Simulation of Gaseous Microscale Transport Phenomena via Kinetic Theory

2010 ◽  
Author(s):  
Sarantis Pantazis ◽  
Dimitris Valougeorgis
Keyword(s):  
Kinetic Theory ◽  
High Speed ◽  
Transport Phenomena ◽  
Kinetic Equations ◽  
Computational Effort ◽  
Flow And Heat Transfer ◽  
Micro Flow ◽  
Microscale Transport ◽  
Transfer Problems ◽  
Nonlinear Kinetic Equations

Kinetic theory of gases, as described by the Boltzmann or model kinetic equations, provides a solid theoretical approach for solving microscale transport phenomena in gases. Due to significant advancement in computational kinetic theory and due to the availability of high speed parallel computers, kinetic equations may be solved numerically with modest computational effort. In this framework, recently developed upgraded discrete velocity algorithms for solving linear and nonlinear kinetic equations are presented. In addition, their applicability in simulating efficiently and accurately multidimensional micro flow and heat transfer problems is demonstrated. Analysis and results are valid in the whole range of the Knudsen number.

Stochastic Particle Dynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Brownian Motion ◽  
Kinetic Theory ◽  
Stochastic Dynamics ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Central Place ◽  
Conclusive Evidence ◽  
Dense Fluids ◽  
Complementary Role ◽  
Collisional Interactions

Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

Thermal Wake of a Single Rising Air Bubble in a Large Body of Stagnant Liquid

2007 ◽  
Author(s):  
Majid Molki ◽  
Bahman Abbasi
Keyword(s):  
High Speed ◽  
Thermal Field ◽  
Large Body ◽  
Heat Transfer Process ◽  
Computational Effort ◽  
Temperature Fields ◽  
High Speed Photography ◽  
Three Dimensional Model ◽  
Surrounding Water ◽  
Air Bubble

A computational effort was undertaken to study the thermal field behind a slowly rising solitary air bubble. Starting from rest, the bubble moves upward in water due to buoyancy force in the gravitational field and induces both internal and external motion. The bubble, being colder than the surrounding water, is heated by water. The upward motion deforms the shape of the bubble and generates a convective heat transfer process. Variation of temperature at the gas-liquid interface causes a local variation of surface tension. Although the problems of this type have been generally treated by the axisymmetric assumption, the present work employs a three-dimensional model that captures the azimuthal variation of flow parameters. High-speed photography was employed to visualize the bubble evolution from the onset until the bubble reached a certain velocity. The computations were performed using the finite-volume and Volume of Fluid (VOF) techniques. The shape and evolution of the bubble as predicted by the computations are compared with those captured on the high-speed photographs. The computations revealed details of the pressure and temperature fields inside and outside the bubble. They also indicated the thermal field in the wake region behind the bubble.

Transport Phenomena and Properties in Treelike Networks

2016 ◽  
Vol 68 (4) ◽  
Author(s):  
Peng Xu ◽  
Agus Pulung Sasmito ◽  
Boming Yu ◽  
Arun Sadashiv Mujumdar
Keyword(s):  
Transport Properties ◽  
Scaling Laws ◽  
Transport Phenomena ◽  
Transport Processes ◽  
Research Progress ◽  
Transport Systems ◽  
Transport Mechanisms ◽  
Branching Structures ◽  
Flow And Heat Transfer ◽  
Flow Heat

Treelike structures abound in natural as well as man-made transport systems, which have fascinated multidisciplinary researchers to study the transport phenomena and properties and understand the transport mechanisms of treelike structures for decades. The fluid flow and heat transfer in treelike networks have received an increasing attention over the past decade as the highly efficient transport processes observed in natural treelike structures can provide useful hints for optimal solutions to many engineering and industrial problems. This review paper attempts to present the background and research progress made in recent years on the transport phenomenon in treelike networks as well as technological applications of treelike structures. The subtopics included are optimization of branching structures, scaling laws of treelike networks, and transport properties for laminar flow, turbulent flow, heat conduction, and heat convection in treelike networks. Analytical expressions for the effective transport properties have been derived based on deterministic treelike networks, and the effect of branching parameters on the transport properties of treelike networks has also been discussed. Furthermore, numerical simulation results for treelike microchannel networks are presented as well. The proposed transport properties may be beneficial to understand the transport mechanisms of branching structures and promote the applications of treelike networks in engineering and industry.

scholarly journals Invariant Imbedding and the Radiation Transfer in a Plane-Parallel Inhomogeneous Atmosphere

