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Author: Henning Struchtrup Publisher: Springer Science & Business Media ISBN: 3540323864 Category : Science Languages : en Pages : 262
Book Description
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.
Author: Henning Struchtrup Publisher: Springer Science & Business Media ISBN: 3540323864 Category : Science Languages : en Pages : 262
Book Description
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.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
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., Kn1. 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 n.
Author: Peyman Taheri Bonab Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: Ching Shen Publisher: Springer Science & Business Media ISBN: 3540272305 Category : Science Languages : en Pages : 406
Book Description
Aerodynamics is a science engaged in the investigation of the motion of air and other gases and their interaction with bodies, and is one of the most important bases of the aeronautic and astronautic techniques. The continuous improvement of the configurations of the airplanes and the space vehicles aid the constant enhancement of their performances are closely related with the development of the aerodynamics. In the design of new flying vehicles the aerodynamics will play more and more important role. The undertakings of aeronautics and astronautics in our country have gained achievements of world interest, the aerodynamics community has made outstanding contributions for the development of these undertakings and the science of aerodynamics. To promote further the development of the aerodynamics, meet the challenge in the new century, summary the experience, cultivate the professional personnel and to serve better the cause of aeronautics and astronautics and the national economy, the present Series of Modern Aerodynamics is organized and published.
Author: Henning Struchtrup Publisher: Springer ISBN: 9783031618673 Category : Science Languages : en Pages : 0
Book Description
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.
Author: K Karamcheti Publisher: Elsevier ISBN: 032314618X Category : Science Languages : en Pages : 562
Book Description
Rarefied Gas Dynamics is a collection of selected papers presented at the Eighth International Symposium on Rarefied Gas Dynamics, held at Stanford University in July 1972. The book is a record of the significant advances in the broad field of Rarefied Gas Dynamics that are considered to be of general and continuing interest. The articles in this compendium are organized under 10 main topics. The text presents research papers on the kinetic theory of gases; studies and experiments on shock structures of gases; use of kinetic theory for the solution of problems in evaporation and condensation; gas expansions and jets; and techniques and methods applied to the study of rarefied gas dynamics. The book also includes works on gas-solid interactions; descriptions of basic notions of current polyatomic gas kinetics; and observation of the gas dynamic phenomena in space. Physicists, aeronautical engineers, mechanical engineers, researchers, and students in the field of aircraft design will find this book a good source of knowledge and information.
Author: Henning Struchtrup
Author: Henning Struchtrup
Author: 
Author: Peyman Taheri Bonab
Author: W. Fiszdon
Author: Ching Shen
Author: Kenneth Raymond Roth
Author: Samuel Albert Schaaf
Author: Henning Struchtrup
Author: O.M. Belotserkovskii
Author: K Karamcheti