Download or read book The Discrete Equation Method DEM for Fully Compressible Two Phase Flows in Ducts of Spatially Varying Cross Section written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Typically, multiphase modeling begins with an averaged (or homogenized) system of partial differential equations (traditionally ill-posed) then discretizes this system to form a numerical scheme. Assuming that the ill-posedness problem is avoided by using a well-posed formulation such as the seven-equation model, this presents problems for the numerical approximation of non-conservative terms at discontinuities (interfaces, shocks) as well as unwieldy treatment of fluxes with seven waves. To solve interface problems without conservation errors and to avoid this questionable determination of average variables and the numerical approximation of the non-conservative terms associated with 2 velocity mixture flows we employ a new homogenization method known as the Discrete Equations Method (DEM). Contrary to conventional methods, the averaged equations for the mixture are not used, and this method directly obtains a (well-posed) discrete equation system from the single-phase system to produce a numerical scheme which accurately computes fluxes for arbitrary numbers of phases and solves non-conservative products. The method effectively uses a sequence of single phase Riemann equation solves. Phase interactions are accounted for by Riemann solvers at each interface. Flow topology can change with changing expressions for the fluxes. Non-conservative terms are correctly approximated. Some of the closure relations missing from the traditional approach are automatically obtained. Lastly, we can often times identify the continuous equation system, resulting from taking the continuous limit with weak wave assumptions, of the discrete equations. This can be very useful from a theoretical standpoint. As a first step toward implict integration of the DEM method in multidimensions, in this paper we construct a DEM model for the flow of two compressible phases in 1-D ducts of spatially varying cross-section to test this approach. To relieve time step size restrictions due to stiffness and to achieve tighter coupling of equations, a fully implicit time integration method is employed. For the first time, we demonstrate on a converging-diverging two-phase nozzle that this well-posed, 2 pressure, 2 velocity DEM model can be integrated to a meaningful steady-state with both phases treated as compressible.

Download or read book Numerical Simulation for Next Generation Thermal Power Plants written by Falah Alobaid and published by Springer. This book was released on 2018-03-29 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides highly specialized researchers and practitioners with a major contribution to mathematical models’ developments for energy systems. First, dynamic process simulation models based on mixture flow and two-fluid models are developed for combined-cycle power plants, pulverised coal-fired power plants, concentrated solar power plant and municipal waste incineration. Operation data, obtained from different power stations, are used to investigate the capability of dynamic models to predict the behaviour of real processes and to analyse the influence of modeling assumptions on simulation results. Then, a computational fluid dynamics (CFD) simulation programme, so-called DEMEST, is developed. Here, the fluid-solid, particle-particle and particle-wall interactions are modeled by tracking all individual particles. To this purpose, the deterministic Euler-Lagrange/Discrete Element Method (DEM) is applied and further improved. An emphasis is given to the determination of inter-phase values, such as volumetric void fraction, momentum and heat transfers, using a new procedure known as the offset-method and to the particle-grid method allowing the refinement of the grid resolution independently from particle size. Model validation is described in detail. Moreover, thermochemical reaction models for solid fuel combustion are developed based on quasi-single-phase, two-fluid and Euler-Lagrange/MP-PIC models. Measurements obtained from actual power plants are used for validation and comparison of the developed numerical models.

Download or read book Nuclear Systems Volume II written by Neil E. Todreas and published by CRC Press. This book was released on 2021-12-13 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides advanced coverage of a wide variety of thermal fluid systems and technologies in nuclear power plants, including discussions of the latest reactor designs and their thermal/fluid technologies. Beyond the thermal hydraulic design and analysis of the core of a nuclear reactor, the book covers other components of nuclear power plants, such as the pressurizer, containment, and the entire primary coolant system. Placing more emphasis on the appropriate models for small-scale resolution of the velocity and temperature fields through computational fluid mechanics, the book shows how this enhances the accuracy of predicted operating conditions in nuclear plants. It introduces considerations of the laws of scaling and uncertainty analysis, along with a wider coverage of the phenomena encountered during accidents. FEATURES Discusses fundamental ideas for various modeling approaches for the macro- and microscale flow conditions in reactors Covers specific design considerations, such as natural convection and core reliability Enables readers to better understand the importance of safety considerations in thermal engineering and analysis of modern nuclear plants Features end-of-chapter problems Includes a solutions manual for adopting instructors This book serves as a textbook for advanced undergraduate and graduate students taking courses in nuclear engineering and studying thermal/hydraulic systems in nuclear power plants.

