Three-Dimensional Simulation of a Tank Filling With a Viscous Fluid Using the VOF Method

This paper presents the results of 3D modeling of a Newtonian fluid flow with a free surface. The PLIC-VOF algorithm, which is developed to solve the problems of two-dimensional fluid flows with a free surface, is generalized to the case of three-dimensional flows. Efficiency of the developed algorithm and reliability of the obtained results are justified by comparing with available data in literature and by testing approximation convergence. Parametric calculations of a rectangular channel filling show that the free surface assumes a steady convex shape over time and then moves along the channel at a constant velocity. As a result of parametric studies, the dependences of geometric characteristics of the free surface shape on problem parameters have been plotted

Existence and static stability of a capillary free surface appearing in a dewetted Bridgman process. Part II.

This paper presents six theoretical results concerning the existence and static stability of a capillary free surface appearing in a dewetted Bridgman crystal growth technique. The results are obtained in an axis-symmetric 2D model for semiconductors for which 𝜃𝜃𝑐𝑐+𝛼𝛼𝑒𝑒>𝜋𝜋 (where:𝜃𝜃𝑐𝑐- wetting angle and 𝛼𝛼𝑒𝑒- growth angle). Numerical results are presented in case of GaSb semiconductor growth. The reported results can help, the practical crystal growers, in better understanding the dependence of the free surface shape and size on the pressure difference across the free surface and the right choice of crystal size, pressure difference and thermal conditions for the growth process.

Existence and static stability of a capillary free surface appearing in a dewetted Bridgman process. Part I.

This paper presents six theoretical results concerning the existence and static stability of a capillary free surface appearing in a dewetted Bridgman crystal growth technique. The results are obtained in an axis-symmetric 2D model for semiconductors for which 𝜃𝜃𝑐𝑐+𝛼𝛼𝑒𝑒<𝜋𝜋 (where:𝜃𝜃𝑐𝑐- wetting angle and 𝛼𝛼𝑒𝑒- growth angle). Numerical results are presented in case of InSb semiconductor growth. The reported results can help, the practical crystal growers, in better understanding the dependence of the free surface shape and size on the pressure difference across the free surface and prepare the appropriate seed size, and thermal conditions before seeding the growth process.

Dynamics of flow structures and surface shapes in the surface switching of rotating fluid

We present a study of the dynamics of the free-surface shape of a flow in a cylinder driven by a rotating bottom. Near the critical Reynolds number of the laminar–turbulent transition of the boundary layer, the free surface exhibits irregular surface switching between axisymmetric and non-axisymmetric shapes, and the switching often occurs with a significant change in the free-surface height. Although such surface deformation is known to be caused by the flow structures, the detailed flow structures of a rotating fluid with a large surface deformation have yet to be analysed. We thus investigate the velocity distribution and surface shape dynamics and show that the flow field during the loss of its axisymmetry is similar to that predicted by the theory of Tophøj et al. (Phys. Rev. Lett., vol. 110, 2013, 194502). The slight difference observed by quantitative comparison is caused by the fact that the basic flow of our study contains a weak rigid-body rotation in addition to the potential flow assumed by the theory. Furthermore, the observed non-axisymmetric surface shape, which has an elliptic horizontal cross-section, is generally associated with a quadrupole vortex structure. It is also found that the relative position between the free surface and the flow structure changes before and after the detachment of the free surface from the bottom. The change just after the detachment is drastic and occurs via a transient dipole-like vortex structure.

Numerical Analysis of Fluid Motion Inside Partially Filled Container Which is Moving in Unsteady Way

The paper describes the behavior of the liquid in a container that moves with a constant speed along a track consisting of three arcs. Such a complicated track shape generates complex form of inertia forces acting on the liquid and generates the sloshing effect. The behavior of the tank container vehicle is affected by the time-dependent inertia forces associated with the transient sloshing motion of the liquid in the non-inertial frame. These internal excitations, acting on a tank construction, can cause a loss of stability of the vehicle. For that reason, the authors analyze the dynamic loads acting on the walls of the tank truck container. The variation of the position of the liquid cargo gravity center, that depends on the filling level of the container, is also analyzed. The simulations were performed according to the varying fill level, which was 20%, 50% and 80% of a liquid in the whole tank volume. The simulations were carried out for a one-compartment container. Another aim of this study was the investigation of the influence of container division (tank with one, two and three compartments) on behavior of the liquid. These simulations considered only the half-filled container which was treated as a dangerous configuration prohibited by the law regulations for one-compartment tank. The results of simulation are presented in the form of visualization of temporary liquid free surface shape, variation of forces and moments, as well as frequency analysis. The results of simulation were analyzed, and some general conclusion were derived, providing the material for future investigation and modifications of the law regulations.

Effect Of Turbulence Modelling In Numerical Analysis Of Melting Process In An Induction Furnace

In this paper, the velocity field and turbulence effects that occur inside a crucible of a typical induction furnace were investigated. In the first part of this work, a free surface shape of the liquid metal was measured in a ceramic crucible. Then a numerical model of aluminium melting process was developed. It took into account coupling of electromagnetic and thermofluid fields that was performed using commercial codes. In the next step, the sensitivity analysis of turbulence modelling in the liquid domain was performed. The obtained numerical results were compared with the measurement data. The performed analysis can be treated as a preliminary approach for more complex mathematical modelling for the melting process optimisation in crucible induction furnaces of different types.