Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common prac...Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common practice in continuum mechanics is not emphasized by the volume averaging technique resulting in the macroscopic balance equations are not capable of comprehensively describing the kinematic behaviors of multiphase porous media due to the loss of essential macroscopic variables. This study derives the macroscopic mass and momentum balance equations for the pore fluid of a fluid-solid porous medium by use of the volume averaging technique. We show(1) if the procedure of the volume averaging is implemented in its traditional manner, only the average flux of the pore fluid described by its mass average velocity is captured;(2) if the work conjugate principle is employed to define a work-conjugate velocity for the pore fluid at the macroscale, both the average flux(described by the mass average velocity) and the dispersive flux(described by the deviation of the mass average velocity from the work-conjugate one) are reproduced. This theoretical analysis demonstrates that the work conjugate principle is an essential thermodynamic constraint to improve the volume averaging technique, in the sense that the macroscopic balance equations are required to be capable of comprehensively describing the macroscopic kinematic behaviors of multiphase porous media.展开更多
Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic o...Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of.conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.展开更多
基金supported by the National Basic Research Program of China(Grant No.2014CB744702)the National Natural Science Foundation of China(Grant No.51678012)
文摘Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common practice in continuum mechanics is not emphasized by the volume averaging technique resulting in the macroscopic balance equations are not capable of comprehensively describing the kinematic behaviors of multiphase porous media due to the loss of essential macroscopic variables. This study derives the macroscopic mass and momentum balance equations for the pore fluid of a fluid-solid porous medium by use of the volume averaging technique. We show(1) if the procedure of the volume averaging is implemented in its traditional manner, only the average flux of the pore fluid described by its mass average velocity is captured;(2) if the work conjugate principle is employed to define a work-conjugate velocity for the pore fluid at the macroscale, both the average flux(described by the mass average velocity) and the dispersive flux(described by the deviation of the mass average velocity from the work-conjugate one) are reproduced. This theoretical analysis demonstrates that the work conjugate principle is an essential thermodynamic constraint to improve the volume averaging technique, in the sense that the macroscopic balance equations are required to be capable of comprehensively describing the macroscopic kinematic behaviors of multiphase porous media.
基金This project is supported by National Natural Science Foundation of China (No.50275017)Provincial Natural Science Foundation of Liaoning, China (No.20051019).
文摘Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of.conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.
