The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube o...The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube of a Francis turbine with splitter blades is not well understood, especially the vortex rope property. This letter presents a prediction of the behavior of the vortex rope in the draft tube of the Francis-99 turbine obtained by the computational fluid dynamics (CFD), where the Liutex/Rortex method, as the most recent vortex definition, is applied to analyze the periodical precession of the vortex rope in the draft tube cone. The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent the vortex rope structurewith the vortex-core lines. Furthermore, since it seems to be very hard to define a sharp boundary surface for the whole vortex structure, it is advantageousfocusing only on the vortex core line,by which different vortex structures can be clearly differentiated. The evolution of the vortex core and the process of the vortex breakdown in the draft tube are revealed, which might help to comprehend the development of the turbulent flow in the draft tube.展开更多
The spatiotemporal evolution of hairpin vortex structures in a fully developed turbulent boundary layer is investigated qualitatively and quantitatively by using two image methods.In this paper,the moving single-frame...The spatiotemporal evolution of hairpin vortex structures in a fully developed turbulent boundary layer is investigated qualitatively and quantitatively by using two image methods.In this paper,the moving single-frame and long-exposure(MSFLE)image method is used to intuitively track the evolution process of a hairpin vortex,while the moving particle image velocimetry(moving-PIV)method is applied for obtaining a moving velocity field for quantitative analysis.According to the structural characteristics of the hairpin vortex,an inclined light sheet with an appropriate inclination of 53°is arranged to capture the complete hairpin vortex structure at Re_(θ)=97–194.In addition,the core size and the rotational strength of a hairpin vortex are further defined and quantified by the Liutex vector method.The evolution process of a complete hairpin vortex structure observed by MSFLE shows that the shear along the normal direction leads to an increasing strength of the hairpin vortex,accompanied by a lifting vortex head and a distance decrease between two vortex legs during the dissipation period.By combining moving-PIV with the Liutex identification,the spatiotemporal evolution of four typical regions of a hairpin vortex projecting into a 53°cross-section is obtained.The results show that the process from the generation to the dissipation of a single hairpin vortex can be well characterized and recorded by the Liutex based on the core size and rotational intensity,and the evolution process is consistent with the MSFLE result.According to the statistics of vortex core size and rotation intensity along time,the evolution of the hairpin vortex necks and legs can be described as a process of enhancement followed by dissipation.For the vortex head,its evolution maintains longer attributed to its far-from-wall position,which consists of an absolute enhancement process(stage 1)with an increasing rotation strength and a constant core size,and an absolute dissipation(stage 2)with a decreasing rotation strength and a constant core size.展开更多
文摘The turbulent flow in the draft tube of a Francis turbine is very complicated while working under off-design conditions. Although the off-design conditions were widely studied, the vortex core line in the draft tube of a Francis turbine with splitter blades is not well understood, especially the vortex rope property. This letter presents a prediction of the behavior of the vortex rope in the draft tube of the Francis-99 turbine obtained by the computational fluid dynamics (CFD), where the Liutex/Rortex method, as the most recent vortex definition, is applied to analyze the periodical precession of the vortex rope in the draft tube cone. The advantage of this Liutex/Rortex method is shown by its enhanced ability to represent the vortex rope structurewith the vortex-core lines. Furthermore, since it seems to be very hard to define a sharp boundary surface for the whole vortex structure, it is advantageousfocusing only on the vortex core line,by which different vortex structures can be clearly differentiated. The evolution of the vortex core and the process of the vortex breakdown in the draft tube are revealed, which might help to comprehend the development of the turbulent flow in the draft tube.
基金Projects supported by the National Natural Science Foundation of China(Grant No.51906154)the National Science and Technology Major Project(Grant No.2017-V-0016-0069)the Natural Science Foundation of Shanghai(Grant No.21ZR1443700).
文摘The spatiotemporal evolution of hairpin vortex structures in a fully developed turbulent boundary layer is investigated qualitatively and quantitatively by using two image methods.In this paper,the moving single-frame and long-exposure(MSFLE)image method is used to intuitively track the evolution process of a hairpin vortex,while the moving particle image velocimetry(moving-PIV)method is applied for obtaining a moving velocity field for quantitative analysis.According to the structural characteristics of the hairpin vortex,an inclined light sheet with an appropriate inclination of 53°is arranged to capture the complete hairpin vortex structure at Re_(θ)=97–194.In addition,the core size and the rotational strength of a hairpin vortex are further defined and quantified by the Liutex vector method.The evolution process of a complete hairpin vortex structure observed by MSFLE shows that the shear along the normal direction leads to an increasing strength of the hairpin vortex,accompanied by a lifting vortex head and a distance decrease between two vortex legs during the dissipation period.By combining moving-PIV with the Liutex identification,the spatiotemporal evolution of four typical regions of a hairpin vortex projecting into a 53°cross-section is obtained.The results show that the process from the generation to the dissipation of a single hairpin vortex can be well characterized and recorded by the Liutex based on the core size and rotational intensity,and the evolution process is consistent with the MSFLE result.According to the statistics of vortex core size and rotation intensity along time,the evolution of the hairpin vortex necks and legs can be described as a process of enhancement followed by dissipation.For the vortex head,its evolution maintains longer attributed to its far-from-wall position,which consists of an absolute enhancement process(stage 1)with an increasing rotation strength and a constant core size,and an absolute dissipation(stage 2)with a decreasing rotation strength and a constant core size.
