Water-model experiments of lance-jet impinging on a liquid free surface were carried out. A cavity was formed on the free surface by the impinging jet and unsteady behavior of the cavity was observed by continuous shooting. Cavity depth and diameter were measured from the photographs. The time average of cavity depth is consistent with the semi-theoretical relation proposed by Banks & Chandrasekhara, and the time average of cavity diameter is consistent with the estimated formula by Tanaka & Okane. The standard deviation of the cavity depth is roughly 10% of the time average of the cavity depth, while the standard deviation of the cavity diameter is roughly 15% of the time average of the cavity diameter.
In this paper we propose a “two-step simulation method” that can solve the dynamics of a sonic or supersonic jet flow and a liquid surface’s behavior simultaneously in a reasonable computing time. With this method, first, we calculate the sonic or supersonic jet flow from a nozzle, as a steady flow and without the water surface. After that, we calculate the liquid surface’s behavior as a two-phase flow, by using the results of the jet flow steady state calculation as boundary conditions. In this method, we can solve a complex flow problem which has multiple flows of different time scales. The simulation results show a good agreement with experimental results.
Numerical simulation of lance-jet impinging on a liquid free surface was carried out and validated against the experimental data of Ueno et al. [Tetsu-to-Hagané, 101 (2015), 74]. Computational domain was separated to lance domain and water-bath domain. Lance domain was solved as single phase of compressible gas and the result was used to inlet boundary condition of water-bath domain by volume of fluid method (VOF) solver. Large eddy simulation (LES) was used and both solver are a part of OpenFOAM, open source CFD toolkit. The time average of depth and diameter of cavity was almost consistent with the experiment. The standard deviation was 10-20% of the time average and slightly larger than that of the experiment. Simulation showed that sloshing of water surface might enhance the spitting phenomena.
The expansion and shape change behaviors of a single rising bubble and continuously rising bubbles in a reduced pressure vessel were observed. The main results obtained are as follows: 1) The aspect ratio, w/h, of a single rising bubble under reduced pressure is almost the same as that under atmospheric pressure. However, the width of the rising bubble expanded to 1.4 times, which is larger than the calculated expansion ratio. This may be explained by the change of the bubble shape while rising. 2) The observed single bubble shapes were ellipsoidal, spherical cap, and breakup of spherical cap. The upward velocity of the bubble increases with the initial volume of the bubble. The upward velocity also increases as the bubble rises.
Numerical analyses have been carried out for a single rising bubble flow in a viscous fluid. It is assumed that both liquid and gas phases are the Newtonian fluid and viscous dissipation is neglected. The dimensionless governing equations for axisymmetric and three-dimensional coordinate systems have been successfully solved using the fractional step method combining with the level set method. The present numerical results exhibit fairly good agreement with experimental results in terms of the bubble shape and rising velocity.
In order to give appropriate assessment of designed systems for secondary refining processes, the predictive methods with computational fluid dynamics are strongly desired. In the present study, a numerical method, called ‘CIP-LSM’ (CIP based Level Set & MARS), was developed to simulate incompressible and compressible two-phase flows including surface tension and gravity effect. With the developed code, the dynamic behavior of bubbles rising in a liquid pool under reduced-pressure condition were tried to be simulated. As to the bubble shape, rising velocity and volume expansion, good agreement was obtained between the computed results and corresponding experiments.
Numerical simulation of bubble rising in reduced pressure vessel was carried out by volume of fluid method (VOF) solver of OpenFOAM, open source CFD toolkit. The result was validated against the experimental data of Kumagai et al. [Tetsu-to-Hagané, 101(2015), 93]. Behaviors of continuous rising bubble at 101.3 kPa, 18.2 kPa, 4.5 kPa were almost consistent with the experiment. The shape of bubble near injection nozzle at 101.3 kPa was more ellipsoidal than that of experiment and the mesh refining decreased the difference. Single bubble rising behavior was also studied. Rising rate and outside appearance were almost consistent, but slight continuous dispersion of gas phase from tail end of bubble was observed in only simulation and it was considered the issue of gas-liquid interface modeling. The cross section of bubble was spherical cap and consistent with the diagram of Grace [Trans. Inst. Chem. Eng., 51(1973), 116]
Experiment and numerical simulation of RH circulation flow was carried out on water model. Helium gas was injected into water in up-leg and flow rate was estimated at the bottom of down-leg. Volume of fluid (VOF) simulation was also performed by compressibleInterFoam solver of OpenFOAM, open source CFD toolbox. Three pairs of diameter of up/down-leg, 100 mm/100 mm, 140 mm/70 mm and 170 mm/30 mm were estimated and the circulation flow rate was compared to Ono et al.’s estimated formula. The flow rate in 100 mm/100 mm and 140 mm/70 mm were almost consistent with that of Ono et al.’s formula, but it was half in 170 mm/30 mm. Simulated flow rate of all pairs were almost consistent with measurement. The visualization of experiment and simulation showed that down flow through up-leg occurred in case of 170 mm/30 mm, and it was thought to cause lower flow rate through down-leg than Ono et al.’s relation. It was important to use sufficiently small mesh for up-leg to get flow rate correctly becase of the necessity of resoluting the shape of bubble. Finally the simulation with scaled up mesh and molten steel properties was carried out. The volume of injected gas became larger according to rising in the up-leg because of hydrostatic pressure distribution and the behavior of gas-liquid interface in vessel was simulated qualitatively.
A coagulation phenomenon is one of important inclusion behaviors in molten steel. It is widely recognized that alumina inclusions aggregate each other, which result in harmful defects in final products. In addition, alumina inclusions often collide with different type inclusions such as slag droplets generated from the slag-metal interface or other oxide particles formed by the complex deoxidation. These types of coagulation, “hetero-coagulation”, are closely related to the means for removal and control of inclusions. Therefore, it is valuable to establish a kinetic model of hetero-coagulation, which is not well developed until now. In the present study, the hetero-coagulation model based on the Smoluchowski’s population balance equation has been developed. Particularly, the present work has focused on a turbulent hetero-coagulation behavior considering the practical steelmaking processes. A new method, called Particle-Size-Grouping for Hetero-coagulation (PSGH) method, has been established, which enables a considerable reduction of a calculation load for the hetero-coagulation with complete conservation in total particle volume. This method has been verified by the comparison with the exact solution of the population balance equation for hetero-coagulation. The change in particle number density with time calculated by PSGH method agreed with that of the exact solution.
A cold model experiment on the hetero-coagulation of inclusion particles in liquid steel has been performed to verify the hetero-coagulation model developed in the previous study. In this study, a cold model experiment of coagulation in electrolyte solution has been conducted in an agitated vessel under turbulent flow condition. Binary suspension of polymethyl methacrylate having different sizes was used in the experiment. Thus, this experiment means a pseudo hetero-coagulation phenomenon. The experimental results have been compared to the calculation ones. As a result, the model has almost agreed with experimental values on a change in particle number density with time. In addition, a generation behavior and a structure of aggregates have been discussed based on the calculation results.
The removal of non-metallic inclusions in the metallurgical process greatly affects the properties of the final products. The structure of inclusion clusters plays a key role in inclusion behaviors of their removal process, such as coagulation, flotation and bubble adhesion. However, it is rare to find reports quantitatively investigating the morphology of inclusion clusters in metal system. On the other hand, to quantitatively estimate the inclusion clusters in metal, it is required to distinguish clusters on two-dimensional (2D) cross-sectional images of the as-polished samples. In this study, TiB2 particle clusters were prepared in a mechanically agitated crucible containing molten Al at 1073 K. The samples of Al-TiB2 were measured by X-ray micro-computed tomography (micro-CT) to obtain the three-dimensional (3D) information of TiB2 particles and clusters in solid Al. The images of 3D particle clusters in solid Al were extracted and reconstructed by self-developed programs. A series of parameters were defined to describe the 3D characteristics of clusters and their 2D cross-sections. The effects of agitation time and speed on the cluster structure were investigated. A program was developed to distinguish clusters in 2D cross-sections through the use of the 3D cluster information (DC-2D-3D) obtained from X-ray micro-CT.
Particle coagulation plays a key role in steel refining process to remove inclusions. Many research works focus on the behaviors of particle coagulation. To reveal its mechanism water model experiments have been performed by some researchers including the author’s group. In this paper, experiments of particle coagulation were carried out with molten Al including SiC particles in a mechanically agitated crucible with two baffles. Particle coagulation and formation of clusters were observed on the microscopy images of as-polished samples. Three-dimensional (3D) analysis of the clusters in solidified Al was implemented by X-ray micro CT available at SPring-8. The methods to distinguish clusters on two-dimensional (2D) cross-sectional images were discussed, which were established in the previous works by the present authors’ group. The characteristics of the 3D SiC clusters and their 2D cross-sections were analyzed. The statistical ranges of the parameters for 2D clusters were used as criteria to distinguish the clusters on 2D microscopy images from the as-polished samples. The kinetics of SiC particle coagulation was studied by the measured cluster number density and size using our computer program to distinguish cluster in 2D cross-sectional images according to 3D information (DC-2D-3D). The calculated and experimental results of the SiC particle coagulation in molten Al agree well with each other.