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Author: Anirudh Singh Rana Publisher: ISBN: Category : Languages : en Pages :
Book Description
It is well established that non-equilibrium flows cannot properly be described by traditional hydrodynamics, namely, the Navier-Stokes-Fourier (NSF) equations. Such flows occur, for example, in micro-electro-mechanical systems (MEMS), and ultra vacuum systems, where the dimensions of the devices are comparable to the mean free path of a gas molecule. Therefore, the study of non-equilibrium effects in gas flows is extremely important. The general interest of the present study is to explore boundary value problems for moderately rarefied gas flows, with an emphasis on numerical solutions of the regularized 13--moment equations (R13). Boundary conditions for the moment equations are derived based on either phenomenological principles or on microscopic gas-surface scattering models, e.g., Maxwell's accommodation model and the isotropic scattering model.Using asymptotic analysis, several non-linear terms in the R13 equations are transformed into algebraic terms. The reduced equations allow us to obtain numerical solutions for multidimensional boundary value problems, with the same set of boundary conditions for the linearized and fully non-linear equations. Some basic flow configurations are employed to investigate steady and unsteady rarefaction effects in rarefied gas flows, namely, planar and cylindrical Couette flow, stationary heat transfer between two plates, unsteady and oscillatory Couette flow. A comparison with the corresponding results obtained previously by the DSMC method is performed. The influence of rarefaction effects in the lid driven cavity problem is investigated. Solutions obtained from several macroscopic models, in particular the classical NSF equations with jump and slip boundary conditions, and the R13--moment equations are compared. The R13 results compare well with those obtained from more costly solvers for rarefied gas dynamics, such as the Direct Simulation Monte Carlo (DSMC) method. Flow and heat transfer in a bottom heated square cavity in a moderately rarefied gas are investigated using the R13 and NSF equations. The results obtained are compared with those from the DSMC method with emphasis on understanding thermal flow characteristics from the slip flow to the early transition regime. The R13 theory gives satisfying results including flow patterns in fair agreement with DSMC in the transition regime, which the conventional Navier-Stokes-Fourier equations are not able to capture.
Author: Anirudh Singh Rana Publisher: ISBN: Category : Languages : en Pages :
Book Description
It is well established that non-equilibrium flows cannot properly be described by traditional hydrodynamics, namely, the Navier-Stokes-Fourier (NSF) equations. Such flows occur, for example, in micro-electro-mechanical systems (MEMS), and ultra vacuum systems, where the dimensions of the devices are comparable to the mean free path of a gas molecule. Therefore, the study of non-equilibrium effects in gas flows is extremely important. The general interest of the present study is to explore boundary value problems for moderately rarefied gas flows, with an emphasis on numerical solutions of the regularized 13--moment equations (R13). Boundary conditions for the moment equations are derived based on either phenomenological principles or on microscopic gas-surface scattering models, e.g., Maxwell's accommodation model and the isotropic scattering model.Using asymptotic analysis, several non-linear terms in the R13 equations are transformed into algebraic terms. The reduced equations allow us to obtain numerical solutions for multidimensional boundary value problems, with the same set of boundary conditions for the linearized and fully non-linear equations. Some basic flow configurations are employed to investigate steady and unsteady rarefaction effects in rarefied gas flows, namely, planar and cylindrical Couette flow, stationary heat transfer between two plates, unsteady and oscillatory Couette flow. A comparison with the corresponding results obtained previously by the DSMC method is performed. The influence of rarefaction effects in the lid driven cavity problem is investigated. Solutions obtained from several macroscopic models, in particular the classical NSF equations with jump and slip boundary conditions, and the R13--moment equations are compared. The R13 results compare well with those obtained from more costly solvers for rarefied gas dynamics, such as the Direct Simulation Monte Carlo (DSMC) method. Flow and heat transfer in a bottom heated square cavity in a moderately rarefied gas are investigated using the R13 and NSF equations. The results obtained are compared with those from the DSMC method with emphasis on understanding thermal flow characteristics from the slip flow to the early transition regime. The R13 theory gives satisfying results including flow patterns in fair agreement with DSMC in the transition regime, which the conventional Navier-Stokes-Fourier equations are not able to capture.
