A robust method for calculating interface curvature and normal vectors using an extracted local level set

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit formulation. It is also said that the interface curvature and normal vectors are easily calculated. This last point is not, however, the case in the moments during a topological change, as several authors have already pointed out. Various methods have been employed to circumvent the problem. In this paper, we present a new such method which retains the implicit level-set representation of the surface and handles general interface configurations. It is demonstrated that the method extends easily to 3D. The method is validated on static interface configurations, and then applied to two-phase flow simulations where the method outperforms the standard method and the results agree well with experiments.Comment: 31 pages, 18 figure

A Volume of Fluid Method for Three Dimensional Direct Numerical Simulations of Immiscible Droplet Collisions

An advanced Volume of Fluid (VOF) method is presented that enables performant three-dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g., binary droplet collisions. One of the challenges associated with the introduction of a third immiscible phase into the VOF method is the reconstruction of the phase boundaries near the triple line in arbitrary arrangements. For this purpose, an efficient method based on a Piecewise Linear Interface Calculation (PLIC) is shown. Moreover, the surface force modeling with the robust Continuous Surface Stress (CSS) model was enhanced to treat such three-phase situations with large topology changes and thin films. A consistent scaling of the fluid properties at the interfaces ensures energy conservation. The implementation of these methods in the multi-phase flow solver Free Surface 3D (FS3D) allowed a successful validation. A qualitative comparison of the morphology in binary collisions of immiscible droplets as well as a quantitative comparison regarding the threshold velocities that distinguish different collision regimes shows excellent agreement with experimental results. These simulations enable the evaluation of experimentally inaccessible data like the contributions of the kinetic, surface and dissipative energy of both immiscible liquids during the collision process. Furthermore, the comparison with binary collisions of the same liquids highlights similarities and differences between the collisions. Both can support the modeling of the immiscible liquid interaction in the future.Comment: dataset on https://doi.org/10.18419/darus-3557; Changes in v2: VOF in title written out as Volume of Fluid, a handful of typos removed and some sentences language polished, keywords added, new citation styl

Moving Polygon Methods for Incompressible Fluid Dynamics

Hybrid particle-mesh numerical approaches are proposed to solve incompressible fluid flows. The methods discussed in this work consist of a collection of particles each wrapped in their own polygon mesh cell, which then move through the domain as the flow evolves. Variables such as pressure, velocity, mass, and momentum are located either on the mesh or on the particles themselves, depending on the specific algorithm described, and each will be shown to have its own advantages and disadvantages. This work explores what is required to obtain local conservation of mass, momentum, and convergence for the velocity and pressure in a particle-mesh CFD simulation method. Current particle methods are explored and analyzed for their benefits and deficiencies, and newly developed methods are described with results and analysis. A new method for generating locally orthogonal polygonal meshes from a set of generator points is presented in which polygon areas are a constraint. The area constraint property is particularly useful for particle methods where moving polygons track a discrete portion of material. Voronoi polygon meshes have some very attractive mathematical and numerical properties for numerical computation, so a generalization of Voronoi polygon meshes is formulated that enforces a polygon area constraint. Area constrained moving polygonal meshes allow one to develop hybrid particle-mesh numerical methods that display some of the most attractive features of each approach. It is shown that this mesh construction method can continuously reconnect a moving, unstructured polygonal mesh in a pseudo-Lagrangian fashion without change in cell area/volume, and the method\u27s ability to simulate various physical scenarios is shown. The advantages are identified for incompressible fluid flow calculations, with demonstration cases that include material discontinuities of all three phases of matter and large density jumps

Numerical Modelling of Transport in Complex Porous Media: Metal Foams to the Human Lung

