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On the Evolution and Physics of Vortex Rings
Author: XiangYang
Tutor: LiuHong
School: Shanghai Jiaotong University
Course: Aircraft design
Keywords: evolution of vortex rings physical features formationtime pinch-off instantaneous force
CLC: O357.1
Type: Master's thesis
Year: 2013
Downloads: 30
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Abstract
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During the past several decades, research on the physical features of vortex ringshas not been well-understood. Shariff (Annu.Rev.Fluid Mech.24:235-79,1992)summarized the researches on the evolution and transmission process of vortex ringsand Dabiri (Annu.Rev.Fluid Mech.41:17-33,2009) further explores the dynamicfeathers of vortex ring and the effect on bio-propulsion system. One of the aims of theresearch on vortex ring is to reveal the fundaments why animals can product high liftforce and large thrust. However, up to now, the formation and evolution of vortex ringand the corresponding fluid dynamics are both lack of thorough analysis. Oneimportant factor is the boundary and physical parameters cannot be determinedclearly.In this thesis, numerical method is applied to simulate the evolution andtransmission of vortex ring, and then the boundary of vortex ring can be determinedon the basis of stream function with body coordinate system. Compared with Gharib s(J.Fluid Mech.360:121-140,1998) experimental results and the analytical results basedon Slug model, stream function method can determine the boundary of vortex ringand the physical parameters of vortex ring reasonably. Meanwhile, combined withexperimental analysis, this paper investigates the physics of vortex ring and drawssome conclusions:1. This thesis studies how formation time (the stroke of piston/the diameter of piston)affects the physics of vortex ring generated by piston-cylinder mechanism. When the formation time of vortex ring is smaller than4, the vortex core radiusincreases with formation time, however, when the formation time is larger than4,the vortex core no longer increases. So the pinch-off of vortex ring really meansthe pinch-off vortex core.2. This thesis studies the growing of vortex core during the evolution of vortex ringand shows there exists three phases during the evolution of vortex core: fastgrowing phase; when the parameterA=Γring/xcoreΔU reaches about one, the growingof vortex core likely undergo a pinch-off phase because of the formation oftrailing vortex ring; the merging phase between vortex ring and the trailing vortexring.3. This thesis studies the instantaneous force during the evolution of vortex ring anddual vortex ring by two strokes. Voticity-moment theorem is applied and studiesindicate the change of momentum is the main source of instantaneous force.Research indicates that the stopping vortex and formation time play an importantrole on the change of instantaneous force. Meanwhile, this paper also shows thatthe instantaneous force during the evolution of the second vortex ring gainsbenefit due to the interaction of the first vortex. Moreover, the benefits ofinstantaneous force show two models: the relative increasing and absoluteincreasing.4. This thesis studies how to judge the performance of biological propulsion fromwake measurement. Two dimensionless parameters ξvandηw, are proposed andthe larger value of ηw means higher efficiency of biological propulsion. Throughthe research on vortex ring flows, we can consider that the two parameters canjudge the efficiency effectively.
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CLC: > Mathematical sciences and chemical > Mechanics > Fluid Mechanics > Viscous fluid > Incompressible viscous fluid
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