A major component of the work has been the study of a water model of a metallurgical bottom blown ladle. This part of the project is closely associated with the subgrid scale multiscale numerical method. The method has been conceptually developed, and followed by the writing of the associated computer code and its testing on the benchmark problem of ellipsoidal rising bubbles. The rising bubble case was treated both by direct numerical simulation, a brute force approach were sufficiently many cells are used to compute even thin (but not too thin, as such cases would be impossible on current computers) boundary layers and by the multiscale subgrid cell approach, with good agreement found between the two approaches, even when the boundary layers become much thinner than the grid cells. The method was then applied to the bottom-blown ladle case. Two different experiments were simulated, with numerical results for mass transfer that match the experiments. The successful application of the subgrid-scale mass-transfer method to such model experiments shows that they are ready to be exploited. The method is disseminated through a freely available dissertation, a paper in the second stage of reviewing, and talks at international conferences, as well as in several individual seminars given by the PI in China, India and the USA. It is also disseminated through the "sandbox" of the Basilisk platform, which provides the method as free code, and finally disseminated through collaboration on a benchmark with other research groups working on mass transfer.
Another major component of the work is the development of better multiphase flow methods, helping perform better atomization simulations. The EBIT method is a complete reworking of the Volume of Fluid (VOF) method existing at the beginning of the project. It allows to parallelize Front Tracking, a very rare feat. It has been disseminated through three scientific papers in top journals for the 2D version and in a submitted paper for the 3D version, at the latest ICTAM and ICMF and is through a sandbox as above. It is however not yet ready for exploitation. Another improvement in multiphase methods directly related to atomization is the ``manifold death'' method, disseminated through a scientific paper, and available through a sandbox. It has been exploited by several other research groups working on atomization, leading to publication in Journal of Fluid Mechanics, and exploited by the PI to study pulsed jet atomization, allowing to obtain better statistical convergence of the simulations upon grid refinement.
The third major component of the project is the study of dynamic contact lines. The PI has developed several new approaches, a Van der Waals diffuse interface method, a simplified model of localized bending in a VOF method mimicking the effect of interface bending and a Generalized Navier Boundary Condition method, all of which have been published and disseminated through papers, the sandbox, conferences and seminars.
A fourth major component is the study of nucleate boiling. We obtained a full simulation of the growth of a vapor bubble on a super-heated surface recovering a reference experiment in the literature. Spray cooling was also studied experimentally and numerically.
