Papers by Katarina Mramor
Metallurgical and Materials Transactions B
The chemical homogeneity and metallurgical structure of vacuum arc remelted (VAR) zirconium ingot... more The chemical homogeneity and metallurgical structure of vacuum arc remelted (VAR) zirconium ingots are directly responsible for product quality. It is therefore important to understand the relationship between these properties and the operating conditions. An in-depth analysis of the modelling of solidification phenomena during the VAR was carried out. Such model, solves a coupled set of transient equations for heat, momentum, solute transport and turbulence in an axisymmetric geometry. The remelting and cooling of a cylindrical ingot are calculated for time-dependent operating parameters. The solidification mechanisms implemented in the model can be applied to multicomponent industrial alloys such as Zircaloy-4, which provides information on the macrosegregation phenomena studied in this paper. The model results were validated, based on the remelting of a specially designed chemically homogeneous Zircaloy-4 electrode. The results illustrate the importance of thermal r radial direction s solid t turbulent z axial direction Ɵ orthoradial direction * * * ,
Science and Technology of Nuclear Installations, 2008
A three-dimensional two-fluid code Neptune_CFD has been validated against the Arizona State Unive... more A three-dimensional two-fluid code Neptune_CFD has been validated against the Arizona State University (ASU) and DEBORA boiling flow experiments. Two-phase flow processes in the subcooled flow boiling regime have been studied on ASU experiments. Within this scope a new wall function has been implemented in the Neptune_CFD code aiming to improve the prediction of flow parameters in the near-wall region. The capability of the code to predict the boiling flow regime close to critical heat flux (CHF) conditions has been verified on selected DEBORA experiments. To predict the onset of CHF regime, a simplified model based on the near-wall values of gas volume fraction was used. The results have shown that the code is able to predict the wall temperature increase and the sharp void fraction peak near the heated wall, which are characteristic phenomena for CHF conditions.
Metals
A large-eddy simulation (LES) based meshless model is developed for the three-dimensional (3D) pr... more A large-eddy simulation (LES) based meshless model is developed for the three-dimensional (3D) problem of continuous casting (CC) of steel billet. The local collocation meshless method based on radial basis functions (RBF) is applied in 3D. The method applies scaled multiquadric (MQ) RBF with a shape parameter on seven nodded local sub-domains. The incompressible turbulent fluid flow is described using mass, energy, and momentum conservation equations and the LES turbulence model. The solidification system is solved with the mixture continuum model. The Boussinesq approximation for buoyancy and the Darcy approximation for porous media are used. Chorin’s fractional step method is used to couple velocity and pressure. The microscopic model is closed with the lever rule model. The LES model is compared to the two-equation Low Re k−ε turbulence Reynolds Averaged Navier–Stokes (RANS) model in terms of temperature, velocity and computational times. The LES model resolves transient charact...
for countless suggestions, discussions and ideas, especially Dr. Robert Vertnik whose advice and ... more for countless suggestions, discussions and ideas, especially Dr. Robert Vertnik whose advice and guidance about the pre-existing numerical model have greatly facilitated my work. My special thanks are extended to the staff of theŠtore Steel d.o.o. company, especially Dr. Robert Vertnik, for providing all the necessary data, relevant for developing the numerical model of their billet casting machine. I am particularly grateful to my employer, Centre of Excellence for Biosensors, Instrumentation and Process Control, for their understanding and support during my Ph.D. studies. The Centre of Excellence for Biosensors, Instrumentation and Process Control is an operation financed by the European Union, European Regional Development Fund and Republic of Slovenia, Ministry of Education, Science and Sport. This doctoral study was partly co-financed by the European Union and by the European Social Fund respectively. The co-financing was carried out within the Human resources development operational programme for years 2007-2013, 1. Developmental priorities: Encouraging entrepreneurship and adaptation; preferential directives 1.3: Scholarship schemes. The least direct but perhaps the most valuable help came from my friends and family. I would like to thank them for their support, understanding and patience, and most importantly their encouragement.