Download or read book Handbook on Thermal Hydraulics in Water Cooled Nuclear Reactors written by Francesco D'Auria and published by Elsevier. This book was released on 2024-07-29 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Thermal Hydraulics of Water-Cooled Nuclear Reactors, Volume 1, Foundations and Principles includes all new chapters which delve deeper into the topic, adding context and practical examples to help readers apply learnings to their own setting. Topics covered include experimental thermal-hydraulics and instrumentation, numerics, scaling and containment in thermal-hydraulics, as well as a title dedicated to good practices in verification and validation. This book will be a valuable reference for graduate and undergraduate students of nuclear or thermal engineering, as well as researchers in nuclear thermal-hydraulics and reactor technology, engineers working in simulation and modeling of nuclear reactors, and more. In addition, nuclear operators, code developers and safety engineers will also benefit from the practical guidance provided. Presents a comprehensive analysis on the connection between nuclear power and thermal hydraulics Includes end-of-chapter questions, quizzes and exercises to confirm understanding and provides solutions in an appendix Covers applicable nuclear reactor safety considerations and design technology throughout

Download or read book On the Formulation and Numerical Evaluation of a Set of Two phase Flow Equations Modelling the Cooldown Process written by Stephen Jarvis and published by . This book was released on 1965 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: A model of transient two-phase flow in a pipe is constructed in Eulerian coordinates assuming a single velocity but independent temperatures in the two phases.Experiments on the numerical integration of the system for Cooldown problem by both Lax and Courant-Isaacson-Rees methods indicate that a very fine spatial difference * net must be used to compensate for the numerical diffusion essential to computational stability if a second surge is to be realized. (Author).

Download or read book Introduction to the Mathematical Theory of Compressible Flow written by Antonín Novotny and published by OUP Oxford. This book was released on 2004-06-17 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.

Download or read book Mathematical Modeling of Disperse Two Phase Flows written by Christophe Morel and published by Springer. This book was released on 2015-07-17 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, amongst others. This book is highly suitable for students in the subject area, but may also be a useful reference text for more advanced scientists and engineers.

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 An Introduction to Compressible Flows with Applications written by José Pontes and published by Springer. This book was released on 2019-12-16 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise and practical survey of the principles governing compressible flows, along with selected applications. It starts with derivation of the time-dependent, three-dimensional equation of compressible potential flows, and a study of weak waves, including evaluation of the sound speed in gases. The following chapter addresses quasi-one-dimensional flows, the study of normal shock waves, and flow in ducts with constant cross section subjected to friction and/or heat transfer. It also investigates the effects of friction and heat transfer in ducts with variable cross section. The chapter ends by pointing to the analogy between one-dimensional compressible flows and open channel hydraulics. Further, the book discusses supersonic flows, including the study of oblique shock waves, and supersonic flows over corners and wedges. It also examines Riemann problems, numerical resolution of the wave equation, and of nonlinear hyperbolic problems, including propagation of strong waves. A subsequent chapter focuses on the small perturbation theory of subsonic, transonic and supersonic flows around slender bodies aligned or almost aligned to the uniform inflow. In particular, it explores subsonic and supersonic flows over a wavy wall. Lastly, an appendix with a short derivation of the Fluid Mechanics basic equations is included. The final chapter addresses the problem of transonic flows where both subsonic and supersonic are present. Lastly, an appendix with a short derivation of the Fluid Mechanics basic equations is included. Illustrated with several practical examples, this book is a valuable tool to understand the most fundamental mathematical principles of compressible flows. Graduate Mathematics, Physics and Engineering students as well as researchers with an interest in the aerospace sciences benefit from this work.

Download or read book Mathematical and Computational Methods for Compressible Flow written by Miloslav Feistauer and published by Oxford University Press, USA. This book was released on 2003 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.

