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Title:Meshless modeling of thermo-mechanics of low-frequency electromagnetic direct chill casting
Authors:ID Šarler, Božidar (Mentor) More about this mentor... New window
ID Mavrič, Boštjan (Author)
Files:.pdf Bostjan_Mavric.pdf (21,30 MB)
MD5: C03BB393BB0268D25251D279578735D6
 
Language:English
Work type:Doctoral dissertation
Typology:2.08 - Doctoral Dissertation
Organization:FPŠ - Graduate School
Abstract:The aim of this dissertation is to devise a meshless model describing the thermomechanical phenomena, which occur during DC casting of aluminium alloys under the influence of electromagnetic stirring. The thermoemchanical phenomena are important, because they can cause several type of defects, which can significantly deteriorate the quality of the resulting billet. The two most important of them are the hot tearing, which causes cracks to appear in the mushy zone, and the porosity, which demonstrates itself as micrometer sized voids in the microstructure of the billet. To calculate the stresses and strains, a computational model of the stationary state of the process, stated in axial symmetry, is formulated. It uses Eulerian formulation by fixing the computational domain to the mold of the casting device allowing the material to move through the computational domain. The stresses are calculated from the stress equilibrium equations. The small strain approximation is used to consider the three contributions to strain. The strain consists of the thermal strain, which is caused by the inhomogeneous thermal profile in the billet, the viscoplastic strain, which is caused by the irreversible deformation because of the large stresses occurring in the billet, and the elastic strain. The spatial discretization of the governing equations is performed by local radial basis function collocation method (LRBFCM) and the temporal discretization is achieved by the method of lines with implicit Euler formula. The method used for spatial discretization uses radial basis functions augmented by monomials to approximate the solution values on localized stencils. This approximation is used to construct the discretization coefficients of the differential operators present in the model. A flexible framework for formulation of multiphysics problems is developed to use the obtained discretization coefficients to construct the temporal discretization of the governing equations. The node arrangement, on which the spatial discretization is performed, was generated by a point-repel algorithm. The performance of the method is tested on several benchmark test cases. The accuracy of the discretization is estimated by comparing the analytic and the numerical solution to several stationary problems in thermomechancis. Of special interest is the performance of the method with respect to the choice of the shape parameter, which determines the spatial scale of the radial basis functions. Besides this, the dependence of the condition number of the interpolation matrix on the shape parameter is studied. The condition number is found fit to replace the condition number as the shape-determining free parameter of the method. The implementation of the solver of time dependent problems is tested on problem of thermoelasticity, which couples the thermal transport with the elastic waves. The results of the problem are compared with the finite element method, showing good agreement of the two methods. The results are also compared with the results obtained by meshless local Petrov-Galerkin method and the proposed local collocation method demonstrated significantly better solution quality in the studied case. The performance of the solver used to solve the system of nonlinear equations given by the viscoplastic constitutive equations is estimated on a quasi zero-dimensional problem. The results are found to match perfectly. Solution of a more complicated problem is obtained with the proposed method and the finite-element method, both methods giving practically the same solution, although some serious limitations of the chosen finite element solver are exposed during the selection of the problem parameters. Finally, the devised method is applied to the problem of DC casting of aluminium alloys. The thermomechanical model relies on a model of heat and mass transfer to obtain the input fields needed in the solver. The required fields are: temperature, pressure, liquid
Keywords:thermomechanics, viscoplasticity, aluminium alloys, direct-chill casting, electromagnetic stirring, hot tearing, porosity, meshless methods, local collocation method, radial basis functions, shape parameter
Place of publishing:Nova Gorica
Year of publishing:2017
PID:20.500.12556/RUNG-3108-7a747fbf-2aaa-307d-7be5-94fad4149715 New window
COBISS.SI-ID:4830971 New window
NUK URN:URN:SI:UNG:REP:MBGTKHGZ
Publication date in RUNG:28.06.2017
Views:5716
Downloads:254
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Secondary language

