Lagrangian Coherent Structures in Vortex Ring Formation
| Main Author: | |
|---|---|
| Language: | English |
| Published: |
The Ohio State University / OhioLINK
2019
|
| Subjects: | |
| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1565828293505214 |
| id |
ndltd-OhioLink-oai-etd.ohiolink.edu-osu1565828293505214 |
|---|---|
| record_format |
oai_dc |
| spelling |
ndltd-OhioLink-oai-etd.ohiolink.edu-osu15658282935052142021-08-03T07:12:25Z Lagrangian Coherent Structures in Vortex Ring Formation Harter, Braxton Nicholas Aerospace Engineering Fluid Dynamics vortex ring vortex ring formation fluid dynamics Lagrangian coherent structures LCS finite-time Lyapunov exponent FTLE vortex identification <p>Vortex rings are among the only consistent natural feature to achieve effective transport of mass, momentum, and energy in fluids. For most scenarios where each of these transport mechanisms are utilized, efficiency of the vortex generator is parameterized by how much vorticity is entrained by the created vortex ring—the more vorticity that a vortex ring entrains during the formation process, the more efficient each of the transport mechanisms will be.</p> <p>They cannot grow indefinitely, however. Vortex ring formation is known to be limited by a dimensionless ratio that compares the length of an ejected slug of fluid <i>L</i> to its diameter <i>D</i>. This ratio is termed <i>formation time</i>, Ţ = <i>L</i>/<i>D</i>, and has a limiting value of approximately 4. The upper limit of ring growth has been justified by the Kelvin-Benjamin variational principle, which states that vortex ring formation is limited due to an energy deficit of the vortex generator in comparison to the translating vortex ring. This principle forms an elegant analytical theory for predicting vortex ring pinch-off; however, a key limitation of findings reported in the literature is the inability to accurately quantify vortex characteristics early in the formation process (especially before pinch-off).</p><p>In this thesis, laminar vortex rings are experimentally studied with a piston-cylinder device for formation times well beyond the limiting ratio of vortex ring pinch-off at Ţ ≈ 4. To answer the question of what the physical limiting processes are, the Lagrangian coherent structures in vortex ring formation are analyzed using both particle image velocimetry and the background-oriented schlieren technique. Utilizing the finite-time Lyapunov exponent calculation, a presently-developed vortex-identification technique is outlined, allowing for the accurate and consistent quantification of vortex formation parameters throughout the entire generation process. A comprehensive examination of the vortex ring limiting process is presented using modern optical measurement and analysis techniques—a study that has previously been absent from literature.</p><p>The dynamics of the system indicate that the process is a highly coupled problem; however, findings show that the process is dependent on the spatial characteristics of the vortex system, as opposed to a temporal parameter that quantifies the volume of fluid ejected (i.e., Ţ). Early in the formation process, the irrotational region of the lead vortex accelerates the trailing jet of fluid, entraining it into the ring. After the vortex has advected beyond a noteworthy axial-location z<i>D</i><sup>-1</sup> ≈ 1, the vortex has advected to a location where the irrotational region can no longer accelerate newly ejected fluid. As such, the lead vortex diverges away from the ejected fluid, leading to a bifurcation in the slug. The jet—and its associated shear layer—stretches at this bifurcation location until it reaches a fatal inflection point and breaks down.</p><p>The proposed limiting process in vortex ring formation is consistent with existing analytical descriptions of pinch-off; present findings reveal the physical phenomena that initialize the process. These insights provide a clear path forward for researchers to maximize vortex ring formation for the effective transport of mass, momentum, and energy in fluids.</p> 2019 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1565828293505214 http://rave.ohiolink.edu/etdc/view?acc_num=osu1565828293505214 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Aerospace Engineering Fluid Dynamics vortex ring vortex ring formation fluid dynamics Lagrangian coherent structures LCS finite-time Lyapunov exponent FTLE vortex identification |
| spellingShingle |
Aerospace Engineering Fluid Dynamics vortex ring vortex ring formation fluid dynamics Lagrangian coherent structures LCS finite-time Lyapunov exponent FTLE vortex identification Harter, Braxton Nicholas Lagrangian Coherent Structures in Vortex Ring Formation |
| author |
Harter, Braxton Nicholas |
| author_facet |
Harter, Braxton Nicholas |
| author_sort |
Harter, Braxton Nicholas |
| title |
Lagrangian Coherent Structures in Vortex Ring Formation |
| title_short |
Lagrangian Coherent Structures in Vortex Ring Formation |
| title_full |
Lagrangian Coherent Structures in Vortex Ring Formation |
| title_fullStr |
Lagrangian Coherent Structures in Vortex Ring Formation |
| title_full_unstemmed |
Lagrangian Coherent Structures in Vortex Ring Formation |
| title_sort |
lagrangian coherent structures in vortex ring formation |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2019 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1565828293505214 |
| work_keys_str_mv |
AT harterbraxtonnicholas lagrangiancoherentstructuresinvortexringformation |
| _version_ |
1719456342288105472 |