Macroscopic Transport Equations For Rarefied Gas Flows

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Macroscopic Transport Equations For Rarefied Gas Flows

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Author : Henning Struchtrup
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-15

Macroscopic Transport Equations For Rarefied Gas Flows written by Henning Struchtrup and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-15 with Science categories.

The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description. This book discusses classical and modern methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equation, for small and moderate Knudsen numbers, i.e. at and above the Navier-Stokes-Fourier level. The main methods discussed are the classical Chapman-Enskog and Grad approaches, as well as the new order of magnitude method, which avoids the short-comings of the classical methods, but retains their benefits. The relations between the various methods are carefully examined, and the resulting equations are compared and tested for a variety of standard problems. The book develops the topic starting from the basic description of an ideal gas, over the derivation of the Boltzmann equation, towards the various methods for deriving macroscopic transport equations, and the test problems which include stability of the equations, shock waves, and Couette flow.

Macroscopic Transport Equations For Rarefied Gas Flows

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Author : Henning Struchtrup
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-15

Macroscopic Transport Equations For Rarefied Gas Flows written by Henning Struchtrup and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Science categories.

The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description. This book discusses classical and modern methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equation, for small and moderate Knudsen numbers, i.e. at and above the Navier-Stokes-Fourier level. The main methods discussed are the classical Chapman-Enskog and Grad approaches, as well as the new order of magnitude method, which avoids the short-comings of the classical methods, but retains their benefits. The relations between the various methods are carefully examined, and the resulting equations are compared and tested for a variety of standard problems. The book develops the topic starting from the basic description of an ideal gas, over the derivation of the Boltzmann equation, towards the various methods for deriving macroscopic transport equations, and the test problems which include stability of the equations, shock waves, and Couette flow.

Macroscopic Description Of Rarefied Gas Flows In The Transition Regime

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Author : Peyman Taheri Bonab
language : en
Publisher:
Release Date : 2010

Macroscopic Description Of Rarefied Gas Flows In The Transition Regime written by Peyman Taheri Bonab and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn?1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation.

Coping With Complexity Model Reduction And Data Analysis

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Author : Alexander N. Gorban
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-21

Coping With Complexity Model Reduction And Data Analysis written by Alexander N. Gorban and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-21 with Mathematics categories.

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.

A Modern Course In Transport Phenomena

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Author : David C. Venerus
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-15

A Modern Course In Transport Phenomena written by David C. Venerus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-15 with Science categories.

Integrating nonequilibrium thermodynamics and kinetic theory, this unique text presents a novel approach to the subject of transport phenomena.

Computational Models For Polydisperse Particulate And Multiphase Systems

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Author : Daniele L. Marchisio
language : en
Publisher: Cambridge University Press
Release Date : 2013-03-28

Computational Models For Polydisperse Particulate And Multiphase Systems written by Daniele L. Marchisio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-28 with Technology & Engineering categories.

Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB® scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away.

A Thermodynamic Introduction To Transport Phenomena

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Author : Henning Struchtrup
language : en
Publisher: Springer Nature
Release Date : 2024-07-08

A Thermodynamic Introduction To Transport Phenomena written by Henning Struchtrup and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-08 with Science categories.

This book presents material for a one semester course on Transport Phenomena for senior undergraduate and graduate students in engineering and applied sciences. The study of Transport Phenomena provides the common ground and explores the connections between Thermodynamics, Fluid Mechanics, and Heat and Mass Transfer, thus giving a sound foundation for all transport equations in the broader area of Thermofluids. The chosen approach highlights the importance of Nonequilibrium Thermodynamics, particularly the second law of thermodynamics, for the development of stable transport equations—global and local balance laws for mass, momentum, energy and entropy— for thermofluidic systems. The study of transport processes through solutions of the equations considers mostly simple materials in simple geometries to allow for analytical solutions. This accessible approach emphasizes the general understanding of Transport Phenomena, visualizes the interplay between the different branches of Thermofluids, and thus enhances the understanding of each field, as well as their interconnections. The material covers classical subjects such as Navier-Stokes-Fourier equations, wave propagation and diffusion, shocks and flames, and includes discussions of nonequilibrium interfaces and extended thermodynamics. Irreversible losses due to entropy generation are highlighted throughout, emphasizing the link to thermodynamics and energy systems. About 140 end-of-chapter problems of varied length and difficulty teach the required technical skills while giving further insight into the multitude of Transport Phenomena.

Entropy And Non Equilibrium Statistical Mechanics

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Author : Antonio M. Scarfone
language : en
Publisher: MDPI
Release Date : 2020-12-15

Entropy And Non Equilibrium Statistical Mechanics written by Antonio M. Scarfone and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Technology & Engineering categories.

Nonequilibrium statistical mechanics has a long history featuring diverse aspects. It has been a major research field in physics and will remain so in the future. Even regarding the concept of entropy, there exists a longstanding problem concerning its definition for a system in a state far from equilibrium. In this Special Issue, we offered the possibility to discuss and present up-to-date problems that were not necessarily restricted to statistical mechanics. Theoretical and experimental papers are both presented, in addition to unifying research works. As the entropy itself is the central element of nonequilibrium processes, papers discuss various formulations of the second law and its consequences. In this Special Issue, recent progress in kinetic approaches to hydrodynamics, rational extended thermodynamics, entropy in a strongly nonequilibrium stationary state, and related topics are reported as both review articles as well as original research works.

Applications Of Chaos And Nonlinear Dynamics In Science And Engineering Vol 4

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Author : Santo Banerjee
language : en
Publisher: Springer
Release Date : 2015-05-04

Applications Of Chaos And Nonlinear Dynamics In Science And Engineering Vol 4 written by Santo Banerjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-04 with Science categories.

Chaos and nonlinear dynamics initially developed as a new emergent field with its foundation in physics and applied mathematics. The highly generic, interdisciplinary quality of the insights gained in the last few decades has spawned myriad applications in almost all branches of science and technology—and even well beyond. Wherever quantitative modeling and analysis of complex, nonlinear phenomena is required, chaos theory and its methods can play a key role. his fourth volume concentrates on reviewing further relevant contemporary applications of chaotic and nonlinear dynamics as they apply to the various cuttingedge branches of science and engineering. This encompasses, but is not limited to, topics such as synchronization in complex networks and chaotic circuits, time series analysis, ecological and biological patterns, stochastic control theory and vibrations in mechanical systems. Featuring contributions from active and leading research groups, this collection is ideal both as a reference and as a ‘recipe book’ full of tried and tested, successful engineering applications.

From Kinetic Theory To Turbulence Modeling

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Author : Paolo Barbante
language : en
Publisher: Springer Nature
Release Date : 2023-04-29

From Kinetic Theory To Turbulence Modeling written by Paolo Barbante and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Mathematics categories.

The book collects relevant contributions presented at a conference, organized in honour of Carlo Cercignani, that took place at Politecnico di Milano on May 24–28, 2021. Different research areas characterizing the scientific work of Carlo Cercignani have been considered with a particular focus on: mathematical and numerical methods for kinetic equations; kinetic modelling of gas mixtures and polyatomic gases; applications of the Boltzmann equation to electron transport, social phenomena and epidemic spread; turbulence modelling; the Einstein Classical Program; Dynamical Systems Theory.