A level-set method for thermal motion of bubbles and droplets

Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.A conservative level-set model for direct simulation of two-phase flows with thermocapillary effects at dynamically deformable interface is presented. The Navier-Stokes equations coupled with the energy conservation equation are solved by means of a finite-volume/level-set method. Some numerical examples including thermocapillary motion of single and multiple fluid particles are computed by means of the present method. The results are compared with analytical solutions and numerical results from the literature as validations of the proposed model.Peer ReviewedPostprint (published version

Numerical simulation of multiphase flows : level-set techniques

This thesis aims at developing numerical methods based on level-set techniques suitable for the direct numerical simulation (DNS) of free surface and interfacial flows, in order to be used on basic research and industrial applications. First, the conservative level-set method for capturing the interface between two fluids is combined with a variable density projection scheme in order to simulate incompressible two-phase flows on unstructured meshes. All equations are discretized by using a finite-volume approximation on a collocated grid arrangement. A high order scheme based on a flux limiter formulation, is adopted for approximating the convective terms, while the diffusive fluxes are centrally differenced. Gradients are computed by the least-squares approach, whereas physical properties are assumed to vary smoothly in a narrow band around the interface to avoid numerical instabilities. Surface tension force is calculated according to the continuous surface force approach. The numerical method is validated against experimental and numerical data reported in the scientific literature. Second, the conservative level-set method is applied to study the gravity-driven bubbly flow. Unlike the cases presented in the first part, a periodic boundary condition is applied in the vertical direction, in order to mimic a channel of infinite length. The shape and terminal velocity of a single bubble which rises in a quiescent liquid are calculated and validated against experimental results reported in the literature. In addition, different initial arrangements of bubble pairs were considered to study its hydrodynamic interaction, and, finally the interaction of multiple bubbles is explored in a periodic vertical duct, allowing their coalescence. In the third part of this thesis, a new methodology is presented for simulation of surface-tension-driven interfacial flows by combining volume-of-fluid with level-set methods. The main idea is to benefit from the advantage of each strategy, which is to minimize mass loss through the volume-of-fluid method, and to keep a fine description of the interface curvature using a level-set function. With the information of the interface given by the volume-of-fluid method, a signed distance function is reconstructed following an iterative geometric algorithm, which is used to compute surface tension force. This numerical method is validated on 2D and 3D test cases well known in the scientific literature. The simulations reveal that numerical schemes afford qualitatively similar results to those obtained by the conservative level-set method. Mass conservation is shown to be excellent, while geometrical accuracy remains satisfactory even for the most complex cases involving topology changes. In the fourth part of the thesis a novel multiple marker level-set method is presented. This method is deployed to perform numerical simulation of deformable fluid particles without numerical coalescence of their interfaces, which is a problem inherent to standard interface tracking methodologies (e.g. level-set and volume of fluid). Each fluid particle is described by a separate level-set function, thus, different interfaces can be solved in the same control volume, avoiding artificial and potentially unphysical coalescence of fluid particles. Therefore, bubbles or droplets are able to approach each other closely, within the size of one grid cell, and can even collide. The proposed algorithm is developed in the context of the conservative levelset method, whereas, surface tension is modeled by the continuous surface force approach. The pressure-velocity coupling is solved by the fractional-step projection method. For validation of the proposed numerical method, the gravity-driven impact of a droplet on a liquid-liquid interface is studied; then, the binary droplet collision with bouncing outcome is examined, and finally, it is applied on simulation of gravity-driven bubbly flow in a vertical column. The study of these cases contributed to shed some light into physics present in bubble and droplet flows.Ésta tesis se enfoca en el desarrollo de métodos numéricos basados en la aplicación de técnicas level-set para la Simulación Numérica Directa (DNS) de flujos interfaciales y flujos de superficie libre, con el objetivo de ser usados tanto en investigación básica como en aplicaciones industriales. Primero, el método level-set conservativo desarrollado para la captura de interfaces entre dos fluidos, es combinado con un esquema de proyección adaptado para un fluido de densidad variable, con el objetivo de simular flujos de dos fases en mallas no estructuradas. Todas las ecuaciones son discretizadas mediante una aproximación de volúmenes finitos sobre un arreglo de malla colocada. Un esquema de alto orden cuya formulación se basa en el uso de limitadores de flujo, es usado para la discretización de los términos convectivos, mientras que los flujos difusivos son calculados mediante diferencias centradas. Los gradientes son calculados mediante el método de los mínimos cuadrados, en tanto que se asume que las propiedades físicas varían suavemente en una zona estrecha alrededor de la interface con el objetivo de evitar inestabilidades numéricas. La tensión superficial es incorporada mediante el enfoque de la fuerza superficial continua. El método numérico es validado con respecto a los datos experimentales y numéricos reportados en la literatura científica. Segundo, el método level-set conservativo es aplicado en el estudio del flujo de burbujas conducidas por la gravedad. A diferencia de los casos precedentes, se aplica una condición de frontera periódica en la dirección vertical, con el objetivo de simular un canal de longitud infinita. La forma y velocidad terminal de una burbuja ascenciendo en un líquido inicialmente en reposo son calculadas y contrastadas con los resultados reportados en la literatura. Adicionalmente se estudia la interacción hidrodinámica de un par de burbujas para diferentes configuraciones, y finalmente se explora la interacción de un emjambre de burbujas ascendiendo en un canal vertical. En la tercera parte de ésta tesis, se presenta una nueva metodología para la simulación de flujos interfaciales conducidos por la tensión superficial, mediante la combinación de los métodos volume-of-fluid y level-set. La idea principal se basa en usar el método volume-of-fluid para advectar la interface, minimizando las pérdidas de masa, mientras que las propiedades geométricas de la interface se calculan a partir de una función level-set obtenida mediante un algoritmo geométrico iterativo. La propiedades geométricas así calculadas son usadas para el cómputo de la tensión superficial. El método numérico es validado mediante casos bi y tri-dimensionales bien conocidos en la literatura científica. La conservación de la masa es excelente en tanto que la precisión del método es altamente satisfactoria incluso en los casos más complejos. En la cuarta parte de ésta tesis se presenta un nuevo método level-set de múltiples marcadores. Éste método es diseñado para llevar a cabo simulaciones numéricas de partículas de fluido deformables, evitando la coalescencia numérica de las interfaces. Cada partícula de fluido es capturada por una función level-set distinta, así, diferentes interfaces pueden ser resueltas en el mismo volumen de control, evitando la coalescencia artificial y potencialmente no-física de las partículas fluidas. Por lo tanto, las burbujas (o gotas) pueden acercarce y colisionar. El algoritmo es propuesto en el contexto del método level-set conservativo, mientras que la tensión superficial se resuelve mediante una adaptación del enfoque de la fuerza superficial continua. Para su validación, se estudia el impacto conducido por la gravedad de una gota sobre una interface líquido-líquido; luego, se estudia la collisión de dos gotas con salida rebotante, y finalmente el método numérico es aplicado para la simulación de un enjambre de burbujas sin coalescencia numérica

