The growth, expansion and collapse of a bubble in a narrow tube are studied using both experiments and numerical simulations. In experiment, the bubble is generated by an electric spark in a water tank and recorded by...The growth, expansion and collapse of a bubble in a narrow tube are studied using both experiments and numerical simulations. In experiment, the bubble is generated by an electric spark in a water tank and recorded by a highspeed camera system. In numerical simulation, the evolution of the bubble is solved by adopting axisymmetric boundary integral equation, considering the surface tension effect. The results of experiments and numerical simulations are compared and good agreements are achieved. Both of them show that a counter-jet forms and penetrates the bubble at the end of the collapse stage, before a ring type bubble forms. Under the attraction of the tube wall due to Bjerknes force, a ring jet is generated, pointing towards the tube. On the basis of this, some physical quantities like the pressure on the tube wall and kinetic energy are calculated in a case study. The effects of tube diameters and tube lengths on the bubble＇s behaviors are also investigated.展开更多
Complex equations of circular ring shells and slender ring shells overall-bending in a meridian plane are presented based on E. L. Axelrad's equations of flexible shells of revolution render asymmetrical lending. ...Complex equations of circular ring shells and slender ring shells overall-bending in a meridian plane are presented based on E. L. Axelrad's equations of flexible shells of revolution render asymmetrical lending. It turns out that the equations are analogous to Novozhilov's equations of symmetrical ring shells, where general sollutions have been given by W. Z. Chien. Therefore, by analogy with Chien's solution, a general solution for equations of the slender ring shells is put forward, which can be used to salve bellow's overall-bending problems.展开更多
A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien...A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien's solution for axial symmetrical slender ring shells to investigate the overall bending problem of Ω shaped bellows subjected to pure bending moments. The values calculated in the present paper are very close to the existing experiment. Thus Chien's work on axial symmetrical problems for ring shells has been extended to overall bending problems.展开更多
基金supported by the Lloyd’s Register Educational Trust(The LRET)the National Natural Foundation of China(10976008)
文摘The growth, expansion and collapse of a bubble in a narrow tube are studied using both experiments and numerical simulations. In experiment, the bubble is generated by an electric spark in a water tank and recorded by a highspeed camera system. In numerical simulation, the evolution of the bubble is solved by adopting axisymmetric boundary integral equation, considering the surface tension effect. The results of experiments and numerical simulations are compared and good agreements are achieved. Both of them show that a counter-jet forms and penetrates the bubble at the end of the collapse stage, before a ring type bubble forms. Under the attraction of the tube wall due to Bjerknes force, a ring jet is generated, pointing towards the tube. On the basis of this, some physical quantities like the pressure on the tube wall and kinetic energy are calculated in a case study. The effects of tube diameters and tube lengths on the bubble＇s behaviors are also investigated.
文摘Complex equations of circular ring shells and slender ring shells overall-bending in a meridian plane are presented based on E. L. Axelrad's equations of flexible shells of revolution render asymmetrical lending. It turns out that the equations are analogous to Novozhilov's equations of symmetrical ring shells, where general sollutions have been given by W. Z. Chien. Therefore, by analogy with Chien's solution, a general solution for equations of the slender ring shells is put forward, which can be used to salve bellow's overall-bending problems.
文摘A linear complex equation for slender ring shells overall bending in a meridian plane is given based on E. L. Axelrad's theory of flexible shells. And the non homogeneous solution is obtained from W. Z. Chien's solution for axial symmetrical slender ring shells to investigate the overall bending problem of Ω shaped bellows subjected to pure bending moments. The values calculated in the present paper are very close to the existing experiment. Thus Chien's work on axial symmetrical problems for ring shells has been extended to overall bending problems.
