Finite element solution of non‐linear heat conduction problems with special reference to phase change

Comini, G.; Guidice, S. Del; Lewis, R. W.; Zienkiewicz, O. C.

doi:10.1002/nme.1620080314

Cited by 490 publications

(142 citation statements)

References 11 publications

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“…both solid and liquid are treated as one continuous material, with different properties, but without any explicit boundary from the mesh point of view [18]. Though the interval of phase transformation T liq -T sol is relatively large according to temperature variations during a time step, the model integrates a general enthalpy method [10,26,31] based the variation of enthalpy per unit mass function where ρ is the density, c the specific heat and L f the latent heat of phase transformation (fusion-solidification) per unit mass. The main advantage of such a formulation is that the size of time step does not influence the result because the conservation of heat is always verified.…”

Section: Constitutive Equationsmentioning

confidence: 99%

Finite element study of the effect of some local defects on the risk of transverse cracking in continuous casting of steel slabs

Pascon

Habraken

2007

Computer Methods in Applied Mechanics and Engineering

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This paper introduces a numerical 2.5D model of continuous casting of steel slabs. This model is based on the finite element method and it has been applied to the study of some local defects in a continuous caster, such as partial blockage of nozzles (leading to a local reduction of secondary cooling rate), locking or misalignment of rolls. The purpose of the study was the evaluation of the effect of such defects on the risk of transverse cracking during bending and unbending operations. To do so, the simulation at macro-scale of the complete process has been first performed in standard conditions to get reference values and then each defect has been introduced. Defining two indexes (indicators) of the risk of transverse cracking, it has been possible to classify the defects in terms of risk increase, helping steel producers to focus on the most critical problems.Keywords: Continuous casting; Transverse crack; Nozzle blockage; Roll locking; Misalignment; Finite element PROCESS PRESENTATION AND CHALLENGESContinuous casting has progressively replaced ingot casting over the years 70s and 80s. Nowadays it is the most common way to produce cast steel thanks to its advantages: better quality, higher yield and lower costs (in manpower and energy). The process is schematically drawn in Fig. 1: it consists in pouring a mould with molten metal, i.e. steel in the present case, that starts solidifying in contact with the walls of the mould (primary cooling). When the process is launched, the bottom of the mould is a dummy that is moving down at a constant speed, so-called casting speed, allowing a constant supplying of the process. When the dummy reaches the exit of the mould, the solidified skin of the strand should be thick and resistant enough to avoid breaking. At this moment, the core of the strand is still liquid. To keep on cooling, the surface of the strand is then sprayed with water at each roll interval (secondary cooling), so that solidification front finally reaches the core of the strand, which can be cut and generally sent to next process (rolling). Once the process has been launched, the caster is continuously supplied in molten steel and the production does not stop until the geometry (cross section) of cast product must be changed. Obviously, this short presentation of continuous casting remains simplified and partial and it does not introduce all the complexity of such a process. For further reading, a lot of information is available in literature as well as on the internet.The quality of continuously cast products is still increasing, thanks to the development and the improvement of the technique. To do so, many studies have been conducted by different teams. Among others, Brimacombe and co-workers are recognized to have helped going ahead in understanding the keys of the process, see [4][5][6]2,3,9,30]. Meanwhile, the growth of computer's potential progressively enabled the advent of powerful numerical models. Thomas and co-workers at University of Illinois have also developed many applications i...

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Section: Constitutive Equationsmentioning

confidence: 99%

Finite element study of the effect of some local defects on the risk of transverse cracking in continuous casting of steel slabs

Pascon

Habraken

2007

Computer Methods in Applied Mechanics and Engineering

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“…In this case the finite element mesh does not change according to time [30]; • methods using mesh adaptation where the edges of the finite elements are systematically adjusted to the shape of the front [31]; • methods based on the diffused front where solidification at a constant temperature is replaced by the process within a narrow temperature range [32,33].…”

Section: Introductionmentioning

confidence: 99%

Effect Of Natural Convection On Directional Solidification Of Pure Metal

Skrzypczak

Węgrzyn-Skrzypczak

Winczek

2015

Archives of Metallurgy and Materials

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The paper is focused on the modeling of the directional solidification process of pure metal. During the process the solidification front is sharp in the shape of the surface separating liquid from solid in three dimensional space or a curve in 2D. The position and shape of the solid-liquid interface change according to time. The local velocity of the interface depends on the values of heat fluxes on the solid and liquid sides. Sharp interface solidification belongs to the phase transition problems which occur due to temperature changes, pressure, etc. Transition from one state to another is discontinuous from the mathematical point of view. Such process can be identified during water freezing, evaporation, melting and solidification of metals and alloys, etc.The influence of natural convection on the temperature distribution and the solid-liquid interface motion during solidification of pure copper is studied. The mathematical model of the process is based on the differential equations of heat transfer with convection, Navier-Stokes equation and the motion of the interface. This system of equations is supplemented by the appropriate initial and boundary conditions. In addition the continuity conditions at the solidification interface must be properly formulated. The solution involves the determination of the temporary temperature and velocity fields and the position of the interface. Typically, it is impossible to obtain the exact solution of such problem. The numerical model of solidification of pure copper in a closed cavity is presented, the influence of the natural convection on the phase change is investigated. Mathematical formulation of the problem is based on the Stefan problem with moving internal boundaries. The equations are spatially discretized with the use of fixed grid by means of the Finite Element Method (FEM). Front advancing technique uses the Level Set Method (LSM). Chorin's projection method is used to solve Navier-Stokes equation. Such approach makes possible to uncouple velocities and pressure. The Petrov-Galerkin formulation is employed to stabilize numerical solutions of the equations. The results of numerical simulations in the 2D region are discussed and compared to the results obtained from the simulation where movement of the liquid phase was neglected.Keywords: Pure Metal, Solidification, Sharp Interface, Natural Convection, Finite Element Method, Level Set Method Praca porusza problematykę modelowania kierunkowego krzepnięcia czystego metalu. Podczas tego procesu obserwuje się formowanie ostrego frontu krzepnięcia w postaci powierzchni separującej ciecz i ciało stałe w przypadku trójwymiarowym lub krzywej w przypadku płaskim. Położenie oraz kształt interfejsu krzepnięcia zmieniają się w czasie a wartości prędkości lokalnych zależą od różnicy intensywności strumieni ciepła po stronie ciała stałego i cieczy. Krzepnięcie z ostrym frontem należy do grupy procesów z przemianami fazowymi, które warunkowane są zmianami temperatury, ciśnienia, itp. Przejście fazowe z jednego stanu w drugi...

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“…The apparent capacity method is usually used for wide solid/liquid phase region alloy. 5,6) The narrower the solid/liquid phase region becomes, the smaller time steps have to be used in order to overcome its shortcoming. Moreover, for pure metals, it is more difficult to realize.…”

Section: Introductionmentioning

confidence: 99%