A level-set model for thermocapillary motion of deformable fluid particles

A new level-set model is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios at dynamically deformable interfaces. The Navier–Stokes equations coupled with the energy conservation equation are solved by means of a finite-volume/level-set approach, adapted to a multiple marker methodology in order to avoid the numerical coalescence of the fluid particles. The temperature field is coupled to the surface tension through an equation of state. Some numerical examples including thermocapillary driven convection in two superimposed fluid layers, and thermocapillary motion of single and multiple fluid particles are computed using the present method. These results are compared against analytical solutions and numerical results from the literature as validations of the proposed model.Peer ReviewedPostprint (author's final draft

Unstructured Level-Set Method For Saturated Liquid-Vapor Phase Change

A novel conservative level-set method for saturated liquid-vapor phase change on unstruc-tured meshes is introduced. Transport equations are discretized by the finite-volume method on col-located unstructured grids. Mass transfer promoted by thermal phase change is computed using theenergy jump condition at the interface, as a function of the temperature gradient. The fractional-stepprojection method is used for solving the pressure-velocity coupling, convective terms are discretized byunstructured flux-limiter schemes, central difference scheme is used for discretization of diffusive terms.Verification and validation cases have been undertaken to prove the accuracy and robustness of the nu-merical methods, including simulation of the Stefan problem, and film boiling on a cylindrical surface.Excellent agreement between numerical solutions against analytical solution and empirical correlationsfrom the literature is reported.Peer ReviewedPostprint (published version

A level-set model for two-phase flow with variable surface tension: thermocapillary and surfactants

An unstructured conservative level-set method for two-phase flow with variable surface tension is introduced. Surface tension is a function of temperature or surfactant concentration on the interface. Consequently, the called Marangoni stresses induced by temperature gradients or surfactant concentration gradients on the interface lead to a coupling of momentum transport equation with thermal energy transport equation or interface surfactant transport equation. The finite-volume method discretizes transport equations on 3D collocated unstructured meshes. The unstructured conservative level-set method is employed for interface capturing, whereas the multiple marker approach avoids the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters are proposed to discretize the convective term of transport equations. A central difference scheme discretizes diffusive terms. Gradients are evaluated by the weighted least-squares method. Verifications and validations are reportedThe main author, N. Balcazar-Arciniega, as a Serra-Húnter Fellow (UPC-LE8027), acknowledges the Catalan Government for the financial support through this programme. Simulations were executed using computing time granted by the RES (IM-2021-1-0013, IM-2020-2-0002) and PRACE 14th Call (2016153612) on the supercomputer MareNostrum IV based in Barcelona, Spain. The authors acknowledge the financial support of the MINECO, Spain (PID2020-115837RB-100).Peer ReviewedPostprint (published version

A comparative study of interface capturing methods with amr for incompressible two-phase flows

This paper presents a comparative study of interface capturing methods with adaptive mesh refinement for Direct Numerical Simulation (DNS) of incompressible two- phase flows. The numerical algorithms for fluid motion and interface capturing methods have been previously introduced in the context of the finite-volume approach for both mass conservative level-set methodology and coupled volume-of-fluid/level-set method for unstructured/structured fixed meshes. The Adaptive Mesh Refinement (AMR) method introduced in consist on a cell-based refinement technique to minimize the number of computational cells and provide the spatial resolution required for the interface capturing methods. The present AMR framework adapts the mesh according to a physics-based refinement criteria defined by the movement of the interface between the fluid-phases. Numerical experiments are presented to evaluate the methods described in this work. This includes a study of the hydrodynamics of single bubbles rising in a quiescent viscous liquid, including its shape, terminal velocity, and wake patterns. These results are validated against experimental and numerical data well established in the scientific literature, as well as a comparison of the different approaches used

Numerical study of droplet deformation in shear flow using a conservative level-set method

This paper is concerned with a numerical study on the behavior of a single Newtonian droplet suspended in another Newtonian fluid, all subjected to a simple shear flow. Conservative finite-volume approximation on a collocated three-dimensional grid along with a conservative Level-set method are used to solve the governing equations. Four parameters of capillary number (Ca), Viscosity ratio (), Reynolds number (Re) and walls confinement ratio are used to physically define the problem. The main focus of the current study is to investigate the effect of viscosity on walls critical confinement ratio. In this paper, the phrase critical is used to specify a state of governing parameters in which divides the parameter space into the subcritical and supercritical regions where droplets attain a steady shape or breakup, respectively. To do so, first, we validate the ability of proposed method on capturing the physics of droplet deformation including: steady-state subcritical deformation of non-confined droplet, breakup of supercritical conditioned droplet, steady-state deformation of moderate confined droplet, subcritical oscillation of highly-confined droplet, and the effect of viscosity ratio on deformation of the droplet. The extracted results are compared with available experimental, analytical and numerical data from the literature. Afterward, for a constant capillary number of 0.3 and a low Reynolds number of 1.0, subcritical (steady-state) and supercritical (breakup) deformations of the droplet for a wide range of walls confinement in different viscosity ratios are studied. The results indicate the existence of two steady-state regions in a viscosity ratio-walls confinement ratio graph which are separated by a breakup region.Peer ReviewedPostprint (author's final draft

