Download or read book Numerical Simulation of Two phase Flow Using the Level Set Approach written by Lan Zhang and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we present numerical schemes in simulating immiscible two-phase flow problems. The goal of this work is to find unified solutions for numerical modeling of any kind of immiscible two-phase flow with moving interface. Fluid flows are modeled using Navier Stokes equations with discontinuous coefficients. We introduce the Volume Fraction method to evaluate discontinuous integrals arise from the variational formulation in the Finite Element method. The use of Volume Fraction method avoids the approximation of the Dirac Delta function, and therefore no regularization procedures are needed. Several operator splitting variants are studied in detail in linearized and non-linearized fashion, when we want to evaluate the discontinuous coefficients. Interface is captured using the Level Set approach, where a transport equation is solved numerically with fourth order scheme without any stabilization terms. The surface tension effect is implemented in a semi-implicit way, thus larger time steps can be used compared with the explicit method. A recent, well-developed re-initialization technique is included as a way to preserve the signed distance property of the Level Set function. All mentioned numerical methods are used to build two-dimensional solvers. Solvers have been tested both with single-phase flow and two-phase flow benchmark problems. In particular, the bubble dynamics are presented to validate stated numerical schemes.

Download or read book Numerical Methods for Two phase Incompressible Flows written by Sven Gross and published by Springer Science & Business Media. This book was released on 2011-04-26 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.

Download or read book Towards Numerical Methods for Two Phase Flow Simulations Undergoing Phase change Phenomena written by China Rama Lakshman Anumolu and published by . This book was released on 2017 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical method to simulate phase-change phenomena is developed using gradient augmented level set strategy (GALS) for advection and reinitialization. Sharp capturing of jump in velocity and pressure is achieved using Ghost Fluid Method. A single phase approach is followed to obtain solution for the energy equation where the governing equation is solved in each fluid phase by explicitly identifying the interface. Explicit identification of the interface is used to properly chose stencil locations in approximating convection and diffusion terms of the energy equation so that a single phase treatment is enforced in the solution procedure. Two approaches to locate the interface are studied in this work; (i) a cubic Hermite interpolating polynomial which is inherent to GALS approach and yields spatially fourth order accurate interface location, (ii) a level set weighted approach which has been used in the level set literature that locates the interface using adjacent level set values as weights along a given axis on a cell edge. The added advantage of cubic Hermite interpolating polynomial over traditional level set weighted approach in approximating the differential terms near the interface is demonstrated. Numerical simulation of phase-change phenomena using level set approach has been the topic of research in the past, however comparison of different numerical strategies with in the category of level set methods have not been presented. Using the level set transport step as the key difference we present a comparative study in this work. Test cases include 1D Stefan problem, 1D absorption problem, 2D bubble growth under a prescribed mass transfer rate, 2D Frank sphere type problem, and a 3D growing bubble subjected to buoyant forces. Both GALS and SLS approaches yielded similar results for 1D test cases due to the choice of the function which is linear and is continuously reinitialized maintaining the signed distance property, resulting in the interface location upto same level of accuracy. Gradient augmented level set based numerical approach resulted in slightly better results for test cases in higher dimensions and with high fluid density ratios.

Download or read book Direct Numerical Simulation of Two phase Flow with Application to Air Layer Drag Reduction written by Dokyun Kim and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An accurate and robust numerical method has been developed to simulate turbulent two-phase flows. The phase interface is tracked by the level-set method to capture frequent topological changes due to breaking or merging. Because of the broad-band characteristics of length scales in two-phase flow, a Lagrangian drop breakup model has been developed, which is coupled to the level-set method. In this approach, small subgrid droplets produced from resolved ligaments are then transferred from the level-set representation to the Lagrangian particles. The further secondary atomization is handled by a stochastic breakup model. When pinching-off of ligaments is not resolved on the level-set grid, a capillary breakup model is used to predict the drop size distribution from the pinching off and inserted as Lagrangian drops. This method improves the mass conservation as well as reducing the computational cost. For a high-fidelity simulation of two-phase flow, a new numerical algorithm has been developed to improve the robustness of the numerical method. The conservative formulation of Navier-Stokes equations is solved with a density correction term in the present method. The density flux terms are calculated from the level-set field for accuracy. In addition, a constant coefficient Poisson system is solved for pressure to satisfy the continuity equation in the fractional-step method. In order to show the capability of the method as an efficient tool in the breakup process, the atomization of a round liquid jet surrounded by a coaxial gas is considered. The numerical results are consistent with the observed breakup mechanisms in the experiment and the stability analysis. The drop size distribution of the resulting spray after breakup is also compared with the experimental data. The subgrid drops are also predicted by the Lagrangian drop breakup model, which shows the applicability of our method for numerical simulation of the atomization process. Both theoretical and numerical approaches are employed to investigate the stability mechanisms of the air layer drag reduction (ALDR) phenomenon. A linear viscous stability analysis is performed by solving the Orr-Sommerfeld equations in a two-dimensional two-phase Couette-Poiseuille flow configuration that mimics the far-downstream region from an air injector. Air-layer stability is reduced as the free-stream velocity, Froude number, and velocity gradients at the air-liquid interface are increased, whereas the air-layer stability is enhanced as the gas flow rate and surface tension force are increased. Nonlinear stability characteristics are also studied using numerical simulations with the same Couette flow configuration as indicated in the linear stability analysis. The study shows that the Weber number has a significant effect on the breakup of the phase interface. As the Weber number increases, the liquid ligaments become thinner, requiring higher grid resolution. Therefore, for simulations of high Weber number flows, the use of a Lagrangian spray breakup model is essential to predict the dynamics of subgrid-scale liquid structures. Direct Numerical Simulation (DNS) of two-phase flow is also performed to investigate the air layer drag reduction (ALDR) phenomenon in turbulent water flow over a backward-facing step. The Reynolds and Weber numbers based on the water properties and step height are 22,800 and 560, respectively. The total number of grid points is about 271 million for DNS. Two different air-flow injection rates are examined to investigate the mechanism and stability of the air layer. For high air-flow rate, the stable air layer is formed on the plate and more than 90% drag reduction is obtained, whereas, in the case of low air-flow rate, the air layer breaks up and ALDR is not achieved. The initial Kelvin-Helmholtz instability causes the streamwise wave structure, while turbulence interaction forms the spawise waves and causes ligament breakups. However, overall rupture of the air layer is mainly determined by the stability of the streamwise wave. The stability of the streamwise wave can be predicted from the stability analysis in the far-downstream region.

Download or read book Numerical Simulation of Multiphase Flows Level set Techniques written by Néstor Vinicio Balcázar Arciniega and published by . This book was released on 2014 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Scientific Computing written by Michael T. Heath and published by SIAM. This book was released on 2018-11-14 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.

Download or read book Numerical Simulation of Multiphase Reactors with Continuous Liquid written by Chao Yang and published by Academic Press. This book was released on 2014-06-13 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of multiphase reactors with continuous liquid phase provides current research and findings in multiphase problems, which will assist researchers and engineers to advance this field. This is an ideal reference book for readers who are interested in design and scale-up of multiphase reactors and crystallizers, and using mathematical model and numerical simulation as tools. Yang and Mao's book focuses on modeling and numerical applications directly in the chemical, petrochemical, and hydrometallurgical industries, rather than theories of multiphase flow. The content will help you to solve reacting flow problems and/or system design/optimization problems. The fundamentals and principles of flow and mass transfer in multiphase reactors with continuous liquid phase are covered, which will aid the reader's understanding of multiphase reaction engineering. Provides practical applications for using multiphase stirred tanks, reactors, and microreactors, with detailed explanation of investigation methods. Presents the most recent research efforts in this highly active field on multiphase reactors and crystallizers. Covers mathematical models, numerical methods and experimental techniques for multiphase flow and mass transfer in reactors and crystallizers.

Download or read book Direct Numerical Simulations of Gas Liquid Multiphase Flows written by Grétar Tryggvason and published by Cambridge University Press. This book was released on 2011-03-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurately predicting the behaviour of multiphase flows is a problem of immense industrial and scientific interest. Modern computers can now study the dynamics in great detail and these simulations yield unprecedented insight. This book provides a comprehensive introduction to direct numerical simulations of multiphase flows for researchers and graduate students. After a brief overview of the context and history the authors review the governing equations. A particular emphasis is placed on the 'one-fluid' formulation where a single set of equations is used to describe the entire flow field and interface terms are included as singularity distributions. Several applications are discussed, showing how direct numerical simulations have helped researchers advance both our understanding and our ability to make predictions. The final chapter gives an overview of recent studies of flows with relatively complex physics, such as mass transfer and chemical reactions, solidification and boiling, and includes extensive references to current work.

