MLPG_R method for modelling 2D flows of two immiscible fluids

This is a first attempt to develop the Meshless Local Petrov-Galerkin method with Rankine source solution (MLPG_R method) to simulate multiphase flows. In this paper, we do not only further develop the MLPG_R method to model two-phase flows but also propose two new techniques to tackle the associated challenges. The first technique is to form an equation for pressure on the explicitly identified interface between different phases by considering the continuity of the pressure and the discontinuity of the pressure gradient (i.e. the ratio of pressure gradient to fluid density), the latter reflecting the fact that the normal velocity is continuous across the interface. The second technique is about solving the algebraic equation for pressure, which gives reasonable solution not only for the cases with low density ratio but also for the cases with very high density ratio, such as more than 1000. The numerical tests show that the results of the newly developed two-phase MLPG_R method agree well with analytical solutions and experimental data in the cases studied. The numerical results also demonstrate that the newly developed method has a second-order convergent rate in the cases for sloshing motion with small amplitudes

Flowbec

publication-status: UnpublishedThis document provides an overview of the resources available for the description of the natural environment at the Wave Hub site, and surrounding region. It aims to provide the reader with an understanding of the mechanisms that have led to the collection of the data resources, and details on how to access them. Detailed information for key research areas is then presented. The document does not aim to provide results of the data collection and analysis, and the reader is referred to the data sources reviewed.NERC FLOWBE

