Macroscopic Transport Equations For Rarefied Gas Flows
DOWNLOAD
Download Macroscopic Transport Equations For Rarefied Gas Flows PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Macroscopic Transport Equations For Rarefied Gas Flows book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Macroscopic Transport Equations For Rarefied Gas Flows
DOWNLOAD
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 Description Of Rarefied Gas Flows In The Transition Regime
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2009
Macroscopic Description Of Rarefied Gas Flows In The Transition Regime written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 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., 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.
Macroscopic Description Of Rarefied Gas Flows In The Transition Regime
DOWNLOAD
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.
Macroscopic Transport Equations For Rarefied Gas Flows
DOWNLOAD
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.
Modeling Evaporation In The Rarefied Gas Regime By Using Macroscopic Transport Equations
DOWNLOAD
Author : Alexander Felix Beckmann
language : en
Publisher:
Release Date : 2018
Modeling Evaporation In The Rarefied Gas Regime By Using Macroscopic Transport Equations written by Alexander Felix Beckmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work.
A Thermodynamic Introduction To Transport Phenomena
DOWNLOAD
Author : Henning Struchtrup
language : en
Publisher: Springer
Release Date : 2024-07-09
A Thermodynamic Introduction To Transport Phenomena written by Henning Struchtrup and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-09 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.
Rarefied Gas Flows Theory And Experiment
DOWNLOAD
Author : W. Fiszdon
language : en
Publisher: Springer
Release Date : 2014-05-04
Rarefied Gas Flows Theory And Experiment written by W. Fiszdon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.
Numerical Studies Of Solutions Of The Boltzmann Transport Equations For Rarefied Gas Flow Problems
DOWNLOAD
Author : Kenneth Raymond Roth
language : en
Publisher:
Release Date : 1969
Numerical Studies Of Solutions Of The Boltzmann Transport Equations For Rarefied Gas Flow Problems written by Kenneth Raymond Roth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with categories.
Moment Method In Rarefied Gas Dynamics
DOWNLOAD
Author : Alireza Mohammadzadeh
language : en
Publisher:
Release Date : 2016
Moment Method In Rarefied Gas Dynamics written by Alireza Mohammadzadeh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, it is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the study of rarefied flows is extremely important. This dissertation includes two main parts. First, we look into the heat transport in solids when the mean free path for phonons are comparable with the length scale of the flow. A set of macroscopic moment equations for heat transport in solids are derived to extend the validity of Fourier's law beyond the hydrodynamics regime. These equations are derived such that they remain valid at room temperature, where the MEMS devices usually work. The system of moment equations for heat transport is then employed to model the thermal grating experiment, recently conducted on a silicon wafer. It turns out that at room temperature, where the experiment was conducted, phonons with high meanfree path significantly contribute to the heat transport. These low frequency phonons are not considered in the classical theory, which leads to failure of the Fourier's law in describing the thermal grating experiment. In contrast, the system of moment equations successfully predict the deviation from the classical theory in the experiment, and suggest the importance of considering both low and high frequency phonons at room temperature to capture the experimental results. In the second part of this study, we look into the gas-surface interactions for conventional gas dynamics when the gas flow is rarefied. An extension to the well-known Maxwell boundary conditions for gas-surface interactions are obtained by considering velocity dependency in the reflection kernel from the surface. This extension improves the Maxwell boundary conditions by providing an extra free parameter that can be fitted to the experimental datafor thermal transpiration effect in non-equilibrium flows. The velocity dependent Maxwell boundary conditions are derived for the Direct Simulation Monte Carlo (DSMC) method and theregularized 13-moment (R13) equations for conventional gas dynamics. Then, athermal cavity is considered to test and study the effect of these boundary conditions on the flow formation in the slip and early transition regime. It turns out that using velocity dependent boundary conditions allows us to change the size and direction of the thermal transpiration force, which leads to marked changes in the balance of transpiration forces and thermal stresses in the flow.
Flow Of Rarefied Gases
DOWNLOAD
Author : Samuel Albert Schaaf
language : en
Publisher:
Release Date : 1961
Flow Of Rarefied Gases written by Samuel Albert Schaaf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Gas flow categories.