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                <title xml:lang="en">Direct numerical simulation of oxide inclusion turbulent deposition at liquid steel/slag interface</title>
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                <term xml:lang="en">free-slip interface</term>
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              <p>The present study focuses on the inclusion behaviour near the liquid metal/slag interface. Inclusion turbulent deposition is investigated using direct numerical simulation of the liquid flow combined with Lagrangian particle tracking under conditions of one-way coupling. The interface is modelled as a non-deformable free-slip surface. Unsheared turbulence is generated by random forcing in a finite-height region parallel to the free-slip surface. In between, the turbulence diffuses toward the free surface. The inclusions are randomly introduced in the forcing region and tracked through the diffusion region up to the interface. In the particle dynamic equation, the buoyancy force, the Stokes drag, the pressure drag and the added mass are considered. Close to the interface, the hydrodynamic interactions (i.e. lubrication effects) between the inclusion and the free surface may be taken into account as well as the Van der Waals forces. Numerical simulations were performed with surface Reynolds numbers ranging from 68 to 235. The inclusion diameter varied between 10-5 m and 5.10-5 m and the particle to liquid density ratio between 0.5 and 1. For these sets of parameters, it appears that the inertia effects are very weak. The deposition of buoyant inclusions is controlled by sedimentation whereas for nonbuoyant inclusions, direct interception is the only deposition mechanism. In the latter case, the deposition velocity strongly depends on. It is shown that the deposition velocity made dimensionless by the free surface characteristic velocity scales as the inclusion diameter made dimensionless by the Kolmogorov length scale calculated at the free surface. Lastly, the effect of lubrication is examined: it can significantly reduce the direct interception contribution of the deposition velocity.</p>
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