An interface capturing method for liquid-gas flows at low-Mach number

Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics is neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method [109]. A nodally perfect matched definition of the interface is used [57, 25] and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.El desarrollo de métodos eficientes para modelar la dinámica de implosión presenta varios desafíos. El primero es una representación eficaz de la dinámica del sistema acoplado de aire-agua. El segundo es que el método tiene que permitir una detección exacta o un seguimiento adecuado de la interfase entre ambas fases. Por último el método tiene que ser capaz de resolver cualquier choque que podría generar en el aire o en el agua, sobre todo en la última fase del colapso. Nosotros presentamos un método numérico compresible y totalmente Lagrangiano para simular la implosión bajo el agua. Tanto el aire como el agua se consideran compresibles y las ecuaciones Lagrangianos para la hidrodinámica del choque se estabilizan mediante un método multiescala que es variacionalmente consistente [109]. Se utiliza una definición de interfase que coincide perfectamente con los nodos [57, 25]. Ésta, nos facilita duplicar eficazmente las variables cinéticas como la presión y la densidad en los nodos de la interfase. Con el fin de obtener suficiente resolución alrededor de la interfase, la malla se genera de forma adaptativa y respetando la posición de la interfase. A continuación el método desarrollado se utiliza para simular la implosión bajo el agua de una burbuja cilíndrica del tamaño de un centímetro. Varios fenómenos se han capturado durante el colapso: un ciclo inmediato de colapso-crecimiento de la burbuja que ocurre en un espacio (0.3mm) y tiempo (0.1ms) bastante limitado, aparición de inestabilidades de tipo Rayleigh-Taylor en la interfase y formaron de varias ondas de choque que viajan tanto en el agua como en el aire. Después, seguimos el desarrollo del método para modelar la implosión bajo el agua de un contenedor metálico considerando una interacción monolítica de fluido y estructura. El cilindro de aluminio, que a su vez contiene aire a presión atmosférica y está rodeada de agua en alta presión, se modelando con elementos de lámina de tres nodos y sin grados de libertad de rotación. El cilindro se somete a deformaciones transitorias suficientemente rápidos y enormes hasta llegar a colapsar. Un nuevo modelo elástico de contacto sin considerar la fricción se ha desarrollado para detectar el contacto y calcular las fuerzas en el dominio discretizado entre las superficies medianas de las laminas. Dos esquemas temporales están considerados, uno es implícito utilizando el método de Bossak y otro es explícito utilizando Forward Euler. Al final los resultados de ambos casos se comparan con los resultados experimentales

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data

Novel reactors for multiphase processes

Process intensification tools, such as the capillary reactor, offer several benefits to the chemical process industries due to the well-defined high specific interfacial area available for heat and mass transfer, which increases the transfer rates, and due to low inventories, they also enhance the safety of the process. This has provided motivation to investigate three such tools, namely the capillary microreactor, spinning disc and rotating tube reactors, in this study.The gas-liquid slug flow capillary microreactor intensifies reactor performance through internal circulation caused by the shear between the continuous phase/wall surface and the slug axis, which enhances the diffusivity and consequently increases the reaction rates. However, integrating the complex hydrodynamics of this reactor with its chemical kinetics is a mathematically challenging task. Therefore, in this study, a simple-to-complex approach, using a set of state-of-the-art computational fluid dynamic tools, has been used. Firstly, simulations were performed without any chemical reaction to ascertain the extent of slug flow regime. The model also clearly captured the slug flow generation mechanism which can be used to structurally optimize the angle of entry in these reactors. Finally, the hydrodynamic model was also capable of estimating the pressure drop and slug lengths. After successfully simulating the hydrodynamics of the system, a reaction model was incorporated to study the chemical reaction kinetics. The results were compared with the published experimental work and were found to be in good agreement.The spinning disc reactor utilizes the centrifugal and shear forces to generate thin liquid films characterized with intense interfering waves. This enables a very high heat transfer coefficients to be realized between the disc and liquid, as well as very high mass transfer between the liquid and the bulk gas phase. The waves formed also produce an intense local mixing with very little back mixing. This makes a spinning disc reactor an ideal contactor for multiphase processes. The focus of this study has been to elucidate the hydrodynamic behaviour of the liquid film flow over the horizontal spinning disc. Investigations were also performed to elaborate the local and overall hydrodynamic characteristics of a fully developed spinning disc reactor. Simulation results showed a continuous linear liquid film on the horizontal spinning disc and intense mixing performance in the annulus of the reactor around the disc surface. Finally, the film thickness data from the simulations were compared with the limited amount of data available for this novel process.Rotating tube reactor also uses centrifugal forces to generate the liquid film and a high degree of mixing along with an improved control over the reactant retention times. In this work we have conducted a CFD analysis to understand the hydrodynamics of this new technology for future developments

Numerical simulation of multifluid flows with the particle finite element method

In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties (density and viscosity), include surface tension, and accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. The interface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations. We have applied the resulting scheme to several academic and geological problems,such as the two-fluid sloshing, extrusion of viscous fluids, bubble rise and breakup,mixing of magmatic liquids and negatively buoyant jets.Postprint (published version