Engineering Analysis with Boundary Elements, 2022
Simulation and control of macrosegregation, deformation and grain size under electromagnetic (EM)... more Simulation and control of macrosegregation, deformation and grain size under electromagnetic (EM) processing conditions is important in industrial solidification systems, since it influences the quality of the casts and consequently the whole downstream processing path. Respectively, a multiphysics and multiscale model is developed for solution of Lorentz force, temperature, velocity, concentration, deformation and grain structure of the casts. The mixture equations with lever rule, linearized phase diagram, and stationary thermoelastic solid phase are assumed, together with EM induction equation for the field imposed by the low frequency EM field or Ohm’s law and charge conservation equation for stationary EM field. Turbulent effects are incorporated through the solution of a low-Re turbulence model. The solidification system is treated by the mixture-continuum model, where the mushy zone is modeled as a Darcy porous media with Kozeny-Karman permeability relation and columnar solid...
Cmes-computer Modeling in Engineering & Sciences, 2013
The purpose of the present paper is to extend and explore the application of a novel meshless Loc... more The purpose of the present paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded subdomains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity with two insulated horizontal and two differentially heated vertical walls with magnetic field applied in the horizontal direction. Numerical predictions are calculated for different Grashof numbers, ranging from 104 to 106, and Hartman numbers, ranging from 0 to 100, at Prandtl numbers 0.71 and 0.14. The results of the method are compared to predictions, obtained by ...
Continuous casting (CC) of steel is a process that nowadays produces more than 95 % [1] of crude ... more Continuous casting (CC) of steel is a process that nowadays produces more than 95 % [1] of crude steel. To further advance this process, electromagnetic (EM) field, which affects the fluid flow as well as the temperature and segregation is added to the CC process. In general, there are two types of electromagnetic devices applicable to the CC process; one are the electromagnetic breakers (EMBR) which implement direct current, and the other are the electromagnetic stirrers (EMS) which implement the alternating current. Which of the process is used depends on what are the desired effects. Both of the processes are modelled by implementing the Lorentz force into the momentum equation and if necessary the Joule heating term into the energy equation. However, the way how these two terms are modelled depend on the type of the implemented device. In case of EMBRs the assumption of low Rem is made and consequently, the current density is calculated by solving the Poisson’s equation for elec...
Cmc-computers Materials & Continua, 2013
This paper explores the application of Local Radial Basis Function Collocation Method (LRBFCM) [Š... more This paper explores the application of Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] for solution of Newtonian incompressible 2D fluid flow for a lid driven cavity problem [Ghia, Ghia, and Shin (1982)] in primitive variables. The involved velocity and pressure fields are represented on overlapping five-noded sub-domains through collocation by using Radial Basis Functions (RBF). The required first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The momentum equation is solved through explicit time stepping. The method is alternatively structured with multiquadrics and inverse multiquadrics RBF’s. In addition, two different approaches are used for pressure velocity coupling (Fractional Step Method (FSM) [Chorin (1968)] and Artificial Compressibility Method (ACM) [Chorin (1967)] with Characteristic Based Split (CBS) [Zienkiewicz and Codina (1995); Zienkiewicz, Morgan, Sai, Codina and Vasquez (1995)]...
The molecules from fullerene family are rapidly becoming a part of our daily lives due to the wid... more The molecules from fullerene family are rapidly becoming a part of our daily lives due to the wide range of their unique properties and extensive field of their potential applications. High demand for these materials revealed a necessity to understand the process of fullerene growth in order to optimize their production. Since the fabrication technique has a large influence on the material proper-ties, several methods have been suggested. The focus of this seminar will be electric-arc discharge method, where fullerens are formed by vaporizing graphite electrodes in a low pressure gas atmosphere. Detailed understanding of growth mechanisms in the arc discharge reactor requires the development of a mathematical model that approximates the physical behaviour of nonequilibrium plasma coupled with nonlinear chemical systems. In this seminar several such models from various authors ([1], [2], [3]) are presented along with chemical kinetics model [Scott, 2004], that describes nucleation an...
The initial results obtained with the local-radial basis-function collocation method (LRBFCM) for... more The initial results obtained with the local-radial basis-function collocation method (LRBFCM) for a two-dimensional (2D), simplified model of continuous casting of steel with an externally applied magnetic field are presented. The multiphysics model is composed of turbulent-solidification equations (mass, momentum, energy, turbulent kinetic energy, turbulent dissipation rate) and Maxwell’s equations that are numerically solved for the non-uniform node arrangement. The numerical procedure is structured using the explicit time stepping and local collocation with multiquadric radial basis functions (MQ RBF) on the overlapping five-node subdomains. The pressure-velocity coupling follows the fractional-step method (FSM) and the convection is treated with adaptive upwinding. The novel LRBFCM has been already verified in several benchmark test cases, such as the natural convection in a cavity with a magnetic field, the lid-driven cavity, and the flow over the backward-facing step with a tr...
