Numerical simulations of primary break-up in two-phase flows

Liquid-Gas interactions and break-up processes are found in many technological and environmental applications, from Internal Combustion and Gas Turbine engines to food processing and manufacturing. Their complete characterisation at realistic Weber and Reynolds numbers is not possible, due to the vast range of scales integrated and the requirement of a ’minimum’ computational mesh size to capture these scales. To this day, a number of questions remain unanswered, with relative research still ongoing. It is crucial to understand such phenomena so that any technological applications can be optimised and the environmental impact can be reduced. Currently, there is a high need to develop appropriate numerical modelling tools that provide both mass conservation and accurate interface topological properties. Two common interface modelling approaches are the Volume of Fluid and the Level Set, typically coupled into CLSVOF methods to ensure improved surface representation and good mass properties. In this work, a novel in-house Mass Conservative Level Set (CMLS) method is developed and validated extensively. The CMLS novelty is in the Level Set coupling with the Volume of Fluid, being processed only when necessary, providing a faster and more robust approach. Doing so, some numerically imposed limitations due to the ’physics’ and ’stability’, are overcome. The novel CMLS is employed for primary break-up investigations, in a single liquid droplet and jets. Single droplet break-up remains a benchmark test case, as it provides good foundations for liquid jet break-up and spray atomisation modelling. In such processes, the main effective parameters considered are the Weber and Reynolds numbers, along with the Ohneshorge (droplets) and Dynamic Pressure ratio (jets). Contrary to most studies, this work employs the surface density evolution using the Σ − Y model. The droplet break-up cases, show a strong correlation between the break-up initiation time and the Ohneshorge number, whilst as the Weber increases so does the droplet complete break-up time. This is of particular interest as at higher Weber numbers, surface density effects be- come negligible and thus by definition the complete break-up time should in fact decrease. However, similar behaviours were noted in previous studies. The droplets surface density evolution shows a ’quasi-independent’ relationship with the gas Weber. In the jets, a strong correlation between the surface density and ligament formation exists. However, the surface density is ’quasi-independent’ of the liquid Reynolds and the gas Weber. The gas boundary layer presence in jets, shows to both reduce and delay any liquid/gas inter- face perturbations and the potential break-up. To summarise, the present investigations are generally in good agreement with previous studies, with minimal contradictions in cases. The novel CMLS capabilities show promising results both in the two- and three- dimensional space. This work provides good foundations for a slightly alternative research approach in two-phase flows modelling.Open Acces

