Transient Fluid Flow Phenomena during Continuous Casting: Part II—Cast Speed Change, Temperature Fluctuation, and Steel Grade Mixing

Abstract

where H is enthalpy or heat content in J/kg, k is thermal conductivity in W/m · K, and T is the temperature in K.Particles were modeled using both Eulerian and Lagrangian approaches. The Eularian approach considers them as continuous phase, whereas the Lagrangian approach treats them as a discrete phase.16) Due to the low volume fraction of particles, the Lagrangian approach is always used to calculate the trajectory of particles by considering the force balance acting on them 17) ......... (2) where u Pi is particle velocity at direction i in m/s, t is time in seconds, C D is a dimensionless drag coefficient, Re P is a particle Reynolds number, d P is particle diameter in m, r P is inclusion density in kg/cm 3 . The first term here is the drag force per unit of particle mass, the second term is gravitational force, the third term is the virtual mass force accelerating the fluid surrounding the particle, 18) and the fourth term is the force stemming from the pressure gradient in the fluid.To incorporate the stochastic effect of turbulent fluctuations on particle motion, the random walk model 19) was used. In this model, particle velocity fluctuations are based on a Gaussian-distributed random number chosen according to the kinetic energy of the local turbulence. The random number is changed, to produce a new instantaneous velocity fluctuation at a frequency equal to the characteristic lifetime of the eddy. (4) where ū is the mean fluid phase velocity in m/s, uЈ is random velocity fluctuation in m/s; x is a random number and k is the local level of turbulent kinetic energy in m 2 /s 2 . The application of Lagrangian approach in discrete phase model requires the particle flow must be dilute (volume fraction Ͻ12 %). Generally, inclusions in molten steel only take a very small volume fraction. If the total oxygen in the molten steel is 30 ppm, and if it is assumed that all of the inclusions are with a density of 3 500 kg/m 3 , then the volume fraction of inclusions in the molten steel is approximately 0.013 %. In our current study, assuming there are 10 000 particles with diameter of 50 mm. where p(x, y) is the pressure at the top surface at location (x, y), p mean is the mean value of the pressure across the entire top surface, r l is the density of the molten steel, r top is the density of the top slag, and g is the gravitational acceleration rate.The dimensions, parameters, and boundary conditions of the slab mold were listed in Table 1. A half mold was simulated. During the iteration, convergence was assumed if all the normalized unscaled residuals were smaller than 10 Ϫ6 . More than 10 000 inclusions with the diameter of 15 mm and 50 mm were injected into the slab mold through the inlet respectively. As boundary conditions for the particle motion, particles escaped from the top surface and the open bottom, and were reflected at the symmetry plane. For the entrapment of the inclusions on the wide or narrow faces, it is very complex; it has received well-deserved attention in recent work. 23,24) There are two cr...

Investigation on Fluid Flow inside a Continuous Slab Casting Mold Using Particle Image Velocimetry

“…In ideal circumstances, fluid flow pattern inside the mold is symmetrical along the central plane. However, in the actual production process, the fluid flow and the surface velocity become asymmetric due to turbulence, slide‐gate or stopper‐rod misalignment, nozzle clogging, and cast speed change . Asymmetric flow causes transient fluctuations, leading to product defects .…”

Modeling on Fluid Flow and Inclusion Motion in Centrifugal Continuous Casting Strands

“…Therefore, in order to understand the steel CCC process of round billets, mathematical modeling of the fluid flow phenomena is a feasible choice. Many turbulent models and multiphase models have been used for the fluid flow in gas-stirred steel refining processes [10][11][12] and steel continuous casting processes [13][14][15][16][17][18][19][20][21][22][23] , as summarized in Table I. However, so far very few investigations on CCC process were reported.…”

“…2008 [20] than well-shaped bottom SEN. [21,22] Ismael VOF Standard k-ε -Effect of deviation of the nozzle towards the inner mold radius on the symmetrical flow pattern and better meniscus control.…”

Steel Thermo‐Fluid‐Dynamics at Tundish Drainage and Quality Features

“…To describe transient flow phenomena, modeling techniques, both physical and numerical, are broadly used, also involving the description of dispersed inclusions path in the steel to estimate their surface floatation tendency 12–22. Water modeling has the advantage of representing in an impressive and immediate way the main flow features, by means of tracers.…”