IOP Conference Series: Materials Science and Engineering, 2020
Engineering Analysis with Boundary Elements, 2020
This paper explores, for the first time, the application of the novel mesh-free local radial basi... more This paper explores, for the first time, the application of the novel mesh-free local radial basis function collocation method (LRBFCM) to the solution of a multi-physics problem in three dimensions. A related benchmark problem is solved by considering the natural convection of an incompressible Newtonian fluid in a differentially heated cubic cavity with and without the application of a magnetic field. The research is limited to typical magnetic fields used in the magnetohydrodynamic processing of liquid metals. For this purpose the assumption of small magnetic Reynolds numbers Re m ≪ 1 is made. Spatial discretization is performed by local non-uniform collocation with scaled multiquadrics radial basis functions (RBFs) with the shape parameter set to a constant value and the explicit Euler formula used to perform the time stepping. The involved temperature, velocity and pressure fields are represented on overlapping seven-nodded sub-domains. The pressure-velocity coupling is resolved by the fractional step method. The originality of the contribution represents LRBFCM solution of the classic threedimensional steady natural convection benchmark for Rayleigh numbers from 10 5 to 10 7 and Prandtl number 0.71, and its extension to Prandtl number 0.1, and Hartman numbers 0, 10, 50 and 100. The accuracy of the LRBFCM is found to be comparable with the published benchmark results obtained using established numerical methods.
MATEC Web of Conferences, 2018
The solidification of binary metallic alloy (Sn-10%Pb) is simulated in 2D with a diffuse approxim... more The solidification of binary metallic alloy (Sn-10%Pb) is simulated in 2D with a diffuse approximate meshless method. The macrosegregation with mesosegregates is described by a coupled set of volume-averaged partial differential equations. The incompressible Newtonian fluid is described by coupled mass and momentum equations and the mushy zone is treated as a Darcy porous media. The energy transport is described with enthalpy formulation and the species transfer is incorporated by considering the Lever rule approximation. The thermo-solutal Boussinesq hypothesis is applied in order to account for the double-diffusive effects in the melt. The mathematical model is solved by a diffusive approximate method on local subdomains with Euler time stepping. Pressure-velocity coupling is incorporated by applying the fractional step method. The instabilities due to the convective terms are smoothed out by applying the upwinding technique. The results are presented on a regular node arrangement...
Engineering Analysis with Boundary Elements, 2019
This paper demonstrates the development of meshless Local Radial Basis Function Collocation Metho... more This paper demonstrates the development of meshless Local Radial Basis Function Collocation Method (LRBFCM) for solution of three dimensional (3D) turbulent molten steel flow and solidification under the influence of electromagnetic stirring (EMS) and its application to continuous casting process of steel billets. A mixture continuum approach is used to formulate the coupled set of macroscopic equations for mass, momentum, energy, turbulent kinetic energy, and dissipation rate in Cartesian coordinates. The mushy zone is treated as a Darcy porous media. The explicit Chorin fractional step method is used to resolve the pressure-velocity coupling. The LRBFCM uses explicit time discretization and spatial discretization with shape-adaptive multiquadrics radial basis functions collocation on non-uniform seven-noded influence domains, and displacement-adaptive upwind scheme. The Lorentz force due to EMS is provided by a one-way coupling by Elmer software. The advantages of the meshless method are trivial adaptation of the nodal densities, simple upgrade to 3D from previous two-dimensional models, and high accuracy. A study on the influence of changing the EMS parameters on the calculated temperature and velocity fields is performed. The paper confirms the ability of LRBFCM meshless solution of a realistic 3D multiphysics industrial problem with complicated swirling flow pattern.
