Adaptive Mesh Refinement Strategies for a Novel Modelof Immiscible Fluid Flow in Fractures

In this paper, we consider two Adaptive Mesh Refinement (AMR) methods to simulate flow through fractures using a novel multiphase model. The approach represents the fluid using a two-dimensional parallel-plate model that employs techniques adapted from lattice-Boltzmann simulations to track the fluid interface. Here, we discuss different mesh refinement strategies for the model and compare their performance to that of a uniform grid. Results from the simulations are demonstrated showing excellent agreement between the model and analytical solutions for both unrefined and refined meshes. We also present results from the study that illustrate the behavior of the AMR front-tracking method. The AMR model is able to accurately track the interfacial properties in cases where uniform fine meshes would significantly increase the simulation cost.The ability of the model to dynamically refine the domain is demonstrated by presenting the results from an example with evolving interfaces.

A numerical study of the solidification process of a retracting fluid filament

In this study, the retraction and solidification of a fluid filament are studied by a front-tracking method/finite difference scheme. The interface between two phases is handled by connected points (Lagrangian grid), which move on a fixed grid domain (Eulerian grid). The Navier-Stokes and energy equations are solved to simulate the problem. Initially, the fluid filament has a shape as half of a cylindrical capsule contact with a cold flat surface. We consider the effect of the aspect ratio (Ar) on the solidification of the fluid filament. It is found that an increase in the aspect ratio (Ar) in the range of 2 – 14 causes the retraction length to increase. The rate of the solidification of a fluid filament decreases when the Ar ratio increases. The solidification time, the solidification height and the tip angle of the fluid filament under the influence of the aspect ratio are also considered. After complete solidification, a small protrusion on the top of the solidified fluid filament is found.

CFD Investigations of Bath Dynamics in a Pilot-Scale TSL Furnace

The hydrodynamics of a Top Submerged Lance (TSL) slag bath are investigated here by means of Computational Fluid Dynamics (CFD) simulation. The object of the study is the pilot-scale furnace located at TU Bergakademie Freiberg, where air is injected beneath the slag bath with a top lance. The fluid dynamics system is evaluated at operating conditions, with experimentally measured slag physical properties and real flow rates. The numerical approach is based on the Volume Of Fluid (VOF) model, a front-tracking method that allows the interface to be geometrically reconstructed. Using a fine computational grid, the multiphase interactions are calculated with a high level of detail, revealing the mechanisms of bubble formation and bath dynamics. Two lance configurations are compared, with and without a swirler, and the effect on the hydrodynamics is discussed with regards to key features of the process, such as bubble dynamics, slag splashing, the interface area, rotational sloshing, and bath mixing. The model predicts bubble frequencies in the range of 2.5 to 3 Hz and captures rotational sloshing waves with half the frequencies of the bubble detachment. These results agree with real furnace data from the literature, proving the reliability of the computing model and adding value to the empirical understanding of the process, thanks to the direct observation of the resolved multiphase flow features. The comparative study indicates that the air swirler has an overall positive effect in addition to the proposed enhancement of lance cooling, with an increase in the bath mixing and a reduction in the splashing.

Dynamics of a contracting fluid compound filament with a variable density ratio

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method

We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in $u$ and the spatial dependency is piecewise constant with finitely many discontinuities. We use this stability result to prove a convergence rate for the front tracking method—a numerical method that is widely used in the field of conservation laws with discontinuous flux. To the best of our knowledge, both of these results are the first of their kind in the literature on conservation laws with discontinuous flux. We also present numerical experiments verifying the convergence rate results and comparing numerical solutions computed with the front tracking method to finite volume approximations.

Analysis of dynamic characteristics of bubble rise under a free surface

The rising process of a bubble occurs in several natural and industrial apparatuses. This process is computationally studied using the front tracking method for a moving interface whose surface properties are solved in terms of an immersed-boundary method. The results show that the free interface does not influence the bubble before the centroid velocity of the bubble reaches the terminal velocity, which reaches a stable value or fluctuates at it, with the distance h (between the centroid of the bubble and the free surface) reaching a certain value. When the Reynolds number increases, the time to reach terminal velocity will decrease, and the influence of the viscous factor on the terminal velocity is also weakened. The dramatic interaction between a bubble and free surface is beneficial to accelerate film draining out. It is also shown that the shape of the bubble gradually becomes an ellipse as the Weber number (We) decreases, and it is beneficial to reduce the resistance of the bubble. The free surface could accelerate the bubble breaking at high We values.