Continuous Casting Problem Research Articles

Solving the steel continuous casting problem using a recurrent neural network model

Solving the steel continuous casting problem using a recurrent neural network model

Solving the steel continuous casting problem using a recurrent neural network model

Solving the steel continuous casting problem using a recurrent neural network model

Development of Three-Dimensional LES Based Meshless Model of Continuous Casting of Steel

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 character of vortices which RANS-type turbulence models are unable to tackle. The computational cost of LES models is considerably higher than in RANS. On the other hand, it results in a much lower computational cost than the direct numerical simulation (DNS). The paper demonstrates the ability of the method to solve realistic industrial 3D examples. Trivial adjustment of nodal densities, high accuracy, and low numerical diffusivity are the main advantages of this meshless method.

An enhanced cross-entropy algorithm for the green scheduling problem of steelmaking and continuous casting with uncertain processing time

Under the mainstream trend of global carbon emission reduction, this paper studies an important steelmaking-continuous casting scheduling problem (SCCSP) considering the practical technological requirements in uncertain production environment. This problem can be modeled as the green SCCSP with uncertain processing time (GSCCSP_UPTHP), whose criteria are to minimize the maximum completion time, the average waiting time, and the carbon emissions simultaneously. An enhanced cross-entropy algorithm (ECEA) is proposed for addressing it. In terms of ECEA’s coding and decoding, a two-segment coding strategy and an adaptive decoding strategy are devised according to the problem’s characteristics. In ECEA’s global search, ECEA adopts two probability models with their own self-adjustment mechanisms to collaboratively learn the valuable information from excellent individuals and quickly guide the search to the promising regions. Moreover, the novel competition and assimilation mechanisms are devised to avoid ECEA falling into local optima early. In ECEA’s local search, a problem-dependent local search based on the key points (PDLS_KP) is proposed to sequentially execute the small neighborhood search (SNS) and the large neighborhood search (LNS) starting from the promising region of each selected key point. Meanwhile, a speed-up scanning method is developed to accelerate the search process of the LNS. Extensive experiments based on both the simulation and the real-world instances from an SCC process are constructed to show the effectiveness of TSOA in solving the GSCCSP_UPTHP.

Evolution of Nonmetallic Inclusion during Steelmaking Process of Cold Heading Steel SWRCH35K

In order to analyze the evolution of the inclusions in the cold heading steel SWRCH35K during the steelmaking process, a systematic sampling of the steelmaking processes in a steel plant was carried out. Both SEM-EDS and the image processing software Image-Pro-Plus6.0 were employed to analyze the chemical composition, morphology, quantity and size of non-metal inclusions in the steel samples. The results show that from BOF tapping to continuous casting tundish, the composition of inclusions in SWRCH35K steel changes from Al2O3 → MgO·Al2O3 → CaO-MgO-Al2O3-CaS, and the typical morphology of the inclusions in the steel gradually changes from irregular blocks and clusters to spherical. The number of inclusions in the BOF argon blowing station is the largest, 213#/mm2, while the number of inclusions at the end of LF refining is the least, about 12#/mm2, and there are basically no inclusions above 5 μm. In addition, LF calcium treatment will adversely affect the size and quantity control of inclusions in steel. In order to effectively reduce the large-size calcium-containing spherical oxide inclusions in cold heading steel, it is necessary to find a technical method that can replace LF calcium treatment to solve the problem of molten steel continuous casting.

Application of the Swarm Intelligence Algorithm for Reconstructing the Cooling Conditions of Steel Ingot Continuous Casting

This paper presents a proposal to apply one of the swarm intelligence algorithms, the artificial bee colony (ABC) algorithm, to solve the inverse problem of steel ingot continuous casting. The discussed task consists of retrieving the cooling conditions of the process on the basis of temperature measurements and by taking into account the macrosegregation phenomenon. The examined process was modeled by using the mathematical model of solidification within the temperature interval. The solution method was based on the implicit scheme of the finite difference method supplemented by the procedure of correcting the field of temperature in the vicinity of liquidus and solidus curves, which was then used for solving the appropriate direct problem. The computational example, illustrating the stability and accuracy of the proposed method, is also presented in the paper.