Download or read book A Simple and Efficient Diffuse Interface Method for Compressible Two Phase Flows written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. For many reasons, to be discussed, there is growing interest in the application of two-phase flow models to provide diffuse, but nevertheless resolved, simulation of interfaces between two immiscible compressible fluids - diffuse interface method (DIM). Because of its ability to dynamically create interfaces and to solve interfaces separating pure media and mixtures for DNS-like (Direct Numerical Simulation) simulations of interfacial flows, we examine the construction of a simple, robust, fast, and accurate numerical formulation for the 5-equation Kapila et al. [1] reduced two-phase model. Though apparently simple, the Kapila et al. model contains a volume fraction differential transport equation containing a nonlinear, non-conservative term which poses serious computational challenges. To circumvent the difficulties encountered with the single velocity and single pressure Kapila et al. [1] multiphase flow model, a 6-equation relaxation hyperbolic model is built to solve interface problems with compressible fluids. In this approach, pressure non-equilibrium is first restored, followed by a relaxation to an asymptotic solution which is convergent to the solutions of the Kapila et al. reduced model. The apparent complexity introduced with this extended hyperbolic model actually leads to considerable simplifications regarding numerical resolution, and the various ingredients used by this method are general enough to consider future extensions to problems involving complex physics.

Download or read book Computational Methods for Two Phase Flows written by Peter D. M. Spelt and published by World Scientific Publishing Company Incorporated. This book was released on 2010 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uniquely presents an overview of methods for the numerical simulation of a wide range of two-phase flows, aimed at a broad readership of engineers and scientists at graduate level. Given that numerous methods have been proposed recently in this field, the new book series could not have been more timely and much needed for an up-to-date overview of the advances, whilst not restricting the focus on two-phase flows or any particular method. The book is written by a team of leading experts who have contributed substantially to the development of the methods and who have also applied the concepts and theories to a diverse range of applications. Computational Methods for Two-Phase Flows is self-contained, and aims to elucidate and analyze the strong relations between the various numerical methods, beyond merely giving detailed summary of the various methods. A unique enhanced feature of the book is that the sample codes that come with the book provide further benefits and ease of use to readers to implement the various numerical methods. The book is the first volume of a new book series entitled Advances in Computational Fluid Dynamics, published by World Scientific.

Download or read book Numerical Modeling of Compressible Two Phase Flows with a Pressure Based Method written by Markus Boger and published by . This book was released on 2014 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elements of Numerical Methods for Compressible Flows written by Doyle Knight and published by Cambridge University Press. This book was released on 2006-08-14 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description

Download or read book Compressible Flow and Euler s Equations written by Demetrios Christodoulou and published by . This book was released on 2014-10-10 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers the classical compressible Euler Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, the authors establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the density of the wave fronts blows up and shocks form. The authors obtain a detailed description of the geometry of this singular boundary, and a detailed analysis of the behavior of the solution there. The approach is geometric, the central concept being that of the acoustical spacetime manifold. Compared to a previous monograph treating the relativistic fluids by the first author, the present monograph not only gives simpler and self-contained proofs but also sharpens some of the results. In addition, it explains in depth the ideas on which the approach is based. Moreover, certain geometric aspects which pertain only to the non-relativistic theory are discussed. Compressible Flow and Euler's Equations will be of interest to scholars working in partial differential equations in general and in fluid mechanics in particular.

Download or read book One Component Two Phase Flow in Horizontal and Vertical Ducts written by and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: For a description and analysis of the flow they consider the conservation equations of the two phases separately, but in thermal and mechanical equilibrium, coupled by the itnerface shear forces (two fluid model, drift flux model). Coupling may be weak or strong, depending on Froude and Mach numbers of the flow. The fluid is highly compressible, not because the individual phases move at such speeds that their individual density changes are significant but because evapiration (phase change) results in large density changes of the system at moderate pressure or temperature changes once flashing occurs. The slip between the phases is caused by unequal wall shear stress, acceleration of the fluid or gravitational forces and is hindered by the interface interaction. if they denote by? the ratio of the liquid density to the vapor density and by? the ratio of the vapor speed to the liquid speed they find that in horizontal flows? =?12 yields the maximum slip (neglecting acceleration effects) that can be reached with no interface force acting (assuming equal friction coefficients for both phases at the wall). If one investigates the conditions of thermodynamic flow similarity between different substances in two phase flow, one finds that the latent heat of vaporization is the principal controlling parameter. Thus, a 5 cm diameter test section in two phase R-114, at room temperature, corresponds to a 30 cm diameter duct in water-steam at boiling conditions at high temperatures such as encountered in geothermal and other power production systems.

Download or read book Physics Briefs written by and published by . This book was released on 1979 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: