Applying of Real-time Heat Transfer and Solidification Model on the Dynamic Control System of Billet Continuous Casting

Abstract

In this paper, a real-time mathematical heat transfer model for billet continuous casting of low carbon steel has been presented and solved by finite volume method. This model can be used to simulate the casting conditions which vary frequently. As taking the variation of superheat of liquid steel into consideration in the water flow rate distribution, the fluctuation of billet surface temperature has been decreased. Meanwhile the fluctuation of measured temperature has been largely reduced when it is measured with thermal imager. The mathematical model has been validated by measuring shell thickness and surface temperature in industrial caster. The on-line model can monitor surface temperature and shell thickness along the caster machine in the casting process, and it has been applied on the dynamic control system to adjust the operation parameters. The billet defect has been decreased greatly and the quality of billet has been obviously improved.KEY WORDS: real-time model; continuous casting; heat transfer; solidification; secondary cooling; dynamic control.......... (1) where T is the billet temperature, t is the time, x, y are the rectangular coordinates, k is the thermal conductivity of steel, c is the specific heat capacity of steel, r is the density of steel, and q is the latent heat source.Owing to the symmetry of heat transfer in square sections, one quarter of billet cross-section is selected as calculation area. The grid division and boundary conditions for cross-section of the billet are presented in Fig. 1. The P is the control volume, and w, e, n, s are the correspondence interfaces.In the time interval (t, tϩDt), Eq. (2) is obtained by finite volume method and the discrete equation group of complete implied format is formulated. 8,9) ... Thermophysical Properties of SteelThe latent heat is generated during phase change between liquidus and solidus temperatures of steel and is ex- where L is the latent heat of fusion, r is the density of steel, f s is the solid fraction in the mushy zone and it can be expressed in accordance with Eq. (4) Equations (4) and (1) giveThe f s 3) of low carbon steel can be expressed by the following equation:... (6) where T L is the liquidus temperature of steel, T S is the solidus temperature of steel.The convective heat transfer in the liquid pool and mushy zone is quite difficult to be calculated by using differential equations. The effective thermal conductivity is given by the following linear relationship 5) :where k eff is the effective thermal conductivity, k is the thermal conductivity of solid steel, A is a constant, and f s is the solid fraction in the mushy zone.The specific heat capacity and density are expressed by the following equations: where sub-indices S and L, respectively, indicates solid and liquid state. The Boundary Conditions (1) Initial ConditionThe boundary condition to the steady state casting has been assumed to be the same as the pouring or casting temperature (T 0 ) of the steel. (10) where T 0 is the steel casting temperature, which is ...

Modeling Solidification Phenomena in the Continuous Casting of Carbon Steels

“…The proposed results could help in the development of more sophisticated 2D finite element models. Once offline computer models are proven correct they can be applied online in real-time applications and minimize internal defects (Ma et al, 2008). Consequently, very advanced types of continuous casting machines have appeared in the international market as a result of these investigations.…”

Real-time Heat Transfer Model Based on Variable Non-uniform Grid for Dynamic Control of Continuous Casting Billets

“…In the calculation before calibration, the parameters are derived from literatures. 16,18) The parameters are not reliable when transfer them from one caster to another, for the spray conditions are quite different, so calibration is a must before online application. The casting steel grade is 65# and the casting speed is 1.75 m/min.…”

“…Numerical solution can be obtained by either finite element method 15) or finite volume method. 16) In FEM, the partial differential equation is transformed to algebraic equations in matrix form and that makes it more difficult to solve the problem in time due to the time consumption of huge memory allocating and large calculation amount. Relatively, according to the calculations, FVM is 10-20 times faster than FEM, and the deference between the calculations of them is quite small, within ±4°C, as shown in Fig.…”

Note: Vignetting calibration and temperature correction for casting billets

“…Meanwhile, both theoretical analysis and experimental results have proved the temperature distribution along the line that is perpendicular to the casting direction present high in the middle and low at two poles, just like a parabolic distribution. 12 Based on these detected uncontaminated temperature points and in combination with the distribution character of surface temperature field of billets, the reconstruction approach can reconstruct temperature contaminated by SIOS, which can be illustrated with Fig. 2, and in math speaking, for any measured temperature distribution T(x) along the line which is perpendicular to the casting direction, its corresponding temperature distribution T R (x) along the same direction after reconstruction could be obtained as following:…”