In-Situ X-Ray Fluoroscopic Observation for Motion of Bubbles in Liquid Fe-C and Fe-C-S for Correction of Drag Coefficient Used in Numerical Simulation

Abstract

Rising of Ar bubble in C-saturated liquid iron was investigated in-situ by employing a high power X-Ray fluoroscope (maximum power of 450 kV and 4.5 mA) coupled with a high speed camera. This analysis enabled to track the actual motion of rising bubble in the liquid iron. After post-processing of X-Ray images, size, shape, velocity, and trajectory of the bubble were obtained. From the initial study on liquid Fe-C, the bubbles were found to be not spherical, but ellipsoidal. Their average size could be estimated about 1.1×10-2 m. The bubbles wobbled during rising and arrived at their terminal velocities within 0.1 sec. The obtained terminal velocities revealed that the governing forces acting on the motion of ellipsoidal bubble were inertia and surface force. This was quite different from that of spherical bubble which was widely used in the assumption for the numerical analysis. As a result, widely applied equation for the drag coefficient (CD = 24(1+0.15Re^0.687 )/Re) is seen to be applicable only for low Re regime, and this was also confirmed by the drag coefficient derived from the present experimental observation. Therefore, it is suggested to use the following equation for the drag coefficient CD = max [24(1+0.15Re^0.687 )/Re, 8Eo / 3(Eo + 4)]. The next study was done for liquid Fe-C and liquid Fe-C-S with the relaxed experimental conditions of widen gas flow rate and broaden crucible cross-section. The observed bubbles were also ellipsoidal and their size could be estimated about at least 1.2×10-2 m in both liquids. In particular, sulfur acted as a surfactant in liquid Fe-C causing the Marangoni stress on the bubble surface, and it significantly contributed the trajectory and shape of bubble. Consequently, the bubble in liquid Fe-C-S rose in more straightforward and had a distorted shape compared to liquid Fe-C. This affected the bubble dynamics and the retardation of terminal velocity by sulfur was observed. Therefore, it is suggested to use the following equation for the drag coefficient CD=max [24(1+0.15Re^0.687 )/Re, min (〖〖((sin〗^(-1) √(1-(E_M )^2 )-E_M √(1-(E_M )^2 ))/(1-(E_M )^2))〗^(-2) 2Eo/(〖E_M〗^(3/2) (1-E^2 )Eo+16〖E_M〗^(4/3)), 8/3)], where the mean bubble aspect ratio EM=1/(1+0.163Eo^0.757). Numerical simulation for the Ar bubble behavior in the three dimensional (3D) continuous casting mold was conducted in order to evaluate the effect of the drag coefficient for the behavior of spherical and ellipsoidal bubbles. The numerical results showed that the increased CD affected the entire fluid pattern in the mold. Therefore, the CD model should be carefully selected for the precise numerical simulation result.