Numerical Simulation of Dendritic Growth of Continuously Cast High Carbon Steel

Abstract

Considering the influence of the latent heat released during the solidification of high carbon liquid steel, a cellular automaton (CA) model coupled with the heat transfer was developed to investigate the growth of equiaxed dendrites which is controlled by the solute diffusion during the continuous casting process. Additionally, the growth of columnar dendrites and primary dendrite arm spacings were predicted and measured. The results show that the CA model is able to describe the growth behavior of equiaxed dendrites, especially at 5 K to 7 K melt undercoolings, and the approach adjusting the cooling medium temperature is reliable to keep the undercooling condition stable for equiaxed dendrites although its hysteresis is reinforced as the pre-set undercooling increases. With the increase of the melt undercooling, the growth of equiaxed dendrites becomes faster, and the thickness of dendritic arms increases slightly, however, the thickness of the diffusion layer in front of dendritic tips keeps constant. The growth of thin and tiny columnar dendrites will be confined due to the competition and absorbed by neighboring strong columnar dendrites, giving rise to the coarsening of columnar dendrites, which is observed both from the experimental observation and the numerical simulation. With the decrease of the cooling intensity, columnar dendrites get sparser, primary dendrite arm spacings increase, and secondary dendritic arms become undeveloped.

Validation and Simulation of Cellular Automaton Model for Dendritic Growth during the Solidification of Fe–C Binary Alloy with Fluid Flow

“…In our previous works, 40,41,48) preliminary validation of the 2D CA-FVM model for dendritic growth controlled by pure solute diffusion in a static melt has been performed with the comparison of the classical LGK analytical model, 49,50) and a good agreement has been obtained over a small range of low undercooling. It should be mentioned here that the capillary effects are neglected and thus the selection parameter, σ 0 * , which is vital for the unique determination of the steady-state dendrite shape, is set to be constant and equal to 1/4π 2 , according to the marginal stability criterion.…”

Development of a CA-FVM Model with Weakened Mesh Anisotropy and Application to Fe–C Alloy

“…Steady tip growth velocities agree with analytical results. Meanwhile, compared with our previous model based on Neumann rule [37,38,41], the accuracy is much improved. However, because the present approach is deterministic and depends on the mesh layout, the mesh size greatly influences the dendritic radius.…”

“…In order to determine the steady state, the average growth velocity V n is defined by the cell size and the time interval as the cell stays at interface state [37]. Figure 2 shows V n of dendritic tips at melt undercoolings of 5 K and 8 K. According to the dendritic growth theory [9,42], the solidification time and length needed by the equiaxed dendrite to reach the steady state should be on the orders of D l V −2 n and 5D l k −1 0 V −1 n , respectively.…”

“…The present work designs a 4 mm × 4 mm domain, meshes it into 2.5 µm × 2.5 µm cells, sets the initial temperature at T l , and cools the domain down with the average heat flux according to the mold cooling condition of SWRH82B steel billet [37], accordingly simulating the unidirectional solidification of Fe-0.82C alloy. Initial and boundary conditions for the solute diffusion are the same as those mentioned above.…”

Numerical Simulation of Latent Heat of Solidification for Low Pressure Casting of Aluminum Alloy Wheels

“…After completing the 3D modeling of the wheel hub, the VE module [17] that comes with ProCAST is used to complete the meshing of the model, and the local mesh refinement of some key parts, which guarantees the mesh quality of the model well While minimizing the number of unnecessary grids. Figure 4 shows the meshing of castings and molds.…”