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Arthur G. Nikoghossian
Keyword(s):  
High Speed ◽  
Radiation Transfer ◽  
Energy Sources ◽  
Invariant Imbedding ◽  
Distributed Energy ◽  
Initial Value ◽  
Radiation Diffusion ◽  
Inhomogeneous Atmosphere ◽  
Plane Parallel ◽  
Transfer Problems

The invariant imbedding technique is applied to the problems of radiation transfer in a plane-parallel inhomogeneous atmosphere. All the parameters which describe the elementary event of scattering and the distribution of the energy sources are allowed to vary with depth. Mathematically, the considered standard problems of the theory are reduced to initial-value problems which are better adapted to capabilities of the modern high speed computers. The reflectance of an atmosphere is shown to play a prominent role in describing the diffusion process since all the other characteristics of the radiation field are expressed through it. Three transfer problems frequently encountered in astrophysical applications are discussed: the radiation diffusion in the source-free medium, in a medium with arbitrarily distributed energy sources, as well as the problem of finding the statistical mean quantities, characteristics of the multiple scattering in the atmosphere.

Beyond the Cahn-Hilliard Equation: a Vacancy-Based Kinetic Theory

2011 ◽  
Vol 172-174 ◽  
pp. 321-330 ◽  
Author(s):  
Maylise Nastar
Keyword(s):  
Kinetic Theory ◽  
Structure Function ◽  
Diffusion Mechanism ◽  
Kinetic Equations ◽  
Mean Field ◽  
Early Time ◽  
Present Theory ◽  
Kinetic Coupling ◽  
Amplification Rate ◽  
Cahn Hilliard Equation

A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description ofthe vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equi-librium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. Theresulting analytical expression of the structure function highlights the contribution of the vacancydiffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, thelinearized SCMF kinetic equations involve three constant rates, first one describing the vacancy re-laxation kinetics, second one related to the kinetic coupling between local concentrations and paircorrelations and the third one representing the spinodal amplification rate. Starting from the same va-cancy diffusion model, we perform kineticMonte Carlo simulations of a Body Centered Cubic (BCC)demixting alloy. The resulting spherically averaged structure function is compared to the SCMF pre-dictions. Both qualitative and quantitative agreements are satisfying.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

Long-term evolution of directional spectra of wind waves modelled by DNS and kinetic equations, and comparison with airborne measurements

2021 ◽  
Author(s):  
Sergei Annenkov ◽  
Victor Shrira ◽  
Leonel Romero ◽  
Ken Melville
Keyword(s):  
Angular Distribution ◽  
Kinetic Equation ◽  
Kinetic Theory ◽  
Wind Waves ◽  
Kinetic Equations ◽  
Spectral Peak ◽  
Angular Width ◽  
Angular Structure ◽  
Airborne Measurements ◽  
Steady Growth

<p>We consider the evolution of directional spectra of waves generated by constant and changing wind, modelling it by direct numerical simulation (DNS), based on the Zakharov equation. Results are compared with numerical simulations performed with the Hasselmann kinetic equation and the generalised kinetic equation, and with airborne measurements of waves generated by offshore wind, collected during the GOTEX experiment off the coast of Mexico. Modelling is performed with wind measured during the experiment, and the initial conditions are taken as the observed spectrum at the moment when wind waves prevail over swell after the initial part of the evolution.</p><p>Directional spreading is characterised by the second moment of the normalised angular distribution function, taken at selected wavenumbers relative to the spectral peak. We show that for scales longer than the spectral peak the angular spread predicted by the DNS is close to that predicted by both kinetic equations, but it underestimates the corresponding measured value, apparently due to the presence of swell. For the spectral peak and shorter waves, the DNS shows good agreement with the data. A notable feature is the steady growth of angular width at the spectral peak with time/fetch, in contrast to nearly constant width in the kinetic equations modelling. Dependence of angular width on wavenumber is shown to be much weaker than predicted by the kinetic equations. A more detailed consideration of the angular structure at the spectral peak at large fetches shows that the kinetic equations predict an angular distribution with a well-defined peak at the central angle, while the DNS reproduces the observed angular structure, with a flat peak over a range of angles.</p><p>In order to study in detail the differences between the predictions of the DNS and the kinetic equations modelling under idealised conditions, we also perform numerical simulations for the case of constant wind forcing. As in the previous case of forcing by real wind, the most striking difference between the kinetic equations and the DNS is the steady growth with time of angular width at the spectral peak, which is demonstrated by the DNS, but is not present in the modelling with the kinetic equations. We show that while the kinetic theory, both in the case of the Hasselmann equation and the generalised kinetic equation, predicts a relatively simple shape of the spectral peak, the DNS shows a more complicated structure, with a flat top and dependence of the peak position on angle. We discuss the approximations employed in the derivation of the kinetic theory and the possible causes of the found differences of directional structure.</p>

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