Numerical study of binary droplets collision in the main collision regimes

Direct numerical simulation of binary droplets collision is done using a conservative level-set method. The Navier-Stokes and level-set equations are solved using a finite-volume method on collocated grids. A novel lamella stabilization approach is introduced to numerically resolve the thin lamella film appeared during a broad range of collision regimes. This direction-independent method proves to be numerically efficient and accurate compared with experimental data. When the droplets collide, the fluid between them is pushed outward, leaving a thin gas layer bounded by the surface of two droplets. This layer progressively gets thinner and depending on the collision regime, may rupture resulting in coalescence of the droplets or may linger resulting in bouncing-off the droplets. Embedded ghost-nodes layer makes it possible to mimic both bouncing and coalescence phenomena of the droplets collision. The numerical tools introduced are validated and verified against different experimental results for a wide range of collision regimes. A very good agreement is observed between the results of this paper and experimental data available in the literature. A detailed study of the energy budget for different shares of kinetic and dissipation energies inside of the droplet and matrix, in addition to the surface tension energy for studied cases, is provided. Supplementary quantitative values of viscous dissipation rate inside of the matrix and droplet, and also the radial expansion of the droplet are presented as well.Peer ReviewedPostprint (published version

DNS of falling droplets in a vertical channel

© 2018 WIT PressThis paper presents Direct Numerical Simulation (DNS) of the falling motion of single and multiple deformable drops in a vertical channel. A systematic study of the wall effect on the motion of single drop is performed for Eötvös number (0.5=Eo=5), Morton number (10-3=M=10-8), and confinement ratio CR = 2. Second, the gravity-driven motion of multiple drops and their interactions are studied in a periodic vertical channel for CR = 4. These simulations are performed using a multiple marker level-set methodology, integrated in a finite-volume framework on a collocated unstructured grid. Each droplet is described by a level-set function, which allows capturing multiple interfaces in the same control volume, avoiding the numerical merging of the droplets. Numerical algorithms for fluid motion and interface capturing have been developed in the context of the finite-volume and level-set methodology, surface tension is modeled by means of the continuous surface force approach, and the pressure-velocity coupling is solved using a fractional-step projection method. DNS of single drop shows that they migrate to the symmetry axis of the channel when the Reynolds number is low, following a monotonic approach or damped oscillations according to the dimensionless parameters. If Eötvös number increases, stronger oscillations around the symmetry axis are observed. Simulations of multiple drops show that the collision of two drops follows the drafting-kissing tumbling (DKT) phenomenon. Deformable drops do not collide with the wall, whereas DKT phenomenon in the droplet swarm leads to the formation of groups which move through the center of the channel.Peer ReviewedPostprint (published version

DNS of the wall effect on the motion of bubble swarms

This paper presents a numerical study of the gravity-driven motion of single bubbles and bubble swarms through a vertical channel, using High-Performance Computing (HPC) and Direct Numerical Simulation (DNS) of the Navier-Stokes equations. A systematic study of the wall effect on the motion of single deformable bubbles is carried out for confinement ratios CR = {2,4,6} in both circular and square channels, for a broad range of flow conditions. Then, the rising motion of a swarm of deformable bubbles in a vertical channel is researched, for void fractions a = {8.3%, 10.4%, 12.5%} and CR = {4, 6}. These simulations are carried out in the framework of a novel multiple marker interface capturing approach, where a conservative level-set function is used to represent each bubble. This method avoids the numerical and potentially unphysical coalescence of the bubbles, allowing for the collision of the fluid particles as well as long time simulations of bubbly flows. Present simulations are performed in a periodic vertical domain discretized by 2 × 106 control volumes (CVs) up to 16.6 × 106 CVs, distributed in 128 up to 2048 processors. The collective and individual behavior of the bubbles are analyzed in detail.Peer ReviewedPostprint (published version