In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated num...In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid （VOF） method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We1,~We2,~We3 and We4, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We 〉We2, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.展开更多
The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipati...The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.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
The group-theorytic approach is applied for solving the problem of the unsteady MHD mixed convective flow past on a moving curved surface. The application of two-parameter groups reduces the number of independent vari...The group-theorytic approach is applied for solving the problem of the unsteady MHD mixed convective flow past on a moving curved surface. The application of two-parameter groups reduces the number of independent variables by two, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effects of varying parameters governing the problem are studied. A comparison with previous work is presented.展开更多
Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical sol...Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.展开更多
基金Supported by National Natural Science Foundation of China （60504026, 60674041） and National High Technology Research and Development Program of China （863 Program） （2006AA04Z173）
基金supported by the National Natural Science Foundation of China (Grant Nos. 10672043 and 10272032)
文摘In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid （VOF） method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We1,~We2,~We3 and We4, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We 〉We2, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.
基金Project supported by the National Natural Science Foundation of China (Nos.50479038 and 50679061)
文摘The turbulent flow of vertical plane wall plume with concentration variation was studied with the finite analytical method. The k-epsilon model with the effect of buoyancy on turbulent kinetic energy and its dissipation rate was adopted. There were similarity solutions in the uniform environment for the system of equations including the equation of continuity, the equation of momentum along the flow direction and concentration, and equations of k, epsilon. The finite analytic method was applied to obtain the similarity solution. The calculated data of velocity, relative density difference, the kinetic energy of turbulence and its dissipation rate distribution for vertical plane plumes are in good agreement with the experimental data at the turbulent Schmidt number equal to 1.0. The variations of their maximum value along the direction of main flow were also given. It shows that the present model is good, i.e., the effect of buoyancy on turbulent kinetic energy and its dissipation rate should be taken into account, and the finite analytic method is effective.
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The group-theorytic approach is applied for solving the problem of the unsteady MHD mixed convective flow past on a moving curved surface. The application of two-parameter groups reduces the number of independent variables by two, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effects of varying parameters governing the problem are studied. A comparison with previous work is presented.
基金the National Natural Science Foundation of China (Grant No. 50576097)the National Basic Research Development Program of China (Grant No. 2007CB206902)
文摘Analytical solutions of governing equations of various phenomena have their irre-placeable theoretical meanings. In addition, they can also be the benchmark solu-tions to verify the outcomes and codes of numerical solutions, and even to develop various numerical methods such as their differencing schemes and grid generation skills as well. A hybrid method of separating variables for simultaneous partial differential equation sets is presented. It is proposed that different methods of separating variables for different independent variables in the simultaneous equa-tion set may be used to improve the solution derivation procedure, for example, using the ordinary separating method for some variables and using extraordinary methods of separating variables, such as the separating variables with addition promoted by the first author, for some other variables. In order to prove the ability of the above-mentioned hybrid method, a lot of analytical exact solutions of two-buoyancy convection in porous media are successfully derived with such a method. The physical features of these solutions are given.