Author: Stephanie Y. Docherty Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Accurate predictions of the flow behaviour in microscale geometries are needed, for example, to design and optimise micro devices, and to ensure their safety/reliability. Rarefied gas flows in such geometries tend, however, to be far from local thermodynamic equilibrium, meaning that the flow behaviour cannot be described by conventional fluid mechanics. Alternative approaches for modelling 'non-equilibrium' gas flows have been proposed in recent years; because analytical solution methods are subject to significant limitations, the direct simulation Monte Carlo (DSMC) method is, at present, the most practical numerical simulation tool for dilute gases. Unfortunately, the computational expense of tracking and computing collisions between thousands (or perhaps millions) of DSMC particles means that simulating the scales of realistic flow problems can require months (or even years) of computing time. This has resulted in the development of continuum-DSMC 'hybrid' methods, which aim to combine the efficiency of a conventional continuum-fluid description with the detail and accuracy of the DSMC method. This thesis focuses on the development of a continuum-DSMC method that offers a more general approach than existing methods. Using a heterogeneous framework with a field-wise coupling strategy, this new method is not subject to the limitations of the well-known domain decomposition framework, or the restrictions of the heterogeneous point-wise coupling approach. The continuum-fluid description is applied across the entire flow field, while the DSMC method is performed in dispersed micro elements that can be any size and at any location; these elements then provide the continuum description with updated constitutive and boundary information. Unlike most methods in the literature, the coupling strategy presented here is able to cope with heat transfer, and so non-isothermal flows can be simulated. Testing and validation of this new continuum-DSMC method is performed by simulating a number of benchmark cases and comparing the results with full DSMC solutions of the same cases. Two 1D flow problems are considered: a micro Fourier flow problem tests the energy coupling procedure of the method, and a high-speed micro Couette flow problem demonstrates the full coupling algorithm. In general, the method's accuracy is found to depend on the arrangement of the micro elements - with sufficient micro resolution, good agreement with the equivalent full DSMC simulations can be obtained. Although the hybrid method offers no computational speed-up over the full DSMC simulations for several of these 1D test cases and only modest speed-ups for the others, both of these 1D ow problems are simulated only to validate the coupling strategy of the method. Considerable speed-ups are offered by the method when simulating a larger and more realistic flow problem: a microchannel with a high-aspect-ratio cross-section acts as a representative geometry for modelling a gas flow through a narrow microscale crack. While the limitations of existing hybrid methods preclude their use for this type of high-aspect-ratio geometry, the new hybrid method is able to model this problem under isothermal and non-isothermal conditions. The implementation of the method is simplified to 2D by assuming that the flow variation in the streamwise direction is negligible, i.e. the method is applied to the microchannel cross-section only. Accurate predictions of the mass flow rate and the streamwise velocity field are obtained for a number of test cases; accurate predictions of the temperature field are also obtained when there is a temperature difference between the bounding walls.
Author: Lucien Baldas Publisher: MDPI ISBN: 3039215426 Category : Technology & Engineering Languages : en Pages : 220
Book Description
The last two decades have witnessed a rapid development of microelectromechanical systems (MEMS) involving gas microflows in various technical fields. Gas microflows can, for example, be observed in microheat exchangers designed for chemical applications or for cooling of electronic components, in fluidic microactuators developed for active flow control purposes, in micronozzles used for the micropropulsion of nano and picosats, in microgas chromatographs, analyzers or separators, in vacuum generators and in Knudsen micropumps, as well as in some organs-on-a-chip, such as artificial lungs. These flows are rarefied due to the small MEMS dimensions, and the rarefaction can be increased by low-pressure conditions. The flows relate to the slip flow, transition or free molecular regimes and can involve monatomic or polyatomic gases and gas mixtures. Hydrodynamics and heat and mass transfer are strongly impacted by rarefaction effects, and temperature-driven microflows offer new opportunities for designing original MEMS for gas pumping or separation. Accordingly, this Special Issue seeks to showcase research papers, short communications, and review articles that focus on novel theoretical and numerical models or data, as well as on new experimental results and technics, for improving knowledge on heat and mass transfer in gas microflows. Papers dealing with the development of original gas MEMS are also welcome.
Author: Alexey Polikarpov Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This work is devoted to the development of the numerical resolution of the kinetic model equations such as BGK, S-model, ES-model by the discrete velocity method. The different approximations of the Boltzmann equation are presented.
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: Anirudh Singh Rana
Author: Anirudh Singh Rana
Author: Chan Hong Chung
Author: Stephanie Y. Docherty
Author: Lucien Baldas
Author: Alexey Polikarpov
Author: 
Author: C. Chung
Author: Peyman Taheri Bonab
Author: 
Author: Tengfei Liang