DNS of multiphase flows: study of atomization and free-surface phenomena

The present thesis focuses on the numerical analysis of some diverse physical set-up that involve the interaction of two -or three immiscible and incompressible phases. The simulations are carried out by means of finite-volume algorithms developed on the in-house Computational Fluid Dynamics platform TermoFluids, developed by the Heat and Mass Transfer Technological Center (CTTC). They are intended to give detailed insights on the physics of the analyzed phenomena by carrying out Direct Numerical Simulations (DNS). In the context of multiphase flows, namely, Computational Multi-Fluid Dynamics (CMFD) field, DNS means that all the interfacial and turbulent scales of the phenomenon must be fully resolved. In the Introduction, a general overview of the engineering applications and the computational methods related to multiphase flows is proposed. The various types of physics analyzed in this work and the numerical approaches applied here to carry out efficient simulations are introduced. In Chapter 2, a low-dissipation convection scheme for the stable discretization of multiphase flow by means of interface-capturing schemes is analyzed. The hybrid form of the convective operator proposed incorporates localized low-dispersion characteristics to limit the growth of spurious flow solutions. Moreover, in comparison to pure-dissipative schemes, the discretization aims at minimizing the differences in kinetic energy preservation with respect to the continuous governing equations. This property plays a fundamental role in the case of flows presenting significant levels of turbulence. The simulation of a turbulent 2D coaxial jet with the low-dissipation convection scheme demonstrates its capability of solving correctly the two-phase turbulent problems. In Chapter 3, all the work carried out on the simulation of two-phase flow with the aid of Adaptive Mesh Refinement (AMR) strategies is described. The model is globally addressed at improving the representation of interfacial and turbulent scales in general multiphase flows. It is first applied to the simulation of simple multiphase phenomena, as 2D and 3D rising bubbles, to demonstrate the convergence of the method and the important computational savings in comparison to static mesh computations. However, its adoption becames essential in the simulation of instability and break-up phenomena, where the necessity of representing accurately the complex structures that appear at the interface, as ligaments and droplets, make the simulation particularly expensive in terms of computational cost. In Chapter 4, we analyze in detail the simulations of 3-D atomizing phenomena, including the coaxial jet case, characterized by the parallel injection of high speed liquid and gas fluxes, and the liquid spray case, characterized by the injection of a high speed liquid inside a still air chamber. In Chapter 5, an original single-phase scheme for the DNS of free-surface problems on 3-D unstructured meshes is presented. The scheme is based on a novel treatment of the interface for the deactivation of the light-phase, allowing an optimization of the classic two-phase model for the cases in which the influence of the lighter phase is negligible. Consequently, the model is particularly addressed at analyzing problems involving the movement of free-surfaces, as the evolution of waves on the sea, and their interaction with fixed and moving obstacles. Some practical cases of application are proposed, as the evaluation of stresses on an object due to the action of a dam-break event, and the interaction of linear waves with an oscillating water column device. In the same Chapter we describe the procedure to couple the single-phase model to the Immersed Boundary Method. The method is aimed at representing the interaction of a solid moving with prescribed velocity and the two-phase flow. The most significant example consists in the simulation of a sliding wedge into a liquid basin.Esta tesis se focaliza en la simulación numérica de algunos set-up físicos que involucran la interacción entre dos o tres fluidos incompresibles y immiscibles. Las simulaciones se realizan por medio de algoritmos de volúmenes-finitos desarrollados en la plataforma propia de Fluido-Dinámica Computacional (CFD) denominada TermoFluids, desarrollada en el Centro Tecnologico de Trasferencia de Calor (CTTC). Las simulaciones quieren estudiar en detalle la física de los fenómenos analizados, realizando su Simulación Numérica Directa (DNS). En el contexto de los flujos multifase, DNS significa que todas las escalas interfaciales y turbulentas del fenómeno han de ser totalmente resueltas. En la Introducción, se propone una panorámica general de las aplicaciones de ingeniería y de los métodos computacionales relacionados con flujos multifases. Se introducen los varios tipos de física analizados en este trabajo y las estrategias numéricas aplicadas aquí para efectuar su simulación de manera eficiente. En el Capitulo 2 se analiza un esquema convectivo de baja-disipación para la discretization de flujo multifase por medio de métodos de interface-capturing. La forma híbrida del operador convectivo propuesto incorpora la característica de una baja dispersión localizada, focalizada en limitar el crecimiento de soluciones numéricas espurias. Además, en comparación con métodos disipativos puros, la discretización apunta a minimizar las diferencias en la conservación de energía cinética en respeto a las ecuaciones continuas que gobiernan el flujo. Esta propiedad juega un papel fundamental en el caso de flujo caracterizado por un alto nivel de turbulencia. La simulación de un jet 2D coaxial turbulento con el método convectivo de baja disipación demuestra su capacidad de resolver correctamente un flujo de dos fases turbulentos. En el Capitulo 3 se reporta todo el trabajo realizado sobre la simulación de flujo multifase con el auxilio de técnicas de refinamiento adaptativo de malla (AMR). El modelo es globalmente dirigido a la mejora de la representación de las escalas turbulentas y interfaciales en flujos multifases en general. Se aplica inicialmente a la simulación de flujos sencillos, como unos casos de burbujas flotantes 2D y 3D, demostrando la convergencia del método y los importantes ahorros computacional en comparación con los cálculos de mallas estáticas. La adopción de la técnica se hace esencial en la simulación de fenómenos de inestabilidad y de ruptura, donde la necesidad de representar sacramentalmente las estructuras complejas que aparecen en la interfaz, como ligamentos o pequeñas gotas, hacen que la simulación sea particularmente pesada en términos de coste computacional. En el Capitulo 4 se reportan en detalle las simulaciones de fenómenos de atomización 3D. Esas incluyen el caso del jet coaxial, caracterizado por la inyección paralela de flujos de aire y liquido de altas velocidades, y el caso del spray liquido, que consiste en la inyección de un liquido dentro de una cámara de aire. En el Capitulo 5 se presenta un esquema de single-phase original, para el DNS de problemas de superficie libre en mallas 3D no-estructuradas. El esquema se basa en un nuevo tratamiento de la interfase para la desactivación de la fase ligera, permitiendo la optimización del solver clásico de dos fases para los casos en que la influencia de la fase mas ligera sea despreciable. En consecuencia, el modelo es particularmente indicado para la análisis de problemas que involucran el movimiento de superficies libres, como la evolución de olas en la superficie marina y su interacción con obstáculos fijos o muebles. Se proponen algunos casos prácticos de aplicación, como la evaluación de las fuerzas sobre un objeto debidos a un episodio de dam-break, o el estudio de las olas generadas por el impacto de un solido deslizante (representado integrando la tecnica de Immersed Boundary con el presente metodo de single-phase) con un embalse de agua

Numerical investigation of breaking waves and their interactions with structures using MLPG_R method

Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) has been developed by Dr. Qingwei Ma (Ma, 2005b) and has been used to simulate the nonlinear water wave problems in 2D cases without the occurrence of the breaking waves. In this thesis, MLPG_R method has been further developed to numerically simulate breaking waves and the interactions between breaking waves and structures in 2D and 3D cases. The main difference between this meshless method and conventional mesh-based methods is that the governing equations are solved in terms of particle interaction models, without the need of computational meshes. Therefore, this method avoids the time-consuming mesh generating and updating procedures which may be necessary and may need to be frequently performed in the mesh-based methods. Furthermore, in order to simulate the breaking waves well, several novel numerical techniques are developed and adopted. The numerical technique for implementing the solid boundary condition for meshless methods is proposed, which is more robust than others in terms of accuracy and efficiency. A technique for meshless interpolation (SFDI scheme) is adopted, which is as accurate as the more costly moving least square (MLS) method generally but requires much less computational time than the latter. A newly developed technique for identifying the free surface particles is presented, which is much more robust than those existing in literature. A semi-analytical method for numerical evaluation of integrals in a local domain and on its surface is presented to form the matrix for the algebraic equations, which makes it possible to modelling the 3D problems on personal computers. The newly extended MLPG_R method is applied to simulate the waves generated by a wave maker and their propagations, overturning and breaking over flat and sloped seabed. And it is also applied to 2D and 3D dam breaking cases and violent sloshing cases. The convergence properties of this method in different cases are investigated. Some of the results have been validated by experimental data and numerical results obtained by other methods. Satisfactory agreements are achieved. Based on these numerical investigations, a number of conclusions have been made, including that the breaking waves can cause large pressure with several peaks when they impact on structures; the behaviour of pressure strongly depends on the relative locations of structures to the breaking point of breaking waves. Breaking waves in a sloshing container can also cause more than one peaks, which is correlated with the direction change of water motion within the container. These investigations can give us better understanding of the impact pressure, breaking wave and interactions between breaking wave and structures