Regularity for a quasilinear continuous casting problem

In this paper, we study the regularity of weak solutions to the continuous casting problem(♯)div(|∇u|p−2∇u−vβ(u))=0 for prescribed constant velocity v and enthalpy β(u) with jump discontinuity at u=0. We establish the following estimates: local log-Lipschitz p>2 for u (and BMO for ∇u) for two phase, Lipschitz p>1 for one phase and linear growth up-to boundary near the contact points. We also prove that the free boundary is continuous curve in the direction of v in two spatial dimensions. The proof is based on a delicate argument exploiting Sard's theorem for W2,2+η,η>0 functions and circumventing the lack of comparison principle for the solutions of (♯).

Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation

In this paper we are concerned with theregularity of weak solutions $u$ to theone phase continuous casting problem$$ div (A(x) \nabla u(X)) = div [\beta (u) v(X)], X\in \mathcal{C}_L$$in the cylindrical domain $\mathcal{C}_L=\Omega\times (0,L)$ where $X=(x,z), x\in \Omega\subset \mathbb{R}^{N-1}, z\in(0,L), L>0$ with given elliptic matrix $A:\Omega \to \mathbb{R}^{N^2}, A_{ij}(x)\in C^{1,\alpha_0}(\Omega), \alpha_0 > 0$,prescribed convection $v$, and the enthalpy function $\beta(u)$. We first establish the optimal regularity ofweak solutions $u\ge 0$ for one phase problem.Furthermore,we show that the free boundary $\partial$ {u > 0} is locallyLipschitz continuous graph provided that $v = e_N$, the direction of $x_N$ coordinate axisand$\partial_{z}u\geq 0$.The latter monotonicity assumption in $z$ variable can be easily obtainedfor a suitable boundary condition.

Optimal regularity for phase transition problems with convection

In this paper we consider a steady state phase transition problem with given convection v. We prove, among other things, that the weak solution is locally Lipschitz continuous provided that v=Dξ and ξ is a harmonic function. Moreover, for continuous casting problem, i.e. when v is constant vector, we show that Lipschitz free boundaries are C1 regular surfaces.

An effective 3-D inverse procedure to retrieve cooling conditions in an aluminium alloy continuous casting problem

The paper discusses a three-dimensional numerical solution of the inverse boundary problem for a continuous casting process of an aluminium alloy. Because verified information of heat flux distribution is crucial for a good mould design, effective cooling system and the whole caster in general, the main goal of the analysis presented within the paper is identifying of the heat fluxes along the external surface of the ingot. To model the solidification process, an enthalpy-porosity technique implemented in a commercial package was used. In this method, the phase change interface was determined based on the liquid fraction approach. In the inverse procedure, a sensitivity analysis was used to estimate the boundary condition retrieval. While the measured temperatures required to solve the problem are always burdened by measurement errors, a comparison of the measured and retrieved values showed a computational high accuracy. The average percentage error of the sensors was considerably lower than the maximum percentage error of the numerically simulated measurements. In addition, the computationally effective method was independent of the mesh size, the starting value of the assumed boundary condition and the maximum error of measurements used for calculations.

Integrated Scheduling System on Steel-Making and Continuous Casting with Application

The integrated scheduling problem of steel-making and continuous casting is discussed. To solve the problem we develop a scheduling system with the architecture of three tiers. Its main functions include: schedule making and adjusting, matching and optimization, abnormal logistics handling and production information management. A hybrid heuristic and optimization algorithm is developed for the solution. The scheduling system had been embedded into the whole MES of a big iron and steel group in China. This approach had been applied to a branch plant of stainless steel. The satisfactory results have been achieved.

Asynchronous domain decomposition methods for continuous casting problem

Two asynchronous domain decomposition methods (which appear to be a two-stage Schwarz alternating algorithms) to solve the finite difference schemes approximating dynamic continuous casting problem are theoretically and numerically studied. Fully implicit and semi-implicit (implicit for the diffusion operator while explicit for the nonlinear convective term) finite difference schemes are considered. Unique solvability of the finite difference schemes as well as a monotone dependence of the solution on the right-hand side (the so-called comparison theorem) are proved. Geometric rate of convergence for the iterative methods is investigated, the comparison theorem being the main tool of this study. Numerical results are included and analyzed.

