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Macroscopic Description of Rarefied Gas Flows in the Transition Regime

Macroscopic Description of Rarefied Gas Flows in the Transition Regime
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Release: 2009
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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

Macroscopic Description of Rarefied Gas Flows in the Transition Regime
Author: Peyman Taheri Bonab
Publisher:
Total Pages:
Release: 2010
Genre:
ISBN:
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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

Macroscopic Transport Equations for Rarefied Gas Flows
Author: Henning Struchtrup
Publisher: Springer Science & Business Media
Total Pages: 262
Release: 2006-06-15
Genre: Science
ISBN: 3540323864
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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.

The Transition Regime of Rarefied Gas Dynamics

The Transition Regime of Rarefied Gas Dynamics
Author: Carlo Cercignani
Publisher:
Total Pages: 13
Release: 1968
Genre:
ISBN:
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This report summarizes the work done in the field of rarefied gas dynamics under contract with A.F.O.S.R. The report essentially consists of a list of the research papers prepared for publication from 1 May 1965 to 31 July 1968; for each paper the full title and an abstract is given, together with the proper reference. This list comprises 25 papers, mainly devoted to the study of specific problems of flows in the transitions regime, i.e., in that regime of rarefaction where the mean free path is of the same order of magnitude as a characteristic length. The main original contributions range from the suggestion of new methods of solution for the Boltzmann equation to the detailed treatment of specific problems of particular interest, such as the Poiseuille and Couette flows in different geometries, flow past an axisymmetric obstacle, influence of the wall accomodation properties on the results of the above problems. (Author).

Rarefied Gas Dynamics

Rarefied Gas Dynamics
Author: O.M. Belotserkovskii
Publisher: Springer
Total Pages: 728
Release: 1999-03-15
Genre: Science
ISBN: 9780306419324
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Rarefied Gas Flows and Dynamic Plasma Phenomena in Electric Propulsion Systems

Rarefied Gas Flows and Dynamic Plasma Phenomena in Electric Propulsion Systems
Author: Juan Esteban Gomez Herrera
Publisher: Cuvillier Verlag
Total Pages: 368
Release: 2020-12-01
Genre: Science
ISBN: 3736963246
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Zu den aktuellen Entwicklungen in der Raumfahrtindustrie zählen das stetig wachsende Interesse an miniaturisierten Satelliten sowie der immer häufigere Einsatz elektrischer Antriebssysteme zu allgemeinen Lage- und Bahnregelungszwecken. Die Entwicklung miniaturisierter Satelliten erfordert ihrerseits den Einsatz von Antriebssystemen, die sehr kleine und präzise zu steuernde Schubkräfte erzeugen. Vor diesem Hintergrund stellen elektrische Triebwerke eine attraktive Option dar, die Antriebsanforderungen von Satelliten sowohl in herkömmlichen als auch in miniaturisierten Größen langfristig zu erfüllen. Bei miniaturisierten Satelliten sind die Schubanforderungen oft mit niedrigen Treibstoff-Massenstromwerten und verhältnismäßig kleinen geometrischen charakteristischen Längen verbunden. Dies kann zu verdünnten Gaszuständen innerhalb der Triebwerksdüsen führen. Wegen der hohen Komplexität der Plasmaphänomene innerhalb elektrischer Triebwerke sowie der typischerweise hohen Rechenanforderungen, die mit der Plasmamodellierung einhergehen, werden elektrische Antriebssysteme oft auf Basis empirischer Modelle und experimenteller Daten entwickelt. Der Fokus der vorliegenden Arbeit liegt auf den oben beschriebenen Herausforderungen und den dazugehörigen Forschungsfeldern: der Untersuchung verdünnter Gaszustände in transsonischen Strömungen sowie der Entwicklung numerischer Modellierungsansätze zur Beschreibung des Plasmaverhaltens innerhalb elektrischer Antriebssysteme. New trends regarding fundamental design approaches of orbital spacecraft have been developing in the space industry in recent years. They include an increased interest in miniaturized satellites as well as a general rise in the use of electric propulsion systems for orbit and attitude control. The successful implementation of miniaturized satellites requires the use of propulsion devices able to provide small and precise thrust and impulse levels. One technical solution able to meet the requirements of both standard-sized as well as miniaturized spacecraft involves the use of highly efficient and precise electric propulsion systems. In the particular case of miniaturized satellites, the propulsion requirements are often associated with low propellant mass flow rates and small characteristic geometrical lengths, potentially leading to the appearance of rarefied conditions inside the nozzles of the propulsion devices. Because of the high complexity of the plasma phenomena taking place inside such systems and the usually very high computational requirements associated with their numerical modelling, electric propulsion systems for space applications are usually designed based on empirical models and experimental data. The present work focuses on two key aspects outlined above: rarefied gas conditions in transonic micronozzle flows as well as the numerical modelling of plasma phenomena inside electric propulsion systems.

Modeling Evaporation in the Rarefied Gas Regime by Using Macroscopic Transport Equations

Modeling Evaporation in the Rarefied Gas Regime by Using Macroscopic Transport Equations
Author: Alexander Felix Beckmann
Publisher:
Total Pages:
Release: 2018
Genre:
ISBN:
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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.

Moment Method in Rarefied Gas Dynamics

Moment Method in Rarefied Gas Dynamics
Author: Alireza Mohammadzadeh
Publisher:
Total Pages:
Release: 2016
Genre:
ISBN:
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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.

Rarefied Gas Dynamics

Rarefied Gas Dynamics
Author: Ching Shen
Publisher: Springer Science & Business Media
Total Pages: 406
Release: 2006-03-30
Genre: Science
ISBN: 3540272305
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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.