Language:Slovenian
Title:Brezmrežno modeliranje termomehanike nizkofrekvenčnega elektromagnetnega polkontinuirnega ulivanja
Abstract:Namen te disertacije je razvoj brezmrežnega modela termomehanskih pojavov, ki so prisotni med DC ulivanjem aluminijevih zlitin pod vplivom elektromagnetnega mešanja. Ti pojavi so pomembni, ker lahko povzročijo več vrst defektov, ki lahko bistveno poslabšajo kvaliteto ulitega droga. Med njimi sta najpomembnejša vroče trganje, ki povzroči pojavljanje razpok v kašastem področju, in poroznost, ki se kaže kot prisotnost mikrometrskih praznin v notranjosti droga. Za izračun napetosti in deformacij je bil razvit osno simetrični računski model. Z Eulerjevim opisom modelira stacionarno stanje med procesom litja. Računska domena je pripeta na kokilo, skoznjo pa se premika strjeni material. Za izračun napetosti se rešuje ravnovesna enačba za napetost zapisana za približek majhnih deformacij. Deformacija je vsota treh prispevkov. Sestavljajo jo termična deformacija, ki je posledica nehomogenega temperaturnega profila, viskoplastična deformacija, ki je posledica nepovratne deformacije zaradi velikih napetosti v drogu, ter elastična deformacija. Prostorska diskretizacija enačb modela je izvedena z lokalno kolokacijo z radialnimi baznimi funkcijami, časovna diskretizacija pa z implicitno Eulerjevo metodo. Metoda, ki jo uporabimo za prostorsko diskretizacijo, ustvari aproksimacijo rešitve na lokaliziranih poddomenah z radialnimi baznimi funkcijami in monomi. Iz dobljene aproksimacije lahko izračunamo diskretizacijske koeficiente za vse diferencialne operatorje, ki so prisotni v enačbah modela. Ti diskretizacijski koeficienti so uporabljeni v razvitem ogrodju, ki omogoča lažjo sklopitev enačb večfizikalnih modelov in njihovo enostavno časovno diskretizacijo. Postavitev točk, na katerem se izvede prostorska diskretizacija je ustvarjena z algoritmom, ki razporeja točke z modeliranjem odbojnih sil med njimi. Učinkovitost razvite metode je bila preverjena na več različnih testnih primerih. Natančnost diskretizacijske metode je bila ocenjena z primerjavo numeričnih in analitičnih rešitev stacionarnih problemov termomehanike. Posebej zanimivo je obnašanje natančnosti ob spreminjanju oblikovnega parametra, ki določa prostorsko skalo radialnih baznih funkcij. Poleg tega je bil proučen vpliv oblikovnega parametra na pogojenostno število interpolacijskih matrik. Pogojenostno število se je izkazalo za primeren nadomestek oblikovnega prametra kot prosti parameter metode. Implementacija postopka reševanja je bila preverjena na problemu sklopljene termoelastičnosti, ki sklaplja transport toplote z elastičnimi valovi. Dobljeni rezultati so bili primerjani z rezultati metode končnih elementov. Rešitvi sta se ujemali za vse obravnavane primere. Ob primerjavi z rešitvijo dobljeno z brezmrežno lokalno metodo Petrov-Galerkin, so se rezultati dobljeni z lokalno kolokacijsko metodo izkazali za bistveno boljše. Učinkovitost postopka reševanja sistema nelinearnih enačb dobljenih iz viskoplastičnega mehanskega modela je bila preverjena na kvazi nič-dimenzionalnem problemu. Ujemanje rezultatov z analitično rešitvijo je bilo popolno. Rešitev istih enačb na geometrijsko bolj zapletenem primeru je bila primerjana z rešitvijo s končnimi elementi. Dobljeni rešitvi ta bili praktično enaki, je pa postopek izbire testnega primera izpostavil nekaj pomanjkljivosti izbranega programa za reševanje s končnimi elementi. Nazadnje je bila razvita metoda uporabljena za reševanje termomehanskega problema DC ulivanja aluminijevih zlitin. Termomehanski model se za pridobitev nekaterih vhodnih fizikalnih polj zanaša na povezan model prenosa toplote in gibalne količine. Potrebna vhodna fizikalna polja so temperatura, tlak, delež tekoče faze in elektromagnetna sila. Termomehanski model rešuje enačbe na mehansko koherentnem delu kašastega območja, pod položajem izoterme koherenčne temperature. Na območju stika med drogom in kokilo model iterativno določi ustrezne robne pogoje. Ko rešitev mehanskega modela doseže stacionarno stanje, se izračunajo še kriteriji vročega trganja ter p
Keywords:brezmrežne metode, termomehanika, viskoplastičnost, aluminijeve zlitine, DC ulivanje, elektromagnetno mešanje, radialne bazne funkcije, vroče trganje, poroznost, lokalna kolokacijska metoda, radialne bazne funkcije, parameter oblike


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