A characteristic Galerkin method with adaptive error control for the continuous casting problem

The continuous casting problem is a convection-dominated nonlinearly degenerate diffusion problem. It is discretized implicitly in time via the method of characteristics, and in space via continuous piecewise linear finite elements. A posteriori error estimates are derived for the L 1 L 1 norm of temperature which exhibit a mild explicit dependence on velocity. The analysis is based on special properties of a linear dual problem in non-divergence form with vanishing diffusion and strong advection. Several simulations with realistic physical parameters illustrate the reliability of the estimators and the flexibility of the proposed adaptive method.

Vertical continuous casting of bars

The problem of vertical continuous casting of bars is considered in this paper. An asymptotic solution is constructed using the ratio of radius of the bar to the solidification length as the small ...

Dual reciprocity boundary element method for convective-diffusive solid-liquid phase change problems, Part 2. Numerical examples

A newly developed dual reciprocity boundary element method for solid-liquid phase change problems has been verified in this paper. Tests include numerical convergence studies for the transient Dirichlet jump problem with and without phase change, and the steady-state convective-diffusive problem with different material properties of the phases and phase change. Results are compared with the existing analytical solutions and with the results obtained by the finite volume and finite element methods. Excellent agreement has been obtained. The method turns out to be robust over the whole broad spectrum of conducted numerical tests. The axisymmeeryryc problem of direct chill continuous casting, where nonuniform meshes have been applied, serves as a ‘real’ problem example exhibiting nonlinear material properties, solidification over a temperature interval, and nonlinear boundary conditions.

THE BIDIMENSIONAL EVOLUTIONARY BOUSSINESQ-STEFAN PROBLEM WITH CONTINUOUS EXTRACTION

In this paper we consider an evolutionary continuous casting problem with convection ∂tχ+b∂yχ−Δk(u)+v→ċ∇u=0 coupled with Stokes equation in the liquid phase ∂tv→−vΔv→+∇p=f→(u).The mixed boundary condition is put on temprature. The existence of a weak solution is obtained by using methods of regularization, temperature dependent penalty form in the Stokes equation and compact arguments.

THE CONTINUOUS CASTING PROBLEM WITH NON-EQUILIBRIUM CONDITIONS

We establish the existence and uniqueness of classical solutions of the continuous casting problem with surface tension and kinetic conditions in a short time interval.

Regularity of the free boundary of a continuous casting problem

Regularity of the free boundary of a continuous casting problem

Finite-element simulation of solidification

The problem of predicting the solidification front and the temperature field for the case of the continuous-casting process is of great practical importance. Due to the release of latent heat during the change of phase, such a problem is non-linear and considerably more difficult to solve than the corresponding single-phase problem. The present work introduces a numerical algorithm which is used in the development of a non-linear transient thermal analysis finite-element program, based on the goal of simulating the foundry casting process, with the inherent phenomena of solidification and phase changes. The continuous-casting problem was investigated experimentally in 1953 by Brandt et al., who used thermocouples in the mould and mould cavity. Their experimentally measured isochronal solidification profiles for low-carbon steel cast into simple “L”-shaped sand moulds are matched in the present work by calculations from a finite-element program, with appropriate physical assumptions. The computations from the heat-transfer model agree with the experimental results with respect to the shape of the isochronal solidification profiles, the time of solidification, the thermal gradients and the temperature profiles.

Finite element simulation of heat flow in continuous casting

This article presents a non-linear transient thermal analysis finite element program which is developed based on the goal in simulating the casting process with the phenomena of solidification and changes of latent heat. The continuous casting problem was experimentally investigated in 1953 by Brandt, Bishop and Pellini 1, who used thermocouples in the mold and mold cavity. The experimentally measured isochronal solidification profiles for low carbon steel cast in simple ‘T’ shaped sand molds were matched by calculations from the finite element program, with appropriate physical assumptions. The computations from the heat transfer model agreed with the experimental results with respect to the shape of the isochronal solidification profiles, time of solidification, thermal gradients and temperature profiles.