The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze th...The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.展开更多
The particle paths of the Lagrangian flow field simulate very well the interface curve of the Yin-Yang balance in the ancient Tal-Chi diagram. There are four forms called the ＂four states＂ in the Tai-Chi diagram. Of...The particle paths of the Lagrangian flow field simulate very well the interface curve of the Yin-Yang balance in the ancient Tal-Chi diagram. There are four forms called the ＂four states＂ in the Tai-Chi diagram. Of the four states, under Yang are the Major Yang and the Minor Yin, and under Yin are the Major Yin and the Minor Yang. The present study provides the proper positions of the four states in the ancient Tal-Chi diagram. The Fu Xi＇s Eight Trigrams Chart located along the ancient Tai-Chi diagram is also developed in the present study. The interface curve of Yin-Yang in the ancient Tai-Chi diagram has never been described mathematically. It can now be formulated by the equations describing the particle paths in the Lagrangian flow field.展开更多
Galaxies are huge families of stars held together by their own gravities. The system M51 is a spiral galaxy. It possesses billions of stars. The range of the spiral arms extends hundred thousand light years. The prese...Galaxies are huge families of stars held together by their own gravities. The system M51 is a spiral galaxy. It possesses billions of stars. The range of the spiral arms extends hundred thousand light years. The present study is in an attempt in using the particle paths of the Lagrangian flow field to simulate the spiral arms of Galaxy M51. The Lagrangian flow field is introduced. The initial locations of fluid particles in the space between two concen- tric cylinders are ftrst specified. Then a linear velocity distribution of the fluid particles is used with different an- gle rotations of the particles to obtain the particle paths in the Lagrangian diagram. For simulating the spiral arms of Galaxy M51, the Lagrangian M51 diagram is developed. The particle paths of the Lagrangian M51 diagram agree quite well with the spiral arms of Galaxy M51.展开更多
The particle paths of the Lagrangian flow field between two cylinders simulate well the spiral arms of Galaxy M51 image [1] and the interface curve of the Yin-Yang balance in the ancient Tai-Cbi diagram [2]. The parti...The particle paths of the Lagrangian flow field between two cylinders simulate well the spiral arms of Galaxy M51 image [1] and the interface curve of the Yin-Yang balance in the ancient Tai-Cbi diagram [2]. The particle paths of the Lagrangian flow field involve four parameters. The normalization of the system of equations significantly simplifies the formulation of the flow process and reduces the original four parameters to only one parameter. Furthermore it provides the similarity between the formulation of the spiral arms of Galaxy M51 and that of the interface curve of the Yin-Yang balance in the ancient Tai-Chi diagram.展开更多
文摘The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.
文摘The particle paths of the Lagrangian flow field simulate very well the interface curve of the Yin-Yang balance in the ancient Tal-Chi diagram. There are four forms called the ＂four states＂ in the Tai-Chi diagram. Of the four states, under Yang are the Major Yang and the Minor Yin, and under Yin are the Major Yin and the Minor Yang. The present study provides the proper positions of the four states in the ancient Tal-Chi diagram. The Fu Xi＇s Eight Trigrams Chart located along the ancient Tai-Chi diagram is also developed in the present study. The interface curve of Yin-Yang in the ancient Tai-Chi diagram has never been described mathematically. It can now be formulated by the equations describing the particle paths in the Lagrangian flow field.
基金the Natural Sciences and Engineering Research Council of Canada
文摘Galaxies are huge families of stars held together by their own gravities. The system M51 is a spiral galaxy. It possesses billions of stars. The range of the spiral arms extends hundred thousand light years. The present study is in an attempt in using the particle paths of the Lagrangian flow field to simulate the spiral arms of Galaxy M51. The Lagrangian flow field is introduced. The initial locations of fluid particles in the space between two concen- tric cylinders are ftrst specified. Then a linear velocity distribution of the fluid particles is used with different an- gle rotations of the particles to obtain the particle paths in the Lagrangian diagram. For simulating the spiral arms of Galaxy M51, the Lagrangian M51 diagram is developed. The particle paths of the Lagrangian M51 diagram agree quite well with the spiral arms of Galaxy M51.
基金sponsored by the Natural SciencesEngineering Research Council of Canada
文摘The particle paths of the Lagrangian flow field between two cylinders simulate well the spiral arms of Galaxy M51 image [1] and the interface curve of the Yin-Yang balance in the ancient Tai-Cbi diagram [2]. The particle paths of the Lagrangian flow field involve four parameters. The normalization of the system of equations significantly simplifies the formulation of the flow process and reduces the original four parameters to only one parameter. Furthermore it provides the similarity between the formulation of the spiral arms of Galaxy M51 and that of the interface curve of the Yin-Yang balance in the ancient Tai-Chi diagram.