An ALE method for simuations of elastic surfaces in flow

Die Dynamik von elastischen Membranen, Kapseln und Schalen hat sich zu einem aktiven Forschungsgebiet in der simulationsgestützten Physik und Biologie entwickelt. Die dünne Oberfläche dieser elastischen Materialien ermöglicht es, sie effizient als Hyperfläche zu approximieren. Solche Oberflächen reagieren auf Dehnungen in Oberflächenrichtung und Verformungen in Normalenrichtung mit einer elastischen Kraft. Zusätzlich können Oberflächenspannungskräfte auftreten. In dieser Arbeit präsentieren wir eine neuartige Arbitrary Lagrangian-Eulerian (ALE) Methode um solche in (Navier-Stokes) Fluiden eingebetteten elastischen Schalen zu simulieren. Dadurch, dass das Gitter an die elastische Oberfläche angepasst ist, kombiniert die vorgeschlagene Methode hohe Genauigkeit mit Effizienz in der Berechnung der Lösungen. Folglich kann man die Simulationen mit einer verhältnismäßig geringen Gitterauflösung durchführen. Der Fokus dieser Arbeit liegt bei achsensymmetrischen Formen und Strömungen, wie sie bei vielen biophysikalischen Anwendungen zu finden sind. Neben einer allgemeinen dreidimensionalen Beschreibung formulieren wir achsensymmetrische Kräfte auf der Oberfläche, für welche wir eine Diskretisierung mit der Finite Differenzen Methode vorschlagen, welche an eine Finite-Elemente Methode für die umgebenden Fluide gekoppelt ist. Weiterhin entwickeln wir eine Strategie zur impliziten Kopplung der Kräfte, um Zeitschrittrestriktionen zu reduzieren. In verschiedenen numerischen Tests werden wir zeigen, dass akkurate Ergebnisse schon in einer Größenordnung von Minuten auf einer Single-Core CPU erreicht werden können. Die Methode wurde in drei aktuellen Anwendungen verwendet, wobei mindestens zwei davon nach unserer Kenntnis im Moment mit keiner anderen numerischen Methode simuliert werden können: Zunächst präsentieren wir Simulationen von biologischen Zellen, die im Zuge eines RT-DC (Real-Time Deformability Cytometry) Experiments durch einen schmalen mikrofluidischen Kanal advektiert und dabei verformt werden. Danach zeigen wir die Ergebnisse erster Simulationen der uniaxialen Kompression biologischer Zellen zwischen zwei parallelen Platten im Zuge eines AFM Experiments. Schließlich präsentieren wir Resultate erster Simulationen von neuartigen mikroschwimmenden Schalen, welche lediglich durch äußere Einflüsse (wie z.B. Ultraschall), zum Schwimmen angeregt werden können.The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. Next to a general three-dimensional description, we formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. Several numerical test cases show that accurate results can be achieved at computational times on the order of minutes on a single core CPU. Three state-of-the-art applications are demonstrated, where to our knowledge at least two of them cannot be simulated with any other numerical method so far. First, simulations of biological cells being advected through a microfluidic channel and therefore being deformed during an RT-DC (Real-Time Deformability Cytometry) experiment are presented. Then, the uniaxial compression of the cortex of a biological cell during an AFM experiment is investigated. Finally, we present the results of first simulations of the observed shape oscillations of novel microswimming shells which can be locomoted by exterior influences (e.g. ultrasound waves) only

A discrete geometric approach for simulating the dynamics of thin viscous threads

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematical constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations is established formally in the limit of a vanishing discretization length. The discrete models lends itself naturally to numerical implementation. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous jets in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension

Numerical solution of the Ericksen-Leslie model for liquid crystalline polymers free surface flows

In this paper we present a finite difference method on a staggered grid for solving two-dimensional free surface flows of liquid crystalline polymers governed by the Ericksen–Leslie dynamic equations. The numerical technique is based on a projection method and employs Cartesian coordinates. The technique solves the governing equations using primitive variables for velocity, pressure, extra-stress tensor and the director. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. Code verification and convergence estimates are effected by solving a flow problem on 5 different meshes. Two free surface problems are tackled: A jet impinging on a flat surface and injection molding. In the first case the buckling phenomenon is examined and shown to be highly dependent on the elasticity of the fluid. In the second case, injection molding of two differently shaped containers is carried out and the director is shown to be strongly dependent on its orientation at the boundaries

Numerical Simulation of High-Density Ratio Bubble Motion with interIsoFoam

The breeding blanket is one of the fundamental components of a nuclear fusion reactor and is responsible for the fuel production, generating tritium through neutronic capture reaction between lithium and neutrons. Lithium is a liquid PbLi alloy and the helium formed as reaction by-product can coalesce into bubbles, generating a two-phase mixture with a high-density ratio (¿¿ ~ O5 ). These bubbles can accumulate and stagnate within the blanket channels with potentially harmful consequences. In this work, the interIsoFoam solver of OpenFOAM v2012 is used to simulate bubble motion for a two-phase mixture representative of the He-PbLi system to test its potential for future developments in the field of fusion. In a first phase, several traditional benchmarks were carried out, both 2D and 3D, and considering the two variants of the VOF method implemented in the solver, isoAdvector and plicRDF. Subsequently, He bubbles of different diameters rising in liquid PbLi (¿¿ = 1.2 × 105 ) were analysed to investigate different regimes. For a Eötvös number (Eo) greater than 10, it was possible to recreate the axisymmetric, skirted, oscillatory regimes and the peripheral and central breakup regimes. For Eo < 10, non-physical deformations of the interface are observed, probably generated by spurious velocities that have a greater impact on the solution for very small bubbles and rising velocities.Peer ReviewedPostprint (published version