Transport in porous media has many practical applications in science and engineering. This work focuses on the development of numerical methods for analyzing porous media flows and uses two major applications, metal foams and the human lung, to demonstrate the capabilities of the methods. Both of these systems involve complex pore geometries and typically involve porous domains of complex shape. Such geometric complexities make the characterization of the relevant effective properties of the porous medium as well as the solution of the governing equations in conjugate fluid-porous domains challenging. In porous domains, there are typically too many individual pores to consider transport processes directly; instead the governing equations are volume-averaged to obtain a new sets of governing equations describing the conservation laws in a bulk sense. There are, however, unknown pore-level terms remaining in the volume-averaged equations that must be characterized using effective properties that account for the effects of processes at the pore level. Once closed, the volume-averaged equations can be solved numerically, however currently available numerical methods for conjugate domains do not perform well at fluid-porous interfaces when using unstructured grids. In light of the preceding discussion, the goals of this work are: (i) to develop a finite-volume-based numerical method for solving fluid flow and non-equilibrium heat transfer problems in conjugate fluid-porous domains that is compatible with general unstructured grids, (ii) to characterize the relevant flow and thermal properties of an idealized graphite foam, (iii) to determine the permeability of an alveolated duct, which is considered as a representative element of the respiratory region of the human lung, and (iv) to conduct simulations of airflow in the human lung using a novel fluid-porous description of the domain. Results show that the numerical method that has been developed for conjugate fluid-porous systems is able to maintain accuracy on all grid types, flow directions, and flow speeds considered. This work also introduces a comprehensive set of correlations for the effective properties of graphite foam, which will be useful for studying the performance of devices incorporating this new material. In order to model air flow in the lung as a porous medium, the permeability of an alveolated duct is obtained using direct pore-level simulations. Finally, simulations of air flow in the lung are presented which use a novel fluid-porous approach wherein the upper airways are considered as a pure fluid region and the smaller airways and alveoli are considered as a porous domain

A generalised immersed boundary method for flows of dense suspension of solid particles

Immersed boundary method (IBM) provides computational advantages in approximating moving solid surfaces on fixed numerical meshes. It has been widely used for fully-resolved simulations of particulate flows. This thesis proposes a generalised formulation of IBM with improved applicability to flows with dense concentrations of particles and unstructured meshes. The new IBM formulation, which is based on the smooth-interface direct forcing approach, directly uses the algebraic discretised terms of the momentum equations in the evaluation of the forces on Lagrangian immersed boundary (IB) points, and evaluate the integral Lagrangian volumes based on these forces. Appropriate reconstructions of the boundary forces are adopted to ensure the compatibility with the momentum-weighted interpolation used for the finite-volume discretisation with a collocated mesh arrangement. A modified direct forcing formulation is also proposed, which results in an efficiency gain of a devised segregated flow-particle coupling scheme. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and arbitrary triangular/tetrahedral meshes, and the results are similar or better than other related methods that are mostly developed for Cartesian meshes. Accurate and stable enforcement of the no-slip condition on the IB at every time-step is demonstrated, even for flows with strong transient behaviour and high velocity and pressure gradients. Local continuity in the vicinity of the IB is also preserved, ensuring local and global mass conservation alongside the local no-slip condition. Adaptations devised for unstructured meshes results in an accuracy close to that obtained on Cartesian meshes. The framework is successfully applied in the simulations of fluidisation of dense particle bed and a rising pack of light particles, showing robust stability. The issues related to the interfering regularised forces of different particle surfaces are not significant using the present formulation, hence eliminate unphysical flow patterns between aggregated particles.Open Acces

Stellar Wind Confinement of Evaporating Exoplanet Atmospheres and Its Signatures in 1083 nm Observations

Atmospheric escape from close-in exoplanets is thought to be crucial in shaping observed planetary populations. Recently, significant progress has been made in observing this process in action through excess absorption in transit spectra and narrowband light curves. We model the escape of initially-homogeneous planetary winds interacting with a stellar wind. The ram pressure balance of the two winds governs this interaction. When the impingement of the stellar wind on the planetary outflow is mild or moderate, the planetary outflow expands nearly spherically through its sonic surface before forming a shocked boundary layer. When the confinement is strong, the planetary outflow is redirected into a cometary tail before it expands to its sonic radius. The resultant transmission spectra at the He 1083 nm line are accurately represented by a 1D spherical wind solution in cases of mild to moderate stellar wind interaction. In cases of strong stellar wind interaction, the degree of absorption is enhanced and the cometary tail leads to an extended egress from transit. The crucial features of the wind--wind interaction are, therefore, encapsulated in the light curve of He 1083 nm equivalent width as a function of time. The possibility of extended He 1083 nm absorption well beyond the optical transit carries important implications for planning "out-of-transit" observations that serve as a baseline for in-transit data.Comment: Accepted for publication in AAS Journals. Associated data and software at: https://zenodo.org/record/5750747 and https://zenodo.org/record/575077