| Author: | Zheng, Haojun |
| Title: | On the kinematics and dynamics of the leading vortex in starting jets |
| Advisors: | Yu, Ching Man Simon (AAE) |
| Degree: | Ph.D. |
| Year: | 2024 |
| Subject: | Vortex-motion Jets -- Fluid dynamics Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Aeronautical and Aviation Engineering |
| Pages: | xxxiii, 111 pages : color illustrations |
| Language: | English |
| Abstract: | The leading vortex is a significant component in wakes of aquatic locomotion and starting jets observed in cardiac flows as well as volcanic eruption. On account of a great interest of vortex formation in starting flows, the kinematic and dynamical properties of the leading vortex have been examined by a number of analytical and experimental studies. In particular, a physical limit for the vortex formation was discovered in axisymmetric flows. At small stroke ratios, jet fluids are eventually accumulated in the leading vortex ring. At large stroke ratios, the vortex ring stops growing and disconnects from the trailing jet at certain time, which indicates not all fluids can be delivered into the vortex bubble in its formation. Associated with the energy maximization principle, the transition between the states occurs at a critical stroke ratio referred to as the formation number. However, the pinch-off process was not be found in two-dimensional flows. To this end, the goal of this thesis is to numerically examine the vortex formation in impulsively started flows including axisymmetric, two-dimensional, three-dimensionally rectangular jets. With better understanding on the kinematics and dynamics of vortex motion, the vortex properties and critical formation time are predicted by analytical studies. For axisymmetric jets, the kinematic and dynamical properties of the leading vortex ring are investigated during the formation and post-formation stages. The effects of the stroke ratio and nozzle geometry are studied at a fixed jet Reynolds number of 2500. The vortex ring with maximum circulation is identified for both tube and orifice configurations. Based on the circulation method, formation numbers for tube and orifice are determined at around 4.4 and 2.1, respectively. Moreover, a new criterion to describe the onset of vortex ring pinch-off process is proposed based on a circulation ratio. During the formation stage, the scaling laws for vortex trajectories and circulation are proposed. The evolution of dimensionless energy is predicted accurately. During the post-formation stage, the scaling laws for vortex properties (e.g., the vortex ring diameter, translational velocity, and circulation) are found to be independent of both the nozzle configuration and vortex Reynolds number. On the grounds of the invariance of impulse in vortex decay, the scaling laws of vortex motion are analytically derived for the non-dimensional energy, circulation, and diffusivity scale of vortex core. For two-dimensional jets, the effects of stroke ratio, nozzle configuration, and Reynolds number (ranging from 500 to 2000) are investigated. A complete vortex pair pinch-off from the trailing jet can be identified in the vorticity fields. Moreover, the maximum vortex circulation and the universal energy level in post-formation stage are proposed. Critical formation numbers (13.6 and 9.3) are determined for straight nozzle and orifice nozzle by circulation criterion. They are further analysed by other four criterions including both global and local analyses. Considering the contraction effect of the orifice flows, critical formation numbers can be transformed into a universal value of 16.5 for both nozzles. The effect of Reynolds number on the formation number is found to be within 12% for parallel flow cases but it will increase up to 27% for non-parallel flow cases due to shear-layer instability. Larger formation number of two-dimensional flows than axisymmetric flows can be attributed to the slower vortex motion without the curvature effect. It is noted that the curvature effect dominates the self-induced velocity and has more contribution than vortex circulation. The effects of boundary layer and over-pressure on total invariants are studied. For two-dimensional flows, a modified contraction-based slug model is proposed, and it can predict accurately the total invariants shedding from the nozzle edge. Analytical estimations on the formation number is proposed by matching predicted total invariants to Pierrehumbert model of steady vortex pairs. By assuming that the pinch-off starts when the vortex motion becomes steady, two analytical models are proposed in terms of vortex impulse and vortex translational velocity. In comparison to the impulse-based model, the kinematic model is more appropriate with errors at about -25%. For rectangular jets, the effects of aspect ratio are investigated at a fixed jet Reynolds number of 1000. For the axis-switching process, the secondary flow induced by the vortex ring deformation plays an important role. During the azimuthal deformation of the leading vortex ring, vortex stretching weakened by the increasing aspect ratio is identified. Based on the method of net vorticity flux, vortex pinch-off on both centerline planes is determined. The formation numbers for the square jet are at about 2.0 on both the diagonal and mid planes. For the rectangular jets with aspect ratios greater than one, the formation number is reduced from 2.3 to 1.5 on the major axis plane by increasing aspect ratio, while it approaches 1.7 on the minor axis plane which is independent of the aspect ratio. It is suggested that the vortex deformation accelerates the pinch-off process on both the major and minor axis planes. In particular, the appearance of secondary vortices on the major plane and the arc-shaped vortices on the minor plane signals the onset of pinch-off. With considerable three-dimensional effects on global flows, the two-dimensional nature is absent on the minor axis plane. |
| Rights: | All rights reserved |
| Access: | open access |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| 7962.pdf | For All Users (off-campus access for PolyU Staff & Students only) | 26.65 MB | Adobe PDF | View/Open |
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