The mathematical model used to simulate the process of CC in a mold with a narrow width is based on the Eulerian–Lagrangian approach. Here, the molten steel is considered the continuous phase, and Ar gas bubbles are treated as the discrete phase. Several reasonable assumptions, which are detailed in our previous paper , are included in the present model to simplify it.
The continuity and momentum equations of molten steel are given by Eqs. (2) and (3):
where ρ is the fluid density, ui and uj are the fluid velocity components (i, j = 1, 2, 3), xi and xj are the direction of components, t is the time, p is the pressure, μ is the effective fluid viscosity, gi is the compnents of gravity acceleration, F is the momentum source, respectively.
μt refers to the turbulent viscosity of fluid, which is computed from
where Cμ = 0.09, k is the instantaneous turbulent kinetic energy, and ε is the turbulent dissipation rate.
The standard k–ε model is used to calculate the turbulence process; k and ε are solved by using the following equations.
where Gk is the generation of turbulent kinetic energy due to the mean velocity gradient, C1 and C2 are constants, σk and σε are the turbulent Prandtl numbers for k and ε, respectively. In the model, σk = 1.0, σε = 1.3, C1 = 1.44, and C2 = 1.92.
In the present paper, the transient transport of Ar gas bubbles is calculated by using Eq. (8), which is Newton’s second law:
where mb is the mass of bubble, and ub is the velocity of bubble. The right-hand side of Eq. (8) includes forces acting on the Ar bubbles. The terms on the right-hand side of Eq. (8) are drag force (Fd), gravitational force (Fg), buoyancy force (Ff), and other forces (Fx). Fx is an additional source term, mainly including virtual mass force, the pressure gradient force, and the lift force. Relevant details of these forces are provided in our previous work .
The mathematical model was solved by using the commercial CFD software ANSYS 16.1, and simulations were conducted on a Windows 10 server equipped with two Intel cores of E5-2630.
Fig. 1 shows the geometry and grids of the computational domain and SEN. The region of the nozzle is partially meshed with refinement to improve the accuracy and stability of the calculations. The number of grids is approximately 570000 cells, and the time step is set to 0.001 s. The calculation domain and parameters are given in Table 1.
Parameters Values Parameters Values Slab length / mm 3000 Fluid density / (kg·m−3) 7020 Slab thickness / mm 230 Fluid dynamic viscosity / (N·s·m−2) 0.0056 Slab width / mm 1040, 1080 Gas density / (kg·m−3) 0.27 Casting speed / (m·min−1) 1.3, 1.5, 1.7 Gas bubble radius / (mm) 0.5 Gas flow rate / (L·min−1) 1, 4, 7 Gravity acceleration / (m·s−2) 9.81 Immersion depth of SEN / mm 140, 170, 190 SEN port angle / (°) 20
Table 1. Geometric and process parameters of simulation and experiment
An initial velocity of the molten steel is set at the top of the SEN on the basis of the casting speed. The boundary condition at the bottom of the mold is outflow. The surface of molten steel is considered to have free-slip conditions. Based on our previous work , the radius of bubbles is 0.5 mm. The walls of the SEN can reflect Ar gas bubbles. Ar gas bubbles can escape from the top surface and outlet of the mold, whereas the walls of the mold can capture these bubbles.
Effects of operating parameters on the flow field in slab continuous casting molds with narrow widths
11 November 2019
Revised: 15 January 2020
Accepted: 17 January 2020
Available online: 11 February 2020
Abstract: Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting (CC) molds with narrow widths for the production of automobile exposed panels. Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process. The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold. Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone. The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min−1 and casting speed of 1.7 m·min−1. Under the present experimental conditions, the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.