The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedin...The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223（5）, 1113- 1116 （2009））. The Lie group theory is applied to the general equation. The group classi- fication with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates.展开更多
重新考察虑了,最早由Pakdemirli[Pakdemirli M.Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2009,223(5):1113-1116]提出的描述最小阻力功的路径方程.将Lie群理论应用...重新考察虑了,最早由Pakdemirli[Pakdemirli M.Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2009,223(5):1113-1116]提出的描述最小阻力功的路径方程.将Lie群理论应用于一般方程,提出了关系任意高程函数群的分类.利用对称性,确定群不变解,并利用正则坐标,降低方程的阶次.展开更多
The concept of field synergy for fluid flow is introduced, which refers to the synergy of the velocity field and the velocity gradient field in an entire flow domain. Analyses show that the flow drag depends not only ...The concept of field synergy for fluid flow is introduced, which refers to the synergy of the velocity field and the velocity gradient field in an entire flow domain. Analyses show that the flow drag depends not only on the velocity and the velocity gradient fields but also on their synergy. The principle of minimum dissipation of mechanical energy is developed, which may be stated as follows: the worse the synergy between the velocity and velocity gradient fields is, the smaller the resistance becomes. Furthermore, based on the principle of minimum dissipation of mechanical energy together with conservation equa-tions, a field synergy equation with a set of specified constraints has been established for optimizing flow processes. The optimal flow field can be obtained by solving the field synergy equation, which leads to the minimum resistance to fluid flow in the fixed flow domain. Finally, as an example, the field synergy analysis for duct flow with two parallel branches is presented. The optimized velocity dis-tributor nearby the fork, which was designed based on the principle of minimum dissipation of me-chanical energy, may reduce the drag of duct flow with two parallel branches.展开更多
文摘The path equation describing the minimum drag work first proposed by Pakdemirli is reconsidered （Pakdemirli, M. The drag work minimization path for a fly- ing object with altitude-dependent drag parameters. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 223（5）, 1113- 1116 （2009））. The Lie group theory is applied to the general equation. The group classi- fication with respect to an altitude-dependent arbitrary function is presented. Using the symmetries, the group-invariant solutions are determined, and the reduction of order is performed by the canonical coordinates.
文摘重新考察虑了,最早由Pakdemirli[Pakdemirli M.Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2009,223(5):1113-1116]提出的描述最小阻力功的路径方程.将Lie群理论应用于一般方程,提出了关系任意高程函数群的分类.利用对称性,确定群不变解,并利用正则坐标,降低方程的阶次.
文摘The concept of field synergy for fluid flow is introduced, which refers to the synergy of the velocity field and the velocity gradient field in an entire flow domain. Analyses show that the flow drag depends not only on the velocity and the velocity gradient fields but also on their synergy. The principle of minimum dissipation of mechanical energy is developed, which may be stated as follows: the worse the synergy between the velocity and velocity gradient fields is, the smaller the resistance becomes. Furthermore, based on the principle of minimum dissipation of mechanical energy together with conservation equa-tions, a field synergy equation with a set of specified constraints has been established for optimizing flow processes. The optimal flow field can be obtained by solving the field synergy equation, which leads to the minimum resistance to fluid flow in the fixed flow domain. Finally, as an example, the field synergy analysis for duct flow with two parallel branches is presented. The optimized velocity dis-tributor nearby the fork, which was designed based on the principle of minimum dissipation of me-chanical energy, may reduce the drag of duct flow with two parallel branches.