Download or read book Small Scale Modeling and Simulation of Incompressible Turbulent Multi Phase Flow written by Stéphane Vincent and published by Springer Nature. This book was released on 2022-10-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides basic and recent research insights concerning the small scale modeling and simulation of turbulent multi-phase flows. By small scale, it has to be understood that the grid size for the simulation is smaller than most of the physical time and space scales of the problem. Small scale modeling of multi-phase flows is a very popular topic since the capabilities of massively parallel computers allows to go deeper into the comprehension and characterization of realistic flow configurations and at the same time, many environmental and industrial applications are concerned such as nuclear industry, material processing, chemical reactors, engine design, ocean dynamics, pollution and erosion in rivers or on beaches. The work proposes a complete and exhaustive presentation of models and numerical methods devoted to small scale simulation of incompressible turbulent multi-phase flows from specialists of the research community. Attention has also been paid to promote illustrations and applications, multi-phase flows and collaborations with industry. The idea is also to bring together developers and users of different numerical approaches and codes to share their experience in the development and validation of the algorithms and discuss the difficulties and limitations of the different methods and their pros and cons. The focus will be mainly on fixed-grid methods, however adaptive grids will be also partly broached, with the aim to compare and validate the different approaches and models.

Download or read book The Finite Element Method Theory Implementation and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Download or read book Bubbly Flows written by Martin Sommerfeld and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book summarises the outcom of a priority research programme: 'Analysis, Modelling and Computation of Multiphase Flows'. The results of 24 individual research projects are presented. The main objective of the research programme was to provide a better understanding of the physical basis for multiphase gas-liquid flows as they are found in numerous chemical and biochemical reactors. The research comprises steady and unsteady multiphase flows in three frequently found reactor configurations, namely bubble columns without interiors, airlift loop reactors, and aerated stirred vessels. For this purpose new and improved measurement techniques were developed. From the resulting knowledge and data, new and refined models for describing the underlying physical processes were developed, which were used for the establishment and improvement of analytic as well as numerical methods for predicting multiphase reactors. Thereby, the development, lay-out and scale-up of such processes should be possible on a more reliable basis.

Download or read book Mechanics written by L D Landau and published by Elsevier. This book was released on 1982-01-29 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics.The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

Download or read book Numerical Methods for Fluid Dynamics written by Institute of Mathematics and Its Applications and published by . This book was released on 1982 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Simulation of Multiphase Reactors with Continuous Liquid Phase written by Chao Yang and published by Academic Press. This book was released on 2014-09-04 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation of multiphase reactors with continuous liquid phase provides current research and findings in multiphase problems, which will assist researchers and engineers to advance this field. This is an ideal reference book for readers who are interested in design and scale-up of multiphase reactors and crystallizers, and using mathematical model and numerical simulation as tools. Yang and Mao’s book focuses on modeling and numerical applications directly in the chemical, petrochemical, and hydrometallurgical industries, rather than theories of multiphase flow. The content will help you to solve reacting flow problems and/or system design/optimization problems. The fundamentals and principles of flow and mass transfer in multiphase reactors with continuous liquid phase are covered, which will aid the reader’s understanding of multiphase reaction engineering. Provides practical applications for using multiphase stirred tanks, reactors, and microreactors, with detailed explanation of investigation methods Presents the most recent research efforts in this highly active field on multiphase reactors and crystallizers Covers mathematical models, numerical methods and experimental techniques for multiphase flow and mass transfer in reactors and crystallizers

Download or read book Computational Methods for Multiphase Flow written by Andrea Prosperetti and published by Cambridge University Press. This book was released on 2009-06-25 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thanks to high-speed computers and advanced algorithms, the important field of modelling multiphase flows is an area of rapid growth. This one-stop account – now in paperback, with corrections from the first printing – is the ideal way to get to grips with this topic, which has significant applications in industry and nature. Each chapter is written by an acknowledged expert and includes extensive references to current research. All of the chapters are essentially independent and so the book can be used for a range of advanced courses and the self-study of specific topics. No other book covers so many topics related to multiphase flow, and it will therefore be warmly welcomed by researchers and graduate students of the subject across engineering, physics, and applied mathematics.

Download or read book Numerical Simulation of Two phase Flow in Pipes Using Godunov Method written by V. Guinot and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: