arXiv subjects

Jacob Maarek

Publications and source records attributed to Jacob Maarek.

4 recordsLinked to original sources

arXiv2025

A multiscale numerical approach to investigate interfacial mass transfer in three phase flow: application to metallurgical bottom-blown ladles

We use direct numerical simulation (DNS) to investigate mass transfer between liquid steel and slag during a metallurgical secondary refinement process through two reduced-scale water experiments, which reproduce the dynamics seen in an industrial bottom-blown ladle. A container is filled with water and topped by a thin layer of oil, representing the molten steel and slag, respectively. The system is agitated by a bubble plume that impinges on the oil layer and forms an open-eye. A tracer species, dissolved in the water, acts as a passive scalar that is progressively absorbed into the oil layer. Both the hydrodynamics and mass transfer in the system are studied and compared with experiments from the literature of different size and geometry. The numerical simulation of mass transfer is challenging due to the high P\'eclet number, leading to extremely thin species boundary layers at the interface. Resolving the boundary layer is prohibitive even with adaptive grid techniques. A subgrid-scale (SGS) boundary layer model corrects the scalar transport equation, allowing us to solve convection-dominated transport on relatively coarse grids. The hydrodynamics is investigated, and we analyze how the resultant flow field governs mass transport. The numerical results recover two flow regimes: a quasi-steady regime at low flow rates with small deformations of the oil-water interface and an atomizing regime at large flow rates. Interfacial species transport is determined to be dominated in an annulus surrounding the open eye caused by a shear layer at the oil-water interface. It is observed that we achieve grid-independent macroscopic quantities that match relatively well with those observed in experiments, allowing use of simulation techniques as a complementary tool going forward.

physics.flu-dyn↗

arXiv2025

Three-dimensional numerical study on hydrogen bubble growth at electrode

Three-dimensional direct numerical simulation of electrolysis is applied to investigate the growth and detachment of bubbles at electrodes. The moving gas-liquid interface is modeled employing the VOF-based method. To ensure the accuracy of the simulations, a mesh-independence study has been performed. The simulations include the growth phase of the bubbles, followed by their detachment from the electrode surface, and the results are validated with analytical models and experimental data. The bubble growth is diffusion-controlled, leading to the scaling \(R\propto t^{1/2}\), but our simulation overpredicts the growth exponent during the initial stage. We further demonstrate that the number of nucleation sites significantly affects gas transport, as quantified by the Sherwood number. The influences of contact angle and nucleation site on bubble detachment are also examined. The predicted detachment radius varies linearly with contact angle, consistent with Fritz's linear relation between the volume-equivalent radius and contact angle, confirming that the surface tension is the dominant attachment force. Finally, as the nucleation sites increase, the induced bubble coalescence accelerates the bubble detachment. Taken together, these findings give us valuable insights into improving gas bubble removal and enhancing overall electrolysis efficiency.

physics.flu-dyn↗

arXiv2023

A hybrid continuum surface force for the three-phase VOF method

We propose a hybrid continuum surface force (CSF) formulation to model the interface interaction within the three-phase volume of fluid (VOF) method. Instead of employing the height function globally, we compute the curvature based on a smooth fraction function near the region of the triple contact line. In addition, we apply the isotropic finite difference method to calculate derivatives, and the current scheme readily accommodates adaptive mesh refinement, greatly enhancing efficiency. We rigorously validate the hybrid CSF using two benchmark problems that have received limited attention in previous studies of the three-phase VOF method. Using the hybrid CSF method, we accurately predict the behavior of a liquid lens under specific surface tension ratios. Furthermore, the simulation results of the equilibrium morphology of two contacting droplets are consistent with the theoretical expectations.

physics.flu-dyn↗

arXiv2021

Manifold death: a Volume of Fluid implementation of controlled topological changes in thin sheets by the signature method

A well-known drawback of the Volume-Of-Fluid (VOF) method is that the breakup of thin liquid films or filaments is mainly caused by numerical aspects rather than by physical ones. The rupture of thin films occurs when their thickness reaches the order of the grid size and by refining the grid the breakup events are delayed. When thin filaments rupture, many droplets are generated due to the mass conserving properties of VOF. Thus, the numerical character of the breakup does not allow obtaining the desired convergence of the droplet size distribution under grid refinement. In this work, we present a novel algorithm to detect and perforate thin structures. First, thin films or ligaments are identified by taking quadratic moments of an indicator obtained from the volume fraction. A multiscale approach allows us to choose the critical film thickness independently of the mesh resolution. Then, the breakup is induced by making holes in the films before their thickness reaches the grid size. We show that the method improves the convergence upon grid refinement of the droplets size distribution and of enstrophy.

physics.flu-dyn↗