Transformation of Nonlinear Waves in the Presence of Wind, Current, and Vegetation

Accurate prediction of extreme wave events is crucial for the safe maritime activities and offshore operations. Improved knowledge of wave dissipation mechanisms due to breaking and vegetation leads to accurate wave forecast, protecting life and property along the coast. The scope of the thesis is to examine the wave transformations in the presence of wind, current, and vegetation, using a two-phase flow solver based on the open-source platform OpenFOAM. The Reynolds-Averaged Navier-Stokes (RANS) equations are coupled with a Volume of Fluid (VOF) surface capturing scheme and a turbulence closure model. This RANS-VOF model is adapted to develop a numerical wind-wave-current flume suitable for studying wind-wave, wave-current, and wave-structure interactions. Proper wind/wave/current boundary conditions are devised, two-equation and Shear Stress Transport (SST) turbulence models modified, and new modules capturing fluid-structure interactions are developed. The wind and current effects on the evolution of a two-dimensional dispersive focusing wave group are examined. The model predictions are validated against experimental measurements with and without following wind. The effects of wind-driven current and opposing wind are investigated based on additional model results. The air flow structure above a plunging breaking wave group is examined. The RANS-VOF model is also applied to investigate the phenomenon of wave breaking and blocking due to strong opposing currents on a flat bottom. The geometric and hydrodynamic characteristics, i.e., the breaking criterion, the wave set-down and set-up, the energy dissipation, and the turbulence and vorticity generated in the wave breaking/blocking process are examined. A new coupled wave-vegetation interaction model is developed by coupling the RANS-VOF wave model with a Finite Element Method (FEM) based structure model using an immersed boundary approach. The wave height decay along and wave kinematics within a vegetation patch are examined. The study has contributed to understanding of the wind effects on the extreme wave formation and breaking, the characteristics of current-induced wave breaking/blocking, and the vegetation effect on wave transformations. Insights gained from this study shed some light on the formation mechanism for rogue waves, and the breaking- and vegetation-induced dissipation formulations in the present wave prediction and circulation models

Numerical Investigation of breaking waves and their interations with structures using MLPG_R method

Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) has been developed by Dr. Qingwei Ma (Ma, 2005b) and has been used to simulate the nonlinear water wave problems in 2D cases without the occurrence of the breaking waves. In this thesis, MLPG_R method has been further developed to numerically simulate breaking waves and the interactions between breaking waves and structures in 2D and 3D cases. The main difference between this meshless method and conventional mesh-based methods is that the governing equations are solved in terms of particle interaction models, without the need of computational meshes. Therefore, this method avoids the time-consuming mesh generating and updating procedures which may be necessary and may need to be frequently performed in the mesh-based methods. Furthermore, in order to simulate the breaking waves well, several novel numerical techniques are developed and adopted. The numerical technique for implementing the solid boundary condition for meshless methods is proposed, which is more robust than others in terms of accuracy and efficiency. A technique for meshless interpolation (SFDI scheme) is adopted, which is as accurate as the more costly moving least square (MLS) method generally but requires much less computational time than the latter. A newly developed technique for identifying the free surface particles is presented, which is much more robust than those existing in literature. A semi-analytical method for numerical evaluation of integrals in a local domain and on its surface is presented to form the matrix for the algebraic equations, which makes it possible to modelling the 3D problems on personal computers. The newly extended MLPG_R method is applied to simulate the waves generated by a wave maker and their propagations, overturning and breaking over flat and sloped seabed. And it is also applied to 2D and 3D dam breaking cases and violent sloshing cases. The convergence properties of this method in different cases are investigated. Some of the results have been validated by experimental data and numerical results obtained by other 14 methods. Satisfactory agreements are achieved. Based on these numerical investigations, a number of conclusions have been made, including that the breaking waves can cause large pressure with several peaks when they impact on structures; the behaviour of pressure strongly depends on the relative locations of structures to the breaking point of breaking waves. Breaking waves in a sloshing container can also cause more than one peaks, which is correlated with the direction change of water motion within the container. These investigations can give us better understanding of the impact pressure, breaking wave and interactions between breaking wave and structures