Materiali in tehnologije, 2015
The application of magnetohydrodynamics in the continuous casting of steel enables improved contr... more The application of magnetohydrodynamics in the continuous casting of steel enables improved control of the quality of the strand. The most common applications are electromagnetic braking (EMBR) and electromagnetic stirring (EMS). The former slows the flow by applying a static magnetic field and thus improves the steel flow pattern, reduces the velocity and the turbulence of the flow, increases the cleanliness of the material, improves the surface quality and reduces the number of inclusions, whereas the latter stirs the flow by applying an alternating magnetic field and thus improves the quality of the strand, reduces the surface and subsurface defects, enhances the solidification and reduces the number of breakouts. In this contribution EMBR in a continuous-casting process is considered. The local radial basis function collocation method (LRBFCM) is used for the solution of coupled mass, energy, turbulent fluid flow, species and magnetic field equations. The explicit Euler time-stepping scheme and the collocation with multiquadrics radial basis functions on the five-noded overlapping influence domains are used to obtain the solution of the partial differential equations. The Abe-Kondoh-Nagano low Reynolds turbulence model is used to describe the turbulent fluid flow, whereas the fractional step method is used to solve the pressurevelocity coupling. The method has been thoroughly tested in several test cases. In the present article the influence of the application of electromagnetic braking on the macro-segregation in the continuous-casting process for carbon steel is presented. Keywords: LRBFCM, continuous casting of steel, turbulent flow, magnetic field, macro-segregation Uporaba magnetohidrodinamike pri kontinuiranem ulivanju jekla omogo~a izbolj{ano kontrolo kakovosti`ile. Najpogostej{i aplikaciji sta elektromagnetno zaviranje (EMBR) in elektromagnetno me{anje (EMS). Prva zavira tok z uporabo stati~nega magnetnega polja in tako izbolj{a tokovni vzorec jekla, zmanj{a hitrost in turbulenco toka, pove~a~istost materiala, izbolj{a kvaliteto povr{ine in zmanj{a {tevilo vklju~kov, medtem ko druga me{a tok z uporabo izmeni~nega magnetnega polja in tako izbolj{a kvaliteto`ile, zmanj{a nepravilnosti na povr{ini in pod njo, pospe{i strjevanje in zmanj{a {tevilo prodorov. V tem prispevku je obravnavano EMBR pri kontinuiranem ulivanju jekla. Lokalna kolokacijska metoda z radialnimi baznimi funkcijami (LRBFCM) je uporabljena za re{evanje sklopljenih ena~b za maso, energijo, turbulenten tok teko~ine, koncentracijo sestavin in magnetno polje. Eksplicitna Euler-jeva~asovna shema in kolokacija z multikvadri~nimi radialnimi baznimi funkcijami na petto~kovnih prekrivajo~ih se poddomenah sta uporabljeni za re{itev parcialnih diferencialnih ena~b. Abe-Kondoh-Naganov turbuletni model za nizka Reynolds-ova {tevila je uporabljen za opis turbulentnega toka, medtem ko je metoda delnih korakov uporabljena za re{itev tla~no-hitrostne sklopitve. Metoda je bila izdatno preizku{ena na ve~preizkusnih primerih. V tem~lanku je predstavljen vpliv elektromagnetnega zaviranja na makroizcejanje pri kontinuiranem ulivanju oglji~nega jekla.
Engineering Analysis with Boundary Elements, 2014
The purpose of the present paper is to extend the use of a novel meshless Local Radial Basis Func... more The purpose of the present paper is to extend the use of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) for solving the two-dimensional, steady, laminar flow over a backward facing step under the influence of the Lorentz force. The incompressible Navier-Stokes equations are under the influence of predetermined static magnetic field numerically solved on a non-uniform node arrangement. In the numerical procedure, local collocation and Multiquadric Radial Basis Functions (MQ RBF) are used on five-nodded subdomains. The coupling between the pressure and the velocity is made by using Fractional Step Method (FSM). The considered problem is calculated for Reynolds numbers (Re) ranging from 300 to 800, Hartman numbers (Ha) ranging from 0 to 100, and for low magnetic Re m number. The numerical results demonstrate excellent agreement with previously published data, obtained with the classical numerical methods, such as Finite Volume Method (FVM) and Finite Element Method (FEM). Simplicity of the numerical implementation, accuracy and the absence of the polygonalisation are the main advantages of the LRBFCM.
IOP Conference Series: Materials Science and Engineering, 2012
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Papers by Katarina Mramor