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Title:Izračun oblike proste površine magnetne tekočine v homogenem magnetnem polju : doktorska disertacija
Authors:ID Trbušić, Mislav (Author)
ID Hamler, Anton (Mentor) More about this mentor... New window
Files:.pdf DOK_Trbusic_Mislav_2020.pdf (4,84 MB)
MD5: 377AF243AC65A3CEDA18467328EDA0FF
 
Language:Slovenian
Work type:Doctoral dissertation (mb31)
Typology:2.08 - Doctoral Dissertation
Organization:FERI - Faculty of Electrical Engineering and Computer Science
Abstract:Doktorska naloga obravnava problematiko izračuna oblike proste površine magnetne tekočine v homogenem in statičnem magnetnem polju. Če magnetno tekočino, ki je stabilna koloidna suspenzija magnetnih nanodelcev, izpostavimo zunanjemu magnetnemu polju, ki presega določeno kritično vrednost, se bodo na prosti površini tekočine ustvarile konicam podobne oblike. Razporeditev in višina konic bo odvisna od jakosti magnetnega polja, kot tudi od lastnosti tekočine. V nalogi sta teoretično in numerično obravnavana dva primera, in sicer primer osamljene konice v dvodimenzionalni osno simetrični postavitvi ter centralne konice v heksagonalnem periodičnem vzorcu, ki je vpeta v tri-razsežnostni prostor. V prvem primeru je vodilna enačba magnetno razširjena nelinearna Young-Laplaceova enačba, pri tem obliko proste površine opisuje polinomska funkcija v valjnem koordinatnem sistemu. Drugi primer temelji na energijskem funkcionalu, ki zajema magnetno, gravitacijsko in površinsko energijo. V tem primeru je površina aproksimirana z valovnimi funkcijami oziroma z vsoto treh ravninskih valov, katerih valovni vektorji so v kartezičnem koordinatnem sistemu krajevno premaknjeni za 2/3. Računska strategija je zastavljena na način, da se najprej ovrednoti magnetno polje v prostoru, za kar je uporabljena metoda končnih elementov in nato deformacija proste površine, pri tem je v slednjem postopku naloga zastavljena kot optimizacijski problem, ki se v primeru osamljene konice v 2D prostoru rešuje s pomočjo algoritma diferenčne evolucije, v primeru centralne konice v heksagonalni razporeditvi pa z uporabo kombinacije algoritma diferenčne evolucije in Ritzove metode. Rezultati numeričnega modela deformacije proste površine magnetne tekočine so primerjani z računskimi in merjenimi vrednostmi, ki so dostopne v literaturi, saj zadovoljivih meritev ni bilo možno izvesti. Eksperimentalno in numerično je bila ovrednotena razporeditev magnetnega polja v ravnini nad konicami magnetne tekočine, s čimer je bilo potrjeno teoretično predvidevanje, da je razporeditev magnetnega polja nad tekočino podobna razporeditvi konic na prosti površini.
Keywords:Rosensweigova nastabilnost, heksagonalna razporeditev, ferofluid, metoda končnih elementov (MKE), diferenčna evolucija (DE), energijski funkcional, Young-Laplaceova enačba, Ritzova metoda
Year of publishing:2020
Place of performance:Maribor
Publisher:[M. Trbušić]
Number of pages:XXV, 104 str.
Source:Maribor
UDC:621.317.41:620.3(043.3)
COBISS.SI-ID:24894979 New window
NUK URN:URN:SI:UM:DK:4WY4ITL3
Publication date in DKUM:11.08.2020
Views:809
Downloads:122
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:KTFMB - FERI
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Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:22.03.2020

Secondary language

Language:English
Title:Computation of a magnetic liquid free surface shape in a homogeneous magnetic field
Abstract:The thesis deals with the computation of a magnetic liquid free surface deformation under the influence of a homogeneous magnetostatic field. When a magnetic liquid, which is a stable colloidal suspension of magnetic nanoparticles, is exposed to an external magnetic field exceeding a certain critical value, spike-like shapes appear on the surface of the liquid. The distribution and the height of the spikes depend on the magnetic field strength, as well as the properties of the magnetic liquid. Two case studies of free surface deformation are covered theoretically and numerically in the thesis. The first case study is devoted to a single spike, where the free surface is described as a polynomial function in cylindrical coordinates with applied cylindrical symmetry. To obtain the shape deformation, a system of nonlinear magnetic augmented Young-Laplace equations is solved iteratively. In the second case study, the research effort is focused on the free surface deformation of a central spike in a periodical hexagonal pattern placed in three-dimensional space (3D). Due to the periodical nature of the problem, the free surface is approximated by three planar waves, whose two-dimensional wave-vectors are mutually displaced by 2/3 in the x-y plane. The surface deformation is achieved through the energy function, with the combination of Differential Evolution and the Ritz method. The computational strategy is divided into two stages. At the first stage, the magnetic field is computed by the Finite Element Method (FEM), while a free surface profile is obtained in the second stage. The numerical results of the magnetic liquid free surface deformation obtained by the proposed methods are compared by the numerical and experimental results published in the References. To support the theoretical predictions as well as numerically obtained results, measurements of the magnetic field were performed at a close distance above the spikes of the magnetic liquid, which show that the magnetic field is distributed in a similar way as a free surface.
Keywords:Rosensweig instability, hexagonal pattern, Ferrofluid, Finite Element Methods (FEM), Differential Evolution (DE), Energy Functional, Young-Laplace equation, Ritz method


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