computed by a nonlinear,inhomogeneous,two-member recurrence formula,initiated from a radiative condition on top.Singularities of the wave equation due to evanescent winds are eliminated by turbulent friction.The method provides an estimation of the minimal vertical resolution,required to attain a stable accurate solution.The areas of application of the developed numerical scheme are high resolution modelling of orographic waves for arbitrary orography in general atmospheric stratification conditions,and testing of adiabatic kernels of numerical weather prediction models.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10672043 and 10272032)
文摘A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） method in the frame of two incompressible and immiscible viscous fluids under the action of gravity, taking into consideration of surface tension effects. A comparison of the numerical results by this method with those by other works indicates the validity of the method. In the frame of inviseid and incompressible fluids without taking into consideration of surface tension effects, the mechanisms of the generation of the liquid jet and the transition from spherical shape to toroidal shape during the bubble or drop deformation, the increase of the ring diameter of the toroidal bubble or drop and the decrease of its cross-section area during its motion, and the effects of the density ratio of the two fluids on the deformation of the bubble or drop are analysed both theoretically and numerically.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10672043, 10272032)supported by the Staff Innovation Foundation of State Nuclear Power Technology Corporation Ltd. (SNP-KJ-CX-2011-0004)
文摘In the inviscid and incompressible fluid flow regime, surface tension effects on the behavior of two initially spherical bubbles with same size rising axisymmetrically in an infinite and initially stationary liquid are investigated numerically with the VOF method. The numerical experiments are performed for two bubbles with two different bubble distances. The ratio of gas density to liquid density is 0.001, which is close to the case of air bubbles rising in water. In the case of Dis = 2.5, where Dis is defined as the ratio of the distance between the bubble centroids to the radius of the bubble, it is found from numerical experiments that there exist four critical Weber numbers We1 , We2 , We3 and We4 , which are in between 10 and 100, 3 and 4, 1.5 and 1.8, and 0.2 and 0.3, respectively. In the case of Dis = 2.3, similar phenomena also appear but the corresponding four critical Weber numbers are lower than those in the case of Dis = 2.5. The mechanism of the above phenomena is analyzed theoretically and numerically.
文摘Density and porosity are fundamental and important physical properties of rocks in various geological problems, and affect the other physical properties. Therefore, measurements of density and porosity of rock samples are important investigation items in both geo-science and geo-engineering areas. Several measurement techniques of the density and porosity are available and being applied currently. To ensure the data quality and to conduct its quality assessment, comparison of measurement results by different measurement techniques is necessary since the techniques are based on different principles and test procedures. In this study, we collected eight types of rock samples including a gabbro, a granite, four sandstones, a welded tuff and a mudstone as study materials, and also prepared several metal specimens for the experimental comparison. The porosities of the eight rocks covered a very wide range from 0.3% to 50% approximately. We employed three methods (caliper, buoyancy and helium-displacement pycnometer) to measure volumes of regularly-shaped specimens and to determine their bulk densities and porosities. As a result, the three techniques yielded almost same bulk densities and porosities for all the specimens. In addition, we also applied mercury intrusion porosimetry to measure density and porosity as well as to determine pore size distribution of the rock samples. Porosity values obtained by the porosimetry method were underestimated in the case of high-porosity (soft) rock samples and overestimated for the very low-porosity rock samples. Ability to determine pore size distribution, however, is a very important advantage of the porosimetry method.
文摘Free convection of a viscous electrically conducting liquid past a vertical stretching surface is investigated in the presence of a transverse magnetic field.Natural convection is driven by both thermal and solutal buoyancy.The original partial differential equations governing the problem are turned into a set of ordinary differential equations through a similar variables transformation.This alternate set of equations is solved through a Differential Transform Method(DTM)and the Pade approximation.The response of the considered physical system to the non-dimensional parameters accounting for the relative importance of different effects is assessed considering different situations.
基金supported by Estonian Science Foundation under Research Grant 5711.
文摘A novel amplitude factorization method is applied to solve a discrete buoyancy wave equation with arbitrary wind and temperature height distribution.The solution is given in the form of a cumulative product of complex factors,which are computed by a nonlinear,inhomogeneous,two-member recurrence formula,initiated from a radiative condition on top.Singularities of the wave equation due to evanescent winds are eliminated by turbulent friction.The method provides an estimation of the minimal vertical resolution,required to attain a stable accurate solution.The areas of application of the developed numerical scheme are high resolution modelling of orographic waves for arbitrary orography in general atmospheric stratification conditions,and testing of adiabatic kernels of numerical weather prediction models.
